Finite Group Databasebeta

← #29696493

Subgroups — #29696493

Order 15616.

1262 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459379C211yesmaximal, characteristic
2M16×C22⋊D61C211yesmaximal, characteristic, complemented
3C4×#14519737C211yesmaximal, characteristic, complemented
4#21446794C211yesmaximal, characteristic, complemented
5#21446761C211yesmaximal, characteristic, complemented
6#21446263C211yesmaximal, characteristic, complemented
7#21446259C211yesmaximal, characteristic, complemented
8#21446118C211yesmaximal, characteristic, complemented
9#21445919C211yesmaximal, characteristic, complemented
10#21445917C211yesmaximal, characteristic, complemented
11#21445837C211yesmaximal, characteristic, complemented
12#104×Dic61C211yesmaximal, characteristic, complemented
13C2×#16839523C211yesmaximal, characteristic, complemented
14#339×D61C211yesmaximal, characteristic, complemented
15C61×#1871C211yesmaximal, characteristic, complemented
16C2×M16×D61C2211yescharacteristic
17#16840483C411yescharacteristic, complemented
18#16840476C411yescharacteristic, complemented
19#16840470C411yescharacteristic, complemented
20#16840464C411yescharacteristic, complemented
21#16840459C411yescharacteristic, complemented
22#16840454C411yescharacteristic, complemented
23#16840449—21no—
24#16840446C411yescharacteristic, complemented
25#16840443—21no—
26#16840435—21no—
27#16840412C411yescharacteristic, complemented
28#16840399—21no—
29#16840315C2211yescharacteristic
30#16840294—21no—
31#16840292—21no—
32#16840292—21no—
33#16840269C2211yescharacteristic
34#41×Dic61C2211yescharacteristic
35C4×#11758224—21no—
36C2×C4×C22⋊D61C2211yescharacteristic
37C2×#14519737—21no—
38C2×#14519736C2211yescharacteristic
39#117×D61C2211yescharacteristic
40C22×C4×Dic61C2211yescharacteristic
41C2×C42×D61C2211yescharacteristic
42#16839838—21no—
43#16839833—21no—
44#16839831—21no—
45C8×C22⋊D61—21no—
46#16839785C2211yescharacteristic
47C2×#14519704C2211yescharacteristic
48C2×#14519704C2211yescharacteristic
49#16839726C2211yescharacteristic
50#16839725C2211yescharacteristic
51M16×Dic61C2211yescharacteristic
52C4×#11758196C2211yescharacteristic
53#16839613—21no—
54C22⋊C4×Dic61—21no—
55C4×#11758198C2211yescharacteristic
56#16839609—21no—
57C42×Dic61C2211yescharacteristic
58#16839523C2211yescharacteristic
59#16839523C2211yescharacteristic
60#16839523C2211yescharacteristic
61#16839523C2211yescharacteristic
62#16839522C2211yescharacteristic
63#16839522C2211yescharacteristic
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×#11758224—21no—
76C22×C22⋊D61D411yescharacteristic
77C23×Dic61—21no—
78C22×C4×D61—21no—
79C22×C4×D61C2311yescharacteristic
80C2×#11758194C2311yescharacteristic
81C2×#11758194C2311yescharacteristic
82C2×#11758189—21no—
83M16×D61—22no—
84M16×D61—41no—
85C2×C8×D61—21no—
86#14519776C2×C411yescharacteristic, complemented
87#14519776C2×C411yescharacteristic, complemented
88#14519772—21no—
89#14519772—21no—
90#14519770—21no—
91#14519770—21no—
92#14519770—21no—
93#14519770—21no—
94#14519768—21no—
95#14519768C2×C411yescharacteristic, complemented
96#14519768C2×C411yescharacteristic, complemented
