Finite Group Databasebeta

← #30611373

Subgroups — #30611373

Order 15616.

1270 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462671C211yesmaximal, characteristic, complemented
2#21462336C211yesmaximal, characteristic, complemented
3#21461255C211yesmaximal, characteristic, complemented
4#21461254C211yesmaximal, characteristic, complemented
5#21461239C211yesmaximal, characteristic, complemented
6#21461238C211yesmaximal, characteristic, complemented
7#21461225C211yesmaximal, characteristic, complemented
8#21461224C211yesmaximal, characteristic, complemented
9#21461215C211yesmaximal, characteristic, complemented
10#21461214C211yesmaximal, characteristic, complemented
11#21461209C211yesmaximal, characteristic, complemented
12#21461208C211yesmaximal, characteristic, complemented
13D61⋊#327C211yesmaximal, characteristic, complemented
14C2×#16840613C211yesmaximal, characteristic, complemented
15#21459575C211yesmaximal, characteristic
16#16840794—21no—
17#16840793—21no—
18#16840792—21no—
19#16840791—21no—
20#16840785C2211yescharacteristic, complemented
21#16840784C2211yescharacteristic, complemented
22#16840734C2211yescharacteristic, complemented
23#16840733C2211yescharacteristic, complemented
24C2×#14519834C2211yescharacteristic, complemented
25D61⋊(C22⋊C8)C2211yescharacteristic, complemented
26#16840712—21no—
27#16840711—21no—
28#16840710—21no—
29#16840707C2211yescharacteristic, complemented
30#16840705C2211yescharacteristic, complemented
31#16840704C2211yescharacteristic, complemented
32C22⋊C4×#6923—21no—
33C4×C22⋊#6923C2211yescharacteristic, complemented
34#16840698C2211yescharacteristic, complemented
35C2×(C2×#6923)⋊C4C2211yescharacteristic, complemented
36#16840614C2211yescharacteristic, complemented
37#16840614C2211yescharacteristic, complemented
38#16840614C2211yescharacteristic, complemented
39#16840614C2211yescharacteristic, complemented
40#16840613C2211yescharacteristic, complemented
41#16840613C2211yescharacteristic, complemented
42#16840613C2211yescharacteristic, complemented
43#16840613C2211yescharacteristic, complemented
44#16840613C2211yescharacteristic, complemented
45#16840613C2211yescharacteristic, complemented
46#16840613C2211yescharacteristic, complemented
47#16840613C2211yescharacteristic, complemented
48#16840613C2211yescharacteristic, complemented
49#16840613C2211yescharacteristic, complemented
50#16840613C2211yescharacteristic, complemented
51#16840613C2211yescharacteristic, complemented
52C2×#14519822—21no—
53#16840417C411yescharacteristic, complemented
54#16840416C411yescharacteristic, complemented
55#16840412C411yescharacteristic, complemented
56#16840412C411yescharacteristic, complemented
57#16840409—21no—
58#16840406—21no—
59#16840399—21no—
60#16840399—21no—
61#16840397C411yescharacteristic, complemented
62D4×C22⋊D61C411yescharacteristic, complemented
63D4×C22⋊D61C411yescharacteristic, complemented
64#16840341—21no—
65#16840322—21no—
66#16840322—21no—
67#16840310C2211yescharacteristic
68#16840309C2211yescharacteristic
69C2×#14519748C2211yescharacteristic
70C2×#14519748C2211yescharacteristic
71#121×D61C2211yescharacteristic
72#121×D61C2211yescharacteristic
73C4×D4×D61C2211yescharacteristic
74D42×C61C411yescharacteristic, complemented
75C23×#6923—21no—
76C2×#11758213—21no—
77C2×#11758217—21no—
78C2×D61⋊C8—21no—
79C22×#92420—21no—
80C2×C4⋊#6923—21no—
81C2×C22⋊#6923—21no—
82C2×C22⋊#6923—21no—
83C2×C22⋊#6923—21no—
84C2×C4×#6923—21no—
85C2×C4×#6923—21no—
86#14519844—21no—
87C4⋊#92420—21no—
88#14519834—21no—
89#14519834—21no—
90#14519834C2311yescharacteristic
91#14519834C2311yescharacteristic
92#14519834C2311yescharacteristic
93#14519834C2311yescharacteristic
94C22⋊#92420—21no—
95C22⋊#92420—21no—
96#14519832—21no—
