Finite Group Databasebeta

← #29647625

Subgroups — #29647625

Order 15616.

1004 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459548C211yesmaximal, characteristic
2#21454479C211yesmaximal, characteristic, complemented
3#21448681C211yesmaximal, characteristic, complemented
4#21444393C211yesmaximal, characteristic, complemented
5#21444377C211yesmaximal, characteristic, complemented
6#21444373C211yesmaximal, characteristic, complemented
7#21444364C211yesmaximal, characteristic, complemented
8#21444354C211yesmaximal, characteristic, complemented
9#21444341C211yesmaximal, characteristic, complemented
10#21444325C211yesmaximal, characteristic, complemented
11#21444324C211yesmaximal, characteristic, complemented
12#21444312C211yesmaximal, characteristic, complemented
13#21444302C211yesmaximal, characteristic, complemented
14C2×#16839496C211yesmaximal, characteristic, complemented
15C61×#1510C211yesmaximal, characteristic, complemented
16#16840476—21no—
17#16840464—21no—
18#16840459—21no—
19#16840438—21no—
20#16840438—21no—
21#16840412—21no—
22#16840406—21no—
23#16840406—21no—
24#16840393C411yescharacteristic, complemented
25#16840379C411yescharacteristic, complemented
26#16840379C411yescharacteristic, complemented
27#16840365C411yescharacteristic, complemented
28#16840365C411yescharacteristic, complemented
29#16840329C411yescharacteristic, complemented
30#16840307C2211yescharacteristic
31#16840307C2211yescharacteristic
32#16840293C2211yescharacteristic
33#16840293C2211yescharacteristic
34#16840273C2211yescharacteristic
35#16840243C411yescharacteristic, complemented
36#16840237C411yescharacteristic, complemented
37C2×#14519736C2211yescharacteristic
38#16839820—21no—
39#16839820—21no—
40#16839816C2211yescharacteristic, complemented
41#16839816C2211yescharacteristic, complemented
42#16839812C2211yescharacteristic, complemented
43#16839812C2211yescharacteristic, complemented
44#16839790—21no—
45C2×C22⋊#92418C2211yescharacteristic
46#16839720—21no—
47#16839647—21no—
48#16839645—21no—
49#16839634—21no—
50#16839629C2211yescharacteristic, complemented
51#16839626C2211yescharacteristic, complemented
52#16839613C2211yescharacteristic, complemented
53C22⋊C4×Dic61—21no—
54#16839607C2211yescharacteristic, complemented
55C2×#14519684C2211yescharacteristic
56#16839500C2211yescharacteristic, complemented
57#16839500C2211yescharacteristic, complemented
58#16839498C2211yescharacteristic, complemented
59#16839498C2211yescharacteristic, complemented
60#16839497C2211yescharacteristic, complemented
61#16839497C2211yescharacteristic, complemented
62#16839496C2211yescharacteristic
63#16839496C2211yescharacteristic
64#16839496C2211yescharacteristic
65#16839496C2211yescharacteristic
66#16839495C2211yescharacteristic, complemented
