Finite Group Databasebeta

← #17001993

Subgroups — #17001993

Order 4352.

944 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14542536C211yesmaximal, characteristic
2#14531644C211yesmaximal, characteristic, complemented
3#14527362C211yesmaximal, characteristic, complemented
4#14527349C211yesmaximal, characteristic, complemented
5#14527341C211yesmaximal, characteristic
6#14527336C211yesmaximal, characteristic, complemented
7#14527323C211yesmaximal, characteristic, complemented
8#14527318C211yesmaximal, characteristic, complemented
9#14527310C211yesmaximal, characteristic, complemented
10#14527297C211yesmaximal, characteristic, complemented
11#14527289C211yesmaximal, characteristic
12#14527284C211yesmaximal, characteristic, complemented
13#14527271C211yesmaximal, characteristic, complemented
14C2×#11762547C211yesmaximal, characteristic, complemented
15C17×#2924C211yesmaximal, characteristic, complemented
16#11763527—21no—
17#11763514—21no—
18#11763498—21no—
19#11763494—21no—
20#11763492—21no—
21#11763492—21no—
22#11763485—21no—
23#11763485—21no—
24#11763437C411yescharacteristic, complemented
25#11763430C411yescharacteristic, complemented
26#11763430C411yescharacteristic, complemented
27#11763421C411yescharacteristic, complemented
28#11763421C411yescharacteristic, complemented
29#11763385C411yescharacteristic, complemented
30#11763366C2211yescharacteristic
31#11763366C2211yescharacteristic
32#11763343C2211yescharacteristic
33#11763343C2211yescharacteristic
34#11763320C2211yescharacteristic
35C2×#10587610C2211yescharacteristic
36#11763289C411yescharacteristic, complemented
37#11763286C411yescharacteristic, complemented
38#11762695—21no—
39#11762695—21no—
40#11762684—21no—
41#11762677C2211yescharacteristic
42#11762675C2211yescharacteristic
43#11762672C2211yescharacteristic
44C4×C4⋊Dic17C2211yescharacteristic
45C22⋊C4×Dic17—21no—
46#11762655C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48#11762547C2211yescharacteristic
49#11762547C2211yescharacteristic
50#11762547C2211yescharacteristic
51#11762547C2211yescharacteristic
52#11762547C2211yescharacteristic
53#11762547C2211yescharacteristic
54#11762547C2211yescharacteristic
55#11762547C2211yescharacteristic
56#11762547C2211yescharacteristic
57#11762547C2211yescharacteristic
58#11762547C2211yescharacteristic
59#11762547C2211yescharacteristic
60#11762544C2211yescharacteristic
61#11762544C2211yescharacteristic
62#11762544C2211yescharacteristic
63#11762544C2211yescharacteristic
64C2×C17×#117C2211yescharacteristic
65C17×#433—21no—
66C17×#433—21no—
67C17×#432C2211yescharacteristic
68C17×#432C2211yescharacteristic
69C17×#431C2211yescharacteristic
70C17×#431C2211yescharacteristic
71C17×#424—21no—
72C17×#407C2211yescharacteristic
