Finite Group Databasebeta

← #29646295

Subgroups — #29646295

Order 15616.

922 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840448C211yesmaximal, characteristic
2#21454909C211yesmaximal, characteristic, complemented
3#21454906C211yesmaximal, characteristic, complemented
4#21444188C211yesmaximal, characteristic, complemented
5#21444185C211yesmaximal, characteristic, complemented
6#21444185C211yesmaximal, characteristic, complemented
7#21444173C211yesmaximal, characteristic, complemented
8#21444173C211yesmaximal, characteristic, complemented
9#21444158C211yesmaximal, characteristic
10#21444152C211yesmaximal, characteristic, complemented
11#21444151C211yesmaximal, characteristic, complemented
12#21444138C211yesmaximal, characteristic
13#21444132C211yesmaximal, characteristic, complemented
14#21444131C211yesmaximal, characteristic, complemented
15C61×#1473C211yesmaximal, characteristic, complemented
16#16840448—21no—
17#16840448—21no—
18#16840448—21no—
19#16840448—21no—
20#16840448—21no—
21#16840448—21no—
22#16840448—21no—
23#16840448—21no—
24C2×#14519770C2211yescharacteristic
25C2×#14519768C411yescharacteristic
26C2×#14519767C411yescharacteristic
27C2×#14519767C2211yescharacteristic
28C2×#14519759C411yescharacteristic
29C2×#14519759C411yescharacteristic
30C2×#14519755C411yescharacteristic
31C2×#14519754C411yescharacteristic
32C2×C4×Dic122C2211yescharacteristic
33C2×#14519737C2211yescharacteristic
34C2×#14519735C2211yescharacteristic
35C2×#14519734C2211yescharacteristic
36C2×#14519733C411yescharacteristic
37C2×C4⋊C4×D61C411yescharacteristic
38#16839892—21no—
39#16839891—21no—
40#16839891—21no—
41#16839890—21no—
42#16839890—21no—
43#16839889—21no—
44C8×Dic122—21no—
45#16839886—21no—
46#16839819C2211yescharacteristic
47#16839816C2211yescharacteristic
48#16839816C2211yescharacteristic
49#16839816C2211yescharacteristic
50#16839816C2211yescharacteristic
51#16839815C2211yescharacteristic
52#16839812C2211yescharacteristic
53#16839812C2211yescharacteristic
54#16839812C2211yescharacteristic
55#16839812C2211yescharacteristic
56#16839488C2211yescharacteristic
57#16839488C2211yescharacteristic
58#16839487C2211yescharacteristic
59#16839487C2211yescharacteristic
60#16839487C2211yescharacteristic
61#16839487C2211yescharacteristic
62#16839486C2211yescharacteristic
63#16839486C2211yescharacteristic
64#16839485C2211yescharacteristic
65#16839485C2211yescharacteristic
66#16839485C2211yescharacteristic
67#16839485C2211yescharacteristic
68C2×#126×C61C2211yescharacteristic
69C61×#432C2211yescharacteristic
70C61×#431C2211yescharacteristic
71C61×#324C2211yescharacteristic
72C61×#324C2211yescharacteristic
73C61×#323C2211yescharacteristic
74C61×#323C2211yescharacteristic
75C22×Dic122C2×C411yescharacteristic
76C22×C22⋊D61C2×C411yescharacteristic
77C23×Dic61C2×C411yescharacteristic
