Finite Group Databasebeta

← #29647567

Subgroups — #29647567

Order 15616.

1046 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459845C211yesmaximal, characteristic
2#21454850C211yesmaximal, characteristic, complemented
3#21448461C211yesmaximal, characteristic, complemented
4#21444385C211yesmaximal, characteristic, complemented
5#21444376C211yesmaximal, characteristic, complemented
6#21444372C211yesmaximal, characteristic, complemented
7#21444360C211yesmaximal, characteristic, complemented
8#21444359C211yesmaximal, characteristic, complemented
9#21444348C211yesmaximal, characteristic, complemented
10#21444346C211yesmaximal, characteristic, complemented
11#21444341C211yesmaximal, characteristic, complemented
12#21444325C211yesmaximal, characteristic, complemented
13#21444312C211yesmaximal, characteristic, complemented
14#21444302C211yesmaximal, characteristic, complemented
15C61×#1519C211yesmaximal, characteristic, complemented
16#16840476C411yescharacteristic, complemented
17#16840467C411yescharacteristic, complemented
18#16840460C411yescharacteristic, complemented
19#16840459C411yescharacteristic, complemented
20#16840455—21no—
21#16840430C411yescharacteristic, complemented
22#16840409C411yescharacteristic, complemented
23#16840406—21no—
24#16840406C411yescharacteristic, complemented
25#16840401—21no—
26D4×C22⋊D61—21no—
27D4×C22⋊D61C411yescharacteristic, complemented
28#16840362—21no—
29#16840350—21no—
30#16840344—21no—
31#16840307C2211yescharacteristic
32#16840293C2211yescharacteristic
33#16840273C2211yescharacteristic
34#16840272C2211yescharacteristic
35#121×D61C2211yescharacteristic
36#16840235—21no—
37C2×C4×C22⋊D61C2211yescharacteristic
38#16839837—21no—
39#16839836—21no—
40#16839833—21no—
41C8×C22⋊D61—21no—
42#16839816C2211yescharacteristic, complemented
43#16839812C2211yescharacteristic, complemented
44#16839726C2211yescharacteristic, complemented
45#16839724C2211yescharacteristic, complemented
46C22⋊C8×D61C2211yescharacteristic, complemented
47#16839662—21no—
48#16839657—21no—
49#16839652—21no—
50#16839650—21no—
51#16839625C2211yescharacteristic, complemented
52#16839624C2211yescharacteristic, complemented
53#16839621C2211yescharacteristic, complemented
54#16839613C2211yescharacteristic, complemented
55#16839607C2211yescharacteristic, complemented
56#16839500C2211yescharacteristic, complemented
57#16839500C2211yescharacteristic, complemented
58#16839498C2211yescharacteristic, complemented
59#16839498C2211yescharacteristic, complemented
60#16839497C2211yescharacteristic, complemented
61#16839497C2211yescharacteristic, complemented
62#16839496C2211yescharacteristic
63#16839496C2211yescharacteristic
64#16839496C2211yescharacteristic, complemented
65#16839496C2211yescharacteristic, complemented
66#16839495C2211yescharacteristic, complemented
67#16839495C2211yescharacteristic, complemented
68C2×#121×C61C2211yescharacteristic
69C2×C22⋊C8×C61C2211yescharacteristic, complemented
