Finite Group Databasebeta

← #29689676

Subgroups — #29689676

Order 15616.

1038 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#21459207C211yesmaximal, characteristic
2#21454382C211yesmaximal, characteristic, complemented
3#21448315C211yesmaximal, characteristic, complemented
4#21446798C211yesmaximal, characteristic, complemented
5#21446794C211yesmaximal, characteristic, complemented
6#21446649C211yesmaximal, characteristic, complemented
7#21446645C211yesmaximal, characteristic, complemented
8#21446122C211yesmaximal, characteristic, complemented
9#21446121C211yesmaximal, characteristic, complemented
10#21446119C211yesmaximal, characteristic, complemented
11#21445838C211yesmaximal, characteristic, complemented
12#21445838C211yesmaximal, characteristic, complemented
13#21445837C211yesmaximal, characteristic, complemented
14#21445837C211yesmaximal, characteristic, complemented
15C61×#1871C211yesmaximal, characteristic, complemented
16C22×#11758194C2211yescharacteristic
17#16840385C411yescharacteristic, complemented
18#16840385C411yescharacteristic, complemented
19#16840379C411yescharacteristic, complemented
20#16840379C411yescharacteristic, complemented
21#16840372C411yescharacteristic, complemented
22#16840372C411yescharacteristic, complemented
23#16840365C411yescharacteristic, complemented
24#16840365C411yescharacteristic, complemented
25#16840356—21no—
26#16840356—21no—
27#16840347—21no—
28#16840347—21no—
29#16840315C2211yescharacteristic
30#16840308C2211yescharacteristic
31#16840294—21no—
32#16840294—21no—
33#16840292—21no—
34#16840292—21no—
35#16840273C2211yescharacteristic
36#41×Dic61C2211yescharacteristic
37#16840230C2211yescharacteristic
38C2×#14519736C2211yescharacteristic
39#16839790—21no—
40#16839790—21no—
41#16839788—21no—
42#16839788—21no—
43#16839785C2211yescharacteristic
44#16839785C2211yescharacteristic
45#16839785C2211yescharacteristic
46#16839785C2211yescharacteristic
47C2×#14519705C2211yescharacteristic
48C2×#14519705C2211yescharacteristic
49C2×#14519704C2211yescharacteristic
50C2×#14519704C2211yescharacteristic
51C2×#14519703C2211yescharacteristic
52C2×#14519703C2211yescharacteristic
53#16839656—21no—
54#16839650—21no—
55#16839647—21no—
56#16839645—21no—
57C4×#11758196C2211yescharacteristic
58C4×#11758196C2211yescharacteristic
59C4×C22⋊Dic61C2211yescharacteristic
60#16839608C2211yescharacteristic
61C42×Dic61C2211yescharacteristic
62#16839523C2211yescharacteristic
63#16839523C2211yescharacteristic
64#16839522C2211yescharacteristic
65#16839522C2211yescharacteristic
66#16839521C2211yescharacteristic
67#16839521C2211yescharacteristic
68C22×M16×C61C2211yescharacteristic
69C61×#525C2211yescharacteristic
70C2×#104×C61C2211yescharacteristic
71C2×#104×C61C2211yescharacteristic
72C4×C22⋊C4×C61C2211yescharacteristic
73C61×#339C2211yescharacteristic
74C61×#339C2211yescharacteristic