78C22×C4×D61C2×C411yescharacteristic
79C22×C4×D61C2×C411yescharacteristic
80C22×C4×D61C2×C411yescharacteristic
81#14519770—21no—
82#14519770—21no—
83#14519770—21no—
84#14519770—21no—
85#14519768—21no—
86#14519768—21no—
87#14519768—21no—
88#14519768—21no—
89#14519767—21no—
90#14519767—21no—
91#14519767—21no—
92#14519767—21no—
93#14519767—21no—
94#14519767—21no—
95#14519767—21no—
96#14519767—21no—
97#14519759—21no—
98#14519759—21no—
99#14519759—21no—
100#14519759—21no—
101#14519759—21no—
102#14519759—21no—
103#14519759—21no—
104#14519759—21no—
105#14519755—21no—
106#14519755—21no—
107#14519755—21no—
108#14519755—21no—
109#14519754—21no—
110#14519754—21no—
111#14519754—21no—
112#14519754—21no—
113C4×Dic122D411yescharacteristic
114C4×Dic122D411yescharacteristic
115C4×Dic122D411yescharacteristic
116C4×Dic122D411yescharacteristic
117C4×Dic122D411yescharacteristic
118C4×Dic122D411yescharacteristic
119C4×Dic122D411yescharacteristic
120C4×Dic122D411yescharacteristic
121#14519737—21no—
122#14519737—21no—
123#14519737—21no—
124#14519737—21no—
125#14519735—21no—
126#14519735—21no—
127#14519735—21no—
128#14519735—21no—
129#14519734—21no—
130#14519734—21no—
131#14519734—21no—
132#14519734—21no—
133#14519733—21no—
134#14519733—21no—
135#14519733—21no—
136#14519733—21no—
137C2×C4⋊Dic61C2×C411yescharacteristic
138C2×C4⋊Dic61C2×C411yescharacteristic
139C2×C4⋊Dic61C2×C411yescharacteristic
140C2×C4⋊Dic61C2×C411yescharacteristic
141C2×#11758196C2×C411yescharacteristic
142C2×#11758196C2×C411yescharacteristic
143C2×#11758196C2×C411yescharacteristic
144C2×#11758196C2×C411yescharacteristic
145C2×#11758196C2×C411yescharacteristic
146C2×#11758196C2×C411yescharacteristic
147C2×#11758196C2×C411yescharacteristic
148C2×#11758196C2×C411yescharacteristic
149C2×#11758196C2311yescharacteristic
150C4⋊C4×D61—21no—
151C4⋊C4×D61—21no—
152C4⋊C4×D61—21no—
153C4⋊C4×D61—21no—
154C2×C22⋊Dic61C2×C411yescharacteristic
155C2×C22⋊Dic61C2×C411yescharacteristic
156C2×#11758198C2×C411yescharacteristic
157C2×#11758198C2×C411yescharacteristic
158C2×#11758198C2311yescharacteristic
159C2×C4×Dic61C2×C411yescharacteristic
160C2×C4×Dic61C2×C411yescharacteristic
161C2×C4×Dic61C2311yescharacteristic
162C2×C4×Dic61C2311yescharacteristic
163C4⋊#92418—21no—
164C4⋊#92418—21no—
165#14519706—21no—
166#14519706—21no—
167#14519706—21no—
168#14519706—21no—
169#14519706—21no—
170#14519706—21no—
171#14519706—21no—
172#14519706—21no—
173C22⋊#92418C2311yescharacteristic
174C22⋊#92418C2311yescharacteristic
175C22⋊#92418C2311yescharacteristic
176C22⋊#92418C2311yescharacteristic
177#14519688—21no—
178#14519687—21no—
179#14519687—21no—
180#14519687—21no—
181#14519687—21no—
182C4×#92418—21no—
183C8×Dic61—21no—
184C8×Dic61—21no—
185C8×Dic61—21no—
186C8×Dic61—21no—
187#126×C61—21no—
188#126×C61—21no—
189#126×C61—21no—
190#126×C61—21no—
