Finite Group Databasebeta

← #17207019

Subgroups — #17207019

Order 4352.

2878 conjugacy classes of subgroups.

The subgroup lattice has 1724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763407C211yesmaximal, characteristic, complemented
2C2×C4×D4×D17C211yesmaximal, characteristic, complemented
3#14537102C211yesmaximal, characteristic, complemented
4#14537091C211yesmaximal, characteristic, complemented
5#14537079C211yesmaximal, characteristic, complemented
6#14537072C211yesmaximal, characteristic, complemented
7#14534706C211yesmaximal, characteristic, complemented
8#14534680C211yesmaximal, characteristic, complemented
9#14534651C211yesmaximal, characteristic, complemented
10#14534630C211yesmaximal, characteristic, complemented
11#14533034C211yesmaximal, characteristic, complemented
12#14532921C211yesmaximal, characteristic, complemented
13#14532820C211yesmaximal, characteristic, complemented
14#14532775C211yesmaximal, characteristic, complemented
15#14532666C211yesmaximal, characteristic, complemented
16#14532598C211yesmaximal, characteristic, complemented
17#14532592C211yesmaximal, characteristic, complemented
18#14532524C211yesmaximal, characteristic, complemented
19#14532446C211yesmaximal, characteristic, complemented
20#14532332C211yesmaximal, characteristic, complemented
21#14532268C211yesmaximal, characteristic, complemented
22#14532253C211yesmaximal, characteristic, complemented
23#14532173C211yesmaximal, characteristic, complemented
24#14532153C211yesmaximal, characteristic
25#14532106C211yesmaximal, characteristic, complemented
26#14531488C211yesmaximal, characteristic, complemented
27#14531454C211yesmaximal, characteristic, complemented
28#14531416C211yesmaximal, characteristic, complemented
29C4×#10587568C211yesmaximal, characteristic, complemented
30D17×#385C211yesmaximal, characteristic, complemented
31C17×#2460C211yesmaximal, characteristic, complemented
32C22×D4×D17C2211yescharacteristic
33C23×C4×D17C2211yescharacteristic
34C23×C4×D17C2211yescharacteristic
35#11763407—28no—
36C2×#10587584C2211yescharacteristic, complemented
37C2×#10587562C2211yescharacteristic, complemented
38C2×#10587575C2211yescharacteristic, complemented
39C2×#10587580C2211yescharacteristic
40C2×#10587580C2211yescharacteristic, complemented
41C2×#10587580C2211yescharacteristic, complemented
42C2×#10587580C2211yescharacteristic, complemented
43C2×#10587580C2211yescharacteristic, complemented
44C2×#10587569C2211yescharacteristic
45C2×#10587583C2211yescharacteristic
46C2×#10587583C2211yescharacteristic, complemented
47C2×#10587610C2211yescharacteristic, complemented
48C2×#10587582C2211yescharacteristic, complemented
49C2×#10587582C2211yescharacteristic, complemented
50C2×#10587581C2211yescharacteristic
51C2×#10587570C2211yescharacteristic
52C2×#10587568C2211yescharacteristic
53C2×#10587568C2211yescharacteristic
54C2×C4×D68C2211yescharacteristic
55C2×C4×D68C2211yescharacteristic
56C2×C4×D68C2211yescharacteristic, complemented
57C2×D4×Dic17C2211yescharacteristic
58C2×#10587579C2211yescharacteristic
59C2×C4×C22⋊D17C2211yescharacteristic
60C2×C4×C22⋊D17C2211yescharacteristic
61C2×C4×C22⋊D17C2211yescharacteristic, complemented
62C2×#10587567C2211yescharacteristic
63C2×#10587567C2211yescharacteristic
64C4×D4×D17—28no—
65C2×C4⋊C4×D17C2211yescharacteristic
66C2×C4⋊C4×D17C2211yescharacteristic, complemented
67C2×C4⋊C4×D17C2211yescharacteristic, complemented
68C2×C22⋊C4×D17C2211yescharacteristic
69C2×C22⋊C4×D17C2211yescharacteristic
70C2×C22⋊C4×D17C2211yescharacteristic
71C2×C22⋊C4×D17C2211yescharacteristic
72C2×C42×D17C2211yescharacteristic
73#11762748C2211yescharacteristic, complemented
74#11762746C2211yescharacteristic, complemented
75#11762745C2211yescharacteristic, complemented
76#11762745C2211yescharacteristic, complemented
77#11762742C2211yescharacteristic, complemented
78#11762741C2211yescharacteristic, complemented
79#11762740C2211yescharacteristic, complemented
80#11762739C2211yescharacteristic, complemented
81#11762737C2211yescharacteristic, complemented
82#11762737C2211yescharacteristic, complemented
83#11762736C2211yescharacteristic, complemented
84#11762736C2211yescharacteristic, complemented
85#11762735C2211yescharacteristic, complemented
86#11762732C2211yescharacteristic, complemented
87#11762732C2211yescharacteristic, complemented
88#11762731C2211yescharacteristic, complemented
89#11762730C2211yescharacteristic, complemented
90#11762727C2211yescharacteristic, complemented
91#11762725C2211yescharacteristic
92#11762725C2211yescharacteristic, complemented
93#11762724C2211yescharacteristic
94#11762724C2211yescharacteristic
95#11762724C2211yescharacteristic, complemented
96#11762724C2211yescharacteristic, complemented
97#11762723C2211yescharacteristic
98#11762721C2211yescharacteristic, complemented
99#11762718C2211yescharacteristic
100#11762717C2211yescharacteristic
101#11762707C2211yescharacteristic, complemented
102#11762706C2211yescharacteristic, complemented
103#11762704C2211yescharacteristic, complemented
104#11762704C2211yescharacteristic, complemented
105#11762703C2211yescharacteristic, complemented
106#11762700C2211yescharacteristic, complemented
107#11762700C2211yescharacteristic, complemented
108#11762699C2211yescharacteristic, complemented
109#11762698C2211yescharacteristic, complemented
110#11762698C2211yescharacteristic, complemented
111#11762696C2211yescharacteristic, complemented
112#11762696C2211yescharacteristic, complemented
113#11762695C2211yescharacteristic, complemented
114#11762693C2211yescharacteristic, complemented
115#11762693C2211yescharacteristic, complemented
116#11762692C2211yescharacteristic, complemented
