Finite Group Databasebeta

← #30611264

Subgroups — #30611264

Order 15616.

996 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462676C211yesmaximal, characteristic, complemented
2#21462301C211yesmaximal, characteristic, complemented
3#21461261C211yesmaximal, characteristic, complemented
4#21461257C211yesmaximal, characteristic, complemented
5#21461253C211yesmaximal, characteristic, complemented
6#21461245C211yesmaximal, characteristic, complemented
7#21461243C211yesmaximal, characteristic, complemented
8#21461234C211yesmaximal, characteristic, complemented
9#21461230C211yesmaximal, characteristic, complemented
10#21461228C211yesmaximal, characteristic, complemented
11#21461217C211yesmaximal, characteristic, complemented
12#21461205C211yesmaximal, characteristic, complemented
13#21461194C211yesmaximal, characteristic, complemented
14D61⋊#328C211yesmaximal, characteristic, complemented
15#21459871C211yesmaximal, characteristic
16#16840795—21no—
17#16840793—21no—
18#16840792—21no—
19#16840789—21no—
20#16840785C2211yescharacteristic
21#16840780C2211yescharacteristic
22#16840734C2211yescharacteristic
23#16840733C2211yescharacteristic
24C2×#14519834C2211yescharacteristic
25D61⋊(C22⋊C8)C2211yescharacteristic
26#16840712—21no—
27#16840711—21no—
28#16840710—21no—
29#16840709—21no—
30#16840707C2211yescharacteristic
31#16840706C2211yescharacteristic
32#16840705C2211yescharacteristic
33#16840704C2211yescharacteristic
34C4×C22⋊#6923C2211yescharacteristic
35C2×(C2×#6923)⋊C4C2211yescharacteristic
36#16840616C2211yescharacteristic
37#16840616C2211yescharacteristic
38#16840616C2211yescharacteristic
39#16840616C2211yescharacteristic
40#16840616C2211yescharacteristic
41#16840616C2211yescharacteristic
42#16840616C2211yescharacteristic
43#16840616C2211yescharacteristic
44#16840615C2211yescharacteristic
45#16840615C2211yescharacteristic
46#16840615C2211yescharacteristic
47#16840615C2211yescharacteristic
48#16840613C2211yescharacteristic
49#16840613C2211yescharacteristic
50#16840613C2211yescharacteristic
51#16840613C2211yescharacteristic
52#16840482C411yescharacteristic, complemented
53#16840467—21no—
54#16840446C411yescharacteristic, complemented
55#16840446C411yescharacteristic, complemented
56#16840440—21no—
57#16840440—21no—
58#16840427C411yescharacteristic, complemented
59#16840419C411yescharacteristic, complemented
60#16840419C411yescharacteristic, complemented
61#16840417C411yescharacteristic, complemented
62#16840409—21no—
63#16840379—21no—
64#16840355—21no—
65#16840355—21no—
66#16840317C2211yescharacteristic
67#16840294C2211yescharacteristic
68#16840269C2211yescharacteristic
69#16840269C2211yescharacteristic
70C22⋊Q8×D61C2211yescharacteristic
71C22⋊Q8×D61C2211yescharacteristic
72#16840243—21no—
73C4×D4×D61C2211yescharacteristic
