Finite Group Databasebeta

← #29647707

Subgroups — #29647707

Order 15616.

930 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459559C211yesmaximal, characteristic
2#21454478C211yesmaximal, characteristic, complemented
3#21448713C211yesmaximal, characteristic, complemented
4#21444396C211yesmaximal, characteristic, complemented
5#21444393C211yesmaximal, characteristic, complemented
6#21444389C211yesmaximal, characteristic, complemented
7#21444371C211yesmaximal, characteristic, complemented
8#21444368C211yesmaximal, characteristic, complemented
9#21444359C211yesmaximal, characteristic
10#21444341C211yesmaximal, characteristic, complemented
11#21444337C211yesmaximal, characteristic, complemented
12#21444317C211yesmaximal, characteristic, complemented
13#21444316C211yesmaximal, characteristic, complemented
14#21444307C211yesmaximal, characteristic
15C61×#1509C211yesmaximal, characteristic, complemented
16#16840479—21no—
17#16840471—21no—
18#16840451—21no—
19#16840449—21no—
20#16840448—21no—
21#16840445—21no—
22#16840441—21no—
23#16840435—21no—
24#16840392C411yescharacteristic, complemented
25#16840381C411yescharacteristic, complemented
26#16840377C411yescharacteristic, complemented
27#16840375C411yescharacteristic, complemented
28#16840370C411yescharacteristic, complemented
29#16840332C411yescharacteristic, complemented
30#16840319C2211yescharacteristic
31#16840314C2211yescharacteristic
32#16840293C2211yescharacteristic
33#16840272C2211yescharacteristic
34C22⋊Q8×D61C2211yescharacteristic
35#16840241C411yescharacteristic, complemented
36#16840238C411yescharacteristic, complemented
37C2×#14519734C2211yescharacteristic
38#16839824—21no—
39#16839822—21no—
40#16839816C2211yescharacteristic
41#16839815C2211yescharacteristic
42#16839812C2211yescharacteristic
43#16839787—21no—
44#16839724C2211yescharacteristic
45C22⋊C8×D61C2211yescharacteristic
46#16839719—21no—
47#16839657—21no—
48#16839653—21no—
49#16839652—21no—
50#16839630C2211yescharacteristic
51#16839629C2211yescharacteristic
52#16839621C2211yescharacteristic
53C4×#11758196—21no—
54#16839613C2211yescharacteristic
55#16839609C2211yescharacteristic
56#16839500C2211yescharacteristic
57#16839500C2211yescharacteristic
58#16839500C2211yescharacteristic
59#16839500C2211yescharacteristic
60#16839499C2211yescharacteristic
61#16839499C2211yescharacteristic
62#16839498C2211yescharacteristic
63#16839498C2211yescharacteristic
64#16839498C2211yescharacteristic
65#16839498C2211yescharacteristic
66#16839496C2211yescharacteristic
67#16839496C2211yescharacteristic
68C61×#529C2211yescharacteristic
69C61×#432C2211yescharacteristic
70C4×C4⋊C4×C61C2211yescharacteristic
71C61×#328C2211yescharacteristic
72C61×#328C2211yescharacteristic
73C61×#327C2211yescharacteristic
74C61×#327C2211yescharacteristic