67#16839495C2211yescharacteristic, complemented
68C2×#121×C61C2211yescharacteristic
69C61×#407C2211yescharacteristic
70C61×#381C2211yescharacteristic
71C61×#327C2211yescharacteristic
72C61×#327C2211yescharacteristic
73C61×#327C2211yescharacteristic
74C61×#327C2211yescharacteristic
75C2×#11758222C2×C411yescharacteristic
76C2×#11758224—21no—
77C2×#11758224—21no—
78C23×Dic61—21no—
79C22×#92418—21no—
80#14519776—21no—
81#14519776C2×C411yescharacteristic, complemented
82#14519776C2×C411yescharacteristic, complemented
83#14519773C2×C411yescharacteristic, complemented
84#14519773C2×C411yescharacteristic, complemented
85#14519770—21no—
86#14519770—21no—
87#14519770—21no—
88#14519770—21no—
89#14519768—21no—
90#14519768C2×C411yescharacteristic, complemented
91#14519768C2×C411yescharacteristic, complemented
92#14519764—21no—
93#14519764—21no—
94#14519764C2×C411yescharacteristic, complemented
95#14519764C2×C411yescharacteristic, complemented
96#14519763—21no—
97#14519763—21no—
98#14519761—21no—
99#14519761—21no—
100#14519760—21no—
101#14519759—21no—
102#14519759—21no—
103#14519758—21no—
104#14519758—21no—
105#14519758—21no—
106#14519758—21no—
107#14519756—21no—
108#14519756—21no—
109#14519756C2×C411yescharacteristic
110#14519756C2311yescharacteristic
111#14519754—21no—
112#14519754—21no—
113#14519751C2×C411yescharacteristic
114#14519751C2311yescharacteristic
115#14519749—21no—
116#14519749—21no—
117#14519749—21no—
118#14519749—21no—
119#14519748—21no—
120#14519748—21no—
121#14519748—21no—
122#14519748—21no—
123#14519746—21no—
124#14519746—21no—
125#14519746—21no—
126#14519742C2×C411yescharacteristic, complemented
127#14519742C2×C411yescharacteristic, complemented
128D4×Dic61—21no—
129D4×Dic61—21no—
130D4×Dic61—21no—
131D4×Dic61—21no—
132D4×Dic61C2×C411yescharacteristic, complemented
133D4×Dic61C2×C411yescharacteristic, complemented
134D4×Dic61C2×C411yescharacteristic, complemented
135D4×Dic61C2×C411yescharacteristic, complemented
136#14519739C2×C411yescharacteristic, complemented
137#14519739C2×C411yescharacteristic, complemented
138C4×C22⋊D61—21no—
139C4×C22⋊D61—21no—
140C4×C22⋊D61—21no—
141C4×C22⋊D61—21no—
142#14519737—21no—
143#14519737—21no—
144#14519736C2×C411yescharacteristic
145#14519736C2×C411yescharacteristic
146#14519736C2×C411yescharacteristic
147#14519736C2×C411yescharacteristic
148#14519736C2×C411yescharacteristic
149#14519736D411yescharacteristic
150#14519736D411yescharacteristic
151#14519736D411yescharacteristic
152#14519736D411yescharacteristic
153#14519735—21no—
154#14519733—21no—
155#14519733—21no—
156C2×C4⋊Dic61D411yescharacteristic
157C2×C4⋊Dic61D411yescharacteristic
158C2×#11758196—21no—
159C2×#11758196—21no—
160C4⋊C4×D61—21no—
161C2×C22⋊Dic61—21no—
162C2×C22⋊Dic61—21no—
163C2×C22⋊Dic61D411yescharacteristic
164C2×C22⋊Dic61D411yescharacteristic
