Finite Group Databasebeta

← #30611377

Subgroups — #30611377

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#21461257C211yesmaximal, characteristic, complemented
4#21461255C211yesmaximal, characteristic, complemented
5#21461235C211yesmaximal, characteristic, complemented
6#21461234C211yesmaximal, characteristic, complemented
7#21461231C211yesmaximal, characteristic, complemented
8#21461230C211yesmaximal, characteristic, complemented
9#21461221C211yesmaximal, characteristic, complemented
10#21461220C211yesmaximal, characteristic, complemented
11#21461205C211yesmaximal, characteristic, complemented
12#21461204C211yesmaximal, characteristic, complemented
13D61⋊#328C211yesmaximal, characteristic, complemented
14C2×#16840613C211yesmaximal, characteristic, complemented
15#21459646C211yesmaximal, 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#16840615C2211yescharacteristic, complemented
41#16840615C2211yescharacteristic, complemented
42#16840615C2211yescharacteristic, complemented
43#16840615C2211yescharacteristic, complemented
44#16840613C2211yescharacteristic
45#16840613C2211yescharacteristic
46#16840613C2211yescharacteristic
47#16840613C2211yescharacteristic
48#16840613C2211yescharacteristic
49#16840613C2211yescharacteristic
50#16840613C2211yescharacteristic
51#16840613C2211yescharacteristic
52#16840462C411yescharacteristic, complemented
53#16840459—21no—
54#16840459C411yescharacteristic, complemented
55#16840457—21no—
56#16840454C411yescharacteristic, complemented
57#16840452C411yescharacteristic, complemented
58#16840443—21no—
59#16840438—21no—
60#16840420C411yescharacteristic, complemented
61#16840419C411yescharacteristic, complemented
62#16840406C411yescharacteristic, complemented
63#16840355—21no—
64#16840344—21no—
65#16840322—21no—
66#16840294C2211yescharacteristic
67#16840291C2211yescharacteristic
68#16840272C2211yescharacteristic
69#16840269C2211yescharacteristic
70C22⋊Q8×D61C2211yescharacteristic
71C2×#14519748C2211yescharacteristic
72#16840235—21no—
73C4×D4×D61C2211yescharacteristic
74C61×#546C411yescharacteristic, 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×#11758224C2×C411yescharacteristic, complemented
109C2×Q8×D61C2×C411yescharacteristic, complemented
110C22×C22⋊D61—21no—
111C2×D4×D61D411yescharacteristic
112C22×C4×D61C2311yescharacteristic
113C22×C4×D61C2311yescharacteristic
114#14519772—21no—
115#14519770—21no—
116#14519770—21no—
117#14519770—21no—
118#14519770—21no—
119#14519770—21no—
120#14519769C2×C411yescharacteristic, complemented
121#14519768—21no—
122#14519768C2×C411yescharacteristic, complemented
123#14519767—21no—
124#14519764—21no—
125#14519764C2×C411yescharacteristic, complemented
126#14519763—21no—
127#14519761—21no—
128#14519760—21no—
129#14519759—21no—
130#14519759—21no—
131#14519759—21no—
132#14519758—21no—
133#14519758—21no—
134#14519758—21no—
135#14519758—21no—
136#14519757C2311yescharacteristic
137#14519756—21no—
138#14519756C2×C411yescharacteristic, complemented
139#14519756C2×C411yescharacteristic, complemented
140#14519755—21no—
141#14519754—21no—
142#14519754—21no—
143#14519753C2×C411yescharacteristic, complemented
144#14519753C2311yescharacteristic
