Finite Group Databasebeta

← #30611324

Subgroups — #30611324

Order 15616.

1298 conjugacy classes of subgroups.

The subgroup lattice has 1066 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462409C211yesmaximal, characteristic, complemented
2#21462322C211yesmaximal, characteristic, complemented
3#21461257C211yesmaximal, characteristic, complemented
4#21461245C211yesmaximal, characteristic, complemented
5#21461244C211yesmaximal, characteristic, complemented
6#21461235C211yesmaximal, characteristic, complemented
7#21461228C211yesmaximal, characteristic, complemented
8#21461227C211yesmaximal, characteristic, complemented
9#21461217C211yesmaximal, characteristic, complemented
10#21461205C211yesmaximal, characteristic, complemented
11#21461204C211yesmaximal, characteristic, complemented
12#21461195C211yesmaximal, characteristic, complemented
13D61⋊#328C211yesmaximal, characteristic, complemented
14C2×#16840615C211yesmaximal, characteristic, complemented
15#21459494C211yesmaximal, characteristic
16C2×#14519864—21no—
17C2×D4×#6923—21no—
18#16840737—21no—
19#16840735—21no—
20#16840735—21no—
21#16840734C2211yescharacteristic
22#16840734C2211yescharacteristic
23#16840733C2211yescharacteristic
24C2×#14519834C2211yescharacteristic
25C2×#14519834C2211yescharacteristic
26D61⋊(C22⋊C8)C2211yescharacteristic
27(C2×#6923)⋊Q8—21no—
28#16840710—21no—
29#16840710—21no—
30#16840705C2211yescharacteristic
31#16840705C2211yescharacteristic
32#16840704C2211yescharacteristic
33C4×C22⋊#6923C2211yescharacteristic
34C2×(C2×#6923)⋊C4C2211yescharacteristic
35C2×(C2×#6923)⋊C4C2211yescharacteristic
36#16840616C2211yescharacteristic
37#16840616C2211yescharacteristic
38#16840616C2211yescharacteristic
39#16840616C2211yescharacteristic
40#16840615C2211yescharacteristic
41#16840615C2211yescharacteristic
42#16840615C2211yescharacteristic
43#16840615C2211yescharacteristic
44#16840615C2211yescharacteristic
45#16840615C2211yescharacteristic
46#16840615C2211yescharacteristic
47#16840615C2211yescharacteristic
48#16840613C2211yescharacteristic
49#16840613C2211yescharacteristic
50#16840613C2211yescharacteristic
51#16840613C2211yescharacteristic
52C2×#14519824C411yescharacteristic, complemented
53C2×#41×D61C2211yescharacteristic
54#16840425—21no—
55#16840418—21no—
56#16840414—21no—
57#16840412—21no—
58#16840412—21no—
59#16840409—21no—
60#16840401—21no—
61#16840401—21no—
62#16840341C411yescharacteristic, complemented
63#16840341C411yescharacteristic, complemented
64#16840335C411yescharacteristic, complemented
65#16840335C411yescharacteristic, complemented
66#16840333C411yescharacteristic, complemented
67#16840272C2211yescharacteristic
68#16840272C2211yescharacteristic
69#16840269C2211yescharacteristic
70C2×#14519757C2211yescharacteristic
71C22⋊Q8×D61C2211yescharacteristic
72C22⋊Q8×D61C2211yescharacteristic
73#16840243C411yescharacteristic, complemented
74C61×#537C411yescharacteristic, complemented
75C23×#6923—21no—
76C23×#6923—21no—
77#14519864—44no—
78C2×#11758213—21no—
79C2×#11758217—21no—
80C2×#11758217—21no—
81C2×D61⋊C8—21no—
82C22×#92420—21no—
83C22×#92420—21no—