117#11762691C2211yescharacteristic, complemented
118#11762688C2211yescharacteristic, complemented
119#11762687C2211yescharacteristic
120#11762687C2211yescharacteristic
121#11762687C2211yescharacteristic
122#11762687C2211yescharacteristic
123#11762687C2211yescharacteristic
124#11762687C2211yescharacteristic
125#11762687C2211yescharacteristic, complemented
126#11762687C2211yescharacteristic, complemented
127#11762686C2211yescharacteristic, complemented
128#11762686C2211yescharacteristic, complemented
129#11762685C2211yescharacteristic
130#11762685C2211yescharacteristic
131#11762685C2211yescharacteristic, complemented
132#11762684C2211yescharacteristic, complemented
133#11762684C2211yescharacteristic, complemented
134#11762684C2211yescharacteristic, complemented
135#11762684C2211yescharacteristic, complemented
136#11762683C2211yescharacteristic
137#11762683C2211yescharacteristic
138#11762683C2211yescharacteristic
139#11762683C2211yescharacteristic
140#11762683C2211yescharacteristic, complemented
141#11762683C2211yescharacteristic, complemented
142#11762683C2211yescharacteristic, complemented
143#11762683C2211yescharacteristic, complemented
144#11762683C2211yescharacteristic, complemented
145#11762683C2211yescharacteristic, complemented
146#11762682C2211yescharacteristic, complemented
147#11762681C2211yescharacteristic, complemented
148#11762681C2211yescharacteristic, complemented
149#11762680C2211yescharacteristic
150#11762680C2211yescharacteristic
151#11762680C2211yescharacteristic
152#11762680C2211yescharacteristic
153#11762680C2211yescharacteristic
154#11762680C2211yescharacteristic
155#11762680C2211yescharacteristic, complemented
156#11762676C2211yescharacteristic, complemented
157#11762673C2211yescharacteristic, complemented
158#11762671C2211yescharacteristic, complemented
159#11762671C2211yescharacteristic, complemented
160#11762671C2211yescharacteristic, complemented
161#11762668C2211yescharacteristic
162#11762668C2211yescharacteristic
163#11762666C2211yescharacteristic
164#11762666C2211yescharacteristic, complemented
165#11762666C2211yescharacteristic, complemented
166#11762664C2211yescharacteristic
167#11762664C2211yescharacteristic
168#11762664C2211yescharacteristic
169#11762664C2211yescharacteristic
170C4×#63227C2211yescharacteristic
171C4×#63227C2211yescharacteristic, complemented
172#95×D17C2211yescharacteristic, complemented
173#95×D17C2211yescharacteristic, complemented
174C2×C17×#125C2211yescharacteristic, complemented
175C2×C4×D4×C17C2211yescharacteristic
176C17×#397C2211yescharacteristic, complemented
177C17×#396C2211yescharacteristic, complemented
178C17×#394C2211yescharacteristic
179C17×#394C2211yescharacteristic
180C17×#388C2211yescharacteristic, complemented
181C17×#388C2211yescharacteristic, complemented
182C17×#387C2211yescharacteristic, complemented
183C17×#387C2211yescharacteristic, complemented
184C17×#387C2211yescharacteristic, complemented
185C17×#385C2211yescharacteristic, complemented
186C17×#385C2211yescharacteristic, complemented
187C17×#380C2211yescharacteristic, complemented
188C4×C22⋊C4×C17C2211yescharacteristic, complemented
189C24×D17C2311yescharacteristic
190C24×D17C2311yescharacteristic
191C22×D4×C17C2311yescharacteristic
192C23×C4×C17C2311yescharacteristic
193C23×C4×C17C2311yescharacteristic
194C22×C22⋊D17C2311yescharacteristic
195C22×C22⋊D17C2311yescharacteristic
196C22×C22⋊D17C2311yescharacteristic
197C22×C22⋊D17C2311yescharacteristic
198C23×Dic17C2311yescharacteristic
199C23×Dic17C2311yescharacteristic
200C2×D4×D17—24no—
201C2×D4×D17—24no—
202C2×D4×D17—24no—
203C22×D68C2311yescharacteristic
204C22×D68C2311yescharacteristic
205C22×D68C2311yescharacteristic
206C22×D68C2311yescharacteristic
207C22×C4×D17—24no—
208C22×C4×D17—24no—
209C22×C4×D17—42no—
210C22×C4×D17—42no—
211C22×C4×D17—42no—
212C22×C4×D17—42no—
213C22×C4×D17C2311yescharacteristic
214C22×C4×D17C2311yescharacteristic
215C22×C4×D17C2311yescharacteristic
216C22×C4×D17C2311yescharacteristic
217C22×C4×D17C2311yescharacteristic
218C22×C4×D17C2311yescharacteristic
219C22×C4×D17C2311yescharacteristic
220C22×C4×D17C2311yescharacteristic
221C22×C4×D17C2311yescharacteristic
222C22×C4×D17C2311yescharacteristic
223C22×C4×D17C2311yescharacteristic
224C22×C4×D17C2311yescharacteristic
225C22×C4×D17C2311yescharacteristic
226C22×C4×D17C2311yescharacteristic
227C22×Dic34C2311yescharacteristic
228C17×#125—24no—
229C4×D4×C17—24no—
230C2×C4⋊C4×C17C2311yescharacteristic
231C2×C4⋊C4×C17C2311yescharacteristic
232C2×C4⋊C4×C17C2311yescharacteristic
233C2×C4⋊C4×C17C2311yescharacteristic
234C2×C4⋊C4×C17C2311yescharacteristic
235C2×C4⋊C4×C17C2311yescharacteristic
236C2×C4⋊C4×C17C2311yescharacteristic
237C2×C4⋊C4×C17C2311yescharacteristic
238C2×C4⋊C4×C17C2311yescharacteristic
239C2×C22⋊C4×C17C2311yescharacteristic
240C2×C22⋊C4×C17C2311yescharacteristic
241C2×C22⋊C4×C17C2311yescharacteristic
242C2×C22⋊C4×C17C2311yescharacteristic
243C2×C22⋊C4×C17C2311yescharacteristic
244C2×C22⋊C4×C17C2311yescharacteristic
245C2×C22⋊C4×C17C2311yescharacteristic
246C2×C22⋊C4×C17C2311yescharacteristic
247C2×C22⋊C4×C17C2311yescharacteristic
248C2×C22⋊C4×C17C2311yescharacteristic
249C2×C42×C17C2311yescharacteristic
250C2×C42×C17C2311yescharacteristic
251C2×C42×C17C2311yescharacteristic
252C2×C22⋊Dic17C2311yescharacteristic
253C2×C22⋊Dic17C2311yescharacteristic
254C2×C22⋊Dic17C2311yescharacteristic
255C2×C22⋊Dic17C2311yescharacteristic
256C2×C22⋊Dic17C2311yescharacteristic
257C2×C22⋊Dic17C2311yescharacteristic
258C2×C22⋊Dic17C2311yescharacteristic
259C2×C22⋊Dic17C2311yescharacteristic
260D4×Dic17—24no—
261C4×C22⋊D17—24no—
262C4×C22⋊D17—24no—
263C4×C22⋊D17—42no—
264C2×#63227C2311yescharacteristic
