Finite Group Databasebeta

← #29696491

Subgroups — #29696491

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#21459373C211yesmaximal, characteristic
2M16×C22⋊D61C211yesmaximal, characteristic, complemented
3C42×C22⋊D61C211yesmaximal, characteristic, complemented
4#21446794C211yesmaximal, characteristic, complemented
5#21446761C211yesmaximal, characteristic, complemented
6#21446262C211yesmaximal, characteristic, complemented
7#21446261C211yesmaximal, characteristic, complemented
8#21446121C211yesmaximal, characteristic, complemented
9#21446120C211yesmaximal, characteristic, complemented
10#21445918C211yesmaximal, characteristic, complemented
11#21445917C211yesmaximal, characteristic, complemented
12#21445838C211yesmaximal, characteristic, complemented
13#21445623C211yesmaximal, characteristic, complemented
14#339×D61C211yesmaximal, characteristic, complemented
15C2×C61×#339C211yesmaximal, characteristic, complemented
16C2×M16×D61C2211yescharacteristic
17#16840480C411yescharacteristic, complemented
18#16840475C411yescharacteristic, complemented
19#16840467C411yescharacteristic, complemented
20#16840460C411yescharacteristic, complemented
21#16840456C411yescharacteristic, complemented
22#16840451C411yescharacteristic, complemented
23#16840447C411yescharacteristic, complemented
24#16840445—21no—
25#16840438—21no—
26#16840436—21no—
27#16840413C411yescharacteristic, complemented
28#16840402—21no—
29#16840315C2211yescharacteristic
30#16840296—21no—
31#16840290—21no—
32#16840290—21no—
33#16840274C2211yescharacteristic
34#16840273C2211yescharacteristic
35C4×#11758222—21no—
36#16840230C2211yescharacteristic
37C2×C4×C22⋊D61—21no—
38C2×C4×C22⋊D61C2211yescharacteristic
39#117×D61C2211yescharacteristic
40C2×C42×D61C2211yescharacteristic
41#16839838—21no—
42#16839833—21no—
43#16839831—21no—
44C8×C22⋊D61—21no—
45#16839785C2211yescharacteristic
46C2×#14519705C2211yescharacteristic
47C2×#14519705C2211yescharacteristic
48C2×#14519703C2211yescharacteristic
49C2×#14519703C2211yescharacteristic
50#16839726C2211yescharacteristic
51#16839725C2211yescharacteristic
52M16×Dic61C2211yescharacteristic
53C4×#11758196—21no—
54C4×#11758196C2211yescharacteristic
55C4×#11758198—21no—
56C4×#11758198C2211yescharacteristic
57C4×C22⋊Dic61—21no—
58C4×C22⋊Dic61C2211yescharacteristic
59C42×Dic61C2211yescharacteristic
60#16839523C2211yescharacteristic
61#16839523C2211yescharacteristic
62#16839522C2211yescharacteristic
63#16839522C2211yescharacteristic
64#16839521C2211yescharacteristic
65#16839521C2211yescharacteristic
66#16839521C2211yescharacteristic
67#16839521C2211yescharacteristic
68C22×M16×C61C2211yescharacteristic
69C2×#117×C61C2211yescharacteristic
70C22×C42×C61C2211yescharacteristic
71C61×#339C2211yescharacteristic
72C61×#339C2211yescharacteristic
73C61×#339C2211yescharacteristic
74C61×#339C2211yescharacteristic
75C2×#11758222—21no—
76C2×#11758222C2311yescharacteristic
77C22×C22⋊D61D411yescharacteristic
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#14519771—21no—
91#14519771—21no—
92#14519770—21no—
93#14519770—21no—
94#14519769—21no—