73C2×C17×C22⋊C8C2211yescharacteristic
74C17×#405—21no—
75C23×C4×C17C2311yescharacteristic
76C23×Dic17—21no—
77C2×#63252C2×C411yescharacteristic
78C22×Dic34C2×C411yescharacteristic
79C2×M16×C17—21no—
80C22×C8×C17—21no—
81C17×#117C2×C411yescharacteristic
82C17×#117C2×C411yescharacteristic
83C17×#117C2×C411yescharacteristic
84C17×#117C2×C411yescharacteristic
85C17×#117D411yescharacteristic
86C17×#117D411yescharacteristic
87C17×#117D411yescharacteristic
88C17×#117D411yescharacteristic
89C2×C4⋊C4×C17D411yescharacteristic
90C2×C4⋊C4×C17D411yescharacteristic
91C2×C22⋊C4×C17D411yescharacteristic
92C2×C22⋊C4×C17D411yescharacteristic
93C2×C42×C17C2311yescharacteristic
94C2×C42×C17C2311yescharacteristic
95#10587639—21no—
96C2×C22⋊Dic17—21no—
97C2×C22⋊Dic17—21no—
98#10587616C2×C411yescharacteristic
99#10587616C2311yescharacteristic
100#10587615—21no—
101#10587615—21no—
102#10587615—21no—
103C4×C22⋊D17—21no—
104C4×C22⋊D17—21no—
105C4×C22⋊D17—21no—
106C4×C22⋊D17—21no—
107#10587612—21no—
108#10587612—21no—
109#10587612C2×C411yescharacteristic
110C2×C4⋊Dic17—21no—
111C2×C4⋊Dic17—21no—
112C2×C4⋊Dic17C2×C411yescharacteristic
113#10587610—21no—
114#10587610—21no—
115#10587610—21no—
116#10587610—21no—
117#10587610C2×C411yescharacteristic
118#10587610C2×C411yescharacteristic
119#10587610C2×C411yescharacteristic
120#10587610C2311yescharacteristic
121#10587610C2311yescharacteristic
122#10587610C2311yescharacteristic
123C2×#63225—21no—
124C2×C4×Dic17—21no—
125C2×C4×Dic17—21no—
126#10587584—21no—
127#10587584—21no—
128#10587583—21no—
129#10587583—21no—
130#10587582—21no—
131#10587582—21no—
132#10587578—21no—
133C4⋊C4×D17—21no—
134#10587576—21no—
135#10587575—21no—
136#10587575—21no—
137#10587575—21no—
138#10587575—21no—
139#10587574—21no—
140#10587573—21no—
141#10587573—21no—
142#10587572—21no—
143#10587572—21no—
144#10587571—21no—
145#10587571—21no—
146#10587569—21no—
147#10587569—21no—
148#10587567—21no—
149#10587567—21no—
150#10587565—21no—
151#10587565—21no—
152#10587565—21no—
153#10587565—21no—
154#10587564—21no—
155#10587564—21no—
156#10587563—21no—
157#10587563—21no—
158#10587562—21no—
159#10587562—21no—
160#10587561C2×C411yescharacteristic, complemented
161#10587561C2×C411yescharacteristic, complemented
162C4×D68C2×C411yescharacteristic, complemented
163C4×D68C2×C411yescharacteristic, complemented
164#10587558—21no—
165#10587558—21no—
166#10587556—21no—
167#10587556—21no—
168#10587556C2×C411yescharacteristic, complemented
169#10587556C2×C411yescharacteristic, complemented
170#10587555C2×C411yescharacteristic, complemented
171#10587555C2×C411yescharacteristic, complemented
172#10587555C2×C411yescharacteristic, complemented
173#10587555C2×C411yescharacteristic, complemented
174C4×Dic34—21no—
