Finite Group Databasebeta

← #30611380

Subgroups — #30611380

Order 15616.

1074 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462671C211yesmaximal, characteristic, complemented
2#21462332C211yesmaximal, characteristic, complemented
3#21461259C211yesmaximal, characteristic, complemented
4#21461254C211yesmaximal, characteristic, complemented
5#21461237C211yesmaximal, characteristic, complemented
6#21461234C211yesmaximal, characteristic, complemented
7#21461232C211yesmaximal, characteristic, complemented
8#21461231C211yesmaximal, characteristic, complemented
9#21461223C211yesmaximal, characteristic, complemented
10#21461220C211yesmaximal, characteristic, complemented
11#21461206C211yesmaximal, characteristic, complemented
12#21461205C211yesmaximal, characteristic, complemented
13C2×#16840616C211yesmaximal, characteristic, complemented
14D61⋊#327C211yesmaximal, characteristic, complemented
15#21459655C211yesmaximal, characteristic
16C2×D4×#6923—21no—
17#16840794—21no—
18#16840793—21no—
19#16840792—21no—
20#16840791—21no—
21#16840785C2211yescharacteristic, complemented
22#16840784C2211yescharacteristic, complemented
23#16840734C2211yescharacteristic, complemented
24#16840733C2211yescharacteristic, complemented
25C2×#14519834C2211yescharacteristic
26D61⋊(C22⋊C8)C2211yescharacteristic
27#16840713—21no—
28#16840709—21no—
29#16840709—21no—
30#16840706C2211yescharacteristic, complemented
31#16840704C2211yescharacteristic
32#16840704C2211yescharacteristic, complemented
33C4×C4⋊#6923C2211yescharacteristic, complemented
34C2×(C2×#6923)⋊C4C2211yescharacteristic
35C2×(C2×#6923)⋊C4C2211yescharacteristic, complemented
36#16840616C2211yescharacteristic, complemented
37#16840616C2211yescharacteristic, complemented
38#16840616C2211yescharacteristic, complemented
39#16840616C2211yescharacteristic, complemented
40#16840616C2211yescharacteristic, complemented
41#16840616C2211yescharacteristic, complemented
42#16840616C2211yescharacteristic, complemented
43#16840616C2211yescharacteristic, complemented
44#16840614C2211yescharacteristic
45#16840614C2211yescharacteristic
46#16840614C2211yescharacteristic
47#16840614C2211yescharacteristic
48#16840613C2211yescharacteristic
49#16840613C2211yescharacteristic
50#16840613C2211yescharacteristic
51#16840613C2211yescharacteristic
52#16840464C411yescharacteristic, complemented
53#16840461—21no—
54#16840458C411yescharacteristic, complemented
55#16840455—21no—
56#16840453C411yescharacteristic, complemented
57#16840446C411yescharacteristic, complemented
58#16840442—21no—
59#16840439—21no—
60#16840423C411yescharacteristic, complemented
61#16840405C411yescharacteristic, complemented
62#16840400C411yescharacteristic, complemented
63#16840358—21no—
64#16840346—21no—
65#16840320—21no—
66#16840299C2211yescharacteristic
67#16840291C2211yescharacteristic
68#16840275C2211yescharacteristic
69#16840269C2211yescharacteristic
70C2×#14519753C2211yescharacteristic
71#121×D61C2211yescharacteristic
72#16840234—21no—