165C2×C4×Dic61—21no—
166C2×C4×Dic61—21no—
167C2×C4×Dic61C2311yescharacteristic
168C2×C4×Dic61C2311yescharacteristic
169#14519706—21no—
170#14519706—21no—
171#14519706—21no—
172#14519706—21no—
173C22⋊#92418—21no—
174C22⋊#92418C2311yescharacteristic
175C22⋊#92418C2311yescharacteristic
176#14519687—21no—
177#14519687—21no—
178C8×Dic61—21no—
179C8×Dic61—21no—
180#14519684—21no—
181#14519684—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
190C2×M16×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×C61C2×C411yescharacteristic
198C2×C22⋊C4×C61—21no—
199C2×C22⋊C4×C61—21no—
200C22⋊C8×C61—21no—
201C22⋊C8×C61C2311yescharacteristic
202C22⋊C8×C61C2311yescharacteristic
203#95×C61—21no—
204#95×C61C2311yescharacteristic
205#95×C61C2311yescharacteristic
206C24×C61—21no—
207C24×C61C2×D411yescharacteristic
208C2×D4×C61—21no—
209C2×D4×C61—21no—
210C2×D4×C61—21no—
211C2×D4×C61—21no—
212C2×D4×C61—21no—
213C2×D4×C61—42no—
214C2×D4×C61—81no—
215C2×D4×C61—81no—
216C2×D4×C61C22×C411yescharacteristic
217C2×D4×C61C22×C411yescharacteristic
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—42no—
222C22×C4×C61C22×C411yescharacteristic
223C22×C4×C61C22×C411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2411yescharacteristic
228C2×C22⋊D61—21no—
229C2×C22⋊D61—21no—
230C2×C22⋊D61—21no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61—21no—
233C2×C22⋊D61—21no—
234C2×C22⋊D61—21no—
235C22×Dic61—21no—
236C22×Dic61—21no—
237C22×Dic61—21no—
238C22×Dic61—21no—
239C22×Dic61—21no—
240C22×Dic61—21no—
241C22×Dic61—42no—
242C22×Dic61—42no—
243C22×Dic61—81no—
244C22×Dic61C2×D411yescharacteristic
245C22×Dic61C2×D411yescharacteristic
246C22×Dic61C2×D411yescharacteristic
247C22×Dic61C2×D411yescharacteristic
248#11758224—81no—
249#11758224—81no—
250#11758224—81no—
251#11758224—81no—
252#11758222—42no—
253C2×D244C22×C411yescharacteristic
254C2×C4×D61—21no—
255C2×C4×D61—21no—
256C2×C4×D61—21no—
257C2×Dic122—21no—
258C2×Dic122—21no—
259C2×Dic122C22×C411yescharacteristic
260M16×C61—42no—
261C2×C8×C61—21no—
262C2×C8×C61—21no—
263C4⋊C4×C61—21no—
264C4⋊C4×C61C22×C411yescharacteristic
265C4⋊C4×C61C22×C411yescharacteristic
266C22⋊C4×C61—21no—
267C22⋊C4×C61—21no—
268C22⋊C4×C61—21no—
269C22⋊C4×C61—21no—
270C22⋊C4×C61—42no—
271C22⋊Dic61—21no—
272C22⋊Dic61—21no—
273C22⋊Dic61—21no—
274C22⋊Dic61—21no—
275C22⋊Dic61—21no—
276C22⋊Dic61—21no—
277C22⋊Dic61—21no—
278C22⋊Dic61—21no—
279C22⋊Dic61—21no—
280C22⋊Dic61—21no—
281C22⋊Dic61—21no—
282C22⋊Dic61C22⋊C411yescharacteristic
283C22⋊Dic61C22⋊C411yescharacteristic
284C22⋊Dic61C22⋊C411yescharacteristic
285C22⋊Dic61C22⋊C411yescharacteristic
286C22⋊Dic61C22⋊C411yescharacteristic
287C22⋊Dic61C22⋊C411yescharacteristic
288C22⋊Dic61C22⋊C411yescharacteristic
289C22⋊Dic61C22⋊C411yescharacteristic
290#11758198—21no—
291#11758198—21no—