175C4×Dic34—21no—
176C4×Dic34C2×C411yescharacteristic, complemented
177C4×Dic34C2×C411yescharacteristic, complemented
178C4×Dic34C2×C411yescharacteristic, complemented
179C4×Dic34C2×C411yescharacteristic, complemented
180C4×Dic34C2×C411yescharacteristic, complemented
181C4×Dic34C2×C411yescharacteristic, complemented
182C17×C4⋊C8—21no—
183C17×C4⋊C8—21no—
184C17×C4⋊C8—21no—
185C17×C4⋊C8—21no—
186C17×C22⋊C8—21no—
187C17×C22⋊C8—21no—
188C17×C22⋊C8C2311yescharacteristic
189C17×C22⋊C8C2311yescharacteristic
190C17×C22⋊C8C2311yescharacteristic
191C17×C22⋊C8C2311yescharacteristic
192C17×#97—21no—
193C17×#97—21no—
194C4×C8×C17—21no—
195C4×C8×C17—21no—
196#10587502—21no—
197#10587502—21no—
198#10587502—21no—
199#10587502—21no—
200#10587502—21no—
201#10587502—21no—
202#10587502C2311yescharacteristic
203#10587502C2311yescharacteristic
204#10587502C2311yescharacteristic
205#10587502C2311yescharacteristic
206C24×C17C2×D411yescharacteristic
207C22×C4×C17—42no—
208C22×C4×C17C22×C411yescharacteristic
209C22×C4×C17C22×C411yescharacteristic
210C22×C4×C17C2×D411yescharacteristic
211C22×C4×C17C2×D411yescharacteristic
212C22×C4×C17C2×D411yescharacteristic
213C22×C4×C17C2×D411yescharacteristic
214C22×C4×C17C2×D411yescharacteristic
215C22×C4×C17C2×D411yescharacteristic
216C22×C4×C17C2×D411yescharacteristic
217C22×C4×C17C2411yescharacteristic
218C2×C22⋊D17—21no—
219C2×C22⋊D17—21no—
220C2×C22⋊D17—21no—
221C22×Dic17—21no—
222C22×Dic17—21no—
223C22×Dic17—21no—
224C22×Dic17—21no—
225C22×Dic17—21no—
226C22×Dic17—21no—
227C22×Dic17—42no—
228C22×Dic17—42no—
229C22×Dic17—81no—
230#63252—42no—
231C2×D68C22×C411yescharacteristic
232C2×C4×D17—21no—
233C2×C4×D17—21no—
234C2×C4×D17—21no—
235C2×Dic34—21no—
236C2×Dic34—21no—
237C2×Dic34—21no—
238C2×Dic34—42no—
239C2×Dic34C22×C411yescharacteristic
240C2×Dic34C22×C411yescharacteristic
241C2×Dic34C22×C411yescharacteristic
242M16×C17—42no—
243C2×C8×C17—21no—
244C2×C8×C17—21no—
245C2×C8×C17—21no—
246C2×C8×C17—21no—
247C2×C8×C17—42no—
248C4⋊C4×C17C22⋊C411yescharacteristic
249C4⋊C4×C17C22⋊C411yescharacteristic
250C4⋊C4×C17C22⋊C411yescharacteristic
251C4⋊C4×C17C22⋊C411yescharacteristic
252C4⋊C4×C17C22⋊C411yescharacteristic
253C4⋊C4×C17C22⋊C411yescharacteristic
254C4⋊C4×C17C22⋊C411yescharacteristic
255C4⋊C4×C17C22⋊C411yescharacteristic
256C22⋊C4×C17C22⋊C411yescharacteristic
257C22⋊C4×C17C22⋊C411yescharacteristic
258C22⋊C4×C17C22⋊C411yescharacteristic
259C22⋊C4×C17C22⋊C411yescharacteristic
260C22⋊C4×C17C22⋊C411yescharacteristic
261C22⋊C4×C17C22⋊C411yescharacteristic
262C22⋊C4×C17C22⋊C411yescharacteristic
263C22⋊C4×C17C22⋊C411yescharacteristic
264C42×C17C22×C411yescharacteristic
265C42×C17C22×C411yescharacteristic
266C42×C17C22×C411yescharacteristic
267C42×C17C22×C411yescharacteristic