70C61×#380C2211yescharacteristic, complemented
71C61×#327C2211yescharacteristic
72C61×#327C2211yescharacteristic
73C61×#327C2211yescharacteristic, complemented
74C61×#327C2211yescharacteristic, complemented
75C2×#11758222C2×C411yescharacteristic
76C2×#11758224—21no—
77C2×#11758224C2×C411yescharacteristic
78C22×C22⋊D61—21no—
79C22×C22⋊D61D411yescharacteristic
80C2×D4×D61—21no—
81C2×D4×D61C2×C411yescharacteristic
82C22×C4×D61C2311yescharacteristic
83C2×#11758194—21no—
84C2×#11758189—21no—
85C2×C8×D61—21no—
86#14519776C2×C411yescharacteristic
87#14519773—21no—
88#14519773C2×C411yescharacteristic
89#14519772—21no—
90#14519770—21no—
91#14519770—21no—
92#14519768C2×C411yescharacteristic
93#14519767—21no—
94#14519764—21no—
95#14519764C2×C411yescharacteristic
96#14519763—21no—
97#14519763—21no—
98#14519762—21no—
99#14519760—21no—
100#14519759—21no—
101#14519759—21no—
102#14519758—21no—
103#14519758—21no—
104#14519758—21no—
105#14519757C2×C411yescharacteristic
106#14519756—21no—
107#14519756C2×C411yescharacteristic
108#14519756C2311yescharacteristic
109#14519755—21no—
110#14519752C2×C411yescharacteristic
111#14519751—21no—
112#14519751C2×C411yescharacteristic
113#14519751C2311yescharacteristic
114#14519750—21no—
115#14519750—21no—
116#14519749—21no—
117#14519749—21no—
118#14519749—21no—
119#14519749—21no—
120#14519749—21no—
121#14519749—21no—
122#14519748—21no—
123#14519748—21no—
124#14519748C2×C411yescharacteristic
125#14519748C2×C411yescharacteristic
126#14519746—21no—
127#14519746—21no—
128#14519746—21no—
129#14519745—21no—
130#14519745—21no—
131#14519745—21no—
132#14519742C2×C411yescharacteristic
133D4×Dic61—21no—
134D4×Dic61—21no—
135D4×Dic61C2×C411yescharacteristic
136D4×Dic61C2×C411yescharacteristic
137#14519739C2×C411yescharacteristic
138C4×C22⋊D61—21no—
139C4×C22⋊D61—21no—
140C4×C22⋊D61—21no—
141C4×C22⋊D61—21no—
142C4×C22⋊D61C2×C411yescharacteristic
143C4×C22⋊D61C2×C411yescharacteristic
144C4×C22⋊D61C2×C411yescharacteristic
145C4×C22⋊D61C2×C411yescharacteristic
146C4×C22⋊D61D411yescharacteristic
147C4×C22⋊D61D411yescharacteristic
148C4×C22⋊D61D411yescharacteristic
149C4×C22⋊D61D411yescharacteristic
150#14519737—21no—
151#14519737—21no—
152#14519737—21no—
153#14519737—21no—
154#14519736C2×C411yescharacteristic
155#14519735C2×C411yescharacteristic
156#14519733—21no—
157#14519733—21no—
158C2×#11758196—21no—
159C2×#11758196—21no—
160C2×#11758196D411yescharacteristic
161C4⋊C4×D61C2×C411yescharacteristic
162C2×C22⋊Dic61—21no—
163C2×C22⋊Dic61—21no—
164C2×C22⋊Dic61D411yescharacteristic
165C2×#11758198—21no—
166C2×#11758198—21no—
167C2×#11758198D411yescharacteristic
168C22⋊C4×D61—21no—
169C22⋊C4×D61—21no—
170C2×C4×Dic61—21no—
171C2×C4×Dic61—21no—
172C2×C4×Dic61C2311yescharacteristic
173#14519706—21no—
174#14519706—21no—
175C22⋊#92418—21no—
176C22⋊#92418C2311yescharacteristic
177C22⋊#92418C2311yescharacteristic
178#14519689—21no—
179#14519689—21no—
180#14519687—21no—
181C8×Dic61—21no—
182#14519684—21no—
