Finite Group Databasebeta

← #29689678

Subgroups — #29689678

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#21459204C211yesmaximal, characteristic
2#21454381C211yesmaximal, characteristic, complemented
3#21448312C211yesmaximal, characteristic, complemented
4#21446798C211yesmaximal, characteristic, complemented
5#21446794C211yesmaximal, characteristic, complemented
6#21446649C211yesmaximal, characteristic, complemented
7#21446645C211yesmaximal, characteristic, complemented
8#21446120C211yesmaximal, characteristic, complemented
9#21446120C211yesmaximal, characteristic, complemented
10#21446118C211yesmaximal, characteristic, complemented
11#21446118C211yesmaximal, characteristic, complemented
12#21445840C211yesmaximal, characteristic, complemented
13#21445839C211yesmaximal, characteristic, complemented
14#21445836C211yesmaximal, characteristic, complemented
15C61×#1806C211yesmaximal, characteristic, complemented
16C2×M16×D61C2211yescharacteristic
17C2×M16×D61C2211yescharacteristic
18#16840384C411yescharacteristic, complemented
19#16840384C411yescharacteristic, complemented
20#16840377C411yescharacteristic, complemented
21#16840377C411yescharacteristic, complemented
22#16840370C411yescharacteristic, complemented
23#16840370C411yescharacteristic, complemented
24#16840363C411yescharacteristic, complemented
25#16840363C411yescharacteristic, complemented
26#16840354—21no—
27#16840354—21no—
28#16840345—21no—
29#16840345—21no—
30#16840315C2211yescharacteristic
31#16840308C2211yescharacteristic
32#16840296—21no—
33#16840296—21no—
34#16840290—21no—
35#16840290—21no—
36#16840274C2211yescharacteristic
37#16840269C2211yescharacteristic
38C4×#11758222C2211yescharacteristic
39C2×#14519734C2211yescharacteristic
40#16839787—21no—
41#16839787—21no—
42#16839787—21no—
43#16839787—21no—
44#16839786C2211yescharacteristic
45#16839785C2211yescharacteristic
46#16839785C2211yescharacteristic
47C2×#14519705C2211yescharacteristic
48C2×#14519705C2211yescharacteristic
49C2×#14519704C2211yescharacteristic
50C2×#14519704C2211yescharacteristic
51C2×#14519703C2211yescharacteristic
52C2×#14519703C2211yescharacteristic
53#16839654—21no—
54#16839652—21no—
55#16839649—21no—
56#16839643—21no—
57C4×C4⋊Dic61C2211yescharacteristic
58C4×#11758198C2211yescharacteristic
59C4×#11758198C2211yescharacteristic
60#16839608C2211yescharacteristic
61C42×Dic61C2211yescharacteristic
62#16839523C2211yescharacteristic
63#16839523C2211yescharacteristic
64#16839522C2211yescharacteristic
65#16839522C2211yescharacteristic
66#16839521C2211yescharacteristic
67#16839521C2211yescharacteristic
68C4×#41×C61C2211yescharacteristic
69C61×#423C2211yescharacteristic
70C2×#104×C61C2211yescharacteristic
71C2×#104×C61C2211yescharacteristic
72C4×C4⋊C4×C61C2211yescharacteristic
73C61×#339C2211yescharacteristic
74C61×#339C2211yescharacteristic
75C2×#11758222C2311yescharacteristic
76C22×C4×D61C2311yescharacteristic
77C2×#11758194C2311yescharacteristic
78C2×#11758194C2311yescharacteristic
79C2×#11758189—21no—
80C2×#11758189—21no—
81M16×D61—41no—
82M16×D61—41no—
83M16×D61—41no—
84M16×D61—41no—
85C2×C8×D61—21no—
86C2×C8×D61—21no—
87#14519776C2×C411yescharacteristic
88#14519776C2×C411yescharacteristic
89#14519775C2×C411yescharacteristic
90#14519773C2×C411yescharacteristic