73C4×D4×D61C2211yescharacteristic
74C61×#548C411yescharacteristic, complemented
75C23×#6923—21no—
76C23×#6923—21no—
77C2×#11758213—21no—
78C2×#11758217—21no—
79C2×D61⋊C8—21no—
80C22×#92420—21no—
81D4×#6923—44no—
82C2×C4⋊#6923—21no—
83C2×C4⋊#6923—21no—
84C2×C4⋊#6923—21no—
85C2×C4⋊#6923—21no—
86C2×C22⋊#6923—21no—
87C2×C22⋊#6923—21no—
88C2×C4×#6923—21no—
89#14519844—21no—
90C4⋊#92420—21no—
91#14519834—21no—
92#14519834—21no—
93#14519834C2311yescharacteristic
94#14519834C2311yescharacteristic
95#14519834C2311yescharacteristic
96#14519834C2311yescharacteristic
97C22⋊#92420—21no—
98C22⋊#92420—21no—
99#14519832—21no—
100#14519832—21no—
101(C2×#6923)⋊C4—21no—
102(C2×#6923)⋊C4—21no—
103(C2×#6923)⋊C4—21no—
104(C2×#6923)⋊C4C2311yescharacteristic
105(C2×#6923)⋊C4C2311yescharacteristic
106(C2×#6923)⋊C4C2311yescharacteristic
107(C2×#6923)⋊C4C2311yescharacteristic
108C2×#11758226C2×C411yescharacteristic, complemented
109C2×D4×D61—21no—
110C2×D4×D61C2×C411yescharacteristic, complemented
111C2×D4×D61D411yescharacteristic
112C22×C4×D61C2311yescharacteristic
113C22×C4×D61C2311yescharacteristic
114#14519772—21no—
115#14519772—21no—
116#14519771—21no—
117#14519770—21no—
118#14519770—21no—
119#14519770—21no—
120#14519769C2×C411yescharacteristic, complemented
121#14519768C2×C411yescharacteristic, complemented
122#14519767—21no—
123#14519767—21no—
124#14519766—21no—
125#14519766C2×C411yescharacteristic, complemented
126#14519762—21no—
127#14519762—21no—
128#14519762—21no—
129#14519761—21no—
130#14519760—21no—
131#14519759—21no—
132#14519759—21no—
133#14519759—21no—
134#14519759—21no—
135#14519758—21no—
136#14519753—21no—
137#14519753—21no—
138#14519753—21no—
139#14519753C2×C411yescharacteristic, complemented
140#14519753C2×C411yescharacteristic, complemented
141#14519753C2×C411yescharacteristic, complemented
142#14519753C2311yescharacteristic
143#14519753C2311yescharacteristic
144#14519752C2311yescharacteristic
145#14519751—21no—
146#14519751C2×C411yescharacteristic, complemented
147#14519751C2×C411yescharacteristic, complemented
148#14519750—21no—
149#14519750—21no—
150#14519749—21no—
151#14519749—21no—
152#14519749—21no—
153#14519749—21no—
154#14519748C2×C411yescharacteristic, complemented
155#14519748C2311yescharacteristic
156#14519747—21no—
157#14519747—21no—
158#14519745—21no—
159#14519745—21no—
160Q8×Dic61C2×C411yescharacteristic, complemented
161C4×D244—21no—
162C4×D244C2×C411yescharacteristic
163C4×D244C2×C411yescharacteristic, complemented
164D4×Dic61—21no—
165D4×Dic61C2×C411yescharacteristic, complemented
166D4×Dic61D411yescharacteristic
167#14519739—21no—
168#14519739D411yescharacteristic
169C4×C22⋊D61—21no—
170C4×C22⋊D61—21no—
171C4×C22⋊D61—21no—
172C4×C22⋊D61C2×C411yescharacteristic
173C4×C22⋊D61C2×C411yescharacteristic
174#14519737—21no—
175#14519737—21no—
176#14519737—21no—
177#14519737D411yescharacteristic
178#14519737D411yescharacteristic
179#14519736C2×C411yescharacteristic, complemented
180#14519735—21no—