268C42×C17C2×D411yescharacteristic
269C42×C17C2×D411yescharacteristic
270C42×C17C2×D411yescharacteristic
271C42×C17C2×D411yescharacteristic
272C22⋊Dic17—21no—
273C22⋊Dic17—21no—
274C22⋊Dic17—21no—
275C22⋊Dic17—21no—
276C22⋊Dic17—21no—
277C22⋊Dic17—21no—
278C22⋊Dic17—21no—
279C22⋊Dic17—42no—
280#63227—21no—
281#63227—21no—
282#63227—21no—
283#63227—21no—
284#63227—21no—
285#63227—21no—
286#63227—21no—
287#63227—21no—
288C4⋊Dic17—21no—
289C4⋊Dic17—21no—
290C4⋊Dic17—21no—
291C4⋊Dic17—21no—
292C4⋊Dic17—21no—
293C4⋊Dic17—21no—
294C4⋊Dic17—21no—
295C4⋊Dic17—42no—
296C4⋊Dic17—81no—
297C4⋊Dic17C22×C411yescharacteristic
298C4⋊Dic17C22×C411yescharacteristic
299C4⋊Dic17C22×C411yescharacteristic
300C4⋊Dic17C22×C411yescharacteristic
301#63225—21no—
302#63225—21no—
303#63225—21no—
304#63225—21no—
305#63225—21no—
306#63225—21no—
307#63225—21no—
308#63225—21no—
309#63225—21no—
310#63225—21no—
311#63225—21no—
312#63225—21no—
313#63225—21no—
314#63225—21no—
315#63225—21no—
316#63225—21no—
317C4×Dic17—21no—
318C4×Dic17—21no—
319C4×Dic17—21no—
320C4×Dic17—21no—
321C4×Dic17—21no—
322C4×Dic17—21no—
323C4×Dic17—21no—
324C4×Dic17—42no—
325C4×Dic17—81no—
326#17609—171nomaximal, Sylow
327C23×C17—21no—
328C23×C17—21no—
329C23×C17—22no—
330C23×C17—41no—
331C23×C17C2×C22⋊C411yescharacteristic
332C23×C17C2×C22⋊C411yescharacteristic
333C23×C17C22×D411yescharacteristic
334C22×D17—21no—
335C2×C4×C17—21no—
336C2×C4×C17—21no—
337C2×C4×C17—21no—
338C2×C4×C17—21no—
339C2×C4×C17—22no—
340C2×C4×C17—22no—
341C2×C4×C17—41no—
342C2×C4×C17—41no—
343C2×C4×C17—41no—
344C2×C4×C17—41no—
345C2×C4×C17—41no—
346C2×C4×C17—41no—
347C2×C4×C17C2×C22⋊C411yescharacteristic
348C2×C4×C17C2×C22⋊C411yescharacteristic
349C2×C4×C17C2×C22⋊C411yescharacteristic
350C2×C4×C17C2×C22⋊C411yescharacteristic
351C2×C4×C17C2×C22⋊C411yescharacteristic
352C2×C4×C17C2×C22⋊C411yescharacteristic
353C2×C4×C17C2×C22⋊C411yescharacteristic
354C2×C4×C17C2×C22⋊C411yescharacteristic
355C2×C4×C17C2×C22⋊C411yescharacteristic
356C2×C4×C17C2×C22⋊C411yescharacteristic
357C2×C4×C17C23×C411yescharacteristic
358C2×C4×C17C22×D411yescharacteristic
359C22⋊D17—41no—
360C22⋊D17—41no—
361C22⋊D17—42no—
362C22⋊D17—81no—
363C2×Dic17—22no—
364C2×Dic17—21no—
365C2×Dic17—21no—
366C2×Dic17—21no—
367C2×Dic17—21no—
368C2×Dic17—21no—
369C2×Dic17—21no—
370C2×Dic17—21no—
371C2×Dic17—41no—
372C2×Dic17—41no—
373C2×Dic17—42no—
374C2×Dic17—41no—
375C2×Dic17—41no—
376C2×Dic17—41no—
377C2×Dic17—41no—
378C2×Dic17—41no—
379C2×Dic17—41no—
380C2×Dic17—41no—
381C2×Dic17—41no—
382C2×Dic17—41no—
383C2×Dic17—81no—
384C2×Dic17—84no—
385D68—41no—
386C4×D17—42no—
387C4×D17—81no—
388C4×D17—81no—
389Dic34—42no—
390Dic34—41no—
391Dic34—41no—
392Dic34—41no—
393Dic34—81no—
394Dic34—81no—
