Finite Group Databasebeta

← #29646246

Subgroups — #29646246

Order 15616.

944 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840449C211yesmaximal, characteristic
2#21454479C211yesmaximal, characteristic, complemented
3#21454473C211yesmaximal, characteristic, complemented
4#21444185C211yesmaximal, characteristic, complemented
5#21444185C211yesmaximal, characteristic, complemented
6#21444173C211yesmaximal, characteristic, complemented
7#21444173C211yesmaximal, characteristic, complemented
8#21444167C211yesmaximal, characteristic
9#21444161C211yesmaximal, characteristic, complemented
10#21444150C211yesmaximal, characteristic, complemented
11#21444148C211yesmaximal, characteristic, complemented
12#21444141C211yesmaximal, characteristic, complemented
13#21444130C211yesmaximal, characteristic, complemented
14C2×#16839487C211yesmaximal, characteristic, complemented
15C61×#1468C211yesmaximal, characteristic
16#16840449—21no—
17#16840449—21no—
18#16840449—21no—
19#16840449—21no—
20#16840449—21no—
21#16840449—21no—
22#16840449—21no—
23#16840449—21no—
24C2×#14519770C411yescharacteristic
25C2×#14519770C2211yescharacteristic
26C2×#14519768C411yescharacteristic
27C2×#14519767C411yescharacteristic
28C2×#14519767C2211yescharacteristic
29C2×#14519758C411yescharacteristic
30C2×#14519754C411yescharacteristic
31C2×#14519754C411yescharacteristic
32C2×#14519742C2211yescharacteristic
33C2×D4×Dic61C411yescharacteristic
34C2×#14519736C2211yescharacteristic
35C2×#14519733C411yescharacteristic
36C2×#14519733C2211yescharacteristic
37C22×#11758196C2211yescharacteristic
38#16839820—21no—
39#16839820—21no—
40#16839820—21no—
41#16839820—21no—
42#16839816C2211yescharacteristic
43#16839816C2211yescharacteristic
44#16839816C2211yescharacteristic
45#16839816C2211yescharacteristic
46#16839812C2211yescharacteristic
47#16839812C2211yescharacteristic
48#16839812C2211yescharacteristic
49#16839812C2211yescharacteristic
50#16839790—21no—
51#16839788—21no—
52#16839726C2211yescharacteristic
53C2×C22⋊#92418C2211yescharacteristic
54#16839720—21no—
55#16839717—21no—
56#16839488C2211yescharacteristic
57#16839488C2211yescharacteristic
58#16839487C2211yescharacteristic
59#16839487C2211yescharacteristic
60#16839487C2211yescharacteristic
61#16839487C2211yescharacteristic
62#16839487C2211yescharacteristic
63#16839487C2211yescharacteristic
64#16839487C2211yescharacteristic
65#16839487C2211yescharacteristic
66#16839486C2211yescharacteristic
67#16839486C2211yescharacteristic
68C2×#123×C61C2211yescharacteristic
69C61×#407C2211yescharacteristic
70C2×C22⋊C8×C61C2211yescharacteristic
71C61×#324C2211yescharacteristic
72C61×#324C2211yescharacteristic
73C61×#323C2211yescharacteristic
74C61×#323C2211yescharacteristic
75C22×Dic122C2×C411yescharacteristic