292#11758198—21no—
293#11758198—21no—
294C4⋊Dic61—21no—
295C4⋊Dic61—21no—
296C4⋊Dic61C22⋊C411yescharacteristic
297C4⋊Dic61C22⋊C411yescharacteristic
298C4⋊Dic61C22⋊C411yescharacteristic
299C4⋊Dic61C22⋊C411yescharacteristic
300C4⋊Dic61C22⋊C411yescharacteristic
301C4⋊Dic61C22⋊C411yescharacteristic
302C4⋊Dic61C22⋊C411yescharacteristic
303C4⋊Dic61C22⋊C411yescharacteristic
304C4⋊Dic61C22×C411yescharacteristic
305C4⋊Dic61C22×C411yescharacteristic
306#11758196—21no—
307#11758196—21no—
308#11758196—21no—
309#11758196—21no—
310#11758196—21no—
311#11758196—21no—
312#11758196—21no—
313#11758196—21no—
314#11758196—42no—
315#11758196—81no—
316C4×Dic61—21no—
317C4×Dic61—21no—
318C4×Dic61—21no—
319C4×Dic61—42no—
320C4×Dic61—81no—
321C4×Dic61C22×C411yescharacteristic
322C4×Dic61C22×C411yescharacteristic
323C4×Dic61C22×C411yescharacteristic
324C4×Dic61C22×C411yescharacteristic
325C4×Dic61C2×D411yescharacteristic
326C4×Dic61C2×D411yescharacteristic
327C4×Dic61C2×D411yescharacteristic
328C4×Dic61C2×D411yescharacteristic
329C2×#92418—21no—
330C2×#92418—21no—
331C2×#92418—42no—
332C23×C61—21no—
333C23×C61—21no—
334C23×C61—22no—
335C23×C61—21no—
336C23×C61—21no—
337C23×C61—41no—
338C23×C61—42no—
339C23×C61—81no—
340C23×C61—81no—
341C23×C61C2×C22⋊C411yescharacteristic
342C23×C61C2×C22⋊C411yescharacteristic
343C23×C61C22×D411yescharacteristic
344C22×D61—21no—
345D4×C61—41no—
346D4×C61—41no—
347D4×C61—42no—
348D4×C61—41no—
349D4×C61—41no—
350D4×C61—41no—
351D4×C61—41no—
352D4×C61—81no—
353D4×C61—81no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—21no—
357C2×C4×C61—21no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61—41no—
366C2×C4×C61—41no—
367C2×C4×C61—41no—
368C2×C4×C61—81no—
369C2×C4×C61C2×C22⋊C411yescharacteristic
370C2×C4×C61C2×C22⋊C411yescharacteristic
371C2×C4×C61C23×C411yescharacteristic
372C2×C4×C61C22×D411yescharacteristic
373C22⋊D61—41no—
374C22⋊D61—41no—
375C22⋊D61—42no—
376C22⋊D61—81no—
377C22⋊D61—81no—
378C22⋊D61—81no—
379C22⋊D61—81no—
380C22⋊D61—81no—
381C2×Dic61—21no—
382C2×Dic61—21no—
383C2×Dic61—21no—
384C2×Dic61—21no—
385C2×Dic61—22no—
386C2×Dic61—21no—
387C2×Dic61—21no—
388C2×Dic61—21no—
389C2×Dic61—41no—
390C2×Dic61—41no—
391C2×Dic61—41no—
392C2×Dic61—41no—
393C2×Dic61—41no—
394C2×Dic61—41no—
395C2×Dic61—41no—
396C2×Dic61—81no—
397C2×Dic61—81no—
398C2×Dic61—81no—
399C2×Dic61—81no—
400C2×Dic61—84no—
401C2×Dic61C2×C22⋊C411yescharacteristic
402C2×Dic61C2×C22⋊C411yescharacteristic
403C2×Dic61C2×C22⋊C411yescharacteristic
404C2×Dic61C2×C22⋊C411yescharacteristic
405C2×Dic61C2×C22⋊C411yescharacteristic
406C2×Dic61C2×C22⋊C411yescharacteristic
407C2×Dic61C2×C22⋊C411yescharacteristic
408C2×Dic61C2×C22⋊C411yescharacteristic
409D244—41no—
410C4×D61—42no—
411C4×D61—81no—
412C4×D61—81no—
413Dic122—41no—
414Dic122—81no—
415Dic122—81no—