145#14519750—21no—
146#14519750—21no—
147#14519749—21no—
148#14519748—21no—
149#14519748—21no—
150#14519748—21no—
151#14519748—21no—
152#14519748C2×C411yescharacteristic, complemented
153#14519748C2×C411yescharacteristic, complemented
154#14519748C2×C411yescharacteristic, complemented
155#14519748C2311yescharacteristic
156#14519748C2311yescharacteristic
157#14519746—21no—
158#14519745—21no—
159#14519745—21no—
160Q8×Dic61C2×C411yescharacteristic, complemented
161C4×Dic122C2×C411yescharacteristic, complemented
162C4×D244C2×C411yescharacteristic
163D4×Dic61—21no—
164D4×Dic61C2×C411yescharacteristic, complemented
165D4×Dic61D411yescharacteristic
166#14519739D411yescharacteristic
167C4×C22⋊D61—21no—
168C4×C22⋊D61—21no—
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#14519737—21no—
178#14519737D411yescharacteristic
179#14519737D411yescharacteristic
180#14519736—21no—
181#14519736C2×C411yescharacteristic, complemented
182#14519735C2×C411yescharacteristic, complemented
183#14519733—21no—
184#14519733—21no—
185#14519733—21no—
186C2×C4⋊Dic61C2×C411yescharacteristic, complemented
187C4⋊C4×D61—21no—
188C4⋊C4×D61C2×C411yescharacteristic, complemented
189C4⋊C4×D61D411yescharacteristic
190C2×C22⋊Dic61—21no—
191C2×C22⋊Dic61—21no—
192C22⋊C4×D61—21no—
193C22⋊C4×D61D411yescharacteristic
194C22⋊C4×D61D411yescharacteristic
195C42×D61C2311yescharacteristic
196C2×#41×C61C2×C411yescharacteristic, complemented
197C22×D4×C61C2×C411yescharacteristic, complemented
198#124×C61C2×C411yescharacteristic, complemented
199#123×C61—21no—
200C22⋊Q8×C61C2×C411yescharacteristic, complemented
201#121×C61—21no—
202#121×C61C2×C411yescharacteristic, complemented
203#120×C61—21no—
204C4×D4×C61C2×C411yescharacteristic
205C4×D4×C61C2×C411yescharacteristic, complemented
206C2×C22⋊C4×C61—21no—
207C24×C61—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×C61C22×C411yescharacteristic
222C2×D4×C61—21no—
223C2×D4×C61—21no—
224C2×D4×C61—21no—
225C2×D4×C61—81no—
226C2×D4×C61C22⋊C411yescharacteristic
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⋊D61—21no—
239C2×C22⋊D61—42no—
240C2×C22⋊D61—42no—
241C2×C22⋊D61C22⋊C411yescharacteristic
242C2×C22⋊D61C22⋊C411yescharacteristic
243C22×Dic61—21no—
244C22×Dic61—21no—
245C22×Dic61—21no—
246C22×Dic61C2×D411yescharacteristic
247C22×Dic61C2×D411yescharacteristic
248Q8×D61—81no—
249#11758224—81no—
250D4×D61—22no—
251D4×D61—22no—
252C2×D244C22⋊C411yescharacteristic
253C2×C4×D61—21no—
254C2×C4×D61—21no—
255C2×C4×D61—81no—
256C2×C4×D61—81no—
257C2×C4×D61C22×C411yescharacteristic
258C2×C4×D61C22×C411yescharacteristic
259C2×C4×D61C2×D411yescharacteristic
260C2×C4×D61C2×D411yescharacteristic
261C2×C4×D61C2×D411yescharacteristic
262C2×C4×D61C2×D411yescharacteristic
263C2×C4×D61C2×D411yescharacteristic
264C2×C4×D61C2×D411yescharacteristic
265C2×C4×D61C2411yescharacteristic
266C2×Dic122—21no—
267C2×Dic122C22×C411yescharacteristic
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×C61C22⋊C411yescharacteristic
285C4⋊C4×C61C22×C411yescharacteristic
286C22⋊C4×C61—21no—
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×C61C22×C411yescharacteristic
294C22⋊Dic61—21no—
295C22⋊Dic61—21no—
296C22⋊Dic61—21no—