75C2×#11758222C2311yescharacteristic
76C2×#11758194—21no—
77C2×#11758194—41no—
78C2×#11758194—41no—
79C2×#11758194C2311yescharacteristic
80C2×#11758194C2311yescharacteristic
81C22×#92418—21no—
82#14519776C2×C411yescharacteristic
83#14519776C2×C411yescharacteristic
84#14519775C2×C411yescharacteristic
85#14519773C2×C411yescharacteristic
86#14519772—21no—
87#14519772—21no—
88#14519770—21no—
89#14519770—21no—
90#14519770—21no—
91#14519770—21no—
92#14519770—21no—
93#14519770—21no—
94#14519768—21no—
95#14519768—21no—
96#14519768C2×C411yescharacteristic
97#14519768C2×C411yescharacteristic
98#14519767—21no—
99#14519767—21no—
100#14519766C2×C411yescharacteristic
101#14519764—21no—
102#14519764—21no—
103#14519764C2×C411yescharacteristic
104#14519763—21no—
105#14519763—21no—
106#14519761—21no—
107#14519761—21no—
108#14519760—21no—
109#14519759—21no—
110#14519759—21no—
111#14519759—21no—
112#14519759—21no—
113#14519758—21no—
114#14519758—21no—
115#14519757—21no—
116#14519757—21no—
117#14519756C2×C411yescharacteristic
118#14519756C2×C411yescharacteristic
119#14519754—21no—
120#14519754—21no—
121#14519754—21no—
122#14519754—21no—
123#14519751C2×C411yescharacteristic
124#14519751C2×C411yescharacteristic
125#14519749—21no—
126#14519749—21no—
127#14519749—21no—
128#14519749—21no—
129#14519748—21no—
130#14519748—21no—
131#14519746—21no—
132Q8×Dic61C2×C411yescharacteristic
133Q8×Dic61C2×C411yescharacteristic
134C4×Dic122—21no—
135C4×Dic122—21no—
136#14519742C2×C411yescharacteristic
137#14519742C2×C411yescharacteristic
138D4×Dic61—21no—
139D4×Dic61—21no—
140D4×Dic61C2×C411yescharacteristic
141D4×Dic61C2×C411yescharacteristic
142#14519739C2×C411yescharacteristic
143#14519739C2×C411yescharacteristic
144C4×C22⋊D61—21no—
145C4×C22⋊D61—21no—
146C4×C22⋊D61—21no—
147C4×C22⋊D61—21no—
148#14519737—21no—
149#14519737—21no—
150#14519736—21no—
151#14519736C2×C411yescharacteristic
152#14519736C2×C411yescharacteristic
153#14519736C2×C411yescharacteristic
154#14519736C2×C411yescharacteristic
155#14519736D411yescharacteristic
156#14519736D411yescharacteristic
157#14519736D411yescharacteristic
158#14519736D411yescharacteristic
159#14519736C2311yescharacteristic
160#14519734—21no—
161C2×C4⋊Dic61D411yescharacteristic
162C2×C4⋊Dic61D411yescharacteristic
163C2×#11758196—21no—
164C2×#11758196—21no—
165C2×C22⋊Dic61—21no—
166C2×C22⋊Dic61D411yescharacteristic
167C2×C22⋊Dic61D411yescharacteristic
168C2×C4×Dic61—21no—
169C2×C4×Dic61—21no—
170C2×C4×Dic61—21no—
171C2×C4×Dic61C2311yescharacteristic
172C2×C4×Dic61C2311yescharacteristic
173C2×C4×Dic61C2311yescharacteristic
174C2×C4×Dic61C2311yescharacteristic
175C42×D61—21no—
176#14519706—21no—
177#14519706—21no—
178#14519706—21no—
179#14519706—21no—
180#14519706—21no—
181#14519706—21no—
182#14519706—21no—
183#14519706—21no—
184#14519705—41no—
185#14519705—41no—
186#14519704—41no—
