Finite Group Databasebeta

← #29696920

Subgroups — #29696920

Order 15616.

1058 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459412C211yesmaximal, characteristic
2M16×Dic122C211yesmaximal, characteristic, complemented
3#21448291C211yesmaximal, characteristic, complemented
4#21446738C211yesmaximal, characteristic, complemented
5#21446736C211yesmaximal, characteristic, complemented
6#21446736C211yesmaximal, characteristic, complemented
7#21446651C211yesmaximal, characteristic, complemented
8#21446649C211yesmaximal, characteristic, complemented
9#21446645C211yesmaximal, characteristic, complemented
10#21445839C211yesmaximal, characteristic, complemented
11#21445838C211yesmaximal, characteristic, complemented
12#21445838C211yesmaximal, characteristic, complemented
13#21445628C211yesmaximal, characteristic, complemented
14#21445623C211yesmaximal, characteristic, complemented
15C61×#1759C211yesmaximal, characteristic, complemented
16#16840497C411yescharacteristic, complemented
17#16840495C411yescharacteristic, complemented
18#16840495C411yescharacteristic, complemented
19#16840490C411yescharacteristic, complemented
20#16840484C411yescharacteristic, complemented
21#16840484C411yescharacteristic, complemented
22#16840482C411yescharacteristic, complemented
23#16840461—21no—
24#16840461—21no—
25#16840458—21no—
26#16840433C411yescharacteristic, complemented
27#16840421—21no—
28#16840312C2211yescharacteristic
29#16840308C2211yescharacteristic
30#16840308C2211yescharacteristic
31#16840296—21no—
32#16840290—21no—
33#16840290—21no—
34C4×#11758222—21no—
35#16840230C2211yescharacteristic
36#16840230C2211yescharacteristic
37C2×C4×Dic122C2211yescharacteristic
38#16839892—21no—
39#16839890—21no—
40#16839890—21no—
41C8×Dic122—21no—
42#16839786C2211yescharacteristic
43#16839785C2211yescharacteristic
44#16839785C2211yescharacteristic
45C2×#14519705C2211yescharacteristic
46C2×#14519705C2211yescharacteristic
47C2×#14519705C2211yescharacteristic
48C2×#14519705C2211yescharacteristic
49C2×#14519704C2211yescharacteristic
50C2×#14519704C2211yescharacteristic
51C2×#14519703C2211yescharacteristic
52C2×#14519703C2211yescharacteristic
53C2×#14519703C2211yescharacteristic
54C2×#14519703C2211yescharacteristic
55M16×Dic61C2211yescharacteristic
56M16×Dic61C2211yescharacteristic
57#16839666—21no—
58#16839659—21no—
59#16839649—21no—
60#16839645—21no—
61C4×#11758196C2211yescharacteristic
62C4×#11758196C2211yescharacteristic
63C4×C4⋊Dic61C2211yescharacteristic
64#16839608C2211yescharacteristic
65C42×Dic61C2211yescharacteristic
66#16839521C2211yescharacteristic
67#16839521C2211yescharacteristic
68C4×#41×C61C2211yescharacteristic
69C2×#104×C61C2211yescharacteristic
70C2×#104×C61C2211yescharacteristic