97#14519767—21no—
98#14519767—21no—
99#14519764—21no—
100#14519763—21no—
101#14519763—21no—
102#14519761—21no—
103#14519761—21no—
104#14519759—21no—
105#14519759—21no—
106#14519758—21no—
107#14519758—21no—
108#14519758—21no—
109#14519757—21no—
110#14519754—21no—
111#14519754—21no—
112#14519754—21no—
113#14519754—21no—
114#14519753C2×C411yescharacteristic, complemented
115#14519753C2×C411yescharacteristic, complemented
116#14519749—21no—
117#14519749—21no—
118#14519748—21no—
119#14519748C2×C411yescharacteristic, complemented
120#14519748C2×C411yescharacteristic, complemented
121#14519745—21no—
122Q8×Dic61C2×C411yescharacteristic, complemented
123Q8×Dic61C2×C411yescharacteristic, complemented
124C4×Dic122—21no—
125C4×Dic122—21no—
126#14519742—21no—
127D4×Dic61—21no—
128D4×Dic61—21no—
129D4×Dic61—21no—
130D4×Dic61C2×C411yescharacteristic, complemented
131D4×Dic61C2×C411yescharacteristic, complemented
132C4×C22⋊D61—21no—
133C4×C22⋊D61—21no—
134C4×C22⋊D61C2×C411yescharacteristic
135C4×C22⋊D61C2×C411yescharacteristic
136C4×C22⋊D61C2×C411yescharacteristic
137C4×C22⋊D61C2×C411yescharacteristic
138C4×C22⋊D61D411yescharacteristic
139C4×C22⋊D61D411yescharacteristic
140C4×C22⋊D61D411yescharacteristic
141C4×C22⋊D61D411yescharacteristic
142#14519737—28no—
143#14519737—21no—
144#14519737—21no—
145#14519736—21no—
146#14519736—21no—
147#14519736—21no—
148#14519736C2×C411yescharacteristic, complemented
149#14519736C2×C411yescharacteristic, complemented
150#14519736C2311yescharacteristic
151#14519736C2311yescharacteristic
152#14519735—21no—
153#14519735C2×C411yescharacteristic, complemented
154#14519735C2×C411yescharacteristic, complemented
155#14519734—21no—
156#14519733—21no—
157#14519733—21no—
158#14519733—21no—
159C2×C4⋊Dic61C2×C411yescharacteristic, complemented
160C2×C4⋊Dic61C2×C411yescharacteristic, complemented
161C2×#11758196—21no—
162C2×#11758196D411yescharacteristic
163C4⋊C4×D61C2×C411yescharacteristic, complemented
164C4⋊C4×D61C2×C411yescharacteristic, complemented
165C2×C22⋊Dic61—21no—
166C2×C22⋊Dic61D411yescharacteristic
167C2×#11758198—21no—
168C2×#11758198D411yescharacteristic
169C22⋊C4×D61—21no—
170C2×C4×Dic61—21no—
171C2×C4×Dic61—21no—
172C2×C4×Dic61—21no—
173C2×C4×Dic61—22no—
174C2×C4×Dic61—21no—
175C2×C4×Dic61—21no—
176C2×C4×Dic61—21no—
177C2×C4×Dic61—41no—
178C2×C4×Dic61C2311yescharacteristic
179C2×C4×Dic61C2311yescharacteristic
180C2×C4×Dic61C2311yescharacteristic
181C42×D61—21no—
182C42×D61—22no—
183C42×D61—41no—
184#14519706—21no—
185#14519706—21no—
186#14519704—22no—
187#14519704—41no—
188C22⋊#92418—21no—
189C22⋊#92418—21no—
190#14519689—21no—
191#14519689—21no—
192#14519687—21no—
193C8×Dic61—21no—
194#14519684—21no—
195#14519684—21no—
196C2×#41×C61C2311yescharacteristic
197C23×C4×C61C2311yescharacteristic
198C2×M16×C61—21no—
199C2×M16×C61—22no—
200C2×M16×C61—41no—
201C2×M16×C61C2311yescharacteristic
202C2×M16×C61C2311yescharacteristic
203C22×C8×C61—21no—
204#123×C61—21no—
205C22⋊Q8×C61C2×C411yescharacteristic, complemented
206C22⋊Q8×C61C2×C411yescharacteristic, complemented
207#121×C61C2×C411yescharacteristic, complemented