395C8×C17—41no—
396C8×C17—41no—
397C8×C17—41no—
398C8×C17—41no—
399#3495—171no—
400#2924D1711yescharacteristic, complemented
401#2343—171no—
402#1521—171no—
403#1518—171no—
404#1516—171no—
405#1515—171no—
406#1512—171no—
407#1511—171no—
408#1509—171no—
409#1506—171no—
410#1504—171no—
411#1503—171no—
412#1500—171no—
413C2×#328—171no—
414C22×C17—21no—
415C22×C17—21no—
416C22×C17—21no—
417C22×C17—21no—
418C22×C17—21no—
419C22×C17—21no—
420C22×C17—21no—
421C22×C17—42no—
422C22×C17—42no—
423C22×C17#41012yes—
424C22×C17C22×C22⋊C411yescharacteristic
425C22×C17#57711yescharacteristic
426C22×C17#57811yescharacteristic
427C2×D17—41no—
428C2×D17—41no—
429C2×D17—41no—
430C4×C17—21no—
431C4×C17—21no—
432C4×C17—21no—
433C4×C17—21no—
434C4×C17—21no—
435C4×C17—21no—
436C4×C17—21no—
437C4×C17—21no—
438C4×C17—21no—
439C4×C17—21no—
440C4×C17—21no—
441C4×C17—21no—
442Dic17—42no—
443Dic17—41no—
444Dic17—41no—
445Dic17—41no—
446Dic17—41no—
447Dic17—41no—
448Dic17—41no—
449Dic17—41no—
450Dic17—81no—
451Dic17—81no—
452Dic17—81no—
453#556—341no—
454#554—341no—
455#552—341no—
456#552—341no—
457#552—341no—
458#552—341no—
459#551—341no—
460#551—341no—
461#544—171no—
462#542—171no—
463#542—171no—
464#541—171no—
465#541—171no—
466#536—171no—
467#533—171no—
468#533—171no—
469#529—171no—
470#529—171no—
471#525—171no—
472C2×C22⋊Q8—171no—
473#520—171no—
474#519—171no—
475C2×#117C2×D1711yescharacteristic
476#433—21no—
477#433—21no—
478#432C2×D1711yescharacteristic
479#432C2×D1711yescharacteristic
480#431C2×D1711yescharacteristic
481#431C2×D1711yescharacteristic
482#424—21no—
483#407C2×D1711yescharacteristic
484C2×C22⋊C8C2×D1711yescharacteristic
485#405—21no—
486#387—341no—
487#387—341no—
488#385—341no—
489#383—171no—
490#382—171no—
491#381—171no—
492C4×C4⋊C4—171no—
493C4×C22⋊C4—341no—
494#376—171no—
495C2×#95—171no—
496#328—171no—
497#328—171no—
498#328—171no—
499#328—171no—
500#328—171no—
501#328—171no—
502#328—171no—
503#328—171no—
504#328—171no—
505#328—171no—
506#328—171no—
507#328—171no—
508#327—171no—
509#327—171no—
510#327—171no—
511#327—171no—
512C2×C17—21no—
513C2×C17—21no—
514C2×C17—22no—
515C2×C17—41no—
516C2×C17C2×#41011yescharacteristic
517C2×C17#289811yescharacteristic
518C2×C17#290111yescharacteristic
519D17—81no—
520C2×#41—171no—
521C22×Q8—171no—
522C23×C4—341no—
523C23×C4C22×D1711yescharacteristic
524C2×M16—21no—
525C22×C8—21no—
526C4⋊Q8—171no—
527C4⋊Q8—171no—
528C4⋊Q8—171no—
529C4⋊Q8—171no—
530C4⋊Q8—341no—
531#126—341no—
532#126—341no—
533#126—341no—
534#126—341no—
535#126—341no—
536#126—341no—
537#126—341no—
538#126—341no—
539#125—171no—
540#125—171no—
541#125—341no—
542#125—341no—
543#125—341no—
544#125—341no—
545#125—341no—
546#125—341no—
547#125—341no—
548#124—171no—
549#124—171no—