71C4×M16×C61C2211yescharacteristic
72C61×#376C2211yescharacteristic
73C61×#339C2211yescharacteristic
74C61×#339C2211yescharacteristic
75C2×#11758222—21no—
76C2×#11758222C2311yescharacteristic
77C2×#11758222C2311yescharacteristic
78C22×Dic122D411yescharacteristic
79C2×#11758194C2311yescharacteristic
80C2×#11758194C2311yescharacteristic
81#14519777C2×C411yescharacteristic
82#14519775C2×C411yescharacteristic
83#14519775C2×C411yescharacteristic
84#14519774C2×C411yescharacteristic
85#14519773C2×C411yescharacteristic
86#14519773C2×C411yescharacteristic
87#14519772—21no—
88#14519772—21no—
89#14519771—21no—
90#14519771—21no—
91#14519770—21no—
92#14519770—21no—
93#14519769—21no—
94#14519767—21no—
95#14519767—21no—
96#14519766C2×C411yescharacteristic
97#14519766C2×C411yescharacteristic
98#14519765—21no—
99#14519765C2×C411yescharacteristic
100#14519765C2×C411yescharacteristic
101#14519764C2×C411yescharacteristic
102#14519764C2×C411yescharacteristic
103#14519763—21no—
104#14519763—21no—
105#14519762—21no—
106#14519762—21no—
107#14519760—21no—
108#14519760—21no—
109#14519759—21no—
110#14519759—21no—
111#14519756—21no—
112#14519755—21no—
113#14519755—21no—
114#14519751—21no—
115#14519751—21no—
116#14519751—21no—
117#14519750—21no—
118#14519750—21no—
119#14519749—21no—
120#14519749—21no—
121#14519749—21no—
122#14519749—21no—
123C4×Dic122—21no—
124C4×Dic122C2×C411yescharacteristic
125C4×Dic122C2×C411yescharacteristic
126C4×Dic122C2×C411yescharacteristic
127C4×Dic122C2×C411yescharacteristic
128C4×Dic122D411yescharacteristic
129C4×Dic122D411yescharacteristic
130C4×Dic122D411yescharacteristic
131C4×Dic122D411yescharacteristic
132#14519742C2×C411yescharacteristic
133#14519742C2×C411yescharacteristic
134#14519742C2×C411yescharacteristic
135#14519742C2×C411yescharacteristic
136C4×D244—21no—
137C4×D244—21no—
138C4×D244—21no—
139#14519739C2×C411yescharacteristic
140#14519739C2×C411yescharacteristic
141#14519739C2×C411yescharacteristic
142#14519739C2×C411yescharacteristic
143C4×C22⋊D61—21no—
144C4×C22⋊D61—21no—
145C4×C22⋊D61—21no—
146C4×C22⋊D61—21no—
147C4×C22⋊D61—21no—
148C4×C22⋊D61—21no—
149#14519737—21no—
150#14519737—21no—
151#14519737—21no—
152#14519737—21no—
153#14519736—21no—
154#14519734—21no—
155#14519734—21no—
156#14519734—21no—
157#14519734—21no—
158C2×C4⋊Dic61—21no—
159C2×C4⋊Dic61D411yescharacteristic
160C2×#11758196—21no—
161C2×#11758196—21no—
162C2×#11758196D411yescharacteristic
163C2×#11758196D411yescharacteristic
164C2×C4×Dic61—21no—
165C2×C4×Dic61—21no—
166C2×C4×Dic61C2311yescharacteristic
167C2×C4×Dic61C2311yescharacteristic
168C2×C4×Dic61C2311yescharacteristic
169C2×C4×Dic61C2311yescharacteristic
170C42×D61—21no—
171C42×D61—21no—
172C4⋊#92418—21no—
173C4⋊#92418—21no—
174#14519706—21no—
