Finite Group Databasebeta

← #17241309

Subgroups — #17241309

Order 4352.

2490 conjugacy classes of subgroups.

The subgroup lattice has 1656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763407C211yesmaximal, characteristic, complemented
2C2×C22⋊Q8×D17C211yesmaximal, characteristic, complemented
3#14537070C211yesmaximal, characteristic, complemented
4#14537067C211yesmaximal, characteristic
5#14535444C211yesmaximal, characteristic, complemented
6#14535442C211yesmaximal, characteristic, complemented
7#14535436C211yesmaximal, characteristic, complemented
8#14535415C211yesmaximal, characteristic, complemented
9#14535413C211yesmaximal, characteristic, complemented
10#14535411C211yesmaximal, characteristic, complemented
11#14535409C211yesmaximal, characteristic, complemented
12#14535158C211yesmaximal, characteristic, complemented
13#14535155C211yesmaximal, characteristic, complemented
14#14535153C211yesmaximal, characteristic, complemented
15#14535153C211yesmaximal, characteristic, complemented
16#14535139C211yesmaximal, characteristic, complemented
17#14535137C211yesmaximal, characteristic, complemented
18#14535131C211yesmaximal, characteristic, complemented
19#14535129C211yesmaximal, characteristic, complemented
20#14534602C211yesmaximal, characteristic, complemented
21#14534527C211yesmaximal, characteristic, complemented
22#14533678C211yesmaximal, characteristic, complemented
23#14533675C211yesmaximal, characteristic, complemented
24#14532188C211yesmaximal, characteristic, complemented
25#14532184C211yesmaximal, characteristic, complemented
26#14532168C211yesmaximal, characteristic, complemented
27#14532164C211yesmaximal, characteristic, complemented
28#14532147C211yesmaximal, characteristic, complemented
29#14532144C211yesmaximal, characteristic, complemented
30#14531399C211yesmaximal, characteristic, complemented
31C17×#2704C211yesmaximal, characteristic, complemented
32C22×Q8×D17C2211yescharacteristic
33C23×C4×D17C2211yescharacteristic
34#11763407—28no—
35C2×#10587584C2211yescharacteristic, complemented
36C2×#10587562C2211yescharacteristic, complemented
37C2×#10587575C2211yescharacteristic, complemented
38C2×#10587580C2211yescharacteristic
39C2×#10587580C2211yescharacteristic
40C2×#10587580C2211yescharacteristic
41C2×#10587580C2211yescharacteristic
42C2×#10587580C2211yescharacteristic, complemented
43C2×#10587580C2211yescharacteristic, complemented
44C2×#10587583C2211yescharacteristic
45C2×#10587583C2211yescharacteristic, complemented
46C2×#10587583C2211yescharacteristic, complemented
47C2×#10587610C2211yescharacteristic
48C2×#10587582C2211yescharacteristic
49C2×#10587582C2211yescharacteristic
50C2×#10587582C2211yescharacteristic
51C2×#10587582C2211yescharacteristic
52C2×#10587582C2211yescharacteristic, complemented
53C2×#10587582C2211yescharacteristic, complemented
54C2×#10587582C2211yescharacteristic, complemented
55C2×#10587564C2211yescharacteristic
56C2×#10587564C2211yescharacteristic
57C2×#10587564C2211yescharacteristic
58C2×#10587632C2211yescharacteristic
59C2×#10587632C2211yescharacteristic, complemented
60C22⋊Q8×D17—28no—
61C2×#10587581C2211yescharacteristic
62C2×#10587581C2211yescharacteristic
63C2×#10587616C2211yescharacteristic
64C2×#10587568C2211yescharacteristic
65C2×#10587568C2211yescharacteristic
66C2×C4×D68C2211yescharacteristic
67C2×#10587579C2211yescharacteristic
68C2×#10587578C2211yescharacteristic
69C2×#10587558C2211yescharacteristic
70C2×C4⋊C4×D17C2211yescharacteristic
71C2×C4⋊C4×D17C2211yescharacteristic
72C2×C4⋊C4×D17C2211yescharacteristic
73C2×C22⋊C4×D17C2211yescharacteristic
74C2×C22⋊C4×D17C2211yescharacteristic
75#11762751C2211yescharacteristic, complemented
76#11762750C2211yescharacteristic, complemented
77#11762743C2211yescharacteristic, complemented
78#11762742C2211yescharacteristic, complemented
79#11762742C2211yescharacteristic, complemented
80#11762742C2211yescharacteristic, complemented
81#11762740C2211yescharacteristic, complemented
82#11762740C2211yescharacteristic, complemented
83#11762739C2211yescharacteristic, complemented
84#11762733C2211yescharacteristic
85#11762733C2211yescharacteristic, complemented
86#11762733C2211yescharacteristic, complemented
87#11762733C2211yescharacteristic, complemented
88#11762732C2211yescharacteristic
89#11762732C2211yescharacteristic
90#11762731C2211yescharacteristic
