Finite Group Databasebeta

← #17241198

Subgroups — #17241198

Order 4352.

2440 conjugacy classes of subgroups.

The subgroup lattice has 1676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763425C211yesmaximal, characteristic, complemented
2C2×#11763319C211yesmaximal, characteristic, complemented
3#14537079C211yesmaximal, characteristic, complemented
4#14537072C211yesmaximal, characteristic, complemented
5#14535336C211yesmaximal, characteristic, complemented
6#14535313C211yesmaximal, characteristic, complemented
7#14535280C211yesmaximal, characteristic, complemented
8#14535242C211yesmaximal, characteristic, complemented
9#14535185C211yesmaximal, characteristic, complemented
10#14535180C211yesmaximal, characteristic, complemented
11#14535159C211yesmaximal, characteristic, complemented
12#14535099C211yesmaximal, characteristic, complemented
13#14535085C211yesmaximal, characteristic, complemented
14#14535072C211yesmaximal, characteristic, complemented
15#14535068C211yesmaximal, characteristic, complemented
16#14535038C211yesmaximal, characteristic, complemented
17#14535019C211yesmaximal, characteristic, complemented
18#14535007C211yesmaximal, characteristic, complemented
19#14534989C211yesmaximal, characteristic, complemented
20#14534706C211yesmaximal, characteristic, complemented
21#14534630C211yesmaximal, characteristic, complemented
22#14534462C211yesmaximal, characteristic, complemented
23#14534397C211yesmaximal, characteristic, complemented
24#14534360C211yesmaximal, characteristic, complemented
25#14534345C211yesmaximal, characteristic, complemented
26#14534140C211yesmaximal, characteristic, complemented
27#14533968C211yesmaximal, characteristic, complemented
28#14532407C211yesmaximal, characteristic, complemented
29#14532392C211yesmaximal, characteristic, complemented
30#14531412C211yesmaximal, characteristic, complemented
31C17×#2691C211yesmaximal, characteristic, complemented
32C22×#63254C2211yescharacteristic
33C23×C4×D17C2211yescharacteristic
34#11763425—28no—
35C2×#10587574C2211yescharacteristic, complemented
36C2×#10587574C2211yescharacteristic, complemented
37C2×#10587584C2211yescharacteristic
38C2×#10587561C2211yescharacteristic
39C2×#10587571C2211yescharacteristic
40C2×#10587571C2211yescharacteristic
41C2×#10587571C2211yescharacteristic, complemented
42#11763319—28no—
43C2×#10587580C2211yescharacteristic
44C2×#10587580C2211yescharacteristic
45C2×#10587572C2211yescharacteristic, complemented
46C2×#10587569C2211yescharacteristic
47C2×#10587569C2211yescharacteristic
48C2×#10587583C2211yescharacteristic
49C2×#10587583C2211yescharacteristic
50C2×#10587583C2211yescharacteristic
51C2×#10587610C2211yescharacteristic
52C2×#10587610C2211yescharacteristic
53C2×#10587582C2211yescharacteristic, complemented
54C2×#10587564C2211yescharacteristic, complemented
55C2×#10587616C2211yescharacteristic
56C2×#10587570C2211yescharacteristic
57C2×#10587625C2211yescharacteristic, complemented
58C2×#10587624C2211yescharacteristic
59C2×#10587568C2211yescharacteristic
60C2×#10587623C2211yescharacteristic
61C2×#10587623C2211yescharacteristic
62C2×C4×Dic34C2211yescharacteristic, complemented
63C2×D4×Dic17C2211yescharacteristic
64C2×D4×Dic17C2211yescharacteristic
65C2×#10587567C2211yescharacteristic
66C2×#10587567C2211yescharacteristic
67C2×#10587578C2211yescharacteristic
68C2×#10587578C2211yescharacteristic, complemented
69#11762751C2211yescharacteristic, complemented
70#11762748C2211yescharacteristic, complemented
71#11762746C2211yescharacteristic, complemented
72#11762745C2211yescharacteristic
73#11762745C2211yescharacteristic
74#11762745C2211yescharacteristic, complemented
75#11762742C2211yescharacteristic, complemented
76#11762742C2211yescharacteristic, complemented
77#11762740C2211yescharacteristic, complemented
78#11762738C2211yescharacteristic
79#11762737C2211yescharacteristic, complemented
80#11762736C2211yescharacteristic
81#11762736C2211yescharacteristic
82#11762735C2211yescharacteristic
83#11762731C2211yescharacteristic
84#11762731C2211yescharacteristic, complemented
85#11762731C2211yescharacteristic, complemented
86#11762730C2211yescharacteristic, complemented
87#11762730C2211yescharacteristic, complemented
88#11762730C2211yescharacteristic, complemented
89#11762730C2211yescharacteristic, complemented
90#11762727C2211yescharacteristic
91#11762726C2211yescharacteristic
92#11762725C2211yescharacteristic
93#11762725C2211yescharacteristic
94#11762725C2211yescharacteristic
95#11762725C2211yescharacteristic, complemented
96#11762725C2211yescharacteristic, complemented
97#11762724C2211yescharacteristic
98#11762724C2211yescharacteristic
99#11762724C2211yescharacteristic
100#11762723C2211yescharacteristic, complemented
101#11762722C2211yescharacteristic
102#11762722C2211yescharacteristic, complemented
103#11762721C2211yescharacteristic
104#11762721C2211yescharacteristic
105#11762721C2211yescharacteristic, complemented
106#11762721C2211yescharacteristic, complemented
107#11762718C2211yescharacteristic