208#121×C61C2×C411yescharacteristic, complemented
209#120×C61—21no—
210C4×D4×C61—21no—
211C4×D4×C61—21no—
212#117×C61C2311yescharacteristic
213C2×C22⋊C4×C61—21no—
214C2×C42×C61C2311yescharacteristic
215C2×C42×C61C2311yescharacteristic
216#104×C61—22no—
217#104×C61—41no—
218#95×C61—21no—
219C24×C61C2×D411yescharacteristic
220C23×D61C2×D411yescharacteristic
221#41×C61—21no—
222#41×C61—21no—
223#41×C61—21no—
224#41×C61—21no—
225C2×Q8×C61C22×C411yescharacteristic
226C2×D4×C61—21no—
227C2×D4×C61—21no—
228C2×D4×C61—21no—
229C2×D4×C61C22×C411yescharacteristic
230C22×C4×C61—21no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—21no—
235C22×C4×C61—21no—
236C22×C4×C61—21no—
237C22×C4×C61C22×C411yescharacteristic
238C22×C4×C61C22×C411yescharacteristic
239C22×C4×C61C2×D411yescharacteristic
240C22×C4×C61C2×D411yescharacteristic
241C22×C4×C61C2×D411yescharacteristic
242C22×C4×C61C2411yescharacteristic
243C2×C22⋊D61—24no—
244C2×C22⋊D61—21no—
245C2×C22⋊D61—21no—
246C2×C22⋊D61C22⋊C411yescharacteristic
247C2×C22⋊D61C22⋊C411yescharacteristic
248C2×C22⋊D61C22⋊C411yescharacteristic
249C2×C22⋊D61C22⋊C411yescharacteristic
250C22×Dic61—21no—
251C22×Dic61—24no—
252C22×Dic61—21no—
253C22×Dic61—21no—
254C22×Dic61—21no—
255C22×Dic61—21no—
256C22×Dic61—21no—
257C22×Dic61—42no—
258C22×Dic61—42no—
259C22×Dic61C2×D411yescharacteristic
260C22×Dic61C2×D411yescharacteristic
261C22×Dic61C2×D411yescharacteristic
262#11758224—44no—
263C2×C4×D61—21no—
264C2×C4×D61—21no—
265C2×C4×D61—21no—
266C2×C4×D61—21no—
267C2×C4×D61—24no—
268C2×C4×D61—21no—
269C2×C4×D61—21no—
270C2×C4×D61—42no—
271C2×C4×D61—42no—
272C2×C4×D61C22×C411yescharacteristic
273C2×C4×D61C22×C411yescharacteristic
274C2×C4×D61C2×D411yescharacteristic
275C2×C4×D61C2×D411yescharacteristic
276C2×Dic122—21no—
277C2×Dic122—21no—
278M16×C61—21no—
279M16×C61—21no—
280M16×C61—21no—
281M16×C61—42no—
282M16×C61#4112yescomplemented
283C2×C8×C61—21no—
284C2×C8×C61—21no—
285C2×C8×C61—42no—
286C4⋊C4×C61—21no—
287C4⋊C4×C61—21no—
288C4⋊C4×C61C22×C411yescharacteristic
289C4⋊C4×C61C22×C411yescharacteristic
290C22⋊C4×C61—24no—
291C22⋊C4×C61—21no—
292C22⋊C4×C61—21no—
293C22⋊C4×C61—21no—
294C22⋊C4×C61—21no—
295C22⋊C4×C61—21no—
296C42×C61—21no—
297C42×C61—21no—
298C42×C61—21no—
299C42×C61—21no—
300C42×C61—21no—
301C22⋊Dic61—21no—
302C22⋊Dic61—21no—
303C22⋊Dic61—21no—
304C22⋊Dic61—21no—
305C22⋊Dic61—21no—
306C22⋊Dic61—21no—
307C22⋊Dic61—21no—
308C22⋊Dic61—21no—
309C22⋊Dic61C22⋊C411yescharacteristic
310C22⋊Dic61C22⋊C411yescharacteristic
311C22⋊Dic61C22⋊C411yescharacteristic
312C22⋊Dic61C22⋊C411yescharacteristic
313#11758198—24no—
314#11758198—21no—
315#11758198—21no—
316#11758198—21no—
317#11758198—21no—
318#11758198C22⋊C411yescharacteristic
319#11758198C22⋊C411yescharacteristic
320#11758198C22⋊C411yescharacteristic
321#11758198C22⋊C411yescharacteristic
322C4⋊Dic61—21no—
323C4⋊Dic61—21no—
324C4⋊Dic61—21no—
325C4⋊Dic61—21no—
326C4⋊Dic61—21no—
327C4⋊Dic61—21no—
328C4⋊Dic61C22×C411yescharacteristic
329C4⋊Dic61C22×C411yescharacteristic
330C4⋊Dic61C22×C411yescharacteristic
331C4⋊Dic61C22×C411yescharacteristic
332#11758196—24no—