550#124—341no—
551#124—341no—
552#123—341no—
553#123—341no—
554#123—341no—
555#123—341no—
556#123—341no—
557#123—341no—
558#123—341no—
559C22⋊Q8—171no—
560C22⋊Q8—171no—
561C22⋊Q8—171no—
562C22⋊Q8—171no—
563C22⋊Q8—171no—
564C22⋊Q8—171no—
565C22⋊Q8—341no—
566C22⋊Q8—341no—
567C22⋊Q8—341no—
568C22⋊Q8—341no—
569C22⋊Q8—341no—
570C22⋊Q8—341no—
571C22⋊Q8—341no—
572C22⋊Q8—341no—
573C22⋊Q8—341no—
574C22⋊Q8—341no—
575#121—171no—
576#121—171no—
577#120—341no—
578C4×Q8—171no—
579C4×Q8—171no—
580C4×Q8—171no—
581C4×Q8—171no—
582C4×Q8—171no—
583C4×Q8—171no—
584C4×Q8—341no—
585C4×Q8—341no—
586C4×Q8—341no—
587C4×Q8—341no—
588C4×D4—171no—
589C4×D4—171no—
590C4×D4—341no—
591C4×D4—341no—
592C4×D4—341no—
593C4×D4—341no—
594C4×D4—341no—
595C4×D4—341no—
596#117—171no—
597#117—341no—
598#117—341no—
599#117—341no—
600#117—341no—
601#117—341no—
602#117—341no—
603#117—341no—
604#117C4×D1711yescharacteristic
605#117C4×D1711yescharacteristic
606#117C4×D1711yescharacteristic
607#117C4×D1711yescharacteristic
608#117C22⋊D1711yescharacteristic
609#117C22⋊D1711yescharacteristic
610#117C22⋊D1711yescharacteristic
611#117C22⋊D1711yescharacteristic
612C2×C4⋊C4—171no—
613C2×C4⋊C4—341no—
614C2×C4⋊C4—341no—
615C2×C4⋊C4—341no—
616C2×C4⋊C4—341no—
617C2×C4⋊C4D6811yescharacteristic
618C2×C4⋊C4D6811yescharacteristic
619C2×C22⋊C4—341no—
620C2×C22⋊C4—341no—
621C2×C22⋊C4D6811yescharacteristic
622C2×C22⋊C4D6811yescharacteristic
623C2×C42—341no—
624C2×C42—341no—
625C2×C42C22×D1711yescharacteristic
626C2×C42C22×D1711yescharacteristic
627C4⋊C8—21no—
628C4⋊C8—21no—
629C4⋊C8—21no—
630C4⋊C8—21no—
631C22⋊C8—21no—
632C22⋊C8—21no—
633C22⋊C8C22×D1711yescharacteristic
634C22⋊C8C22×D1711yescharacteristic
635C22⋊C8C22×D1711yescharacteristic
636C22⋊C8C22×D1711yescharacteristic
637#97—21no—
638#97—21no—
639C4×C8—21no—
640C4×C8—21no—
641#95—171no—
642#95—171no—
643#95—171no—
644#95—171no—
645#95—341no—
646#95—341no—
647#95—341no—
648#95—341no—
649#95—341no—
650#95—341no—
651C17#1760911yescharacteristic, complemented, Sylow
652C24C2×D6811yescharacteristic
653#41—682no—
654C2×Q8—171no—
655C2×Q8—171no—
656C2×Q8—171no—
657C2×Q8—341no—
658C2×Q8—341no—
659C2×Q8—341no—
660C2×Q8—682no—
661C2×D4—171no—
662C2×D4—341no—
663C2×D4—341no—
664C2×D4—341no—
665C22×C4—42no—
666C22×C4—341no—
667C22×C4—341no—
668C22×C4—341no—
669C22×C4—341no—
670C22×C4—341no—
671C22×C4—341no—
672C22×C4—341no—
673C22×C4—341no—
674C22×C4—341no—
675C22×C4—682no—
676C22×C4—682no—
677C22×C4—1361no—
678C22×C4C2×C4×D1711yescharacteristic
679C22×C4C2×C4×D1711yescharacteristic
680C22×C4C2×D6811yescharacteristic
681C22×C4C2×D6811yescharacteristic
682C22×C4C2×D6811yescharacteristic
683C22×C4C2×D6811yescharacteristic
684C22×C4C2×D6811yescharacteristic
685C22×C4C2×C22⋊D1711yescharacteristic