91#11762731C2211yescharacteristic
92#11762731C2211yescharacteristic
93#11762731C2211yescharacteristic, complemented
94#11762731C2211yescharacteristic, complemented
95#11762731C2211yescharacteristic, complemented
96#11762731C2211yescharacteristic, complemented
97#11762731C2211yescharacteristic, complemented
98#11762730C2211yescharacteristic, complemented
99#11762730C2211yescharacteristic, complemented
100#11762730C2211yescharacteristic, complemented
101#11762729C2211yescharacteristic, complemented
102#11762729C2211yescharacteristic, complemented
103#11762727C2211yescharacteristic
104#11762727C2211yescharacteristic
105#11762727C2211yescharacteristic, complemented
106#11762726C2211yescharacteristic
107#11762726C2211yescharacteristic
108#11762726C2211yescharacteristic, complemented
109#11762725C2211yescharacteristic
110#11762725C2211yescharacteristic
111#11762724C2211yescharacteristic
112#11762724C2211yescharacteristic
113#11762722C2211yescharacteristic, complemented
114#11762722C2211yescharacteristic, complemented
115#11762722C2211yescharacteristic, complemented
116#11762720C2211yescharacteristic, complemented
117#11762715C2211yescharacteristic, complemented
118#11762713C2211yescharacteristic, complemented
119#11762713C2211yescharacteristic, complemented
120#11762711C2211yescharacteristic
121#11762710C2211yescharacteristic
122#11762709C2211yescharacteristic
123#11762709C2211yescharacteristic
124#11762708C2211yescharacteristic, complemented
125#11762707C2211yescharacteristic, complemented
126#11762706C2211yescharacteristic, complemented
127#11762706C2211yescharacteristic, complemented
128#11762706C2211yescharacteristic, complemented
129#11762705C2211yescharacteristic, complemented
130#11762705C2211yescharacteristic, complemented
131#11762704C2211yescharacteristic, complemented
132#11762704C2211yescharacteristic, complemented
133#11762704C2211yescharacteristic, complemented
134#11762703C2211yescharacteristic
135#11762701C2211yescharacteristic, complemented
136#11762700C2211yescharacteristic
137#11762700C2211yescharacteristic, complemented
138#11762699C2211yescharacteristic
139#11762699C2211yescharacteristic
140#11762699C2211yescharacteristic, complemented
141#11762698C2211yescharacteristic
142#11762698C2211yescharacteristic, complemented
143#11762697C2211yescharacteristic
144#11762687C2211yescharacteristic
145#11762687C2211yescharacteristic
146#11762687C2211yescharacteristic
147#11762687C2211yescharacteristic
148#11762687C2211yescharacteristic
149#11762687C2211yescharacteristic
150#11762687C2211yescharacteristic
151#11762687C2211yescharacteristic
152#11762686C2211yescharacteristic
153#11762686C2211yescharacteristic
154#11762685C2211yescharacteristic
155#11762685C2211yescharacteristic
156#11762683C2211yescharacteristic
157#11762683C2211yescharacteristic
158#11762683C2211yescharacteristic
159#11762682C2211yescharacteristic
160#11762680C2211yescharacteristic
161#11762680C2211yescharacteristic
162#11762680C2211yescharacteristic
163#11762671C2211yescharacteristic
164#11762671C2211yescharacteristic
165#11762668C2211yescharacteristic
166#11762668C2211yescharacteristic
167#11762668C2211yescharacteristic
168#11762667C2211yescharacteristic
169#11762666C2211yescharacteristic
170#11762666C2211yescharacteristic
171#11762666C2211yescharacteristic
172#11762664C2211yescharacteristic
173#11762664C2211yescharacteristic
174C2×C17×#125C2211yescharacteristic, complemented
175C2×C17×C22⋊Q8C2211yescharacteristic
176C17×#398C2211yescharacteristic, complemented
177C17×#398C2211yescharacteristic, complemented
178C17×#398C2211yescharacteristic, complemented
179C17×#396C2211yescharacteristic
180C17×#396C2211yescharacteristic
181C17×#395C2211yescharacteristic, complemented
182C17×#391C2211yescharacteristic, complemented
183C17×#389C2211yescharacteristic, complemented
184C17×#389C2211yescharacteristic, complemented
185C17×#388C2211yescharacteristic
186C17×#388C2211yescharacteristic
187C17×#385C2211yescharacteristic
188C17×#380C2211yescharacteristic
189C24×D17C2311yescharacteristic
190C22×Q8×C17C2311yescharacteristic
191C23×C4×C17C2311yescharacteristic
192C22×C22⋊D17C2311yescharacteristic
193C22×C22⋊D17C2311yescharacteristic
194C23×Dic17C2311yescharacteristic
195C2×Q8×D17—24no—
196C2×Q8×D17—42no—
197C2×Q8×D17—42no—
198C22×D68C2311yescharacteristic
199C22×D68C2311yescharacteristic