75C2×#11758224C2×C411yescharacteristic
76C2×Q8×D61C2×C411yescharacteristic
77C22×C4×D61C2311yescharacteristic
78C2×#11758189—21no—
79C2×C8×D61—21no—
80#14519777C2×C411yescharacteristic
81#14519777C2×C411yescharacteristic
82#14519776—21no—
83#14519776C2×C411yescharacteristic
84#14519775C2×C411yescharacteristic
85#14519772—21no—
86#14519772—21no—
87#14519772—21no—
88#14519771—21no—
89#14519770—21no—
90#14519770—21no—
91#14519770—21no—
92#14519769—21no—
93#14519769—21no—
94#14519768—21no—
95#14519768—21no—
96#14519768C2×C411yescharacteristic
97#14519767—21no—
98#14519767—21no—
99#14519767—21no—
100#14519764C2×C411yescharacteristic
101#14519763—21no—
102#14519763—21no—
103#14519761—21no—
104#14519760—21no—
105#14519759—21no—
106#14519759—21no—
107#14519759—21no—
108#14519758—21no—
109#14519757—21no—
110#14519757C2×C411yescharacteristic
111#14519757C2×C411yescharacteristic
112#14519756—21no—
113#14519756—21no—
114#14519756C2311yescharacteristic
115#14519756C2311yescharacteristic
116#14519755—21no—
117#14519755—21no—
118#14519754—21no—
119#14519754—21no—
120#14519754—21no—
121#14519754—21no—
122#14519754—21no—
123#14519753C2×C411yescharacteristic
124#14519748C2×C411yescharacteristic
125#14519745—21no—
126Q8×Dic61C2×C411yescharacteristic
127C4×Dic122—21no—
128C4×Dic122—21no—
129C4×Dic122C2×C411yescharacteristic
130C4×Dic122C2×C411yescharacteristic
131#14519742—21no—
132#14519742—21no—
133#14519742C2×C411yescharacteristic
134#14519742C2×C411yescharacteristic
135D4×Dic61—21no—
136D4×Dic61—21no—
137D4×Dic61C2×C411yescharacteristic
138C4×C22⋊D61—21no—
139#14519737—21no—
140#14519737—21no—
141#14519736—21no—
142#14519735—21no—
143#14519735C2×C411yescharacteristic
144#14519734—21no—
145#14519734C2×C411yescharacteristic
146#14519734C2×C411yescharacteristic
147#14519734C2×C411yescharacteristic
148#14519734C2×C411yescharacteristic
149#14519734D411yescharacteristic
150#14519734D411yescharacteristic
151#14519734D411yescharacteristic
152#14519734D411yescharacteristic
153#14519733—21no—
154#14519733—21no—
155#14519733—21no—
156C2×#11758196—21no—
157C2×#11758196—21no—
158C2×#11758196—21no—
159C2×#11758196D411yescharacteristic
160C2×#11758196D411yescharacteristic
161C4⋊C4×D61—21no—
162C4⋊C4×D61C2×C411yescharacteristic
163C2×#11758198—21no—
164C2×#11758198—21no—
165C2×#11758198D411yescharacteristic
166C2×#11758198D411yescharacteristic
167C22⋊C4×D61—21no—
168C2×C4×Dic61—21no—
169C2×C4×Dic61—21no—
170C2×C4×Dic61C2311yescharacteristic
171C4⋊#92418—21no—
172#14519706—21no—
173#14519706—21no—
174C22⋊#92418C2311yescharacteristic
175C22⋊#92418C2311yescharacteristic
176#14519689—21no—
177#14519689—21no—
178#14519687—21no—
179C4×#92418—21no—
180C8×Dic61—21no—
181#14519684—21no—
182#14519684—21no—
183#14519684—21no—
184#14519684—21no—
185#14519684C2311yescharacteristic
186#14519684C2311yescharacteristic