265C2×#63227C2311yescharacteristic
266C2×#63227C2311yescharacteristic
267C2×#63227C2311yescharacteristic
268C2×#63227C2311yescharacteristic
269C2×#63227C2311yescharacteristic
270C2×#63227C2311yescharacteristic
271C2×#63227C2311yescharacteristic
272C2×#63227C2311yescharacteristic
273C2×#63227C2311yescharacteristic
274C2×#63227C2311yescharacteristic
275C2×#63227C2311yescharacteristic
276C2×#63227C2311yescharacteristic
277C2×#63227C2311yescharacteristic
278C2×#63227C2311yescharacteristic
279C2×#63227C2311yescharacteristic
280C2×#63227C2311yescharacteristic
281C2×#63227C2311yescharacteristic
282C2×#63227C2311yescharacteristic
283C2×#63227C2311yescharacteristic
284C2×#63227C2311yescharacteristic
285C2×#63227C2311yescharacteristic
286C2×#63227C2311yescharacteristic
287C2×#63227C2311yescharacteristic
288C2×#63227C2311yescharacteristic
289C2×#63227C2311yescharacteristic
290C2×#63227C2311yescharacteristic
291C2×#63227C2311yescharacteristic
292C2×#63227C2311yescharacteristic
293C2×#63227C2311yescharacteristic
294C2×C4⋊Dic17C2311yescharacteristic
295C2×C4⋊Dic17C2311yescharacteristic
296C2×C4⋊Dic17C2311yescharacteristic
297C2×C4⋊Dic17C2311yescharacteristic
298C2×C4⋊Dic17C2311yescharacteristic
299C2×C4⋊Dic17C2311yescharacteristic
300C2×C4⋊Dic17C2311yescharacteristic
301C2×C4⋊Dic17C2311yescharacteristic
302C2×C4⋊Dic17C2311yescharacteristic
303#10587610—42no—
304C2×#63225C2311yescharacteristic
305C2×#63225C2311yescharacteristic
306C2×#63225C2311yescharacteristic
307C2×#63225C2311yescharacteristic
308C2×#63225C2311yescharacteristic
309C2×#63225C2311yescharacteristic
310C2×#63225C2311yescharacteristic
311C2×#63225C2311yescharacteristic
312C2×#63225C2311yescharacteristic
313C2×#63225C2311yescharacteristic
314C2×#63225C2311yescharacteristic
315C2×#63225C2311yescharacteristic
316C2×#63225C2311yescharacteristic
317C2×#63225C2311yescharacteristic
318C2×#63225C2311yescharacteristic
319C2×#63225C2311yescharacteristic
320C2×C4×Dic17C2311yescharacteristic
321C2×C4×Dic17C2311yescharacteristic
322C2×C4×Dic17C2311yescharacteristic
323C2×C4×Dic17C2311yescharacteristic
324#10587584—24no—
325#10587583—24no—
326#10587583—42no—
327#10587582—24no—
328#10587582—24no—
329#10587581—24no—
330#10587580—24no—
331#10587580—24no—
332#10587580—24no—
333#10587580—24no—
334#10587580—42no—
335#10587579D418yescomplemented
336C4⋊C4×D17—24no—
337C4⋊C4×D17—24no—
338C4⋊C4×D17—42no—
339#10587575—24no—
340#10587570—24no—
341#10587569—24no—
342#10587568—24no—
343#10587568—42no—
344#10587567—24no—
345#10587567—24no—
346C22⋊C4×D17—24no—
347C22⋊C4×D17—24no—
348C22⋊C4×D17—24no—
349C22⋊C4×D17—42no—
350#10587562—24no—
351C4×D68—24no—
352C4×D68—24no—
353C4×D68—42no—
354C42×D17—24no—
355C17×#95C2311yescharacteristic
356C17×#95C2311yescharacteristic
357C17×#95C2311yescharacteristic
358C17×#95C2311yescharacteristic
359C17×#95C2311yescharacteristic
360C17×#95C2311yescharacteristic
361C17×#95C2311yescharacteristic
362C17×#95C2311yescharacteristic
363C17×#95C2311yescharacteristic
364C17×#95C2311yescharacteristic
365#10587502C2311yescharacteristic
366#10587502C2311yescharacteristic
367#10587502C2311yescharacteristic
368#10587502C2311yescharacteristic
369#10587502C2311yescharacteristic
370#10587502C2311yescharacteristic
371#10587502C2311yescharacteristic
372#10587502C2311yescharacteristic
373#10587502C2311yescharacteristic
374#10587502C2311yescharacteristic
375#10587502C2311yescharacteristic
376#10587502C2311yescharacteristic
377#10587502C2311yescharacteristic
378#10587502C2311yescharacteristic
379#10587502C2311yescharacteristic
380#10587502C2311yescharacteristic
381#10587502C2311yescharacteristic
382#10587502C2311yescharacteristic
383#10587502C2311yescharacteristic
384#10587502C2311yescharacteristic
385#10587502C2311yescharacteristic
386#10587502C2311yescharacteristic
387#10587502C2311yescharacteristic
388#10587502C2311yescharacteristic
389#10587502C2311yescharacteristic
390#10587502C2311yescharacteristic
391C24×C17C2411yescharacteristic
392C24×C17C2411yescharacteristic
393C23×D17—22no—
394C23×D17—22no—
395C23×D17—22no—
396C23×D17—22no—
397C23×D17—22no—
398C23×D17—22no—
399C23×D17—22no—
400C23×D17—22no—
401C23×D17—22no—
402C23×D17—41no—
403C23×D17—41no—
404C23×D17—41no—
405C23×D17—41no—
406C23×D17#4114yes—
407C23×D17C2411yescharacteristic
408C23×D17C2411yescharacteristic
409C23×D17C2411yescharacteristic
410C23×D17C2411yescharacteristic
411C2×D4×C17—22no—
412C2×D4×C17—22no—
413C2×D4×C17—22no—
414C22×C4×C17—22no—
415C22×C4×C17—22no—
416C22×C4×C17—22no—
417C22×C4×C17—22no—
418C22×C4×C17—41no—
419C22×C4×C17—41no—
420C22×C4×C17C2411yescharacteristic
421C22×C4×C17C2411yescharacteristic
422C22×C4×C17C2411yescharacteristic
423C22×C4×C17C2411yescharacteristic
424C22×C4×C17C2411yescharacteristic
425C22×C4×C17C2411yescharacteristic
426C22×C4×C17C2411yescharacteristic
427C22×C4×C17C2411yescharacteristic
428C22×C4×C17C2411yescharacteristic
429C22×C4×C17C2411yescharacteristic
430C22×C4×C17C2411yescharacteristic
431C22×C4×C17C2411yescharacteristic
432C22×C4×C17C2411yescharacteristic
433C2×C22⋊D17—22no—
434C2×C22⋊D17—22no—
435C2×C22⋊D17—22no—
436C2×C22⋊D17—22no—
437C2×C22⋊D17—22no—
438C2×C22⋊D17—22no—
439C2×C22⋊D17—22no—
440C2×C22⋊D17—41no—
441C2×C22⋊D17—41no—
442C2×C22⋊D17—41no—
443C2×C22⋊D17—41no—
444C2×C22⋊D17#4114yes—
445C22×Dic17—22no—
446C22×Dic17—22no—
447C22×Dic17—41no—
448C22×Dic17—41no—
449C22×Dic17—41no—
450C22×Dic17—41no—
451C22×Dic17C2411yescharacteristic
452C22×Dic17C2411yescharacteristic
453C22×Dic17C2411yescharacteristic
454C22×Dic17C2411yescharacteristic
455C22×Dic17C2411yescharacteristic
456C22×Dic17C2411yescharacteristic
457C22×Dic17C2411yescharacteristic
458C22×Dic17C2411yescharacteristic
459C22×Dic17C2411yescharacteristic