76C23×Dic61C2×C411yescharacteristic
77C23×Dic61C2×C411yescharacteristic
78C23×Dic61C2×C411yescharacteristic
79C2×#11758194—21no—
80C22×#92418—21no—
81#14519770—21no—
82#14519770—21no—
83#14519770—21no—
84#14519770—21no—
85#14519770—21no—
86#14519770—21no—
87#14519770—21no—
88#14519770—21no—
89#14519768—21no—
90#14519768—21no—
91#14519768—21no—
92#14519768—21no—
93#14519767—21no—
94#14519767—21no—
95#14519767—21no—
96#14519767—21no—
97#14519767—21no—
98#14519767—21no—
99#14519767—21no—
100#14519767—21no—
101#14519758—21no—
102#14519758—21no—
103#14519758—21no—
104#14519758—21no—
105#14519754—21no—
106#14519754—21no—
107#14519754—21no—
108#14519754—21no—
109#14519754—21no—
110#14519754—21no—
111#14519754—21no—
112#14519754—21no—
113#14519742—21no—
114#14519742—21no—
115#14519742—21no—
116#14519742—21no—
117D4×Dic61—21no—
118D4×Dic61—21no—
119D4×Dic61—21no—
120D4×Dic61—21no—
121#14519736D411yescharacteristic
122#14519736D411yescharacteristic
123#14519736D411yescharacteristic
124#14519736D411yescharacteristic
125#14519736D411yescharacteristic
126#14519736D411yescharacteristic
127#14519736D411yescharacteristic
128#14519736D411yescharacteristic
129#14519733—21no—
130#14519733—21no—
131#14519733—21no—
132#14519733—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×#11758196—21no—
142C2×#11758196—21no—
143C2×#11758196—21no—
144C2×#11758196—21no—
145C2×#11758196C2×C411yescharacteristic
146C2×#11758196C2×C411yescharacteristic
147C2×#11758196C2×C411yescharacteristic
148C2×#11758196C2×C411yescharacteristic
149C2×#11758196C2×C411yescharacteristic
150C2×#11758196C2×C411yescharacteristic
151C2×#11758196C2×C411yescharacteristic
152C2×#11758196C2×C411yescharacteristic
153C2×#11758196C2311yescharacteristic
154C2×#11758196C2311yescharacteristic
155C2×C22⋊Dic61C2×C411yescharacteristic
156C2×C22⋊Dic61C2×C411yescharacteristic
157C2×C22⋊Dic61C2×C411yescharacteristic
158C2×C22⋊Dic61C2×C411yescharacteristic
159C2×C22⋊Dic61C2×C411yescharacteristic
160C2×C4×Dic61C2×C411yescharacteristic
161C2×C4×Dic61C2×C411yescharacteristic
162C2×C4×Dic61C2×C411yescharacteristic
163C2×C4×Dic61C2311yescharacteristic
164C2×C4×Dic61C2311yescharacteristic
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⋊#92418—21no—
174C22⋊#92418—21no—
175C22⋊#92418C2311yescharacteristic
176C22⋊#92418C2311yescharacteristic
177C22⋊#92418C2311yescharacteristic
178C22⋊#92418C2311yescharacteristic
179#14519687—21no—
180#14519687—21no—
181#14519687—21no—
182#14519687—21no—
183C8×Dic61—21no—
184C8×Dic61—21no—
185C8×Dic61—21no—
186C8×Dic61—21no—
187C22×D4×C61C2×C411yescharacteristic
188C23×C4×C61C2311yescharacteristic
189C2×M16×C61—21no—
190C22×C8×C61—21no—
191#123×C61—21no—
192#123×C61—21no—
193#123×C61—21no—
194#123×C61—21no—
195C2×C4⋊C4×C61C2×C411yescharacteristic