181#14519735C2×C411yescharacteristic, complemented
182#14519734—21no—
183#14519734—21no—
184#14519733—21no—
185C2×C4⋊Dic61C2×C411yescharacteristic, complemented
186C2×#11758196—21no—
187C4⋊C4×D61C2×C411yescharacteristic, complemented
188C4⋊C4×D61D411yescharacteristic
189C2×#11758198—21no—
190C2×#11758198—21no—
191C22⋊C4×D61—21no—
192C22⋊C4×D61—21no—
193C22⋊C4×D61D411yescharacteristic
194C22⋊C4×D61D411yescharacteristic
195C42×D61C2311yescharacteristic
196C2×#41×C61C2×C411yescharacteristic, complemented
197C22×Q8×C61C2×C411yescharacteristic, complemented
198#124×C61—21no—
199#124×C61C2×C411yescharacteristic, complemented
200C22⋊Q8×C61—21no—
201C22⋊Q8×C61C2×C411yescharacteristic, complemented
202#121×C61—21no—
203#121×C61C2×C411yescharacteristic, complemented
204C4×Q8×C61C2×C411yescharacteristic, complemented
205C4×D4×C61—21no—
206C4×D4×C61C2×C411yescharacteristic
207C23×D61—21no—
208C23×D61C2×D411yescharacteristic
209C23×D61C2×D411yescharacteristic
210C22×#6923—21no—
211C22×#6923—21no—
212C22×#6923—21no—
213C22×#6923—21no—
214C22×#6923—42no—
215C22×#6923—42no—
216C22×#6923—42no—
217C22×#6923—42no—
218C22×#6923—81no—
219C22×#6923—81no—
220#41×C61—81no—
221C2×Q8×C61—21no—
222C2×Q8×C61—81no—
223C2×Q8×C61C22×C411yescharacteristic
224C2×Q8×C61C22×C411yescharacteristic
225C2×D4×C61—21no—
226C2×D4×C61—21no—
227C2×D4×C61C22⋊C411yescharacteristic
228C2×D4×C61C22×C411yescharacteristic
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61C22×C411yescharacteristic
232C22×C4×C61C22×C411yescharacteristic
233C2×C22⋊D61—21no—
234C2×C22⋊D61—21no—
235C2×C22⋊D61—21no—
236C2×C22⋊D61—21no—
237C2×C22⋊D61—21no—
238C2×C22⋊D61C22⋊C411yescharacteristic
239C2×C22⋊D61C22⋊C411yescharacteristic
240C22×Dic61—21no—
241C22×Dic61—21no—
242C22×Dic61C2×D411yescharacteristic
243C22×Dic61C2×D411yescharacteristic
244#11758226—81no—
245D4×D61—22no—
246D4×D61—22no—
247D4×D61—42no—
248D4×D61—42no—
249D4×D61—81no—
250C2×D244—21no—
251C2×D244—21no—
252C2×D244C22⋊C411yescharacteristic
253C2×D244C22×C411yescharacteristic
254C2×C4×D61—21no—
255C2×C4×D61—21no—
256C2×C4×D61—21no—
257C2×C4×D61—81no—
258C2×C4×D61—81no—
259C2×C4×D61C22×C411yescharacteristic
260C2×C4×D61C22×C411yescharacteristic
261C2×C4×D61C2×D411yescharacteristic
262C2×C4×D61C2×D411yescharacteristic
263C2×C4×D61C2×D411yescharacteristic
264C2×C4×D61C2×D411yescharacteristic
265C2×C4×D61C2×D411yescharacteristic
266C2×C4×D61C2×D411yescharacteristic
267C2×C4×D61C2411yescharacteristic
268C22⋊#6923—42no—
269C22⋊#6923—42no—
270#11758217—81no—
271C2×#92420—21no—
272C2×#92420—21no—
273C2×#92420—21no—
274C2×#92420—21no—
275C2×#92420—81no—
276C4⋊#6923—42no—
277C4⋊#6923—42no—
278C4⋊#6923—81no—
279C4⋊#6923—81no—
280C4×#6923—42no—
281#11758213—81no—
282D61⋊C8—81no—
283C4⋊C4×C61—21no—
284C4⋊C4×C61—21no—
285C4⋊C4×C61C22⋊C411yescharacteristic
286C4⋊C4×C61C22×C411yescharacteristic
287C22⋊C4×C61—21no—
288C22⋊C4×C61—21no—
289C22⋊C4×C61—21no—
290C22⋊C4×C61—21no—
291C22⋊C4×C61C22⋊C411yescharacteristic
292C22⋊C4×C61C22⋊C411yescharacteristic