200C22×D68C2311yescharacteristic
201C22×D68C2311yescharacteristic
202C22×D68C2311yescharacteristic
203C22×C4×D17—24no—
204C22×C4×D17—42no—
205C22×C4×D17—42no—
206C22×C4×D17C2311yescharacteristic
207C22×C4×D17C2311yescharacteristic
208C22×C4×D17C2311yescharacteristic
209C22×C4×D17C2311yescharacteristic
210C22×C4×D17C2311yescharacteristic
211C22×C4×D17C2311yescharacteristic
212C22×C4×D17C2311yescharacteristic
213C22×C4×D17C2311yescharacteristic
214C22×C4×D17C2311yescharacteristic
215C22×C4×D17C2311yescharacteristic
216C22×Dic34C2311yescharacteristic
217C22×Dic34C2311yescharacteristic
218C22×Dic34C2311yescharacteristic
219C22×Dic34C2311yescharacteristic
220C17×#125—24no—
221C17×C22⋊Q8—24no—
222C2×C4⋊C4×C17C2311yescharacteristic
223C2×C4⋊C4×C17C2311yescharacteristic
224C2×C4⋊C4×C17C2311yescharacteristic
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×C4⋊C4×C17C2311yescharacteristic
234C2×C4⋊C4×C17C2311yescharacteristic
235C2×C4⋊C4×C17C2311yescharacteristic
236C2×C4⋊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×C42×C17C2311yescharacteristic
244C2×C42×C17C2311yescharacteristic
245C2×C22⋊Dic17C2311yescharacteristic
246C2×C22⋊Dic17C2311yescharacteristic
247C2×C22⋊Dic17C2311yescharacteristic
248C2×C22⋊Dic17C2311yescharacteristic
249#10587632—24no—
250#10587632—42no—
251#10587616—42no—
252C2×#63227C2311yescharacteristic
253C2×#63227C2311yescharacteristic
254C2×#63227C2311yescharacteristic
255C2×#63227C2311yescharacteristic
256C2×#63227C2311yescharacteristic
257C2×#63227C2311yescharacteristic
258C2×#63227C2311yescharacteristic
259C2×#63227C2311yescharacteristic
260C2×#63227C2311yescharacteristic
261C2×#63227C2311yescharacteristic
262C2×#63227C2311yescharacteristic
263C2×#63227C2311yescharacteristic
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×C4⋊Dic17C2311yescharacteristic
289C2×C4⋊Dic17C2311yescharacteristic
290C2×C4⋊Dic17C2311yescharacteristic
291C2×C4⋊Dic17C2311yescharacteristic
292C2×C4⋊Dic17C2311yescharacteristic
293C2×C4⋊Dic17C2311yescharacteristic
294C2×C4⋊Dic17C2311yescharacteristic
295C2×C4⋊Dic17C2311yescharacteristic
296C2×C4⋊Dic17C2311yescharacteristic
297#10587610—24no—
298C2×#63225C2311yescharacteristic
299C2×#63225C2311yescharacteristic
300C2×#63225C2311yescharacteristic
301C2×#63225C2311yescharacteristic
302C2×#63225C2311yescharacteristic
303C2×#63225C2311yescharacteristic
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—24no—
327#10587583—42no—
328#10587582—24no—
329#10587582—24no—
330#10587582—24no—
331#10587582—24no—
332#10587582—42no—
333#10587582—42no—
334#10587582—42no—
335#10587581—24no—
336#10587581—42no—
337#10587580—24no—
338#10587580—24no—
339#10587580—24no—
340#10587580—24no—
341#10587580—42no—
342#10587580—42no—
343#10587579—24no—
344#10587578—42no—
345C4⋊C4×D17—24no—
346C4⋊C4×D17—24no—
347C4⋊C4×D17D418yescomplemented
348#10587575—24no—
349#10587568—42no—
350#10587568—42no—
351C22⋊C4×D17—24no—
352C22⋊C4×D17—24no—
353#10587564—24no—
354#10587564—24no—
355#10587564—42no—
356#10587562—24no—
357C4×D68—24no—
358#10587558—42no—
359C17×#95C2311yescharacteristic
360C17×#95C2311yescharacteristic
361C17×#95C2311yescharacteristic
362C17×#95C2311yescharacteristic
363C17×#95C2311yescharacteristic
364C17×#95C2311yescharacteristic
365C17×#95C2311yescharacteristic
366C17×#95C2311yescharacteristic
367C17×#95C2311yescharacteristic
368C17×#95C2311yescharacteristic
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
392C23×D17—22no—
393C23×D17—22no—
394C23×D17—22no—
395C23×D17—22no—
396C23×D17—22no—
397C23×D17—41no—
398C23×D17—41no—
399C23×D17C2411yescharacteristic
400C23×D17C2411yescharacteristic
401C23×D17C2411yescharacteristic
402C23×D17C2411yescharacteristic
403C2×Q8×C17—22no—
404C2×Q8×C17—22no—
405C2×Q8×C17—41no—
406C22×C4×C17—22no—
407C22×C4×C17—22no—
408C22×C4×C17—41no—
409C22×C4×C17C2411yescharacteristic
410C22×C4×C17C2411yescharacteristic
411C22×C4×C17C2411yescharacteristic
412C22×C4×C17C2411yescharacteristic
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
423C2×C22⋊D17—22no—
424C2×C22⋊D17—22no—
425C2×C22⋊D17—41no—
426C2×C22⋊D17—41no—
427C2×C22⋊D17—41no—
428C2×C22⋊D17—41no—
429C22×Dic17—22no—
430C22×Dic17—22no—
431C22×Dic17—41no—
432C22×Dic17C2411yescharacteristic
433C22×Dic17C2411yescharacteristic
434C22×Dic17C2411yescharacteristic
435C22×Dic17C2411yescharacteristic
