Finite Group Databasebeta

← #29646268

Subgroups — #29646268

Order 15616.

938 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×#16840479C211yesmaximal, characteristic
2#21454478C211yesmaximal, characteristic, complemented
3#21454472C211yesmaximal, characteristic, complemented
4#21444188C211yesmaximal, characteristic, complemented
5#21444185C211yesmaximal, characteristic, complemented
6#21444185C211yesmaximal, characteristic, complemented
7#21444181C211yesmaximal, characteristic, complemented
8#21444181C211yesmaximal, characteristic, complemented
9#21444162C211yesmaximal, characteristic, complemented
10#21444161C211yesmaximal, characteristic, complemented
11#21444154C211yesmaximal, characteristic
12#21444142C211yesmaximal, characteristic, complemented
13#21444141C211yesmaximal, characteristic, complemented
14#21444134C211yesmaximal, characteristic
15C61×#1473C211yesmaximal, characteristic, complemented
16#16840479—21no—
17#16840479—21no—
18#16840479—21no—
19#16840479—21no—
20#16840479—21no—
21#16840479—21no—
22#16840479—21no—
23#16840479—21no—
24C2×#14519776C411yescharacteristic
25C2×#14519772C411yescharacteristic
26C2×#14519772C411yescharacteristic
27C2×#14519770C2211yescharacteristic
28C2×#14519763C411yescharacteristic
29C2×#14519763C411yescharacteristic
30C2×#14519755C2211yescharacteristic
31C2×#14519754C411yescharacteristic
32C2×C4×Dic122C2211yescharacteristic
33C2×#14519742C411yescharacteristic
34C2×#14519742C2211yescharacteristic
35C2×#14519737C2211yescharacteristic
36C2×#14519734C2211yescharacteristic
37C2×#14519733C411yescharacteristic
38#16839824—21no—
39#16839822—21no—
40#16839822—21no—
41#16839821—21no—
42#16839819C2211yescharacteristic
43#16839816C2211yescharacteristic
44#16839816C2211yescharacteristic
45#16839815C2211yescharacteristic
46#16839812C2211yescharacteristic
47#16839812C2211yescharacteristic
48#16839787—21no—
49#16839787—21no—
50#16839724C2211yescharacteristic
51#16839724C2211yescharacteristic
52C22⋊C8×D61C2211yescharacteristic
53C22⋊C8×D61C2211yescharacteristic
54#16839719—21no—
55#16839716—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×#126×C61C2211yescharacteristic
69C61×#432C2211yescharacteristic
70C61×#431C2211yescharacteristic
71C61×#324C2211yescharacteristic
72C61×#324C2211yescharacteristic
73C61×#323C2211yescharacteristic
74C61×#323C2211yescharacteristic
75C22×Dic122C2×C411yescharacteristic
76C22×Dic122C2×C411yescharacteristic
77C22×Dic122C2×C411yescharacteristic
78C22×C22⋊D61C2×C411yescharacteristic
79C23×Dic61C2×C411yescharacteristic
80C22×C4×D61C2311yescharacteristic
81C2×#11758189—21no—
82C2×#11758189—21no—
83C2×C8×D61—21no—
84C2×C8×D61—21no—
85#14519776—21no—
86#14519776—21no—
87#14519776—21no—
88#14519776—21no—
89#14519772—21no—
90#14519772—21no—
91#14519772—21no—
92#14519772—21no—
93#14519772—21no—
94#14519772—21no—
95#14519772—21no—
96#14519772—21no—
97#14519770—21no—
98#14519770—21no—
99#14519770—21no—
100#14519770—21no—
101#14519763—21no—
102#14519763—21no—
103#14519763—21no—
104#14519763—21no—
105#14519763—21no—
106#14519763—21no—
107#14519763—21no—
108#14519763—21no—
109#14519755—21no—
110#14519755—21no—
111#14519755—21no—
112#14519755—21no—
113#14519754—21no—
114#14519754—21no—
115#14519754—21no—
116#14519754—21no—
117C4×Dic122—21no—
118C4×Dic122—21no—
119C4×Dic122—21no—
120C4×Dic122—21no—