293C42×C61—21no—
294C42×C61C22×C411yescharacteristic
295C22⋊Dic61—21no—
296C22⋊Dic61—21no—
297C22⋊Dic61—21no—
298C22⋊Dic61—21no—
299C22⋊Dic61C22⋊C411yescharacteristic
300C22⋊Dic61C22⋊C411yescharacteristic
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—
311#11758198—21no—
312#11758198—21no—
313#11758198C22⋊C411yescharacteristic
314#11758198C22⋊C411yescharacteristic
315#11758198C22⋊C411yescharacteristic
316#11758198C22⋊C411yescharacteristic
317C4⋊Dic61—21no—
318C4⋊Dic61—21no—
319C4⋊Dic61—21no—
320C4⋊Dic61C22⋊C411yescharacteristic
321C4⋊Dic61C22×C411yescharacteristic
322C4⋊Dic61C22×C411yescharacteristic
323C4⋊Dic61C22×C411yescharacteristic
324#11758196—21no—
325#11758196—21no—
326#11758196—21no—
327#11758196—21no—
328#11758196—21no—
329#11758196—21no—
330#11758196—21no—
331#11758196—21no—
332#11758196—21no—
333#11758196C22⋊C411yescharacteristic
334#11758196C22⋊C411yescharacteristic
335C4×Dic61—21no—
336C4×Dic61—21no—
337C4×Dic61—21no—
338C4×Dic61C22×C411yescharacteristic
339C4×Dic61C2×D411yescharacteristic
340C4×Dic61C2×D411yescharacteristic
341C23×C61—21no—
342C23×C61C2×C22⋊C411yescharacteristic
343C23×C61C2×C22⋊C411yescharacteristic
344C22×D61—21no—
345C22×D61—21no—
346C22×D61—21no—
347C22×D61—41no—
348C22×D61—41no—
349C22×D61—41no—
350C22×D61—41no—
351C22×D61—42no—
352C22×D61—81no—
353C22×D61—81no—
354C22×D61C2×C22⋊C411yescharacteristic
355C22×D61C2×C22⋊C411yescharacteristic
356C22×D61AGL(1,ℤ/8)12yes—
357C22×D61#13712yes—
358C22×D61C22×D411yescharacteristic
359C2×#6923—22no—
360C2×#6923—41no—
361C2×#6923—41no—
362C2×#6923—41no—
363C2×#6923—41no—
364C2×#6923—41no—
365C2×#6923—41no—
366C2×#6923—41no—
367C2×#6923—41no—
368C2×#6923—41no—
369C2×#6923—41no—
370C2×#6923—41no—
371C2×#6923—84no—
372C2×#6923—84no—
373Q8×C61—41no—
374Q8×C61—41no—
375Q8×C61—81no—
376D4×C61—22no—
377D4×C61—41no—
378D4×C61—42no—
379D4×C61—81no—
380C2×C4×C61—21no—
381C2×C4×C61—21no—
382C2×C4×C61—21no—
383C2×C4×C61—41no—
384C2×C4×C61—41no—
385C2×C4×C61—81no—
386C2×C4×C61—81no—
387C2×C4×C61C2×C22⋊C411yescharacteristic
388C2×C4×C61C2×C22⋊C411yescharacteristic
389C2×C4×C61C2×C22⋊C411yescharacteristic
390C2×C4×C61C2×C22⋊C411yescharacteristic
391C2×C4×C61C23×C411yescharacteristic
392C22⋊D61—22no—
393C22⋊D61—22no—
394C22⋊D61—42no—
395C22⋊D61—41no—
396C22⋊D61—41no—
397C22⋊D61—81no—
398C22⋊D61—81no—
399C22⋊D61—81no—
400C2×Dic61—21no—
401C2×Dic61—21no—
402C2×Dic61—21no—
403C2×Dic61—41no—
404C2×Dic61—41no—
405C2×Dic61—81no—
406C2×Dic61—81no—
407C2×Dic61C2×C22⋊C411yescharacteristic
408C2×Dic61C2×C22⋊C411yescharacteristic
409C2×Dic61C2×C22⋊C411yescharacteristic
410C2×Dic61C2×C22⋊C411yescharacteristic
411C2×Dic61C22×D411yescharacteristic
412D244—22no—
413D244—41no—
414D244—41no—
415D244—41no—
416D244—81no—
417C4×D61—21no—
418C4×D61—21no—
419C4×D61—41no—
420C4×D61—41no—
421C4×D61—41no—
422C4×D61—41no—
423C4×D61—41no—
424C4×D61—41no—
425C4×D61—41no—
426C4×D61—41no—
427C4×D61—42no—
428C4×D61—81no—
429C4×D61—81no—
430#92420—41no—
431#92420—41no—
432#92420—41no—