191C2×C4⋊C4×C61C2×C411yescharacteristic
192C2×C4⋊C4×C61C2×C411yescharacteristic
193C2×C4⋊C4×C61C2311yescharacteristic
194C2×C22⋊C4×C61C2×C411yescharacteristic
195C2×C22⋊C4×C61C2×C411yescharacteristic
196C2×C22⋊C4×C61C2311yescharacteristic
197C2×C42×C61C2311yescharacteristic
198C4⋊C8×C61—21no—
199C4⋊C8×C61—21no—
200C22⋊C8×C61C2311yescharacteristic
201C22⋊C8×C61C2311yescharacteristic
202C22⋊C8×C61C2311yescharacteristic
203C22⋊C8×C61C2311yescharacteristic
204#97×C61—21no—
205C4×C8×C61—21no—
206C24×C61C22×C411yescharacteristic
207C23×D61C22×C411yescharacteristic
208C22×C4×C61C22×C411yescharacteristic
209C22×C4×C61C22×C411yescharacteristic
210C22×C4×C61C22×C411yescharacteristic
211C22×C4×C61C22×C411yescharacteristic
212C22×C4×C61C22×C411yescharacteristic
213C22×C4×C61C2411yescharacteristic
214C2×C22⋊D61—22no—
215C2×C22⋊D61—21no—
216C2×C22⋊D61—21no—
217C2×C22⋊D61—41no—
218C22×Dic61—21no—
219C22×Dic61—21no—
220C22×Dic61—42no—
221C22×Dic61C22×C411yescharacteristic
222C22×Dic61C22×C411yescharacteristic
223C22×Dic61C22×C411yescharacteristic
224C22×Dic61C22×C411yescharacteristic
225C22×Dic61C22×C411yescharacteristic
226C22×Dic61C22×C411yescharacteristic
227C22×Dic61C22×C411yescharacteristic
228C2×C4×D61—22no—
229C2×C4×D61—22no—
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×C4×D61—21no—
235C2×C4×D61—21no—
236C2×C4×D61—41no—
237C2×C4×D61—41no—
238C2×C4×D61—42no—
239C2×Dic122—42no—
240C2×Dic122C22⋊C411yescharacteristic
241C2×Dic122C22⋊C411yescharacteristic
242C2×Dic122C22⋊C411yescharacteristic
243C2×Dic122C22⋊C411yescharacteristic
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C22⋊C4×C61—21no—
255C22⋊C4×C61—21no—
256C22⋊C4×C61—21no—
257C22⋊C4×C61—21no—
258C22⋊C4×C61—21no—
259C22⋊C4×C61—21no—
260C42×C61C2×D411yescharacteristic
261C42×C61C2×D411yescharacteristic
262C42×C61C2×D411yescharacteristic
263C42×C61C2×D411yescharacteristic
264C22⋊Dic61—21no—
265C22⋊Dic61—21no—
266C22⋊Dic61—21no—
267C22⋊Dic61—21no—
268#11758198—21no—
269#11758198—21no—
270#11758198—21no—
271#11758198—21no—
272#11758198—21no—
273#11758198—21no—
274C4⋊Dic61—21no—
275C4⋊Dic61—21no—
276C4⋊Dic61—21no—
277C4⋊Dic61—21no—
278C4⋊Dic61—21no—
279C4⋊Dic61—21no—
280C4⋊Dic61C22⋊C411yescharacteristic
281C4⋊Dic61C22⋊C411yescharacteristic
282C4⋊Dic61C22⋊C411yescharacteristic
283C4⋊Dic61C22⋊C411yescharacteristic
284#11758196—21no—
285#11758196—21no—
286#11758196—21no—
287#11758196—21no—
288#11758196—21no—
289#11758196—21no—
290#11758196—21no—
291#11758196—21no—
292#11758196—21no—
293#11758196—21no—
294#11758196—21no—
295#11758196—21no—
296#11758196—21no—
297#11758196—21no—
298#11758196C22⋊C411yescharacteristic
299#11758196C22⋊C411yescharacteristic
300#11758196C22⋊C411yescharacteristic
301#11758196C22⋊C411yescharacteristic
302#11758196C22⋊C411yescharacteristic
303#11758196C22⋊C411yescharacteristic
304#11758196C22⋊C411yescharacteristic