187#14519704—41no—
188#14519703—41no—
189#14519703—41no—
190#14519684—21no—
191#14519684—21no—
192#14519684—21no—
193#14519684—21no—
194#14519684—21no—
195C2×#41×C61C2311yescharacteristic
196C23×C4×C61C2311yescharacteristic
197C2×M16×C61—21no—
198C2×M16×C61—41no—
199C2×M16×C61—41no—
200C2×M16×C61C2311yescharacteristic
201C2×M16×C61C2311yescharacteristic
202C22×C8×C61—21no—
203#123×C61—21no—
204C22⋊Q8×C61C2×C411yescharacteristic
205C22⋊Q8×C61C2×C411yescharacteristic
206#121×C61C2×C411yescharacteristic
207#121×C61C2×C411yescharacteristic
208#120×C61—21no—
209C4×D4×C61—21no—
210C4×D4×C61—21no—
211#117×C61C2311yescharacteristic
212C2×C22⋊C4×C61—21no—
213C2×C42×C61C2311yescharacteristic
214C2×C42×C61C2311yescharacteristic
215#104×C61—41no—
216#104×C61—41no—
217#95×C61—21no—
218C24×C61C2×D411yescharacteristic
219#41×C61—21no—
220#41×C61—21no—
221#41×C61—21no—
222#41×C61—21no—
223C2×Q8×C61C22×C411yescharacteristic
224C2×D4×C61—21no—
225C2×D4×C61—21no—
226C2×D4×C61—21no—
227C2×D4×C61C22×C411yescharacteristic
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—21no—
235C22×C4×C61C22×C411yescharacteristic
236C22×C4×C61C22×C411yescharacteristic
237C22×C4×C61C2×D411yescharacteristic
238C22×C4×C61C2×D411yescharacteristic
239C22×C4×C61C2×D411yescharacteristic
240C22×C4×C61C2411yescharacteristic
241C2×C22⋊D61—21no—
242C2×C22⋊D61—21no—
243C2×C22⋊D61—21no—
244C2×C22⋊D61—21no—
245C2×C22⋊D61—21no—
246C22×Dic61—21no—
247C22×Dic61—21no—
248C22×Dic61—21no—
249C22×Dic61—21no—
250C22×Dic61C2×D411yescharacteristic
251C22×Dic61C2×D411yescharacteristic
252C22×Dic61C2×D411yescharacteristic
253C22×Dic61C2×D411yescharacteristic
254#11758222—21no—
255#11758222—21no—
256#11758222—21no—
257#11758222—21no—
258C2×D244C22×C411yescharacteristic
259C2×C4×D61—21no—
260C2×C4×D61—21no—
261C2×C4×D61—21no—
262C2×Dic122—21no—
263C2×Dic122—21no—
264C2×Dic122C22×C411yescharacteristic
265M16×C61—21no—
266M16×C61—21no—
267M16×C61—21no—
268M16×C61—21no—
269M16×C61—42no—
270C2×C8×C61—21no—
271C2×C8×C61—21no—
272C2×C8×C61—42no—
273C4⋊C4×C61—21no—
274C4⋊C4×C61—21no—
275C4⋊C4×C61C22×C411yescharacteristic
276C4⋊C4×C61C22×C411yescharacteristic
277C22⋊C4×C61—21no—
278C22⋊C4×C61—21no—
279C22⋊C4×C61—21no—
280C22⋊C4×C61—21no—
281C22⋊C4×C61—21no—
282C22⋊C4×C61—42no—
283C42×C61—21no—
284C42×C61—21no—
285C42×C61—21no—
286C42×C61—21no—
287C42×C61—21no—
288C22⋊Dic61—21no—
289C22⋊Dic61—21no—
290C22⋊Dic61—21no—
291C22⋊Dic61—21no—
292C22⋊Dic61—21no—
293C22⋊Dic61—21no—
294C22⋊Dic61—21no—
295C22⋊Dic61—42no—
296C22⋊Dic61C22⋊C411yescharacteristic
297C22⋊Dic61C22⋊C411yescharacteristic
298C22⋊Dic61C22⋊C411yescharacteristic
299C22⋊Dic61C22⋊C411yescharacteristic
300C22⋊Dic61C22⋊C411yescharacteristic
301C22⋊Dic61C22⋊C411yescharacteristic
302C22⋊Dic61C22⋊C411yescharacteristic
303C22⋊Dic61C22⋊C411yescharacteristic
304#11758198—21no—
305#11758198—21no—