187#126×C61—21no—
188#125×C61C2×C411yescharacteristic
189#124×C61C2×C411yescharacteristic
190#123×C61—21no—
191C22⋊Q8×C61C2311yescharacteristic
192#121×C61C2311yescharacteristic
193C4×Q8×C61C2×C411yescharacteristic
194C4×D4×C61—21no—
195C4×D4×C61C2×C411yescharacteristic
196#117×C61—21no—
197C2×C4⋊C4×C61—21no—
198C2×C42×C61—21no—
199C2×C42×C61C2311yescharacteristic
200C4⋊C8×C61—21no—
201C22⋊C8×C61C2311yescharacteristic
202C22⋊C8×C61C2311yescharacteristic
203#97×C61—21no—
204#95×C61C2311yescharacteristic
205#95×C61C2311yescharacteristic
206C23×D61C2×D411yescharacteristic
207C2×Q8×C61C22×C411yescharacteristic
208C2×D4×C61—21no—
209C2×D4×C61C22×C411yescharacteristic
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—21no—
213C22×C4×C61C2×D411yescharacteristic
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2411yescharacteristic
216C2×C22⋊D61—21no—
217C2×C22⋊D61—21no—
218C22×Dic61—21no—
219C22×Dic61—21no—
220C22×Dic61—21no—
221C22×Dic61—21no—
222C22×Dic61C2×D411yescharacteristic
223C22×Dic61C2×D411yescharacteristic
224C22×Dic61C2×D411yescharacteristic
225Q8×D61—42no—
226#11758224—42no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—42no—
230C2×C4×D61C22×C411yescharacteristic
231C2×C4×D61C22×C411yescharacteristic
232C2×C4×D61C2×D411yescharacteristic
233C2×C4×D61C2×D411yescharacteristic
234C2×Dic122—21no—
235C2×Dic122—21no—
236C2×Dic122—21no—
237C2×Dic122C22×C411yescharacteristic
238C2×Dic122C22×C411yescharacteristic
239C2×C8×C61—21no—
240C2×C8×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—42no—
246C4⋊C4×C61C22×C411yescharacteristic
247C4⋊C4×C61C22×C411yescharacteristic
248C22⋊C4×C61—21no—
249C22⋊C4×C61—21no—
250C22⋊C4×C61—21no—
251C22⋊C4×C61—21no—
252C22⋊C4×C61—21no—
253C42×C61—21no—
254C42×C61—81no—
255C42×C61C22×C411yescharacteristic
256C42×C61C22×C411yescharacteristic
257C42×C61C2×D411yescharacteristic
258C42×C61C2×D411yescharacteristic
259C22⋊Dic61—21no—
260C22⋊Dic61—21no—
261C22⋊Dic61—21no—
262C22⋊Dic61—21no—
263C22⋊Dic61—21no—
264C22⋊Dic61—21no—
265#11758198—21no—
266#11758198—21no—
267#11758198—21no—
268#11758198—21no—
269#11758198—42no—
270#11758198—81no—
271#11758198C22⋊C411yescharacteristic
272#11758198C22⋊C411yescharacteristic
273#11758198C22⋊C411yescharacteristic
274#11758198C22⋊C411yescharacteristic
275#11758198C22⋊C411yescharacteristic
276#11758198C22⋊C411yescharacteristic
277#11758198C22⋊C411yescharacteristic
278#11758198C22⋊C411yescharacteristic
279C4⋊Dic61—21no—
280C4⋊Dic61—21no—
281C4⋊Dic61—21no—
282C4⋊Dic61—21no—
283C4⋊Dic61—21no—
284C4⋊Dic61—21no—
285C4⋊Dic61—21no—
286C4⋊Dic61C22×C411yescharacteristic
287C4⋊Dic61C22×C411yescharacteristic
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—42no—
301#11758196—42no—
302#11758196C22⋊C411yescharacteristic
303#11758196C22⋊C411yescharacteristic