175#14519706—21no—
176#14519706—21no—
177#14519706—21no—
178#14519705—22no—
179#14519705—22no—
180#14519705—41no—
181#14519705—41no—
182#14519704—41no—
183#14519704—41no—
184#14519703—22no—
185#14519703—22no—
186#14519703—41no—
187#14519703—41no—
188#14519687—21no—
189#14519687—21no—
190C8×Dic61—21no—
191C8×Dic61—21no—
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×C42×C61—21no—
209C2×C42×C61C2311yescharacteristic
210C2×C42×C61C2311yescharacteristic
211C2×C42×C61C2311yescharacteristic
212#104×C61—22no—
213#104×C61—22no—
214#97×C61—21no—
215C4×C8×C61—21no—
216#95×C61—21no—
217#95×C61—21no—
218#41×C61—21no—
219#41×C61—21no—
220#41×C61—21no—
221#41×C61—21no—
222C2×Q8×C61C22×C411yescharacteristic
223C2×D4×C61—21no—
224C2×D4×C61C22×C411yescharacteristic
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61C2×D411yescharacteristic
231C22×C4×C61C2×D411yescharacteristic
232C22×C4×C61C2411yescharacteristic
233C2×C22⋊D61—21no—
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
244C22×Dic61C2×D411yescharacteristic
245#11758222—21no—
246#11758222—21no—
247#11758222—21no—
248#11758222—21no—
249#11758222—21no—
250#11758222—21no—
251#11758222—21no—
252#11758222—21no—
253#11758222—44no—
254C2×D244—21no—
255C2×D244—21no—
256C2×D244C22×C411yescharacteristic
257C2×D244C22×C411yescharacteristic
258C2×C4×D61—21no—
259C2×C4×D61—21no—
260C2×C4×D61—21no—
261C2×C4×D61—21no—
262C2×C4×D61—21no—
263C2×C4×D61—21no—
264C2×Dic122—42no—
265C2×Dic122C22⋊C411yescharacteristic
266C2×Dic122C22⋊C411yescharacteristic
267C2×Dic122C22⋊C411yescharacteristic
268C2×Dic122C22⋊C411yescharacteristic
269C2×Dic122C22×C411yescharacteristic
270C2×Dic122C22×C411yescharacteristic
271M16×C61—21no—
272M16×C61—21no—
273M16×C61—21no—
274M16×C61#4112yescomplemented
275C2×C8×C61—21no—
276C2×C8×C61—21no—
277C4⋊C4×C61—21no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61C22×C411yescharacteristic
280C4⋊C4×C61C22×C411yescharacteristic
281C22⋊C4×C61—21no—
282C22⋊C4×C61—21no—
283C22⋊C4×C61—21no—
284C42×C61—21no—
285C42×C61—21no—
286C42×C61—21no—
287C42×C61—21no—
288C42×C61—21no—
289C42×C61—21no—
290C42×C61C22×C411yescharacteristic
291C42×C61C22×C411yescharacteristic
292C42×C61C2×D411yescharacteristic
293C42×C61C2×D411yescharacteristic
294C42×C61#4112yescomplemented
295C22⋊Dic61—21no—
296C22⋊Dic61—21no—
297C22⋊Dic61—21no—
298C22⋊Dic61—21no—
299#11758198—21no—
300#11758198—21no—
301#11758198—21no—
302#11758198—21no—
303#11758198—21no—
304#11758198—21no—
305#11758198—21no—
306#11758198—21no—
307#11758198—21no—
308#11758198—21no—
309#11758198—21no—
310#11758198—21no—
311C4⋊Dic61—21no—
312C4⋊Dic61—21no—
313C4⋊Dic61—42no—
314C4⋊Dic61C22⋊C411yescharacteristic
315C4⋊Dic61C22⋊C411yescharacteristic
316C4⋊Dic61C22⋊C411yescharacteristic