91#14519772—21no—
92#14519772—21no—
93#14519771—21no—
94#14519771—21no—
95#14519771—21no—
96#14519771—21no—
97#14519770—21no—
98#14519770—21no—
99#14519769—21no—
100#14519769—21no—
101#14519768C2×C411yescharacteristic
102#14519768C2×C411yescharacteristic
103#14519767—21no—
104#14519767—21no—
105#14519766C2×C411yescharacteristic
106#14519765—21no—
107#14519765—21no—
108#14519764C2×C411yescharacteristic
109#14519763—21no—
110#14519763—21no—
111#14519762—21no—
112#14519762—21no—
113#14519761—21no—
114#14519760—21no—
115#14519760—21no—
116#14519760—21no—
117#14519760—21no—
118#14519759—21no—
119#14519759—21no—
120#14519758—21no—
121#14519757C2×C411yescharacteristic
122#14519757C2×C411yescharacteristic
123#14519756—21no—
124#14519756—21no—
125#14519755—21no—
126#14519755—21no—
127#14519754—21no—
128#14519754—21no—
129#14519753C2×C411yescharacteristic
130#14519753C2×C411yescharacteristic
131#14519752C2×C411yescharacteristic
132#14519752C2×C411yescharacteristic
133#14519751—21no—
134#14519751—21no—
135#14519750—21no—
136#14519750—21no—
137#14519749—21no—
138#14519749—21no—
139#14519748C2×C411yescharacteristic
140#14519748C2×C411yescharacteristic
141#14519747—21no—
142#14519745—21no—
143C4×Dic122—21no—
144C4×Dic122—21no—
145C4×Dic122C2×C411yescharacteristic
146C4×Dic122C2×C411yescharacteristic
147C4×D244—21no—
148C4×D244—21no—
149C4×D244C2×C411yescharacteristic
150C4×D244C2×C411yescharacteristic
151C4×C22⋊D61—21no—
152C4×C22⋊D61—21no—
153C4×C22⋊D61—21no—
154C4×C22⋊D61—21no—
155C4×C22⋊D61—21no—
156C4×C22⋊D61—21no—
157#14519736C2311yescharacteristic
158#14519734—21no—
159#14519734C2×C411yescharacteristic
160#14519734C2×C411yescharacteristic
161#14519734C2×C411yescharacteristic
162#14519734C2×C411yescharacteristic
163#14519734D411yescharacteristic
164#14519734D411yescharacteristic
165#14519734D411yescharacteristic
166#14519734D411yescharacteristic
167C2×C4⋊Dic61—21no—
168C2×#11758196D411yescharacteristic
169C2×#11758196D411yescharacteristic
170C2×#11758198—21no—
171C2×#11758198—21no—
172C2×#11758198D411yescharacteristic
173C2×#11758198D411yescharacteristic
174C2×C4×Dic61—21no—
175C2×C4×Dic61—21no—
176C2×C4×Dic61C2311yescharacteristic
177C2×C4×Dic61C2311yescharacteristic
178C2×C4×Dic61C2311yescharacteristic
179C42×D61—21no—
180C4⋊#92418—21no—
181C4⋊#92418—21no—
182#14519706—21no—
183#14519706—21no—
184#14519706—21no—
185#14519706—21no—
186#14519705—41no—
187#14519705—41no—
188#14519704—41no—
189#14519704—41no—
190#14519703—41no—
191#14519703—41no—
192#14519684—21no—
193#14519684—21no—
194#14519684—21no—
195#14519684—21no—
196#14519684—21no—
197C2×#41×C61C2311yescharacteristic
198C2×M16×C61C2311yescharacteristic
199C2×M16×C61C2311yescharacteristic
200C4×Q8×C61C2×C411yescharacteristic
201C4×Q8×C61C2×C411yescharacteristic
202C4×D4×C61—21no—
203C4×D4×C61—21no—
204C4×D4×C61C2×C411yescharacteristic
205C4×D4×C61C2×C411yescharacteristic
206#117×C61—21no—
207#117×C61C2311yescharacteristic
208C2×C4⋊C4×C61—21no—
209C2×C42×C61—21no—
210C2×C42×C61C2311yescharacteristic
211C2×C42×C61C2311yescharacteristic
212C2×C42×C61C2311yescharacteristic
213C4⋊C8×C61—21no—
214C4⋊C8×C61—21no—
215#104×C61—41no—
216#104×C61—41no—
217#95×C61—21no—
218C23×D61C2×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×C61C22×C411yescharacteristic