305#11758196C22⋊C411yescharacteristic
306C4×Dic61—21no—
307C4×Dic61—21no—
308C4×Dic61—21no—
309C4×Dic61—21no—
310C4×Dic61C2×D411yescharacteristic
311C4×Dic61C2×D411yescharacteristic
312C4×Dic61C2×D411yescharacteristic
313C4×Dic61C2×D411yescharacteristic
314C4×Dic61C2×D411yescharacteristic
315C4×Dic61C2×D411yescharacteristic
316C4×Dic61C2×D411yescharacteristic
317C4×Dic61C2×D411yescharacteristic
318C2×#92418—21no—
319C2×#92418—21no—
320C2×#92418—21no—
321C2×#92418—21no—
322C23×C61—21no—
323C23×C61—21no—
324C23×C61—21no—
325C23×C61—41no—
326C23×C61—41no—
327C23×C61C23×C411yescharacteristic
328C22×D61—21no—
329C22×D61—21no—
330C22×D61—41no—
331C22×D61—41no—
332C22×D61#13112yes—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61C2×C22⋊C411yescharacteristic
345C2×C4×C61C2×C22⋊C411yescharacteristic
346C2×C4×C61C2×C22⋊C411yescharacteristic
347C2×C4×C61C2×C22⋊C411yescharacteristic
348C2×C4×C61C22×D411yescharacteristic
349C2×C4×C61C22×D411yescharacteristic
350C22⋊D61—42no—
351C22⋊D61—42no—
352C2×Dic61—21no—
353C2×Dic61—21no—
354C2×Dic61—21no—
355C2×Dic61—21no—
356C2×Dic61—22no—
357C2×Dic61—21no—
358C2×Dic61—21no—
359C2×Dic61—21no—
360C2×Dic61—21no—
361C2×Dic61—21no—
362C2×Dic61—41no—
363C2×Dic61—42no—
364C2×Dic61—42no—
365C2×Dic61—41no—
366C2×Dic61—41no—
367C2×Dic61C2×C22⋊C411yescharacteristic
368C2×Dic61C2×C22⋊C411yescharacteristic
369C2×Dic61C2×C22⋊C411yescharacteristic
370C2×Dic61C2×C22⋊C411yescharacteristic
371C2×Dic61C2×C22⋊C411yescharacteristic
372C2×Dic61C2×C22⋊C411yescharacteristic
373C2×Dic61C2×C22⋊C411yescharacteristic
374C2×Dic61C2×C22⋊C411yescharacteristic
375C4×D61—42no—
376C4×D61—42no—
377C4×D61—42no—
378C4×D61—42no—
379C4×D61—42no—
380C4×D61—42no—
381Dic122—22no—
382Dic122—22no—
383Dic122—41no—
384Dic122—41no—
385C8×C61—41no—
386C8×C61—41no—
387C8×C61—41no—
388C8×C61—41no—
389#92418—41no—
390#92418—41no—
391#92418—41no—
392#92418—41no—
393#17423—611nomaximal, Sylow
394C22×C61—21no—
395C22×C61—21no—
396C22×C61—41no—
397C22×C61—41no—
398C22×C61—41no—
399C22×C61—81no—
400C22×C61—81no—
401C22×C61C22×C22⋊C411yescharacteristic
402C22×C61C2×#13111yescharacteristic
403C22×C61#56811yescharacteristic
404C2×D61—22no—
405C2×D61—42no—
406C2×D61—41no—
407C2×D61—41no—
408C2×D61—42no—
409C4×C61—21no—
410C4×C61—21no—
411C4×C61—21no—
412C4×C61—21no—
413C4×C61—21no—
414C4×C61—21no—
415C4×C61—41no—
416C4×C61—41no—
417C4×C61—41no—
418Dic61—21no—
419Dic61—21no—
420Dic61—21no—
421Dic61—21no—
422Dic61—21no—
423Dic61—21no—
424Dic61—21no—
425Dic61—41no—
426Dic61—41no—
427Dic61—41no—
428Dic61#41312yes—
429C2×#552—611no—
430#2984—611no—
431#2984—611no—
432#1473—611no—
433#1473—611no—
434#1473—611no—
435#1473D6111yescharacteristic, complemented
436#1470—611no—
437#1470—611no—
438#1466—611no—
439#1464—611no—
440#1464—611no—
441#1460—611no—
442#1458—611no—
443#1458—611no—