95#14519768C2×C411yescharacteristic, complemented
96#14519768C2×C411yescharacteristic, complemented
97#14519767—21no—
98#14519767—21no—
99#14519765—21no—
100#14519763—21no—
101#14519763—21no—
102#14519762—21no—
103#14519762—21no—
104#14519761—21no—
105#14519760—21no—
106#14519760—21no—
107#14519760—21no—
108#14519759—21no—
109#14519759—21no—
110#14519757C2×C411yescharacteristic, complemented
111#14519757C2×C411yescharacteristic, complemented
112#14519756—21no—
113#14519756C2×C411yescharacteristic, complemented
114#14519756C2×C411yescharacteristic, complemented
115#14519755—21no—
116#14519755—21no—
117#14519754—21no—
118#14519754—21no—
119#14519752C2×C411yescharacteristic, complemented
120#14519752C2×C411yescharacteristic, complemented
121#14519751—21no—
122#14519751C2×C411yescharacteristic, complemented
123#14519751C2×C411yescharacteristic, complemented
124#14519750—21no—
125#14519750—21no—
126#14519747—21no—
127#14519746—21no—
128C4×Dic122—21no—
129C4×Dic122—21no—
130C4×Dic122—21no—
131#14519742C2×C411yescharacteristic, complemented
132#14519742C2×C411yescharacteristic, complemented
133C4×D244—21no—
134C4×D244—21no—
135C4×D244—21no—
136#14519739C2×C411yescharacteristic, complemented
137#14519739C2×C411yescharacteristic, complemented
138C4×C22⋊D61—28no—
139C4×C22⋊D61—21no—
140C4×C22⋊D61—21no—
141C4×C22⋊D61—21no—
142C4×C22⋊D61—21no—
143C4×C22⋊D61C2×C411yescharacteristic
144C4×C22⋊D61C2×C411yescharacteristic
145C4×C22⋊D61C2×C411yescharacteristic
146C4×C22⋊D61C2×C411yescharacteristic
147C4×C22⋊D61D411yescharacteristic
148C4×C22⋊D61D411yescharacteristic
149C4×C22⋊D61D411yescharacteristic
150C4×C22⋊D61D411yescharacteristic
151#14519737—21no—
152#14519737—21no—
153#14519736—21no—
154#14519736C2311yescharacteristic
155#14519735C2×C411yescharacteristic, complemented
156#14519735C2×C411yescharacteristic, complemented
157#14519734—21no—
158#14519734—21no—
159#14519734—21no—
160#14519734—21no—
161#14519733—21no—
162C2×#11758196—21no—
163C2×#11758196D411yescharacteristic
164C4⋊C4×D61C2×C411yescharacteristic, complemented
165C4⋊C4×D61C2×C411yescharacteristic, complemented
166C2×C22⋊Dic61—21no—
167C2×C22⋊Dic61D411yescharacteristic
168C2×#11758198—21no—
169C2×#11758198D411yescharacteristic
170C22⋊C4×D61—21no—
171C2×C4×Dic61—21no—
172C2×C4×Dic61—21no—
173C2×C4×Dic61—21no—
174C2×C4×Dic61C2311yescharacteristic
175C2×C4×Dic61C2311yescharacteristic
176C2×C4×Dic61C2311yescharacteristic
177C42×D61—21no—
178C42×D61—21no—
179C42×D61—22no—
180C42×D61—41no—
181#14519706—21no—
182#14519706—21no—
183#14519705—22no—
184#14519705—41no—
185#14519703—22no—
186#14519703—41no—
187C22⋊#92418—21no—
188C22⋊#92418—21no—
189#14519689—21no—
190#14519689—21no—
191#14519687—21no—
192C8×Dic61—21no—
193#14519684—21no—
194#14519684—21no—
195#14519684—21no—
196C23×C4×C61—21no—
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#117×C61—21no—
205#117×C61—21no—
206#117×C61C2×C411yescharacteristic, complemented
207#117×C61C2×C411yescharacteristic, complemented
208#117×C61C2311yescharacteristic
209#117×C61C2311yescharacteristic
210C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