317C4⋊Dic61C22⋊C411yescharacteristic
318#11758196—21no—
319#11758196—21no—
320#11758196—21no—
321#11758196—21no—
322#11758196—21no—
323#11758196—21no—
324#11758196—21no—
325#11758196—21no—
326#11758196—42no—
327#11758196—42no—
328#11758196C22⋊C411yescharacteristic
329#11758196C22⋊C411yescharacteristic
330#11758196C22⋊C411yescharacteristic
331#11758196C22⋊C411yescharacteristic
332#11758196C22⋊C411yescharacteristic
333#11758196C22⋊C411yescharacteristic
334#11758196C22⋊C411yescharacteristic
335#11758196C22⋊C411yescharacteristic
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—42no—
345C4×Dic61—42no—
346C4×Dic61C22×C411yescharacteristic
347C4×Dic61C22×C411yescharacteristic
348C4×Dic61C22×C411yescharacteristic
349C4×Dic61C22×C411yescharacteristic
350C4×Dic61C2×D411yescharacteristic
351C4×Dic61C2×D411yescharacteristic
352C4×Dic61C2×D411yescharacteristic
353C4×Dic61C2×D411yescharacteristic
354#11758194—21no—
355#11758194—21no—
356#11758194—21no—
357#11758194—21no—
358C2×#92418—21no—
359C2×#92418—21no—
360C23×C61—21no—
361C23×C61C22×D411yescharacteristic
362C22×D61—21no—
363C22×D61—21no—
364Q8×C61—21no—
365Q8×C61—21no—
366D4×C61—21no—
367D4×C61—21no—
368D4×C61—41no—
369D4×C61—41no—
370C2×C4×C61—21no—
371C2×C4×C61—21no—
372C2×C4×C61—21no—
373C2×C4×C61—22no—
374C2×C4×C61—41no—
375C2×C4×C61—41no—
376C2×C4×C61—42no—
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—81no—
385C2×C4×C61C2×C22⋊C411yescharacteristic
386C2×C4×C61C2×C22⋊C411yescharacteristic
387C2×C4×C61C2×C22⋊C411yescharacteristic
388C2×C4×C61C2×C22⋊C411yescharacteristic
389C2×C4×C61C23×C411yescharacteristic
390C2×C4×C61C22×D411yescharacteristic
391C2×C4×C61C2×#4111yescharacteristic
392C2×C4×C61C2×#4111yescharacteristic
393C2×C4×C61H(5,𝔽2)11yescharacteristic
394C2×C4×C612−1+411yescharacteristic
395C22⋊D61—42no—
396C22⋊D61—41no—
397C22⋊D61—41no—
398C22⋊D61—41no—
399C22⋊D61—41no—
400C22⋊D61—42no—
401C22⋊D61—81no—
402C22⋊D61—81no—
403C2×Dic61—22no—
404C2×Dic61—22no—
405C2×Dic61—21no—
406C2×Dic61—21no—
407C2×Dic61—41no—
408C2×Dic61—41no—
409C2×Dic61—41no—
410C2×Dic61—41no—
411C2×Dic61—41no—
412C2×Dic61—41no—
413C2×Dic61—41no—
414C2×Dic61—41no—
415C2×Dic61C2×C22⋊C411yescharacteristic
416C2×Dic61C2×C22⋊C411yescharacteristic
417C2×Dic61C2×C22⋊C411yescharacteristic
418C2×Dic61C2×C22⋊C411yescharacteristic
419C2×Dic61C2×C22⋊C411yescharacteristic
420C2×Dic61C2×C22⋊C411yescharacteristic
421C2×Dic61C2×C22⋊C411yescharacteristic
422C2×Dic61C2×C22⋊C411yescharacteristic
423D244—21no—
424D244—21no—
425D244—21no—
426D244—21no—
427D244—42no—
428D244—81no—
429C4×D61—42no—
430C4×D61—41no—
431C4×D61—41no—
432C4×D61—41no—
433C4×D61—41no—
434C4×D61—42no—
435C4×D61—81no—
436C4×D61—81no—
437Dic122—22no—
438Dic122—22no—