183#14519684—21no—
184#14519684—21no—
185#14519684C2311yescharacteristic
186#14519684C2311yescharacteristic
187C22×D4×C61—21no—
188C22×D4×C61C2×C411yescharacteristic
189C23×C4×C61C2311yescharacteristic
190C22×C8×C61—21no—
191#121×C61—21no—
192#121×C61—21no—
193#121×C61C2×C411yescharacteristic
194#121×C61C2×C411yescharacteristic
195#121×C61C2311yescharacteristic
196#121×C61C2311yescharacteristic
197C2×C4⋊C4×C61—21no—
198C2×C4⋊C4×C61C2×C411yescharacteristic
199C2×C22⋊C4×C61—21no—
200C2×C22⋊C4×C61—21no—
201C22⋊C8×C61—21no—
202C22⋊C8×C61C2311yescharacteristic
203C22⋊C8×C61C2311yescharacteristic
204#95×C61C2311yescharacteristic
205#95×C61C2311yescharacteristic
206C24×C61—21no—
207C24×C61C2×D411yescharacteristic
208C23×D61—21no—
209C23×D61C2×D411yescharacteristic
210C2×D4×C61—21no—
211C2×D4×C61—21no—
212C2×D4×C61—21no—
213C2×D4×C61—21no—
214C2×D4×C61—21no—
215C2×D4×C61—81no—
216C2×D4×C61—81no—
217C2×D4×C61—81no—
218C2×D4×C61C22×C411yescharacteristic
219C2×D4×C61C22×C411yescharacteristic
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—81no—
224C22×C4×C61C22×C411yescharacteristic
225C22×C4×C61C22×C411yescharacteristic
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2411yescharacteristic
230C2×C22⋊D61—21no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61—21no—
233C2×C22⋊D61—21no—
234C2×C22⋊D61—21no—
235C2×C22⋊D61—21no—
236C2×C22⋊D61—21no—
237C2×C22⋊D61—21no—
238C2×C22⋊D61—21no—
239C2×C22⋊D61—42no—
240C2×C22⋊D61—44no—
241C2×C22⋊D61C22⋊C411yescharacteristic
242C2×C22⋊D61C22⋊C411yescharacteristic
243C2×C22⋊D61C22⋊C411yescharacteristic
244C2×C22⋊D61C22⋊C411yescharacteristic
245C22×Dic61—21no—
246C22×Dic61—21no—
247C22×Dic61—21no—
248C22×Dic61—21no—
249C22×Dic61—21no—
250C22×Dic61C2×D411yescharacteristic
251C22×Dic61C2×D411yescharacteristic
252C22×Dic61C2×D411yescharacteristic
253#11758224—81no—
254#11758224—81no—
255#11758224—81no—
256D4×D61—81no—
257D4×D61—81no—
258D4×D61—81no—
259#11758222—81no—
260C2×D244—21no—
261C2×D244C22×C411yescharacteristic
262C2×C4×D61—21no—
263C2×C4×D61—21no—
264C2×C4×D61—21no—
265C2×C4×D61—81no—
266C2×C4×D61C22×C411yescharacteristic
267C2×C4×D61C22×C411yescharacteristic
268C2×C4×D61C2×D411yescharacteristic
269C2×C4×D61C2×D411yescharacteristic
270C2×Dic122—21no—
271C2×Dic122C22×C411yescharacteristic
272C2×C8×C61—21no—
273C2×C8×C61—21no—
274C2×C8×C61—81no—
275C4⋊C4×C61—21no—
276C4⋊C4×C61—81no—
277C4⋊C4×C61C22×C411yescharacteristic
278C4⋊C4×C61C22×C411yescharacteristic
279C22⋊C4×C61—21no—
280C22⋊C4×C61—21no—
281C22⋊C4×C61—21no—
282C22⋊C4×C61—21no—
283C22⋊C4×C61—81no—
284C22⋊Dic61—21no—
285C22⋊Dic61—21no—
286C22⋊Dic61—21no—
287C22⋊Dic61—21no—
288C22⋊Dic61—21no—
289C22⋊Dic61—21no—
290C22⋊Dic61—21no—
291C22⋊Dic61—21no—
292C22⋊Dic61—21no—
293C22⋊Dic61—81no—
294C22⋊Dic61C22⋊C411yescharacteristic
295C22⋊Dic61C22⋊C411yescharacteristic
296C22⋊Dic61C22⋊C411yescharacteristic
297C22⋊Dic61C22⋊C411yescharacteristic
298#11758198—21no—
299#11758198—21no—
300#11758198—21no—
301#11758198—21no—