211C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
212C2×C22⋊C4×C61—21no—
213C2×C42×C61—21no—
214C2×C42×C61—22no—
215C2×C42×C61—21no—
216C2×C42×C61—41no—
217C2×C42×C61C2311yescharacteristic
218C2×C42×C61C2311yescharacteristic
219C24×C61C2×D411yescharacteristic
220C23×D61C2×D411yescharacteristic
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—24no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—42no—
231C22×C4×C61—42no—
232C22×C4×C61C22×C411yescharacteristic
233C22×C4×C61C22×C411yescharacteristic
234C22×C4×C61C2×D411yescharacteristic
235C22×C4×C61C2×D411yescharacteristic
236C22×C4×C61C2×D411yescharacteristic
237C22×C4×C61C2411yescharacteristic
238C2×C22⋊D61—24no—
239C2×C22⋊D61—21no—
240C2×C22⋊D61—21no—
241C2×C22⋊D61—21no—
242C2×C22⋊D61C22⋊C411yescharacteristic
243C2×C22⋊D61C22⋊C411yescharacteristic
244C2×C22⋊D61C22⋊C411yescharacteristic
245C2×C22⋊D61C22⋊C411yescharacteristic
246C22×Dic61—21no—
247C22×Dic61—21no—
248C22×Dic61C2×D411yescharacteristic
249C22×Dic61C2×D411yescharacteristic
250C22×Dic61C2×D411yescharacteristic
251#11758222—21no—
252#11758222—21no—
253#11758222—21no—
254#11758222—21no—
255#11758222—44no—
256C2×D244—21no—
257C2×D244—21no—
258C2×D244C22×C411yescharacteristic
259C2×C4×D61—21no—
260C2×C4×D61—21no—
261C2×C4×D61—21no—
262C2×C4×D61—21no—
263C2×C4×D61—24no—
264C2×C4×D61—21no—
265C2×C4×D61—21no—
266C2×C4×D61—21no—
267C2×C4×D61—21no—
268C2×C4×D61—21no—
269C2×C4×D61—42no—
270C2×C4×D61—42no—
271C2×C4×D61C22×C411yescharacteristic
272C2×C4×D61C22×C411yescharacteristic
273C2×C4×D61C2×D411yescharacteristic
274C2×C4×D61C2×D411yescharacteristic
275C2×Dic122—21no—
276C2×Dic122—21no—
277C2×Dic122C22×C411yescharacteristic
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
290C4⋊C4×C61C22×C411yescharacteristic
291C4⋊C4×C61C22×C411yescharacteristic
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—
301C42×C61—21no—
302C42×C61—21no—
303C42×C61—42no—
304C42×C61#4112yescomplemented
305C22⋊Dic61—24no—
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#11758198—21no—
319#11758198—21no—
320#11758198—21no—
321#11758198—21no—
322#11758198—21no—
323#11758198—21no—
324#11758198C22⋊C411yescharacteristic
325#11758198C22⋊C411yescharacteristic
326#11758198C22⋊C411yescharacteristic
327#11758198C22⋊C411yescharacteristic
328C4⋊Dic61—21no—
329C4⋊Dic61—21no—
330C4⋊Dic61—21no—
331C4⋊Dic61—21no—
332C4⋊Dic61C22×C411yescharacteristic
333C4⋊Dic61C22×C411yescharacteristic
334#11758196—24no—
335#11758196—21no—
336#11758196—21no—
337#11758196—21no—
338#11758196—21no—
339#11758196—21no—
340#11758196—21no—
341#11758196—21no—
342#11758196—21no—
343#11758196—21no—
344#11758196—21no—
345#11758196C22⋊C411yescharacteristic
346#11758196C22⋊C411yescharacteristic
347#11758196C22⋊C411yescharacteristic
348#11758196C22⋊C411yescharacteristic
349C4×Dic61—24no—
350C4×Dic61—21no—
351C4×Dic61—21no—
352C4×Dic61—21no—
353C4×Dic61—21no—
354C4×Dic61—21no—
355C4×Dic61—21no—
356C4×Dic61—21no—
357C4×Dic61—21no—
358C4×Dic61—21no—
359C4×Dic61—42no—
360C4×Dic61—42no—
361C4×Dic61C22×C411yescharacteristic
362C4×Dic61C22×C411yescharacteristic