460C22×Dic17C2411yescharacteristic
461C22×Dic17C2411yescharacteristic
462C22×Dic17C2411yescharacteristic
463D4×D17—232no—
464C2×D68—22no—
465C2×D68—22no—
466C2×D68—22no—
467C2×D68—22no—
468C2×D68—22no—
469C2×D68—22no—
470C2×D68—22no—
471C2×D68—22no—
472C2×D68—22no—
473C2×D68—41no—
474C2×D68—41no—
475C2×D68C2×D414yes—
476C2×C4×D17—22no—
477C2×C4×D17—22no—
478C2×C4×D17—22no—
479C2×C4×D17—22no—
480C2×C4×D17—22no—
481C2×C4×D17—22no—
482C2×C4×D17—22no—
483C2×C4×D17—22no—
484C2×C4×D17—22no—
485C2×C4×D17—22no—
486C2×C4×D17—22no—
487C2×C4×D17—22no—
488C2×C4×D17—22no—
489C2×C4×D17—22no—
490C2×C4×D17—22no—
491C2×C4×D17—22no—
492C2×C4×D17—22no—
493C2×C4×D17—22no—
494C2×C4×D17—22no—
495C2×C4×D17—22no—
496C2×C4×D17—22no—
497C2×C4×D17—22no—
498C2×C4×D17—22no—
499C2×C4×D17—416no—
500C2×C4×D17—416no—
501C2×C4×D17—41no—
502C2×C4×D17—41no—
503C2×C4×D17—41no—
504C2×C4×D17—41no—
505C2×C4×D17—41no—
506C2×C4×D17—41no—
507C2×C4×D17—41no—
508C2×C4×D17—41no—
509C2×C4×D17—41no—
510C2×C4×D17—41no—
511C2×C4×D17—41no—
512C2×C4×D17—41no—
513C2×C4×D17—41no—
514C2×C4×D17—41no—
515C2×C4×D17—41no—
516C2×C4×D17—41no—
517C2×C4×D17—41no—
518C2×C4×D17C2×D414yes—
519C2×C4×D17C2×D414yes—
520C2×Dic34—22no—
521C2×Dic34—41no—
522C2×Dic34—41no—
523C4⋊C4×C17—22no—
524C4⋊C4×C17—22no—
525C4⋊C4×C17—22no—
526C4⋊C4×C17—22no—
527C4⋊C4×C17—22no—
528C4⋊C4×C17—22no—
529C4⋊C4×C17—41no—
530C4⋊C4×C17—41no—
531C4⋊C4×C17C2×D414yes—
532C22⋊C4×C17—22no—
533C22⋊C4×C17—22no—
534C22⋊C4×C17—22no—
535C22⋊C4×C17—22no—
536C22⋊C4×C17—22no—
537C22⋊C4×C17—22no—
538C22⋊C4×C17—41no—
539C22⋊C4×C17—41no—
540C22⋊C4×C17—41no—
541C22⋊C4×C17—41no—
542C42×C17—22no—
543C42×C17—22no—
544C42×C17—41no—
545C22⋊Dic17—22no—
546C22⋊Dic17—22no—
547C22⋊Dic17—22no—
548C22⋊Dic17—22no—
549C22⋊Dic17—41no—
550C22⋊Dic17—41no—
551C22⋊Dic17—41no—
552C22⋊Dic17—41no—
553#63227—22no—
554#63227—22no—
555#63227—22no—
556#63227—22no—
557#63227—22no—
558#63227—22no—
559#63227—22no—
560#63227—22no—
561#63227—22no—
562#63227—22no—
563#63227—22no—
564#63227—22no—
565#63227—22no—
566#63227—22no—
567#63227—22no—
568#63227—22no—
569#63227—22no—
570#63227—22no—
571#63227—22no—
572#63227—22no—
573#63227—22no—
574#63227—41no—
575#63227—41no—
576#63227—41no—
577#63227—41no—
578#63227—41no—
579#63227—41no—
580#63227—41no—
581#63227C2×D414yes—
582#63227C2×D414yes—
583C4⋊Dic17—22no—
584C4⋊Dic17—22no—
585C4⋊Dic17—22no—
586C4⋊Dic17—22no—
587C4⋊Dic17—41no—
588C4⋊Dic17—41no—
589C4⋊Dic17—41no—
590C4⋊Dic17—41no—
591C4⋊Dic17—41no—
592#63225—22no—
593#63225—22no—
594#63225—22no—
595#63225—22no—
596#63225—22no—
597#63225—22no—
598#63225—22no—
599#63225—22no—
600#63225—22no—
601#63225—22no—
602#63225—22no—
603#63225—22no—
604#63225—41no—
605#63225—41no—
606#63225—41no—
607#63225—41no—
608C4×Dic17—22no—
609C4×Dic17—22no—
610C4×Dic17—41no—
611C4×Dic17C2×D414yes—
612#34991—171nomaximal, Sylow
613C23×C17—21no—
614C23×C17—21no—
615C23×C17—21no—
616C23×C17—21no—
617C23×C17—21no—
618C23×C17—21no—
619C23×C17—21no—
620C23×C17—21no—
621C23×C17—21no—
622C23×C17—21no—
623C23×C17—21no—
624C23×C17—21no—
625C23×C17C2×#4112yes—
626C23×C17C2×#4112yes—
627C23×C17C2511yescharacteristic
628C22×D17—21no—
629C22×D17—21no—
630C22×D17—21no—
631C22×D17—21no—
632C22×D17—21no—
633C22×D17—21no—
634C22×D17—21no—
635C22×D17—21no—
636C22×D17—28no—
637C22×D17—21no—
638C22×D17—21no—
639C22×D17—21no—
640C22×D17—21no—
641C22×D17—21no—
642C22×D17—21no—
643C22×D17—28no—
644C22×D17—28no—
645C22×D17—21no—
646C22×D17—21no—
647C22×D17—21no—
648C22×D17—21no—
649C22×D17—21no—
650C22×D17—21no—
651C22×D17—21no—
652C22×D17—44no—
653C22×D17—44no—
654C22×D17—44no—
655C22×D17—44no—
656C22×D17—44no—
657C22×D17—44no—
658C22×D17—44no—
659C22×D17—44no—
660C22×D17—44no—
661C22×D17—44no—
662C22×D17—44no—
663C22×D17C22×D412yes—
664C22×D17C22×D412yes—
665C22×D17C2×#4112yes—
666C22×D17C2×#4112yes—
667C22×D17C2×#4112yes—
668C22×D17H(5,𝔽2)12yes—
669C22×D172−1+412yes—
670D4×C17—28no—
671C2×C4×C17—21no—
672C2×C4×C17—21no—
673C2×C4×C17—21no—
674C2×C4×C17—21no—
675C2×C4×C17—21no—
676C2×C4×C17—21no—
677C2×C4×C17—21no—
678C2×C4×C17—21no—
679C2×C4×C17—21no—
680C2×C4×C17—21no—
681C2×C4×C17—21no—
682C2×C4×C17—21no—
683C2×C4×C17—21no—
684C2×C4×C17—21no—
685C2×C4×C17—21no—
686C2×C4×C17—21no—
687C2×C4×C17—21no—
688C2×C4×C17—21no—
689C2×C4×C17—21no—
690C2×C4×C17—21no—
691C2×C4×C17—21no—
692C2×C4×C17—21no—
693C2×C4×C17—21no—
694C2×C4×C17—21no—
695C2×C4×C17—21no—
696C2×C4×C17—21no—
697C2×C4×C17—21no—
698C2×C4×C17—21no—
699C2×C4×C17—21no—
700C2×C4×C17—21no—
701C2×C4×C17—21no—
702C2×C4×C17—21no—
703C2×C4×C17—21no—
704C2×C4×C17—21no—
705C2×C4×C17—21no—
706C2×C4×C17—44no—
707C2×C4×C17—44no—
708C2×C4×C17C22×D412yes—
709C2×C4×C17C22×D412yes—
710C2×C4×C17C22×D412yes—
711C2×C4×C17H(5,𝔽2)12yes—
712C22⋊D17—28no—
713C22⋊D17—28no—
714C22⋊D17—44no—
715C22⋊D17—82no—
716C2×Dic17—21no—
717C2×Dic17—21no—
718C2×Dic17—21no—
719C2×Dic17—21no—
720C2×Dic17—21no—
721C2×Dic17—21no—
722C2×Dic17—21no—
723C2×Dic17—21no—
724C2×Dic17—21no—
725C2×Dic17—21no—
726C2×Dic17—21no—
727C2×Dic17—21no—
728C2×Dic17—21no—
729C2×Dic17—21no—
730C2×Dic17—21no—
731C2×Dic17—21no—
732C2×Dic17—21no—
733C2×Dic17—21no—
734C2×Dic17—21no—
735C2×Dic17—21no—
736C2×Dic17—21no—
737C2×Dic17—21no—
738C2×Dic17—21no—
739C2×Dic17—21no—
740C2×Dic17—21no—
741C2×Dic17—21no—
742C2×Dic17—21no—
743C2×Dic17—21no—
744C2×Dic17—21no—
745C2×Dic17—21no—
746C2×Dic17—21no—
747C2×Dic17—21no—
748C2×Dic17—21no—
749C2×Dic17—44no—
750C2×Dic17—44no—
751C2×Dic17C22×D412yes—
752C2×Dic17C22×D412yes—
753C2×Dic17C2×#4112yes—
754D68—28no—
755D68—44no—
756D68—44no—
757D68—82no—
758C4×D17—28no—
759C4×D17—28no—
760C4×D17—44no—
761C4×D17—44no—
762C4×D17—44no—
763C4×D17—44no—
764C4×D17—44no—
765C4×D17—44no—