686C22×C4C2×C22⋊D1711yescharacteristic
687C22×C4C23×D1711yescharacteristic
688M16—42no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—42no—
694C4⋊C4—171no—
695C4⋊C4—171no—
696C4⋊C4—171no—
697C4⋊C4—171no—
698C4⋊C4—341no—
699C4⋊C4—341no—
700C4⋊C4—341no—
701C4⋊C4—341no—
702C4⋊C4—341no—
703C4⋊C4—341no—
704C4⋊C4—341no—
705C4⋊C4—341no—
706C4⋊C4—341no—
707C4⋊C4—341no—
708C4⋊C4—341no—
709C4⋊C4—341no—
710C4⋊C4—341no—
711C4⋊C4—341no—
712C4⋊C4—341no—
713C4⋊C4—341no—
714C4⋊C4—341no—
715C4⋊C4—341no—
716C4⋊C4—341no—
717C4⋊C4—341no—
718C4⋊C4—341no—
719C4⋊C4—341no—
720C4⋊C4—341no—
721C4⋊C4—682no—
722C4⋊C4—1361no—
723C4⋊C4#6322711yescharacteristic
724C4⋊C4#6322711yescharacteristic
725C4⋊C4#6322711yescharacteristic
726C4⋊C4#6322711yescharacteristic
727C4⋊C4#6322711yescharacteristic
728C4⋊C4#6322711yescharacteristic
729C4⋊C4#6322711yescharacteristic
730C4⋊C4#6322711yescharacteristic
731C22⋊C4—341no—
732C22⋊C4—341no—
733C22⋊C4—341no—
734C22⋊C4—341no—
735C22⋊C4—341no—
736C22⋊C4—341no—
737C22⋊C4—341no—
738C22⋊C4—341no—
739C22⋊C4—341no—
740C22⋊C4—341no—
741C22⋊C4—341no—
742C22⋊C4—341no—
743C22⋊C4—341no—
744C22⋊C4—341no—
745C22⋊C4—341no—
746C22⋊C4—682no—
747C22⋊C4#6322711yescharacteristic
748C22⋊C4#6322711yescharacteristic
749C22⋊C4#6322711yescharacteristic
750C22⋊C4#6322711yescharacteristic
751C22⋊C4#6322711yescharacteristic
752C22⋊C4#6322711yescharacteristic
753C22⋊C4#6322711yescharacteristic
754C22⋊C4#6322711yescharacteristic
755C42—341no—
756C42—341no—
757C42—341no—
758C42—341no—
759C42—341no—
760C42—341no—
761C42—341no—
762C42—682no—
763C42—1361no—
764C42C2×C4×D1711yescharacteristic
765C42C2×C4×D1711yescharacteristic
766C42C2×C4×D1711yescharacteristic
767C42C2×C4×D1711yescharacteristic
768C42C2×C22⋊D1711yescharacteristic
769C42C2×C22⋊D1711yescharacteristic
770C42C2×C22⋊D1711yescharacteristic
771C42C2×C22⋊D1711yescharacteristic
772C23—22no—
773C23—21no—
774C23—21no—
775C23—41no—
776C23—341no—
777C23C2×#6322711yescharacteristic
778C23C2×#6322711yescharacteristic
779C23C22×D6811yescharacteristic
780Q8—681no—
781Q8—681no—
782Q8—681no—
783Q8—682no—
784Q8—1361no—
785Q8—1361no—
786D4—681no—
787D4—682no—
788D4—681no—
789D4—681no—
790D4—1361no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—342no—
804C2×C4—341no—
805C2×C4—341no—
806C2×C4—341no—
807C2×C4—341no—
808C2×C4—341no—
809C2×C4—341no—
810C2×C4—341no—
811C2×C4—682no—
812C2×C4—681no—
813C2×C4—682no—
814C2×C4—681no—
815C2×C4—681no—
816C2×C4—681no—
817C2×C4—681no—
818C2×C4—681no—
819C2×C4—681no—
820C2×C4—681no—
821C2×C4—681no—
822C2×C4—681no—
823C2×C4—681no—
824C2×C4—1361no—
825C2×C4—1361no—
826C2×C4—1361no—
827C2×C4—1364no—
828C2×C4C2×#6322711yescharacteristic
829C2×C4C2×#6322711yescharacteristic
830C2×C4C2×#6322711yescharacteristic