416C8×C61—41no—
417C8×C61—41no—
418#92418—41no—
419#92418—41no—
420#17604—611nomaximal, Sylow
421C22×C61—21no—
422C22×C61—21no—
423C22×C61—21no—
424C22×C61—21no—
425C22×C61—21no—
426C22×C61—21no—
427C22×C61—21no—
428C22×C61—42no—
429C22×C61—42no—
430C22×C61—41no—
431C22×C61—41no—
432C22×C61—41no—
433C22×C61—41no—
434C22×C61—41no—
435C22×C61—41no—
436C22×C61—162no—
437C22×C61#41012yes—
438C22×C61C22×C22⋊C411yescharacteristic
439C22×C61#57611yescharacteristic
440C22×C61#57711yescharacteristic
441C2×D61—41no—
442C2×D61—41no—
443C2×D61—41no—
444C4×C61—21no—
445C4×C61—21no—
446C4×C61—21no—
447C4×C61—21no—
448C4×C61—41no—
449C4×C61—41no—
450C4×C61—81no—
451C4×C61—81no—
452Dic61—21no—
453Dic61—21no—
454Dic61—21no—
455Dic61—21no—
456Dic61—21no—
457Dic61—21no—
458Dic61—21no—
459Dic61—21no—
460Dic61—42no—
461Dic61—41no—
462Dic61—41no—
463Dic61—41no—
464Dic61—81no—
465#3494—611no—
466#2924—611no—
467#2343—611no—
468#1521—611no—
469#1517—611no—
470#1516—611no—
471#1514—611no—
472#1512—611no—
473#1510D6111yescharacteristic, complemented
474#1509—611no—
475#1505—611no—
476#1504—611no—
477#1502—611no—
478#1500—611no—
479C2×#327—611no—
480C2×C61—21no—
481C2×C61—21no—
482C2×C61—22no—
483C2×C61—41no—
484C2×C61—81no—
485C2×C61—81no—
486C2×C61C2×#41011yescharacteristic
487C2×C61#289711yescharacteristic
488C2×C61#290111yescharacteristic
489D61—81no—
490#555—1221no—
491#553—1221no—
492#553—1221no—
493#551—1221no—
494#551—1221no—
495#547—1221no—
496#546—1221no—
497#546—1221no—
498#544—611no—
499#542—611no—
500#542—611no—
501#540—611no—
502#540—611no—
503#535—611no—
504#532—611no—
505#532—611no—
506#529—611no—
507#529—611no—
508#525—611no—
509C2×#121C2×D6111yescharacteristic
510#520—611no—
511#518—611no—
512C2×#117—611no—
513#433—1221no—
514#433—1221no—
515#432—611no—
516#432—611no—
517#431—611no—
518#431—611no—
519#424—1221no—
520#407C2×D6111yescharacteristic
521C2×C22⋊C8—611no—
522#405—1221no—
523#387—1221no—
524#387—1221no—
525#385—1221no—
526#383—611no—
527#382—611no—
528#381C2×D6111yescharacteristic
529C4×C4⋊C4—611no—
530C4×C22⋊C4—1221no—
531#376—611no—
532C2×#95—611no—
533#328—611no—
534#328—611no—
535#328—611no—
536#328—611no—
537#327—611no—
538#327—611no—
539#327—611no—
540#327—611no—
541#327—611no—
542#327—611no—
543#327—611no—
544#327—611no—
545#327C2×D6111yescharacteristic
546#327C2×D6111yescharacteristic
547#327C2×D6111yescharacteristic
548#327C2×D6111yescharacteristic
549C61#1760411yescharacteristic, complemented, Sylow
550C2×#41—611no—
551C2×#41—1221no—
552C2×#41—1221no—
553C22×D4—21no—
554C22×D4C4×D6111yescharacteristic
555C23×C4—1221no—
556C23×C4C22×D6111yescharacteristic
557C2×M16—21no—
558C22×C8—1221no—
559C4⋊Q8—611no—
560C4⋊Q8—611no—
561C4⋊Q8—1221no—
562#127—611no—
563#127—611no—
564#126—1221no—
565#126—1221no—
566#126—1221no—