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61C2×D411yescharacteristic
232C22×C4×C61C2×D411yescharacteristic
233C22×C4×C61C2411yescharacteristic
234C2×C22⋊D61—21no—
235C2×C22⋊D61—21no—
236C2×C22⋊D61—21no—
237C2×C22⋊D61—21no—
238C2×C22⋊D61—21no—
239C22×Dic61—21no—
240C22×Dic61—21no—
241C22×Dic61C2×D411yescharacteristic
242C22×Dic61C2×D411yescharacteristic
243C22×Dic61C2×D411yescharacteristic
244#11758222—21no—
245#11758222—21no—
246#11758222—21no—
247#11758222—21no—
248C2×D244—21no—
249C2×D244—21no—
250C2×D244C22×C411yescharacteristic
251C2×C4×D61—21no—
252C2×C4×D61—21no—
253C2×C4×D61—21no—
254C2×C4×D61—21no—
255C2×C4×D61—21no—
256C2×C4×D61—21no—
257C2×C4×D61—21no—
258C2×C4×D61C22×C411yescharacteristic
259C2×C4×D61C22×C411yescharacteristic
260C2×C4×D61C2×D411yescharacteristic
261C2×C4×D61C2×D411yescharacteristic
262C2×Dic122—21no—
263C2×Dic122—21no—
264C2×Dic122C22×C411yescharacteristic
265M16×C61—21no—
266M16×C61—21no—
267M16×C61—21no—
268M16×C61—21no—
269C2×C8×C61—21no—
270C2×C8×C61—21no—
271C4⋊C4×C61—21no—
272C4⋊C4×C61—21no—
273C4⋊C4×C61—42no—
274C4⋊C4×C61C22×C411yescharacteristic
275C4⋊C4×C61C22×C411yescharacteristic
276C22⋊C4×C61—21no—
277C22⋊C4×C61—21no—
278C22⋊C4×C61—21no—
279C42×C61—21no—
280C42×C61—21no—
281C42×C61—21no—
282C42×C61—21no—
283C42×C61—21no—
284C42×C61—21no—
285C42×C61—21no—
286C42×C61C22×C411yescharacteristic
287C42×C61C22×C411yescharacteristic
288C42×C61C2×D411yescharacteristic
289C42×C61C2×D411yescharacteristic
290C22⋊Dic61—21no—
291C22⋊Dic61—21no—
292C22⋊Dic61—21no—
293C22⋊Dic61—21no—
294C22⋊Dic61—21no—
295#11758198—21no—
296#11758198—21no—
297#11758198—21no—
298#11758198—21no—
299#11758198—21no—
300#11758198—21no—
301#11758198—21no—
302#11758198—21no—
303#11758198—21no—
304#11758198—21no—
305#11758198—42no—
306#11758198—42no—
307#11758198C22⋊C411yescharacteristic
308#11758198C22⋊C411yescharacteristic
309#11758198C22⋊C411yescharacteristic
310#11758198C22⋊C411yescharacteristic
311#11758198C22⋊C411yescharacteristic
312#11758198C22⋊C411yescharacteristic
313#11758198C22⋊C411yescharacteristic
314#11758198C22⋊C411yescharacteristic
315C4⋊Dic61—21no—
316C4⋊Dic61—21no—
317C4⋊Dic61—21no—
318C4⋊Dic61—21no—
319C4⋊Dic61—42no—
320C4⋊Dic61C22×C411yescharacteristic
321C4⋊Dic61C22×C411yescharacteristic
322#11758196—21no—
323#11758196—21no—
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#11758196C22⋊C411yescharacteristic
333#11758196C22⋊C411yescharacteristic
334#11758196C22⋊C411yescharacteristic
335#11758196C22⋊C411yescharacteristic
336#11758196C22⋊C411yescharacteristic
337#11758196C22⋊C411yescharacteristic
338#11758196C22⋊C411yescharacteristic
339#11758196C22⋊C411yescharacteristic
340C4×Dic61—21no—
341C4×Dic61—21no—
342C4×Dic61—21no—
343C4×Dic61—21no—
344C4×Dic61—21no—
345C4×Dic61—21no—
346C4×Dic61—21no—
347C4×Dic61—42no—
348C4×Dic61—42no—
349C4×Dic61C22×C411yescharacteristic
350C4×Dic61C22×C411yescharacteristic
351C4×Dic61C2×D411yescharacteristic
352C4×Dic61C2×D411yescharacteristic
353#11758194—21no—
354#11758194—21no—
355#11758194—21no—
356#11758194—21no—
357C2×#92418—21no—
358C2×#92418—21no—
359#11758189—42no—
360#11758189—42no—
361C8×D61—42no—
362C8×D61—42no—
363C23×C61—21no—
364C23×C61C22×D411yescharacteristic
365C22×D61—21no—
366C22×D61—21no—
367C22×D61—21no—
368C22×D61—41no—
369C22×D61—41no—