306#11758198—21no—
307#11758198—21no—
308#11758198—21no—
309#11758198—21no—
310C4⋊Dic61—21no—
311C4⋊Dic61—21no—
312C4⋊Dic61—21no—
313C4⋊Dic61—21no—
314C4⋊Dic61C22⋊C411yescharacteristic
315C4⋊Dic61C22⋊C411yescharacteristic
316C4⋊Dic61C22⋊C411yescharacteristic
317C4⋊Dic61C22⋊C411yescharacteristic
318C4⋊Dic61C22⋊C411yescharacteristic
319C4⋊Dic61C22⋊C411yescharacteristic
320C4⋊Dic61C22⋊C411yescharacteristic
321C4⋊Dic61C22⋊C411yescharacteristic
322C4⋊Dic61C22×C411yescharacteristic
323C4⋊Dic61C22×C411yescharacteristic
324#11758196—21no—
325#11758196—21no—
326#11758196—21no—
327#11758196—21no—
328#11758196—21no—
329#11758196—21no—
330#11758196—21no—
331#11758196—21no—
332#11758196—21no—
333#11758196—21no—
334#11758196—42no—
335#11758196—42no—
336C4×Dic61—21no—
337C4×Dic61—21no—
338C4×Dic61—21no—
339C4×Dic61—21no—
340C4×Dic61—21no—
341C4×Dic61—21no—
342C4×Dic61—21no—
343C4×Dic61—21no—
344C4×Dic61—21no—
345C4×Dic61—42no—
346C4×Dic61—42no—
347C4×Dic61C22×C411yescharacteristic
348C4×Dic61C22×C411yescharacteristic
349C4×Dic61C22×C411yescharacteristic
350C4×Dic61C22×C411yescharacteristic
351C4×Dic61C2×D411yescharacteristic
352C4×Dic61C2×D411yescharacteristic
353C4×Dic61C2×D411yescharacteristic
354C4×Dic61C2×D411yescharacteristic
355#11758194—21no—
356#11758194—21no—
357#11758194—21no—
358#11758194—21no—
359#11758194—42no—
360C2×#92418—21no—
361C2×#92418—21no—
362C2×#92418—42no—
363C23×C61—21no—
364C23×C61—21no—
365C23×C61—21no—
366C23×C61—41no—
367C23×C61—41no—
368C23×C61C2×C22⋊C411yescharacteristic
369C23×C61C2×C22⋊C411yescharacteristic
370C23×C61C22×D411yescharacteristic
371C22×D61—21no—
372Q8×C61—21no—
373Q8×C61—21no—
374D4×C61—21no—
375D4×C61—21no—
376D4×C61—41no—
377D4×C61—41no—
378D4×C61—81no—
379D4×C61—81no—
380C2×C4×C61—21no—
381C2×C4×C61—21no—
382C2×C4×C61—21no—
383C2×C4×C61—21no—
384C2×C4×C61—21no—
385C2×C4×C61—21no—
386C2×C4×C61—21no—
387C2×C4×C61—21no—
388C2×C4×C61—21no—
389C2×C4×C61—21no—
390C2×C4×C61—22no—
391C2×C4×C61—21no—
392C2×C4×C61—21no—
393C2×C4×C61—21no—
394C2×C4×C61—41no—
395C2×C4×C61—41no—
396C2×C4×C61—41no—
397C2×C4×C61—41no—
398C2×C4×C61—41no—
399C2×C4×C61—41no—
400C2×C4×C61—41no—
401C2×C4×C61C2×C22⋊C411yescharacteristic
402C2×C4×C61C2×C22⋊C411yescharacteristic
403C2×C4×C61C23×C411yescharacteristic
404C2×C4×C61C22×D411yescharacteristic
405C2×C4×C61H(5,𝔽2)11yescharacteristic
406C2×C4×C61H(5,𝔽2)11yescharacteristic
407C2×C4×C612−1+411yescharacteristic
408C2×C4×C612−1+411yescharacteristic
409C22⋊D61—41no—
410C22⋊D61—41no—
411C22⋊D61—81no—
412C22⋊D61—81no—
413C22⋊D61—81no—
414C22⋊D61—81no—
415C2×Dic61—22no—
416C2×Dic61—21no—
417C2×Dic61—21no—
418C2×Dic61—21no—
419C2×Dic61—41no—
420C2×Dic61—41no—
421C2×Dic61—41no—
422C2×Dic61—41no—
423C2×Dic61—41no—
424C2×Dic61—41no—
425C2×Dic61—41no—
426C2×Dic61—41no—
427C2×Dic61—41no—
428C2×Dic61—81no—
429C2×Dic61—81no—
430C2×Dic61C2×C22⋊C411yescharacteristic