333#11758196—21no—
334#11758196—21no—
335#11758196—21no—
336#11758196—21no—
337#11758196—21no—
338#11758196—21no—
339#11758196—21no—
340#11758196—21no—
341#11758196C22⋊C411yescharacteristic
342#11758196C22⋊C411yescharacteristic
343#11758196C22⋊C411yescharacteristic
344#11758196C22⋊C411yescharacteristic
345C4×Dic61—24no—
346C4×Dic61—21no—
347C4×Dic61—21no—
348C4×Dic61—21no—
349C4×Dic61—21no—
350C4×Dic61—21no—
351C4×Dic61—21no—
352C4×Dic61—21no—
353C4×Dic61—21no—
354C4×Dic61—21no—
355C4×Dic61—21no—
356C4×Dic61—21no—
357C4×Dic61—42no—
358C4×Dic61—42no—
359C4×Dic61—42no—
360C4×Dic61C22×C411yescharacteristic
361C4×Dic61C22×C411yescharacteristic
362C4×Dic61C2×D411yescharacteristic
363C4×Dic61C2×D411yescharacteristic
364C4×Dic61#4112yescomplemented
365#11758194—21no—
366#11758194—21no—
367#11758194—21no—
368#11758194—21no—
369C2×#92418—21no—
370C2×#92418—21no—
371#11758189—42no—
372C8×D61—42no—
373C23×C61—21no—
374C23×C61—21no—
375C23×C61—22no—
376C23×C61—21no—
377C23×C61—41no—
378C23×C61C2×C22⋊C411yescharacteristic
379C23×C61C2×C22⋊C411yescharacteristic
380C23×C61C22×D411yescharacteristic
381C22×D61—21no—
382C22×D61—21no—
383C22×D61—22no—
384C22×D61—41no—
385C22×D61C2×C22⋊C411yescharacteristic
386C22×D61C2×C22⋊C411yescharacteristic
387Q8×C61—21no—
388Q8×C61—21no—
389D4×C61—21no—
390D4×C61—21no—
391D4×C61—41no—
392D4×C61—41no—
393D4×C61—42no—
394D4×C61—81no—
395C2×C4×C61—21no—
396C2×C4×C61—21no—
397C2×C4×C61—21no—
398C2×C4×C61—21no—
399C2×C4×C61—21no—
400C2×C4×C61—21no—
401C2×C4×C61—21no—
402C2×C4×C61—21no—
403C2×C4×C61—21no—
404C2×C4×C61—21no—
405C2×C4×C61—22no—
406C2×C4×C61—22no—
407C2×C4×C61—21no—
408C2×C4×C61—21no—
409C2×C4×C61—21no—
410C2×C4×C61—41no—
411C2×C4×C61—41no—
412C2×C4×C61—41no—
413C2×C4×C61—41no—
414C2×C4×C61—41no—
415C2×C4×C61—41no—
416C2×C4×C61C2×C22⋊C411yescharacteristic
417C2×C4×C61C2×C22⋊C411yescharacteristic
418C2×C4×C61C23×C411yescharacteristic
419C2×C4×C61C22×D411yescharacteristic
420C2×C4×C61C2×#4111yescharacteristic
421C2×C4×C61C2×#4111yescharacteristic
422C2×C4×C61H(5,𝔽2)11yescharacteristic
423C2×C4×C612−1+411yescharacteristic
424C22⋊D61—22no—
425C22⋊D61—22no—
426C22⋊D61—22no—
427C22⋊D61—42no—
428C22⋊D61—81no—
429C22⋊D61#10414yescomplemented
430C2×Dic61—22no—
431C2×Dic61—22no—
432C2×Dic61—22no—
433C2×Dic61—21no—
434C2×Dic61—21no—
435C2×Dic61—22no—
436C2×Dic61—22no—
437C2×Dic61—21no—
438C2×Dic61—21no—
439C2×Dic61—21no—
440C2×Dic61—21no—
441C2×Dic61—41no—
442C2×Dic61—48no—
443C2×Dic61—41no—
444C2×Dic61—41no—
445C2×Dic61—42no—
446C2×Dic61—42no—
447C2×Dic61—81no—
448C2×Dic61—81no—
449C2×Dic61C2×C22⋊C411yescharacteristic
450C2×Dic61C2×C22⋊C411yescharacteristic
451C2×Dic61C2×C22⋊C411yescharacteristic
452C2×Dic61C2×C22⋊C411yescharacteristic
453C2×Dic61C2×C22⋊C411yescharacteristic
454C2×Dic61C2×C22⋊C411yescharacteristic
455C4×D61—21no—
456C4×D61—21no—
457C4×D61—21no—
458C4×D61—21no—
459C4×D61—21no—
460C4×D61—21no—
461C4×D61—21no—
462C4×D61—21no—
463C4×D61—48no—
464C4×D61—42no—
465C4×D61—81no—
466Dic122—42no—
467Dic122—81no—
468C8×C61—22no—
469C8×C61—41no—
470#92418—41no—
471#92418—41no—
472#22505—611nomaximal, Sylow
473C22×C61—21no—