302#11758198—21no—
303#11758198—21no—
304#11758198—81no—
305#11758198—81no—
306#11758198C22⋊C411yescharacteristic
307#11758198C22⋊C411yescharacteristic
308#11758198C22⋊C411yescharacteristic
309#11758198C22⋊C411yescharacteristic
310C4⋊Dic61—21no—
311C4⋊Dic61—21no—
312C4⋊Dic61C22×C411yescharacteristic
313C4⋊Dic61C22×C411yescharacteristic
314#11758196—21no—
315#11758196—21no—
316#11758196—21no—
317#11758196—21no—
318#11758196—21no—
319#11758196—21no—
320#11758196—42no—
321#11758196—81no—
322#11758196C22⋊C411yescharacteristic
323#11758196C22⋊C411yescharacteristic
324#11758196C22⋊C411yescharacteristic
325#11758196C22⋊C411yescharacteristic
326C4×Dic61—21no—
327C4×Dic61—21no—
328C4×Dic61—21no—
329C4×Dic61—42no—
330C4×Dic61—81no—
331C4×Dic61C22×C411yescharacteristic
332C4×Dic61C22×C411yescharacteristic
333C4×Dic61C2×D411yescharacteristic
334C4×Dic61C2×D411yescharacteristic
335#11758194—81no—
336C2×#92418—21no—
337C2×#92418—21no—
338#11758189—81no—
339C8×D61—81no—
340C23×C61—21no—
341C23×C61—21no—
342C23×C61—21no—
343C23×C61—21no—
344C23×C61—41no—
345C23×C61—41no—
346C23×C61—42no—
347C23×C61—81no—
348C23×C61—81no—
349C23×C61C2×C22⋊C411yescharacteristic
350C23×C61C2×C22⋊C411yescharacteristic
351C23×C61C22×D411yescharacteristic
352C22×D61—21no—
353C22×D61—21no—
354C22×D61—21no—
355C22×D61—41no—
356C22×D61—41no—
357C22×D61—42no—
358C22×D61—81no—
359C22×D61—81no—
360C22×D61C2×C22⋊C411yescharacteristic
361C22×D61C2×C22⋊C411yescharacteristic
362D4×C61—41no—
363D4×C61—41no—
364D4×C61—41no—
365D4×C61—41no—
366D4×C61—41no—
367D4×C61—41no—
368D4×C61—81no—
369D4×C61—81no—
370D4×C61—81no—
371C2×C4×C61—21no—
372C2×C4×C61—21no—
373C2×C4×C61—41no—
374C2×C4×C61—41no—
375C2×C4×C61—41no—
376C2×C4×C61—41no—
377C2×C4×C61—41no—
378C2×C4×C61—41no—
379C2×C4×C61—41no—
380C2×C4×C61—41no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
383C2×C4×C61—41no—
384C2×C4×C61—41no—
385C2×C4×C61—81no—
386C2×C4×C61C2×C22⋊C411yescharacteristic
387C2×C4×C61C2×C22⋊C411yescharacteristic
388C2×C4×C61C23×C411yescharacteristic
389C2×C4×C61C22×D411yescharacteristic
390C22⋊D61—22no—
391C22⋊D61—22no—
392C22⋊D61—41no—
393C22⋊D61—41no—
394C22⋊D61—42no—
395C22⋊D61—42no—
396C22⋊D61—41no—
397C22⋊D61—41no—
398C22⋊D61—42no—
399C22⋊D61—81no—
400C22⋊D61—81no—
401C22⋊D61—81no—
402C22⋊D61—81no—
403C22⋊D61—81no—
404C2×Dic61—21no—
405C2×Dic61—21no—
406C2×Dic61—22no—
407C2×Dic61—21no—
408C2×Dic61—21no—
409C2×Dic61—21no—
410C2×Dic61—41no—
411C2×Dic61—42no—
412C2×Dic61—41no—
413C2×Dic61—41no—
414C2×Dic61—41no—
415C2×Dic61—41no—
416C2×Dic61—41no—
417C2×Dic61—41no—
418C2×Dic61—81no—
419C2×Dic61—81no—
420C2×Dic61C2×C22⋊C411yescharacteristic
421C2×Dic61C2×C22⋊C411yescharacteristic
422C2×Dic61C2×C22⋊C411yescharacteristic
423C2×Dic61C2×C22⋊C411yescharacteristic
424C2×Dic61C2×C22⋊C411yescharacteristic
425C2×Dic61C2×C22⋊C411yescharacteristic
426D244—41no—
427D244—81no—
428C4×D61—41no—
429C4×D61—41no—
430C4×D61—41no—
431C4×D61—41no—
432C4×D61—81no—
433C4×D61—81no—