108#11762718C2211yescharacteristic
109#11762717C2211yescharacteristic
110#11762717C2211yescharacteristic
111#11762713C2211yescharacteristic, complemented
112#11762712C2211yescharacteristic
113#11762709C2211yescharacteristic
114#11762709C2211yescharacteristic
115#11762708C2211yescharacteristic, complemented
116#11762708C2211yescharacteristic, complemented
117#11762707C2211yescharacteristic, complemented
118#11762702C2211yescharacteristic
119#11762702C2211yescharacteristic
120#11762702C2211yescharacteristic, complemented
121#11762701C2211yescharacteristic
122#11762701C2211yescharacteristic
123#11762701C2211yescharacteristic, complemented
124#11762700C2211yescharacteristic
125#11762699C2211yescharacteristic
126#11762699C2211yescharacteristic
127#11762699C2211yescharacteristic, complemented
128#11762696C2211yescharacteristic, complemented
129#11762696C2211yescharacteristic, complemented
130#11762696C2211yescharacteristic, complemented
131#11762696C2211yescharacteristic, complemented
132#11762692C2211yescharacteristic, complemented
133#11762690C2211yescharacteristic, complemented
134#11762690C2211yescharacteristic, complemented
135#11762689C2211yescharacteristic
136#11762688C2211yescharacteristic
137#11762688C2211yescharacteristic
138#11762687C2211yescharacteristic
139#11762687C2211yescharacteristic
140#11762687C2211yescharacteristic
141#11762686C2211yescharacteristic
142#11762686C2211yescharacteristic
143#11762686C2211yescharacteristic
144#11762686C2211yescharacteristic, complemented
145#11762685C2211yescharacteristic
146#11762685C2211yescharacteristic, complemented
147#11762684C2211yescharacteristic
148#11762684C2211yescharacteristic
149#11762684C2211yescharacteristic, complemented
150#11762684C2211yescharacteristic, complemented
151#11762684C2211yescharacteristic, complemented
152#11762683C2211yescharacteristic
153#11762683C2211yescharacteristic
154#11762683C2211yescharacteristic
155#11762683C2211yescharacteristic
156#11762683C2211yescharacteristic, complemented
157#11762681C2211yescharacteristic
158#11762681C2211yescharacteristic, complemented
159#11762680C2211yescharacteristic
160#11762680C2211yescharacteristic
161#11762676C2211yescharacteristic, complemented
162#11762674C2211yescharacteristic, complemented
163#11762671C2211yescharacteristic
164#11762671C2211yescharacteristic
165#11762669C2211yescharacteristic, complemented
166#11762667C2211yescharacteristic, complemented
167#11762666C2211yescharacteristic
168#11762666C2211yescharacteristic
169#11762664C2211yescharacteristic
170#11762664C2211yescharacteristic
171#11762664C2211yescharacteristic
172C22⋊C4×Dic17C2211yescharacteristic, complemented
173C2×#10587502C2211yescharacteristic, complemented
174C2×C17×#126C2211yescharacteristic, complemented
175C2×C17×#121C2211yescharacteristic
176C17×#398C2211yescharacteristic, complemented
177C17×#397C2211yescharacteristic, complemented
178C17×#396C2211yescharacteristic, complemented
179C17×#394C2211yescharacteristic
180C17×#394C2211yescharacteristic
181C17×#394C2211yescharacteristic, complemented
182C17×#390C2211yescharacteristic
183C17×#387C2211yescharacteristic, complemented
184C17×#386C2211yescharacteristic
185C17×#386C2211yescharacteristic, complemented
186C17×#385C2211yescharacteristic
187C17×#385C2211yescharacteristic, complemented
188C17×#380C2211yescharacteristic
189C24×D17C2311yescharacteristic
190C22×D4×C17C2311yescharacteristic
191C22×D4×C17C2311yescharacteristic
192C22×D4×C17C2311yescharacteristic
193C23×C4×C17C2311yescharacteristic
194C23×C4×C17C2311yescharacteristic
195C22×C22⋊D17C2311yescharacteristic
196C22×C22⋊D17C2311yescharacteristic
197C22×C22⋊D17C2311yescharacteristic
198C22×C22⋊D17C2311yescharacteristic
199C22×C22⋊D17C2311yescharacteristic
200C22×C22⋊D17C2311yescharacteristic
201C22×C22⋊D17C2311yescharacteristic
202C23×Dic17C2311yescharacteristic
203C23×Dic17C2311yescharacteristic
204C23×Dic17C2311yescharacteristic
205C23×Dic17C2311yescharacteristic
206C2×#63254—24no—
207C2×#63254—42no—
208C2×#63254—42no—
209C22×D68C2311yescharacteristic
210C22×D68C2311yescharacteristic
211C22×C4×D17—24no—
212C22×C4×D17—42no—
213C22×C4×D17—42no—
214C22×C4×D17C2311yescharacteristic
215C22×C4×D17C2311yescharacteristic
216C22×C4×D17C2311yescharacteristic
217C22×C4×D17C2311yescharacteristic
218C22×C4×D17C2311yescharacteristic
219C22×Dic34C2311yescharacteristic
220C22×Dic34C2311yescharacteristic
221C22×Dic34C2311yescharacteristic
222C22×Dic34C2311yescharacteristic
223C17×#126—24no—
224C17×#121—24no—
225C2×C4⋊C4×C17C2311yescharacteristic
226C2×C4⋊C4×C17C2311yescharacteristic
227C2×C4⋊C4×C17C2311yescharacteristic
228C2×C4⋊C4×C17C2311yescharacteristic
229C2×C4⋊C4×C17C2311yescharacteristic
230C2×C4⋊C4×C17C2311yescharacteristic
231C2×C4⋊C4×C17C2311yescharacteristic
232C2×C4⋊C4×C17C2311yescharacteristic
233C2×C22⋊C4×C17C2311yescharacteristic
234C2×C22⋊C4×C17C2311yescharacteristic
235C2×C22⋊C4×C17C2311yescharacteristic
236C2×C22⋊C4×C17C2311yescharacteristic
237C2×C22⋊C4×C17C2311yescharacteristic