474C22×C61—21no—
475C22×C61—21no—
476C22×C61—21no—
477C22×C61—21no—
478C22×C61—21no—
479C22×C61—21no—
480C22×C61—42no—
481C22×C61—42no—
482C22×C61—41no—
483C22×C61—41no—
484C22×C61—41no—
485C22×C61C2×#10412yes—
486C22×C61C22×C22⋊C411yescharacteristic
487C22×C61#54611yescharacteristic
488C22×C61#54711yescharacteristic
489C2×D61—21no—
490C2×D61—21no—
491C2×D61—21no—
492C2×D61—21no—
493C2×D61—21no—
494C2×D61—42no—
495C2×D61—42no—
496C2×D61C2×#10412yes—
497C4×C61—21no—
498C4×C61—21no—
499C4×C61—42no—
500C4×C61—42no—
501C4×C61—41no—
502C4×C61—41no—
503C4×C61—41no—
504C4×C61C4×#4111yescharacteristic
505C4×C61#52011yescharacteristic
506C4×C61#54611yescharacteristic
507C4×C61#54711yescharacteristic
508Dic61—24no—
509Dic61—21no—
510Dic61—21no—
511Dic61—21no—
512Dic61—21no—
513Dic61—21no—
514Dic61—42no—
515Dic61—41no—
516Dic61—41no—
517Dic61—41no—
518Dic61—41no—
519Dic61C2×#10412yes—
520#3475—611no—
521D4×M16—611no—
522C42×D4—611no—
523#1994—611no—
524#1986—611no—
525#1896—611no—
526#1896—611no—
527#1871—611no—
528#1871D6111yescharacteristic, complemented
529#1826—611no—
530#1826—611no—
531#1806—611no—
532C4×#104—611no—
533C2×#339—611no—
534C2×#339—611no—
535C2×C61—21no—
536C2×C61—21no—
537C2×C61—22no—
538C2×C61—41no—
539C2×C61—81no—
540C2×C61#233911yescharacteristic
541C2×C61C22×#10411yescharacteristic
542C2×C61#290111yescharacteristic
543D61—22no—
544D61—41no—
545C22×M16—611no—
546C22×M16C2×D6111yescharacteristic
547#556—611no—
548#555—611no—
549#554—611no—
550#553—611no—
551#553—611no—
552#552—611no—
553#552—611no—
554#552—1221no—
555#551—1221no—
556#551—1221no—
557#547—611no—
558#546—1221no—
559#533—611no—
560#529—1221no—
561#529—1221no—
562#529—1221no—
563#525—611no—
564#525C2×D6111yescharacteristic
565C4×#41—611no—
566C4×#41—1221no—
567C2×C4×D4—611no—
568C2×C4×D4—1221no—
569C2×#117—611no—
570C2×#117—611no—
571C22×C42—611no—
572C22×C42—611no—
573#436—1221no—
574#435—1221no—
575#435—1221no—
576C8×D4—1221no—
577#423—611no—
578C2×#104—611no—
579C2×#104—611no—
580C2×#104C2×D6111yescharacteristic
581C2×#104C2×D6111yescharacteristic
582#407—611no—
583#407—611no—
584C4×M16—611no—
585C4×C4⋊C4—611no—
586C4×C4⋊C4—1221no—
587C4×C22⋊C4—611no—
588C4×C22⋊C4—1221no—
589C4×C22⋊C4—1221no—
590C4×C22⋊C4C2×D6111yescharacteristic
591C43—611no—
592#339—611no—
593#339—611no—
594#339—611no—
595#339—611no—
596#339—611no—
597#339—611no—
598#339—611no—
599#339—611no—
600#339—611no—
601#339—611no—
602#339C2×D6111yescharacteristic
603#339C2×D6111yescharacteristic
604C61#2250511yescharacteristic, complemented, Sylow
605C2×#41—1221no—
606C2×#41C22×D6111yescharacteristic
607C22×D4—611no—
608C23×C4—611no—
609C23×C4—1221no—
610C23×C4—1221no—
611C23×C4C22×D6111yescharacteristic
612C2×M16—21no—
613C2×M16—22no—
614C2×M16—41no—
615C2×M16—611no—
616C2×M16—611no—
617C2×M16—1221no—
618C2×M16—1222no—
619C2×M16—2441no—
620C2×M16C22×D6111yescharacteristic
621C2×M16C22×D6111yescharacteristic
622C22×C8—21no—
623C22×C8—1221no—
624C4⋊Q8—611no—
625C4⋊Q8—611no—
626#126—1221no—
627#126—1221no—
628#126—1221no—
629#126—1221no—
630#126—1221no—
631#126—1221no—
632#125—611no—
633#125—611no—
634#125—1221no—