74C61×#547C411yescharacteristic, complemented
75C23×#6923—21no—
76C2×#11758213—21no—
77C2×#11758217—21no—
78C2×D61⋊C8—21no—
79C22×#92420—21no—
80C2×C4⋊#6923—21no—
81C2×C4⋊#6923—21no—
82C2×C22⋊#6923—21no—
83C2×C22⋊#6923—21no—
84C2×C22⋊#6923—21no—
85C2×C4×#6923—21no—
86#14519844—21no—
87#14519844—21no—
88#14519834—21no—
89#14519834—21no—
90#14519834C2311yescharacteristic
91#14519834C2311yescharacteristic
92#14519834C2311yescharacteristic
93#14519834C2311yescharacteristic
94C22⋊#92420—21no—
95C22⋊#92420—21no—
96#14519832—21no—
97C4×#92420—21no—
98(C2×#6923)⋊C4—21no—
99(C2×#6923)⋊C4—21no—
100(C2×#6923)⋊C4—21no—
101(C2×#6923)⋊C4—21no—
102(C2×#6923)⋊C4—21no—
103(C2×#6923)⋊C4C2311yescharacteristic
104(C2×#6923)⋊C4C2311yescharacteristic
105(C2×#6923)⋊C4C2311yescharacteristic
106(C2×#6923)⋊C4C2311yescharacteristic
107C2×#11758222—21no—
108C2×Q8×D61C2×C411yescharacteristic
109C2×Q8×D61C2×C411yescharacteristic, complemented
110C2×D4×D61D411yescharacteristic
111C22×C4×D61C2311yescharacteristic
112C22×C4×D61C2311yescharacteristic
113#14519777C2×C411yescharacteristic, complemented
114#14519776—21no—
115#14519770—21no—
116#14519770—21no—
117#14519770—21no—
118#14519770—21no—
119#14519770—21no—
120#14519768—21no—
121#14519768C2×C411yescharacteristic, complemented
122#14519767—21no—
123#14519767—21no—
124#14519764—21no—
125#14519764—21no—
126#14519764—21no—
127#14519764C2×C411yescharacteristic, complemented
128#14519759—21no—
129#14519759—21no—
130#14519759—21no—
131#14519759—21no—
132#14519759—21no—
133#14519758—21no—
134#14519758—21no—
135#14519757—21no—
136#14519757C2311yescharacteristic
137#14519756—21no—
138#14519756—21no—
139#14519756—21no—
140#14519756C2×C411yescharacteristic
141#14519756C2×C411yescharacteristic, complemented
142#14519755—21no—
143#14519755—21no—
144#14519755—21no—
145#14519755—21no—
146#14519754—21no—
147#14519754—21no—
148#14519753C2×C411yescharacteristic
149#14519753C2×C411yescharacteristic, complemented
150#14519753C2311yescharacteristic
151#14519753C2311yescharacteristic
152#14519748—21no—
153#14519748—21no—
154#14519748C2×C411yescharacteristic
155#14519748C2×C411yescharacteristic, complemented
156#14519748C2311yescharacteristic
157#14519745—21no—
158#14519745—21no—
159Q8×Dic61C2×C411yescharacteristic, complemented
160Q8×Dic61C2×C411yescharacteristic, complemented
161C4×Dic122C2×C411yescharacteristic, complemented
162#14519742—21no—
163#14519742—21no—
164C4×D244C2×C411yescharacteristic
165D4×Dic61D411yescharacteristic
166#14519739—21no—
167#14519739D411yescharacteristic
168C4×C22⋊D61—21no—
169C4×C22⋊D61—21no—
170C4×C22⋊D61—21no—
171C4×C22⋊D61—21no—
172C4×C22⋊D61—21no—
173C4×C22⋊D61—21no—
174C4×C22⋊D61—21no—
175C4×C22⋊D61C2×C411yescharacteristic
176C4×C22⋊D61C2×C411yescharacteristic
177#14519737D411yescharacteristic