238C2×C22⋊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×C42×C17C2311yescharacteristic
247C2×C22⋊Dic17C2311yescharacteristic
248C2×C22⋊Dic17C2311yescharacteristic
249C2×C22⋊Dic17C2311yescharacteristic
250C2×C22⋊Dic17C2311yescharacteristic
251C2×C22⋊Dic17C2311yescharacteristic
252C2×C22⋊Dic17C2311yescharacteristic
253C2×C22⋊Dic17C2311yescharacteristic
254C2×C22⋊Dic17C2311yescharacteristic
255C2×C22⋊Dic17C2311yescharacteristic
256C2×C22⋊Dic17C2311yescharacteristic
257C2×C22⋊Dic17C2311yescharacteristic
258C2×C22⋊Dic17C2311yescharacteristic
259#10587625—42no—
260#10587624—24no—
261#10587623—24no—
262#10587623—24no—
263D4×Dic17—24no—
264D4×Dic17—24no—
265#10587616—42no—
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×C4⋊Dic17C2311yescharacteristic
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
303C2×C4⋊Dic17C2311yescharacteristic
304C2×C4⋊Dic17C2311yescharacteristic
305C2×C4⋊Dic17C2311yescharacteristic
306#10587610—24no—
307#10587610—42no—
308C2×#63225C2311yescharacteristic
309C2×#63225C2311yescharacteristic
310C2×#63225C2311yescharacteristic
311C2×#63225C2311yescharacteristic
312C2×#63225C2311yescharacteristic
313C2×#63225C2311yescharacteristic
314C2×#63225C2311yescharacteristic
315C2×#63225C2311yescharacteristic
316C2×#63225C2311yescharacteristic
317C2×#63225C2311yescharacteristic
318C2×#63225C2311yescharacteristic
319C2×C4×Dic17C2311yescharacteristic
320C2×C4×Dic17C2311yescharacteristic
321C2×C4×Dic17C2311yescharacteristic
322C2×C4×Dic17C2311yescharacteristic
323C2×C4×Dic17C2311yescharacteristic
324C2×C4×Dic17C2311yescharacteristic
325#10587584—24no—
326#10587583—24no—
327#10587583—24no—
328#10587583—42no—
329#10587582—24no—
330#10587580—24no—
331#10587580—42no—
332#10587578—24no—
333#10587578—24no—
334#10587574—24no—
335#10587574—42no—
336#10587572—24no—
337#10587571—24no—
338#10587571—24no—
339#10587571—42no—
340#10587570—24no—
341#10587569—24no—
342#10587569—24no—
343#10587568—42no—
344#10587567—24no—
345#10587567D418yescomplemented
346#10587564—24no—
347#10587561—24no—
348C4×Dic34—24no—
349C17×#95C2311yescharacteristic
350C17×#95C2311yescharacteristic
351C17×#95C2311yescharacteristic
352C17×#95C2311yescharacteristic
353C17×#95C2311yescharacteristic
354C17×#95C2311yescharacteristic
355C17×#95C2311yescharacteristic
356C17×#95C2311yescharacteristic
357#10587502C2311yescharacteristic
358#10587502C2311yescharacteristic
359#10587502C2311yescharacteristic
360#10587502C2311yescharacteristic
361#10587502C2311yescharacteristic
362#10587502C2311yescharacteristic
363#10587502C2311yescharacteristic
364#10587502C2311yescharacteristic
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
385C24×C17C2411yescharacteristic
386C24×C17C2411yescharacteristic
387C24×C17C2411yescharacteristic
388C23×D17—22no—
389C23×D17—22no—
390C23×D17—22no—
391C23×D17—41no—
392C23×D17—41no—
393C23×D17—41no—
394C23×D17—41no—
395C23×D17C2411yescharacteristic
396C23×D17C2411yescharacteristic
397C23×D17C2411yescharacteristic
398C2×D4×C17—22no—
399C2×D4×C17—22no—
400C2×D4×C17—22no—
401C2×D4×C17—22no—
402C2×D4×C17—22no—
403C2×D4×C17—22no—
404C2×D4×C17—41no—
405C2×D4×C17—41no—
406C2×D4×C17—41no—
407C22×C4×C17—22no—
408C22×C4×C17—22no—
409C22×C4×C17—41no—
410C22×C4×C17—41no—
411C22×C4×C17—41no—
412C22×C4×C17—41no—
413C22×C4×C17C2411yescharacteristic
414C22×C4×C17C2411yescharacteristic
415C22×C4×C17C2411yescharacteristic
416C22×C4×C17C2411yescharacteristic
417C22×C4×C17C2411yescharacteristic
418C22×C4×C17C2411yescharacteristic
419C22×C4×C17C2411yescharacteristic
420C22×C4×C17C2411yescharacteristic
421C22×C4×C17C2411yescharacteristic
422C22×C4×C17C2411yescharacteristic
423C22×C4×C17C2411yescharacteristic
424C22×C4×C17C2411yescharacteristic
425C2×C22⋊D17—22no—
426C2×C22⋊D17—22no—
427C2×C22⋊D17—22no—
428C2×C22⋊D17—22no—
429C2×C22⋊D17—22no—
430C2×C22⋊D17—22no—
431C2×C22⋊D17—22no—
432C2×C22⋊D17—41no—
433C2×C22⋊D17—41no—
434C2×C22⋊D17—41no—
435C2×C22⋊D17—41no—
436C2×C22⋊D17—41no—
437C2×C22⋊D17—41no—
438C2×C22⋊D17—41no—
439C2×C22⋊D17—41no—
440C2×C22⋊D17—41no—
441C2×C22⋊D17—41no—
442C2×C22⋊D17—41no—
443C2×C22⋊D17—41no—
444C2×C22⋊D17—41no—
445C2×C22⋊D17C2×D414yes—
446C22×Dic17—22no—
447C22×Dic17—22no—
448C22×Dic17—41no—
449C22×Dic17—41no—
450C22×Dic17—41no—
451C22×Dic17—41no—
452C22×Dic17—41no—
453C22×Dic17—41no—
454C22×Dic17—41no—
455C22×Dic17—41no—
456C22×Dic17—41no—
457C22×Dic17C2×D414yes—
458C22×Dic17C2411yescharacteristic
459C22×Dic17C2411yescharacteristic
460C22×Dic17C2411yescharacteristic
461C22×Dic17C2411yescharacteristic
462C22×Dic17C2411yescharacteristic
463C22×Dic17C2411yescharacteristic
464C22×Dic17C2411yescharacteristic
465C22×Dic17C2411yescharacteristic
466C22×Dic17C2411yescharacteristic
467C22×Dic17C2411yescharacteristic
468C22×Dic17C2411yescharacteristic
469C22×Dic17C2411yescharacteristic
470C22×Dic17C2411yescharacteristic
471#63254—416no—
472C2×D68—22no—
473C2×D68—22no—
474C2×D68—41no—
475C2×D68—41no—
476C2×D68—41no—
477C2×D68—41no—
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—416no—
487C2×C4×D17—41no—
488C2×C4×D17—41no—