635#125—1221no—
636#125—1221no—
637#124—1221no—
638#124—1221no—
639#124—1221no—
640#123—21no—
641#123—1221no—
642#123—1221no—
643#123—1221no—
644#123—1221no—
645#123—1221no—
646#123—1221no—
647#123—1221no—
648C22⋊Q8—611no—
649C22⋊Q8—611no—
650C22⋊Q8—1221no—
651C22⋊Q8—1221no—
652C22⋊Q8—1221no—
653C22⋊Q8—1221no—
654C22⋊Q8—1221no—
655C22⋊Q8C4×D6111yescharacteristic, complemented
656C22⋊Q8C4×D6111yescharacteristic, complemented
657#121—611no—
658#121—611no—
659#121—1221no—
660#121—1221no—
661#121—1221no—
662#121C4×D6111yescharacteristic, complemented
663#121C4×D6111yescharacteristic, complemented
664#120—21no—
665#120—1221no—
666C4×Q8—611no—
667C4×Q8—611no—
668C4×Q8—1221no—
669C4×Q8—1221no—
670C4×Q8—1221no—
671C4×D4—21no—
672C4×D4—21no—
673C4×D4—611no—
674C4×D4—611no—
675C4×D4—611no—
676C4×D4—611no—
677C4×D4—611no—
678C4×D4—611no—
679C4×D4—611no—
680C4×D4—611no—
681C4×D4—611no—
682C4×D4—611no—
683C4×D4—1221no—
684C4×D4—1221no—
685C4×D4—1228no—
686C4×D4—1221no—
687C4×D4—1221no—
688C4×D4—1221no—
689C4×D4—1221no—
690C4×D4—1221no—
691#117—611no—
692#117—611no—
693#117—611no—
694#117—611no—
695#117—611no—
696#117—611no—
697#117—1221no—
698#117—1221no—
699#117—1221no—
700#117—1221no—
701#117—1221no—
702#117—1221no—
703#117—1221no—
704#117—1221no—
705#117C22×D6111yescharacteristic
706C2×C4⋊C4—611no—
707C2×C4⋊C4—611no—
708C2×C4⋊C4—611no—
709C2×C4⋊C4—611no—
710C2×C4⋊C4—611no—
711C2×C4⋊C4—1221no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—611no—
714C2×C22⋊C4—611no—
715C2×C22⋊C4—1221no—
716C2×C22⋊C4—1221no—
717C2×C22⋊C4—1221no—
718C2×C42—611no—
719C2×C42—611no—
720C2×C42—611no—
721C2×C42—1222no—
722C2×C42—1221no—
723C2×C42—1221no—
724C2×C42—1222no—
725C2×C42—1221no—
726C2×C42—1221no—
727C2×C42—1221no—
728C2×C42—1221no—
729C2×C42—1221no—
730C2×C42—2441no—
731C2×C42—2441no—
732C2×C42C22×D6111yescharacteristic
733C2×C42C22×D6111yescharacteristic
734C4⋊C8—1221no—
735C4⋊C8—1221no—
736#104—22no—
737#104—41no—
738#104—1222no—
739#104—2441no—
740C22⋊C8—1221no—
741C22⋊C8—1221no—
742C22⋊C8—1221no—
743C22⋊C8—1221no—
744#97—1221no—
745C4×C8—1221no—
746#95—21no—
747#95—1221no—
748#95—1221no—
749C24—611no—
750C24D4×D6111yescharacteristic
751#41—21no—
752#41—21no—
753#41—21no—
754#41—21no—
755#41—2444no—
756C2×Q8—1221no—
757C2×Q8—1221no—
758C2×Q8C2×C4×D6111yescharacteristic
759C2×D4—21no—
760C2×D4—21no—
761C2×D4—21no—
762C2×D4—611no—
763C2×D4—611no—
764C2×D4—611no—
765C2×D4—611no—
766C2×D4—1224no—
767C2×D4—1221no—
768C2×D4—1221no—
769C2×D4C2×C4×D6111yescharacteristic
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—611no—
778C22×C4—611no—
779C22×C4—611no—
780C22×C4—611no—
781C22×C4—611no—
782C22×C4—611no—
783C22×C4—611no—
784C22×C4—1221no—
785C22×C4—1221no—
786C22×C4—1224no—
787C22×C4—1221no—
788C22×C4—1221no—
789C22×C4—1221no—
790C22×C4—1221no—
791C22×C4—1221no—
792C22×C4—1221no—
793C22×C4—1221no—
794C22×C4—1221no—
795C22×C4—1224no—
796C22×C4—1221no—
797C22×C4—1221no—
798C22×C4—2442no—
799C22×C4—2442no—
800C22×C4—2442no—
801C22×C4—2442no—
802C22×C4C2×C4×D6111yescharacteristic
803C22×C4C2×C4×D6111yescharacteristic
804C22×C4D4×D6111yescharacteristic