196C2×C4⋊C4×C61C2311yescharacteristic
197C2×C22⋊C4×C61C2×C411yescharacteristic
198C2×C22⋊C4×C61C2×C411yescharacteristic
199C2×C22⋊C4×C61C2311yescharacteristic
200C22⋊C8×C61—21no—
201C22⋊C8×C61—21no—
202C22⋊C8×C61C2311yescharacteristic
203C22⋊C8×C61C2311yescharacteristic
204C22⋊C8×C61C2311yescharacteristic
205C22⋊C8×C61C2311yescharacteristic
206C24×C61C22×C411yescharacteristic
207C24×C61C22×C411yescharacteristic
208C2×D4×C61—21no—
209C2×D4×C61—21no—
210C2×D4×C61—42no—
211C22×C4×C61—42no—
212C22×C4×C61C22×C411yescharacteristic
213C22×C4×C61C22×C411yescharacteristic
214C22×C4×C61C22×C411yescharacteristic
215C22×C4×C61C22×C411yescharacteristic
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2×D411yescharacteristic
219C22×C4×C61C2×D411yescharacteristic
220C22×C4×C61C2411yescharacteristic
221C22×Dic61—21no—
222C22×Dic61—21no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61—21no—
226C22×Dic61—21no—
227C22×Dic61—22no—
228C22×Dic61—22no—
229C22×Dic61—41no—
230C22×Dic61—41no—
231C22×Dic61—42no—
232C22×Dic61C22×C411yescharacteristic
233C22×Dic61C22×C411yescharacteristic
234C22×Dic61C22×C411yescharacteristic
235C22×Dic61C22×C411yescharacteristic
236C22×Dic61C22×C411yescharacteristic
237C22×Dic61C22×C411yescharacteristic
238C22×Dic61C22×C411yescharacteristic
239C22×Dic61C22×C411yescharacteristic
240C2×Dic122—21no—
241C2×Dic122—21no—
242C2×Dic122—22no—
243C2×Dic122—41no—
244M16×C61—42no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C2×C8×C61—42no—
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—
260C22⋊Dic61—21no—
261C22⋊Dic61—21no—
262C22⋊Dic61—21no—
263C22⋊Dic61—21no—
264C22⋊Dic61—21no—
265C22⋊Dic61—21no—
266C22⋊Dic61C22⋊C411yescharacteristic
267C22⋊Dic61C22⋊C411yescharacteristic
268C22⋊Dic61C22⋊C411yescharacteristic
269C22⋊Dic61C22⋊C411yescharacteristic
270C22⋊Dic61C22⋊C411yescharacteristic
271C22⋊Dic61C22⋊C411yescharacteristic
272C22⋊Dic61C22⋊C411yescharacteristic
273C22⋊Dic61C22⋊C411yescharacteristic
274C4⋊Dic61—21no—
275C4⋊Dic61—21no—
276C4⋊Dic61—21no—
277C4⋊Dic61—21no—
278C4⋊Dic61C22⋊C411yescharacteristic
279C4⋊Dic61C22⋊C411yescharacteristic
280C4⋊Dic61C22⋊C411yescharacteristic
281C4⋊Dic61C22⋊C411yescharacteristic
282C4⋊Dic61C22⋊C411yescharacteristic
283C4⋊Dic61C22⋊C411yescharacteristic
284C4⋊Dic61C22⋊C411yescharacteristic
285C4⋊Dic61C22⋊C411yescharacteristic
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#11758196—21no—
299#11758196—21no—
300#11758196—21no—
301#11758196—21no—
302#11758196—21no—
303#11758196—21no—
304#11758196—21no—
305#11758196—21no—
306C4×Dic61—21no—
307C4×Dic61—21no—
308C4×Dic61—21no—
309C4×Dic61—21no—
310C4×Dic61—21no—
311C4×Dic61—21no—
312C4×Dic61C2×D411yescharacteristic
313C4×Dic61C2×D411yescharacteristic
314C4×Dic61C2×D411yescharacteristic
315C4×Dic61C2×D411yescharacteristic