297C22⋊Dic61—21no—
298C22⋊Dic61—21no—
299C22⋊Dic61—21no—
300C22⋊Dic61—21no—
301C22⋊Dic61—21no—
302C22⋊Dic61—21no—
303C22⋊Dic61—21no—
304C22⋊Dic61—21no—
305C22⋊Dic61C22⋊C411yescharacteristic
306C22⋊Dic61C22⋊C411yescharacteristic
307#11758198—21no—
308#11758198—21no—
309#11758198—21no—
310#11758198—21no—
311#11758198C22⋊C411yescharacteristic
312#11758198C22⋊C411yescharacteristic
313#11758198C22⋊C411yescharacteristic
314#11758198C22⋊C411yescharacteristic
315C4⋊Dic61—21no—
316C4⋊Dic61—21no—
317C4⋊Dic61—21no—
318C4⋊Dic61—21no—
319C4⋊Dic61C22⋊C411yescharacteristic
320C4⋊Dic61C22×C411yescharacteristic
321C4⋊Dic61C22×C411yescharacteristic
322C4⋊Dic61C22×C411yescharacteristic
323#11758196—21no—
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#11758196C22⋊C411yescharacteristic
333#11758196C22⋊C411yescharacteristic
334C4×Dic61—21no—
335C4×Dic61—21no—
336C4×Dic61—21no—
337C4×Dic61—21no—
338C4×Dic61C22×C411yescharacteristic
339C4×Dic61C2×D411yescharacteristic
340C4×Dic61C2×D411yescharacteristic
341C23×C61—21no—
342C23×C61—21no—
343C23×C61—42no—
344C23×C61—81no—
345C23×C61—81no—
346C23×C61C2×C22⋊C411yescharacteristic
347C23×C61C2×C22⋊C411yescharacteristic
348C22×D61—21no—
349C22×D61—21no—
350C22×D61—41no—
351C22×D61—41no—
352C22×D61—41no—
353C22×D61—41no—
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—
374D4×C61—22no—
375D4×C61—41no—
376D4×C61—41no—
377D4×C61—81no—
378D4×C61—81no—
379D4×C61—81no—
380C2×C4×C61—21no—
381C2×C4×C61—21no—
382C2×C4×C61—41no—
383C2×C4×C61—41no—
384C2×C4×C61—81no—
385C2×C4×C61—81no—
386C2×C4×C61C2×C22⋊C411yescharacteristic
387C2×C4×C61C2×C22⋊C411yescharacteristic
388C2×C4×C61C2×C22⋊C411yescharacteristic
389C2×C4×C61C2×C22⋊C411yescharacteristic
390C2×C4×C61C23×C411yescharacteristic
391C22⋊D61—22no—
392C22⋊D61—22no—
393C22⋊D61—41no—
394C22⋊D61—41no—
395C22⋊D61—41no—
396C22⋊D61—41no—
397C22⋊D61—42no—
398C22⋊D61—42no—
399C22⋊D61—81no—
400C22⋊D61—81no—
401C2×Dic61—21no—
402C2×Dic61—21no—
403C2×Dic61—21no—
404C2×Dic61—21no—
405C2×Dic61—41no—
406C2×Dic61—41no—
407C2×Dic61—42no—
408C2×Dic61—81no—
409C2×Dic61—81no—
410C2×Dic61C2×C22⋊C411yescharacteristic
411C2×Dic61C2×C22⋊C411yescharacteristic
412C2×Dic61C2×C22⋊C411yescharacteristic
413C2×Dic61C2×C22⋊C411yescharacteristic
414C2×Dic61C22×D411yescharacteristic
415D244—22no—
416C4×D61—21no—
417C4×D61—21no—
418C4×D61—41no—
419C4×D61—41no—
420C4×D61—41no—
421C4×D61—41no—
422C4×D61—41no—
423C4×D61—41no—
424C4×D61—41no—
425C4×D61—41no—
426C4×D61—81no—
427C4×D61—81no—
428Dic122—41no—
429Dic122—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—41no—
444C22×C61—41no—
445C22×C61—41no—
446C22×C61—162no—
447C22×C61#41712yes—
448C22×C61C22×C22⋊C411yescharacteristic
449C2×D61—21no—
450C2×D61—21no—
451C2×D61—21no—
452C2×D61—21no—
453C2×D61—21no—
454C2×D61—21no—
455C2×D61—21no—
456C2×D61—42no—
457C2×D61—42no—
458C2×D61—42no—
459C2×D61—42no—
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—
474Dic61—21no—
475Dic61—21no—
476Dic61—21no—
477Dic61—21no—
478Dic61—21no—
479Dic61—41no—
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—81no—
502C2×C61#288311yescharacteristic
503C2×C61C2×#41711yescharacteristic
504C2×C61#290111yescharacteristic