363C4×Dic61C2×D411yescharacteristic
364C4×Dic61C2×D411yescharacteristic
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—41no—
377C23×C61C2×C22⋊C411yescharacteristic
378C23×C61C2×C22⋊C411yescharacteristic
379C23×C61C22×D411yescharacteristic
380C22×D61—21no—
381C22×D61—21no—
382C22×D61—22no—
383C22×D61—21no—
384C22×D61—41no—
385C22×D61C2×C22⋊C411yescharacteristic
386C22×D61C2×C22⋊C411yescharacteristic
387C2×C4×C61—22no—
388C2×C4×C61—22no—
389C2×C4×C61—22no—
390C2×C4×C61—21no—
391C2×C4×C61—21no—
392C2×C4×C61—21no—
393C2×C4×C61—21no—
394C2×C4×C61—21no—
395C2×C4×C61—21no—
396C2×C4×C61—21no—
397C2×C4×C61—21no—
398C2×C4×C61—21no—
399C2×C4×C61—21no—
400C2×C4×C61—22no—
401C2×C4×C61—21no—
402C2×C4×C61—21no—
403C2×C4×C61—21no—
404C2×C4×C61—21no—
405C2×C4×C61—48no—
406C2×C4×C61—41no—
407C2×C4×C61—41no—
408C2×C4×C61—42no—
409C2×C4×C61—81no—
410C2×C4×C61C2×C22⋊C411yescharacteristic
411C2×C4×C61C2×C22⋊C411yescharacteristic
412C2×C4×C61C23×C411yescharacteristic
413C2×C4×C61C22×D411yescharacteristic
414C2×C4×C61C2×#4111yescharacteristic
415C2×C4×C61C2×#4111yescharacteristic
416C2×C4×C61H(5,𝔽2)11yescharacteristic
417C2×C4×C612−1+411yescharacteristic
418C22⋊D61—22no—
419C22⋊D61—22no—
420C22⋊D61—22no—
421C22⋊D61—41no—
422C22⋊D61—41no—
423C22⋊D61—42no—
424C22⋊D61—81no—
425C22⋊D61#10414yescomplemented
426C2×Dic61—21no—
427C2×Dic61—21no—
428C2×Dic61—22no—
429C2×Dic61—22no—
430C2×Dic61—22no—
431C2×Dic61—21no—
432C2×Dic61—21no—
433C2×Dic61—21no—
434C2×Dic61—41no—
435C2×Dic61—41no—
436C2×Dic61—41no—
437C2×Dic61—41no—
438C2×Dic61—41no—
439C2×Dic61C2×C22⋊C411yescharacteristic
440C2×Dic61C2×C22⋊C411yescharacteristic
441C2×Dic61C2×C22⋊C411yescharacteristic
442C2×Dic61C2×C22⋊C411yescharacteristic
443C2×Dic61C2×C22⋊C411yescharacteristic
444C2×Dic61C2×C22⋊C411yescharacteristic
445D244—21no—
446D244—21no—
447D244—42no—
448D244—81no—
449C4×D61—21no—
450C4×D61—21no—
451C4×D61—21no—
452C4×D61—21no—
453C4×D61—21no—
454C4×D61—21no—
455C4×D61—21no—
456C4×D61—21no—
457C4×D61—48no—
458C4×D61—42no—
459C4×D61—41no—
460C4×D61—41no—
461C4×D61—42no—
462C4×D61—81no—
463C4×D61—81no—
464Dic122—21no—
465Dic122—21no—
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×C61C2×#10412yes—
483C22×C61C22×C22⋊C411yescharacteristic
484C22×C61#54611yescharacteristic
485C22×C61#54711yescharacteristic
486C2×D61—21no—
487C2×D61—21no—
488C2×D61—21no—
489C2×D61—21no—
490C2×D61—21no—
491C2×D61—42no—
492C2×D61—42no—
493C2×D61—41no—
494C2×D61—41no—
495C2×D61—41no—
496C2×D61C2×#10412yes—
497C4×C61—24no—
498C4×C61—21no—
499C4×C61—21no—
500C4×C61—42no—
501C4×C61—41no—
502C4×C61—41no—
503C4×C61—41no—
504C4×C61—41no—
505C4×C61C4×#4111yescharacteristic
506C4×C61#52011yescharacteristic
507C4×C61#54611yescharacteristic
508C4×C61#54711yescharacteristic
509Dic61—21no—
510Dic61—21no—
511Dic61—21no—
512Dic61—21no—
513Dic61—21no—
514Dic61—42no—
515Dic61—42no—
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#1871—611no—
529#1826—611no—
530#1826—611no—
531#1806—611no—
532C4×#104—611no—
533C2×#339—611no—
534C2×#339D6111yescharacteristic, complemented
535C2×C61—21no—
536C2×C61—21no—
537C2×C61—22no—