433#92420—41no—
434#17622—611nomaximal, Sylow
435C22×C61—21no—
436C22×C61—21no—
437C22×C61—21no—
438C22×C61—21no—
439C22×C61—21no—
440C22×C61—41no—
441C22×C61—41no—
442C22×C61—41no—
443C22×C61#41712yes—
444C22×C61C22×C22⋊C411yescharacteristic
445C2×D61—21no—
446C2×D61—21no—
447C2×D61—21no—
448C2×D61—21no—
449C2×D61—21no—
450C2×D61—21no—
451C2×D61—21no—
452C2×D61—42no—
453C2×D61—42no—
454C2×D61—42no—
455C2×D61—42no—
456C2×D61—41no—
457C2×D61—41no—
458C2×D61—41no—
459C2×D61—162no—
460C2×D61#41712yes—
461C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
462C2×D61C2×#13711yescharacteristic
463#6923—42no—
464#6923—81no—
465#6923—81no—
466#6923—81no—
467C4×C61—21no—
468C4×C61—21no—
469C4×C61—21no—
470C4×C61—21no—
471C4×C61—21no—
472C4×C61—41no—
473C4×C61—41no—
474C4×C61—41no—
475Dic61—21no—
476Dic61—21no—
477Dic61—21no—
478Dic61—21no—
479Dic61—21no—
480Dic61—41no—
481Dic61—41no—
482Dic61—41no—
483#3505—611no—
484#2973—611no—
485#2349—611no—
486#1520—611no—
487#1519—611no—
488#1513—611no—
489#1513—611no—
490#1512—611no—
491#1512—611no—
492#1509—611no—
493#1509—611no—
494#1504—611no—
495#1504—611no—
496C2×#328—611no—
497C2×#327—611no—
498C2×C61—22no—
499C2×C61—41no—
500C2×C61—81no—
501C2×C61#288311yescharacteristic
502C2×C61C2×#41711yescharacteristic
503C2×C61#290111yescharacteristic
504D61—21no—
505D61—21no—
506D61—22no—
507D61—41no—
508D61—81no—
509#553—611no—
510#553—611no—
511#553—1221no—
512#553—1221no—
513#552—611no—
514#552—611no—
515#551—1221no—
516#551—1221no—
517#548—611no—
518#548#692311yescharacteristic, complemented
519#546—611no—
520#546—611no—
521#539—1221no—
522#538—1221no—
523#534—1221no—
524#529—611no—
525#529—611no—
526#525—611no—
527#525—611no—
528C2×C22⋊Q8—611no—
529C2×#121—611no—
530#518—1221no—
531C2×C4×D4—611no—
532C2×C4×D4—1221no—
533#435—1221no—
534#435—1221no—
535#435—1221no—
536#435—1221no—
537#432—611no—
538#432—611no—
539#407—611no—
540#407—611no—
541C2×C22⋊C8—611no—
542C2×C22⋊C8—611no—
543#389—1221no—
544#385—1221no—
545#385—1221no—
546#382—611no—
547#380—611no—
548#380—611no—
549C4×C4⋊C4—611no—
550C2×#95—611no—
551C2×#95—611no—
552#328—611no—
553#328—611no—
554#328—611no—
555#328—611no—
556#328—611no—
557#328—611no—
558#328—611no—
559#328—611no—
560#327—611no—
561#327—611no—
562#327—611no—
563#327—611no—
564#327—611no—
565#327—611no—
566#327—611no—
567#327—611no—
568C61#1762211yescharacteristic, complemented, Sylow
569C2×#41—611no—
570C2×#41C2×#692311yescharacteristic, complemented
571C22×Q8C2×#692311yescharacteristic, complemented
572C22×D4—611no—
573C22×D4—611no—
574C22×D4—1221no—
575C23×C4—611no—
576C23×C4—611no—
577C23×C4—1221no—
578C23×C4—1221no—
579C2×M16—1221no—
580C2×M16—1221no—
581C22×C8—1221no—
582C22×C8—1221no—
583#126—1221no—
584#126—1221no—
585#126—1221no—
586#126—1221no—
587#126—1221no—
588#126—1221no—
589#125—611no—
590#125—611no—
591#125—1221no—
592#125—1221no—
593#124—21no—
594#124—611no—
595#124—1221no—
596#124C2×#692311yescharacteristic, complemented
597#123—1221no—