489C2×C4×D17—41no—
490C2×C4×D17—41no—
491C2×C4×D17—41no—
492C2×C4×D17—41no—
493C2×C4×D17C2×D414yes—
494C2×Dic34—22no—
495C2×Dic34—22no—
496C2×Dic34—22no—
497C2×Dic34—22no—
498C2×Dic34—22no—
499C2×Dic34—41no—
500C2×Dic34—41no—
501C2×Dic34—41no—
502C2×Dic34—41no—
503C2×Dic34—41no—
504C2×Dic34—41no—
505C2×Dic34—41no—
506C4⋊C4×C17—22no—
507C4⋊C4×C17—22no—
508C4⋊C4×C17—22no—
509C4⋊C4×C17—22no—
510C4⋊C4×C17—22no—
511C4⋊C4×C17—41no—
512C4⋊C4×C17—41no—
513C4⋊C4×C17—41no—
514C22⋊C4×C17—22no—
515C22⋊C4×C17—22no—
516C22⋊C4×C17—22no—
517C22⋊C4×C17—22no—
518C22⋊C4×C17—41no—
519C22⋊C4×C17—41no—
520C22⋊C4×C17—41no—
521C22⋊C4×C17—41no—
522C22⋊C4×C17—41no—
523C22⋊C4×C17—41no—
524C22⋊C4×C17—41no—
525C22⋊C4×C17—41no—
526C22⋊C4×C17C2×D414yes—
527C42×C17—22no—
528C22⋊Dic17—22no—
529C22⋊Dic17—22no—
530C22⋊Dic17—22no—
531C22⋊Dic17—22no—
532C22⋊Dic17—22no—
533C22⋊Dic17—41no—
534C22⋊Dic17—41no—
535C22⋊Dic17—41no—
536C22⋊Dic17—41no—
537C22⋊Dic17—41no—
538C22⋊Dic17—41no—
539C22⋊Dic17—41no—
540#63227—22no—
541#63227—22no—
542#63227—22no—
543#63227—22no—
544#63227—22no—
545#63227—22no—
546#63227—22no—
547#63227—22no—
548#63227—22no—
549#63227—22no—
550#63227—22no—
551#63227—22no—
552#63227—22no—
553#63227—22no—
554#63227—41no—
555#63227—41no—
556#63227—41no—
557#63227—41no—
558#63227—41no—
559#63227—41no—
560#63227—41no—
561#63227—41no—
562#63227—41no—
563#63227—41no—
564#63227—41no—
565#63227—41no—
566#63227C2×D414yes—
567C4⋊Dic17—22no—
568C4⋊Dic17—22no—
569C4⋊Dic17—22no—
570C4⋊Dic17—22no—
571C4⋊Dic17—22no—
572C4⋊Dic17—22no—
573C4⋊Dic17—41no—
574C4⋊Dic17—41no—
575C4⋊Dic17—41no—
576C4⋊Dic17—41no—
577C4⋊Dic17—41no—
578C4⋊Dic17—41no—
579C4⋊Dic17—41no—
580#63225—22no—
581#63225—22no—
582#63225—22no—
583#63225—22no—
584#63225—22no—
585#63225—22no—
586#63225—41no—
587#63225—41no—
588#63225—41no—
589#63225—41no—
590#63225C2×D414yes—
591C4×Dic17—22no—
592C4×Dic17—22no—
593C4×Dic17—22no—
594C4×Dic17—41no—
595C4×Dic17—41no—
596C4×Dic17C2×D414yes—
597#36712—171nomaximal, Sylow
598C23×C17—21no—
599C23×C17—21no—
600C23×C17—21no—
601C23×C17—21no—
602C23×C17—21no—
603C23×C17—21no—
604C23×C17—21no—
605C23×C17—21no—
606C23×C17—21no—
607C23×C17—21no—
608C23×C17—21no—
609C23×C17—21no—
610C23×C17—21no—
611C23×C17—21no—
612C23×C17—21no—
613C23×C17—21no—
614C23×C17—21no—
615C23×C17—21no—
616C23×C17—21no—
617C23×C17C22×D412yes—
618C23×C172−1+412yes—
619C23×C17C2511yescharacteristic
620C22×D17—21no—
621C22×D17—21no—
622C22×D17—21no—
623C22×D17—21no—
624C22×D17—21no—
625C22×D17—21no—
626C22×D17—21no—
627C22×D17—21no—
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—21no—
637C22×D17—21no—
638C22×D17—21no—
639C22×D17—44no—
640C22×D17—44no—
641C22×D17—44no—
642C22×D17—44no—
643C22×D17—44no—
644C22×D17—44no—
645C22×D17—44no—
646C22×D17C22×D412yes—
647C22×D17H(5,𝔽2)12yes—
648D4×C17—44no—
649D4×C17—44no—
650D4×C17—44no—
651C2×C4×C17—21no—
652C2×C4×C17—21no—
653C2×C4×C17—21no—
654C2×C4×C17—21no—
655C2×C4×C17—21no—
656C2×C4×C17—21no—
657C2×C4×C17—21no—
658C2×C4×C17—21no—
659C2×C4×C17—21no—
660C2×C4×C17—21no—
661C2×C4×C17—21no—
662C2×C4×C17—21no—
663C2×C4×C17—21no—
664C2×C4×C17—21no—
665C2×C4×C17—21no—
666C2×C4×C17—21no—
667C2×C4×C17—21no—
668C2×C4×C17—21no—
669C2×C4×C17—21no—
670C2×C4×C17—21no—
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—44no—
685C2×C4×C17—82no—
686C2×C4×C17C22×D412yes—
687C2×C4×C17C22×D412yes—
688C2×C4×C17H(5,𝔽2)12yes—
689C22⋊D17—44no—
690C22⋊D17—44no—
691C22⋊D17—44no—
692C22⋊D17—44no—
693C22⋊D17—82no—
694C22⋊D17—82no—
695C22⋊D17—82no—
696C2×Dic17—21no—
697C2×Dic17—21no—
698C2×Dic17—21no—
699C2×Dic17—21no—
700C2×Dic17—21no—
701C2×Dic17—21no—
702C2×Dic17—21no—
703C2×Dic17—21no—
704C2×Dic17—21no—
705C2×Dic17—21no—
706C2×Dic17—21no—
707C2×Dic17—21no—
708C2×Dic17—21no—
709C2×Dic17—21no—
710C2×Dic17—21no—
711C2×Dic17—21no—
712C2×Dic17—21no—
713C2×Dic17—21no—
714C2×Dic17—21no—
715C2×Dic17—21no—
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—44no—
733C2×Dic17—44no—
734C2×Dic17—44no—
735C2×Dic17—82no—
736C2×Dic17C22×D412yes—
737C2×Dic17C22×D412yes—
738C2×Dic17C22×D412yes—
739D68—82no—
740D68—82no—
741C4×D17—28no—
742C4×D17—44no—
743C4×D17—44no—
744C4×D17—44no—
745C4×D17—44no—
746Dic34—44no—
747Dic34—44no—
748Dic34—82no—
749Dic34—82no—
750C2×#542—171no—
751C2×#525—171no—
752#2849—171no—
753#2848—171no—
754#2696—171no—
755#2695—171no—
756#2692—171no—
757#2691D1711yescharacteristic, complemented
758#2689—171no—
759#2686—171no—
760#2685—171no—
761#2684—171no—
762#2677—171no—
763#2676—171no—
764#2674—171no—
765#2674—171no—
766#2672—171no—
767#2671—171no—
768#2670—171no—
769#2668—171no—
770#2638—171no—
771#2630—171no—
772#2609—171no—
773#2602—171no—
774#2599—171no—
775#2598—171no—
776#2580—171no—
777#2564—171no—
778#2432—171no—
779#2430—171no—
780#2318—171no—
781C22×C17—22no—
782C22×C17—22no—
783C22×C17—22no—
784C22×C17—22no—
785C22×C17—22no—
786C22×C17—22no—
787C22×C17—41no—
788C22×C17—41no—
789C22×C17—41no—
790C22×C17—41no—
791C22×C17—41no—
792C22×C17—41no—
793C22×C17—41no—
794C22×C17—41no—
795C22×C17—41no—