178#14519737D411yescharacteristic
179#14519736—21no—
180#14519736C2×C411yescharacteristic
181#14519736C2×C411yescharacteristic, complemented
182#14519735—21no—
183#14519735—21no—
184#14519735—21no—
185C4⋊C4×D61—21no—
186C4⋊C4×D61—21no—
187C4⋊C4×D61C2×C411yescharacteristic
188C4⋊C4×D61C2×C411yescharacteristic, complemented
189C4⋊C4×D61D411yescharacteristic
190C22⋊C4×D61—21no—
191C22⋊C4×D61—21no—
192C22⋊C4×D61D411yescharacteristic
193C22⋊C4×D61D411yescharacteristic
194C42×D61C2311yescharacteristic
195C2×#41×C61C2×C411yescharacteristic
196C2×#41×C61C2×C411yescharacteristic, complemented
197C4⋊Q8×C61C2×C411yescharacteristic, complemented
198#123×C61—21no—
199#123×C61—21no—
200C22⋊Q8×C61C2×C411yescharacteristic
201C22⋊Q8×C61C2×C411yescharacteristic, complemented
202#121×C61—21no—
203C4×D4×C61C2×C411yescharacteristic
204C4×D4×C61C2×C411yescharacteristic, complemented
205C2×C4⋊C4×C61—21no—
206C23×D61C2×D411yescharacteristic
207C23×D61C2×D411yescharacteristic
208C22×#6923—21no—
209C22×#6923—21no—
210C22×#6923—21no—
211C22×#6923—21no—
212C22×#6923—42no—
213C22×#6923—81no—
214C22×#6923—81no—
215#41×C61—81no—
216#41×C61—81no—
217C2×Q8×C61C22×C411yescharacteristic
218C2×Q8×C61C22×C411yescharacteristic
219C2×D4×C61—21no—
220C2×D4×C61—21no—
221C2×D4×C61C22⋊C411yescharacteristic
222C2×D4×C61C22×C411yescharacteristic
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61C22×C411yescharacteristic
227C22×C4×C61C22×C411yescharacteristic
228C2×C22⋊D61—21no—
229C2×C22⋊D61—21no—
230C2×C22⋊D61—21no—
231C2×C22⋊D61C22⋊C411yescharacteristic
232C2×C22⋊D61C22⋊C411yescharacteristic
233C22×Dic61C2×D411yescharacteristic
234C22×Dic61C2×D411yescharacteristic
235Q8×D61—81no—
236Q8×D61—81no—
237D4×D61—42no—
238#11758222—44no—
239C2×D244C22⋊C411yescharacteristic
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×C4×D61—21no—
243C2×C4×D61—21no—
244C2×C4×D61—81no—
245C2×C4×D61—81no—
246C2×C4×D61C22×C411yescharacteristic
247C2×C4×D61C22×C411yescharacteristic
248C2×C4×D61C2×D411yescharacteristic
249C2×C4×D61C2×D411yescharacteristic
250C2×C4×D61C2×D411yescharacteristic
251C2×C4×D61C2×D411yescharacteristic
252C2×C4×D61C2×D411yescharacteristic
253C2×C4×D61C2×D411yescharacteristic
254C2×C4×D61C2411yescharacteristic
255C2×Dic122—21no—
256C2×Dic122—21no—
257C2×Dic122—21no—
258C2×Dic122C22×C411yescharacteristic
259C22⋊#6923—42no—
260C22⋊#6923—81no—
261C22⋊#6923—81no—
262#11758217—81no—
263C2×#92420—21no—
264C2×#92420—21no—
265C2×#92420—21no—
266C2×#92420—21no—
267C2×#92420—81no—
268C4⋊#6923—81no—
269C4⋊#6923—81no—
270C4×#6923—81no—
271#11758213—81no—
272D61⋊C8—81no—
273C4⋊C4×C61—21no—
274C4⋊C4×C61—21no—
275C4⋊C4×C61—21no—
276C4⋊C4×C61—21no—
277C4⋊C4×C61C22⋊C411yescharacteristic
278C4⋊C4×C61C22×C411yescharacteristic
279C22⋊C4×C61—21no—
280C22⋊C4×C61—21no—
281C22⋊C4×C61—21no—