370C22×D61C2×C22⋊C411yescharacteristic
371C22×D61C2×C22⋊C411yescharacteristic
372Q8×C61—21no—
373Q8×C61—21no—
374D4×C61—21no—
375D4×C61—21no—
376D4×C61—41no—
377D4×C61—41no—
378C2×C4×C61—22no—
379C2×C4×C61—21no—
380C2×C4×C61—21no—
381C2×C4×C61—21no—
382C2×C4×C61—41no—
383C2×C4×C61—41no—
384C2×C4×C61—41no—
385C2×C4×C61—41no—
386C2×C4×C61—41no—
387C2×C4×C61—41no—
388C2×C4×C61—41no—
389C2×C4×C61—41no—
390C2×C4×C61—41no—
391C2×C4×C61—81no—
392C2×C4×C61—81no—
393C2×C4×C61C2×C22⋊C411yescharacteristic
394C2×C4×C61C2×C22⋊C411yescharacteristic
395C2×C4×C61C2×C22⋊C411yescharacteristic
396C2×C4×C61C2×C22⋊C411yescharacteristic
397C2×C4×C61C23×C411yescharacteristic
398C2×C4×C61C22×D411yescharacteristic
399C2×C4×C61H(5,𝔽2)11yescharacteristic
400C2×C4×C61H(5,𝔽2)11yescharacteristic
401C2×C4×C612−1+411yescharacteristic
402C2×C4×C612−1+411yescharacteristic
403C22⋊D61—41no—
404C22⋊D61—41no—
405C22⋊D61—81no—
406C22⋊D61—81no—
407C22⋊D61—81no—
408C22⋊D61—81no—
409C2×Dic61—21no—
410C2×Dic61—21no—
411C2×Dic61—22no—
412C2×Dic61—21no—
413C2×Dic61—21no—
414C2×Dic61—21no—
415C2×Dic61—41no—
416C2×Dic61—41no—
417C2×Dic61—41no—
418C2×Dic61—41no—
419C2×Dic61—41no—
420C2×Dic61—41no—
421C2×Dic61—41no—
422C2×Dic61C2×C22⋊C411yescharacteristic
423C2×Dic61C2×C22⋊C411yescharacteristic
424C2×Dic61C2×C22⋊C411yescharacteristic
425C2×Dic61C2×C22⋊C411yescharacteristic
426C2×Dic61C2×C22⋊C411yescharacteristic
427C2×Dic61C2×C22⋊C411yescharacteristic
428D244—21no—
429D244—21no—
430D244—81no—
431D244—81no—
432C4×D61—21no—
433C4×D61—21no—
434C4×D61—21no—
435C4×D61—21no—
436C4×D61—21no—
437C4×D61—21no—
438C4×D61—21no—
439C4×D61—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—41no—
456C22×C61—41no—
457C22×C61—41no—
458C22×C61C22×C22⋊C411yescharacteristic
459C22×C61#53711yescharacteristic
460C22×C61#53711yescharacteristic
461C2×D61—21no—
462C2×D61—21no—
463C2×D61—21no—
464C2×D61—21no—
465C2×D61—21no—
466C2×D61—21no—
467C2×D61—41no—
468C2×D61—41no—
469C2×D61—41no—
470C2×D61—81no—
471C2×D61—81no—
472C4×C61—21no—
473C4×C61—21no—
474C4×C61—21no—
475C4×C61—21no—
476C4×C61—42no—
477C4×C61—41no—
478C4×C61—41no—
479C4×C61—41no—
480C4×C61—81no—
481C4×C61#52011yescharacteristic
482C4×C61#52011yescharacteristic
483C4×C61#53511yescharacteristic
484C4×C61#53611yescharacteristic
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#1871—611no—
507#1806—611no—
508#1806—611no—
509#1806—611no—
510#1806D6111yescharacteristic, complemented
511C2×C61—21no—
512C2×C61—21no—
513C2×C61—81no—
514C2×C61#231111yescharacteristic
515C2×C61#290111yescharacteristic
516C2×C61#290111yescharacteristic
517D61—41no—
518D61—41no—
519D61—81no—
520C22×M16—611no—
521C22×M16—611no—
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#525—611no—
542C4×#41—611no—
543C4×#41C2×D6111yescharacteristic
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#423C2×D6111yescharacteristic
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⋊C4C2×D6111yescharacteristic
567C4×C22⋊C4—611no—
568C4×C22⋊C4—611no—
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×C4—611no—
583C2×M16—611no—
584C2×M16—611no—
585C2×M16—1221no—
586C2×M16—1221no—
587C2×M16—2441no—
588C2×M16—2441no—
589C2×M16—2441no—
590C2×M16—2441no—
591C2×M16C22×D6111yescharacteristic
592C2×M16C22×D6111yescharacteristic
593C22×C8—1221no—