796C22×C17—41no—
797C22×C17—41no—
798C22×C17—41no—
799C22×C17—41no—
800C22×C17—41no—
801C22×C17—41no—
802C22×C17C23×D411yescharacteristic
803C22×C17C2×H(5,𝔽2)11yescharacteristic
804C22×C17C2×H(5,𝔽2)11yescharacteristic
805C22×C17C2×2−1+411yescharacteristic
806C22×C17#58511yescharacteristic
807C22×C17#58511yescharacteristic
808C22×C17#58511yescharacteristic
809C2×D17—22no—
810C2×D17—22no—
811C2×D17—22no—
812C2×D17—22no—
813C2×D17—22no—
814C2×D17—22no—
815C2×D17—416no—
816C2×D17—41no—
817C2×D17—41no—
818C2×D17—41no—
819C2×D17—41no—
820C2×D17—41no—
821C2×D17—41no—
822C2×D17—41no—
823C2×D17—41no—
824C2×D17—41no—
825C2×D17—41no—
826C2×D17—41no—
827C2×D17—41no—
828C2×D17—41no—
829C2×D17—41no—
830C2×D17—41no—
831C4×C17—22no—
832C4×C17—22no—
833C4×C17—22no—
834C4×C17—41no—
835C4×C17—41no—
836C4×C17—41no—
837C4×C17—41no—
838C4×C17—41no—
839C4×C17—41no—
840C4×C17—41no—
841C4×C17—41no—
842C4×C17—41no—
843Dic17—22no—
844Dic17—22no—
845Dic17—22no—
846Dic17—41no—
847Dic17—41no—
848Dic17—41no—
849Dic17—41no—
850Dic17—41no—
851Dic17—41no—
852Dic17—41no—
853Dic17—41no—
854Dic17—41no—
855Dic17—41no—
856C22×#41—171no—
857C24×C4—171no—
858#542—348no—
859C2×C4⋊Q8—171no—
860C2×C4⋊Q8—171no—
861C2×#126—171no—
862C2×#126C2×D1711yescharacteristic, complemented
863C2×#124—171no—
864C2×#124—171no—
865C2×#124—171no—
866C2×#124—171no—
867#525—348no—
868C2×#123—171no—
869C2×#123—171no—
870C2×#123—171no—
871C2×#123—171no—
872C2×#123—171no—
873C2×C22⋊Q8—171no—
874C2×C22⋊Q8—171no—
875C2×C22⋊Q8—171no—
876C2×C22⋊Q8—171no—
877C2×C22⋊Q8—171no—
878C2×C22⋊Q8—171no—
879C2×C22⋊Q8—171no—
880C2×#121—171no—
881C2×#121—171no—
882C2×#121—171no—
883C2×#121—171no—
884C2×#121C2×D1711yescharacteristic
885C2×#120—171no—
886C2×#120—171no—
887C2×#120—171no—
888C2×C4×Q8—171no—
889C2×C4×D4—171no—
890C2×C4×D4—171no—
891C2×C4×D4—171no—
892C2×C4×D4—171no—
893C2×#117—171no—
894C2×#117—171no—
895#400—171no—
896#400—171no—
897#399—171no—
898#399—171no—
899#399—171no—
900#399—171no—
901#398—171no—
902#398—171no—
903#398—171no—
904#398C2×D1711yescharacteristic, complemented
905#397—171no—
906#397—171no—
907#397—171no—
908#397—171no—
909#397—171no—
910#397C2×D1711yescharacteristic, complemented
911#396—171no—
912#396—171no—
913#396—171no—
914#396C2×D1711yescharacteristic, complemented
915#395—171no—
916#395—171no—
917#395—171no—
918#395—171no—
919#394—171no—
920#394—171no—
921#394—171no—
922#394—171no—
923#394—171no—
924#394—171no—
925#394—171no—
926#394—171no—
927#394—171no—
928#394—171no—
929#394—171no—
930#394C2×D1711yescharacteristic
931#394C2×D1711yescharacteristic
932#394C2×D1711yescharacteristic, complemented
933#393—171no—
934#393—171no—
935#393—171no—
936#393—171no—
937#393—171no—
938#393—171no—
939#392—171no—
940#392—171no—
941#392—171no—
942#392—171no—
943#391—171no—
944#390—171no—
945#390—171no—
946#390—171no—
947#390C2×D1711yescharacteristic
948#389—171no—
949#389—171no—
950#389—171no—
951#388—171no—
952#388—171no—
953#388—171no—
954#388—171no—
955#388—171no—
956#388—171no—
957#388—171no—
958#388—171no—
959#388—171no—
960#388—171no—
961#387—171no—
962#387—171no—
963#387—171no—
964#387—171no—
965#387—171no—
966#387—171no—
967#387—171no—
968#387C2×D1711yescharacteristic, complemented
969#386—171no—
970#386—171no—
971#386—171no—
972#386—171no—
973#386—171no—
974#386—171no—
975#386—171no—
976#386—171no—
977#386—171no—
978#386—171no—
979#386—171no—
980#386—171no—
981#386C2×D1711yescharacteristic
982#386C2×D1711yescharacteristic, complemented
983#385—171no—
984#385—171no—
985#385—171no—
986#385—171no—
987#385—171no—
988#385—171no—
989#385—171no—
990#385—171no—
991#385—171no—
992#385—171no—
993#385—171no—
994#385—171no—
995#385—171no—
996#385—171no—
997#385C2×D1711yescharacteristic
998#385C2×D1711yescharacteristic, complemented
999#383—171no—
1000#382—171no—
1001#381—171no—
1002#381—171no—
1003#380—171no—
1004#380—171no—
1005#380—171no—
1006#380—171no—
1007#380C2×D1711yescharacteristic
1008#379—171no—
1009#379—171no—
1010#379—171no—
1011C4×C22⋊C4—171no—
1012C2×#95—171no—
1013C2×C17—42no—
1014C2×C17—42no—
1015C2×C17—81no—
1016C2×C17#344911yescharacteristic
1017C2×C17#348411yescharacteristic
1018C2×C17#348911yescharacteristic
1019C2×C17#353311yescharacteristic
1020C2×C17#353511yescharacteristic
1021C2×C17#354011yescharacteristic
1022C2×C17#354111yescharacteristic
1023D17—42no—
1024D17—42no—
1025D17—81no—
1026C25—171no—
1027C2×#41—344no—
1028C2×#41—682no—
1029C2×#41—682no—
1030C22×Q8—171no—
1031C22×Q8—171no—
1032C22×Q8—171no—
1033C22×Q8—171no—
1034C22×D4—171no—
1035C22×D4—171no—
1036C22×D4—171no—
1037C22×D4—171no—
1038C22×D4—171no—
1039C22×D4—171no—
1040C22×D4—171no—
1041C22×D4—171no—
1042C22×D4—171no—
1043C22×D4C22×D1711yescharacteristic
1044C22×D4C22×D1711yescharacteristic
1045C22×D4C22×D1711yescharacteristic
1046C23×C4—171no—
1047C23×C4—171no—
1048C23×C4—171no—
1049C23×C4—171no—
1050C23×C4—171no—
1051C23×C4—171no—
1052C23×C4—171no—
1053C23×C4—171no—
1054C23×C4—171no—
1055C23×C4—344no—
1056C23×C4—682no—
1057C23×C4—682no—
1058C23×C4C22×D1711yescharacteristic