84D4×#6923—44no—
85C2×C4⋊#6923—21no—
86C2×C22⋊#6923—21no—
87C2×C22⋊#6923—21no—
88C2×C22⋊#6923—21no—
89C2×C22⋊#6923—21no—
90C2×C4×#6923—21no—
91#14519834—21no—
92#14519834—21no—
93#14519834—21no—
94#14519834—21no—
95#14519834C2311yescharacteristic
96#14519834C2311yescharacteristic
97#14519834C2311yescharacteristic
98#14519834C2311yescharacteristic
99C22⋊#92420—21no—
100C22⋊#92420—21no—
101(C2×#6923)⋊C4—21no—
102(C2×#6923)⋊C4—21no—
103(C2×#6923)⋊C4—21no—
104(C2×#6923)⋊C4—21no—
105(C2×#6923)⋊C4C2311yescharacteristic
106(C2×#6923)⋊C4C2311yescharacteristic
107(C2×#6923)⋊C4C2311yescharacteristic
108(C2×#6923)⋊C4C2311yescharacteristic
109#14519824—44no—
110C2×#11758226D411yescharacteristic
111C2×#11758222—21no—
112C2×#11758222C2×C411yescharacteristic
113C2×#11758222C2×C411yescharacteristic
114C2×#11758222C2×C411yescharacteristic
115C2×#11758224—21no—
116C2×#11758224—21no—
117C2×#11758224C2×C411yescharacteristic, complemented
118C2×#11758224C2×C411yescharacteristic, complemented
119C2×#11758224D411yescharacteristic
120C2×#11758224D411yescharacteristic
121C2×#11758224D411yescharacteristic
122#41×D61—44no—
123C22×Dic122—21no—
124C22×Dic122C2×C411yescharacteristic, complemented
125C2×Q8×D61C2×C411yescharacteristic, complemented
126C2×Q8×D61C2×C411yescharacteristic, complemented
127C2×Q8×D61D411yescharacteristic
128C2×D4×D61D411yescharacteristic
129C2×D4×D61D411yescharacteristic
130C2×D4×D61D411yescharacteristic
131C22×C4×D61C2311yescharacteristic
132C22×C4×D61C2311yescharacteristic
133C22×C4×D61C2311yescharacteristic
134#14519776—21no—
135#14519776—21no—
136#14519775—21no—
137#14519764—21no—
138#14519763—21no—
139#14519763—21no—
140#14519762—21no—
141#14519762—21no—
142#14519759—21no—
143#14519759—21no—
144#14519759—21no—
145#14519759—21no—
146#14519758—21no—
147#14519758—21no—
148#14519758—21no—
149#14519757—21no—
150#14519757—21no—
151#14519757C2×C411yescharacteristic, complemented
152#14519757C2×C411yescharacteristic, complemented
153#14519757C2311yescharacteristic
154#14519757C2311yescharacteristic
155#14519756C2×C411yescharacteristic, complemented
156#14519756C2×C411yescharacteristic, complemented
157#14519756C2×C411yescharacteristic, complemented
158#14519756C2×C411yescharacteristic, complemented
159#14519755—21no—
160#14519755—21no—
161#14519754—21no—
162#14519754—21no—
163#14519754—21no—
164#14519754—21no—
165#14519753C2×C411yescharacteristic, complemented
166#14519753C2311yescharacteristic
167#14519750—21no—
168#14519750—21no—
169#14519749—21no—
170#14519749—21no—
171#14519748—21no—
172#14519748—21no—
173#14519748C2×C411yescharacteristic, complemented
174#14519748C2311yescharacteristic
175#14519745—21no—
176#14519745—21no—
177#14519745—21no—
178#14519742—21no—
179D4×Dic61—21no—
180D4×Dic61—21no—
181#14519739—21no—
182C4×C22⋊D61—21no—
183C4×C22⋊D61—21no—
184C4×C22⋊D61—21no—
185C4×C22⋊D61—21no—
186#14519737—21no—
187#14519737—21no—
188#14519736C2×C411yescharacteristic, complemented
189#14519735C2×C411yescharacteristic, complemented
190#14519735C2×C411yescharacteristic, complemented
191C2×C4⋊Dic61—21no—
192C4⋊C4×D61—21no—
193C4⋊C4×D61—21no—