598#123—1221no—
599#123—1221no—
600#123—1221no—
601#123—1221no—
602#123—1221no—
603#123—1221no—
604#123—1221no—
605#123—1221no—
606#123—1221no—
607C22⋊Q8—21no—
608C22⋊Q8—611no—
609C22⋊Q8—611no—
610C22⋊Q8—611no—
611C22⋊Q8—611no—
612C22⋊Q8—611no—
613C22⋊Q8—1221no—
614C22⋊Q8—1221no—
615C22⋊Q8—1221no—
616C22⋊Q8C2×#692311yescharacteristic, complemented
617#121—21no—
618#121—611no—
619#121—611no—
620#121—611no—
621#121—611no—
622#121—611no—
623#121—1221no—
624#121—1221no—
625#121—1221no—
626#121—1221no—
627#121—1221no—
628#121—1221no—
629#121—1221no—
630#121C2×#692311yescharacteristic, complemented
631#120—1221no—
632#120—1221no—
633#120—1221no—
634#120—1221no—
635C4×Q8—611no—
636C4×Q8C2×#692311yescharacteristic, complemented
637C4×D4—21no—
638C4×D4—611no—
639C4×D4—611no—
640C4×D4—611no—
641C4×D4—611no—
642C4×D4—611no—
643C4×D4—611no—
644C4×D4—611no—
645C4×D4—611no—
646C4×D4—611no—
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—2444no—
657C4×D4C2×#692311yescharacteristic
658#117—611no—
659#117—611no—
660#117—1221no—
661#117—1221no—
662#117—1221no—
663#117—1221no—
664C2×C4⋊C4—611no—
665C2×C4⋊C4—611no—
666C2×C4⋊C4—611no—
667C2×C4⋊C4—1221no—
668C2×C4⋊C4—1221no—
669C2×C4⋊C4—1221no—
670C2×C4⋊C4—1221no—
671C2×C4⋊C4—1221no—
672C2×C22⋊C4—611no—
673C2×C22⋊C4—611no—
674C2×C22⋊C4—1221no—
675C2×C22⋊C4—1221no—
676C2×C22⋊C4—1221no—
677C2×C22⋊C4—1221no—
678C2×C22⋊C4—1221no—
679C2×C22⋊C4—1221no—
680C2×C42—611no—
681C2×C42—1221no—
682C4⋊C8—1221no—
683C4⋊C8—1221no—
684C22⋊C8—611no—
685C22⋊C8—611no—
686C22⋊C8—611no—
687C22⋊C8—611no—
688C22⋊C8—1221no—
689C22⋊C8—1221no—
690C22⋊C8—1221no—
691C22⋊C8—1221no—
692#97—1221no—
693#97—1221no—
694#95—611no—
695#95—611no—
696#95—611no—
697#95—611no—
698#95—1221no—
699#95—1221no—
700#95—1221no—
701C24—611no—
702C24—611no—
703C24—1221no—
704#41—81no—
705#41—4881no—
706C2×Q8—21no—
707C2×Q8—81no—
708C2×Q8C22×#692311yescharacteristic
709C2×Q8C22×#692311yescharacteristic
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—611no—
713C2×D4—611no—
714C2×D4—611no—
715C2×D4—611no—
716C2×D4—1221no—
717C2×D4—1221no—
718C2×D4—1221no—
719C2×D4—1222no—
720C2×D4—1222no—
721C2×D4—1221no—
722C2×D4—1221no—
723C2×D4—1221no—
724C2×D4—1221no—
725C2×D4—4881no—
726C2×D4—2442no—
727C2×D4—2442no—
728C2×D4C22⋊#692311yescharacteristic
729C2×D4C22×#692311yescharacteristic
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—611no—
733C22×C4—611no—
734C22×C4—611no—
735C22×C4—611no—
736C22×C4—611no—
737C22×C4—611no—
738C22×C4—611no—
739C22×C4—611no—
740C22×C4—611no—
741C22×C4—611no—
742C22×C4—611no—
743C22×C4—1221no—
744C22×C4—1221no—
745C22×C4—1221no—
746C22×C4—1221no—
747C22×C4—1221no—
748C22×C4—1221no—
749C22×C4—1221no—
750C22×C4—1221no—
751C22×C4—1221no—
752C22×C4—4881no—
753C22×C4—4881no—
754C22×C4—4881no—
755C22×C4—4881no—
756C22×C4—2442no—
757C22×C4—2442no—
758C22×C4—2442no—
759C22×C4—2442no—
760C22×C4C22×#692311yescharacteristic
761C22×C4C22×#692311yescharacteristic
762M16—4881no—
763M16—4881no—
764C2×C8—1221no—
765C2×C8—1221no—