1059C23×C4C22×D1711yescharacteristic
1060C4⋊Q8—344no—
1061C4⋊Q8—682no—
1062#126—24no—
1063#126—344no—
1064#124—344no—
1065#124—344no—
1066#124—344no—
1067#124—682no—
1068#123—344no—
1069#123—344no—
1070#123—344no—
1071#123—344no—
1072#123—682no—
1073C22⋊Q8—344no—
1074C22⋊Q8—344no—
1075C22⋊Q8—344no—
1076C22⋊Q8—344no—
1077C22⋊Q8—344no—
1078C22⋊Q8—682no—
1079C22⋊Q8—682no—
1080#121—24no—
1081#121—344no—
1082#121—344no—
1083#121—682no—
1084#121—682no—
1085#120—344no—
1086#120—344no—
1087#120—682no—
1088C4×Q8—344no—
1089C4×D4—178no—
1090C4×D4—344no—
1091C4×D4—344no—
1092C4×D4—344no—
1093#117—344no—
1094#117—344no—
1095C2×C4⋊C4—171no—
1096C2×C4⋊C4—171no—
1097C2×C4⋊C4—171no—
1098C2×C4⋊C4—171no—
1099C2×C4⋊C4—171no—
1100C2×C4⋊C4—171no—
1101C2×C4⋊C4—171no—
1102C2×C4⋊C4—171no—
1103C2×C4⋊C4—171no—
1104C2×C4⋊C4—171no—
1105C2×C4⋊C4—171no—
1106C2×C4⋊C4—171no—
1107C2×C4⋊C4—171no—
1108C2×C4⋊C4—171no—
1109C2×C4⋊C4—171no—
1110C2×C4⋊C4—171no—
1111C2×C4⋊C4—171no—
1112C2×C4⋊C4—171no—
1113C2×C4⋊C4—171no—
1114C2×C4⋊C4—171no—
1115C2×C4⋊C4—171no—
1116C2×C4⋊C4—171no—
1117C2×C4⋊C4—171no—
1118C2×C4⋊C4—171no—
1119C2×C4⋊C4C22×D1711yescharacteristic
1120C2×C4⋊C4C22×D1711yescharacteristic
1121C2×C4⋊C4C22×D1711yescharacteristic
1122C2×C4⋊C4C22×D1711yescharacteristic
1123C2×C4⋊C4C22×D1711yescharacteristic
1124C2×C4⋊C4C22×D1711yescharacteristic
1125C2×C4⋊C4C22×D1711yescharacteristic
1126C2×C4⋊C4C22×D1711yescharacteristic
1127C2×C22⋊C4—171no—
1128C2×C22⋊C4—171no—
1129C2×C22⋊C4—171no—
1130C2×C22⋊C4—171no—
1131C2×C22⋊C4—171no—
1132C2×C22⋊C4—171no—
1133C2×C22⋊C4—171no—
1134C2×C22⋊C4—171no—
1135C2×C22⋊C4—171no—
1136C2×C22⋊C4—171no—
1137C2×C22⋊C4—171no—
1138C2×C22⋊C4—171no—
1139C2×C22⋊C4—171no—
1140C2×C22⋊C4—171no—
1141C2×C22⋊C4—171no—
1142C2×C22⋊C4—171no—
1143C2×C22⋊C4—171no—
1144C2×C22⋊C4—171no—
1145C2×C22⋊C4—171no—
1146C2×C22⋊C4—171no—
1147C2×C22⋊C4—171no—
1148C2×C22⋊C4—171no—
1149C2×C22⋊C4—171no—
1150C2×C22⋊C4—171no—
1151C2×C22⋊C4—171no—
1152C2×C22⋊C4—171no—
1153C2×C22⋊C4—171no—
1154C2×C22⋊C4—171no—
1155C2×C22⋊C4—171no—
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⋊C4C22×D1711yescharacteristic
1167C2×C22⋊C4C22×D1711yescharacteristic
1168C2×C22⋊C4C22×D1711yescharacteristic
1169C2×C22⋊C4C22×D1711yescharacteristic
1170C2×C22⋊C4C22×D1711yescharacteristic
1171C2×C22⋊C4C22×D1711yescharacteristic
1172C2×C22⋊C4C22×D1711yescharacteristic
1173C2×C22⋊C4C22×D1711yescharacteristic
1174C2×C22⋊C4C22×D1711yescharacteristic
1175C2×C22⋊C4C22×D1711yescharacteristic
1176C2×C22⋊C4C22×D1711yescharacteristic
1177C2×C22⋊C4C22×D1711yescharacteristic
1178C2×C22⋊C4C22×D1711yescharacteristic
1179C2×C42—171no—
1180C2×C42—171no—
1181C2×C42—171no—
1182C2×C42—171no—
1183C2×C42—171no—
1184C2×C42—171no—
1185C2×C42C22×D1711yescharacteristic
1186#95—171no—
1187#95—171no—
1188#95—171no—
1189#95—171no—
1190#95—171no—
1191#95—171no—
1192#95—171no—
1193#95—171no—
1194#95—171no—
1195#95—171no—
1196#95—171no—
1197#95—171no—
1198#95—171no—
1199#95—171no—
1200#95—171no—
1201#95—171no—
1202#95—171no—
1203#95—171no—
1204#95—171no—
1205#95—171no—
1206#95—171no—
1207#95—171no—
1208#95—171no—
1209#95—171no—
1210#95—171no—
1211#95—171no—
1212#95—171no—
1213#95—171no—
1214#95C22×D1711yescharacteristic
1215#95C22×D1711yescharacteristic
1216#95C22×D1711yescharacteristic
1217#95C22×D1711yescharacteristic
1218#95C22×D1711yescharacteristic
1219#95C22×D1711yescharacteristic
1220#95C22×D1711yescharacteristic
1221#95C22×D1711yescharacteristic
1222C17#3671211yescharacteristic, complemented, Sylow
1223C24—171no—
1224C24—171no—
1225C24—171no—
1226C24—342no—
1227C24—342no—
1228C24—342no—
1229C24—681no—
1230C24—681no—
1231C24—681no—
1232C24—681no—
1233C24C23×D1711yescharacteristic
1234C24C23×D1711yescharacteristic
1235C24C23×D1711yescharacteristic
1236#41—6816no—
1237C2×Q8—342no—
1238C2×Q8—342no—
1239C2×Q8—342no—
1240C2×Q8—342no—
1241C2×Q8—342no—
1242C2×Q8—681no—
1243C2×Q8—681no—
1244C2×Q8—681no—
1245C2×Q8—681no—
1246C2×Q8—681no—
1247C2×Q8—681no—
1248C2×Q8—681no—
1249C2×D4—22no—
1250C2×D4—22no—
1251C2×D4—22no—
1252C2×D4—22no—
1253C2×D4—22no—
1254C2×D4—22no—
1255C2×D4—41no—
1256C2×D4—41no—
1257C2×D4—41no—
1258C2×D4—174no—
1259C2×D4—342no—
1260C2×D4—342no—
1261C2×D4—342no—
1262C2×D4—342no—
1263C2×D4—342no—
1264C2×D4—342no—
1265C2×D4—342no—
1266C2×D4—342no—
1267C2×D4—342no—
1268C2×D4—681no—
1269C2×D4—681no—
1270C2×D4—681no—
1271C2×D4—681no—
1272C2×D4—681no—
1273C2×D4—681no—
1274C2×D4—681no—
1275C2×D4—681no—
1276C2×D4—681no—
1277C2×D4—681no—
1278C2×D4—681no—
1279C2×D4—681no—
1280C2×D4—681no—
1281C2×D4—681no—
1282C2×D4—681no—
1283C2×D4—681no—
1284C2×D4—681no—
1285C22×C4—22no—
1286C22×C4—22no—
1287C22×C4—41no—
1288C22×C4—41no—
1289C22×C4—41no—
1290C22×C4—41no—
1291C22×C4—171no—
1292C22×C4—171no—
1293C22×C4—171no—
1294C22×C4—174no—
1295C22×C4—174no—
1296C22×C4—171no—
1297C22×C4—171no—
1298C22×C4—171no—
1299C22×C4—171no—
1300C22×C4—171no—
1301C22×C4—171no—
1302C22×C4—171no—
1303C22×C4—171no—
1304C22×C4—171no—
1305C22×C4—171no—
1306C22×C4—342no—
1307C22×C4—342no—
1308C22×C4—342no—
1309C22×C4—342no—