316C4×Dic61C2×D411yescharacteristic
317C4×Dic61C2×D411yescharacteristic
318C4×Dic61C2×D411yescharacteristic
319C4×Dic61C2×D411yescharacteristic
320#11758194—42no—
321C2×#92418—21no—
322C2×#92418—21no—
323C2×#92418—21no—
324C2×#92418—21no—
325C2×#92418—42no—
326C23×C61—21no—
327C23×C61—21no—
328C23×C61—22no—
329C23×C61—21no—
330C23×C61—21no—
331C23×C61—21no—
332C23×C61—41no—
333C23×C61—41no—
334C23×C61—41no—
335C23×C61C2×C22⋊C411yescharacteristic
336C23×C61C2×C22⋊C411yescharacteristic
337C23×C61C23×C411yescharacteristic
338D4×C61—42no—
339D4×C61—42no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—21no—
345C2×C4×C61—21no—
346C2×C4×C61—21no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61—41no—
352C2×C4×C61—41no—
353C2×C4×C61C2×C22⋊C411yescharacteristic
354C2×C4×C61C2×C22⋊C411yescharacteristic
355C2×C4×C61C22×D411yescharacteristic
356C2×C4×C61C22×D411yescharacteristic
357C2×Dic61—21no—
358C2×Dic61—21no—
359C2×Dic61—21no—
360C2×Dic61—21no—
361C2×Dic61—21no—
362C2×Dic61—21no—
363C2×Dic61—21no—
364C2×Dic61—21no—
365C2×Dic61—21no—
366C2×Dic61—21no—
367C2×Dic61—21no—
368C2×Dic61—41no—
369C2×Dic61—41no—
370C2×Dic61—42no—
371C2×Dic61—42no—
372C2×Dic61—42no—
373C2×Dic61—42no—
374C2×Dic61—42no—
375C2×Dic61—42no—
376C2×Dic61—41no—
377C2×Dic61—41no—
378C2×Dic61C2×C22⋊C411yescharacteristic
379C2×Dic61C2×C22⋊C411yescharacteristic
380C2×Dic61C2×C22⋊C411yescharacteristic
381C2×Dic61C2×C22⋊C411yescharacteristic
382C2×Dic61C2×C22⋊C411yescharacteristic
383C2×Dic61C2×C22⋊C411yescharacteristic
384C2×Dic61C2×C22⋊C411yescharacteristic
385C2×Dic61C2×C22⋊C411yescharacteristic
386C2×Dic61#13112yes—
387Dic122—42no—
388Dic122—42no—
389C8×C61—41no—
390C8×C61—41no—
391C8×C61—41no—
392C8×C61—41no—
393#92418—41no—
394#92418—41no—
395#92418—41no—
396#92418—41no—
397#17417—611nomaximal, Sylow
398C22×C61—21no—
399C22×C61—21no—
400C22×C61—21no—
401C22×C61—21no—
402C22×C61—21no—
403C22×C61—21no—
404C22×C61—21no—
405C22×C61—42no—
406C22×C61—42no—
407C22×C61—41no—
408C22×C61—41no—
409C22×C61—41no—
410C22×C61—81no—
411C22×C61—81no—
412C22×C61#41012yes—
413C22×C61C22×C22⋊C411yescharacteristic
414C22×C61C2×#13111yescharacteristic
415C22×C61#56811yescharacteristic
416C4×C61—21no—
417C4×C61—21no—
418C4×C61—21no—
419C4×C61—21no—
420C4×C61—41no—
421C4×C61—41no—
422C4×C61—41no—
423Dic61—22no—
424Dic61—21no—
425Dic61—21no—
426Dic61—21no—
427Dic61—21no—
428Dic61—21no—
429Dic61—21no—
430Dic61—21no—
431Dic61—21no—
432Dic61—41no—
433Dic61—41no—
434Dic61—41no—
435C2×#552—611no—
436#2924—611no—
437#2924—611no—
438#1473—611no—
439#1473—611no—
440#1470—611no—
441#1470—611no—
442#1468—611no—
443#1468D6111yescharacteristic
444#1467—611no—
445#1464—611no—
446#1463—611no—
447#1461—611no—
448#1458—611no—
449C2×#324—611no—
450C2×C61—21no—
451C2×C61—21no—