304#11758196C22⋊C411yescharacteristic
305#11758196C22⋊C411yescharacteristic
306#11758196C22⋊C411yescharacteristic
307#11758196C22⋊C411yescharacteristic
308#11758196C22⋊C411yescharacteristic
309#11758196C22⋊C411yescharacteristic
310C4×Dic61—21no—
311C4×Dic61—21no—
312C4×Dic61—21no—
313C4×Dic61—21no—
314C4×Dic61—21no—
315C4×Dic61—21no—
316C4×Dic61—42no—
317C4×Dic61—81no—
318C4×Dic61C22×C411yescharacteristic
319C4×Dic61C22×C411yescharacteristic
320C4×Dic61C2×D411yescharacteristic
321C4×Dic61C2×D411yescharacteristic
322C2×#92418—21no—
323C2×#92418—21no—
324#11758189—42no—
325C8×D61—42no—
326C23×C61—21no—
327C23×C61C22×D411yescharacteristic
328C22×D61—21no—
329C22×D61—21no—
330C22×D61—41no—
331C22×D61—41no—
332C22×D61C2×C22⋊C411yescharacteristic
333C22×D61C2×C22⋊C411yescharacteristic
334Q8×C61—41no—
335D4×C61—41no—
336D4×C61—41no—
337D4×C61—41no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—22no—
341C2×C4×C61—21no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61—81no—
352C2×C4×C61C2×C22⋊C411yescharacteristic
353C2×C4×C61C2×C22⋊C411yescharacteristic
354C2×C4×C61C2×C22⋊C411yescharacteristic
355C2×C4×C61C2×C22⋊C411yescharacteristic
356C2×C4×C61C23×C411yescharacteristic
357C2×C4×C61C22×D411yescharacteristic
358C22⋊D61—42no—
359C22⋊D61—81no—
360C2×Dic61—21no—
361C2×Dic61—21no—
362C2×Dic61—22no—
363C2×Dic61—21no—
364C2×Dic61—21no—
365C2×Dic61—21no—
366C2×Dic61—21no—
367C2×Dic61—41no—
368C2×Dic61—42no—
369C2×Dic61—41no—
370C2×Dic61—41no—
371C2×Dic61—41no—
372C2×Dic61—41no—
373C2×Dic61—41no—
374C2×Dic61—41no—
375C2×Dic61—81no—
376C2×Dic61C2×C22⋊C411yescharacteristic
377C2×Dic61C2×C22⋊C411yescharacteristic
378C2×Dic61C2×C22⋊C411yescharacteristic
379C2×Dic61C2×C22⋊C411yescharacteristic
380C2×Dic61C2×C22⋊C411yescharacteristic
381C2×Dic61C2×C22⋊C411yescharacteristic
382C4×D61—22no—
383C4×D61—22no—
384C4×D61—41no—
385C4×D61—41no—
386C4×D61—42no—
387C4×D61—81no—
388Dic122—42no—
389Dic122—41no—
390Dic122—41no—
391Dic122—81no—
392Dic122—81no—
393C8×C61—41no—
394C8×C61—41no—
395#92418—41no—
396#92418—41no—
397#17612—611nomaximal, Sylow
398C22×C61—21no—
399C22×C61—21no—
400C22×C61—41no—
401C22×C61—41no—
402C22×C61—41no—
403C22×C61C22×C22⋊C411yescharacteristic
404C22×C61#57711yescharacteristic
405C22×C61#57811yescharacteristic
406C2×D61—21no—
407C2×D61—21no—
408C2×D61—21no—
409C2×D61—21no—
410C2×D61—21no—
411C2×D61—21no—
412C2×D61—81no—
413C2×D61—81no—
414C4×C61—21no—
415C4×C61—21no—
416C4×C61—21no—
417C4×C61—21no—
418C4×C61—21no—
419C4×C61—21no—
420C4×C61—42no—
421C4×C61—41no—
422C4×C61—41no—
423C4×C61—41no—
424C4×C61—81no—
425Dic61—21no—
426Dic61—21no—
427Dic61—21no—
428Dic61—21no—
429Dic61—21no—
430Dic61—41no—
431Dic61—41no—
432Dic61—41no—
433Dic61—41no—
434Dic61—81no—
435Dic61—81no—
436Dic61#41012yes—
437#3495—611no—
438#2924—611no—
439#2347—611no—