282C22⋊C4×C61C22⋊C411yescharacteristic
283C22⋊C4×C61C22⋊C411yescharacteristic
284C42×C61C22×C411yescharacteristic
285C22⋊Dic61—21no—
286C22⋊Dic61—21no—
287C22⋊Dic61—21no—
288C22⋊Dic61—21no—
289C22⋊Dic61—21no—
290C22⋊Dic61—21no—
291C22⋊Dic61—21no—
292C22⋊Dic61—21no—
293C22⋊Dic61—21no—
294C22⋊Dic61C22⋊C411yescharacteristic
295C22⋊Dic61C22⋊C411yescharacteristic
296#11758198—21no—
297#11758198—21no—
298#11758198—21no—
299#11758198—21no—
300#11758198—21no—
301#11758198C22⋊C411yescharacteristic
302#11758198C22⋊C411yescharacteristic
303#11758198C22⋊C411yescharacteristic
304#11758198C22⋊C411yescharacteristic
305C4⋊Dic61—21no—
306C4⋊Dic61—21no—
307C4⋊Dic61—21no—
308C4⋊Dic61—21no—
309C4⋊Dic61—21no—
310C4⋊Dic61C22⋊C411yescharacteristic
311C4⋊Dic61C22×C411yescharacteristic
312C4⋊Dic61C22×C411yescharacteristic
313C4⋊Dic61C22×C411yescharacteristic
314#11758196—21no—
315#11758196—21no—
316#11758196—21no—
317#11758196—21no—
318#11758196—21no—
319#11758196—21no—
320#11758196—21no—
321#11758196—21no—
322#11758196—21no—
323#11758196—21no—
324#11758196C22⋊C411yescharacteristic
325#11758196C22⋊C411yescharacteristic
326C4×Dic61—21no—
327C4×Dic61—21no—
328C4×Dic61—21no—
329C4×Dic61—21no—
330C4×Dic61—21no—
331C4×Dic61C22×C411yescharacteristic
332C4×Dic61C2×D411yescharacteristic
333C4×Dic61C2×D411yescharacteristic
334C23×C61—21no—
335C23×C61C2×C22⋊C411yescharacteristic
336C23×C61C2×C22⋊C411yescharacteristic
337C22×D61—21no—
338C22×D61—21no—
339C22×D61—22no—
340C22×D61—21no—
341C22×D61—21no—
342C22×D61—41no—
343C22×D61—41no—
344C22×D61—41no—
345C22×D61C2×C22⋊C411yescharacteristic
346C22×D61C2×C22⋊C411yescharacteristic
347C22×D61C22×D411yescharacteristic
348C2×#6923—41no—
349C2×#6923—41no—
350C2×#6923—41no—
351C2×#6923—41no—
352C2×#6923—41no—
353C2×#6923—41no—
354C2×#6923—41no—
355C2×#6923—41no—
356C2×#6923—41no—
357C2×#6923—41no—
358C2×#6923—41no—
359C2×#6923—41no—
360C2×#6923—84no—
361Q8×C61—41no—
362Q8×C61—41no—
363D4×C61—41no—
364D4×C61—41no—
365D4×C61—81no—
366D4×C61—81no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—21no—
370C2×C4×C61—41no—
371C2×C4×C61—41no—
372C2×C4×C61—42no—
373C2×C4×C61—81no—
374C2×C4×C61—81no—
375C2×C4×C61C2×C22⋊C411yescharacteristic
376C2×C4×C61C2×C22⋊C411yescharacteristic
377C2×C4×C61C2×C22⋊C411yescharacteristic
378C2×C4×C61C2×C22⋊C411yescharacteristic
379C2×C4×C61C23×C411yescharacteristic
380C22⋊D61—22no—
381C22⋊D61—41no—
382C22⋊D61—42no—
383C22⋊D61—41no—
384C22⋊D61—41no—
385C22⋊D61—42no—
386C2×Dic61—21no—
387C2×Dic61—21no—
388C2×Dic61—21no—
389C2×Dic61—21no—
390C2×Dic61—41no—
391C2×Dic61—41no—
392C2×Dic61C2×C22⋊C411yescharacteristic
393C2×Dic61C2×C22⋊C411yescharacteristic
394C2×Dic61C2×C22⋊C411yescharacteristic
395C2×Dic61C2×C22⋊C411yescharacteristic
396C2×Dic61C22×D411yescharacteristic
397D244—22no—
398C4×D61—21no—