538C2×C61—41no—
539C2×C61#233911yescharacteristic
540C2×C61C22×#10411yescharacteristic
541C2×C61#290111yescharacteristic
542D61—22no—
543D61—41no—
544D61—81no—
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#525—611no—
565C4×#41—611no—
566C4×#41—1221no—
567C2×C4×D4—611no—
568C2×C4×D4—1221no—
569C2×#117—611no—
570C2×#117C2×D6111yescharacteristic
571C22×C42—611no—
572C22×C42C2×D6111yescharacteristic
573#436—1221no—
574#435—1221no—
575#435—1221no—
576C8×D4—1221no—
577#423—611no—
578C2×#104—611no—
579C2×#104—611no—
580C2×#104—611no—
581C2×#104—611no—
582#407—611no—
583#407—611no—
584C4×M16—611no—
585C4×C4⋊C4—611no—
586C4×C4⋊C4—1221no—
587C4×C22⋊C4—611no—
588C4×C22⋊C4—611no—
589C4×C22⋊C4—1221no—
590C4×C22⋊C4—1221no—
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#339C2×D6111yescharacteristic
601#339C2×D6111yescharacteristic
602#339C2×D6111yescharacteristic
603#339C2×D6111yescharacteristic
604C61#2250511yescharacteristic, complemented, Sylow
605C2×#41—611no—
606C2×#41—1221no—
607C22×D4—611no—
608C23×C4—21no—
609C23×C4—611no—
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—1221no—
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—611no—
651C22⋊Q8—611no—
652C22⋊Q8—1221no—
653C22⋊Q8—1221no—
654C22⋊Q8—1221no—
655C22⋊Q8—1221no—
656C22⋊Q8—1221no—
657#121—611no—
658#121—611no—
659#121—611no—
660#121—611no—
661#121—1221no—
662#121—1221no—
663#121—1221no—
664#120—1221no—
665#120—1221no—
666C4×Q8—611no—
667C4×Q8—611no—
668C4×Q8—1221no—
669C4×Q8—1221no—
670C4×Q8—1221no—
671C4×D4—611no—
672C4×D4—611no—
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—1221no—
682C4×D4—1221no—
683C4×D4—1221no—
684C4×D4—1221no—
685C4×D4—1221no—
686C4×D4—1221no—
687C4×D4—1221no—
688C4×D4—1228no—
689C4×D4—1221no—
690C4×D4—1221no—
691#117—21no—
692#117—21no—
693#117—611no—
694#117—611no—
695#117—611no—
696#117—1221no—
697#117—1221no—
698#117—1221no—
699#117—1221no—
700#117—1221no—
701#117—1221no—
702#117C4×D6111yescharacteristic, complemented
703#117C4×D6111yescharacteristic, complemented
704#117C22×D6111yescharacteristic
705#117C22×D6111yescharacteristic
706C2×C4⋊C4—611no—
707C2×C4⋊C4—611no—
708C2×C4⋊C4—611no—
709C2×C4⋊C4—1221no—
710C2×C4⋊C4C4×D6111yescharacteristic, complemented
711C2×C4⋊C4C4×D6111yescharacteristic, complemented
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—21no—
719C2×C42—22no—
720C2×C42—21no—
721C2×C42—41no—
722C2×C42—611no—
723C2×C42—611no—
724C2×C42—611no—
725C2×C42—1221no—
726C2×C42—1221no—
727C2×C42—1221no—
728C2×C42—1222no—
729C2×C42—1221no—
730C2×C42—1221no—
731C2×C42—2441no—
732C2×C42C22×D6111yescharacteristic
733C2×C42C22×D6111yescharacteristic
734C4⋊C8—1221no—
735C4⋊C8—1221no—
736#104—1222no—
737#104—1222no—
738#104—2441no—
739#104—2441no—
740C22⋊C8—1221no—
741C22⋊C8—1221no—
742C22⋊C8—1221no—
743C22⋊C8—1221no—
744#97—1221no—
745C4×C8—1221no—
746#95—1221no—
747#95—1221no—
748#95—1221no—
749C24—611no—
750C24D4×D6111yescharacteristic
751#41—1221no—
752#41—1221no—
753#41—1221no—
754#41—1221no—
755#41—2444no—
756C2×Q8—611no—
757C2×Q8—1221no—
758C2×Q8—1221no—
759C2×D4—611no—
760C2×D4—611no—
761C2×D4—611no—