440#1521—611no—
441#1521—611no—
442#1520—611no—
443#1515—611no—
444#1515—611no—
445#1513—611no—
446#1509—611no—
447#1509D6111yescharacteristic, complemented
448#1508—611no—
449#1503—611no—
450#1503—611no—
451#1501—611no—
452C2×C61—21no—
453C2×C61—21no—
454C2×C61—81no—
455C2×C61C2×#41011yescharacteristic
456C2×C61#289811yescharacteristic
457C2×C61#290111yescharacteristic
458D61—41no—
459D61—41no—
460#556—1221no—
461#554—1221no—
462#552—1221no—
463#552—1221no—
464#552—1221no—
465#552—1221no—
466#551—1221no—
467#551—1221no—
468#544—611no—
469#542—611no—
470#542—611no—
471#541—611no—
472#541—611no—
473#536—611no—
474#533—611no—
475#533—611no—
476#529—611no—
477#529C2×D6111yescharacteristic
478#525—611no—
479C2×C22⋊Q8—611no—
480#520—611no—
481#519—611no—
482C2×#117—611no—
483#433—1221no—
484#433—1221no—
485#432—611no—
486#432C2×D6111yescharacteristic
487#431—611no—
488#431—611no—
489#424—1221no—
490#407—611no—
491C2×C22⋊C8—611no—
492#405—1221no—
493#389—1221no—
494#388—1221no—
495#388—1221no—
496#383—611no—
497#383—611no—
498#380—611no—
499C4×C4⋊C4—611no—
500C4×C4⋊C4—1221no—
501C4×C4⋊C4C2×D6111yescharacteristic
502C4×C22⋊C4—611no—
503#328—611no—
504#328—611no—
505#328—611no—
506#328—611no—
507#328—611no—
508#328—611no—
509#328—611no—
510#328—611no—
511#328—611no—
512#328—611no—
513#328C2×D6111yescharacteristic
514#328C2×D6111yescharacteristic
515#327—611no—
516#327—611no—
517#327C2×D6111yescharacteristic
518#327C2×D6111yescharacteristic
519C61#1761211yescharacteristic, complemented, Sylow
520C2×#41—611no—
521C22×Q8—611no—
522C23×C4—611no—
523C2×M16—1221no—
524C22×C8—1221no—
525C4⋊Q8—611no—
526C4⋊Q8—611no—
527C4⋊Q8—611no—
528C4⋊Q8—611no—
529C4⋊Q8—1221no—
530#126—21no—
531#126—1221no—
532#126—1221no—
533#126—1221no—
534#126—1221no—
535#126—1221no—
536#126—1221no—
537#126—1221no—
538#125—611no—
539#125—1221no—
540#125—1221no—
541#125—1221no—
542#125—1221no—
543#125—1221no—
544#125—1221no—
545#125—1221no—
546#125C4×D6111yescharacteristic
547#124—611no—
548#124—1221no—
549#124—1221no—
550#124C4×D6111yescharacteristic
551#123—21no—
552#123—1221no—
553#123—1221no—
554#123—1221no—
555#123—1221no—
556#123—1221no—
557#123—1221no—
558C22⋊Q8—611no—
559C22⋊Q8—611no—
560C22⋊Q8—611no—
561C22⋊Q8—611no—
562C22⋊Q8—611no—
563C22⋊Q8—1221no—
564C22⋊Q8—1221no—
565C22⋊Q8—1221no—
566C22⋊Q8—1221no—
567C22⋊Q8—1221no—
568C22⋊Q8—1221no—
569C22⋊Q8—1221no—
570C22⋊Q8—1221no—
571C22⋊Q8—1221no—
572C22⋊Q8—1221no—
573C22⋊Q8C22×D6111yescharacteristic
574#121—611no—
575#121C22×D6111yescharacteristic
576#120—1221no—
577C4×Q8—611no—
578C4×Q8—611no—
579C4×Q8—611no—
580C4×Q8—611no—
581C4×Q8—611no—
582C4×Q8—1221no—
583C4×Q8—1221no—
584C4×Q8—1221no—
585C4×Q8—1221no—
586C4×Q8C4×D6111yescharacteristic
587C4×D4—21no—
588C4×D4—611no—
589C4×D4—1221no—
590C4×D4—1221no—
591C4×D4—1221no—
592C4×D4—1221no—