444C2×C61—21no—
445C2×C61—21no—
446C2×C61—81no—
447C2×C61#288011yescharacteristic
448C2×C61#288411yescharacteristic
449C2×C61C2×#41311yescharacteristic
450D61—42no—
451#552—1221no—
452#552—1221no—
453#552—1221no—
454#552—1221no—
455#552—1221no—
456#552—1221no—
457#552—1221no—
458#552—1221no—
459C2×#126—611no—
460C2×#126C2×D6111yescharacteristic
461C2×#125—611no—
462C2×#125—611no—
463C2×#125—611no—
464C2×#123—611no—
465C2×#123—611no—
466C2×C22⋊Q8—611no—
467C2×C22⋊Q8—611no—
468C2×C4×Q8—611no—
469C2×C4×D4—611no—
470C2×#117—611no—
471C2×#117—611no—
472C2×#117—611no—
473C22×C4⋊C4—611no—
474#446—1221no—
475#446—1221no—
476#446—1221no—
477#446—1221no—
478#446—1221no—
479#446—1221no—
480C8×Q8—1221no—
481C8×Q8—1221no—
482#432—611no—
483#432—611no—
484#432—611no—
485#432—611no—
486#432—611no—
487#432C2×D6111yescharacteristic
488#431—611no—
489#431—611no—
490#431—611no—
491#431—611no—
492#431—611no—
493#431C2×D6111yescharacteristic
494#324—611no—
495#324—611no—
496#324—611no—
497#324—611no—
498#324—611no—
499#324—611no—
500#324C2×D6111yescharacteristic
501#324C2×D6111yescharacteristic
502#323—611no—
503#323—611no—
504#323—611no—
505#323—611no—
506#323—611no—
507#323—611no—
508#323C2×D6111yescharacteristic
509#323C2×D6111yescharacteristic
510C61#1742311yescharacteristic, complemented, Sylow
511C22×Q8—611no—
512C22×D4—611no—
513C23×C4—611no—
514C23×C4—611no—
515C23×C4—611no—
516C23×C4—611no—
517#126—21no—
518#126—21no—
519#126—21no—
520#126—21no—
521#126—1221no—
522#126—1221no—
523#126—1221no—
524#126—1221no—
525#125—1221no—
526#125—1221no—
527#125—1221no—
528#125—1221no—
529#125—1221no—
530#125—1221no—
531#125—1221no—
532#125—1221no—
533#125—1221no—
534#125—1221no—
535#125—1221no—
536#125—1221no—
537#123—1221no—
538#123—1221no—
539#123—1221no—
540#123—1221no—
541#123—1221no—
542#123—1221no—
543#123—1221no—
544#123—1221no—
545C22⋊Q8—1221no—
546C22⋊Q8—1221no—
547C22⋊Q8—1221no—
548C22⋊Q8—1221no—
549C22⋊Q8—1221no—
550C22⋊Q8—1221no—
551C22⋊Q8—1221no—
552C22⋊Q8—1221no—
553C4×Q8—611no—
554C4×Q8—611no—
555C4×Q8—611no—
556C4×Q8—611no—
557C4×Q8—611no—
558C4×Q8—611no—
559C4×Q8—611no—
560C4×Q8—611no—
561C4×D4—1221no—
562C4×D4—1221no—
563C4×D4—1221no—
564C4×D4—1221no—
565#117—1221no—
566#117—1221no—
567#117—1221no—
568#117—1221no—
569#117—1221no—
570#117—1221no—
571#117—1221no—
572#117—1221no—
573#117—1221no—
574#117—1221no—
575#117—1221no—
576#117—1221no—
577C2×C4⋊C4—611no—
578C2×C4⋊C4—611no—
579C2×C4⋊C4—611no—
580C2×C4⋊C4—611no—
581C2×C4⋊C4—611no—
582C2×C4⋊C4—611no—
583C2×C4⋊C4—611no—
584C2×C4⋊C4—611no—
585C2×C4⋊C4—611no—
586C2×C4⋊C4—611no—
587C2×C4⋊C4—611no—
588C2×C4⋊C4—611no—
589C2×C4⋊C4—611no—
590C2×C4⋊C4—1221no—
591C2×C4⋊C4—1221no—
592C2×C4⋊C4—1221no—
593C2×C4⋊C4—1221no—
594C2×C4⋊C4C4×D6111yescharacteristic
595C2×C4⋊C4C4×D6111yescharacteristic
596C2×C4⋊C4C22×D6111yescharacteristic