399C4×D61—21no—
400C4×D61—41no—
401C4×D61—41no—
402C4×D61—41no—
403C4×D61—41no—
404C4×D61—41no—
405C4×D61—41no—
406C4×D61—41no—
407C4×D61—41no—
408C4×D61—42no—
409C4×D61—42no—
410C4×D61—81no—
411C4×D61—81no—
412Dic122—42no—
413Dic122—41no—
414Dic122—81no—
415Dic122—81no—
416#92420—41no—
417#92420—41no—
418#92420—41no—
419#92420—41no—
420#17598—611nomaximal, Sylow
421C22×C61—21no—
422C22×C61—21no—
423C22×C61—21no—
424C22×C61—21no—
425C22×C61—21no—
426C22×C61—21no—
427C22×C61—41no—
428C22×C61—41no—
429C22×C61—41no—
430C22×C61C22×C22⋊C411yescharacteristic
431C2×D61—21no—
432C2×D61—21no—
433C2×D61—21no—
434C2×D61—21no—
435C2×D61—21no—
436C2×D61—21no—
437C2×D61—21no—
438C2×D61—42no—
439C2×D61—42no—
440C2×D61—81no—
441C2×D61—81no—
442C2×D61#42112yes—
443C2×D61#57711yescharacteristic
444C2×D61#57811yescharacteristic
445#6923—81no—
446#6923—81no—
447#6923—81no—
448#6923—81no—
449C4×C61—21no—
450C4×C61—21no—
451C4×C61—21no—
452C4×C61—21no—
453C4×C61—21no—
454C4×C61—41no—
455C4×C61—41no—
456C4×C61—41no—
457Dic61—21no—
458Dic61—21no—
459Dic61—21no—
460Dic61—21no—
461Dic61—21no—
462Dic61—41no—
463Dic61—41no—
464Dic61—41no—
465Dic61—41no—
466#3520—611no—
467#2974—611no—
468#2318—611no—
469#1521—611no—
470#1520—611no—
471#1518—611no—
472#1516—611no—
473#1515—611no—
474#1513—611no—
475#1512—611no—
476#1511—611no—
477#1508—611no—
478#1504—611no—
479#1501—611no—
480C2×#328—611no—
481C2×C61—41no—
482C2×C61—41no—
483C2×C61—81no—
484C2×C61#288311yescharacteristic
485C2×C61#289811yescharacteristic
486C2×C61C2×#42111yescharacteristic
487D61—21no—
488D61—21no—
489D61—22no—
490D61—41no—
491#556—611no—
492#554—1221no—
493#552—611no—
494#552—611no—
495#551—1221no—
496#551—1221no—
497D4×Q8—611no—
498#548—611no—
499#548—611no—
500#547—611no—
501#547#692311yescharacteristic, complemented
502#546—1221no—
503#542—1221no—
504#539—1221no—
505#539—1221no—
506#533—611no—
507#529—611no—
508#525—611no—
509#525—611no—
510C2×C22⋊Q8—611no—
511C2×C22⋊Q8—611no—
512#520—1221no—
513C2×C4×D4—611no—
514#436—1221no—
515#435—1221no—
516#435—1221no—
517C8×D4—1221no—
518#432—611no—
519#431—611no—
520#407—611no—
521#407—611no—
522C2×C22⋊C8—611no—
523C2×C22⋊C8—611no—
524#388—1221no—
525#387—1221no—
526#386—1221no—
527#385—1221no—
528#383—611no—
529#382—611no—
530#381—611no—
531#380—611no—
532C4×C22⋊C4—611no—
533C2×#95—611no—
534#328—611no—
535#328—611no—
536#328—611no—
537#328—611no—
538#328—611no—
539#328—611no—
540#328—611no—
541#328—611no—
542#328—611no—
543#328—611no—
544#328—611no—
545#328—611no—
546#327—611no—
547#327—611no—
548#327—611no—
549#327—611no—
550C61#1759811yescharacteristic, complemented, Sylow
551C2×#41—1221no—
552C2×#41C2×#692311yescharacteristic
553C2×#41C2×#692311yescharacteristic, complemented
554C22×Q8—611no—
555C22×Q8—611no—
556C22×D4—611no—
557C23×C4—611no—