121#14519742—21no—
122#14519742—21no—
123#14519742—21no—
124#14519742—21no—
125#14519742—21no—
126#14519742—21no—
127#14519742—21no—
128#14519742—21no—
129#14519737—21no—
130#14519737—21no—
131#14519737—21no—
132#14519737—21no—
133#14519734D411yescharacteristic
134#14519734D411yescharacteristic
135#14519734D411yescharacteristic
136#14519734D411yescharacteristic
137#14519734D411yescharacteristic
138#14519734D411yescharacteristic
139#14519734D411yescharacteristic
140#14519734D411yescharacteristic
141#14519733—21no—
142#14519733—21no—
143#14519733—21no—
144#14519733—21no—
145C2×C4⋊Dic61C2×C411yescharacteristic
146C2×C4⋊Dic61C2×C411yescharacteristic
147C2×#11758196C2×C411yescharacteristic
148C2×#11758196C2×C411yescharacteristic
149C2×#11758196C2×C411yescharacteristic
150C2×#11758196C2×C411yescharacteristic
151C2×#11758196C2×C411yescharacteristic
152C2×#11758196C2311yescharacteristic
153C2×#11758196C2311yescharacteristic
154C2×C22⋊Dic61C2×C411yescharacteristic
155C2×C22⋊Dic61C2×C411yescharacteristic
156C2×#11758198C2×C411yescharacteristic
157C2×#11758198C2×C411yescharacteristic
158C2×#11758198C2×C411yescharacteristic
159C2×#11758198C2×C411yescharacteristic
160C2×#11758198C2×C411yescharacteristic
161C2×C4×Dic61C2×C411yescharacteristic
162C2×C4×Dic61C2×C411yescharacteristic
163C2×C4×Dic61C2×C411yescharacteristic
164C2×C4×Dic61C2×C411yescharacteristic
165C2×C4×Dic61C2×C411yescharacteristic
166C2×C4×Dic61C2311yescharacteristic
167C4⋊#92418—21no—
168C4⋊#92418—21no—
169#14519706—21no—
170#14519706—21no—
171#14519706—21no—
172#14519706—21no—
173C22⋊#92418C2311yescharacteristic
174C22⋊#92418C2311yescharacteristic
175C22⋊#92418C2311yescharacteristic
176C22⋊#92418C2311yescharacteristic
177#14519689—21no—
178#14519689—21no—
179#14519689—21no—
180#14519689—21no—
181#14519688—21no—
182#14519687—21no—
183#14519687—21no—
184C4×#92418—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—21no—
215C2×C22⋊D61—21no—
216C2×C22⋊D61—22no—
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—42no—
229C2×C4×D61C2×D411yescharacteristic
230C2×C4×D61C2×D411yescharacteristic
231C2×C4×D61C2×D411yescharacteristic
232C2×C4×D61C2×D411yescharacteristic
233C2×Dic122—21no—
234C2×Dic122—21no—
235C2×Dic122—21no—
236C2×Dic122—21no—
237C2×Dic122—21no—
238C2×Dic122—21no—
239C2×Dic122—22no—
240C2×Dic122—22no—
241C2×Dic122—41no—
242C2×Dic122—41no—
243C2×Dic122—42no—
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—
274#11758198C22⋊C411yescharacteristic
275#11758198C22⋊C411yescharacteristic
276#11758198C22⋊C411yescharacteristic
277#11758198C22⋊C411yescharacteristic
278#11758198C22⋊C411yescharacteristic
279#11758198C22⋊C411yescharacteristic
280#11758198C22⋊C411yescharacteristic
281#11758198C22⋊C411yescharacteristic
282C4⋊Dic61—21no—
283C4⋊Dic61—21no—
284C4⋊Dic61—21no—
285C4⋊Dic61—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#11758196C22⋊C411yescharacteristic
297#11758196C22⋊C411yescharacteristic
298#11758196C22⋊C411yescharacteristic
299#11758196C22⋊C411yescharacteristic
300#11758196C22⋊C411yescharacteristic
301#11758196C22⋊C411yescharacteristic
302#11758196C22⋊C411yescharacteristic
303#11758196C22⋊C411yescharacteristic
304C4×Dic61—21no—
305C4×Dic61—21no—
306C4×Dic61—21no—
307C4×Dic61—21no—
308C4×Dic61—21no—
309C4×Dic61—21no—
310C4×Dic61—21no—
311C4×Dic61—21no—
312C4×Dic61—21no—
313C4×Dic61—21no—