436C22×Dic17C2411yescharacteristic
437C22×Dic17C2411yescharacteristic
438C22×Dic17C2411yescharacteristic
439C22×Dic17C2411yescharacteristic
440C22×Dic17C2411yescharacteristic
441C22×Dic17C2411yescharacteristic
442C22×Dic17C2411yescharacteristic
443C22×Dic17C2411yescharacteristic
444Q8×D17—416no—
445C2×D68—22no—
446C2×D68—22no—
447C2×D68—22no—
448C2×D68—22no—
449C2×D68—22no—
450C2×D68—22no—
451C2×D68—22no—
452C2×D68—22no—
453C2×D68—22no—
454C2×D68—41no—
455C2×D68—41no—
456C2×D68—41no—
457C2×D68—41no—
458C2×D68—41no—
459C2×D68—41no—
460C2×C4×D17—22no—
461C2×C4×D17—22no—
462C2×C4×D17—22no—
463C2×C4×D17—22no—
464C2×C4×D17—22no—
465C2×C4×D17—22no—
466C2×C4×D17—22no—
467C2×C4×D17—22no—
468C2×C4×D17—22no—
469C2×C4×D17—22no—
470C2×C4×D17—22no—
471C2×C4×D17—22no—
472C2×C4×D17—22no—
473C2×C4×D17—22no—
474C2×C4×D17—22no—
475C2×C4×D17—416no—
476C2×C4×D17—41no—
477C2×C4×D17—41no—
478C2×C4×D17—41no—
479C2×C4×D17—41no—
480C2×C4×D17—41no—
481C2×C4×D17—41no—
482C2×C4×D17—41no—
483C2×C4×D17—41no—
484C2×C4×D17—41no—
485C2×C4×D17—41no—
486C2×C4×D17—41no—
487C2×C4×D17—41no—
488C2×C4×D17C2×D414yes—
489C2×C4×D17C2×D414yes—
490C2×C4×D17C2×D414yes—
491C2×Dic34—22no—
492C2×Dic34—22no—
493C2×Dic34—22no—
494C2×Dic34—22no—
495C2×Dic34—22no—
496C2×Dic34—22no—
497C2×Dic34—22no—
498C2×Dic34—41no—
499C2×Dic34—41no—
500C2×Dic34—41no—
501C2×Dic34—41no—
502C2×Dic34—41no—
503C4⋊C4×C17—22no—
504C4⋊C4×C17—22no—
505C4⋊C4×C17—22no—
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—
514C4⋊C4×C17—41no—
515C4⋊C4×C17—41no—
516C4⋊C4×C17—41no—
517C4⋊C4×C17C2×D414yes—
518C22⋊C4×C17—22no—
519C22⋊C4×C17—22no—
520C22⋊C4×C17—22no—
521C22⋊C4×C17—41no—
522C22⋊C4×C17—41no—
523C22⋊C4×C17—41no—
524C42×C17—22no—
525C42×C17—41no—
526C22⋊Dic17—22no—
527C22⋊Dic17—22no—
528C22⋊Dic17—22no—
529C22⋊Dic17—41no—
530#63227—22no—
531#63227—22no—
532#63227—22no—
533#63227—22no—
534#63227—22no—
535#63227—22no—
536#63227—22no—
537#63227—22no—
538#63227—22no—
539#63227—22no—
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—
566C4⋊Dic17—22no—
567C4⋊Dic17—22no—
568C4⋊Dic17—22no—
569C4⋊Dic17—22no—
570C4⋊Dic17—41no—
571C4⋊Dic17—41no—
572C4⋊Dic17—41no—
573C4⋊Dic17—41no—
574C4⋊Dic17C2×D414yes—
575#63225—22no—
576#63225—22no—
577#63225—22no—
578#63225—22no—
579#63225—22no—
580#63225—22no—
581#63225—22no—
582#63225—22no—
583#63225—22no—
584#63225—22no—
585#63225—41no—
586#63225—41no—
587#63225—41no—
588#63225—41no—
589#63225—41no—
590#63225—41no—
591#63225—41no—
592#63225—41no—
593#63225—41no—
594#63225—41no—
595#63225C2×D414yes—
596#63225C2×D414yes—
597C4×Dic17—22no—
598C4×Dic17—41no—
599C4×Dic17—41no—
600C4×Dic17—41no—
601#36719—171nomaximal, Sylow
602C23×C17—21no—
603C23×C17—21no—
604C23×C17—21no—
605C23×C17—21no—
606C23×C17—21no—
607C23×C17—21no—
608C23×C172−1+412yes—
609C23×C17C2511yescharacteristic
610C22×D17—21no—
611C22×D17—21no—
612C22×D17—21no—
613C22×D17—21no—
614C22×D17—28no—
615C22×D17—21no—
616C22×D17—21no—
617C22×D17—21no—
618C22×D17—21no—
619C22×D17—21no—
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—44no—
636C22×D17—44no—
637C22×D17—44no—
638C22×D17—44no—
639C22×D17—44no—
640C22×D17—44no—
641C22×D17C22×D412yes—
642C22×D17H(5,𝔽2)12yes—
643C22×D172−1+412yes—
644C22×D172−1+412yes—
645Q8×C17—44no—
646C2×C4×C17—21no—
647C2×C4×C17—21no—
648C2×C4×C17—21no—
649C2×C4×C17—21no—
650C2×C4×C17—21no—
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×C17C22×D412yes—
686C2×C4×C17C22×D412yes—
687C2×C4×C17C22×D412yes—
688C2×C4×C17H(5,𝔽2)12yes—
689C22⋊D17—82no—
690C22⋊D17—82no—
691C2×Dic17—21no—
692C2×Dic17—21no—
693C2×Dic17—21no—
694C2×Dic17—21no—
695C2×Dic17—21no—
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—44no—
724C2×Dic17C22×D412yes—
725C2×Dic17C22×D412yes—
726C2×Dic17C22×D412yes—
727C2×Dic17H(5,𝔽2)12yes—
728D68—44no—
729D68—44no—
730D68—82no—
731D68—82no—
732D68—82no—
733C4×D17—28no—
734C4×D17—28no—
735C4×D17—44no—
736C4×D17—44no—
737C4×D17—44no—
738C4×D17—44no—
739C4×D17—44no—
740C4×D17—44no—
741C4×D17—82no—
742C4×D17—82no—
743Dic34—44no—
744Dic34—44no—
745Dic34—44no—
746Dic34—82no—
747C2×#539—171no—
748C22×C22⋊Q8—171no—
749#2848—171no—
750#2847—171no—
751#2704—171no—
752#2704—171no—
753#2704—171no—
754#2704D1711yescharacteristic, complemented
755#2702—171no—
756#2702—171no—
757#2702—171no—
758#2702—171no—
759#2683—171no—
760#2683—171no—
761#2683—171no—
762#2683—171no—
763#2681—171no—
764#2681—171no—