431C2×Dic61C2×C22⋊C411yescharacteristic
432C2×Dic61C2×C22⋊C411yescharacteristic
433C2×Dic61C2×C22⋊C411yescharacteristic
434C2×Dic61C2×C22⋊C411yescharacteristic
435C2×Dic61C2×C22⋊C411yescharacteristic
436C2×Dic61C2×C22⋊C411yescharacteristic
437C2×Dic61C2×C22⋊C411yescharacteristic
438D244—21no—
439D244—21no—
440C4×D61—41no—
441C4×D61—41no—
442C4×D61—81no—
443C4×D61—81no—
444Dic122—21no—
445Dic122—21no—
446Dic122—81no—
447Dic122—81no—
448C8×C61—41no—
449C8×C61—41no—
450#92418—41no—
451#92418—41no—
452#21858—611nomaximal, Sylow
453C22×C61—21no—
454C22×C61—21no—
455C22×C61—21no—
456C22×C61—21no—
457C22×C61—21no—
458C22×C61—21no—
459C22×C61—21no—
460C22×C61—21no—
461C22×C61—41no—
462C22×C61—41no—
463C22×C61—41no—
464C22×C61—81no—
465C22×C61—81no—
466C22×C61C22×C22⋊C411yescharacteristic
467C22×C61#53711yescharacteristic
468C22×C61#53711yescharacteristic
469C2×D61—41no—
470C2×D61—41no—
471C2×D61—41no—
472C4×C61—21no—
473C4×C61—21no—
474C4×C61—42no—
475C4×C61—41no—
476C4×C61—41no—
477C4×C61—41no—
478C4×C61—81no—
479C4×C61#52011yescharacteristic
480C4×C61#52011yescharacteristic
481C4×C61#53511yescharacteristic
482C4×C61#53611yescharacteristic
483Dic61—21no—
484Dic61—21no—
485Dic61—21no—
486Dic61—21no—
487Dic61—21no—
488Dic61—21no—
489Dic61—21no—
490Dic61—21no—
491Dic61—42no—
492Dic61—41no—
493Dic61—41no—
494Dic61—41no—
495Dic61—81no—
496#3455—611no—
497#2905—611no—
498#2298—611no—
499#1995—611no—
500#1994—611no—
501#1963—611no—
502#1962—611no—
503#1871—611no—
504#1871—611no—
505#1871—611no—
506#1871D6111yescharacteristic, complemented
507#1806—611no—
508#1806—611no—
509#1806—611no—
510#1806—611no—
511C2×C61—21no—
512C2×C61—21no—
513C2×C61—41no—
514C2×C61—41no—
515C2×C61—81no—
516C2×C61#231111yescharacteristic
517C2×C61#290111yescharacteristic
518C2×C61#290111yescharacteristic
519D61—81no—
520C22×M16—611no—
521C22×M16C2×D6111yescharacteristic
522#542—611no—
523#542—611no—
524#542—611no—
525#542—611no—
526#541—611no—
527#541—611no—
528#540—611no—
529#540—611no—
530#539—1221no—
531#539—1221no—
532#538—1221no—
533#538—1221no—
534#533—611no—
535#532—611no—
536#529—1221no—
537#529—1221no—
538#529—1221no—
539#529—1221no—
540#525—611no—
541#525C2×D6111yescharacteristic
542C4×#41—611no—
543C4×#41—611no—
544C2×#117—611no—
545#424—1221no—
546#424—1221no—
547#424—1221no—
548#424—1221no—
549#423—611no—
550#423—611no—
551#423—611no—
552#423—611no—
553C2×#104—611no—
554C2×#104—611no—
555C2×#104—611no—
556C2×#104—611no—
557C2×#104—611no—
558C2×#104—611no—
559C2×#104C2×D6111yescharacteristic
560C2×#104C2×D6111yescharacteristic
561#388—1221no—
562#388—1221no—
563#387—1221no—
564#387—1221no—
565C4×C4⋊C4—611no—
566C4×C4⋊C4—611no—
567C4×C22⋊C4—611no—
568C4×C22⋊C4C2×D6111yescharacteristic
569#376—611no—
570C43—611no—
571#339—611no—
572#339—611no—
573#339—611no—
574#339—611no—
575#339—611no—
576#339—611no—