558C23×C4—611no—
559C23×C4—1221no—
560C2×M16—1221no—
561C2×M16—1221no—
562C22×C8—1221no—
563C22×C8—1221no—
564C4⋊Q8—611no—
565C4⋊Q8—1221no—
566C4⋊Q8C2×#692311yescharacteristic, complemented
567#126—1221no—
568#126—1221no—
569#126—1221no—
570#126—1221no—
571#126—1221no—
572#125—611no—
573#125—1221no—
574#125—1221no—
575#125—1221no—
576#124—611no—
577#124—1221no—
578#124—1221no—
579#124—1221no—
580#123—21no—
581#123—21no—
582#123—1221no—
583#123—1221no—
584#123—1221no—
585#123—1221no—
586#123—1221no—
587#123—1221no—
588#123—1221no—
589C22⋊Q8—611no—
590C22⋊Q8—611no—
591C22⋊Q8—611no—
592C22⋊Q8—611no—
593C22⋊Q8—611no—
594C22⋊Q8—611no—
595C22⋊Q8—611no—
596C22⋊Q8—1221no—
597C22⋊Q8—1221no—
598C22⋊Q8—1221no—
599C22⋊Q8—1221no—
600C22⋊Q8—1221no—
601C22⋊Q8—1221no—
602C22⋊Q8—1221no—
603C22⋊Q8—1221no—
604C22⋊Q8—1221no—
605C22⋊Q8—1221no—
606C22⋊Q8C2×#692311yescharacteristic
607C22⋊Q8C2×#692311yescharacteristic, complemented
608#121—21no—
609#121—611no—
610#121—611no—
611#121—611no—
612#121—1221no—
613#121—1221no—
614#120—1221no—
615#120—1221no—
616C4×Q8—611no—
617C4×Q8—611no—
618C4×Q8—611no—
619C4×Q8—1221no—
620C4×Q8—1221no—
621C4×D4—611no—
622C4×D4—611no—
623C4×D4—611no—
624C4×D4—611no—
625C4×D4—611no—
626C4×D4—611no—
627C4×D4—611no—
628C4×D4—1221no—
629C4×D4—1221no—
630C4×D4—1221no—
631C4×D4—1221no—
632C4×D4—1221no—
633C4×D4—1221no—
634C4×D4—1221no—
635C4×D4—1221no—
636C4×D4C2×#692311yescharacteristic
637C4×D4C2×#692311yescharacteristic, complemented
638#117—611no—
639#117—611no—
640#117—1221no—
641#117—1221no—
642#117—1221no—
643#117—1221no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—611no—
646C2×C4⋊C4—611no—
647C2×C4⋊C4—611no—
648C2×C4⋊C4—1221no—
649C2×C4⋊C4—1221no—
650C2×C4⋊C4—1221no—
651C2×C4⋊C4—1221no—
652C2×C22⋊C4—611no—
653C2×C22⋊C4—611no—
654C2×C22⋊C4—1221no—
655C2×C22⋊C4—1221no—
656C2×C22⋊C4—1221no—
657C2×C22⋊C4—1221no—
658C2×C22⋊C4—1221no—
659C2×C42—611no—
660C2×C42—1221no—
661C4⋊C8—1221no—
662C4⋊C8—1221no—
663C22⋊C8—611no—
664C22⋊C8—611no—
665C22⋊C8—611no—
666C22⋊C8—611no—
667C22⋊C8—1221no—
668C22⋊C8—1221no—
669C22⋊C8—1221no—
670C22⋊C8—1221no—
671#97—1221no—
672C4×C8—1221no—
673#95—611no—
674#95—611no—
675#95—611no—
676#95—611no—
677#95—1221no—
678#95—1221no—
679#95—1221no—
680#95—1221no—
681#95—1221no—
682C24—611no—
683C24—611no—
684#41—81no—
685#41—81no—
686#41—2444no—
687C2×Q8—611no—
688C2×Q8—1221no—
689C2×Q8—1221no—
690C2×Q8—1221no—
691C2×Q8—4881no—
692C2×Q8—4881no—
693C2×Q8C22×#692311yescharacteristic
694C2×Q8C22×#692311yescharacteristic
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—611no—
698C2×D4—611no—
699C2×D4—611no—
700C2×D4—1221no—
701C2×D4—1221no—
702C2×D4—1221no—
703C2×D4—2442no—
704C2×D4C22⋊#692311yescharacteristic
705C2×D4C22×#692311yescharacteristic
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—611no—