765#2681—171no—
766#2681—171no—
767#2627—171no—
768#2618—171no—
769#2534—171no—
770#2534—171no—
771#2413—171no—
772#2413—171no—
773#2411—171no—
774#2411—171no—
775#2409—171no—
776#2409—171no—
777#2316—171no—
778C22×C17—22no—
779C22×C17—22no—
780C22×C17—22no—
781C22×C17—41no—
782C22×C17—41no—
783C22×C17—41no—
784C22×C17—41no—
785C22×C17C23×D411yescharacteristic
786C22×C17C2×H(5,𝔽2)11yescharacteristic
787C22×C17C2×H(5,𝔽2)11yescharacteristic
788C22×C17C2×H(5,𝔽2)11yescharacteristic
789C22×C17C2×2−1+411yescharacteristic
790C22×C17C2×2−1+411yescharacteristic
791C22×C17C2×2−1+411yescharacteristic
792C2×D17—22no—
793C2×D17—22no—
794C2×D17—22no—
795C2×D17—22no—
796C2×D17—22no—
797C2×D17—22no—
798C2×D17—22no—
799C2×D17—22no—
800C2×D17—22no—
801C2×D17—416no—
802C2×D17—41no—
803C2×D17—41no—
804C2×D17—41no—
805C2×D17—41no—
806C2×D17—41no—
807C2×D17—41no—
808C2×D17—41no—
809C2×D17—41no—
810C2×D17—41no—
811C2×D17—41no—
812C2×D17—41no—
813C2×D17—41no—
814C2×D17—41no—
815C2×D17—41no—
816C2×D17—41no—
817C2×D17—41no—
818C2×D17—41no—
819C2×D17—41no—
820C2×D17#53714yes—
821C4×C17—22no—
822C4×C17—22no—
823C4×C17—22no—
824C4×C17—22no—
825C4×C17—41no—
826C4×C17—41no—
827C4×C17—41no—
828C4×C17—41no—
829C4×C17—41no—
830C4×C17—41no—
831C4×C17—41no—
832C4×C17—41no—
833C4×C17—41no—
834C4×C17—41no—
835Dic17—22no—
836Dic17—22no—
837Dic17—22no—
838Dic17—22no—
839Dic17—41no—
840Dic17—41no—
841Dic17—41no—
842Dic17—41no—
843Dic17—41no—
844Dic17—41no—
845Dic17—41no—
846Dic17—41no—
847C23×Q8—171no—
848C24×C4—171no—
849#539—348no—
850C2×#126—171no—
851C2×#126—171no—
852C2×#125—171no—
853C2×#125C2×D1711yescharacteristic, complemented
854C2×#123—171no—
855C2×#123—171no—
856C2×#123—171no—
857C2×#123—171no—
858C2×#123—171no—
859C2×#123—171no—
860C2×C22⋊Q8—171no—
861C2×C22⋊Q8—171no—
862C2×C22⋊Q8—171no—
863C2×C22⋊Q8—171no—
864C2×C22⋊Q8—171no—
865C2×C22⋊Q8—171no—
866C2×C22⋊Q8—171no—
867C2×C22⋊Q8—171no—
868C2×C22⋊Q8—171no—
869C2×C22⋊Q8—171no—
870C2×C22⋊Q8—171no—
871C2×C22⋊Q8—171no—
872C2×C22⋊Q8—171no—
873C2×C22⋊Q8—171no—
874C2×C22⋊Q8—171no—
875C2×C22⋊Q8—171no—
876C2×C22⋊Q8—348no—
877C2×C22⋊Q8C2×D1711yescharacteristic
878C2×#121—171no—
879C2×#121—171no—
880C2×#121—171no—
881C2×#120—171no—
882C2×#120—171no—
883C2×C4×D4—171no—
884C2×C4×D4—171no—
885C2×#117—171no—
886C2×#117—171no—
887C22×C4⋊C4—171no—
888C22×C4⋊C4—171no—
889C22×C4⋊C4—171no—
890C22×C22⋊C4—171no—
891C22×C22⋊C4—171no—
892#400—171no—
893#400—171no—
894#398—171no—
895#398—171no—
896#398—171no—
897#398—171no—
898#398—171no—
899#398—171no—
900#398—171no—
901#398C2×D1711yescharacteristic, complemented
902#398C2×D1711yescharacteristic, complemented
903#398C2×D1711yescharacteristic, complemented
904#396—171no—
905#396—171no—
906#396—171no—
907#396—171no—
908#396—171no—
909#396—171no—
910#396—171no—
911#396—171no—
912#396—171no—
913#396—171no—
914#396—171no—
915#396—171no—
916#396—171no—
917#396—171no—
918#396C2×D1711yescharacteristic
919#396C2×D1711yescharacteristic
920#395—171no—
921#395—171no—
922#395—171no—
923#395—171no—
924#395—171no—
925#395C2×D1711yescharacteristic, complemented
926#394—171no—
927#394—171no—
928#394—171no—
929#394—171no—
930#394—171no—
931#394—171no—
932#394—171no—
933#394—171no—
934#394—171no—
935#394—171no—
936#393—171no—
937#393—171no—
938#393—171no—
939#393—171no—
940#391—171no—
941#391—171no—
942#391—171no—
943#391C2×D1711yescharacteristic, complemented
944#390—171no—
945#390—171no—
946#390—171no—
947#390—171no—
948#389—171no—
949#389—171no—
950#389—171no—
951#389—171no—
952#389—171no—
953#389—171no—
954#389—171no—
955#389—171no—
956#389—171no—
957#389—171no—
958#389C2×D1711yescharacteristic, complemented
959#389C2×D1711yescharacteristic, complemented
960#388—171no—
961#388—171no—
962#388—171no—
963#388—171no—
964#388—171no—
965#388—171no—
966#388—171no—
967#388—171no—
968#388—171no—
969#388—171no—
970#388C2×D1711yescharacteristic
971#388C2×D1711yescharacteristic
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#386—171no—
982#386—171no—
983#386—171no—
984#385—171no—
985#385—171no—
986#385—171no—
987#385—171no—
988#385—171no—
989#385—171no—
990#385—171no—
991#385C2×D1711yescharacteristic
992#381—171no—
993#381—171no—
994#380—171no—
995#380—171no—
996#380—171no—
997#380—171no—
998#380—171no—
999#380—171no—
1000#380—171no—
1001#380C2×D1711yescharacteristic
1002#379—171no—
1003#379—171no—
1004C2×C17—42no—