577#339C2×D6111yescharacteristic
578#339C2×D6111yescharacteristic
579C61#2185811yescharacteristic, complemented, Sylow
580C2×#41—611no—
581C2×#41C22×D6111yescharacteristic
582C23×C4C22×D6111yescharacteristic
583C2×M16—21no—
584C2×M16—41no—
585C2×M16—41no—
586C2×M16—611no—
587C2×M16—611no—
588C2×M16—1221no—
589C2×M16—2441no—
590C2×M16—2441no—
591C2×M16C22×D6111yescharacteristic
592C2×M16C22×D6111yescharacteristic
593C22×C8—21no—
594C22×C8—1221no—
595C4⋊Q8—611no—
596C4⋊Q8—611no—
597C4⋊Q8—611no—
598#127—611no—
599#126—1221no—
600#126—1221no—
601#126—1221no—
602#126—1221no—
603#126—1221no—
604#126—1221no—
605#126—1221no—
606#126—1221no—
607#125—611no—
608#125—611no—
609#125—1221no—
610#125—1221no—
611#125—1221no—
612#125—1221no—
613#124—611no—
614#124—611no—
615#124—1221no—
616#124—1221no—
617#124—1221no—
618#124—1221no—
619#123—21no—
620#123—1221no—
621#123—1221no—
622#123—1221no—
623#123—1221no—
624#123—1221no—
625#123—1221no—
626#123—1221no—
627#123—1221no—
628#123—1221no—
629C22⋊Q8—611no—
630C22⋊Q8—611no—
631C22⋊Q8—1221no—
632C22⋊Q8—1221no—
633C22⋊Q8—1221no—
634C22⋊Q8—1221no—
635C22⋊Q8—1221no—
636C22⋊Q8—1221no—
637C22⋊Q8C4×D6111yescharacteristic
638C22⋊Q8C4×D6111yescharacteristic
639#121—611no—
640#121—611no—
641#121—1221no—
642#121—1221no—
643#121—1221no—
644#121—1221no—
645#121—1221no—
646#121—1221no—
647#121C4×D6111yescharacteristic
648#121C4×D6111yescharacteristic
649#120—21no—
650#120—1221no—
651C4×Q8—611no—
652C4×Q8—611no—
653C4×Q8—611no—
654C4×Q8—611no—
655C4×Q8—1221no—
656C4×Q8—1221no—
657C4×D4—21no—
658C4×D4—21no—
659C4×D4—611no—
660C4×D4—611no—
661C4×D4—611no—
662C4×D4—611no—
663C4×D4—1221no—
664C4×D4—1221no—
665C4×D4—1221no—
666C4×D4—1221no—
667C4×D4—1221no—
668C4×D4—1221no—
669C4×D4—1221no—
670C4×D4—1221no—
671#117—611no—
672#117—611no—
673#117—611no—
674#117—611no—
675#117—611no—
676#117—611no—
677#117—611no—
678#117—611no—
679#117—611no—
680#117—1221no—
681#117—1221no—
682#117C22×D6111yescharacteristic
683C2×C4⋊C4—611no—
684C2×C4⋊C4—611no—
685C2×C4⋊C4—1221no—
686C2×C4⋊C4—1221no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—611no—
689C2×C22⋊C4—611no—
690C2×C22⋊C4—1221no—
691C2×C42—611no—
692C2×C42—611no—
693C2×C42—611no—
694C2×C42—611no—
695C2×C42—1221no—
696C2×C42—1221no—
697C2×C42—1221no—
698C2×C42—1221no—
699C2×C42C22×D6111yescharacteristic
700C2×C42C22×D6111yescharacteristic
701C4⋊C8—1221no—
702C4⋊C8—1221no—
703C4⋊C8—1221no—
704C4⋊C8—1221no—
705C4⋊C8—1221no—
706C4⋊C8—1221no—
707C4⋊C8—1221no—
708C4⋊C8—1221no—
709#104—41no—
710#104—41no—
711#104—2441no—
712#104—2441no—
713#104—2441no—
714#104—2441no—
715#104—2441no—
716#104—2441no—
717#95—21no—
718#95—1221no—
719#95—1221no—
720#95—1221no—
721#95—1221no—
722#95—1221no—
723C24D4×D6111yescharacteristic
724#41—21no—
725#41—21no—
726#41—21no—
727#41—21no—
728#41—1221no—
729#41—1221no—
730#41—1221no—
731#41—1221no—