567#126—1221no—
568#125—611no—
569#125—611no—
570#125—1221no—
571#124—611no—
572#124—611no—
573#124—1221no—
574#124—1221no—
575#124—1221no—
576#124—1221no—
577#123—1221no—
578#123—1221no—
579#123—1221no—
580#123—1221no—
581#123—1221no—
582#123—1221no—
583#123—1221no—
584#123—1221no—
585#123—1221no—
586C22⋊Q8—611no—
587C22⋊Q8—611no—
588C22⋊Q8—1221no—
589C22⋊Q8—1221no—
590C22⋊Q8—1221no—
591C22⋊Q8—1221no—
592#121—21no—
593#121—21no—
594#121—611no—
595#121—611no—
596#121—1221no—
597#121—1221no—
598#121—1221no—
599#121—1221no—
600#121—1221no—
601#121—1221no—
602#121—1221no—
603#121—1221no—
604#121C4×D6111yescharacteristic
605#121C4×D6111yescharacteristic
606#121C22×D6111yescharacteristic
607#121C22×D6111yescharacteristic
608#120—1221no—
609#120—1221no—
610#120—1221no—
611C4×Q8—611no—
612C4×Q8—611no—
613C4×D4—611no—
614C4×D4—611no—
615C4×D4—611no—
616C4×D4—611no—
617C4×D4—611no—
618C4×D4—611no—
619C4×D4—1221no—
620C4×D4—1221no—
621C4×D4—1221no—
622C4×D4—1221no—
623C4×D4—1221no—
624C4×D4—1221no—
625C4×D4—1221no—
626C4×D4—1221no—
627C4×D4—1221no—
628C4×D4—1221no—
629#117—611no—
630#117—611no—
631#117—611no—
632#117—611no—
633#117—611no—
634#117—611no—
635#117—611no—
636#117—611no—
637#117—611no—
638#117—1221no—
639#117—1221no—
640#117—1221no—
641C2×C4⋊C4—611no—
642C2×C4⋊C4—611no—
643C2×C4⋊C4—1221no—
644C2×C4⋊C4—1221no—
645C2×C4⋊C4—1221no—
646C2×C4⋊C4C4×D6111yescharacteristic
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—611no—
650C2×C22⋊C4—611no—
651C2×C22⋊C4—1221no—
652C2×C22⋊C4—1221no—
653C2×C42—611no—
654C2×C42—611no—
655C2×C42—1221no—
656C2×C42—1221no—
657C4⋊C8—1221no—
658C4⋊C8—1221no—
659C4⋊C8—1221no—
660C4⋊C8—1221no—
661C22⋊C8—21no—
662C22⋊C8—611no—
663C22⋊C8—611no—
664C22⋊C8—1221no—
665C22⋊C8C22×D6111yescharacteristic
666C22⋊C8C22×D6111yescharacteristic
667#97—1221no—
668#97—1221no—
669C4×C8—1221no—
670C4×C8—1221no—
671#95—21no—
672#95—611no—
673#95—611no—
674#95—1221no—
675#95—1221no—
676#95—1221no—
677#95—1221no—
678#95—1221no—
679#95C22×D6111yescharacteristic
680#95C22×D6111yescharacteristic
681C24—21no—
682C24D4×D6111yescharacteristic
683#41—4881no—
684#41—4881no—
685#41—4881no—
686#41—4881no—
687#41—2442no—
688C2×Q8—611no—
689C2×Q8—1221no—
690C2×Q8—1221no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—42no—
697C2×D4—81no—
698C2×D4—81no—
699C2×D4—611no—
700C2×D4—1221no—
701C2×D4—1221no—
702C2×D4—1221no—
703C2×D4—1221no—
704C2×D4—1221no—
705C2×D4—1221no—
706C2×D4—1221no—
707C2×D4C2×C4×D6111yescharacteristic
708C2×D4C2×C4×D6111yescharacteristic
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—42no—
713C22×C4—611no—
714C22×C4—611no—
715C22×C4—611no—
716C22×C4—611no—
717C22×C4—1221no—
718C22×C4—1221no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—4881no—
727C22×C4—2442no—
728C22×C4—2442no—