194C4⋊C4×D61C2×C411yescharacteristic, complemented
195C4⋊C4×D61C2×C411yescharacteristic, complemented
196C2×#11758198—21no—
197C22⋊C4×D61—21no—
198C22⋊C4×D61—21no—
199C2×#41×C61C2×C411yescharacteristic
200C2×#41×C61C2×C411yescharacteristic, complemented
201C22⋊Q8×C61—21no—
202C22⋊Q8×C61C2×C411yescharacteristic, complemented
203C22⋊Q8×C61C2×C411yescharacteristic, complemented
204#121×C61—21no—
205#121×C61—21no—
206#121×C61—21no—
207#121×C61C2×C411yescharacteristic, complemented
208#121×C61C2×C411yescharacteristic, complemented
209C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
210C23×D61C2×D411yescharacteristic
211C23×D61C2×D411yescharacteristic
212C23×D61C2×D411yescharacteristic
213C22×#6923—21no—
214C22×#6923—21no—
215C22×#6923—21no—
216C22×#6923—21no—
217C22×#6923—42no—
218C22×#6923—42no—
219C22×#6923—42no—
220C22×#6923—42no—
221C22×#6923—81no—
222C22×#6923—81no—
223#41×C61—42no—
224#41×C61—42no—
225C2×Q8×C61C22⋊C411yescharacteristic
226C2×Q8×C61C22×C411yescharacteristic
227C2×D4×C61—21no—
228C2×D4×C61—21no—
229C2×D4×C61—21no—
230C2×D4×C61C22⋊C411yescharacteristic
231C2×D4×C61C22⋊C411yescharacteristic
232C2×D4×C61C22⋊C411yescharacteristic
233C2×D4×C61C22×C411yescharacteristic
234C22×C4×C61—21no—
235C22×C4×C61—21no—
236C22×C4×C61C22×C411yescharacteristic
237C22×C4×C61C22×C411yescharacteristic
238C22×C4×C61C22×C411yescharacteristic
239C2×C22⋊D61—21no—
240C2×C22⋊D61—21no—
241C2×C22⋊D61—21no—
242C2×C22⋊D61—21no—
243C2×C22⋊D61C22⋊C411yescharacteristic
244C2×C22⋊D61C22⋊C411yescharacteristic
245C2×C22⋊D61C22⋊C411yescharacteristic
246C2×C22⋊D61C22⋊C411yescharacteristic
247C2×C22⋊D61C22⋊C411yescharacteristic
248C2×C22⋊D61C22⋊C411yescharacteristic
249C22×Dic61—21no—
250C22×Dic61—21no—
251C22×Dic61—21no—
252C22×Dic61C2×D411yescharacteristic
253C22×Dic61C2×D411yescharacteristic
254C22×Dic61C2×D411yescharacteristic
255#11758226—42no—
256Q8×D61—42no—
257Q8×D61—42no—
258Q8×D61—42no—
259#11758224—24no—
260#11758224—42no—
261#11758224—42no—
262#11758224—42no—
263#11758224—42no—
264#11758224—44no—
265#11758224—44no—
266D4×D61—24no—
267D4×D61—42no—
268D4×D61—42no—
269#11758222—24no—
270#11758222—42no—
271#11758222—42no—
272#11758222—44no—
273C2×D244C22⋊C411yescharacteristic
274C2×D244C22⋊C411yescharacteristic
275C2×D244C22⋊C411yescharacteristic
276C2×C4×D61—21no—
277C2×C4×D61—21no—
278C2×C4×D61—21no—
279C2×C4×D61—21no—
280C2×C4×D61—42no—
281C2×C4×D61—42no—
282C2×C4×D61—42no—
283C2×C4×D61C22×C411yescharacteristic
284C2×C4×D61C22×C411yescharacteristic
285C2×C4×D61C22×C411yescharacteristic
286C2×C4×D61C2×D411yescharacteristic
287C2×C4×D61C2×D411yescharacteristic
288C2×C4×D61C2×D411yescharacteristic
289C2×C4×D61C2×D411yescharacteristic
290C2×C4×D61C2×D411yescharacteristic
291C2×C4×D61C2×D411yescharacteristic
292C2×C4×D61C2411yescharacteristic
293C2×Dic122—21no—
294C2×Dic122—21no—
295C2×Dic122—21no—
296C2×Dic122—44no—
297C2×Dic122—42no—
298C2×Dic122C22⋊C411yescharacteristic
299C2×Dic122C22⋊C411yescharacteristic
300C2×Dic122C22⋊C411yescharacteristic
301C2×Dic122C22×C411yescharacteristic
302C2×Dic122C22×C411yescharacteristic
303C22⋊#6923—42no—
304C22⋊#6923—42no—