597C2×C22⋊C4—611no—
598C2×C22⋊C4—611no—
599C2×C22⋊C4—611no—
600C2×C22⋊C4—611no—
601C2×C22⋊C4—611no—
602C2×C22⋊C4C4×D6111yescharacteristic
603C2×C22⋊C4C4×D6111yescharacteristic
604C2×C22⋊C4C22×D6111yescharacteristic
605C2×C42—611no—
606C2×C42—611no—
607C2×C42—611no—
608C2×C42—611no—
609C2×C42C22×D6111yescharacteristic
610C4⋊C8—21no—
611C4⋊C8—21no—
612C4⋊C8—1221no—
613C4⋊C8—1221no—
614C4⋊C8—1221no—
615C4⋊C8—1221no—
616C4⋊C8—1221no—
617C4⋊C8—1221no—
618C4⋊C8—1221no—
619C4⋊C8—1221no—
620C4⋊C8—1221no—
621C4⋊C8—1221no—
622C22⋊C8—611no—
623C22⋊C8—611no—
624C22⋊C8—611no—
625C22⋊C8—611no—
626C22⋊C8C22×D6111yescharacteristic
627C22⋊C8C22×D6111yescharacteristic
628C22⋊C8C22×D6111yescharacteristic
629C22⋊C8C22×D6111yescharacteristic
630#97—21no—
631#97—1221no—
632#97—1221no—
633#97—1221no—
634#97—1221no—
635#97—1221no—
636C4×C8—21no—
637C4×C8—1221no—
638C4×C8—1221no—
639C4×C8—1221no—
640C4×C8—1221no—
641C4×C8—1221no—
642C24—611no—
643C24C2×C4×D6111yescharacteristic
644C2×Q8—611no—
645C2×Q8—611no—
646C2×Q8—611no—
647C2×Q8—611no—
648C2×Q8—2442no—
649C2×D4—1221no—
650C2×D4—1221no—
651C2×D4—1222no—
652C2×D4—2441no—
653C22×C4—611no—
654C22×C4—611no—
655C22×C4—611no—
656C22×C4—611no—
657C22×C4—611no—
658C22×C4—611no—
659C22×C4—611no—
660C22×C4—1221no—
661C22×C4—1221no—
662C22×C4—1221no—
663C22×C4—1221no—
664C22×C4—1222no—
665C22×C4—1222no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—2441no—
671C22×C4—2441no—
672C22×C4—2442no—
673C22×C4—2442no—
674C22×C4C2×C4×D6111yescharacteristic
675C22×C4C2×C4×D6111yescharacteristic
676C22×C4C2×C4×D6111yescharacteristic
677C22×C4C2×C4×D6111yescharacteristic
678C22×C4C2×C4×D6111yescharacteristic
679C22×C4C23×D6111yescharacteristic
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—1221no—
685C2×C8—1221no—
686C2×C8—1221no—
687C2×C8—1221no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—611no—
695C4⋊C4—611no—
696C4⋊C4—611no—
697C4⋊C4—611no—
698C4⋊C4—611no—
699C4⋊C4—611no—
700C4⋊C4—611no—
701C4⋊C4—611no—
702C4⋊C4—611no—
703C4⋊C4—611no—
704C4⋊C4—611no—
705C4⋊C4—611no—
706C4⋊C4—1221no—
707C4⋊C4—1221no—
708C4⋊C4—1221no—
709C4⋊C4—1221no—
710C4⋊C4—1221no—
711C4⋊C4—1221no—
712C4⋊C4—1221no—
713C4⋊C4—1221no—
714C4⋊C4—1221no—
715C4⋊C4—1221no—
716C4⋊C4—1221no—
717C4⋊C4—1221no—
718C4⋊C4—1221no—
719C4⋊C4—1221no—
720C4⋊C4—1221no—
721C4⋊C4—1221no—
722C4⋊C4—1221no—
723C4⋊C4—1221no—
724C4⋊C4—1221no—
725C4⋊C4—1221no—
726C22⋊C4—21no—
727C22⋊C4—21no—
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—21no—
732C22⋊C4—1221no—
733C22⋊C4—1221no—
734C22⋊C4—1221no—
735C22⋊C4—1221no—
736C22⋊C4—1221no—
737C22⋊C4—1221no—
738C22⋊C4—1221no—
739C22⋊C4—1221no—
740C22⋊C4—1221no—
741C22⋊C4—1221no—
742C42—611no—
743C42—611no—
744C42—611no—
745C42—611no—
746C42—611no—
747C42—611no—
748C42—611no—
749C42—611no—
750C42—1221no—
751C42—1221no—
752C42—1221no—
753C42—1221no—