434C4×D61—81no—
435Dic122—41no—
436Dic122—81no—
437C8×C61—41no—
438C8×C61—41no—
439#92418—41no—
440#92418—41no—
441#17599—611nomaximal, Sylow
442C22×C61—21no—
443C22×C61—21no—
444C22×C61—21no—
445C22×C61—21no—
446C22×C61—21no—
447C22×C61—21no—
448C22×C61—21no—
449C22×C61—21no—
450C22×C61—41no—
451C22×C61—41no—
452C22×C61—41no—
453C22×C61—41no—
454C22×C61—41no—
455C22×C61—41no—
456C22×C61—81no—
457C22×C61—81no—
458C22×C61—162no—
459C22×C61C22×C22⋊C411yescharacteristic
460C22×C61#57611yescharacteristic
461C22×C61#57711yescharacteristic
462C2×D61—21no—
463C2×D61—21no—
464C2×D61—21no—
465C2×D61—21no—
466C2×D61—21no—
467C2×D61—21no—
468C2×D61—41no—
469C2×D61—41no—
470C2×D61—41no—
471C2×D61—81no—
472C2×D61—81no—
473C2×D61—162no—
474C4×C61—21no—
475C4×C61—21no—
476C4×C61—21no—
477C4×C61—21no—
478C4×C61—41no—
479C4×C61—41no—
480C4×C61—81no—
481C4×C61—81no—
482Dic61—21no—
483Dic61—21no—
484Dic61—21no—
485Dic61—21no—
486Dic61—21no—
487Dic61—41no—
488Dic61—41no—
489Dic61—41no—
490Dic61—81no—
491Dic61—81no—
492Dic61#42112yes—
493#3519—611no—
494#2974—611no—
495#2319—611no—
496#1519—611no—
497#1519D6111yescharacteristic, complemented
498#1516—611no—
499#1516—611no—
500#1513—611no—
501#1513—611no—
502#1510—611no—
503#1510—611no—
504#1509—611no—
505#1505—611no—
506#1502—611no—
507#1500—611no—
508C2×C61—21no—
509C2×C61—21no—
510C2×C61—41no—
511C2×C61—41no—
512C2×C61—81no—
513C2×C61—81no—
514C2×C61#288311yescharacteristic
515C2×C61#289711yescharacteristic
516C2×C61C2×#42111yescharacteristic
517D61—41no—
518D61—41no—
519D61—81no—
520#555—611no—
521#554—611no—
522#553—611no—
523#553—611no—
524#553—1221no—
525#550—611no—
526#546—611no—
527#546—611no—
528#546—1221no—
529#546—1221no—
530D42—611no—
531D42—1221no—
532#540—1221no—
533#538—1221no—
534#538—1221no—
535#532—611no—
536#529—611no—
537#525—611no—
538#525—611no—
539C2×#121—611no—
540C2×#121C2×D6111yescharacteristic
541#518—1221no—
542C2×C4×D4—611no—
543#436—1221no—
544#435—1221no—
545#435—1221no—
546C8×D4—1221no—
547#432—611no—
548#431—611no—
549#407—611no—
550#407—611no—
551C2×C22⋊C8—611no—
552C2×C22⋊C8C2×D6111yescharacteristic, complemented
553#390—1221no—
554#389—1221no—
555#388—1221no—
556#388—1221no—
557#381—611no—
558#381—611no—
559#380—611no—
560#380C2×D6111yescharacteristic, complemented
561C4×C4⋊C4—611no—
562#376—611no—
563#328—611no—
564#328—611no—
565#328—611no—
566#328—611no—
567#327—611no—
568#327—611no—
569#327—611no—
570#327—611no—
571#327—611no—
572#327—611no—
573#327—611no—
574#327—611no—
575#327C2×D6111yescharacteristic
576#327C2×D6111yescharacteristic
577#327C2×D6111yescharacteristic, complemented
578#327C2×D6111yescharacteristic, complemented
579C61#1759911yescharacteristic, complemented, Sylow
580C2×#41—611no—
581C2×#41—611no—
582C2×#41—1221no—
583C22×D4—21no—
584C22×D4—611no—
585C22×D4—611no—
586C22×D4—1221no—
587C22×D4—1221no—
588C22×D4C4×D6111yescharacteristic
589C23×C4—611no—
590C23×C4C22×D6111yescharacteristic
591C2×M16—1221no—