766C4×D17—44no—
767C4×D17—44no—
768C4×D17—44no—
769C4×D17—82no—
770C4×D17—82no—
771C4×D17—82no—
772Dic34—82no—
773C2×#539—171no—
774C22×C4×D4—171no—
775#2852—171no—
776#2851—171no—
777#2849—171no—
778#2848—171no—
779#2638—171no—
780#2636—171no—
781#2633—171no—
782#2630—171no—
783#2480—171no—
784#2473—171no—
785#2466—171no—
786#2463—171no—
787#2460D1711yescharacteristic, complemented
788#2455—171no—
789#2449—171no—
790#2449—171no—
791#2443—171no—
792#2437—171no—
793#2425—171no—
794#2419—171no—
795#2418—171no—
796#2412—171no—
797#2410—171no—
798#2405—171no—
799#2325—171no—
800#2322—171no—
801#2318—171no—
802C4×#120—171no—
803C2×#385—171no—
804C22×C17—22no—
805C22×C17—22no—
806C22×C17—22no—
807C22×C17—22no—
808C22×C17—22no—
809C22×C17—22no—
810C22×C17—41no—
811C22×C17—41no—
812C22×C17—41no—
813C22×C17—41no—
814C22×C17—41no—
815C22×C17—41no—
816C22×C17—41no—
817C22×C17—41no—
818C22×C17C23×D411yescharacteristic
819C22×C17C22×#4111yescharacteristic
820C22×C17C22×#4111yescharacteristic
821C22×C17C2×H(5,𝔽2)11yescharacteristic
822C22×C17C2×H(5,𝔽2)11yescharacteristic
823C22×C17C2×2−1+411yescharacteristic
824C22×C17#58511yescharacteristic
825C2×D17—22no—
826C2×D17—22no—
827C2×D17—22no—
828C2×D17—22no—
829C2×D17—22no—
830C2×D17—22no—
831C2×D17—22no—
832C2×D17—22no—
833C2×D17—22no—
834C2×D17—22no—
835C2×D17—22no—
836C2×D17—22no—
837C2×D17—22no—
838C2×D17—22no—
839C2×D17—22no—
840C2×D17—416no—
841C2×D17—416no—
842C2×D17—41no—
843C2×D17—41no—
844C2×D17—41no—
845C2×D17—41no—
846C2×D17—41no—
847C2×D17—41no—
848C2×D17—41no—
849C2×D17—41no—
850C2×D17—41no—
851C2×D17—41no—
852C2×D17—41no—
853C2×D17#52514yes—
854C2×D17#53914yescomplemented
855C4×C17—22no—
856C4×C17—22no—
857C4×C17—22no—
858C4×C17—22no—
859C4×C17—41no—
860C4×C17—41no—
861C4×C17—41no—
862C4×C17—41no—
863C4×C17—41no—
864C4×C17—41no—
865C4×C17—41no—
866C4×C17—41no—
867C4×C17—41no—
868Dic17—22no—
869Dic17—22no—
870Dic17—22no—
871Dic17—41no—
872Dic17—41no—
873Dic17—41no—
874Dic17—41no—
875Dic17—41no—
876Dic17—41no—
877Dic17—41no—
878Dic17—41no—
879Dic17—41no—
880C23×D4—171no—
881C24×C4—171no—
882C24×C4—171no—
883#539—348no—
884C2×#126—171no—
885C2×#126—171no—
886C2×#125—171no—
887C2×#125C2×D1711yescharacteristic, complemented
888C2×#123—171no—
889C2×#123—171no—
890C2×#123—171no—
891C2×#123—171no—
892C2×#123—171no—
893C2×#123—171no—
894C2×C22⋊Q8—171no—
895C2×C22⋊Q8—171no—
896C2×C22⋊Q8—171no—
897C2×C22⋊Q8—171no—
898C2×C22⋊Q8—171no—
899C2×#121—171no—
900C2×#121—171no—
901C2×#120—171no—
902C2×#120—171no—
903C2×C4×D4—171no—
904C2×C4×D4—171no—
905C2×C4×D4—171no—
906C2×C4×D4—171no—
907C2×C4×D4—171no—
908C2×C4×D4—171no—
909C2×C4×D4—171no—
910C2×C4×D4—171no—
911C2×C4×D4—171no—
912C2×C4×D4—171no—
913C2×C4×D4—348no—
914C2×C4×D4C2×D1711yescharacteristic
915C22×C4⋊C4—171no—
916C22×C4⋊C4—171no—
917C22×C4⋊C4—171no—
918C22×C22⋊C4—171no—
919C22×C22⋊C4—171no—
920C22×C22⋊C4—171no—
921C22×C22⋊C4—171no—
922C22×C42—171no—
923#400—171no—
924#399—171no—
925#399—171no—
926#399—171no—
927#398—171no—
928#398—171no—
929#398—171no—
930#398—171no—
931#397—171no—
932#397—171no—
933#397—171no—
934#397—171no—
935#397—171no—
936#397C2×D1711yescharacteristic, complemented
937#396—171no—
938#396—171no—
939#396—171no—
940#396C2×D1711yescharacteristic, complemented
941#395—171no—
942#394—171no—
943#394—171no—
944#394—171no—
945#394—171no—
946#394—171no—
947#394—171no—
948#394—171no—
949#394—171no—
950#394C2×D1711yescharacteristic
951#394C2×D1711yescharacteristic
952#393—171no—
953#392—171no—
954#392—171no—
955#389—171no—
956#389—171no—
957#389—171no—
958#389—171no—
959#388—171no—
960#388—171no—
961#388—171no—
962#388—171no—
963#388—171no—
964#388—171no—
965#388C2×D1711yescharacteristic, complemented
966#388C2×D1711yescharacteristic, complemented
967#387—171no—
968#387—171no—
969#387—171no—
970#387—171no—
971#387—171no—
972#387—171no—
973#387—171no—
974#387C2×D1711yescharacteristic, complemented
975#387C2×D1711yescharacteristic, complemented
976#387C2×D1711yescharacteristic, complemented
977#386—171no—
978#386—171no—
979#386—171no—
980#386—171no—
981#386—171no—
982#386—171no—
983#386—171no—
984#386—171no—
985#386—171no—
986#386—171no—
987#386—171no—
988#386—171no—
989#386—171no—
990#386—171no—
991#385—171no—
992#385—171no—
993#385—171no—
994#385—171no—
995#385—171no—
996#385—171no—
997#385—171no—
998#385—171no—
999#385—171no—
1000#385—171no—
1001#385—171no—
1002#385—171no—
1003#385—171no—
1004#385—171no—
1005#385—171no—
1006#385—171no—
1007#385—171no—
1008#385—171no—
1009#385—171no—
1010#385—171no—
1011#385—171no—
1012#385—171no—
1013#385—171no—
1014#385—171no—
1015#385C2×D1711yescharacteristic, complemented
1016#385C2×D1711yescharacteristic, complemented
1017#383—171no—
1018#382—171no—
1019#381—171no—
1020#381—171no—
1021#381—171no—
1022#380—171no—
1023#380—171no—
1024#380—171no—
1025#380—171no—
1026#380—171no—
1027#380C2×D1711yescharacteristic, complemented
1028#379—171no—
1029#379—171no—
1030#379—171no—
1031#379—171no—
1032C4×C22⋊C4—171no—
1033C4×C22⋊C4—171no—
1034C4×C22⋊C4C2×D1711yescharacteristic, complemented
1035C2×#95—171no—
1036C2×#95—171no—
1037C2×C17—42no—
1038C2×C17—42no—
1039C2×C17C2×#52511yescharacteristic
1040C2×C17C2×#53911yescharacteristic
1041C2×C17#345911yescharacteristic
1042C2×C17#348411yescharacteristic
1043C2×C17#348911yescharacteristic
1044C2×C17#351311yescharacteristic
1045C2×C17#352011yescharacteristic
1046D17—24no—
1047D17—24no—
1048D17—42no—
1049D17—81no—
1050C25—171no—
1051C25—171no—
1052C22×Q8—171no—
1053C22×D4—171no—
1054C22×D4—171no—
1055C22×D4—171no—
1056C22×D4—171no—
1057C22×D4—171no—
1058C22×D4—171no—
1059C22×D4—171no—
1060C22×D4—171no—
1061C22×D4—344no—
1062C22×D4—344no—
1063C22×D4—344no—