710C22×C4—611no—
711C22×C4—611no—
712C22×C4—611no—
713C22×C4—611no—
714C22×C4—611no—
715C22×C4—611no—
716C22×C4—611no—
717C22×C4—611no—
718C22×C4—611no—
719C22×C4—611no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—4881no—
729C22×C4—4881no—
730C22×C4—4881no—
731C22×C4—4881no—
732C22×C4—2442no—
733C22×C4C22×#692311yescharacteristic
734C22×C4C22×#692311yescharacteristic
735M16—4881no—
736M16—4881no—
737C2×C8—1221no—
738C2×C8—1221no—
739C2×C8—1221no—
740C2×C8—1221no—
741C2×C8—4881no—
742C2×C8—4881no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—611no—
748C4⋊C4—611no—
749C4⋊C4—611no—
750C4⋊C4—611no—
751C4⋊C4—611no—
752C4⋊C4—611no—
753C4⋊C4—1221no—
754C4⋊C4—1221no—
755C4⋊C4—1221no—
756C4⋊C4—1221no—
757C4⋊C4—1221no—
758C4⋊C4—1221no—
759C4⋊C4—1221no—
760C4⋊C4—1221no—
761C4⋊C4—1221no—
762C4⋊C4—1221no—
763C4⋊C4—1221no—
764C4⋊C4—1221no—
765C4⋊C4—1221no—
766C4⋊C4—1221no—
767C4⋊C4—1221no—
768C4⋊C4—4881no—
769C4⋊C4—4881no—
770C4⋊C4C22⋊#692311yescharacteristic
771C4⋊C4C22×#692311yescharacteristic
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—611no—
776C22⋊C4—611no—
777C22⋊C4—611no—
778C22⋊C4—611no—
779C22⋊C4—611no—
780C22⋊C4—611no—
781C22⋊C4—1221no—
782C22⋊C4—1221no—
783C22⋊C4—1221no—
784C22⋊C4—1221no—
785C22⋊C4—1221no—
786C22⋊C4—1221no—
787C22⋊C4—1221no—
788C22⋊C4—1221no—
789C22⋊C4—1221no—
790C22⋊C4—1221no—
791C22⋊C4—1221no—
792C22⋊C4—1221no—
793C22⋊C4—1221no—
794C22⋊C4—1221no—
795C22⋊C4—4881no—
796C22⋊C4—4881no—
797C22⋊C4—2442no—
798C22⋊C4C22⋊#692311yescharacteristic
799C22⋊C4C22⋊#692311yescharacteristic
800C42—611no—
801C42—611no—
802C42—611no—
803C42—1221no—
804C42—1221no—
805C42—1221no—
806C42—1221no—
807C42—1221no—
808C42—4881no—
809C42C22×#692311yescharacteristic
810C23—21no—
811C23—611no—
812C23—611no—
813C23—611no—
814C23—1221no—
815C23—1221no—
816C23—1222no—
817C23—1221no—
818C23—1221no—
819C23—2441no—
820C23—2441no—
821C23—2441no—
822C23C2×C22⋊#692311yescharacteristic
823C23C2×C22⋊#692311yescharacteristic
824Q8—41no—
825Q8—41no—
826Q8—4881no—
827Q8—4881no—
828Q8—2441no—
829Q8—2442no—
830D4—41no—
831D4—41no—
832D4—81no—
833D4—81no—
834D4—1222no—
835D4—1222no—
836D4—2441no—
837D4—2441no—
838D4—2441no—
839D4—2442no—
840D4—2442no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—42no—
847C2×C4—81no—
848C2×C4—81no—
849C2×C4—611no—
850C2×C4—611no—
851C2×C4—611no—
852C2×C4—611no—
853C2×C4—611no—
854C2×C4—1221no—
855C2×C4—1221no—
856C2×C4—1221no—
857C2×C4—1221no—
858C2×C4—1221no—
859C2×C4—1221no—
860C2×C4—4881no—
861C2×C4—4881no—
862C2×C4—4884no—
863C2×C4—2441no—
864C2×C4—2441no—
865C2×C4—2441no—
866C2×C4—2441no—
867C2×C4—2441no—
868C2×C4—2441no—
869C2×C4—2441no—
870C2×C4—2441no—
871C2×C4—2442no—
872C2×C4—2442no—
873C2×C4—2441no—
874C2×C4—2441no—
875C2×C4—2441no—
876C2×C4—2441no—
877C2×C4—2441no—