452C2×C61—22no—
453C2×C61—41no—
454C2×C61—81no—
455C2×C61#288011yescharacteristic
456C2×C61C2×#41011yescharacteristic
457C2×C61#288911yescharacteristic
458#552—1221no—
459#552—1221no—
460#552—1221no—
461#552—1221no—
462#552—1221no—
463#552—1221no—
464#552—1221no—
465#552—1221no—
466C2×#126—611no—
467C2×#126—611no—
468C2×#125—611no—
469C2×#125—611no—
470C2×#125—611no—
471C2×#123—611no—
472C2×#123C2×D6111yescharacteristic
473C2×C22⋊Q8—611no—
474C2×C22⋊Q8—611no—
475C2×C4×Q8—611no—
476C2×C4×D4—611no—
477C2×#117—611no—
478C2×#117—611no—
479C2×#117—611no—
480C22×C4⋊C4—611no—
481#433—1221no—
482#433—1221no—
483#433—1221no—
484#433—1221no—
485#432—611no—
486#432—611no—
487#432—611no—
488#432—611no—
489#431—611no—
490#431—611no—
491#431—611no—
492#431—611no—
493#424—1221no—
494#424—1221no—
495#407—611no—
496#407C2×D6111yescharacteristic
497C2×C22⋊C8—611no—
498C2×C22⋊C8C2×D6111yescharacteristic
499#405—1221no—
500#405—1221no—
501#324—611no—
502#324—611no—
503#324—611no—
504#324—611no—
505#324—611no—
506#324—611no—
507#324—611no—
508#324—611no—
509#324—611no—
510#324—611no—
511#324C2×D6111yescharacteristic
512#324C2×D6111yescharacteristic
513#323—611no—
514#323—611no—
515#323C2×D6111yescharacteristic
516#323C2×D6111yescharacteristic
517C61#1741711yescharacteristic, complemented, Sylow
518C22×Q8—611no—
519C22×D4C4×D6111yescharacteristic
520C23×C4—611no—
521C23×C4—611no—
522C23×C4—611no—
523C23×C4C22×D6111yescharacteristic
524C2×M16—21no—
525C2×M16—1221no—
526C22×C8—21no—
527C22×C8—1221no—
528#126—1221no—
529#126—1221no—
530#126—1221no—
531#126—1221no—
532#126—1221no—
533#126—1221no—
534#126—1221no—
535#126—1221no—
536#125—1221no—
537#125—1221no—
538#125—1221no—
539#125—1221no—
540#125—1221no—
541#125—1221no—
542#125—1221no—
543#125—1221no—
544#125—1221no—
545#125—1221no—
546#125—1221no—
547#125—1221no—
548#123—21no—
549#123—21no—
550#123—21no—
551#123—21no—
552#123—1221no—
553#123—1221no—
554#123—1221no—
555#123—1221no—
556C22⋊Q8—1221no—
557C22⋊Q8—1221no—
558C22⋊Q8—1221no—
559C22⋊Q8—1221no—
560C22⋊Q8—1221no—
561C22⋊Q8—1221no—
562C22⋊Q8—1221no—
563C22⋊Q8—1221no—
564C4×Q8—1221no—
565C4×Q8—1221no—
566C4×Q8—1221no—
567C4×Q8—1221no—
568C4×D4—1221no—
569C4×D4—1221no—
570C4×D4—1221no—
571C4×D4—1221no—
572#117—611no—
573#117—611no—
574#117—611no—
575#117—611no—
576#117—611no—
577#117—611no—
578#117—611no—
579#117—611no—
580#117—1221no—
581#117—1221no—
582#117—1221no—
583#117—1221no—
584#117—1221no—
585#117—1221no—
586#117—1221no—
587#117—1221no—
588C2×C4⋊C4—611no—
589C2×C4⋊C4—611no—
590C2×C4⋊C4—611no—
591C2×C4⋊C4—611no—
592C2×C4⋊C4—611no—
593C2×C4⋊C4—611no—
594C2×C4⋊C4—611no—
595C2×C4⋊C4—611no—
596C2×C4⋊C4—611no—
597C2×C4⋊C4—611no—
598C2×C4⋊C4—611no—
599C2×C4⋊C4—611no—
600C2×C4⋊C4—611no—
601C2×C4⋊C4—611no—
602C2×C4⋊C4—1221no—