1064C22×D4C22×D1711yescharacteristic
1065C23×C4—171no—
1066C23×C4—171no—
1067C23×C4—171no—
1068C23×C4—171no—
1069C23×C4—171no—
1070C23×C4—171no—
1071C23×C4—171no—
1072C23×C4—171no—
1073C23×C4—171no—
1074C23×C4—171no—
1075C23×C4—171no—
1076C23×C4—171no—
1077C23×C4—171no—
1078C23×C4—171no—
1079C23×C4—171no—
1080C23×C4—171no—
1081C23×C4—344no—
1082C23×C4—344no—
1083C23×C4—682no—
1084C23×C4—682no—
1085C23×C4—682no—
1086C23×C4—682no—
1087C23×C4C22×D1711yescharacteristic
1088C23×C4C22×D1711yescharacteristic
1089#126—344no—
1090#126—344no—
1091#125—24no—
1092#125—344no—
1093#123—344no—
1094#123—344no—
1095#123—344no—
1096#123—344no—
1097#123—344no—
1098#123—682no—
1099C22⋊Q8—344no—
1100C22⋊Q8—344no—
1101C22⋊Q8—344no—
1102C22⋊Q8—682no—
1103C22⋊Q8—682no—
1104#121—344no—
1105#121—344no—
1106#120—344no—
1107#120—682no—
1108C4×D4—24no—
1109C4×D4—178no—
1110C4×D4—344no—
1111C4×D4—344no—
1112C4×D4—344no—
1113C4×D4—344no—
1114C4×D4—344no—
1115C4×D4—344no—
1116C4×D4—344no—
1117C4×D4—682no—
1118C4×D4—682no—
1119C2×C4⋊C4—171no—
1120C2×C4⋊C4—171no—
1121C2×C4⋊C4—171no—
1122C2×C4⋊C4—171no—
1123C2×C4⋊C4—171no—
1124C2×C4⋊C4—171no—
1125C2×C4⋊C4—171no—
1126C2×C4⋊C4—171no—
1127C2×C4⋊C4—171no—
1128C2×C4⋊C4—171no—
1129C2×C4⋊C4—171no—
1130C2×C4⋊C4—171no—
1131C2×C4⋊C4—171no—
1132C2×C4⋊C4—171no—
1133C2×C4⋊C4—171no—
1134C2×C4⋊C4—171no—
1135C2×C4⋊C4—171no—
1136C2×C4⋊C4—171no—
1137C2×C4⋊C4—171no—
1138C2×C4⋊C4—171no—
1139C2×C4⋊C4—171no—
1140C2×C4⋊C4—171no—
1141C2×C4⋊C4—171no—
1142C2×C4⋊C4—171no—
1143C2×C4⋊C4—171no—
1144C2×C4⋊C4—344no—
1145C2×C4⋊C4—344no—
1146C2×C4⋊C4—682no—
1147C2×C4⋊C4C22×D1711yescharacteristic
1148C2×C4⋊C4C22×D1711yescharacteristic
1149C2×C4⋊C4C22×D1711yescharacteristic
1150C2×C4⋊C4C22×D1711yescharacteristic
1151C2×C4⋊C4C22×D1711yescharacteristic
1152C2×C4⋊C4C22×D1711yescharacteristic
1153C2×C4⋊C4C22×D1711yescharacteristic
1154C2×C4⋊C4C22×D1711yescharacteristic
1155C2×C4⋊C4C22×D1711yescharacteristic
1156C2×C22⋊C4—171no—
1157C2×C22⋊C4—171no—
1158C2×C22⋊C4—171no—
1159C2×C22⋊C4—171no—
1160C2×C22⋊C4—171no—
1161C2×C22⋊C4—171no—
1162C2×C22⋊C4—171no—
1163C2×C22⋊C4—171no—
1164C2×C22⋊C4—171no—
1165C2×C22⋊C4—171no—
1166C2×C22⋊C4—171no—
1167C2×C22⋊C4—171no—
1168C2×C22⋊C4—171no—
1169C2×C22⋊C4—171no—
1170C2×C22⋊C4—171no—
1171C2×C22⋊C4—171no—
1172C2×C22⋊C4—171no—
1173C2×C22⋊C4—171no—
1174C2×C22⋊C4—171no—
1175C2×C22⋊C4—171no—
1176C2×C22⋊C4—171no—
1177C2×C22⋊C4—171no—
1178C2×C22⋊C4—171no—
1179C2×C22⋊C4—171no—
1180C2×C22⋊C4—171no—
1181C2×C22⋊C4—171no—
1182C2×C22⋊C4—171no—
1183C2×C22⋊C4—171no—
1184C2×C22⋊C4—171no—
1185C2×C22⋊C4—171no—
1186C2×C22⋊C4—171no—
1187C2×C22⋊C4—171no—
1188C2×C22⋊C4—171no—
1189C2×C22⋊C4—171no—
1190C2×C22⋊C4—171no—
1191C2×C22⋊C4—171no—
1192C2×C22⋊C4—171no—
1193C2×C22⋊C4—171no—
1194C2×C22⋊C4—344no—
1195C2×C22⋊C4—344no—
1196C2×C22⋊C4—344no—
1197C2×C22⋊C4—682no—
1198C2×C22⋊C4C22×D1711yescharacteristic
1199C2×C22⋊C4C22×D1711yescharacteristic
1200C2×C22⋊C4C22×D1711yescharacteristic
1201C2×C22⋊C4C22×D1711yescharacteristic
1202C2×C22⋊C4C22×D1711yescharacteristic
1203C2×C22⋊C4C22×D1711yescharacteristic
1204C2×C22⋊C4C22×D1711yescharacteristic
1205C2×C22⋊C4C22×D1711yescharacteristic
1206C2×C22⋊C4C22×D1711yescharacteristic
1207C2×C22⋊C4C22×D1711yescharacteristic
1208C2×C42—171no—
1209C2×C42—171no—
1210C2×C42—171no—
1211C2×C42—171no—
1212C2×C42—344no—
1213C2×C42C22×D1711yescharacteristic
1214C2×C42C22×D1711yescharacteristic
1215C2×C42C22×D1711yescharacteristic
1216#95—171no—
1217#95—171no—
1218#95—171no—
1219#95—171no—
1220#95—171no—
1221#95—171no—
1222#95—171no—
1223#95—171no—
1224#95—171no—
1225#95—171no—
1226#95—171no—
1227#95—171no—
1228#95—171no—
1229#95—171no—
1230#95—171no—
1231#95—171no—
1232#95—171no—
1233#95—171no—
1234#95—171no—
1235#95—171no—
1236#95—171no—
1237#95—171no—
1238#95—171no—
1239#95—171no—
1240#95—171no—
1241#95—171no—
1242#95C22×D1711yescharacteristic
1243#95C22×D1711yescharacteristic
1244#95C22×D1711yescharacteristic
1245#95C22×D1711yescharacteristic
1246#95C22×D1711yescharacteristic
1247#95C22×D1711yescharacteristic
1248#95C22×D1711yescharacteristic
1249#95C22×D1711yescharacteristic
1250#95C22×D1711yescharacteristic
1251#95C22×D1711yescharacteristic
1252C17#3499111yescharacteristic, complemented, Sylow
1253C24—171no—
1254C24—171no—
1255C24—171no—
1256C24—174no—
1257C24—171no—
1258C24—342no—
1259C24—342no—
1260C24—342no—
1261C24—342no—
1262C24—342no—
1263C24—342no—
1264C24—342no—
1265C24—342no—
1266C24—342no—
1267C24—681no—
1268C24—681no—
1269C24—681no—
1270C24—681no—
1271C24C23×D1711yescharacteristic
1272C24C23×D1711yescharacteristic
1273C2×Q8—342no—
1274C2×Q8—681no—
1275C2×Q8—681no—
1276C2×D4—22no—
1277C2×D4—22no—
1278C2×D4—22no—
1279C2×D4—174no—
1280C2×D4—174no—
1281C2×D4—342no—
1282C2×D4—342no—
1283C2×D4—342no—
1284C2×D4—342no—
1285C2×D4—342no—
1286C2×D4—342no—
1287C2×D4—342no—
1288C2×D4—342no—
1289C2×D4—342no—
1290C2×D4—342no—
1291C2×D4—3432no—
1292C2×D4—342no—
1293C2×D4—342no—
1294C2×D4—342no—
1295C2×D4—342no—
1296C2×D4—342no—
1297C2×D4—342no—
1298C2×D4—681no—
1299C2×D4—681no—
1300C2×D4—681no—
1301C2×D4—681no—
1302C2×D4—681no—
1303C2×D4—681no—
1304C22×C4—22no—
1305C22×C4—22no—
1306C22×C4—22no—
1307C22×C4—22no—
1308C22×C4—41no—
1309C22×C4—41no—
1310C22×C4—171no—
1311C22×C4—171no—
1312C22×C4—171no—
1313C22×C4—174no—
1314C22×C4—174no—
1315C22×C4—171no—
1316C22×C4—171no—
1317C22×C4—171no—
1318C22×C4—171no—
1319C22×C4—171no—
1320C22×C4—171no—
1321C22×C4—171no—
1322C22×C4—171no—
1323C22×C4—171no—
1324C22×C4—342no—
1325C22×C4—342no—
1326C22×C4—342no—
1327C22×C4—342no—
1328C22×C4—342no—
1329C22×C4—342no—
1330C22×C4—342no—
1331C22×C4—342no—
1332C22×C4—342no—
1333C22×C4—342no—
1334C22×C4—342no—
1335C22×C4—342no—
1336C22×C4—342no—
1337C22×C4—342no—