439Dic122—21no—
440Dic122—21no—
441Dic122—21no—
442Dic122—21no—
443Dic122—41no—
444Dic122—41no—
445C8×C61—22no—
446C8×C61—41no—
447#92418—41no—
448#92418—41no—
449#22551—611nomaximal, Sylow
450C22×C61—21no—
451C22×C61—21no—
452C22×C61—41no—
453C22×C61—41no—
454C22×C61—41no—
455C22×C61C22×C22⋊C411yescharacteristic
456C22×C61#54811yescharacteristic
457C22×C61#55011yescharacteristic
458C2×D61—41no—
459C2×D61—41no—
460C2×D61—41no—
461C2×D61—41no—
462C2×D61—41no—
463C2×D61—41no—
464C4×C61—21no—
465C4×C61—21no—
466C4×C61—21no—
467C4×C61—21no—
468C4×C61—42no—
469C4×C61—41no—
470C4×C61—41no—
471C4×C61—41no—
472C4×C61—81no—
473C4×C61C4×#4111yescharacteristic
474C4×C61#52011yescharacteristic
475C4×C61#54811yescharacteristic
476C4×C61#55011yescharacteristic
477Dic61—21no—
478Dic61—21no—
479Dic61—21no—
480Dic61—21no—
481Dic61—21no—
482Dic61—21no—
483Dic61—21no—
484Dic61—42no—
485Dic61—41no—
486Dic61—41no—
487Dic61—81no—
488Dic61#42112yes—
489#3480—611no—
490Q8×M16—611no—
491#2295—611no—
492#1980—611no—
493#1980—611no—
494#1980—611no—
495#1963—611no—
496#1963—611no—
497#1962—611no—
498#1806—611no—
499#1806—611no—
500#1806—611no—
501#1759—611no—
502#1759D6111yescharacteristic, complemented
503C4×#104—611no—
504C2×C61—21no—
505C2×C61—21no—
506C2×C61—81no—
507C2×C61#234111yescharacteristic
508C2×C61C2×#42111yescharacteristic
509C2×C61#290111yescharacteristic
510D61—81no—
511D61—81no—
512#559—611no—
513#559—611no—
514#559—611no—
515#557—611no—
516#556—611no—
517#556—611no—
518#556—611no—
519#553—1221no—
520#553—1221no—
521#553—1221no—
522#550—611no—
523#548—1221no—
524#532—611no—
525#532—611no—
526#532—611no—
527#529—1221no—
528#529—1221no—
529#529—1221no—
530C4×#41—611no—
531C4×#41—611no—
532C4×#41—1221no—
533C4×#41C2×D6111yescharacteristic
534C2×C4×Q8—611no—
535#446—1221no—
536#446—1221no—
537#446—1221no—
538C8×Q8—1221no—
539#423—611no—
540#423—611no—
541#423—611no—
542C2×#104—611no—
543C2×#104—611no—
544C2×#104—611no—
545C2×#104—611no—
546C2×#104—611no—
547C2×#104—611no—
548C2×#104—611no—
549C2×#104—611no—
550C2×#104—611no—
551C2×#104—611no—
552C2×#104C2×D6111yescharacteristic
553C2×#104C2×D6111yescharacteristic
554C4×M16—611no—
555C4×M16—611no—
556C4×M16C2×D6111yescharacteristic
557#391—1221no—
558#389—1221no—
559#387—1221no—
560#387—1221no—
561C4×C4⋊C4—611no—
562C4×C4⋊C4—611no—
563C4×C4⋊C4—611no—
564#376—611no—
565#376C2×D6111yescharacteristic
566C43—611no—
567#339—611no—
568#339—611no—
569#339C2×D6111yescharacteristic
570#339C2×D6111yescharacteristic
571C61#2255111yescharacteristic, complemented, Sylow
572C2×#41—611no—
573C2×#41—611no—
574C2×#41—1221no—
575C2×#41C22×D6111yescharacteristic
576C22×Q8—611no—
577C2×M16—611no—
578C2×M16—611no—
579C2×M16C22×D6111yescharacteristic