505D61—21no—
506D61—21no—
507D61—22no—
508D61—41no—
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—611no—
519#546—611no—
520#546#692311yescharacteristic, complemented
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×Q8—611no—
572C22×D4—611no—
573C22×D4—1221no—
574C22×D4C2×#692311yescharacteristic, complemented
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—611no—
594#124—1221no—
595#124—1221no—
596#124C2×#692311yescharacteristic, complemented
597#123—21no—
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—611no—
608C22⋊Q8—611no—
609C22⋊Q8—611no—
610C22⋊Q8—611no—
611C22⋊Q8—611no—
612C22⋊Q8—1221no—
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—21no—
632#120—1221no—
633#120—1221no—
634#120—1221no—
635C4×Q8—611no—
636C4×Q8—611no—
637C4×D4—611no—
638C4×D4—611no—
639C4×D4—611no—
640C4×D4—611no—
641C4×D4—611no—
642C4×D4—611no—
643C4×D4—611no—
644C4×D4—611no—
645C4×D4—1221no—
646C4×D4—1221no—
647C4×D4—1221no—
648C4×D4—1221no—
649C4×D4—1221no—
650C4×D4—1221no—
651C4×D4—1221no—
652C4×D4—1221no—
653C4×D4—1221no—
654C4×D4—1221no—
655C4×D4—2444no—
656C4×D4C2×#692311yescharacteristic
657C4×D4C2×#692311yescharacteristic, complemented
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—21no—
673C2×C22⋊C4—611no—
674C2×C22⋊C4—611no—
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—21no—
702C24—611no—
703C24—611no—
704#41—81no—
705#41—4881no—
706C2×Q8—611no—
707C2×Q8—1221no—
708C2×Q8—4881no—
709C2×Q8C22×#692311yescharacteristic
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—81no—
714C2×D4—611no—
715C2×D4—611no—
716C2×D4—611no—
717C2×D4—1222no—
718C2×D4—1222no—
719C2×D4—1221no—
720C2×D4—1221no—
721C2×D4—1221no—
722C2×D4—1221no—
723C2×D4—1221no—
724C2×D4—1221no—
725C2×D4—2442no—
726C2×D4—2442no—
727C2×D4C22⋊#692311yescharacteristic
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—611no—
772C4⋊C4—611no—
773C4⋊C4—611no—
774C4⋊C4—611no—
775C4⋊C4—611no—
776C4⋊C4—611no—
777C4⋊C4—1221no—
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—21no—
801C22⋊C4—611no—
802C22⋊C4—611no—
803C22⋊C4—611no—
804C22⋊C4—611no—
805C22⋊C4—611no—
806C22⋊C4—611no—
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—611no—
827C42—611no—
828C42—611no—
829C42—1221no—
830C42—1221no—
831C42—1221no—
832C42—1221no—
833C42—2442no—
834C42C22×#692311yescharacteristic
835C23—21no—
836C23—21no—
837C23—42no—
838C23—81no—
839C23—81no—
840C23—611no—
841C23—611no—
842C23—612no—
843C23—612no—
844C23—611no—
845C23—1221no—
846C23—1221no—
847C23—2441no—
848C23—2441no—
849C23—2441no—
850C23—2441no—
851C23C2×C22⋊#692311yescharacteristic
852C23C2×C22⋊#692311yescharacteristic
853Q8—41no—
854Q8—4881no—
855Q8—2441no—
856D4—22no—
857D4—41no—
858D4—41no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—1222no—
863D4—1222no—
864D4—1222no—
865D4—4881no—
866D4—4881no—
867D4—2441no—
868D4—2441no—
869D4—2441no—
870D4—2441no—
871D4—2442no—
872D4—2442no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—81no—
878C2×C4—81no—
879C2×C4—611no—
880C2×C4—611no—
881C2×C4—611no—
882C2×C4—611no—
883C2×C4—611no—
884C2×C4—1221no—
885C2×C4—1221no—
886C2×C4—1222no—
887C2×C4—1221no—
888C2×C4—1221no—
889C2×C4—1221no—
890C2×C4—1221no—