592C2×M16—1221no—
593C22×C8—21no—
594C22×C8—1221no—
595C4⋊Q8—611no—
596#127—611no—
597#127—1221no—
598#126—1221no—
599#126—1221no—
600#126—1221no—
601#125—611no—
602#125—1221no—
603#124—611no—
604#124—1221no—
605#124—1221no—
606#124—1221no—
607#123—1221no—
608#123—1221no—
609#123—1221no—
610#123—1221no—
611#123—1221no—
612#123—1221no—
613#123—1221no—
614C22⋊Q8—611no—
615C22⋊Q8—611no—
616C22⋊Q8—611no—
617C22⋊Q8—1221no—
618C22⋊Q8—1221no—
619#121—21no—
620#121—21no—
621#121—611no—
622#121—611no—
623#121—611no—
624#121—611no—
625#121—611no—
626#121—1221no—
627#121—1221no—
628#121—1221no—
629#121—1221no—
630#121—1221no—
631#121—1221no—
632#121—1221no—
633#121—1221no—
634#121—1221no—
635#121—1221no—
636#121—1221no—
637#121C4×D6111yescharacteristic
638#121C4×D6111yescharacteristic
639#121C22×D6111yescharacteristic
640#121C22×D6111yescharacteristic
641#120—1221no—
642#120—1221no—
643#120—1221no—
644#120—1221no—
645#120—1221no—
646#120—1221no—
647C4×Q8—611no—
648C4×D4—611no—
649C4×D4—611no—
650C4×D4—611no—
651C4×D4—611no—
652C4×D4—611no—
653C4×D4—611no—
654C4×D4—611no—
655C4×D4—611no—
656C4×D4—611no—
657C4×D4—611no—
658C4×D4—611no—
659C4×D4—1221no—
660C4×D4—1221no—
661C4×D4—1221no—
662C4×D4—1221no—
663C4×D4—1221no—
664C4×D4—1221no—
665C4×D4—1221no—
666C4×D4—1221no—
667C4×D4—1221no—
668C4×D4—1221no—
669#117—611no—
670#117—611no—
671#117—1221no—
672#117—1221no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—611no—
675C2×C4⋊C4—611no—
676C2×C4⋊C4—1221no—
677C2×C4⋊C4—1221no—
678C2×C4⋊C4C4×D6111yescharacteristic
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—611no—
682C2×C22⋊C4—611no—
683C2×C22⋊C4—1221no—
684C2×C22⋊C4—1221no—
685C2×C22⋊C4—1221no—
686C2×C22⋊C4—1221no—
687C2×C22⋊C4—1221no—
688C2×C22⋊C4—1221no—
689C2×C42—611no—
690C2×C42—1221no—
691C2×C42—1221no—
692C4⋊C8—1221no—
693C4⋊C8—1221no—
694C22⋊C8—21no—
695C22⋊C8—611no—
696C22⋊C8—611no—
697C22⋊C8—1221no—
698C22⋊C8—1221no—
699C22⋊C8—1221no—
700C22⋊C8C22×D6111yescharacteristic
701C22⋊C8C22×D6111yescharacteristic
702#97—1221no—
703C4×C8—1221no—
704#95—611no—
705#95—611no—
706#95—1221no—
707#95—1221no—
708#95—1221no—
709#95C22×D6111yescharacteristic
710#95C22×D6111yescharacteristic
711C24—21no—
712C24—611no—
713C24—1221no—
714C24D4×D6111yescharacteristic
715#41—4881no—
716#41—4881no—
717#41—4881no—
718#41—4881no—
719C2×Q8—611no—
720C2×Q8—1221no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—81no—
727C2×D4—81no—
728C2×D4—81no—
729C2×D4—611no—
730C2×D4—611no—
731C2×D4—611no—
732C2×D4—611no—
733C2×D4—611no—
734C2×D4—1221no—
735C2×D4—1221no—
736C2×D4—1221no—
737C2×D4—1221no—
738C2×D4—1221no—
739C2×D4—1221no—
740C2×D4—1221no—
741C2×D4—1221no—
742C2×D4—1221no—
743C2×D4—1221no—
744C2×D4—4881no—
745C2×D4—4881no—
746C2×D4—4881no—
747C2×D4—2442no—
748C2×D4—2444no—
749C2×D4C2×C4×D6111yescharacteristic
750C2×D4C2×C4×D6111yescharacteristic
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—81no—
755C22×C4—611no—
756C22×C4—611no—
757C22×C4—611no—