314C4×Dic61C2×D411yescharacteristic
315C4×Dic61C2×D411yescharacteristic
316C4×Dic61C2×D411yescharacteristic
317C4×Dic61C2×D411yescharacteristic
318C2×#92418—21no—
319C2×#92418—21no—
320C2×#92418—21no—
321C2×#92418—21no—
322#11758189—42no—
323#11758189—42no—
324C8×D61—42no—
325C8×D61—42no—
326C23×C61—21no—
327C23×C61—21no—
328C23×C61—21no—
329C23×C61—41no—
330C23×C61—41no—
331C23×C61C23×C411yescharacteristic
332C22×D61—21no—
333C22×D61—21no—
334C22×D61—41no—
335C22×D61—41no—
336C22×D61C2×C22⋊C411yescharacteristic
337C22×D61C2×C22⋊C411yescharacteristic
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—21no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—21no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61C2×C22⋊C411yescharacteristic
350C2×C4×C61C2×C22⋊C411yescharacteristic
351C2×C4×C61C2×C22⋊C411yescharacteristic
352C2×C4×C61C2×C22⋊C411yescharacteristic
353C2×C4×C61C22×D411yescharacteristic
354C2×C4×C61C22×D411yescharacteristic
355C22⋊D61—42no—
356C22⋊D61—42no—
357C2×Dic61—21no—
358C2×Dic61—21no—
359C2×Dic61—21no—
360C2×Dic61—21no—
361C2×Dic61—22no—
362C2×Dic61—21no—
363C2×Dic61—21no—
364C2×Dic61—21no—
365C2×Dic61—21no—
366C2×Dic61—21no—
367C2×Dic61—41no—
368C2×Dic61—42no—
369C2×Dic61—42no—
370C2×Dic61—41no—
371C2×Dic61—41no—
372C2×Dic61C2×C22⋊C411yescharacteristic
373C2×Dic61C2×C22⋊C411yescharacteristic
374C2×Dic61C2×C22⋊C411yescharacteristic
375C2×Dic61C2×C22⋊C411yescharacteristic
376C2×Dic61C2×C22⋊C411yescharacteristic
377C2×Dic61C2×C22⋊C411yescharacteristic
378C2×Dic61#13112yes—
379C4×D61—22no—
380C4×D61—22no—
381C4×D61—41no—
382C4×D61—41no—
383Dic122—42no—
384Dic122—42no—
385Dic122—42no—
386Dic122—42no—
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#17420—611nomaximal, Sylow
398C22×C61—21no—
399C22×C61—21no—
400C22×C61—41no—
401C22×C61—41no—
402C22×C61—41no—
403C22×C61—81no—
404C22×C61—81no—
405C22×C61C22×C22⋊C411yescharacteristic
406C22×C61C2×#13111yescharacteristic
407C22×C61#56811yescharacteristic
408C2×D61—21no—
409C2×D61—21no—
410C2×D61—21no—
411C2×D61—21no—
412C2×D61—21no—
413C2×D61—21no—
414C2×D61—81no—
415C2×D61—81no—
416C4×C61—21no—
417C4×C61—21no—
418C4×C61—21no—
419C4×C61—21no—
420C4×C61—21no—
421C4×C61—21no—
422C4×C61—41no—
423C4×C61—41no—
424C4×C61—41no—
425Dic61—22no—
426Dic61—21no—
427Dic61—21no—
428Dic61—21no—
429Dic61—21no—
430Dic61—21no—
431Dic61—41no—
432Dic61—41no—
433Dic61—41no—
434Dic61#41012yes—
435C2×#556—611no—
436#2924—611no—
437#2924—611no—
438#1473—611no—
439#1473—611no—
440#1473—611no—
441#1473D6111yescharacteristic, complemented
442#1472—611no—
443#1472—611no—
444#1467—611no—
445#1467—611no—
446#1465—611no—
447#1461—611no—
448#1461—611no—
449#1459—611no—
450C2×C61—21no—
451C2×C61—21no—
452C2×C61—81no—
453C2×C61#288011yescharacteristic
454C2×C61C2×#41011yescharacteristic
455C2×C61#288911yescharacteristic
456D61—41no—
457D61—41no—
458#556—1221no—
459#556—1221no—
460#556—1221no—
461#556—1221no—
462#556—1221no—
463#556—1221no—
464#556—1221no—
465#556—1221no—
466C2×C4⋊Q8—611no—
467C2×#126—611no—
468C2×#126—611no—
469C2×#126—611no—
470C2×#126C2×D6111yescharacteristic
471C2×#124—611no—
472C2×#124—611no—
473C2×C22⋊Q8—611no—
474C2×C22⋊Q8—611no—
475C2×C4×Q8—611no—
476C2×C4×Q8—611no—
477C2×C4×Q8—611no—
478C2×C4×D4—611no—
479C2×#117—611no—
480C2×#117—611no—
481#433—1221no—
482#433—1221no—
483#433—1221no—