305C22⋊#6923—42no—
306C22⋊#6923—81no—
307#11758217—42no—
308#11758217—42no—
309C2×#92420—21no—
310C2×#92420—21no—
311C2×#92420—21no—
312C2×#92420—21no—
313C2×#92420—42no—
314C2×#92420—42no—
315C4⋊#6923—42no—
316C4×#6923—42no—
317#11758213—42no—
318D61⋊C8—42no—
319C4⋊C4×C61—21no—
320C4⋊C4×C61—21no—
321C4⋊C4×C61—21no—
322C4⋊C4×C61C22×C411yescharacteristic
323C4⋊C4×C61C22×C411yescharacteristic
324C22⋊C4×C61—21no—
325C22⋊C4×C61—21no—
326C22⋊C4×C61—21no—
327C22⋊C4×C61—21no—
328C22⋊Dic61—21no—
329C22⋊Dic61—21no—
330C22⋊Dic61—21no—
331C22⋊Dic61—21no—
332C22⋊Dic61—21no—
333C22⋊Dic61—21no—
334C22⋊Dic61—21no—
335#11758198—21no—
336#11758198—21no—
337#11758198—21no—
338#11758198—21no—
339#11758198—21no—
340#11758198—21no—
341#11758198—21no—
342#11758198—21no—
343C4⋊Dic61—21no—
344C4⋊Dic61—21no—
345C4⋊Dic61—21no—
346C4⋊Dic61—21no—
347C4⋊Dic61C22×C411yescharacteristic
348C4⋊Dic61C22×C411yescharacteristic
349#11758196—21no—
350#11758196—21no—
351#11758196—21no—
352#11758196—21no—
353#11758196—21no—
354#11758196—21no—
355#11758196—21no—
356#11758196—21no—
357C4×Dic61—21no—
358C4×Dic61—21no—
359C4×Dic61—21no—
360C23×C61—21no—
361C23×C61C2×C22⋊C411yescharacteristic
362C23×C61C2×C22⋊C411yescharacteristic
363C23×C61C2×C22⋊C411yescharacteristic
364C22×D61—22no—
365C22×D61—21no—
366C22×D61—21no—
367C22×D61—21no—
368C22×D61—21no—
369C22×D61—22no—
370C22×D61—21no—
371C22×D61—21no—
372C22×D61—41no—
373C22×D61—41no—
374C22×D61—41no—
375C22×D61—41no—
376C22×D61C2×C22⋊C411yescharacteristic
377C22×D61C2×C22⋊C411yescharacteristic
378C22×D61C2×C22⋊C411yescharacteristic
379C22×D61C22×D411yescharacteristic
380C2×#6923—22no—
381C2×#6923—41no—
382C2×#6923—41no—
383C2×#6923—41no—
384C2×#6923—41no—
385C2×#6923—41no—
386C2×#6923—41no—
387C2×#6923—41no—
388C2×#6923—41no—
389C2×#6923—41no—
390C2×#6923—41no—
391C2×#6923—41no—
392C2×#6923—84no—
393C2×#6923—84no—
394Q8×C61—41no—
395Q8×C61—41no—
396D4×C61—22no—
397D4×C61—22no—
398D4×C61—41no—
399D4×C61—41no—
400D4×C61—42no—
401D4×C61—81no—
402D4×C61—81no—
403C2×C4×C61—22no—
404C2×C4×C61—21no—
405C2×C4×C61—21no—
406C2×C4×C61—21no—
407C2×C4×C61—41no—
408C2×C4×C61—41no—
409C2×C4×C61—42no—
410C2×C4×C61—81no—
411C2×C4×C61C2×C22⋊C411yescharacteristic
412C2×C4×C61C2×C22⋊C411yescharacteristic
413C2×C4×C61C2×C22⋊C411yescharacteristic
414C2×C4×C61C23×C411yescharacteristic
415C22⋊D61—22no—
416C22⋊D61—22no—
417C22⋊D61—22no—
418C22⋊D61—41no—
419C22⋊D61—41no—
420C22⋊D61—42no—
421C22⋊D61—41no—
422C22⋊D61—41no—
423C22⋊D61—42no—
424C22⋊D61—81no—
425C22⋊D61#9914yes—
426C2×Dic61—22no—
427C2×Dic61—22no—
428C2×Dic61—21no—
429C2×Dic61—21no—
430C2×Dic61—21no—
431C2×Dic61—21no—
432C2×Dic61—41no—
433C2×Dic61—42no—
434C2×Dic61—42no—
435C2×Dic61—42no—
436C2×Dic61C2×C22⋊C411yescharacteristic
437C2×Dic61C2×C22⋊C411yescharacteristic
438C2×Dic61C2×C22⋊C411yescharacteristic
439C2×Dic61C22×D411yescharacteristic
440D244—22no—
441D244—22no—
442D244—41no—
443C4×D61—22no—
444C4×D61—22no—
445C4×D61—22no—
446C4×D61—22no—
447C4×D61—41no—
448C4×D61—41no—
449C4×D61—41no—
450C4×D61—41no—
451C4×D61—41no—
452C4×D61—41no—
453C4×D61—42no—
454C4×D61—42no—
455C4×D61—81no—