762C2×D4—611no—
763C2×D4—611no—
764C2×D4—1221no—
765C2×D4—1221no—
766C2×D4—1224no—
767C2×D4—1221no—
768C2×D4—1221no—
769C2×D4—1221no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—24no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—611no—
782C22×C4—611no—
783C22×C4—611no—
784C22×C4—611no—
785C22×C4—611no—
786C22×C4—611no—
787C22×C4—611no—
788C22×C4—1221no—
789C22×C4—1221no—
790C22×C4—1221no—
791C22×C4—1221no—
792C22×C4—1224no—
793C22×C4—1221no—
794C22×C4—1221no—
795C22×C4—1221no—
796C22×C4—1221no—
797C22×C4—1221no—
798C22×C4—1221no—
799C22×C4—1221no—
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#1175822212yescomplemented
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—1221no—
833C4⋊C4—1221no—
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—1224no—
845C4⋊C4—1221no—
846C4⋊C4—1221no—
847C4⋊C4C2×C4×D6111yescharacteristic
848C4⋊C4C2×C4×D6111yescharacteristic
849C4⋊C4C2×C4×D6111yescharacteristic
850C4⋊C4C2×C4×D6111yescharacteristic
851C22⋊C4—21no—
852C22⋊C4—21no—
853C22⋊C4—21no—
854C22⋊C4—21no—
855C22⋊C4—611no—
856C22⋊C4—611no—
857C22⋊C4—611no—
858C22⋊C4—611no—
859C22⋊C4—611no—
860C22⋊C4—611no—
861C22⋊C4—611no—
862C22⋊C4—611no—
863C22⋊C4—1221no—
864C22⋊C4—1221no—
865C22⋊C4—1221no—
866C22⋊C4—1221no—
867C22⋊C4—1221no—
868C22⋊C4—1221no—
869C22⋊C4—1221no—
870C22⋊C4—1221no—
871C22⋊C4—1224no—
872C22⋊C4—1224no—
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—21no—
884C42—21no—
885C42—42no—
886C42—611no—
887C42—611no—
888C42—611no—
889C42—611no—
890C42—1221no—
891C42—1221no—
892C42—1221no—
893C42—1221no—
894C42—1224no—
895C42—1221no—
896C42—1221no—
897C42—1221no—
898C42—1221no—
899C42—1221no—
900C42—2442no—
901C42—2442no—
902C42#1175822212yescomplemented
903C23—22no—
904C23—21no—
905C23—21no—
906C23—41no—
907C23—611no—
908C23—611no—
909C23—1222no—
910C23—1221no—
911C23—1221no—
912C23—1221no—
913C23—2441no—
914C23C22⋊C4×D6111yescharacteristic
915C23C22⋊C4×D6111yescharacteristic
916C23C2×D4×D6111yescharacteristic
917Q8—1221no—
918Q8—1221no—
919Q8—4881no—
920Q8—2442no—
921D4—614no—
922D4—1222no—
923D4—1222no—
924D4—1222no—
925D4—1221no—
926D4—1221no—
927D4—4881no—
928D4—4881no—
929D4—2442no—
930D4—2442no—
931D4—2441no—
932D4—2441no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—22no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—48no—
952C2×C4—41no—
953C2×C4—42no—
954C2×C4—41no—
955C2×C4—81no—
956C2×C4—611no—
957C2×C4—611no—
958C2×C4—611no—
959C2×C4—611no—
960C2×C4—611no—
961C2×C4—611no—
962C2×C4—1222no—
963C2×C4—1221no—
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—1222no—
974C2×C4—1222no—
975C2×C4—1221no—
976C2×C4—1221no—
977C2×C4—1221no—
978C2×C4—4881no—
979C2×C4—4881no—
980C2×C4—2448no—
981C2×C4—2442no—
982C2×C4—2442no—
983C2×C4—2441no—
984C2×C4—2441no—
985C2×C4—2441no—
986C2×C4—2441no—
987C2×C4—2441no—
988C2×C4—2441no—
989C2×C4—2441no—
990C2×C4C22⋊C4×D6111yescharacteristic
991C2×C4C22⋊C4×D6111yescharacteristic
992C2×C4C22×C4×D6111yescharacteristic
993C2×C4C2×D4×D6111yescharacteristic
994C2×C4C2×#1175822211yescharacteristic
995C2×C4C2×#1175822211yescharacteristic
996C2×C4#1451982211yescharacteristic