484#433—1221no—
485#432—611no—
486#432—611no—
487#432—611no—
488#432C2×D6111yescharacteristic
489#431—611no—
490#431—611no—
491#431—611no—
492#431C2×D6111yescharacteristic
493#424—1221no—
494#424—1221no—
495#407—611no—
496#407—611no—
497C2×C22⋊C8—611no—
498C2×C22⋊C8—611no—
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#1742011yescharacteristic, complemented, Sylow
518C22×Q8—611no—
519C22×Q8—611no—
520C22×Q8—611no—
521C22×D4—611no—
522C23×C4—611no—
523C23×C4—611no—
524C2×M16—1221no—
525C2×M16—1221no—
526C22×C8—1221no—
527C22×C8—1221no—
528C4⋊Q8—1221no—
529C4⋊Q8—1221no—
530C4⋊Q8—1221no—
531C4⋊Q8—1221no—
532#126—21no—
533#126—21no—
534#126—21no—
535#126—21no—
536#126—1221no—
537#126—1221no—
538#126—1221no—
539#126—1221no—
540#126—1221no—
541#126—1221no—
542#126—1221no—
543#126—1221no—
544#126—1221no—
545#126—1221no—
546#126—1221no—
547#126—1221no—
548#124—1221no—
549#124—1221no—
550#124—1221no—
551#124—1221no—
552#124—1221no—
553#124—1221no—
554#124—1221no—
555#124—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×Q8—1221no—
569C4×Q8—1221no—
570C4×Q8—1221no—
571C4×Q8—1221no—
572C4×Q8—1221no—
573C4×Q8—1221no—
574C4×Q8—1221no—
575C4×Q8—1221no—
576C4×D4—1221no—
577C4×D4—1221no—
578C4×D4—1221no—
579C4×D4—1221no—
580#117—611no—
581#117—611no—
582#117—611no—
583#117—611no—
584#117—611no—
585#117—611no—
586#117—611no—
587#117—611no—
588#117—1221no—
589#117—1221no—
590#117—1221no—
591#117—1221no—
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⋊C4C4×D6111yescharacteristic
602C2×C4⋊C4C4×D6111yescharacteristic
603C2×C4⋊C4C22×D6111yescharacteristic
604C2×C22⋊C4—611no—
605C2×C22⋊C4—611no—
606C2×C22⋊C4—611no—
607C2×C22⋊C4—611no—
608C2×C22⋊C4—611no—
609C2×C22⋊C4—611no—
610C2×C22⋊C4—611no—
611C2×C22⋊C4C4×D6111yescharacteristic
612C2×C22⋊C4C4×D6111yescharacteristic
613C2×C22⋊C4C22×D6111yescharacteristic
614C2×C42—611no—
615C2×C42—611no—
616C2×C42—611no—
617C2×C42—611no—
618C2×C42—611no—
619C2×C42—611no—
620C2×C42C22×D6111yescharacteristic
621C4⋊C8—21no—
622C4⋊C8—21no—
623C4⋊C8—1221no—
624C4⋊C8—1221no—
625C4⋊C8—1221no—
626C4⋊C8—1221no—
627C4⋊C8—1221no—
628C4⋊C8—1221no—
629C22⋊C8—611no—
630C22⋊C8—611no—
631C22⋊C8—611no—
632C22⋊C8—611no—
633C22⋊C8—1221no—
634C22⋊C8—1221no—
635C22⋊C8—1221no—
636C22⋊C8—1221no—
637C22⋊C8C22×D6111yescharacteristic
638C22⋊C8C22×D6111yescharacteristic
639C22⋊C8C22×D6111yescharacteristic
640C22⋊C8C22×D6111yescharacteristic
641#97—21no—
642#97—1221no—
643#97—1221no—
644#97—1221no—
645C4×C8—21no—
646C4×C8—1221no—
647C4×C8—1221no—
648C4×C8—1221no—
649C24—611no—
650C24C2×C4×D6111yescharacteristic
651C2×Q8—1221no—
652C2×Q8—1221no—
653C2×Q8—1221no—
654C2×Q8—1221no—
655C2×Q8—1222no—
656C2×Q8—1222no—
657C2×Q8—1221no—
658C2×Q8—1221no—
659C2×Q8—2441no—
660C2×Q8—2441no—
661C2×Q8—2442no—
662C2×D4—1222no—
663C2×D4—1221no—
664C2×D4—1221no—
665C2×D4—2441no—
666C22×C4—611no—
667C22×C4—611no—
668C22×C4—611no—
669C22×C4—611no—
670C22×C4—611no—
671C22×C4—611no—
672C22×C4—611no—
673C22×C4—611no—
674C22×C4—611no—
675C22×C4—611no—
676C22×C4—611no—
677C22×C4—1221no—
678C22×C4—1221no—
679C22×C4—2442no—
680C22×C4—2442no—
681C22×C4C2×C4×D6111yescharacteristic
682C22×C4C2×C4×D6111yescharacteristic
683C22×C4C2×C4×D6111yescharacteristic
684C22×C4C2×C4×D6111yescharacteristic
685C22×C4C2×C4×D6111yescharacteristic
686C22×C4C23×D6111yescharacteristic
687M16—2442no—