758C22×C4—611no—
759C22×C4—611no—
760C22×C4—611no—
761C22×C4—611no—
762C22×C4—1221no—
763C22×C4—1221no—
764C22×C4—1221no—
765C22×C4—1221no—
766C22×C4—1221no—
767C22×C4—1221no—
768C22×C4—1221no—
769C22×C4—1221no—
770C22×C4—4881no—
771C22×C4C2×C4×D6111yescharacteristic
772C22×C4C2×C4×D6111yescharacteristic
773C22×C4D4×D6111yescharacteristic
774C22×C4D4×D6111yescharacteristic
775C22×C4D4×D6111yescharacteristic
776C22×C4C23×D6111yescharacteristic
777M16—4881no—
778M16—4881no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—81no—
782C2×C8—1221no—
783C2×C8—1221no—
784C2×C8—4881no—
785C4⋊C4—21no—
786C4⋊C4—81no—
787C4⋊C4—611no—
788C4⋊C4—611no—
789C4⋊C4—611no—
790C4⋊C4—611no—
791C4⋊C4—611no—
792C4⋊C4—611no—
793C4⋊C4—1221no—
794C4⋊C4—1221no—
795C4⋊C4—1221no—
796C4⋊C4—1221no—
797C4⋊C4—1221no—
798C4⋊C4—1221no—
799C4⋊C4—1221no—
800C4⋊C4—1221no—
801C4⋊C4—4881no—
802C4⋊C4—2442no—
803C4⋊C4C2×C4×D6111yescharacteristic
804C4⋊C4C2×C4×D6111yescharacteristic
805C22⋊C4—21no—
806C22⋊C4—21no—
807C22⋊C4—21no—
808C22⋊C4—21no—
809C22⋊C4—81no—
810C22⋊C4—611no—
811C22⋊C4—611no—
812C22⋊C4—611no—
813C22⋊C4—611no—
814C22⋊C4—611no—
815C22⋊C4—611no—
816C22⋊C4—611no—
817C22⋊C4—611no—
818C22⋊C4—1221no—
819C22⋊C4—1221no—
820C22⋊C4—1221no—
821C22⋊C4—1221no—
822C22⋊C4—1221no—
823C22⋊C4—1221no—
824C22⋊C4—1221no—
825C22⋊C4—1221no—
826C22⋊C4—1221no—
827C22⋊C4—1221no—
828C22⋊C4—1221no—
829C22⋊C4—1221no—
830C22⋊C4—1221no—
831C22⋊C4—1221no—
832C22⋊C4—1221no—
833C22⋊C4—4881no—
834C22⋊C4—4881no—
835C22⋊C4—4881no—
836C42—611no—
837C42—611no—
838C42—611no—
839C42—611no—
840C42—1221no—
841C42—1221no—
842C42—1221no—
843C42—4881no—
844C42—2442no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—41no—
850C23—41no—
851C23—42no—
852C23—81no—
853C23—81no—
854C23—611no—
855C23—611no—
856C23—1221no—
857C23—1221no—
858C23—1221no—
859C23—4881no—
860C23—4881no—
861C23—2441no—
862C23—2441no—
863C23—2442no—
864C23C22⋊C4×D6111yescharacteristic
865C23C22⋊C4×D6111yescharacteristic
866C23C2×D4×D6111yescharacteristic
867Q8—4881no—
868Q8—2441no—
869D4—41no—
870D4—41no—
871D4—41no—
872D4—41no—
873D4—41no—
874D4—41no—
875D4—81no—
876D4—81no—
877D4—81no—
878D4—1222no—
879D4—1222no—
880D4—4881no—
881D4—4881no—
882D4—4881no—
883D4—4881no—
884D4—4881no—
885D4—4881no—
886D4—2441no—
887D4—2442no—
888D4—2441no—
889D4—2441no—
890D4—2442no—
891D4—2442no—
892D4—2441no—
893D4—2441no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—81no—
909C2×C4—611no—
910C2×C4—611no—
911C2×C4—611no—
912C2×C4—611no—
913C2×C4—611no—
914C2×C4—611no—
915C2×C4—1222no—
916C2×C4—1221no—
917C2×C4—1221no—
918C2×C4—1221no—
919C2×C4—1221no—
920C2×C4—1221no—
921C2×C4—4881no—
922C2×C4—4881no—
923C2×C4—4881no—
924C2×C4—4881no—
925C2×C4—4881no—
926C2×C4—2441no—
927C2×C4—2441no—
928C2×C4—2441no—
929C2×C4—2441no—
930C2×C4—2442no—
931C2×C4—2441no—
932C2×C4—2441no—
933C2×C4—2441no—
934C2×C4—2441no—
935C2×C4—2441no—
936C2×C4—2441no—
937C2×C4—2441no—
938C2×C4C22⋊C4×D6111yescharacteristic