456C4×D61—81no—
457Dic122—22no—
458Dic122—22no—
459Dic122—41no—
460Dic122—42no—
461Dic122—42no—
462Dic122—42no—
463Dic122—41no—
464Dic122—41no—
465#92420—41no—
466#92420—41no—
467#92420—41no—
468#92420—41no—
469#17608—611nomaximal, Sylow
470C22×C61—21no—
471C22×C61—21no—
472C22×C61—21no—
473C22×C61—21no—
474C22×C61—21no—
475C22×C61—21no—
476C22×C61—21no—
477C22×C61—21no—
478C22×C61—41no—
479C22×C61—41no—
480C22×C61—41no—
481C22×C61C2×#9912yes—
482C22×C61C22×C22⋊C411yescharacteristic
483C2×D61—21no—
484C2×D61—21no—
485C2×D61—21no—
486C2×D61—21no—
487C2×D61—21no—
488C2×D61—21no—
489C2×D61—21no—
490C2×D61—21no—
491C2×D61—21no—
492C2×D61—21no—
493C2×D61—42no—
494C2×D61—42no—
495C2×D61—42no—
496C2×D61—42no—
497C2×D61—81no—
498C2×D61—81no—
499C2×D61C2×#9912yes—
500C2×D61#57711yescharacteristic
501C2×D61#57811yescharacteristic
502#6923—42no—
503#6923—81no—
504#6923—81no—
505#6923—81no—
506C4×C61—21no—
507C4×C61—21no—
508C4×C61—21no—
509C4×C61—21no—
510C4×C61—41no—
511C4×C61—41no—
512C4×C61—41no—
513Dic61—21no—
514Dic61—21no—
515Dic61—21no—
516Dic61—41no—
517Dic61—41no—
518Dic61—41no—
519Dic61—41no—
520Dic61C2×#9912yes—
521#3489—611no—
522#2880—611no—
523#2339—611no—
524#1520—611no—
525#1516—611no—
526#1516—611no—
527#1513—611no—
528#1511—611no—
529#1511—611no—
530#1508—611no—
531#1504—611no—
532#1504—611no—
533#1501—611no—
534C2×#328—611no—
535C2×#328—611no—
536C2×C61—22no—
537C2×C61—41no—
538C2×C61—41no—
539C2×C61—81no—
540C2×C61C22×#9911yescharacteristic
541C2×C61#289811yescharacteristic
542C2×C61#290111yescharacteristic
543D61—21no—
544D61—21no—
545D61—22no—
546D61—41no—
547D61—41no—
548C2×2−1+4—611no—
549C22×#41—611no—
550C2×#131—1221no—
551D4×Q8—1221no—
552#548—1221no—
553#547—1221no—
554#547—1221no—
555#547—1221no—
556#546—1221no—
557#546—1221no—
558#546—1221no—
559#537—611no—
560#537—611no—
561#537#692311yescharacteristic, complemented
562#536—611no—
563#536—611no—
564#536—611no—
565#525—611no—
566#525—611no—
567#525—611no—
568C2×C22⋊Q8—611no—
569C2×C22⋊Q8—611no—
570C2×C22⋊Q8—611no—
571#520—611no—
572C2×C4×D4—1221no—
573#408—1221no—
574#408—1221no—
575#408—1221no—
576#407—611no—
577#407—611no—
578#407—611no—
579C2×C22⋊C8—611no—
580C2×C22⋊C8—611no—
581C2×C22⋊C8—611no—
582#391—1221no—
583#386—1221no—
584#386—1221no—
585#381—611no—
586#381—611no—
587#380—611no—
588C4×C22⋊C4—611no—
589C2×#95—611no—
590C2×#95—611no—
591#328—611no—
592#328—611no—
593#328—611no—
594#328—611no—
595#328—611no—
596#328—611no—
597#328—611no—
598#328—611no—
599#328—611no—
600#328—611no—
601#328—611no—
602#328—611no—
603#327—611no—
604#327—611no—
605#327—611no—
606#327—611no—
607C61#1760811yescharacteristic, complemented, Sylow
6082−1+4—2444no—
609C2×#41—611no—
610C2×#41—611no—
611C2×#41—611no—
612C2×#41—611no—
613C2×#41—611no—
614C2×#41—611no—
615C2×#41—611no—
616C2×#41—611no—
617C2×#41—611no—
618C2×#41—1221no—
619C2×#41—1221no—
620C2×#41—1221no—
621C2×#41—2444no—
622C2×#41C2×#692311yescharacteristic
623C2×#41C2×#692311yescharacteristic, complemented
624C22×Q8—611no—
625C22×Q8—611no—
626C22×Q8—611no—
627C22×Q8—611no—
628C22×Q8—1221no—
629C22×D4—611no—
630C22×D4—611no—