805C22×C4D4×D6111yescharacteristic
806C22×C4D4×D6111yescharacteristic
807C22×C4C23×D6111yescharacteristic
808M16—21no—
809M16—21no—
810M16—21no—
811M16—42no—
812M16—1221no—
813M16—1221no—
814M16—1221no—
815M16—1221no—
816M16—2442no—
817M16#1175822412yescomplemented
818C2×C8—21no—
819C2×C8—21no—
820C2×C8—42no—
821C2×C8—1221no—
822C2×C8—1221no—
823C2×C8—2442no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—611no—
827C4⋊C4—611no—
828C4⋊C4—611no—
829C4⋊C4—611no—
830C4⋊C4—611no—
831C4⋊C4—611no—
832C4⋊C4—611no—
833C4⋊C4—611no—
834C4⋊C4—1221no—
835C4⋊C4—1221no—
836C4⋊C4—1221no—
837C4⋊C4—1221no—
838C4⋊C4—1221no—
839C4⋊C4—1221no—
840C4⋊C4—1221no—
841C4⋊C4—1221no—
842C4⋊C4—1221no—
843C4⋊C4—1221no—
844C4⋊C4—1221no—
845C4⋊C4—1221no—
846C4⋊C4—1224no—
847C4⋊C4—1221no—
848C4⋊C4—1221no—
849C4⋊C4C2×C4×D6111yescharacteristic
850C4⋊C4C2×C4×D6111yescharacteristic
851C22⋊C4—24no—
852C22⋊C4—21no—
853C22⋊C4—21no—
854C22⋊C4—21no—
855C22⋊C4—21no—
856C22⋊C4—21no—
857C22⋊C4—611no—
858C22⋊C4—611no—
859C22⋊C4—611no—
860C22⋊C4—611no—
861C22⋊C4—611no—
862C22⋊C4—611no—
863C22⋊C4—611no—
864C22⋊C4—611no—
865C22⋊C4—1221no—
866C22⋊C4—1221no—
867C22⋊C4—1221no—
868C22⋊C4—1221no—
869C22⋊C4—1224no—
870C22⋊C4—1221no—
871C22⋊C4—1221no—
872C22⋊C4—1221no—
873C22⋊C4—1221no—
874C22⋊C4—1221no—
875C22⋊C4—1221no—
876C22⋊C4—1221no—
877C22⋊C4—1221no—
878C42—21no—
879C42—21no—
880C42—21no—
881C42—21no—
882C42—21no—
883C42—611no—
884C42—611no—
885C42—611no—
886C42—611no—
887C42—612no—
888C42—1221no—
889C42—1221no—
890C42—1221no—
891C42—1221no—
892C42—1224no—
893C42—1221no—
894C42—1221no—
895C42—1221no—
896C42—1221no—
897C42—1221no—
898C42—1221no—
899C42—1221no—
900C42—2442no—
901C42—2442no—
902C42—2442no—
903C23—22no—
904C23—21no—
905C23—21no—
906C23—21no—
907C23—41no—
908C23—611no—
909C23—611no—
910C23—1222no—
911C23—1221no—
912C23—1221no—
913C23—2441no—
914C23C22⋊C4×D6111yescharacteristic
915C23C22⋊C4×D6111yescharacteristic
916C23C2×D4×D6111yescharacteristic
917Q8—21no—
918Q8—21no—
919Q8—4881no—
920Q8—2442no—
921D4—21no—
922D4—21no—
923D4—42no—
924D4—41no—
925D4—41no—
926D4—81no—
927D4—614no—
928D4—1222no—
929D4—1222no—
930D4—1222no—
931D4—4881no—
932D4—2442no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—611no—
955C2×C4—611no—
956C2×C4—611no—
957C2×C4—611no—
958C2×C4—611no—
959C2×C4—611no—
960C2×C4—1222no—
961C2×C4—1222no—
962C2×C4—1222no—
963C2×C4—1222no—
964C2×C4—1221no—
965C2×C4—1221no—
966C2×C4—1221no—
967C2×C4—1221no—
968C2×C4—1221no—
969C2×C4—1221no—
970C2×C4—1221no—
971C2×C4—1221no—
972C2×C4—1221no—
973C2×C4—1221no—
974C2×C4—1222no—
975C2×C4—1221no—
976C2×C4—1221no—
977C2×C4—1221no—
978C2×C4—1221no—
979C2×C4—4881no—
980C2×C4—4881no—
981C2×C4—4881no—
982C2×C4—2448no—
983C2×C4—2442no—
984C2×C4—2442no—
985C2×C4—2441no—
986C2×C4—2448no—
987C2×C4—2441no—
988C2×C4—2442no—
989C2×C4—2441no—
990C2×C4C22⋊C4×D6111yescharacteristic
991C2×C4C22⋊C4×D6111yescharacteristic
992C2×C4C22×C4×D6111yescharacteristic
993C2×C4C2×D4×D6111yescharacteristic
994C2×C4#41×D6111yescharacteristic
995C2×C4C2×#1175822411yescharacteristic
996C2×C4#1451982211yescharacteristic
997C2×C4#1451982411yescharacteristic