1338C22×C4—342no—
1339C22×C4—342no—
1340C22×C4—342no—
1341C22×C4—342no—
1342C22×C4—342no—
1343C22×C4—342no—
1344C22×C4—342no—
1345C22×C4—342no—
1346C22×C4—342no—
1347C22×C4—342no—
1348C22×C4—342no—
1349C22×C4—681no—
1350C22×C4—681no—
1351C22×C4—681no—
1352C22×C4—681no—
1353C22×C4—681no—
1354C22×C4—681no—
1355C22×C4—681no—
1356C22×C4—681no—
1357C22×C4—681no—
1358C22×C4—681no—
1359C22×C4—681no—
1360C22×C4—681no—
1361C22×C4—681no—
1362C22×C4—681no—
1363C22×C4—681no—
1364C22×C4—681no—
1365C22×C4—681no—
1366C22×C4—6816no—
1367C22×C4—6816no—
1368C22×C4—681no—
1369C22×C4—681no—
1370C22×C4—681no—
1371C22×C4—681no—
1372C22×C4C23×D1711yescharacteristic
1373C22×C4C23×D1711yescharacteristic
1374C22×C4C23×D1711yescharacteristic
1375C22×C4C23×D1711yescharacteristic
1376C22×C4C23×D1711yescharacteristic
1377C22×C4C23×D1711yescharacteristic
1378C22×C4C23×D1711yescharacteristic
1379C22×C4C23×D1711yescharacteristic
1380C22×C4C23×D1711yescharacteristic
1381C22×C4C23×D1711yescharacteristic
1382C22×C4C23×D1711yescharacteristic
1383C22×C4C23×D1711yescharacteristic
1384C22×C4C23×D1711yescharacteristic
1385C4⋊C4—22no—
1386C4⋊C4—22no—
1387C4⋊C4—22no—
1388C4⋊C4—22no—
1389C4⋊C4—22no—
1390C4⋊C4—22no—
1391C4⋊C4—41no—
1392C4⋊C4—41no—
1393C4⋊C4—342no—
1394C4⋊C4—342no—
1395C4⋊C4—342no—
1396C4⋊C4—342no—
1397C4⋊C4—342no—
1398C4⋊C4—342no—
1399C4⋊C4—342no—
1400C4⋊C4—342no—
1401C4⋊C4—342no—
1402C4⋊C4—342no—
1403C4⋊C4—342no—
1404C4⋊C4—342no—
1405C4⋊C4—342no—
1406C4⋊C4—342no—
1407C4⋊C4—342no—
1408C4⋊C4—342no—
1409C4⋊C4—681no—
1410C4⋊C4—681no—
1411C4⋊C4—681no—
1412C4⋊C4—681no—
1413C4⋊C4—681no—
1414C4⋊C4—681no—
1415C4⋊C4—681no—
1416C4⋊C4—681no—
1417C4⋊C4—681no—
1418C4⋊C4D4×D1714yes—
1419C22⋊C4—22no—
1420C22⋊C4—22no—
1421C22⋊C4—22no—
1422C22⋊C4—22no—
1423C22⋊C4—22no—
1424C22⋊C4—22no—
1425C22⋊C4—41no—
1426C22⋊C4—41no—
1427C22⋊C4—41no—
1428C22⋊C4—41no—
1429C22⋊C4—174no—
1430C22⋊C4—174no—
1431C22⋊C4—342no—
1432C22⋊C4—342no—
1433C22⋊C4—342no—
1434C22⋊C4—342no—
1435C22⋊C4—342no—
1436C22⋊C4—342no—
1437C22⋊C4—342no—
1438C22⋊C4—342no—
1439C22⋊C4—342no—
1440C22⋊C4—342no—
1441C22⋊C4—342no—
1442C22⋊C4—342no—
1443C22⋊C4—342no—
1444C22⋊C4—342no—
1445C22⋊C4—342no—
1446C22⋊C4—342no—
1447C22⋊C4—342no—
1448C22⋊C4—342no—
1449C22⋊C4—342no—
1450C22⋊C4—342no—
1451C22⋊C4—342no—
1452C22⋊C4—342no—
1453C22⋊C4—342no—
1454C22⋊C4—342no—
1455C22⋊C4—342no—
1456C22⋊C4—681no—
1457C22⋊C4—681no—
1458C22⋊C4—681no—
1459C22⋊C4—681no—
1460C22⋊C4—681no—
1461C22⋊C4—681no—
1462C22⋊C4—681no—
1463C22⋊C4—681no—
1464C22⋊C4—681no—
1465C22⋊C4—681no—
1466C22⋊C4—681no—
1467C42—22no—
1468C42—22no—
1469C42—41no—
1470C42—174no—
1471C42—342no—
1472C42—342no—
1473C42—681no—
1474C23—21no—
1475C23—21no—
1476C23—21no—
1477C23—21no—
1478C23—21no—
1479C23—21no—
1480C23—21no—
1481C23—21no—
1482C23—21no—
1483C23—21no—
1484C23—21no—
1485C23—21no—
1486C23—172no—
1487C23—172no—
1488C23—172no—
1489C23—172no—
1490C23—172no—
1491C23—172no—
1492C23—172no—
1493C23—348no—
1494C23—348no—
1495C23—348no—
1496C23—341no—
1497C23—341no—
1498C23—341no—
1499C23—341no—
1500C23—341no—
1501C23—341no—
1502C23—341no—
1503C23—341no—
1504C23—341no—
1505C23—341no—
1506C23—341no—
1507C23—341no—
1508C23—341no—
1509C23—341no—
1510C23—341no—
1511C23—341no—
1512C23—341no—
1513C23—341no—
1514C23—341no—
1515C23—341no—
1516C23—341no—
1517C23—684no—
1518C23—684no—
1519C23—684no—
1520C23—684no—
1521C23—684no—
1522C23—684no—
1523C23—684no—
1524C23—684no—
1525C23—684no—
1526C23—684no—
1527C23—684no—
1528C23#41×D1712yes—
1529C23#41×D1712yes—
1530C23C24×D1711yescharacteristic
1531Q8—1362no—
1532D4—28no—
1533D4—348no—
1534D4—348no—
1535D4—348no—
1536D4—684no—
1537D4—684no—
1538D4—684no—
1539D4—1362no—
1540D4—1362no—
1541C2×C4—21no—
1542C2×C4—21no—
1543C2×C4—21no—
1544C2×C4—21no—
1545C2×C4—21no—
1546C2×C4—21no—
1547C2×C4—21no—
1548C2×C4—21no—
1549C2×C4—21no—
1550C2×C4—21no—
1551C2×C4—21no—
1552C2×C4—21no—
1553C2×C4—21no—
1554C2×C4—21no—
1555C2×C4—21no—
1556C2×C4—21no—
1557C2×C4—21no—
1558C2×C4—21no—
1559C2×C4—21no—
1560C2×C4—21no—
1561C2×C4—21no—
1562C2×C4—21no—
1563C2×C4—21no—
1564C2×C4—21no—
1565C2×C4—21no—
1566C2×C4—21no—
1567C2×C4—21no—
1568C2×C4—21no—
1569C2×C4—21no—
1570C2×C4—21no—
1571C2×C4—21no—
1572C2×C4—21no—
1573C2×C4—21no—
1574C2×C4—21no—
1575C2×C4—21no—
1576C2×C4—44no—
1577C2×C4—44no—
1578C2×C4—172no—
1579C2×C4—172no—
1580C2×C4—172no—
1581C2×C4—348no—
1582C2×C4—348no—
1583C2×C4—341no—
1584C2×C4—341no—
1585C2×C4—341no—
1586C2×C4—341no—
1587C2×C4—341no—
1588C2×C4—341no—
1589C2×C4—341no—
1590C2×C4—341no—
1591C2×C4—341no—
1592C2×C4—341no—
1593C2×C4—341no—
1594C2×C4—341no—
1595C2×C4—341no—
1596C2×C4—341no—
1597C2×C4—341no—
1598C2×C4—341no—
1599C2×C4—341no—
1600C2×C4—341no—
1601C2×C4—341no—
1602C2×C4—341no—
1603C2×C4—341no—
1604C2×C4—341no—
1605C2×C4—341no—
1606C2×C4—341no—
1607C2×C4—341no—
1608C2×C4—341no—
1609C2×C4—341no—
1610C2×C4—341no—
1611C2×C4—341no—
1612C2×C4—341no—
1613C2×C4—341no—
1614C2×C4—341no—
1615C2×C4—341no—
1616C2×C4—684no—
1617C2×C4—684no—
1618C2×C4—684no—
1619C2×C4—684no—
1620C2×C4—684no—
1621C2×C4—684no—
1622C2×C4—684no—
1623C2×C4—684no—
1624C2×C4—684no—
1625C2×C4—684no—
1626C2×C4—684no—
1627C2×C4—1362no—
1628C2×C4—1362no—
1629C2×C4—1362no—
1630C2×C4C2×D4×D1712yes—
1631C2×C4C2×D4×D1712yes—
1632C2×C4C2×D4×D1712yes—
1633C2×C4#1058769612yes—
1634C22—22no—
1635C22—22no—
1636C22—22no—
1637C22—22no—
1638C22—22no—
1639C22—22no—
1640C22—41no—
1641C22—41no—
1642C22—41no—
1643C22—41no—
1644C22—41no—
1645C22—41no—
1646C22—41no—
1647C22—41no—
1648C22—174no—
1649C22—174no—
1650C22—342no—
1651C22—342no—
1652C22—342no—
1653C22—342no—
1654C22—342no—
1655C22—342no—
1656C22—342no—
1657C22—342no—
1658C22—342no—
1659C22—342no—
1660C22—342no—
1661C22—342no—
1662C22—342no—
1663C22—342no—