631C22×D4—611no—
632C23×C4—611no—
633C23×C4—611no—
634C23×C4—611no—
635C23×C4—1221no—
636C23×C4—1221no—
637#131—2444no—
638C2×M16—1221no—
639C2×M16—1221no—
640C2×M16—1221no—
641C22×C8—1221no—
642C22×C8—1221no—
643C22×C8—1221no—
644C4⋊Q8—1221no—
645C4⋊Q8—1221no—
646C4⋊Q8—1221no—
647#124—1221no—
648#124—1221no—
649#124—1221no—
650#123—1221no—
651#123—1221no—
652#123—1221no—
653#123—1221no—
654#123—1221no—
655#123—1221no—
656#123—1221no—
657#123—1221no—
658#123—1221no—
659C22⋊Q8—21no—
660C22⋊Q8—611no—
661C22⋊Q8—611no—
662C22⋊Q8—611no—
663C22⋊Q8—611no—
664C22⋊Q8—611no—
665C22⋊Q8—611no—
666C22⋊Q8—611no—
667C22⋊Q8—611no—
668C22⋊Q8—611no—
669C22⋊Q8—611no—
670C22⋊Q8—1221no—
671C22⋊Q8—1221no—
672C22⋊Q8—1221no—
673C22⋊Q8—1221no—
674C22⋊Q8—1221no—
675C22⋊Q8—1221no—
676C22⋊Q8—1221no—
677C22⋊Q8—1221no—
678C22⋊Q8C2×#692311yescharacteristic, complemented
679C22⋊Q8C2×#692311yescharacteristic, complemented
680#121—21no—
681#121—21no—
682#121—21no—
683#121—611no—
684#121—611no—
685#121—1221no—
686#121—1221no—
687#121—1221no—
688#121—1221no—
689#121—1221no—
690#121—1221no—
691#121C2×#692311yescharacteristic, complemented
692#121C2×#692311yescharacteristic, complemented
693#120—1221no—
694#120—1221no—
695#120—1221no—
696C4×Q8—1221no—
697C4×D4—1221no—
698C4×D4—1221no—
699C4×D4—1221no—
700C4×D4—1221no—
701C4×D4—1221no—
702C4×D4—1221no—
703C4×D4—1221no—
704C4×D4—1221no—
705C4×D4—1221no—
706C4×D4—2444no—
707#117—611no—
708#117—611no—
709#117—611no—
710C2×C4⋊C4—611no—
711C2×C4⋊C4—611no—
712C2×C4⋊C4—1221no—
713C2×C4⋊C4—1221no—
714C2×C4⋊C4—1221no—
715C2×C4⋊C4—1221no—
716C2×C4⋊C4C2×#692311yescharacteristic, complemented
717C2×C22⋊C4—1221no—
718C2×C22⋊C4—1221no—
719C2×C22⋊C4—1221no—
720C2×C22⋊C4—1221no—
721C2×C22⋊C4—1221no—
722C2×C22⋊C4—1221no—
723C2×C22⋊C4—1221no—
724C2×C42—1221no—
725C22⋊C8—611no—
726C22⋊C8—611no—
727C22⋊C8—611no—
728C22⋊C8—611no—
729C22⋊C8—1221no—
730C22⋊C8—1221no—
731C22⋊C8—1221no—
732C22⋊C8—1221no—
733C22⋊C8—1221no—
734C22⋊C8—1221no—
735#95—611no—
736#95—611no—
737#95—611no—
738#95—611no—
739#95—1221no—
740#95—1221no—
741#95—1221no—
742#95—1221no—
743C24—611no—
744C24—611no—
745C24—611no—
746#41—42no—
747#41—42no—
748#41—1224no—
749#41—1224no—
750#41—2442no—
751#41—2442no—
752#41—2444no—
753#41—2442no—
754#41—2442no—
755#41—2442no—
756#41—2442no—
757#41—2442no—
758#41—2444no—
759#41—2444no—
760C2×Q8—611no—
761C2×Q8—611no—
762C2×Q8—611no—
763C2×Q8—611no—
764C2×Q8—611no—
765C2×Q8—1221no—
766C2×Q8—1221no—
767C2×Q8—1221no—
768C2×Q8—2442no—
769C2×Q8—2444no—
770C2×Q8—2442no—
771C2×Q8—2442no—
772C2×Q8—2442no—
773C2×Q8C22⋊#692311yescharacteristic
774C2×Q8C22×#692311yescharacteristic
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—611no—
779C2×D4—611no—
780C2×D4—611no—
781C2×D4—611no—
782C2×D4—611no—
783C2×D4—611no—
784C2×D4—611no—
785C2×D4—611no—
786C2×D4—611no—
787C2×D4—1224no—
788C2×D4—1221no—
789C2×D4—1221no—
790C2×D4—1221no—
791C2×D4—1221no—
792C2×D4—2442no—
793C2×D4—2442no—
794C2×D4C22⋊#692311yescharacteristic
795C2×D4C22⋊#692311yescharacteristic
796C2×D4C22⋊#692311yescharacteristic
797C2×D4C22×#692311yescharacteristic