593C4×D4—1221no—
594C4×D4C4×D6111yescharacteristic
595#117—21no—
596#117—611no—
597#117—611no—
598#117—611no—
599#117—611no—
600#117—611no—
601#117—611no—
602#117—611no—
603#117—611no—
604#117—611no—
605#117—1221no—
606#117—1221no—
607#117—1221no—
608#117—1221no—
609#117—1221no—
610#117—1221no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—611no—
613C2×C4⋊C4—611no—
614C2×C4⋊C4—611no—
615C2×C4⋊C4—1221no—
616C2×C4⋊C4—1221no—
617C2×C4⋊C4—1221no—
618C2×C4⋊C4—1221no—
619C2×C22⋊C4—611no—
620C2×C22⋊C4—611no—
621C2×C22⋊C4—1221no—
622C2×C22⋊C4—1221no—
623C2×C22⋊C4—1221no—
624C2×C42—21no—
625C2×C42—611no—
626C2×C42—1221no—
627C2×C42—1221no—
628C2×C42C22×D6111yescharacteristic
629C4⋊C8—21no—
630C4⋊C8—1221no—
631C4⋊C8—1221no—
632C4⋊C8—1221no—
633C22⋊C8—611no—
634C22⋊C8—611no—
635C22⋊C8—1221no—
636C22⋊C8—1221no—
637C22⋊C8C22×D6111yescharacteristic
638C22⋊C8C22×D6111yescharacteristic
639#97—21no—
640#97—1221no—
641C4×C8—1221no—
642C4×C8—1221no—
643#95—611no—
644#95—611no—
645#95—1221no—
646#95—1221no—
647#95—1221no—
648#95—1221no—
649#95C22×D6111yescharacteristic
650#95C22×D6111yescharacteristic
651C24—611no—
652#41—2442no—
653C2×Q8—611no—
654C2×Q8—611no—
655C2×Q8—1221no—
656C2×Q8—1221no—
657C2×Q8—1221no—
658C2×Q8—2442no—
659C2×Q8C2×C4×D6111yescharacteristic
660C2×D4—21no—
661C2×D4—1221no—
662C2×D4—1221no—
663C2×D4C2×C4×D6111yescharacteristic
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—611no—
668C22×C4—611no—
669C22×C4—611no—
670C22×C4—611no—
671C22×C4—611no—
672C22×C4—611no—
673C22×C4—611no—
674C22×C4—1221no—
675C22×C4—1221no—
676C22×C4—1221no—
677C22×C4—1221no—
678C22×C4—1221no—
679C22×C4—1221no—
680C22×C4—2442no—
681C22×C4D4×D6111yescharacteristic
682C22×C4D4×D6111yescharacteristic
683C22×C4C23×D6111yescharacteristic
684M16—2442no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—1221no—
688C2×C8—1221no—
689C2×C8—2442no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—42no—
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—1221no—
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—2442no—
725C4⋊C4—2442no—
726C4⋊C4C2×C4×D6111yescharacteristic
727C4⋊C4C2×C4×D6111yescharacteristic
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—
751C22⋊C4—4881no—
752C22⋊C4—2442no—
753C42—21no—
754C42—81no—
755C42—611no—
756C42—611no—
757C42—611no—
758C42—611no—
759C42—1221no—
760C42—1221no—
761C42—1221no—
762C42—1221no—
763C42—1221no—
764C42—1221no—
765C42—4881no—
766C42—2442no—
767C42C2×C4×D6111yescharacteristic
768C42C2×C4×D6111yescharacteristic
769C42D4×D6111yescharacteristic
770C42D4×D6111yescharacteristic
771C23—21no—
772C23—611no—
773C23—611no—
774C23—1221no—
775C23—1221no—
776C23—2441no—
777C23—2441no—
778C23C2×D4×D6111yescharacteristic
779Q8—41no—
780Q8—4881no—
781Q8—4881no—
782Q8—2441no—
783Q8—2441no—
784Q8—2442no—
785D4—41no—