997C2×C4#1451982511yescharacteristic
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—612no—
1012C22—1221no—
1013C22—1221no—
1014C22—1221no—
1015C22—1221no—
1016C22—1221no—
1017C22—2442no—
1018C22—2442no—
1019C22—2441no—
1020C22—2441no—
1021C22—2441no—
1022C22#104×D6112yes—
1023C22C2×C22⋊C4×D6111yescharacteristic
1024C22#1684040211yescharacteristic
1025C22#1684041311yescharacteristic
1026C4—24no—
1027C4—21no—
1028C4—21no—
1029C4—42no—
1030C4—41no—
1031C4—41no—
1032C4—41no—
1033C4—41no—
1034C4—612no—
1035C4—1221no—
1036C4—1221no—
1037C4—1221no—
1038C4—1221no—
1039C4—1221no—
1040C4—2442no—
1041C4—2442no—
1042C4—2441no—
1043C4—2441no—
1044C4—2441no—
1045C4C4×#1175822211yescharacteristic
1046C4#1684024311yescharacteristic
1047C4#1684040211yescharacteristic
1048C4#1684041311yescharacteristic
1049C2—21no—
1050C2—21no—
1051C2—22no—
1052C2—41no—
1053C2—1222no—
1054C2—4881no—
1055C2—2441no—
1056C2#2144864611yescharacteristic
1057C2C2×#104×D6111yescharacteristic
1058C2#2145436311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#339C2
socleC22×C61C22×C22⋊C4
prime radical#21459373C2
cosocleC22×C4×C61C24
hypercenterC2×#339D61
hypocenterC61#22505
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
2. M16×C22⋊D61C2semidirect
3. C42×C22⋊D61C2semidirect
4. #21446794C2semidirect
5. #21446761C2semidirect
6. #21446262C2semidirect
7. #21446261C2semidirect
8. #21446121C2semidirect
9. #21446120C2semidirect
10. #21445918C2semidirect
11. #21445917C2semidirect
12. #21445838C2semidirect
13. #21445623C2semidirect
14. #339×D61C2semidirect
15. C2×C61×#339C2semidirect
17. #16840480C4semidirect
18. #16840475C4semidirect
19. #16840467C4semidirect
20. #16840460C4semidirect
21. #16840456C4semidirect
22. #16840451C4semidirect
23. #16840447C4semidirect
27. #16840413C4semidirect
86. #14519776C2×C4semidirect
87. #14519776C2×C4semidirect
95. #14519768C2×C4semidirect
96. #14519768C2×C4semidirect
110. #14519757C2×C4semidirect
111. #14519757C2×C4semidirect
113. #14519756C2×C4semidirect
114. #14519756C2×C4semidirect
119. #14519752C2×C4semidirect
120. #14519752C2×C4semidirect
122. #14519751C2×C4semidirect
123. #14519751C2×C4semidirect
131. #14519742C2×C4semidirect
132. #14519742C2×C4semidirect
136. #14519739C2×C4semidirect
137. #14519739C2×C4semidirect
155. #14519735C2×C4semidirect
156. #14519735C2×C4semidirect
164. C4⋊C4×D61C2×C4semidirect
165. C4⋊C4×D61C2×C4semidirect
206. #117×C61C2×C4semidirect
207. #117×C61C2×C4semidirect
210. C2×C4⋊C4×C61C2×C4semidirect
211. C2×C4⋊C4×C61C2×C4semidirect
282. M16×C61#41semidirect
304. C42×C61#41semidirect
425. C22⋊D61#104semidirect
534. C2×#339D61semidirect
604. C61#22505semidirect
702. #117C4×D61semidirect
703. #117C4×D61semidirect
710. C2×C4⋊C4C4×D61semidirect
711. C2×C4⋊C4C4×D61semidirect
817. M16#11758222semidirect
902. C42#11758222semidirect

Maximal subgroups

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

subgroupindex
#214593732
M16×C22⋊D612
C42×C22⋊D612
#214467942
#214467612
#214462622
#214462612
#214461212
#214461202
#214459182
#214459172
#214458382
#214456232
#339×D612
C2×C61×#3392
#2250561