732C2×Q8—611no—
733C2×Q8—1221no—
734C2×Q8—1221no—
735C2×Q8C2×C4×D6111yescharacteristic
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—611no—
740C2×D4—1221no—
741C2×D4—1221no—
742C2×D4—1221no—
743C2×D4—1221no—
744C2×D4—1221no—
745C2×D4C2×C4×D6111yescharacteristic
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—611no—
754C22×C4—611no—
755C22×C4—611no—
756C22×C4—611no—
757C22×C4—1221no—
758C22×C4—1221no—
759C22×C4—1221no—
760C22×C4—1221no—
761C22×C4—1221no—
762C22×C4—1221no—
763C22×C4—1221no—
764C22×C4C2×C4×D6111yescharacteristic
765C22×C4C2×C4×D6111yescharacteristic
766C22×C4D4×D6111yescharacteristic
767C22×C4D4×D6111yescharacteristic
768C22×C4D4×D6111yescharacteristic
769C22×C4C23×D6111yescharacteristic
770M16—21no—
771M16—21no—
772M16—21no—
773M16—21no—
774M16—42no—
775M16—1221no—
776M16—1221no—
777M16—1221no—
778M16—1221no—
779M16—2442no—
780C2×C8—21no—
781C2×C8—21no—
782C2×C8—42no—
783C2×C8—1221no—
784C2×C8—1221no—
785C2×C8—2442no—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—611no—
789C4⋊C4—611no—
790C4⋊C4—611no—
791C4⋊C4—611no—
792C4⋊C4—611no—
793C4⋊C4—611no—
794C4⋊C4—611no—
795C4⋊C4—611no—
796C4⋊C4—611no—
797C4⋊C4—611no—
798C4⋊C4—1221no—
799C4⋊C4—1221no—
800C4⋊C4—1221no—
801C4⋊C4—1221no—
802C4⋊C4—1221no—
803C4⋊C4—1221no—
804C4⋊C4—1221no—
805C4⋊C4—1221no—
806C4⋊C4—1221no—
807C4⋊C4—1221no—
808C4⋊C4—1221no—
809C4⋊C4—1221no—
810C4⋊C4—1221no—
811C4⋊C4—1221no—
812C4⋊C4—2442no—
813C4⋊C4—2442no—
814C4⋊C4C2×C4×D6111yescharacteristic
815C4⋊C4C2×C4×D6111yescharacteristic
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—42no—
822C22⋊C4—611no—
823C22⋊C4—611no—
824C22⋊C4—611no—
825C22⋊C4—611no—
826C22⋊C4—611no—
827C22⋊C4—611no—
828C22⋊C4—611no—
829C22⋊C4—611no—
830C22⋊C4—1221no—
831C22⋊C4—1221no—
832C22⋊C4—1221no—
833C22⋊C4—1221no—
834C22⋊C4—1221no—
835C22⋊C4—1221no—
836C22⋊C4—1221no—
837C22⋊C4—1221no—
838C22⋊C4—1221no—
839C22⋊C4—1221no—
840C22⋊C4—1221no—
841C22⋊C4—1221no—
842C22⋊C4—1221no—
843C22⋊C4—2442no—
844C42—21no—
845C42—21no—
846C42—21no—
847C42—21no—
848C42—21no—
849C42—611no—
850C42—611no—
851C42—611no—
852C42—611no—
853C42—611no—
854C42—611no—
855C42—611no—
856C42—611no—
857C42—1221no—
858C42—1221no—
859C42—1221no—
860C42—1221no—
861C42—1221no—
862C42—1221no—
863C42—1221no—
864C42—1221no—
865C42—1221no—
866C42—2442no—
867C42—2442no—
868C23—21no—
869C23—21no—
870C23—21no—
871C23—41no—
872C23—41no—
873C23—1221no—
874C23C22⋊C4×D6111yescharacteristic
875C23C22⋊C4×D6111yescharacteristic
876C23C2×D4×D6111yescharacteristic
877Q8—21no—
878Q8—21no—
879Q8—1221no—
880Q8—1221no—
881Q8—4881no—
882Q8—4881no—
883D4—21no—
884D4—21no—
885D4—41no—
886D4—41no—
887D4—81no—
888D4—81no—
889D4—1221no—
890D4—1221no—
891D4—4881no—
892D4—4881no—
893D4—4881no—
894D4—4881no—
895D4—2441no—
896D4—2441no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—22no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—611no—