891C2×C4—4881no—
892C2×C4—4881no—
893C2×C4—4881no—
894C2×C4—4881no—
895C2×C4—4884no—
896C2×C4—4884no—
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—2441no—
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—2442no—
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—41no—
937C22—41no—
938C22—41no—
939C22—162no—
940C22—611no—
941C22—611no—
942C22—612no—
943C22—1221no—
944C22—1221no—
945C22—1221no—
946C22—1221no—
947C22—1221no—
948C22—1221no—
949C22—1221no—
950C22—2442no—
951C22—2442no—
952C22—2442no—
953C22—2442no—
954C22#1684075312yes—
955C22C22×C22⋊#692311yescharacteristic
956C4—21no—
957C4—21no—
958C4—21no—
959C4—21no—
960C4—21no—
961C4—41no—
962C4—41no—
963C4—1221no—
964C4—1221no—
965C4—1221no—
966C4—1221no—
967C4—1221no—
968C4—4881no—
969C4—4881no—
970C4—4881no—
971C4—2442no—
972C4—2441no—
973C4—2441no—
974C4—2441no—
975C4—2441no—
976C2—22no—
977C2—41no—
978C2—81no—
979C2—81no—
980C2—1221no—
981C2—1221no—
982C2—1222no—
983C2—2441no—
984C2#2146241811yescharacteristic
985C2C2×#1684075311yescharacteristic
986C2#2146244911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#546C4
socleC22×C61C22×C22⋊C4
prime radical#21459646C2
cosocleC2×C4×D61C24
hypercenter#546#6923
hypocenterC61#17622
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. #21462671C2semidirect
2. #21462332C2semidirect
3. #21461257C2semidirect
4. #21461255C2semidirect
5. #21461235C2semidirect
6. #21461234C2semidirect
7. #21461231C2semidirect
8. #21461230C2semidirect
9. #21461221C2semidirect
10. #21461220C2semidirect
11. #21461205C2semidirect
12. #21461204C2semidirect
13. D61⋊#328C2semidirect
14. C2×#16840613C2semidirect
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. #16840615C22semidirect
41. #16840615C22semidirect
42. #16840615C22semidirect
43. #16840615C22semidirect
52. #16840462C4semidirect
54. #16840459C4semidirect
56. #16840454C4semidirect
57. #16840452C4semidirect
60. #16840420C4semidirect
61. #16840419C4semidirect
62. #16840406C4semidirect
74. C61×#546C4semidirect
108. C2×#11758224C2×C4semidirect
109. C2×Q8×D61C2×C4semidirect
120. #14519769C2×C4semidirect
122. #14519768C2×C4semidirect
125. #14519764C2×C4semidirect
138. #14519756C2×C4semidirect
139. #14519756C2×C4semidirect
143. #14519753C2×C4semidirect
152. #14519748C2×C4semidirect
153. #14519748C2×C4semidirect
154. #14519748C2×C4semidirect
160. Q8×Dic61C2×C4semidirect
161. C4×Dic122C2×C4semidirect
164. D4×Dic61C2×C4semidirect
181. #14519736C2×C4semidirect
182. #14519735C2×C4semidirect
186. C2×C4⋊Dic61C2×C4semidirect
188. C4⋊C4×D61C2×C4semidirect
196. C2×#41×C61C2×C4semidirect
197. C22×D4×C61C2×C4semidirect
198. #124×C61C2×C4semidirect
200. C22⋊Q8×C61C2×C4semidirect
202. #121×C61C2×C4semidirect
205. C4×D4×C61C2×C4semidirect
520. #546#6923semidirect
568. C61#17622semidirect
570. C2×#41C2×#6923semidirect
574. C22×D4C2×#6923semidirect
596. #124C2×#6923semidirect
616. C22⋊Q8C2×#6923semidirect
630. #121C2×#6923semidirect
657. C4×D4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214626712
#214623322
#214612572
#214612552
#214612352
#214612342
#214612312
#214612302
#214612212
#214612202
#214612052
#214612042
D61⋊#3282
C2×#168406132
#214596462
#1762261