998C8—22no—
999C8—41no—
1000C8—2441no—
1001C8—2441no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—21no—
1008C22—21no—
1009C22—42no—
1010C22—42no—
1011C22—41no—
1012C22—41no—
1013C22—41no—
1014C22—612no—
1015C22—1221no—
1016C22—1221no—
1017C22—1221no—
1018C22—1221no—
1019C22—1221no—
1020C22—2442no—
1021C22—2442no—
1022C22#104×D6112yes—
1023C22C2×C22⋊C4×D6111yescharacteristic
1024C22#1684040111yescharacteristic
1025C22#1684041211yescharacteristic
1026C4—21no—
1027C4—21no—
1028C4—42no—
1029C4—42no—
1030C4—41no—
1031C4—41no—
1032C4—41no—
1033C4—612no—
1034C4—1224no—
1035C4—1221no—
1036C4—1221no—
1037C4—1221no—
1038C4—1221no—
1039C4—1221no—
1040C4—2442no—
1041C4—2441no—
1042C4—2441no—
1043C4—2441no—
1044C4—2441no—
1045C4C4×#1175822411yescharacteristic
1046C4#1684024111yescharacteristic
1047C4#1684039911yescharacteristic
1048C4#1684041011yescharacteristic
1049C2—21no—
1050C2—21no—
1051C2—22no—
1052C2—41no—
1053C2—81no—
1054C2—1222no—
1055C2—2441no—
1056C2#2144864511yescharacteristic
1057C2C2×#104×D6111yescharacteristic
1058C2#2145436511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1871C2
socleC22×C61C22×C22⋊C4
prime radical#21459379C2
cosocleC22×C4×C61C24
hypercenter#1871D61
hypocenterC61#22505
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. M16×C22⋊D61C2semidirect
3. C4×#14519737C2semidirect
4. #21446794C2semidirect
5. #21446761C2semidirect
6. #21446263C2semidirect
7. #21446259C2semidirect
8. #21446118C2semidirect
9. #21445919C2semidirect
10. #21445917C2semidirect
11. #21445837C2semidirect
12. #104×Dic61C2semidirect
13. C2×#16839523C2semidirect
14. #339×D61C2semidirect
15. C61×#1871C2semidirect
17. #16840483C4semidirect
18. #16840476C4semidirect
19. #16840470C4semidirect
20. #16840464C4semidirect
21. #16840459C4semidirect
22. #16840454C4semidirect
24. #16840446C4semidirect
27. #16840412C4semidirect
86. #14519776C2×C4semidirect
87. #14519776C2×C4semidirect
95. #14519768C2×C4semidirect
96. #14519768C2×C4semidirect
114. #14519753C2×C4semidirect
115. #14519753C2×C4semidirect
119. #14519748C2×C4semidirect
120. #14519748C2×C4semidirect
122. Q8×Dic61C2×C4semidirect
123. Q8×Dic61C2×C4semidirect
130. D4×Dic61C2×C4semidirect
131. D4×Dic61C2×C4semidirect
148. #14519736C2×C4semidirect
149. #14519736C2×C4semidirect
153. #14519735C2×C4semidirect
154. #14519735C2×C4semidirect
159. C2×C4⋊Dic61C2×C4semidirect
160. C2×C4⋊Dic61C2×C4semidirect
163. C4⋊C4×D61C2×C4semidirect
164. C4⋊C4×D61C2×C4semidirect
205. C22⋊Q8×C61C2×C4semidirect
206. C22⋊Q8×C61C2×C4semidirect
207. #121×C61C2×C4semidirect
208. #121×C61C2×C4semidirect
282. M16×C61#41semidirect
364. C4×Dic61#41semidirect
429. C22⋊D61#104semidirect
528. #1871D61semidirect
604. C61#22505semidirect
655. C22⋊Q8C4×D61semidirect
656. C22⋊Q8C4×D61semidirect
662. #121C4×D61semidirect
663. #121C4×D61semidirect
817. M16#11758224semidirect

Maximal subgroups

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

subgroupindex
#214593792
M16×C22⋊D612
C4×#145197372
#214467942
#214467612
#214462632
#214462592
#214461182
#214459192
#214459172
#214458372
#104×Dic612
C2×#168395232
#339×D612
C61×#18712
#2250561