729C22×C4C2×C4×D6111yescharacteristic
730C22×C4C2×C4×D6111yescharacteristic
731C22×C4D4×D6111yescharacteristic
732C22×C4D4×D6111yescharacteristic
733C22×C4D4×D6111yescharacteristic
734C22×C4C23×D6111yescharacteristic
735M16—42no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—1221no—
739C2×C8—1221no—
740C2×C8—2442no—
741C4⋊C4—21no—
742C4⋊C4—611no—
743C4⋊C4—611no—
744C4⋊C4—611no—
745C4⋊C4—611no—
746C4⋊C4—611no—
747C4⋊C4—611no—
748C4⋊C4—611no—
749C4⋊C4—611no—
750C4⋊C4—611no—
751C4⋊C4—611no—
752C4⋊C4—1221no—
753C4⋊C4—1221no—
754C4⋊C4—1221no—
755C4⋊C4—1221no—
756C4⋊C4—1221no—
757C4⋊C4—1221no—
758C4⋊C4—1221no—
759C4⋊C4—1221no—
760C4⋊C4—1221no—
761C4⋊C4—1221no—
762C4⋊C4—4881no—
763C4⋊C4—2442no—
764C4⋊C4C2×C4×D6111yescharacteristic
765C4⋊C4C2×C4×D6111yescharacteristic
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—42no—
771C22⋊C4—611no—
772C22⋊C4—611no—
773C22⋊C4—611no—
774C22⋊C4—611no—
775C22⋊C4—611no—
776C22⋊C4—611no—
777C22⋊C4—611no—
778C22⋊C4—611no—
779C22⋊C4—1221no—
780C22⋊C4—1221no—
781C22⋊C4—1221no—
782C22⋊C4—1221no—
783C22⋊C4—1221no—
784C22⋊C4—1221no—
785C22⋊C4—1221no—
786C22⋊C4—1221no—
787C22⋊C4—1221no—
788C22⋊C4—1221no—
789C22⋊C4—1221no—
790C22⋊C4—1221no—
791C22⋊C4—1221no—
792C22⋊C4—1221no—
793C22⋊C4—1221no—
794C42—611no—
795C42—611no—
796C42—611no—
797C42—611no—
798C42—611no—
799C42—611no—
800C42—611no—
801C42—611no—
802C42—1221no—
803C42—1221no—
804C42—1221no—
805C42—4881no—
806C42—2442no—
807C23—22no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—41no—
813C23—42no—
814C23—81no—
815C23—81no—
816C23—1221no—
817C23C22⋊C4×D6111yescharacteristic
818C23C22⋊C4×D6111yescharacteristic
819C23C2×D4×D6111yescharacteristic
820Q8—4881no—
821Q8—4881no—
822Q8—2441no—
823D4—41no—
824D4—41no—
825D4—42no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—81no—
831D4—81no—
832D4—4881no—
833D4—4881no—
834D4—4881no—
835D4—4881no—
836D4—4881no—
837D4—2441no—
838D4—2442no—
839D4—2441no—
840D4—2441no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—81no—
856C2×C4—611no—
857C2×C4—611no—
858C2×C4—611no—
859C2×C4—611no—
860C2×C4—611no—
861C2×C4—611no—
862C2×C4—611no—
863C2×C4—611no—
864C2×C4—1221no—
865C2×C4—1221no—
866C2×C4—1221no—
867C2×C4—1221no—
868C2×C4—1222no—
869C2×C4—1221no—
870C2×C4—1221no—
871C2×C4—1221no—
872C2×C4—4881no—
873C2×C4—4881no—
874C2×C4—4881no—
875C2×C4—4881no—
876C2×C4—4881no—
877C2×C4—4881no—
878C2×C4—4884no—
879C2×C4—2442no—
880C2×C4—2441no—
881C2×C4—2441no—
882C2×C4—2441no—
883C2×C4—2441no—
884C2×C4—2441no—
885C2×C4—2441no—
886C2×C4—2441no—
887C2×C4C22⋊C4×D6111yescharacteristic
888C2×C4C22⋊C4×D6111yescharacteristic
889C2×C4C22×C4×D6111yescharacteristic
890C2×C4C2×D4×D6111yescharacteristic
891C8—41no—
892C8—41no—
893C8—2441no—
894C8—2441no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—42no—