919C2×C4—611no—
920C2×C4—611no—
921C2×C4—611no—
922C2×C4—611no—
923C2×C4—611no—
924C2×C4—611no—
925C2×C4—611no—
926C2×C4—1222no—
927C2×C4—1221no—
928C2×C4—1221no—
929C2×C4—1221no—
930C2×C4—4881no—
931C2×C4—4881no—
932C2×C4—4881no—
933C2×C4—4881no—
934C2×C4—2441no—
935C2×C4—2441no—
936C2×C4—2441no—
937C2×C4—2441no—
938C2×C4—2441no—
939C2×C4—2441no—
940C2×C4—2441no—
941C2×C4—2441no—
942C2×C4—2441no—
943C2×C4—2441no—
944C2×C4—2441no—
945C2×C4C22⋊C4×D6111yescharacteristic
946C2×C4C22⋊C4×D6111yescharacteristic
947C2×C4C22×C4×D6111yescharacteristic
948C2×C4C2×D4×D6111yescharacteristic
949C2×C4#1451982211yescharacteristic
950C2×C4#1451982211yescharacteristic
951C2×C4#1451982411yescharacteristic
952C2×C4#1451982411yescharacteristic
953C8—41no—
954C8—41no—
955C8—2441no—
956C8—2441no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—21no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—81no—
969C22—81no—
970C22—2441no—
971C22—2441no—
972C22—2441no—
973C22C2×C22⋊C4×D6111yescharacteristic
974C22#1684033911yescharacteristic
975C22#1684033911yescharacteristic
976C4—21no—
977C4—21no—
978C4—42no—
979C4—41no—
980C4—41no—
981C4—41no—
982C4—81no—
983C4—1221no—
984C4—1221no—
985C4—1221no—
986C4—1221no—
987C4—1221no—
988C4—1221no—
989C4—1221no—
990C4—1221no—
991C4—4881no—
992C4—2442no—
993C4—2441no—
994C4—2441no—
995C4—2441no—
996C4#1684024111yescharacteristic
997C4#1684024111yescharacteristic
998C4#1684032711yescharacteristic
999C4#1684033411yescharacteristic
1000C2—21no—
1001C2—21no—
1002C2—41no—
1003C2—41no—
1004C2—81no—
1005C2—4881no—
1006C2#2144840611yescharacteristic
1007C2#2145436311yescharacteristic
1008C2#2145436511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1871C2
socleC22×C61C22×C22⋊C4
prime radical#21459207C2
cosocleC22×C4×C61C24
hypercenter#1871D61
hypocenterC61#21858
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1871

Complements

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

NH ≅ G/Ntype
2. #21454382C2semidirect
3. #21448315C2semidirect
4. #21446798C2semidirect
5. #21446794C2semidirect
6. #21446649C2semidirect
7. #21446645C2semidirect
8. #21446122C2semidirect
9. #21446121C2semidirect
10. #21446119C2semidirect
11. #21445838C2semidirect
12. #21445838C2semidirect
13. #21445837C2semidirect
14. #21445837C2semidirect
15. C61×#1871C2semidirect
17. #16840385C4semidirect
18. #16840385C4semidirect
19. #16840379C4semidirect
20. #16840379C4semidirect
21. #16840372C4semidirect
22. #16840372C4semidirect
23. #16840365C4semidirect
24. #16840365C4semidirect
506. #1871D61semidirect
579. C61#21858semidirect

Maximal subgroups

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

subgroupindex
#214592072
#214543822
#214483152
#214467982
#214467942
#214466492
#214466452
#214461222
#214461212
#214461192
#214458382
#214458372
C61×#18712
#2185861