603C2×C4⋊C4—1221no—
604C2×C4⋊C4—1221no—
605C2×C4⋊C4—1221no—
606C2×C4⋊C4C4×D6111yescharacteristic
607C2×C4⋊C4C22×D6111yescharacteristic
608C2×C22⋊C4—611no—
609C2×C22⋊C4—611no—
610C2×C22⋊C4—611no—
611C2×C22⋊C4—611no—
612C2×C22⋊C4—611no—
613C2×C22⋊C4C4×D6111yescharacteristic
614C2×C22⋊C4C4×D6111yescharacteristic
615C2×C22⋊C4C22×D6111yescharacteristic
616C2×C42—611no—
617C2×C42—611no—
618C2×C42—611no—
619C2×C42—611no—
620C2×C42—611no—
621C4⋊C8—1221no—
622C4⋊C8—1221no—
623C4⋊C8—1221no—
624C4⋊C8—1221no—
625C4⋊C8—1221no—
626C4⋊C8—1221no—
627C4⋊C8—1221no—
628C4⋊C8—1221no—
629C22⋊C8—21no—
630C22⋊C8—21no—
631C22⋊C8—611no—
632C22⋊C8—611no—
633C22⋊C8—611no—
634C22⋊C8—611no—
635C22⋊C8—1221no—
636C22⋊C8—1221no—
637C22⋊C8C22×D6111yescharacteristic
638C22⋊C8C22×D6111yescharacteristic
639C22⋊C8C22×D6111yescharacteristic
640C22⋊C8C22×D6111yescharacteristic
641#97—1221no—
642#97—1221no—
643#97—1221no—
644#97—1221no—
645C4×C8—1221no—
646C4×C8—1221no—
647C4×C8—1221no—
648C4×C8—1221no—
649C24C2×C4×D6111yescharacteristic
650C24C2×C4×D6111yescharacteristic
651C2×Q8—1221no—
652C2×Q8—1221no—
653C2×Q8—1222no—
654C2×Q8—2441no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—42no—
658C22×C4—42no—
659C22×C4—611no—
660C22×C4—611no—
661C22×C4—611no—
662C22×C4—611no—
663C22×C4—611no—
664C22×C4—611no—
665C22×C4—611no—
666C22×C4—611no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—1222no—
670C22×C4—1222no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—1221no—
674C22×C4—1221no—
675C22×C4—2441no—
676C22×C4—2441no—
677C22×C4—2442no—
678C22×C4C2×C4×D6111yescharacteristic
679C22×C4C2×C4×D6111yescharacteristic
680C22×C4C2×C4×D6111yescharacteristic
681C22×C4C2×C4×D6111yescharacteristic
682C22×C4D4×D6111yescharacteristic
683C22×C4D4×D6111yescharacteristic
684C22×C4D4×D6111yescharacteristic
685C22×C4D4×D6111yescharacteristic
686C22×C4C23×D6111yescharacteristic
687M16—42no—
688M16—2442no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—42no—
694C2×C8—1221no—
695C2×C8—1221no—
696C2×C8—1221no—
697C2×C8—1221no—
698C2×C8—2442no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—611no—
704C4⋊C4—611no—
705C4⋊C4—611no—
706C4⋊C4—611no—
707C4⋊C4—611no—
708C4⋊C4—611no—
709C4⋊C4—611no—
710C4⋊C4—611no—
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—
726C4⋊C4—1221no—
727C4⋊C4—1221no—
728C4⋊C4—1221no—
729C4⋊C4—1221no—
730C4⋊C4—1221no—
731C4⋊C4—1221no—
732C4⋊C4—1221no—
733C4⋊C4—1221no—
734C4⋊C4—1221no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—611no—
742C22⋊C4—611no—
743C22⋊C4—611no—
744C22⋊C4—611no—
745C22⋊C4—611no—
746C22⋊C4—611no—
747C22⋊C4—611no—
748C22⋊C4—611no—
749C22⋊C4—1221no—
750C22⋊C4—1221no—
751C22⋊C4—1221no—
752C22⋊C4—1221no—
753C22⋊C4—1221no—
754C22⋊C4—1221no—
755C42—611no—
756C42—611no—
757C42—611no—
758C42—611no—
759C42—611no—