939C2×C4C22⋊C4×D6111yescharacteristic
940C2×C4C22×C4×D6111yescharacteristic
941C2×C4C2×D4×D6111yescharacteristic
942C8—41no—
943C8—41no—
944C8—2441no—
945C8—2441no—
946C22—21no—
947C22—21no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—81no—
961C22—81no—
962C22—162no—
963C22—1221no—
964C22—1221no—
965C22—1221no—
966C22—1221no—
967C22—1221no—
968C22—1221no—
969C22—9762no—
970C22—4881no—
971C22—4881no—
972C22—2441no—
973C22—2441no—
974C22—2441no—
975C22C2×C22⋊C4×D6111yescharacteristic
976C22#1684056311yescharacteristic
977C22#1684056811yescharacteristic
978C4—21no—
979C4—21no—
980C4—21no—
981C4—21no—
982C4—41no—
983C4—41no—
984C4—81no—
985C4—81no—
986C4—612no—
987C4—1221no—
988C4—1221no—
989C4—1221no—
990C4—1221no—
991C4—1221no—
992C4—4881no—
993C4—4881no—
994C4—2441no—
995C4—2441no—
996C4—2441no—
997C2—21no—
998C2—21no—
999C2—41no—
1000C2—41no—
1001C2—81no—
1002C2—81no—
1003C2—4881no—
1004C2—2441no—
1005C2—2441no—
1006C2#2145427711yescharacteristic
1007C2#2145434011yescharacteristic
1008C2#421×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1519C2
socleC22×C61C22×C22⋊C4
prime radical#21459845C2
cosocleC22×C4×C61C24
hypercenter#1519D61
hypocenterC61#17599
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1519

Complements

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

NH ≅ G/Ntype
2. #21454850C2semidirect
3. #21448461C2semidirect
4. #21444385C2semidirect
5. #21444376C2semidirect
6. #21444372C2semidirect
7. #21444360C2semidirect
8. #21444359C2semidirect
9. #21444348C2semidirect
10. #21444346C2semidirect
11. #21444341C2semidirect
12. #21444325C2semidirect
13. #21444312C2semidirect
14. #21444302C2semidirect
15. C61×#1519C2semidirect
16. #16840476C4semidirect
17. #16840467C4semidirect
18. #16840460C4semidirect
19. #16840459C4semidirect
21. #16840430C4semidirect
22. #16840409C4semidirect
24. #16840406C4semidirect
27. D4×C22⋊D61C4semidirect
42. #16839816C22semidirect
43. #16839812C22semidirect
44. #16839726C22semidirect
45. #16839724C22semidirect
46. C22⋊C8×D61C22semidirect
51. #16839625C22semidirect
52. #16839624C22semidirect
53. #16839621C22semidirect
54. #16839613C22semidirect
55. #16839607C22semidirect
56. #16839500C22semidirect
57. #16839500C22semidirect
58. #16839498C22semidirect
59. #16839498C22semidirect
60. #16839497C22semidirect
61. #16839497C22semidirect
64. #16839496C22semidirect
65. #16839496C22semidirect
66. #16839495C22semidirect
67. #16839495C22semidirect
69. C2×C22⋊C8×C61C22semidirect
70. C61×#380C22semidirect
73. C61×#327C22semidirect
74. C61×#327C22semidirect
497. #1519D61semidirect
552. C2×C22⋊C8C2×D61semidirect
560. #380C2×D61semidirect
577. #327C2×D61semidirect
578. #327C2×D61semidirect
579. C61#17599semidirect

Maximal subgroups

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

subgroupindex
#214598452
#214548502
#214484612
#214443852
#214443762
#214443722
#214443602
#214443592
#214443482
#214443462
#214443412
#214443252
#214443122
#214443022
C61×#15192
#1759961