688M16—2442no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—1221no—
694C2×C8—1221no—
695C2×C8—1221no—
696C2×C8—1221no—
697C2×C8—2442no—
698C2×C8—2442no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—611no—
706C4⋊C4—611no—
707C4⋊C4—611no—
708C4⋊C4—611no—
709C4⋊C4—611no—
710C4⋊C4—611no—
711C4⋊C4—611no—
712C4⋊C4—611no—
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—
727C22⋊C4—21no—
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—611no—
734C22⋊C4—611no—
735C22⋊C4—611no—
736C22⋊C4—611no—
737C22⋊C4—611no—
738C22⋊C4—611no—
739C22⋊C4—611no—
740C22⋊C4—611no—
741C22⋊C4—1221no—
742C22⋊C4—1221no—
743C22⋊C4—1221no—
744C22⋊C4—1221no—
745C22⋊C4—1221no—
746C22⋊C4—1221no—
747C22⋊C4—1221no—
748C22⋊C4—1221no—
749C22⋊C4—1221no—
750C22⋊C4—1221no—
751C42—611no—
752C42—611no—
753C42—611no—
754C42—611no—
755C42—1221no—
756C42—1221no—
757C42—1221no—
758C42—1221no—
759C42—1221no—
760C42—1221no—
761C42—1221no—
762C42—1221no—
763C42—1221no—
764C42—1221no—
765C42D4×D6111yescharacteristic
766C42D4×D6111yescharacteristic
767C42D4×D6111yescharacteristic
768C42D4×D6111yescharacteristic
769C23—21no—
770C23—21no—
771C23—21no—
772C23—41no—
773C23—41no—
774C23—611no—
775C23—611no—
776C23—1221no—
777C23—1221no—
778C23—2441no—
779C23—2441no—
780C23C22×C4×D6111yescharacteristic
781Q8—2442no—
782Q8—2442no—
783Q8—2442no—
784Q8—2442no—
785Q8—2442no—
786Q8—2442no—
787D4—2442no—
788D4—2442no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—611no—
801C2×C4—611no—
802C2×C4—611no—
803C2×C4—611no—
804C2×C4—611no—
805C2×C4—611no—
806C2×C4—612no—
807C2×C4—1222no—
808C2×C4—1222no—
809C2×C4—1222no—
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—1221no—
819C2×C4—2441no—
820C2×C4—2441no—
821C2×C4—2442no—
822C2×C4—2441no—
823C2×C4—2442no—
824C2×C4—2441no—
825C2×C4—2441no—
826C2×C4C22⋊C4×D6111yescharacteristic
827C2×C4C22⋊C4×D6111yescharacteristic
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—41no—
843C22—41no—
844C22—41no—
845C22—81no—
846C22—81no—
847C22—1221no—
848C22—1221no—
849C22—1221no—
850C22—1221no—
851C22—1221no—
852C22—1221no—
853C22—4881no—
854C22—4881no—
855C22C2×C22⋊C4×D6111yescharacteristic
856C22#131×D6111yescharacteristic
857C22#1684052711yescharacteristic
858C4—21no—
859C4—21no—
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—41no—
865C4—41no—
866C4—41no—
867C4—612no—
868C4—1222no—
869C4—1221no—
870C4—1221no—
871C4—1221no—
872C4—1221no—
873C4—1221no—
874C4—2441no—
875C4—2441no—
876C4—2441no—
877C2—21no—
878C2—21no—
879C2—81no—
880C2—2441no—
881C2—2441no—
882C2#2145426711yescharacteristic
883C2#410×D6111yescharacteristic
884C2#2145430011yescharacteristic
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#17420
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. #21454478C2semidirect
3. #21454472C2semidirect
4. #21444188C2semidirect
5. #21444185C2semidirect
6. #21444185C2semidirect
7. #21444181C2semidirect
8. #21444181C2semidirect
9. #21444162C2semidirect
10. #21444161C2semidirect
12. #21444142C2semidirect
13. #21444141C2semidirect
15. C61×#1473C2semidirect
441. #1473D61semidirect
517. C61#17420semidirect

Maximal subgroups

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

subgroupindex
C2×#168404792
#214544782
#214544722
#214441882
#214441852
#214441812
#214441622
#214441612
#214441542
#214441422
#214441412
#214441342
C61×#14732
#1742061