766C2×C8—1221no—
767C2×C8—1221no—
768C2×C8—4881no—
769C2×C8—4881no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—611no—
773C4⋊C4—611no—
774C4⋊C4—611no—
775C4⋊C4—611no—
776C4⋊C4—611no—
777C4⋊C4—611no—
778C4⋊C4—1221no—
779C4⋊C4—1221no—
780C4⋊C4—1221no—
781C4⋊C4—1221no—
782C4⋊C4—1221no—
783C4⋊C4—1221no—
784C4⋊C4—1221no—
785C4⋊C4—1221no—
786C4⋊C4—1221no—
787C4⋊C4—1221no—
788C4⋊C4—1221no—
789C4⋊C4—1221no—
790C4⋊C4—4881no—
791C4⋊C4—4881no—
792C4⋊C4—2442no—
793C4⋊C4—2442no—
794C4⋊C4C22⋊#692311yescharacteristic
795C4⋊C4C22×#692311yescharacteristic
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—611no—
801C22⋊C4—611no—
802C22⋊C4—611no—
803C22⋊C4—611no—
804C22⋊C4—611no—
805C22⋊C4—611no—
806C22⋊C4—1221no—
807C22⋊C4—1221no—
808C22⋊C4—1221no—
809C22⋊C4—1221no—
810C22⋊C4—1221no—
811C22⋊C4—1221no—
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—2442no—
823C22⋊C4—2442no—
824C22⋊C4C22⋊#692311yescharacteristic
825C22⋊C4C22⋊#692311yescharacteristic
826C42—21no—
827C42—611no—
828C42—611no—
829C42—611no—
830C42—1221no—
831C42—1221no—
832C42—1221no—
833C42—2442no—
834C42C22×#692311yescharacteristic
835C23—21no—
836C23—611no—
837C23—611no—
838C23—612no—
839C23—612no—
840C23—611no—
841C23—1221no—
842C23—1221no—
843C23—1221no—
844C23—4881no—
845C23—4881no—
846C23—2441no—
847C23—2441no—
848C23—2441no—
849C23—2441no—
850C23—2442no—
851C23C2×C22⋊#692311yescharacteristic
852C23C2×C22⋊#692311yescharacteristic
853Q8—41no—
854Q8—41no—
855Q8—81no—
856D4—22no—
857D4—41no—
858D4—42no—
859D4—81no—
860D4—1222no—
861D4—1222no—
862D4—1222no—
863D4—4881no—
864D4—4881no—
865D4—4881no—
866D4—4881no—
867D4—2441no—
868D4—2441no—
869D4—2441no—
870D4—2441no—
871D4—2441no—
872D4—2442no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—81no—
879C2×C4—81no—
880C2×C4—611no—
881C2×C4—611no—
882C2×C4—611no—
883C2×C4—611no—
884C2×C4—611no—
885C2×C4—1221no—
886C2×C4—1221no—
887C2×C4—1222no—
888C2×C4—1221no—
889C2×C4—1221no—
890C2×C4—1221no—
891C2×C4—4881no—
892C2×C4—4881no—
893C2×C4—4881no—
894C2×C4—4884no—
895C2×C4—4884no—
896C2×C4—4881no—
897C2×C4—2441no—
898C2×C4—2441no—
899C2×C4—2441no—
900C2×C4—2441no—
901C2×C4—2441no—
902C2×C4—2441no—
903C2×C4—2441no—
904C2×C4—2441no—
905C2×C4—2442no—
906C2×C4—2441no—
907C2×C4—2441no—
908C2×C4—2441no—
909C2×C4—2441no—
910C2×C4—2441no—
911C2×C4—2441no—
912C2×C4—2441no—
913C2×C4—2441no—
914C2×C4—2441no—
915C2×C4—2441no—
916C2×C4—2441no—
917C2×C4—2441no—
918C2×C4—2441no—
919C2×C4C2×C22⋊#692311yescharacteristic
920C2×C4C2×C22⋊#692311yescharacteristic
921C2×C4C2×C22⋊#692311yescharacteristic
922C2×C4C2×C22⋊#692311yescharacteristic
923C2×C4C23×#692311yescharacteristic
924C8—2441no—
925C8—2441no—
926C8—2441no—
927C8—2441no—
928C22—21no—
929C22—21no—
930C22—21no—
931C22—21no—
932C22—21no—
933C22—41no—
934C22—41no—
935C22—41no—
936C22—611no—
937C22—611no—
938C22—612no—
939C22—1221no—
940C22—1221no—
941C22—1221no—
942C22—1221no—
943C22—1221no—
944C22—1221no—
945C22—1221no—
946C22—9762no—
947C22—2442no—
948C22—2442no—