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—1221no—
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—611no—
632C22⋊Q8—611no—
633C22⋊Q8—1221no—
634C22⋊Q8—1221no—
635C22⋊Q8—1221no—
636C22⋊Q8—1221no—
637C22⋊Q8—1221no—
638C22⋊Q8—1221no—
639#121—611no—
640#121—611no—
641#121—611no—
642#121—611no—
643#121—1221no—
644#121—1221no—
645#121—1221no—
646#121—1221no—
647#121—1221no—
648#121—1221no—
649#120—1221no—
650#120—1221no—
651C4×Q8—611no—
652C4×Q8—611no—
653C4×Q8—1221no—
654C4×Q8—1221no—
655C4×Q8C4×D6111yescharacteristic
656C4×Q8C4×D6111yescharacteristic
657C4×D4—21no—
658C4×D4—21no—
659C4×D4—611no—
660C4×D4—611no—
661C4×D4—1221no—
662C4×D4—1221no—
663C4×D4—1221no—
664C4×D4—1221no—
665C4×D4—1221no—
666C4×D4—1221no—
667C4×D4—1221no—
668C4×D4—1221no—
669C4×D4C4×D6111yescharacteristic
670C4×D4C4×D6111yescharacteristic
671#117—21no—
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—611no—
681#117—1221no—
682#117C22×D6111yescharacteristic
683C2×C4⋊C4—21no—
684C2×C4⋊C4—611no—
685C2×C4⋊C4—611no—
686C2×C4⋊C4—1221no—
687C2×C22⋊C4—611no—
688C2×C22⋊C4—611no—
689C2×C22⋊C4—1221no—
690C2×C22⋊C4—1221no—
691C2×C42—21no—
692C2×C42—611no—
693C2×C42—611no—
694C2×C42—611no—
695C2×C42—1221no—
696C2×C42—1221no—
697C2×C42—1221no—
698C2×C42C22×D6111yescharacteristic
699C2×C42C22×D6111yescharacteristic
700C2×C42C22×D6111yescharacteristic
701C4⋊C8—21no—
702C4⋊C8—21no—
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—
723C24—611no—
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—611no—
738C2×D4—1221no—
739C2×D4—1221no—
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—611no—
752C22×C4—611no—
753C22×C4—611no—
754C22×C4—611no—
755C22×C4—611no—
756C22×C4—611no—
757C22×C4—611no—
758C22×C4—1221no—
759C22×C4—1221no—
760C22×C4—1221no—
761C22×C4—1221no—
762C22×C4—1221no—
763C22×C4—1221no—
764C22×C4—1221no—
765C22×C4—1221no—
766C22×C4—1221no—
767C22×C4D4×D6111yescharacteristic
768C22×C4D4×D6111yescharacteristic
769C22×C4C23×D6111yescharacteristic
770M16—21no—
771M16—21no—
772M16—21no—
773M16—21no—
774M16—1221no—
775M16—1221no—
776M16—1221no—
777M16—1221no—
778M16—2442no—
779M16—2442no—
780C2×C8—21no—
781C2×C8—21no—
782C2×C8—1221no—
783C2×C8—1221no—
784C2×C8—2442no—
785C2×C8—2442no—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—42no—
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—611no—
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—1221no—
813C4⋊C4—2442no—
814C4⋊C4C2×C4×D6111yescharacteristic
815C4⋊C4C2×C4×D6111yescharacteristic
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—611no—
820C22⋊C4—611no—
821C22⋊C4—611no—
822C22⋊C4—611no—
823C22⋊C4—611no—
824C22⋊C4—611no—
825C22⋊C4—611no—
826C22⋊C4—611no—
827C22⋊C4—1221no—
828C22⋊C4—1221no—
829C22⋊C4—1221no—
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—2442no—
843C22⋊C4—2442no—
844C42—21no—
845C42—21no—
846C42—21no—
847C42—21no—
848C42—21no—
849C42—21no—
850C42—21no—
851C42—611no—
852C42—611no—
853C42—611no—
854C42—611no—
855C42—1221no—
856C42—1221no—
857C42—1221no—
858C42—1221no—
859C42—1221no—
860C42—1221no—
861C42—1221no—
862C42—2442no—
863C42—2442no—
864C42C2×C4×D6111yescharacteristic
865C42C2×C4×D6111yescharacteristic
866C42D4×D6111yescharacteristic
867C42D4×D6111yescharacteristic
868C23—21no—
869C23—611no—
870C23—611no—