1664C22—342no—
1665C22—6816no—
1666C22—6816no—
1667C22—681no—
1668C22—681no—
1669C22—681no—
1670C22—681no—
1671C22—681no—
1672C22—681no—
1673C22—681no—
1674C22—681no—
1675C22—681no—
1676C22—681no—
1677C22—681no—
1678C22C22×D4×D1711yescharacteristic
1679C22C2×#41×D1711yescharacteristic
1680C22C2×#41×D1711yescharacteristic
1681C22H(5,𝔽2)×D1711yescharacteristic
1682C22C2×#1058769611yescharacteristic
1683C222−1+4×D1711yescharacteristic
1684C22#1176364511yescharacteristic
1685C4—22no—
1686C4—22no—
1687C4—22no—
1688C4—22no—
1689C4—41no—
1690C4—41no—
1691C4—41no—
1692C4—41no—
1693C4—41no—
1694C4—41no—
1695C4—41no—
1696C4—41no—
1697C4—41no—
1698C4—342no—
1699C4—342no—
1700C4—342no—
1701C4—681no—
1702C4—681no—
1703C4—681no—
1704C4—681no—
1705C4—681no—
1706C4—681no—
1707C4—681no—
1708C4—681no—
1709C4—681no—
1710C2—42no—
1711C2—42no—
1712C2—344no—
1713C2—344no—
1714C2—682no—
1715C2—1361no—
1716C2D17×#52511yescharacteristic
1717C2D17×#53911yescharacteristic
1718C2#1454219411yescharacteristic
1719C2#1454241411yescharacteristic
1720C2#1454246311yescharacteristic
1721C2#1454271511yescharacteristic
1722C2#1454283011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2460C2
prime radical#14532153C2
hypercenter#2460D17
hypocenterC17#34991
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2460

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#11763407C2semidirect
2. C2×C4×D4×D17C2semidirect
3. #14537102C2semidirect
4. #14537091C2semidirect
5. #14537079C2semidirect
6. #14537072C2semidirect
7. #14534706C2semidirect
8. #14534680C2semidirect
9. #14534651C2semidirect
10. #14534630C2semidirect
11. #14533034C2semidirect
12. #14532921C2semidirect
13. #14532820C2semidirect
14. #14532775C2semidirect
15. #14532666C2semidirect
16. #14532598C2semidirect
17. #14532592C2semidirect
18. #14532524C2semidirect
19. #14532446C2semidirect
20. #14532332C2semidirect
21. #14532268C2semidirect
22. #14532253C2semidirect
23. #14532173C2semidirect
25. #14532106C2semidirect
26. #14531488C2semidirect
27. #14531454C2semidirect
28. #14531416C2semidirect
29. C4×#10587568C2semidirect
30. D17×#385C2semidirect
31. C17×#2460C2semidirect
36. C2×#10587584C22semidirect
37. C2×#10587562C22semidirect
38. C2×#10587575C22semidirect
40. C2×#10587580C22semidirect
41. C2×#10587580C22semidirect
42. C2×#10587580C22semidirect
43. C2×#10587580C22semidirect
46. C2×#10587583C22semidirect
47. C2×#10587610C22semidirect
48. C2×#10587582C22semidirect
49. C2×#10587582C22semidirect
56. C2×C4×D68C22semidirect
61. C2×C4×C22⋊D17C22semidirect
66. C2×C4⋊C4×D17C22semidirect
67. C2×C4⋊C4×D17C22semidirect
73. #11762748C22semidirect
74. #11762746C22semidirect
75. #11762745C22semidirect
76. #11762745C22semidirect
77. #11762742C22semidirect
78. #11762741C22semidirect
79. #11762740C22semidirect
80. #11762739C22semidirect
81. #11762737C22semidirect
82. #11762737C22semidirect
83. #11762736C22semidirect
84. #11762736C22semidirect
85. #11762735C22semidirect
86. #11762732C22semidirect
87. #11762732C22semidirect
88. #11762731C22semidirect
89. #11762730C22semidirect
90. #11762727C22semidirect
92. #11762725C22semidirect
95. #11762724C22semidirect
96. #11762724C22semidirect
98. #11762721C22semidirect
101. #11762707C22semidirect
102. #11762706C22semidirect
103. #11762704C22semidirect
104. #11762704C22semidirect
105. #11762703C22semidirect
106. #11762700C22semidirect
107. #11762700C22semidirect
108. #11762699C22semidirect
109. #11762698C22semidirect
110. #11762698C22semidirect
111. #11762696C22semidirect
112. #11762696C22semidirect
113. #11762695C22semidirect
114. #11762693C22semidirect
115. #11762693C22semidirect
116. #11762692C22semidirect
117. #11762691C22semidirect
118. #11762688C22semidirect
125. #11762687C22semidirect
126. #11762687C22semidirect
127. #11762686C22semidirect
128. #11762686C22semidirect
131. #11762685C22semidirect
132. #11762684C22semidirect
133. #11762684C22semidirect
134. #11762684C22semidirect
135. #11762684C22semidirect
140. #11762683C22semidirect
141. #11762683C22semidirect
142. #11762683C22semidirect
143. #11762683C22semidirect
144. #11762683C22semidirect
145. #11762683C22semidirect
146. #11762682C22semidirect
147. #11762681C22semidirect
148. #11762681C22semidirect
155. #11762680C22semidirect
156. #11762676C22semidirect
157. #11762673C22semidirect
158. #11762671C22semidirect
159. #11762671C22semidirect
160. #11762671C22semidirect
164. #11762666C22semidirect
165. #11762666C22semidirect
171. C4×#63227C22semidirect
172. #95×D17C22semidirect
173. #95×D17C22semidirect
174. C2×C17×#125C22semidirect
176. C17×#397C22semidirect
177. C17×#396C22semidirect
180. C17×#388C22semidirect
181. C17×#388C22semidirect
182. C17×#387C22semidirect
183. C17×#387C22semidirect
184. C17×#387C22semidirect
185. C17×#385C22semidirect
186. C17×#385C22semidirect
187. C17×#380C22semidirect
188. C4×C22⋊C4×C17C22semidirect
335. #10587579D4semidirect
787. #2460D17semidirect
854. C2×D17#539semidirect
887. C2×#125C2×D17semidirect
936. #397C2×D17semidirect
940. #396C2×D17semidirect
965. #388C2×D17semidirect
966. #388C2×D17semidirect
974. #387C2×D17semidirect
975. #387C2×D17semidirect
976. #387C2×D17semidirect
1015. #385C2×D17semidirect
1016. #385C2×D17semidirect
1027. #380C2×D17semidirect
1034. C4×C22⋊C4C2×D17semidirect
1252. C17#34991semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117634072
C2×C4×D4×D172
#145371022
#145370912
#145370792
#145370722
#145347062
#145346802
#145346512
#145346302
#145330342
#145329212
#145328202
#145327752
#145326662
#145325982
#145325922
#145325242
#145324462
#145323322
#145322682
#145322532
#145321732
#145321532
#145321062
#145314882
#145314542
#145314162
C4×#105875682
D17×#3852
C17×#24602
#3499117