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—611no—
807C22×C4—611no—
808C22×C4—611no—
809C22×C4—611no—
810C22×C4—611no—
811C22×C4—611no—
812C22×C4—611no—
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—1221no—
823C22×C4—1221no—
824C22×C4—4881no—
825C22×C4—4881no—
826C22×C4—2442no—
827C22×C4—2442no—
828C22×C4—2442no—
829C22×C4—2442no—
830C22×C4—2442no—
831C22×C4—2442no—
832C22×C4—2442no—
833C22×C4C22×#692311yescharacteristic
834C22×C4C22×#692311yescharacteristic
835C22×C4C22×#692311yescharacteristic
836M16—2442no—
837M16—2442no—
838M16—2442no—
839C2×C8—1221no—
840C2×C8—1221no—
841C2×C8—1221no—
842C2×C8—1221no—
843C2×C8—2442no—
844C2×C8—2442no—
845C2×C8—2442no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—611no—
850C4⋊C4—611no—
851C4⋊C4—1221no—
852C4⋊C4—1221no—
853C4⋊C4—1221no—
854C4⋊C4—1221no—
855C4⋊C4—1221no—
856C4⋊C4—1221no—
857C4⋊C4—1221no—
858C4⋊C4—1221no—
859C4⋊C4—1221no—
860C4⋊C4—1221no—
861C4⋊C4—1221no—
862C4⋊C4—1221no—
863C4⋊C4—2442no—
864C4⋊C4C22×#692311yescharacteristic
865C4⋊C4C22×#692311yescharacteristic
866C22⋊C4—21no—
867C22⋊C4—21no—
868C22⋊C4—21no—
869C22⋊C4—21no—
870C22⋊C4—1221no—
871C22⋊C4—1221no—
872C22⋊C4—1221no—
873C22⋊C4—1221no—
874C22⋊C4—1221no—
875C22⋊C4—1221no—
876C22⋊C4—1221no—
877C22⋊C4—1221no—
878C22⋊C4—1221no—
879C22⋊C4—1221no—
880C22⋊C4—1221no—
881C22⋊C4—1221no—
882C22⋊C4—1221no—
883C22⋊C4—1221no—
884C22⋊C4—1221no—
885C22⋊C4—4881no—
886C22⋊C4—2442no—
887C22⋊C4—2442no—
888C22⋊C4—2442no—
889C42—1221no—
890C42—1221no—
891C42—1221no—
892C42—2442no—
893C23—21no—
894C23—611no—
895C23—611no—
896C23—611no—
897C23—611no—
898C23—1221no—
899C23—1221no—
900C23—1222no—
901C23—1221no—
902C23—1221no—
903C23—1221no—
904C23—1221no—
905C23—1222no—
906C23—2441no—
907C23—2441no—
908C23—2441no—
909C23—2441no—
910C23C2×C22⋊#692311yescharacteristic
911C23C2×C22⋊#692311yescharacteristic
912C23C2×C22⋊#692311yescharacteristic
913Q8—41no—
914Q8—41no—
915Q8—1222no—
916Q8—1222no—
917Q8—2441no—
918Q8—2441no—
919Q8—2441no—
920Q8—2442no—
921Q8—2442no—
922Q8—2442no—
923D4—22no—
924D4—22no—
925D4—41no—
926D4—41no—
927D4—42no—
928D4—81no—
929D4—81no—
930D4—614no—
931D4—1222no—
932D4—1222no—
933D4—1222no—
934D4—1222no—
935D4—1222no—
936D4—4881no—
937D4—2441no—
938D4—2441no—
939D4—2441no—
940D4—2441no—
941D4—2441no—
942D4—2442no—
943D4—2442no—
944C2×C4—22no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—42no—
951C2×C4—81no—
952C2×C4—611no—
953C2×C4—611no—
954C2×C4—611no—
955C2×C4—611no—
956C2×C4—1222no—
957C2×C4—1222no—
958C2×C4—1222no—
959C2×C4—1222no—
960C2×C4—1222no—
961C2×C4—1222no—
962C2×C4—1222no—
963C2×C4—1221no—
964C2×C4—1221no—
965C2×C4—1221no—
966C2×C4—1221no—
967C2×C4—4881no—
968C2×C4—4881no—
969C2×C4—4884no—
970C2×C4—4884no—
971C2×C4—2441no—
972C2×C4—2441no—
973C2×C4—2441no—
974C2×C4—2441no—
975C2×C4—2441no—
976C2×C4—2441no—
977C2×C4—2442no—
978C2×C4—2442no—
979C2×C4—2442no—
980C2×C4—2441no—
981C2×C4—2442no—
982C2×C4—2441no—
983C2×C4—2441no—
984C2×C4—2441no—
985C2×C4—2441no—
986C2×C4—2441no—
987C2×C4—2441no—
988C2×C4—2441no—
989C2×C4—2441no—
990C2×C4—2441no—
991C2×C4—2441no—
992C2×C4—2441no—
993C2×C4—2442no—