871C23—1221no—
872C23—1221no—
873C23—1221no—
874C23—2441no—
875C23—2441no—
876C23C2×D4×D6111yescharacteristic
877Q8—21no—
878Q8—21no—
879Q8—1221no—
880Q8—1221no—
881Q8—4881no—
882Q8—4881no—
883D4—21no—
884D4—21no—
885D4—41no—
886D4—41no—
887D4—1221no—
888D4—1221no—
889D4—4881no—
890D4—4881no—
891D4—4881no—
892D4—4881no—
893D4—4881no—
894D4—4881no—
895D4—2441no—
896D4—2441no—
897C2×C4—22no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—81no—
911C2×C4—81no—
912C2×C4—611no—
913C2×C4—611no—
914C2×C4—611no—
915C2×C4—611no—
916C2×C4—611no—
917C2×C4—611no—
918C2×C4—1221no—
919C2×C4—1221no—
920C2×C4—1221no—
921C2×C4—1221no—
922C2×C4—1221no—
923C2×C4—1221no—
924C2×C4—1221no—
925C2×C4—1221no—
926C2×C4—1221no—
927C2×C4—1221no—
928C2×C4—1222no—
929C2×C4—1221no—
930C2×C4—1221no—
931C2×C4—1221no—
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×C4C22⋊C4×D6111yescharacteristic
944C2×C4C22⋊C4×D6111yescharacteristic
945C2×C4C22⋊C4×D6111yescharacteristic
946C2×C4C22⋊C4×D6111yescharacteristic
947C2×C4C22×C4×D6111yescharacteristic
948C2×C4C2×D4×D6111yescharacteristic
949C2×C4#1451982211yescharacteristic
950C2×C4#1451982311yescharacteristic
951C2×C4#1451982411yescharacteristic
952C2×C4#1451982511yescharacteristic
953C8—41no—
954C8—41no—
955C8—2441no—
956C8—2441no—
957C22—21no—
958C22—21no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—1221no—
963C22—1221no—
964C22—1221no—
965C22—1221no—
966C22—1221no—
967C22—1221no—
968C22—4881no—
969C22—4881no—
970C22—2441no—
971C22—2441no—
972C22—2441no—
973C22C2×C22⋊C4×D6111yescharacteristic
974C22#1684034111yescharacteristic
975C22#1684034211yescharacteristic
976C4—21no—
977C4—21no—
978C4—21no—
979C4—21no—
980C4—42no—
981C4—41no—
982C4—41no—
983C4—41no—
984C4—81no—
985C4—1221no—
986C4—1221no—
987C4—1221no—
988C4—1221no—
989C4—1221no—
990C4—1221no—
991C4—4881no—
992C4—2442no—
993C4—2441no—
994C4—2441no—
995C4—2441no—
996C4#1684024211yescharacteristic
997C4#1684024311yescharacteristic
998C4#1684032811yescharacteristic
999C4#1684033511yescharacteristic
1000C2—21no—
1001C2—21no—
1002C2—81no—
1003C2—4881no—
1004C2—2441no—
1005C2—2441no—
1006C2#2144840811yescharacteristic
1007C2#2145436311yescharacteristic
1008C2#2145436511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1806C2
socleC22×C61C22×C22⋊C4
prime radical#21459204C2
cosocleC22×C4×C61C24
hypercenter#1806D61
hypocenterC61#21858
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
2. #21454381C2semidirect
3. #21448312C2semidirect
4. #21446798C2semidirect
5. #21446794C2semidirect
6. #21446649C2semidirect
7. #21446645C2semidirect
8. #21446120C2semidirect
9. #21446120C2semidirect
10. #21446118C2semidirect
11. #21446118C2semidirect
12. #21445840C2semidirect
13. #21445839C2semidirect
14. #21445836C2semidirect
15. C61×#1806C2semidirect
18. #16840384C4semidirect
19. #16840384C4semidirect
20. #16840377C4semidirect
21. #16840377C4semidirect
22. #16840370C4semidirect
23. #16840370C4semidirect
24. #16840363C4semidirect
25. #16840363C4semidirect
510. #1806D61semidirect
579. C61#21858semidirect

Maximal subgroups

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

subgroupindex
#214592042
#214543812
#214483122
#214467982
#214467942
#214466492
#214466452
#214461202
#214461182
#214458402
#214458392
#214458362
C61×#18062
#2185861