1310C22×C4—342no—
1311C22×C4—342no—
1312C22×C4—342no—
1313C22×C4—342no—
1314C22×C4—342no—
1315C22×C4—342no—
1316C22×C4—681no—
1317C22×C4—681no—
1318C22×C4—681no—
1319C22×C4—681no—
1320C22×C4—681no—
1321C22×C4—681no—
1322C22×C4—6816no—
1323C22×C4—681no—
1324C22×C4—681no—
1325C22×C4—681no—
1326C22×C4—681no—
1327C22×C4—681no—
1328C22×C4—681no—
1329C22×C4—681no—
1330C22×C4—681no—
1331C22×C4—681no—
1332C22×C4C23×D1711yescharacteristic
1333C22×C4C23×D1711yescharacteristic
1334C22×C4C23×D1711yescharacteristic
1335C22×C4C23×D1711yescharacteristic
1336C22×C4C23×D1711yescharacteristic
1337C22×C4C23×D1711yescharacteristic
1338C22×C4C23×D1711yescharacteristic
1339C22×C4C23×D1711yescharacteristic
1340C22×C4C23×D1711yescharacteristic
1341C22×C4C23×D1711yescharacteristic
1342C22×C4C23×D1711yescharacteristic
1343C22×C4C23×D1711yescharacteristic
1344C4⋊C4—22no—
1345C4⋊C4—22no—
1346C4⋊C4—22no—
1347C4⋊C4—22no—
1348C4⋊C4—22no—
1349C4⋊C4—41no—
1350C4⋊C4—41no—
1351C4⋊C4—41no—
1352C4⋊C4—174no—
1353C4⋊C4—342no—
1354C4⋊C4—342no—
1355C4⋊C4—342no—
1356C4⋊C4—342no—
1357C4⋊C4—342no—
1358C4⋊C4—342no—
1359C4⋊C4—342no—
1360C4⋊C4—342no—
1361C4⋊C4—342no—
1362C4⋊C4—342no—
1363C4⋊C4—342no—
1364C4⋊C4—342no—
1365C4⋊C4—681no—
1366C4⋊C4—681no—
1367C4⋊C4—681no—
1368C4⋊C4—681no—
1369C4⋊C4—681no—
1370C4⋊C4—681no—
1371C4⋊C4—681no—
1372C4⋊C4—681no—
1373C4⋊C4—681no—
1374C4⋊C4—681no—
1375C4⋊C4—681no—
1376C22⋊C4—22no—
1377C22⋊C4—22no—
1378C22⋊C4—22no—
1379C22⋊C4—22no—
1380C22⋊C4—41no—
1381C22⋊C4—41no—
1382C22⋊C4—41no—
1383C22⋊C4—41no—
1384C22⋊C4—41no—
1385C22⋊C4—41no—
1386C22⋊C4—41no—
1387C22⋊C4—41no—
1388C22⋊C4—174no—
1389C22⋊C4—342no—
1390C22⋊C4—342no—
1391C22⋊C4—342no—
1392C22⋊C4—342no—
1393C22⋊C4—342no—
1394C22⋊C4—342no—
1395C22⋊C4—342no—
1396C22⋊C4—342no—
1397C22⋊C4—342no—
1398C22⋊C4—342no—
1399C22⋊C4—342no—
1400C22⋊C4—342no—
1401C22⋊C4—342no—
1402C22⋊C4—342no—
1403C22⋊C4—342no—
1404C22⋊C4—342no—
1405C22⋊C4—342no—
1406C22⋊C4—342no—
1407C22⋊C4—342no—
1408C22⋊C4—681no—
1409C22⋊C4—681no—
1410C22⋊C4—681no—
1411C22⋊C4—681no—
1412C22⋊C4—681no—
1413C22⋊C4—681no—
1414C22⋊C4—681no—
1415C22⋊C4—681no—
1416C22⋊C4—681no—
1417C22⋊C4—681no—
1418C22⋊C4—681no—
1419C22⋊C4—681no—
1420C22⋊C4—681no—
1421C22⋊C4—681no—
1422C22⋊C4—681no—
1423C22⋊C4—681no—
1424C22⋊C4—681no—
1425C22⋊C4—681no—
1426C22⋊C4—681no—
1427C22⋊C4D4×D1714yes—
1428C42—22no—
1429C42—174no—
1430C42—342no—
1431C42—342no—
1432C42—342no—
1433C42—681no—
1434C42—681no—
1435C23—21no—
1436C23—21no—
1437C23—21no—
1438C23—21no—
1439C23—21no—
1440C23—21no—
1441C23—21no—
1442C23—21no—
1443C23—21no—
1444C23—21no—
1445C23—21no—
1446C23—21no—
1447C23—21no—
1448C23—21no—
1449C23—21no—
1450C23—21no—
1451C23—21no—
1452C23—21no—
1453C23—21no—
1454C23—172no—
1455C23—172no—
1456C23—341no—
1457C23—341no—
1458C23—341no—
1459C23—341no—
1460C23—341no—
1461C23—341no—
1462C23—341no—
1463C23—341no—
1464C23—341no—
1465C23—341no—
1466C23—341no—
1467C23—341no—
1468C23—341no—
1469C23—341no—
1470C23—341no—
1471C23—341no—
1472C23—341no—
1473C23—341no—
1474C23—341no—
1475C23—684no—
1476C23—684no—
1477C23—684no—
1478C23—684no—
1479C23—684no—
1480C23—684no—
1481C23—684no—
1482C23C2×D4×D1712yes—
1483C23#1058769712yes—
1484C23C24×D1711yescharacteristic
1485Q8—684no—
1486Q8—684no—
1487Q8—1362no—
1488Q8—1362no—
1489D4—44no—
1490D4—44no—
1491D4—44no—
1492D4—684no—
1493D4—684no—
1494D4—684no—
1495D4—684no—
1496D4—1362no—
1497D4—1362no—
1498D4—1362no—
1499D4—1362no—
1500D4—1362no—
1501C2×C4—21no—
1502C2×C4—21no—
1503C2×C4—21no—
1504C2×C4—21no—
1505C2×C4—21no—
1506C2×C4—21no—
1507C2×C4—21no—
1508C2×C4—21no—
1509C2×C4—21no—
1510C2×C4—21no—
1511C2×C4—21no—
1512C2×C4—21no—
1513C2×C4—21no—
1514C2×C4—21no—
1515C2×C4—21no—
1516C2×C4—21no—
1517C2×C4—21no—
1518C2×C4—21no—
1519C2×C4—21no—
1520C2×C4—21no—
1521C2×C4—21no—
1522C2×C4—21no—
1523C2×C4—21no—
1524C2×C4—21no—
1525C2×C4—21no—
1526C2×C4—21no—
1527C2×C4—21no—
1528C2×C4—21no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—21no—
1532C2×C4—21no—
1533C2×C4—21no—
1534C2×C4—44no—
1535C2×C4—82no—
1536C2×C4—172no—
1537C2×C4—172no—
1538C2×C4—172no—
1539C2×C4—348no—
1540C2×C4—341no—
1541C2×C4—341no—
1542C2×C4—341no—
1543C2×C4—341no—
1544C2×C4—341no—
1545C2×C4—341no—
1546C2×C4—341no—
1547C2×C4—341no—
1548C2×C4—341no—
1549C2×C4—341no—
1550C2×C4—341no—
1551C2×C4—341no—
1552C2×C4—341no—
1553C2×C4—341no—
1554C2×C4—341no—
1555C2×C4—341no—
1556C2×C4—341no—
1557C2×C4—341no—
1558C2×C4—341no—
1559C2×C4—341no—
1560C2×C4—341no—
1561C2×C4—341no—
1562C2×C4—341no—
1563C2×C4—341no—
1564C2×C4—341no—
1565C2×C4—341no—
1566C2×C4—341no—
1567C2×C4—341no—
1568C2×C4—341no—
1569C2×C4—341no—
1570C2×C4—341no—
1571C2×C4—341no—
1572C2×C4—341no—
1573C2×C4—341no—
1574C2×C4—341no—
1575C2×C4—341no—
1576C2×C4—684no—
1577C2×C4—684no—
1578C2×C4—684no—
1579C2×C4—684no—
1580C2×C4—684no—
1581C2×C4—684no—
1582C2×C4—684no—
1583C2×C4—1362no—
1584C2×C4C2×D4×D1712yes—
1585C2×C4C2×D4×D1712yes—
1586C2×C4#1058769612yes—
1587C22—22no—
1588C22—22no—
1589C22—22no—
1590C22—22no—
1591C22—22no—
1592C22—22no—
1593C22—41no—
1594C22—41no—