580C2×M16C22×D6111yescharacteristic
581C4⋊Q8—611no—
582C4⋊Q8—611no—
583C4⋊Q8—611no—
584#127—611no—
585#127—611no—
586#127—611no—
587#126—1221no—
588#126—1221no—
589#126—1221no—
590#126—1221no—
591#126—1221no—
592#126—1221no—
593#125—1221no—
594#125—1221no—
595#125—1221no—
596#124—611no—
597#124—611no—
598#124—611no—
599#124—611no—
600#124—611no—
601#124—611no—
602#124—1221no—
603#124—1221no—
604#124—1221no—
605#123—1221no—
606#123—1221no—
607#123—1221no—
608#123—1221no—
609#123—1221no—
610#123—1221no—
611C22⋊Q8—1221no—
612C22⋊Q8—1221no—
613C22⋊Q8—1221no—
614#121—1221no—
615#121—1221no—
616#121—1221no—
617#121—1221no—
618#121—1221no—
619#121—1221no—
620#121—1221no—
621#121—1221no—
622#121—1221no—
623C4×Q8—611no—
624C4×Q8—611no—
625C4×Q8—611no—
626C4×Q8—611no—
627C4×Q8—611no—
628C4×Q8—611no—
629C4×Q8—611no—
630C4×Q8—611no—
631C4×Q8—611no—
632C4×Q8—611no—
633C4×Q8—611no—
634C4×Q8—611no—
635C4×Q8—1221no—
636C4×Q8C4×D6111yescharacteristic
637C4×Q8C4×D6111yescharacteristic
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—611no—
641C4×D4—611no—
642C4×D4—611no—
643C4×D4—611no—
644C4×D4—1221no—
645C4×D4—1221no—
646C4×D4—1221no—
647C4×D4—1221no—
648C4×D4—1221no—
649C4×D4—1221no—
650C4×D4—1221no—
651C4×D4—1221no—
652C4×D4—1221no—
653C4×D4—1221no—
654C4×D4—1221no—
655C4×D4—1221no—
656C4×D4—1221no—
657C4×D4C4×D6111yescharacteristic
658C4×D4C4×D6111yescharacteristic
659#117—21no—
660#117—1221no—
661#117—1221no—
662#117—1221no—
663#117—1221no—
664#117—1221no—
665#117C22×D6111yescharacteristic
666C2×C4⋊C4—611no—
667C2×C4⋊C4—611no—
668C2×C4⋊C4—611no—
669C2×C4⋊C4—1221no—
670C2×C4⋊C4—1221no—
671C2×C4⋊C4—1221no—
672C2×C42—21no—
673C2×C42—611no—
674C2×C42—611no—
675C2×C42—611no—
676C2×C42—611no—
677C2×C42—1221no—
678C2×C42—1221no—
679C2×C42—1221no—
680C2×C42—1221no—
681C2×C42C22×D6111yescharacteristic
682C2×C42C22×D6111yescharacteristic
683C2×C42C22×D6111yescharacteristic
684C4⋊C8—1221no—
685C4⋊C8—1221no—
686C4⋊C8—1221no—
687C4⋊C8—1221no—
688C4⋊C8—1221no—
689C4⋊C8—1221no—
690#104—22no—
691#104—22no—
692#104—1222no—
693#104—1222no—
694#104—1222no—
695#104—1222no—
696#104—2441no—
697#104—2441no—
698#104—2441no—
699#104—2441no—
700#104—2441no—
701#104—2441no—
702#97—21no—
703#97—1221no—
704#97—1221no—
705C4×C8—21no—
706C4×C8—1221no—
707C4×C8—1221no—
708#95—21no—
709#95—21no—
710#95—1221no—
711#95—1221no—
712#95—1221no—
713#95—1221no—
714#95—1221no—
715#41—21no—
716#41—21no—
717#41—21no—
718#41—21no—
719#41—1221no—
720#41—1221no—
721#41—1221no—
722#41—1221no—
723#41—1221no—
724#41—1221no—
725#41—1221no—
726#41—1221no—
727#41—2444no—
728C2×Q8—611no—
729C2×Q8—611no—
730C2×Q8—611no—
731C2×Q8—611no—
732C2×Q8—611no—
733C2×Q8—611no—
734C2×Q8—2442no—
735C2×Q8C2×C4×D6111yescharacteristic
736C2×D4—21no—
737C2×D4—611no—