903C22—42no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—162no—
911C22—2441no—
912C22—2441no—
913C22—2441no—
914C22#1683973412yes—
915C22C2×C22⋊C4×D6111yescharacteristic
916C22#1684056611yescharacteristic
917C22#1684057211yescharacteristic
918C4—21no—
919C4—21no—
920C4—21no—
921C4—21no—
922C4—41no—
923C4—41no—
924C4—81no—
925C4—81no—
926C4—1221no—
927C4—1221no—
928C4—1221no—
929C4—1221no—
930C4—1221no—
931C4—1221no—
932C4—1221no—
933C4—1221no—
934C4—4881no—
935C4—2442no—
936C4—2441no—
937C4—2441no—
938C4—2441no—
939C2—21no—
940C2—21no—
941C2—22no—
942C2—41no—
943C2—81no—
944C2—81no—
945C2—4881no—
946C2C2×#1683973411yescharacteristic
947C2#2145434411yescharacteristic
948C2#2145436511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1510C2
socleC22×C61C22×C22⋊C4
prime radical#21459548C2
cosocleC22×C4×C61C24
hypercenter#1510D61
hypocenterC61#17604
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1510

Complements

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

NH ≅ G/Ntype
2. #21454479C2semidirect
3. #21448681C2semidirect
4. #21444393C2semidirect
5. #21444377C2semidirect
6. #21444373C2semidirect
7. #21444364C2semidirect
8. #21444354C2semidirect
9. #21444341C2semidirect
10. #21444325C2semidirect
11. #21444324C2semidirect
12. #21444312C2semidirect
13. #21444302C2semidirect
14. C2×#16839496C2semidirect
15. C61×#1510C2semidirect
24. #16840393C4semidirect
25. #16840379C4semidirect
26. #16840379C4semidirect
27. #16840365C4semidirect
28. #16840365C4semidirect
29. #16840329C4semidirect
35. #16840243C4semidirect
36. #16840237C4semidirect
40. #16839816C22semidirect
41. #16839816C22semidirect
42. #16839812C22semidirect
43. #16839812C22semidirect
50. #16839629C22semidirect
51. #16839626C22semidirect
52. #16839613C22semidirect
54. #16839607C22semidirect
56. #16839500C22semidirect
57. #16839500C22semidirect
58. #16839498C22semidirect
59. #16839498C22semidirect
60. #16839497C22semidirect
61. #16839497C22semidirect
66. #16839495C22semidirect
67. #16839495C22semidirect
81. #14519776C2×C4semidirect
82. #14519776C2×C4semidirect
83. #14519773C2×C4semidirect
84. #14519773C2×C4semidirect
90. #14519768C2×C4semidirect
91. #14519768C2×C4semidirect
94. #14519764C2×C4semidirect
95. #14519764C2×C4semidirect
126. #14519742C2×C4semidirect
127. #14519742C2×C4semidirect
132. D4×Dic61C2×C4semidirect
133. D4×Dic61C2×C4semidirect
134. D4×Dic61C2×C4semidirect
135. D4×Dic61C2×C4semidirect
136. #14519739C2×C4semidirect
137. #14519739C2×C4semidirect
473. #1510D61semidirect
549. C61#17604semidirect

Maximal subgroups

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

subgroupindex
#214595482
#214544792
#214486812
#214443932
#214443772
#214443732
#214443642
#214443542
#214443412
#214443252
#214443242
#214443122
#214443022
C2×#168394962
C61×#15102
#1760461