1005C2×C17C2×#53711yescharacteristic
1006C2×C17#348411yescharacteristic
1007C2×C17#348611yescharacteristic
1008C2×C17#353611yescharacteristic
1009C2×C17#353611yescharacteristic
1010C2×C17#353811yescharacteristic
1011C2×C17#353811yescharacteristic
1012D17—24no—
1013D17—42no—
1014D17—81no—
1015D17—81no—
1016C25—171no—
1017C22×Q8—171no—
1018C22×Q8—171no—
1019C22×Q8—171no—
1020C22×Q8—171no—
1021C22×Q8—344no—
1022C22×Q8—682no—
1023C22×Q8—682no—
1024C22×Q8C22×D1711yescharacteristic
1025C22×D4—171no—
1026C22×D4—171no—
1027C22×D4—171no—
1028C22×D4—171no—
1029C22×D4—171no—
1030C22×D4—171no—
1031C22×D4—171no—
1032C23×C4—171no—
1033C23×C4—171no—
1034C23×C4—171no—
1035C23×C4—171no—
1036C23×C4—171no—
1037C23×C4—171no—
1038C23×C4—171no—
1039C23×C4—171no—
1040C23×C4—171no—
1041C23×C4—171no—
1042C23×C4—171no—
1043C23×C4—344no—
1044C23×C4—682no—
1045C23×C4—682no—
1046C23×C4C22×D1711yescharacteristic
1047#126—344no—
1048#126—344no—
1049#125—24no—
1050#125—344no—
1051#123—344no—
1052#123—344no—
1053#123—344no—
1054#123—344no—
1055#123—682no—
1056#123—682no—
1057C22⋊Q8—24no—
1058C22⋊Q8—344no—
1059C22⋊Q8—344no—
1060C22⋊Q8—344no—
1061C22⋊Q8—344no—
1062C22⋊Q8—344no—
1063C22⋊Q8—344no—
1064C22⋊Q8—344no—
1065C22⋊Q8—344no—
1066C22⋊Q8—344no—
1067C22⋊Q8—344no—
1068C22⋊Q8—682no—
1069C22⋊Q8—682no—
1070C22⋊Q8—682no—
1071C22⋊Q8—682no—
1072C22⋊Q8—682no—
1073C22⋊Q8—682no—
1074#121—344no—
1075#121—682no—
1076#121—682no—
1077#120—682no—
1078#120—682no—
1079C4×D4—344no—
1080C4×D4—344no—
1081#117—682no—
1082#117—682no—
1083C2×C4⋊C4—171no—
1084C2×C4⋊C4—171no—
1085C2×C4⋊C4—171no—
1086C2×C4⋊C4—178no—
1087C2×C4⋊C4—171no—
1088C2×C4⋊C4—171no—
1089C2×C4⋊C4—171no—
1090C2×C4⋊C4—171no—
1091C2×C4⋊C4—171no—
1092C2×C4⋊C4—171no—
1093C2×C4⋊C4—171no—
1094C2×C4⋊C4—171no—
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—344no—
1116C2×C4⋊C4—344no—
1117C2×C4⋊C4C22×D1711yescharacteristic
1118C2×C4⋊C4C22×D1711yescharacteristic
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×C4⋊C4C22×D1711yescharacteristic
1128C2×C4⋊C4C22×D1711yescharacteristic
1129C2×C4⋊C4C22×D1711yescharacteristic
1130C2×C4⋊C4C22×D1711yescharacteristic
1131C2×C4⋊C4C22×D1711yescharacteristic
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⋊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—344no—
1173C2×C22⋊C4—344no—
1174C2×C22⋊C4C22×D1711yescharacteristic
1175C2×C22⋊C4C22×D1711yescharacteristic
1176C2×C22⋊C4C22×D1711yescharacteristic
1177C2×C22⋊C4C22×D1711yescharacteristic
1178C2×C22⋊C4C22×D1711yescharacteristic
1179C2×C22⋊C4C22×D1711yescharacteristic
1180C2×C42—171no—
1181C2×C42—171no—
1182C2×C42—171no—
1183C2×C42—171no—
1184C2×C42C22×D1711yescharacteristic
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#95C22×D1711yescharacteristic
1209#95C22×D1711yescharacteristic
1210#95C22×D1711yescharacteristic
1211#95C22×D1711yescharacteristic
1212#95C22×D1711yescharacteristic
1213#95C22×D1711yescharacteristic
1214#95C22×D1711yescharacteristic
1215#95C22×D1711yescharacteristic
1216#95C22×D1711yescharacteristic
1217#95C22×D1711yescharacteristic
1218C17#3671911yescharacteristic, complemented, Sylow
1219C24—171no—
1220C24—171no—
1221C24—171no—
1222C24—171no—
1223C24—342no—
1224C24—342no—
1225C24—342no—
1226C24—342no—
1227C24—342no—
1228C24—681no—
1229C24—681no—
1230C24C23×D1711yescharacteristic
1231C2×Q8—22no—
1232C2×Q8—22no—
1233C2×Q8—41no—
1234C2×Q8—342no—
1235C2×Q8—342no—
1236C2×Q8—342no—
1237C2×Q8—342no—
1238C2×Q8—342no—
1239C2×Q8—342no—
1240C2×Q8—342no—
1241C2×Q8—681no—
1242C2×Q8—681no—
1243C2×Q8—681no—
1244C2×Q8—681no—
1245C2×Q8—681no—
1246C2×Q8—6816no—
1247C2×D4—342no—
1248C2×D4—342no—
1249C2×D4—342no—
1250C2×D4—342no—
1251C2×D4—342no—
1252C2×D4—342no—
1253C2×D4—342no—
1254C2×D4—342no—
1255C2×D4—342no—
1256C2×D4—342no—
1257C2×D4—342no—
1258C2×D4—681no—
1259C2×D4—681no—
1260C2×D4—681no—
1261C2×D4—681no—
1262C2×D4—681no—
1263C2×D4—681no—
1264C2×D4—681no—
1265C2×D4—681no—
1266C2×D4—681no—
1267C2×D4—681no—
1268C22×C4—22no—
1269C22×C4—22no—
1270C22×C4—41no—
1271C22×C4—171no—
1272C22×C4—171no—
1273C22×C4—171no—
1274C22×C4—171no—
1275C22×C4—174no—
1276C22×C4—174no—
1277C22×C4—174no—
1278C22×C4—171no—
1279C22×C4—171no—
1280C22×C4—171no—
1281C22×C4—171no—
1282C22×C4—171no—
1283C22×C4—171no—
1284C22×C4—171no—
1285C22×C4—171no—
1286C22×C4—342no—
1287C22×C4—342no—
1288C22×C4—342no—
1289C22×C4—342no—
1290C22×C4—342no—