738C2×D4—611no—
739C2×D4—1221no—
740C2×D4—1221no—
741C2×D4—1221no—
742C2×D4—1221no—
743C2×D4—1221no—
744C2×D4—1221no—
745C2×D4—1221no—
746C2×D4—1221no—
747C2×D4C2×C4×D6111yescharacteristic
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×C4—1221no—
765C22×C4D4×D6111yescharacteristic
766C22×C4D4×D6111yescharacteristic
767C22×C4C23×D6111yescharacteristic
768M16—21no—
769M16—21no—
770M16—21no—
771M16—1221no—
772M16—1221no—
773M16—1221no—
774M16—1221no—
775M16#1175822212yescomplemented
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—1221no—
779C2×C8—1221no—
780C4⋊C4—21no—
781C4⋊C4—21no—
782C4⋊C4—611no—
783C4⋊C4—611no—
784C4⋊C4—611no—
785C4⋊C4—611no—
786C4⋊C4—611no—
787C4⋊C4—611no—
788C4⋊C4—611no—
789C4⋊C4—611no—
790C4⋊C4—611no—
791C4⋊C4—611no—
792C4⋊C4—611no—
793C4⋊C4—611no—
794C4⋊C4—1221no—
795C4⋊C4—1221no—
796C4⋊C4—1221no—
797C4⋊C4—1221no—
798C4⋊C4—1221no—
799C4⋊C4—1221no—
800C4⋊C4—1221no—
801C4⋊C4—1221no—
802C4⋊C4—1221no—
803C4⋊C4—1221no—
804C4⋊C4—2442no—
805C4⋊C4—2442no—
806C4⋊C4—2442no—
807C4⋊C4C2×C4×D6111yescharacteristic
808C4⋊C4C2×C4×D6111yescharacteristic
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—1221no—
813C22⋊C4—1221no—
814C22⋊C4—1221no—
815C22⋊C4—1221no—
816C22⋊C4—1221no—
817C22⋊C4—1221no—
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—
828C42—21no—
829C42—21no—
830C42—21no—
831C42—21no—
832C42—21no—
833C42—21no—
834C42—611no—
835C42—611no—
836C42—611no—
837C42—611no—
838C42—611no—
839C42—611no—
840C42—611no—
841C42—611no—
842C42—1221no—
843C42—1221no—
844C42—1221no—
845C42—1221no—
846C42—1221no—
847C42—1221no—
848C42—1221no—
849C42—1221no—
850C42—2442no—
851C42—2442no—
852C42C2×C4×D6111yescharacteristic
853C42C2×C4×D6111yescharacteristic
854C42#1175822212yescomplemented
855C42D4×D6111yescharacteristic
856C42D4×D6111yescharacteristic
857C23—21no—
858C23—1221no—
859C23—1221no—
860C23C2×D4×D6111yescharacteristic
861Q8—21no—
862Q8—21no—
863Q8—1222no—
864Q8—1222no—
865Q8—1221no—
866Q8—1221no—
867Q8—1221no—
868Q8—1221no—
869Q8—2441no—
870Q8—2441no—
871D4—21no—
872D4—21no—
873D4—41no—
874D4—41no—
875D4—1221no—
876D4—1221no—
877D4—1221no—
878D4—1221no—
879D4—4881no—
880D4—4881no—
881D4—4881no—
882D4—2442no—
883D4—2442no—
884D4—2442no—
885D4—2441no—
886D4—2441no—
887D4—2441no—
888D4—2441no—
889C2×C4—21no—
890C2×C4—21no—
891C2×C4—21no—
892C2×C4—22no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—42no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—81no—
904C2×C4—611no—
905C2×C4—611no—
906C2×C4—611no—
907C2×C4—611no—
908C2×C4—611no—
909C2×C4—611no—
910C2×C4—611no—
911C2×C4—611no—
912C2×C4—1222no—
913C2×C4—1222no—
914C2×C4—1221no—
915C2×C4—1221no—
916C2×C4—4881no—
917C2×C4—4881no—
918C2×C4—2442no—
919C2×C4—2442no—
920C2×C4—2441no—