754C42D4×D6111yescharacteristic
755C42D4×D6111yescharacteristic
756C42D4×D6111yescharacteristic
757C42D4×D6111yescharacteristic
758C23—21no—
759C23—21no—
760C23—21no—
761C23—41no—
762C23—41no—
763C23—612no—
764C23—1221no—
765C23—1221no—
766C23—2441no—
767C23—2441no—
768C23C22×C4×D6111yescharacteristic
769Q8—1222no—
770Q8—1222no—
771Q8—2441no—
772Q8—2441no—
773D4—2442no—
774D4—2442no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—611no—
787C2×C4—611no—
788C2×C4—611no—
789C2×C4—611no—
790C2×C4—611no—
791C2×C4—611no—
792C2×C4—611no—
793C2×C4—611no—
794C2×C4—1222no—
795C2×C4—1221no—
796C2×C4—1221no—
797C2×C4—1221no—
798C2×C4—1221no—
799C2×C4—1221no—
800C2×C4—1221no—
801C2×C4—1221no—
802C2×C4—1221no—
803C2×C4—1221no—
804C2×C4—2442no—
805C2×C4—2442no—
806C2×C4—2442no—
807C2×C4—2442no—
808C2×C4—2442no—
809C2×C4—2442no—
810C2×C4—2442no—
811C2×C4—2441no—
812C2×C4—2442no—
813C2×C4—2441no—
814C2×C4—2441no—
815C2×C4C22⋊C4×D6111yescharacteristic
816C2×C4C22⋊C4×D6111yescharacteristic
817C2×C4C22⋊C4×D6111yescharacteristic
818C2×C4C22⋊C4×D6111yescharacteristic
819C2×C4C2×D4×D6111yescharacteristic
820C2×C4C2×D4×D6111yescharacteristic
821C8—41no—
822C8—41no—
823C8—41no—
824C8—41no—
825C8—2441no—
826C8—2441no—
827C8—2441no—
828C8—2441no—
829C22—21no—
830C22—21no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—81no—
835C22—81no—
836C22—1222no—
837C22—2442no—
838C22—2442no—
839C22—2441no—
840C22—2441no—
841C22C2×C22⋊C4×D6111yescharacteristic
842C22#131×D6111yescharacteristic
843C22#1684052711yescharacteristic
844C4—21no—
845C4—21no—
846C4—21no—
847C4—21no—
848C4—21no—
849C4—21no—
850C4—41no—
851C4—41no—
852C4—41no—
853C4—612no—
854C4—1221no—
855C4—1221no—
856C4—1221no—
857C4—1221no—
858C4—1221no—
859C4—1221no—
860C4—1221no—
861C4—2441no—
862C4—2441no—
863C4—2441no—
864C2—21no—
865C2—21no—
866C2—81no—
867C2—2442no—
868C2#2145426711yescharacteristic
869C2#2145428111yescharacteristic
870C2#413×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1473C2
socleC22×C61C22×C22⋊C4
prime radicalC22×C22⋊D61C2×C4
cosocleC22×C4×C61C24
hypercenter#1473D61
hypocenterC61#17423
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1473

Complements

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

NH ≅ G/Ntype
2. #21454909C2semidirect
3. #21454906C2semidirect
4. #21444188C2semidirect
5. #21444185C2semidirect
6. #21444185C2semidirect
7. #21444173C2semidirect
8. #21444173C2semidirect
10. #21444152C2semidirect
11. #21444151C2semidirect
13. #21444132C2semidirect
14. #21444131C2semidirect
15. C61×#1473C2semidirect
435. #1473D61semidirect
510. C61#17423semidirect

Maximal subgroups

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

subgroupindex
C2×#168404482
#214549092
#214549062
#214441882
#214441852
#214441732
#214441582
#214441522
#214441512
#214441382
#214441322
#214441312
C61×#14732
#1742361