831C2×C4C2×#6322711yescharacteristic
832C2×C4C2×#6322711yescharacteristic
833C2×C4C2×#6322711yescharacteristic
834C2×C4C2×#6322711yescharacteristic
835C2×C4C2×#6322711yescharacteristic
836C2×C4C2×#6322711yescharacteristic
837C2×C4C2×#6322711yescharacteristic
838C2×C4C22×C4×D1711yescharacteristic
839C2×C4C22×C22⋊D1711yescharacteristic
840C8—41no—
841C8—41no—
842C8—41no—
843C8—41no—
844C22—21no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—42no—
852C22—42no—
853C22—681no—
854C22—681no—
855C22—681no—
856C22#1176278212yes—
857C22C22×#6322711yescharacteristic
858C22#1176362111yescharacteristic
859C22#1176362611yescharacteristic
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—21no—
865C4—21no—
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—682no—
873C4—681no—
874C4—681no—
875C4—681no—
876C4—681no—
877C4—681no—
878C4—681no—
879C4—681no—
880C4—1361no—
881C4—1361no—
882C4—1361no—
883C2—21no—
884C2—21no—
885C2—22no—
886C2—41no—
887C2—1361no—
888C2C2×#1176278211yescharacteristic
889C2#1453731811yescharacteristic
890C2#1453732911yescharacteristic
subgroupG/H
centerC22C22×#63227
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#2924C2
socleC22×C17C22×C22⋊C4
prime radical#11763320C22
cosocleC22×C4×C17C24
hypercenter#2924D17
hypocenterC17#17609
LCSG ▷ C2×C4×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2924

Complements

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

NH ≅ G/Ntype
2. #14531644C2semidirect
3. #14527362C2semidirect
4. #14527349C2semidirect
6. #14527336C2semidirect
7. #14527323C2semidirect
8. #14527318C2semidirect
9. #14527310C2semidirect
10. #14527297C2semidirect
12. #14527284C2semidirect
13. #14527271C2semidirect
14. C2×#11762547C2semidirect
15. C17×#2924C2semidirect
24. #11763437C4semidirect
25. #11763430C4semidirect
26. #11763430C4semidirect
27. #11763421C4semidirect
28. #11763421C4semidirect
29. #11763385C4semidirect
36. #11763289C4semidirect
37. #11763286C4semidirect
160. #10587561C2×C4semidirect
161. #10587561C2×C4semidirect
162. C4×D68C2×C4semidirect
163. C4×D68C2×C4semidirect
168. #10587556C2×C4semidirect
169. #10587556C2×C4semidirect
170. #10587555C2×C4semidirect
171. #10587555C2×C4semidirect
172. #10587555C2×C4semidirect
173. #10587555C2×C4semidirect
176. C4×Dic34C2×C4semidirect
177. C4×Dic34C2×C4semidirect
178. C4×Dic34C2×C4semidirect
179. C4×Dic34C2×C4semidirect
180. C4×Dic34C2×C4semidirect
181. C4×Dic34C2×C4semidirect
400. #2924D17semidirect
651. C17#17609semidirect

Maximal subgroups

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

subgroupindex
#145425362
#145316442
#145273622
#145273492
#145273412
#145273362
#145273232
#145273182
#145273102
#145272972
#145272892
#145272842
#145272712
C2×#117625472
C17×#29242
#1760917