921C2×C4—2441no—
922C2×C4—2441no—
923C2×C4—2441no—
924C2×C4—2441no—
925C2×C4—2441no—
926C2×C4—2441no—
927C2×C4—2441no—
928C2×C4—2441no—
929C2×C4—2441no—
930C2×C4—2441no—
931C2×C4—2441no—
932C2×C4C22⋊C4×D6111yescharacteristic
933C2×C4C22⋊C4×D6111yescharacteristic
934C2×C4C22⋊C4×D6111yescharacteristic
935C2×C4C22⋊C4×D6111yescharacteristic
936C2×C4C22×C4×D6111yescharacteristic
937C2×C4C2×D4×D6111yescharacteristic
938C2×C4C2×#1175822211yescharacteristic
939C2×C4C2×#1175822211yescharacteristic
940C2×C4#1451982311yescharacteristic
941C2×C4#1451982411yescharacteristic
942C8—22no—
943C8—41no—
944C8—2441no—
945C8—2441no—
946C22—21no—
947C22—21no—
948C22—41no—
949C22—41no—
950C22—41no—
951C22—2441no—
952C22—2441no—
953C22—2441no—
954C22—2441no—
955C22—2441no—
956C22—2441no—
957C22C2×C22⋊C4×D6111yescharacteristic
958C22#1684042111yescharacteristic
959C22#1684043311yescharacteristic
960C4—21no—
961C4—21no—
962C4—21no—
963C4—21no—
964C4—42no—
965C4—41no—
966C4—41no—
967C4—41no—
968C4—81no—
969C4—612no—
970C4—1221no—
971C4—1221no—
972C4—1221no—
973C4—1221no—
974C4—1221no—
975C4—1221no—
976C4—1221no—
977C4—4881no—
978C4—2442no—
979C4—2441no—
980C4—2441no—
981C4C4×#1175822211yescharacteristic
982C4#1684024211yescharacteristic
983C4#1684042111yescharacteristic
984C4#1684043311yescharacteristic
985C2—21no—
986C2—21no—
987C2—81no—
988C2—4881no—
989C2—4881no—
990C2#2144865911yescharacteristic
991C2#421×D6111yescharacteristic
992C2#2145436511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1759C2
socleC22×C61C22×C22⋊C4
prime radical#21459412C2
cosocleC22×C4×C61C24
hypercenter#1759D61
hypocenterC61#22551
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1759

Complements

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

NH ≅ G/Ntype
2. M16×Dic122C2semidirect
3. #21448291C2semidirect
4. #21446738C2semidirect
5. #21446736C2semidirect
6. #21446736C2semidirect
7. #21446651C2semidirect
8. #21446649C2semidirect
9. #21446645C2semidirect
10. #21445839C2semidirect
11. #21445838C2semidirect
12. #21445838C2semidirect
13. #21445628C2semidirect
14. #21445623C2semidirect
15. C61×#1759C2semidirect
16. #16840497C4semidirect
17. #16840495C4semidirect
18. #16840495C4semidirect
19. #16840490C4semidirect
20. #16840484C4semidirect
21. #16840484C4semidirect
22. #16840482C4semidirect
26. #16840433C4semidirect
274. M16×C61#41semidirect
294. C42×C61#41semidirect
502. #1759D61semidirect
571. C61#22551semidirect
775. M16#11758222semidirect
854. C42#11758222semidirect

Maximal subgroups

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

subgroupindex
#214594122
M16×Dic1222
#214482912
#214467382
#214467362
#214466512
#214466492
#214466452
#214458392
#214458382
#214456282
#214456232
C61×#17592
#2255161