1595C22—41no—
1596C22—41no—
1597C22—41no—
1598C22—41no—
1599C22—41no—
1600C22—41no—
1601C22—41no—
1602C22—41no—
1603C22—41no—
1604C22—41no—
1605C22—41no—
1606C22—41no—
1607C22—41no—
1608C22—342no—
1609C22—342no—
1610C22—342no—
1611C22—342no—
1612C22—342no—
1613C22—342no—
1614C22—6816no—
1615C22—681no—
1616C22—681no—
1617C22—681no—
1618C22—681no—
1619C22—681no—
1620C22—681no—
1621C22—681no—
1622C22—681no—
1623C22—681no—
1624C22—681no—
1625C22—681no—
1626C22—681no—
1627C22—681no—
1628C22—681no—
1629C22—681no—
1630C22C22×D4×D1711yescharacteristic
1631C22H(5,𝔽2)×D1711yescharacteristic
1632C22C2×#1058769611yescharacteristic
1633C22C2×#1058769711yescharacteristic
1634C22#1176364411yescharacteristic
1635C22#1176364411yescharacteristic
1636C22#1176364611yescharacteristic
1637C4—22no—
1638C4—22no—
1639C4—22no—
1640C4—41no—
1641C4—41no—
1642C4—41no—
1643C4—41no—
1644C4—41no—
1645C4—41no—
1646C4—41no—
1647C4—41no—
1648C4—41no—
1649C4—342no—
1650C4—342no—
1651C4—342no—
1652C4—681no—
1653C4—681no—
1654C4—681no—
1655C4—681no—
1656C4—681no—
1657C4—681no—
1658C4—681no—
1659C4—681no—
1660C4—681no—
1661C4—681no—
1662C2—42no—
1663C2—42no—
1664C2—81no—
1665C2—682no—
1666C2—682no—
1667C2—1361no—
1668C2#1454211211yescharacteristic
1669C2#1454241411yescharacteristic
1670C2#1454245511yescharacteristic
1671C2#1454295311yescharacteristic
1672C2#1454299011yescharacteristic
1673C2#1454305611yescharacteristic
1674C2#1454307111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2691C2
hypercenter#2691D17
hypocenterC17#36712
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2691

Complements

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

NH ≅ G/Ntype
1. C2×#11763425C2semidirect
2. C2×#11763319C2semidirect
3. #14537079C2semidirect
4. #14537072C2semidirect
5. #14535336C2semidirect
6. #14535313C2semidirect
7. #14535280C2semidirect
8. #14535242C2semidirect
9. #14535185C2semidirect
10. #14535180C2semidirect
11. #14535159C2semidirect
12. #14535099C2semidirect
13. #14535085C2semidirect
14. #14535072C2semidirect
15. #14535068C2semidirect
16. #14535038C2semidirect
17. #14535019C2semidirect
18. #14535007C2semidirect
19. #14534989C2semidirect
20. #14534706C2semidirect
21. #14534630C2semidirect
22. #14534462C2semidirect
23. #14534397C2semidirect
24. #14534360C2semidirect
25. #14534345C2semidirect
26. #14534140C2semidirect
27. #14533968C2semidirect
28. #14532407C2semidirect
29. #14532392C2semidirect
30. #14531412C2semidirect
31. C17×#2691C2semidirect
35. C2×#10587574C22semidirect
36. C2×#10587574C22semidirect
41. C2×#10587571C22semidirect
45. C2×#10587572C22semidirect
53. C2×#10587582C22semidirect
54. C2×#10587564C22semidirect
57. C2×#10587625C22semidirect
62. C2×C4×Dic34C22semidirect
68. C2×#10587578C22semidirect
69. #11762751C22semidirect
70. #11762748C22semidirect
71. #11762746C22semidirect
74. #11762745C22semidirect
75. #11762742C22semidirect
76. #11762742C22semidirect
77. #11762740C22semidirect
79. #11762737C22semidirect
84. #11762731C22semidirect
85. #11762731C22semidirect
86. #11762730C22semidirect
87. #11762730C22semidirect
88. #11762730C22semidirect
89. #11762730C22semidirect
95. #11762725C22semidirect
96. #11762725C22semidirect
100. #11762723C22semidirect
102. #11762722C22semidirect
105. #11762721C22semidirect
106. #11762721C22semidirect
111. #11762713C22semidirect
115. #11762708C22semidirect
116. #11762708C22semidirect
117. #11762707C22semidirect
120. #11762702C22semidirect
123. #11762701C22semidirect
127. #11762699C22semidirect
128. #11762696C22semidirect
129. #11762696C22semidirect
130. #11762696C22semidirect
131. #11762696C22semidirect
132. #11762692C22semidirect
133. #11762690C22semidirect
134. #11762690C22semidirect
144. #11762686C22semidirect
146. #11762685C22semidirect
149. #11762684C22semidirect
150. #11762684C22semidirect
151. #11762684C22semidirect
156. #11762683C22semidirect
158. #11762681C22semidirect
161. #11762676C22semidirect
162. #11762674C22semidirect
165. #11762669C22semidirect
166. #11762667C22semidirect
172. C22⋊C4×Dic17C22semidirect
173. C2×#10587502C22semidirect
174. C2×C17×#126C22semidirect
176. C17×#398C22semidirect
177. C17×#397C22semidirect
178. C17×#396C22semidirect
181. C17×#394C22semidirect
183. C17×#387C22semidirect
185. C17×#386C22semidirect
187. C17×#385C22semidirect
345. #10587567D4semidirect
757. #2691D17semidirect
862. C2×#126C2×D17semidirect
904. #398C2×D17semidirect
910. #397C2×D17semidirect
914. #396C2×D17semidirect
932. #394C2×D17semidirect
968. #387C2×D17semidirect
982. #386C2×D17semidirect
998. #385C2×D17semidirect
1222. C17#36712semidirect

Maximal subgroups

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

subgroupindex
C2×#117634252
C2×#117633192
#145370792
#145370722
#145353362
#145353132
#145352802
#145352422
#145351852
#145351802
#145351592
#145350992
#145350852
#145350722
#145350682
#145350382
#145350192
#145350072
#145349892
#145347062
#145346302
#145344622
#145343972
#145343602
#145343452
#145341402
#145339682
#145324072
#145323922
#145314122
C17×#26912
#3671217