786D4—41no—
787D4—41no—
788D4—4881no—
789D4—2442no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—22no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—81no—
804C2×C4—611no—
805C2×C4—611no—
806C2×C4—611no—
807C2×C4—611no—
808C2×C4—611no—
809C2×C4—611no—
810C2×C4—1222no—
811C2×C4—1222no—
812C2×C4—1222no—
813C2×C4—1221no—
814C2×C4—1221no—
815C2×C4—1221no—
816C2×C4—1221no—
817C2×C4—1221no—
818C2×C4—1221no—
819C2×C4—4881no—
820C2×C4—4881no—
821C2×C4—2441no—
822C2×C4—2441no—
823C2×C4—2442no—
824C2×C4—2442no—
825C2×C4—2441no—
826C2×C4—2441no—
827C2×C4—2441no—
828C2×C4—2441no—
829C2×C4—2441no—
830C2×C4—2441no—
831C2×C4—2441no—
832C2×C4C22⋊C4×D6111yescharacteristic
833C2×C4C22⋊C4×D6111yescharacteristic
834C2×C4C22⋊C4×D6111yescharacteristic
835C2×C4C22⋊C4×D6111yescharacteristic
836C2×C4C22×C4×D6111yescharacteristic
837C2×C4C2×D4×D6111yescharacteristic
838C8—41no—
839C8—41no—
840C8—2441no—
841C8—2441no—
842C22—21no—
843C22—21no—
844C22—41no—
845C22—41no—
846C22—41no—
847C22—1221no—
848C22—1221no—
849C22—1221no—
850C22—1221no—
851C22—1221no—
852C22—1221no—
853C22—4881no—
854C22—4881no—
855C22C2×C22⋊C4×D6111yescharacteristic
856C22#1684057211yescharacteristic
857C22#1684057811yescharacteristic
858C4—21no—
859C4—21no—
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—42no—
865C4—41no—
866C4—41no—
867C4—41no—
868C4—81no—
869C4—612no—
870C4—1221no—
871C4—1221no—
872C4—1221no—
873C4—1221no—
874C4—1221no—
875C4—4881no—
876C4—4881no—
877C4—2441no—
878C4—2441no—
879C4—2441no—
880C4—2441no—
881C2—21no—
882C2—21no—
883C2—81no—
884C2—2441no—
885C2—2441no—
886C2#410×D6111yescharacteristic
887C2#2145435011yescharacteristic
888C2#2145436311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1509C2
socleC22×C61C22×C22⋊C4
prime radical#16840272C22
cosocleC22×C4×C61C24
hypercenter#1509D61
hypocenterC61#17612
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1509

Complements

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

NH ≅ G/Ntype
2. #21454478C2semidirect
3. #21448713C2semidirect
4. #21444396C2semidirect
5. #21444393C2semidirect
6. #21444389C2semidirect
7. #21444371C2semidirect
8. #21444368C2semidirect
10. #21444341C2semidirect
11. #21444337C2semidirect
12. #21444317C2semidirect
13. #21444316C2semidirect
15. C61×#1509C2semidirect
24. #16840392C4semidirect
25. #16840381C4semidirect
26. #16840377C4semidirect
27. #16840375C4semidirect
28. #16840370C4semidirect
29. #16840332C4semidirect
35. #16840241C4semidirect
36. #16840238C4semidirect
447. #1509D61semidirect
519. C61#17612semidirect

Maximal subgroups

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

subgroupindex
#214595592
#214544782
#214487132
#214443962
#214443932
#214443892
#214443712
#214443682
#214443592
#214443412
#214443372
#214443172
#214443162
#214443072
C61×#15092
#1761261