994C2×C4C2×C22⋊#692311yescharacteristic
995C2×C4C2×C22⋊#692311yescharacteristic
996C2×C4C2×C22⋊#692311yescharacteristic
997C2×C4C23×#692311yescharacteristic
998C8—2441no—
999C8—2441no—
1000C8—2441no—
1001C8—2441no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—41no—
1011C22—41no—
1012C22—41no—
1013C22—612no—
1014C22—611no—
1015C22—611no—
1016C22—1221no—
1017C22—1221no—
1018C22—1221no—
1019C22—1221no—
1020C22—1221no—
1021C22—1221no—
1022C22—1221no—
1023C22—1221no—
1024C22—1221no—
1025C22—1221no—
1026C22—4881no—
1027C22—4881no—
1028C22—2442no—
1029C22—2442no—
1030C22—2442no—
1031C22—2442no—
1032C22D61⋊#9912yes—
1033C22C22×C22⋊#692311yescharacteristic
1034C4—21no—
1035C4—21no—
1036C4—21no—
1037C4—21no—
1038C4—41no—
1039C4—41no—
1040C4—41no—
1041C4—612no—
1042C4—1221no—
1043C4—1221no—
1044C4—1221no—
1045C4—4881no—
1046C4—4881no—
1047C4—4881no—
1048C4—2442no—
1049C4—2441no—
1050C4—2441no—
1051C4—2441no—
1052C4—2441no—
1053C2—22no—
1054C2—41no—
1055C2—41no—
1056C2—81no—
1057C2—1221no—
1058C2—1221no—
1059C2—1222no—
1060C2—2441no—
1061C2—2441no—
1062C2C2×D61⋊#9911yescharacteristic
1063C2#2146244111yescharacteristic
1064C2#2146244911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#537C4
socleC22×C61C22×C22⋊C4
prime radical#21459494C2
cosocleC2×C4×D61C24
hypercenter#537#6923
hypocenterC61#17608
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #21462409C2semidirect
2. #21462322C2semidirect
3. #21461257C2semidirect
4. #21461245C2semidirect
5. #21461244C2semidirect
6. #21461235C2semidirect
7. #21461228C2semidirect
8. #21461227C2semidirect
9. #21461217C2semidirect
10. #21461205C2semidirect
11. #21461204C2semidirect
12. #21461195C2semidirect
13. D61⋊#328C2semidirect
14. C2×#16840615C2semidirect
52. C2×#14519824C4semidirect
62. #16840341C4semidirect
63. #16840341C4semidirect
64. #16840335C4semidirect
65. #16840335C4semidirect
66. #16840333C4semidirect
73. #16840243C4semidirect
74. C61×#537C4semidirect
117. C2×#11758224C2×C4semidirect
118. C2×#11758224C2×C4semidirect
124. C22×Dic122C2×C4semidirect
125. C2×Q8×D61C2×C4semidirect
126. C2×Q8×D61C2×C4semidirect
151. #14519757C2×C4semidirect
152. #14519757C2×C4semidirect
155. #14519756C2×C4semidirect
156. #14519756C2×C4semidirect
157. #14519756C2×C4semidirect
158. #14519756C2×C4semidirect
165. #14519753C2×C4semidirect
173. #14519748C2×C4semidirect
188. #14519736C2×C4semidirect
189. #14519735C2×C4semidirect
190. #14519735C2×C4semidirect
194. C4⋊C4×D61C2×C4semidirect
195. C4⋊C4×D61C2×C4semidirect
200. C2×#41×C61C2×C4semidirect
202. C22⋊Q8×C61C2×C4semidirect
203. C22⋊Q8×C61C2×C4semidirect
207. #121×C61C2×C4semidirect
208. #121×C61C2×C4semidirect
209. C2×C4⋊C4×C61C2×C4semidirect
561. #537#6923semidirect
607. C61#17608semidirect
623. C2×#41C2×#6923semidirect
678. C22⋊Q8C2×#6923semidirect
679. C22⋊Q8C2×#6923semidirect
691. #121C2×#6923semidirect
692. #121C2×#6923semidirect
716. C2×C4⋊C4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214624092
#214623222
#214612572
#214612452
#214612442
#214612352
#214612282
#214612272
#214612172
#214612052
#214612042
#214611952
D61⋊#3282
C2×#168406152
#214594942
#1760861