949C22—2442no—
950C22—2442no—
951C22—2441no—
952C22—2441no—
953C22—2441no—
954C22#1684075312yes—
955C22C22×C22⋊#692311yescharacteristic
956C4—21no—
957C4—21no—
958C4—21no—
959C4—21no—
960C4—21no—
961C4—41no—
962C4—41no—
963C4—41no—
964C4—1221no—
965C4—1221no—
966C4—1221no—
967C4—1221no—
968C4—1221no—
969C4—4881no—
970C4—4881no—
971C4—4881no—
972C4—2442no—
973C4—2441no—
974C4—2441no—
975C4—2441no—
976C2—22no—
977C2—41no—
978C2—81no—
979C2—1221no—
980C2—1222no—
981C2—1221no—
982C2—4881no—
983C2—2441no—
984C2#2146241811yescharacteristic
985C2C2×#1684075311yescharacteristic
986C2#2146245011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#548C4
socleC22×C61C22×C22⋊C4
prime radical#21459655C2
cosocleC2×C4×D61C24
hypercenter#548#6923
hypocenterC61#17622
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #21462671C2semidirect
2. #21462332C2semidirect
3. #21461259C2semidirect
4. #21461254C2semidirect
5. #21461237C2semidirect
6. #21461234C2semidirect
7. #21461232C2semidirect
8. #21461231C2semidirect
9. #21461223C2semidirect
10. #21461220C2semidirect
11. #21461206C2semidirect
12. #21461205C2semidirect
13. C2×#16840616C2semidirect
14. D61⋊#327C2semidirect
21. #16840785C22semidirect
22. #16840784C22semidirect
23. #16840734C22semidirect
24. #16840733C22semidirect
30. #16840706C22semidirect
32. #16840704C22semidirect
33. C4×C4⋊#6923C22semidirect
35. C2×(C2×#6923)⋊C4C22semidirect
36. #16840616C22semidirect
37. #16840616C22semidirect
38. #16840616C22semidirect
39. #16840616C22semidirect
40. #16840616C22semidirect
41. #16840616C22semidirect
42. #16840616C22semidirect
43. #16840616C22semidirect
52. #16840464C4semidirect
54. #16840458C4semidirect
56. #16840453C4semidirect
57. #16840446C4semidirect
60. #16840423C4semidirect
61. #16840405C4semidirect
62. #16840400C4semidirect
74. C61×#548C4semidirect
108. C2×#11758226C2×C4semidirect
110. C2×D4×D61C2×C4semidirect
120. #14519769C2×C4semidirect
121. #14519768C2×C4semidirect
125. #14519766C2×C4semidirect
139. #14519753C2×C4semidirect
140. #14519753C2×C4semidirect
141. #14519753C2×C4semidirect
146. #14519751C2×C4semidirect
147. #14519751C2×C4semidirect
154. #14519748C2×C4semidirect
160. Q8×Dic61C2×C4semidirect
163. C4×D244C2×C4semidirect
165. D4×Dic61C2×C4semidirect
179. #14519736C2×C4semidirect
181. #14519735C2×C4semidirect
185. C2×C4⋊Dic61C2×C4semidirect
187. C4⋊C4×D61C2×C4semidirect
196. C2×#41×C61C2×C4semidirect
197. C22×Q8×C61C2×C4semidirect
199. #124×C61C2×C4semidirect
201. C22⋊Q8×C61C2×C4semidirect
203. #121×C61C2×C4semidirect
204. C4×Q8×C61C2×C4semidirect
518. #548#6923semidirect
568. C61#17622semidirect
570. C2×#41C2×#6923semidirect
571. C22×Q8C2×#6923semidirect
596. #124C2×#6923semidirect
616. C22⋊Q8C2×#6923semidirect
630. #121C2×#6923semidirect
636. C4×Q8C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214626712
#214623322
#214612592
#214612542
#214612372
#214612342
#214612322
#214612312
#214612232
#214612202
#214612062
#214612052
C2×#168406162
D61⋊#3272
#214596552
#1762261