1291C22×C4—342no—
1292C22×C4—342no—
1293C22×C4—342no—
1294C22×C4—342no—
1295C22×C4—342no—
1296C22×C4—342no—
1297C22×C4—342no—
1298C22×C4—342no—
1299C22×C4—342no—
1300C22×C4—342no—
1301C22×C4—342no—
1302C22×C4—342no—
1303C22×C4—681no—
1304C22×C4—681no—
1305C22×C4—681no—
1306C22×C4—681no—
1307C22×C4—681no—
1308C22×C4—681no—
1309C22×C4—681no—
1310C22×C4—681no—
1311C22×C4—681no—
1312C22×C4—681no—
1313C22×C4—681no—
1314C22×C4—681no—
1315C22×C4—6816no—
1316C22×C4—681no—
1317C22×C4C23×D1711yescharacteristic
1318C22×C4C23×D1711yescharacteristic
1319C22×C4C23×D1711yescharacteristic
1320C22×C4C23×D1711yescharacteristic
1321C22×C4C23×D1711yescharacteristic
1322C22×C4C23×D1711yescharacteristic
1323C22×C4C23×D1711yescharacteristic
1324C22×C4C23×D1711yescharacteristic
1325C22×C4C23×D1711yescharacteristic
1326C22×C4C23×D1711yescharacteristic
1327C22×C4C23×D1711yescharacteristic
1328C22×C4C23×D1711yescharacteristic
1329C22×C4C23×D1711yescharacteristic
1330C22×C4C23×D1711yescharacteristic
1331C4⋊C4—22no—
1332C4⋊C4—22no—
1333C4⋊C4—22no—
1334C4⋊C4—22no—
1335C4⋊C4—22no—
1336C4⋊C4—22no—
1337C4⋊C4—22no—
1338C4⋊C4—22no—
1339C4⋊C4—41no—
1340C4⋊C4—41no—
1341C4⋊C4—41no—
1342C4⋊C4—41no—
1343C4⋊C4—41no—
1344C4⋊C4—41no—
1345C4⋊C4—174no—
1346C4⋊C4—174no—
1347C4⋊C4—174no—
1348C4⋊C4—342no—
1349C4⋊C4—342no—
1350C4⋊C4—342no—
1351C4⋊C4—342no—
1352C4⋊C4—342no—
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—681no—
1363C4⋊C4—681no—
1364C4⋊C4—681no—
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—
1376C4⋊C4D4×D1714yes—
1377C22⋊C4—22no—
1378C22⋊C4—22no—
1379C22⋊C4—22no—
1380C22⋊C4—41no—
1381C22⋊C4—41no—
1382C22⋊C4—41no—
1383C22⋊C4—342no—
1384C22⋊C4—342no—
1385C22⋊C4—342no—
1386C22⋊C4—342no—
1387C22⋊C4—342no—
1388C22⋊C4—342no—
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—342no—
1409C22⋊C4—342no—
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—
1423C42—22no—
1424C42—41no—
1425C42—342no—
1426C42—681no—
1427C42—681no—
1428C42—681no—
1429C23—21no—
1430C23—21no—
1431C23—21no—
1432C23—21no—
1433C23—21no—
1434C23—21no—
1435C23—172no—
1436C23—172no—
1437C23—172no—
1438C23—172no—
1439C23—348no—
1440C23—341no—
1441C23—341no—
1442C23—341no—
1443C23—341no—
1444C23—341no—
1445C23—341no—
1446C23—341no—
1447C23—341no—
1448C23—341no—
1449C23—341no—
1450C23—341no—
1451C23—341no—
1452C23—341no—
1453C23—341no—
1454C23—341no—
1455C23—341no—
1456C23—341no—
1457C23—341no—
1458C23—341no—
1459C23—341no—
1460C23—341no—
1461C23—341no—
1462C23—341no—
1463C23—341no—
1464C23—684no—
1465C23—684no—
1466C23—684no—
1467C23—684no—
1468C23—684no—
1469C23—684no—
1470C23#1058769412yes—
1471C23C24×D1711yescharacteristic
1472Q8—44no—
1473Q8—684no—
1474Q8—684no—
1475Q8—684no—
1476Q8—1362no—
1477D4—684no—
1478D4—684no—
1479D4—1362no—
1480D4—1362no—
1481D4—1362no—
1482D4—1362no—
1483D4—1362no—
1484C2×C4—21no—
1485C2×C4—21no—
1486C2×C4—21no—
1487C2×C4—21no—
1488C2×C4—21no—
1489C2×C4—21no—
1490C2×C4—21no—
1491C2×C4—21no—
1492C2×C4—21no—
1493C2×C4—21no—
1494C2×C4—21no—
1495C2×C4—21no—
1496C2×C4—21no—
1497C2×C4—21no—
1498C2×C4—21no—
1499C2×C4—21no—
1500C2×C4—21no—
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—44no—
1523C2×C4—172no—
1524C2×C4—172no—
1525C2×C4—172no—
1526C2×C4—172no—
1527C2×C4—348no—
1528C2×C4—348no—
1529C2×C4—341no—
1530C2×C4—341no—
1531C2×C4—341no—
1532C2×C4—341no—
1533C2×C4—341no—
1534C2×C4—341no—
1535C2×C4—341no—
1536C2×C4—341no—
1537C2×C4—341no—
1538C2×C4—341no—
1539C2×C4—341no—
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—684no—
1562C2×C4—684no—
1563C2×C4—684no—
1564C2×C4—684no—
1565C2×C4—684no—
1566C2×C4—684no—
1567C2×C4—684no—
1568C2×C4—1362no—
1569C2×C4—1362no—
1570C2×C4C2×D4×D1712yes—
1571C2×C4C2×D4×D1712yes—
1572C2×C4C2×D4×D1712yes—
1573C2×C4#1058769612yes—
1574C22—22no—
1575C22—22no—
1576C22—22no—
1577C22—41no—
1578C22—41no—
1579C22—41no—
1580C22—41no—
1581C22—174no—
1582C22—342no—
1583C22—342no—
1584C22—342no—
1585C22—342no—
1586C22—342no—
1587C22—342no—
1588C22—342no—
1589C22—342no—
1590C22—342no—
1591C22—6816no—
1592C22—681no—
1593C22—681no—
1594C22—681no—
1595C22—681no—
1596C22—681no—
1597C22—681no—
1598C22—681no—
1599C22—681no—
1600C22—681no—
1601C22—681no—
1602C22—681no—
1603C22—681no—
1604C22—681no—
1605C22—681no—
1606C22—681no—
1607C22—681no—
1608C22—681no—
1609C22—681no—
1610C22C22×D4×D1711yescharacteristic
1611C22H(5,𝔽2)×D1711yescharacteristic