878C2×C4—2441no—
879C2×C4—2441no—
880C2×C4—2441no—
881C2×C4—2441no—
882C2×C4—2441no—
883C2×C4—2441no—
884C2×C4—2441no—
885C2×C4—2441no—
886C2×C4—2441no—
887C2×C4C2×C22⋊#692311yescharacteristic
888C2×C4C2×C22⋊#692311yescharacteristic
889C2×C4C2×C22⋊#692311yescharacteristic
890C2×C4C2×C22⋊#692311yescharacteristic
891C2×C4C23×#692311yescharacteristic
892C8—2441no—
893C8—2441no—
894C8—2441no—
895C8—2441no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—611no—
906C22—611no—
907C22—612no—
908C22—1221no—
909C22—1221no—
910C22—1221no—
911C22—1221no—
912C22—1221no—
913C22—1221no—
914C22—1221no—
915C22—4881no—
916C22—4881no—
917C22—2442no—
918C22—2442no—
919C22C22×C22⋊#692311yescharacteristic
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—21no—
925C4—41no—
926C4—41no—
927C4—41no—
928C4—1221no—
929C4—1221no—
930C4—1221no—
931C4—1221no—
932C4—1221no—
933C4—4881no—
934C4—4881no—
935C4—4881no—
936C4—4881no—
937C4—2441no—
938C4—2441no—
939C4—2441no—
940C4—2441no—
941C2—41no—
942C2—41no—
943C2—81no—
944C2—1221no—
945C2—1221no—
946C2—1222no—
947C2—2441no—
948C2#2146241811yescharacteristic
949C2#2146244111yescharacteristic
950C2D61⋊#42111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#547C4
socleC22×C61C22×C22⋊C4
prime radical#21459871C2
cosocleC2×C4×D61C24
hypercenter#547#6923
hypocenterC61#17598
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #21462676C2semidirect
2. #21462301C2semidirect
3. #21461261C2semidirect
4. #21461257C2semidirect
5. #21461253C2semidirect
6. #21461245C2semidirect
7. #21461243C2semidirect
8. #21461234C2semidirect
9. #21461230C2semidirect
10. #21461228C2semidirect
11. #21461217C2semidirect
12. #21461205C2semidirect
13. #21461194C2semidirect
14. D61⋊#328C2semidirect
52. #16840482C4semidirect
54. #16840446C4semidirect
55. #16840446C4semidirect
58. #16840427C4semidirect
59. #16840419C4semidirect
60. #16840419C4semidirect
61. #16840417C4semidirect
74. C61×#547C4semidirect
109. C2×Q8×D61C2×C4semidirect
113. #14519777C2×C4semidirect
121. #14519768C2×C4semidirect
127. #14519764C2×C4semidirect
141. #14519756C2×C4semidirect
149. #14519753C2×C4semidirect
155. #14519748C2×C4semidirect
159. Q8×Dic61C2×C4semidirect
160. Q8×Dic61C2×C4semidirect
161. C4×Dic122C2×C4semidirect
181. #14519736C2×C4semidirect
188. C4⋊C4×D61C2×C4semidirect
196. C2×#41×C61C2×C4semidirect
197. C4⋊Q8×C61C2×C4semidirect
201. C22⋊Q8×C61C2×C4semidirect
204. C4×D4×C61C2×C4semidirect
501. #547#6923semidirect
550. C61#17598semidirect
553. C2×#41C2×#6923semidirect
566. C4⋊Q8C2×#6923semidirect
607. C22⋊Q8C2×#6923semidirect
637. C4×D4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214626762
#214623012
#214612612
#214612572
#214612532
#214612452
#214612432
#214612342
#214612302
#214612282
#214612172
#214612052
#214611942
D61⋊#3282
#214598712
#1759861