760C42—611no—
761C42—611no—
762C42—611no—
763C42—1221no—
764C42—1221no—
765C42—1221no—
766C42—1221no—
767C42—1221no—
768C42—1221no—
769C23—22no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23C22⋊C4×D6111yescharacteristic
779C23C22⋊C4×D6111yescharacteristic
780C23C22×C4×D6111yescharacteristic
781Q8—2442no—
782Q8—2442no—
783D4—42no—
784D4—42no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—611no—
799C2×C4—611no—
800C2×C4—611no—
801C2×C4—611no—
802C2×C4—611no—
803C2×C4—611no—
804C2×C4—611no—
805C2×C4—611no—
806C2×C4—612no—
807C2×C4—1221no—
808C2×C4—1221no—
809C2×C4—1221no—
810C2×C4—1221no—
811C2×C4—1221no—
812C2×C4—1221no—
813C2×C4—1221no—
814C2×C4—1221no—
815C2×C4—1221no—
816C2×C4—1221no—
817C2×C4—1221no—
818C2×C4—2441no—
819C2×C4—2441no—
820C2×C4—2442no—
821C2×C4—2442no—
822C2×C4—2442no—
823C2×C4—2442no—
824C2×C4—2442no—
825C2×C4—2442no—
826C2×C4—2441no—
827C2×C4—2441no—
828C2×C4C22⋊C4×D6111yescharacteristic
829C2×C4C22⋊C4×D6111yescharacteristic
830C2×C4C2×D4×D6111yescharacteristic
831C2×C4C2×D4×D6111yescharacteristic
832C8—41no—
833C8—41no—
834C8—41no—
835C8—41no—
836C8—2441no—
837C8—2441no—
838C8—2441no—
839C8—2441no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—21no—
845C22—21no—
846C22—21no—
847C22—42no—
848C22—42no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—81no—
853C22—81no—
854C22#1683973412yes—
855C22C2×C22⋊C4×D6111yescharacteristic
856C22#131×D6111yescharacteristic
857C22#1684052711yescharacteristic
858C4—21no—
859C4—21no—
860C4—21no—
861C4—21no—
862C4—41no—
863C4—41no—
864C4—41no—
865C4—1221no—
866C4—1221no—
867C4—1222no—
868C4—1221no—
869C4—1221no—
870C4—1221no—
871C4—1221no—
872C4—1221no—
873C4—1221no—
874C4—2441no—
875C4—2441no—
876C4—2441no—
877C2—21no—
878C2—21no—
879C2—22no—
880C2—41no—
881C2—81no—
882C2#2145426711yescharacteristic
883C2C2×#1683973411yescharacteristic
884C2#2145430011yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1468C2
socleC22×C61C22×C22⋊C4
prime radicalC22×D4×C61C2×C4
cosocleC22×C4×C61C24
hypercenter#1468D61
hypocenterC61#17417
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1468

Complements

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

NH ≅ G/Ntype
2. #21454479C2semidirect
3. #21454473C2semidirect
4. #21444185C2semidirect
5. #21444185C2semidirect
6. #21444173C2semidirect
7. #21444173C2semidirect
9. #21444161C2semidirect
10. #21444150C2semidirect
11. #21444148C2semidirect
12. #21444141C2semidirect
13. #21444130C2semidirect
14. C2×#16839487C2semidirect
517. C61#17417semidirect

Maximal subgroups

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

subgroupindex
C2×#168404492
#214544792
#214544732
#214441852
#214441732
#214441672
#214441612
#214441502
#214441482
#214441412
#214441302
C2×#168394872
C61×#14682
#1741761