1612C22H(5,𝔽2)×D1711yescharacteristic
1613C22C2×#1058769611yescharacteristic
1614C222−1+4×D1711yescharacteristic
1615C222−1+4×D1711yescharacteristic
1616C22C2×#1058769411yescharacteristic
1617C4—22no—
1618C4—22no—
1619C4—22no—
1620C4—22no—
1621C4—41no—
1622C4—41no—
1623C4—41no—
1624C4—41no—
1625C4—41no—
1626C4—41no—
1627C4—41no—
1628C4—41no—
1629C4—41no—
1630C4—41no—
1631C4—342no—
1632C4—342no—
1633C4—342no—
1634C4—342no—
1635C4—681no—
1636C4—681no—
1637C4—681no—
1638C4—681no—
1639C4—681no—
1640C4—681no—
1641C4—681no—
1642C4—681no—
1643C2—42no—
1644C2—344no—
1645C2—682no—
1646C2—1361no—
1647C2—1361no—
1648C2D17×#53711yescharacteristic
1649C2#1454241411yescharacteristic
1650C2#1454243411yescharacteristic
1651C2#1454300311yescharacteristic
1652C2#1454301211yescharacteristic
1653C2#1454302611yescharacteristic
1654C2#1454303211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutator, socle, cosocleC23×C17C25
FittingC17×#2704C2
prime radical#14537067C2
hypercenter#2704D17
hypocenterC17#36719
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2704

Complements

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

NH ≅ G/Ntype
1. C2×#11763407C2semidirect
2. C2×C22⋊Q8×D17C2semidirect
3. #14537070C2semidirect
5. #14535444C2semidirect
6. #14535442C2semidirect
7. #14535436C2semidirect
8. #14535415C2semidirect
9. #14535413C2semidirect
10. #14535411C2semidirect
11. #14535409C2semidirect
12. #14535158C2semidirect
13. #14535155C2semidirect
14. #14535153C2semidirect
15. #14535153C2semidirect
16. #14535139C2semidirect
17. #14535137C2semidirect
18. #14535131C2semidirect
19. #14535129C2semidirect
20. #14534602C2semidirect
21. #14534527C2semidirect
22. #14533678C2semidirect
23. #14533675C2semidirect
24. #14532188C2semidirect
25. #14532184C2semidirect
26. #14532168C2semidirect
27. #14532164C2semidirect
28. #14532147C2semidirect
29. #14532144C2semidirect
30. #14531399C2semidirect
31. C17×#2704C2semidirect
35. C2×#10587584C22semidirect
36. C2×#10587562C22semidirect
37. C2×#10587575C22semidirect
42. C2×#10587580C22semidirect
43. C2×#10587580C22semidirect
45. C2×#10587583C22semidirect
46. C2×#10587583C22semidirect
52. C2×#10587582C22semidirect
53. C2×#10587582C22semidirect
54. C2×#10587582C22semidirect
59. C2×#10587632C22semidirect
75. #11762751C22semidirect
76. #11762750C22semidirect
77. #11762743C22semidirect
78. #11762742C22semidirect
79. #11762742C22semidirect
80. #11762742C22semidirect
81. #11762740C22semidirect
82. #11762740C22semidirect
83. #11762739C22semidirect
85. #11762733C22semidirect
86. #11762733C22semidirect
87. #11762733C22semidirect
93. #11762731C22semidirect
94. #11762731C22semidirect
95. #11762731C22semidirect
96. #11762731C22semidirect
97. #11762731C22semidirect
98. #11762730C22semidirect
99. #11762730C22semidirect
100. #11762730C22semidirect
101. #11762729C22semidirect
102. #11762729C22semidirect
105. #11762727C22semidirect
108. #11762726C22semidirect
113. #11762722C22semidirect
114. #11762722C22semidirect
115. #11762722C22semidirect
116. #11762720C22semidirect
117. #11762715C22semidirect
118. #11762713C22semidirect
119. #11762713C22semidirect
124. #11762708C22semidirect
125. #11762707C22semidirect
126. #11762706C22semidirect
127. #11762706C22semidirect
128. #11762706C22semidirect
129. #11762705C22semidirect
130. #11762705C22semidirect
131. #11762704C22semidirect
132. #11762704C22semidirect
133. #11762704C22semidirect
135. #11762701C22semidirect
137. #11762700C22semidirect
140. #11762699C22semidirect
142. #11762698C22semidirect
174. C2×C17×#125C22semidirect
176. C17×#398C22semidirect
177. C17×#398C22semidirect
178. C17×#398C22semidirect
181. C17×#395C22semidirect
182. C17×#391C22semidirect
183. C17×#389C22semidirect
184. C17×#389C22semidirect
347. C4⋊C4×D17D4semidirect
754. #2704D17semidirect
853. C2×#125C2×D17semidirect
901. #398C2×D17semidirect
902. #398C2×D17semidirect
903. #398C2×D17semidirect
925. #395C2×D17semidirect
943. #391C2×D17semidirect
958. #389C2×D17semidirect
959. #389C2×D17semidirect
1218. C17#36719semidirect

Maximal subgroups

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

subgroupindex
C2×#117634072
C2×C22⋊Q8×D172
#145370702
#145370672
#145354442
#145354422
#145354362
#145354152
#145354132
#145354112
#145354092
#145351582
#145351552
#145351532
#145351392
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