97#14519832—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
107#14519822—44no—
108#14519822—44no—
109C2×#11758222—21no—
110C2×#11758222—21no—
111C2×#11758224—21no—
112C2×#11758224—21no—
113C2×#11758224—21no—
114C2×#11758224—21no—
115C22×C22⋊D61—21no—
116C22×C22⋊D61—21no—
117C22×C22⋊D61—21no—
118C22×C22⋊D61—21no—
119C2×D4×D61—21no—
120C2×D4×D61—21no—
121C2×D4×D61—21no—
122C2×D4×D61C2×C411yescharacteristic
123C2×D4×D61C2×C411yescharacteristic, complemented
124C2×D4×D61D411yescharacteristic
125C22×C4×D61C2311yescharacteristic
126C22×C4×D61C2311yescharacteristic
127#14519777C2×C411yescharacteristic, complemented
128#14519776C2×C411yescharacteristic, complemented
129#14519773C2×C411yescharacteristic, complemented
130#14519764—21no—
131#14519763—21no—
132#14519761—21no—
133#14519761—21no—
134#14519759—21no—
135#14519759—21no—
136#14519759—21no—
137#14519759—21no—
138#14519758—21no—
139#14519758—21no—
140#14519757—21no—
141#14519756—21no—
142#14519754—21no—
143#14519754—21no—
144#14519752C2311yescharacteristic
145#14519751C2×C411yescharacteristic
146#14519751C2×C411yescharacteristic, complemented
147#14519750—21no—
148#14519750—21no—
149#14519750—21no—
150#14519749—21no—
151#14519749—21no—
152#14519749—21no—
153#14519749—21no—
154#14519748—21no—
155#14519748—21no—
156#14519748—21no—
157#14519748—21no—
158#14519748—21no—
159#14519748—21no—
160#14519748C2×C411yescharacteristic
161#14519748C2×C411yescharacteristic
162#14519748C2×C411yescharacteristic, complemented
163#14519748C2×C411yescharacteristic, complemented
164#14519748C2311yescharacteristic
165#14519748C2311yescharacteristic
166#14519748C2311yescharacteristic
167#14519746—21no—
168#14519746—21no—
169#14519745—21no—
170#14519745—21no—
171#14519745—21no—
172#14519745—21no—
173C4×D244C2×C411yescharacteristic
174C4×D244C2×C411yescharacteristic, complemented
175D4×Dic61—21no—
176D4×Dic61C2×C411yescharacteristic, complemented
177D4×Dic61C2×C411yescharacteristic, complemented
178D4×Dic61D411yescharacteristic
179#14519739D411yescharacteristic
180C4×C22⋊D61—21no—
181C4×C22⋊D61C2×C411yescharacteristic
182C4×C22⋊D61C2×C411yescharacteristic
183#14519737D411yescharacteristic
184#14519737D411yescharacteristic
185C2×C4⋊Dic61C2×C411yescharacteristic
186C2×C4⋊Dic61C2×C411yescharacteristic, complemented
187C4⋊C4×D61C2×C411yescharacteristic
188C4⋊C4×D61C2×C411yescharacteristic, complemented
189C4⋊C4×D61D411yescharacteristic
190C2×C22⋊Dic61—21no—
191C2×C22⋊Dic61—21no—
192C22⋊C4×D61—21no—
193C22⋊C4×D61—21no—
194C22⋊C4×D61D411yescharacteristic
195C22⋊C4×D61D411yescharacteristic
196C42×D61C2311yescharacteristic
197C22×D4×C61—21no—
198C22×D4×C61C2×C411yescharacteristic
199C22×D4×C61C2×C411yescharacteristic, complemented
200#127×C61C2×C411yescharacteristic, complemented
201#121×C61—21no—
202#121×C61C2×C411yescharacteristic
203#121×C61C2×C411yescharacteristic, complemented
204#120×C61—21no—
205#120×C61—21no—
206C4×D4×C61C2×C411yescharacteristic
207C4×D4×C61C2×C411yescharacteristic, complemented
208C24×C61—21no—
209C24×C61—21no—
210C23×D61—21no—
211C23×D61—21no—
212C23×D61C2×D411yescharacteristic
213C23×D61C2×D411yescharacteristic
214C22×#6923—21no—
215C22×#6923—21no—
216C22×#6923—21no—
217C22×#6923—21no—
218C22×#6923—42no—
219C22×#6923—42no—
220C22×#6923—81no—
221C2×D4×C61—21no—
222C2×D4×C61—21no—
223C2×D4×C61—21no—
224C2×D4×C61—21no—
225C2×D4×C61—21no—
226C2×D4×C61—21no—
227C2×D4×C61—44no—
228C2×D4×C61—81no—
229C2×D4×C61—81no—
230C2×D4×C61C22⋊C411yescharacteristic
231C2×D4×C61C22×C411yescharacteristic
232C2×D4×C61C22×C411yescharacteristic
233C2×D4×C61C22×C411yescharacteristic
234C22×C4×C61—21no—
235C22×C4×C61C22×C411yescharacteristic
236C22×C4×C61C22×C411yescharacteristic
237C2×C22⋊D61—21no—
238C2×C22⋊D61—21no—
239C2×C22⋊D61—21no—
240C2×C22⋊D61—21no—
241C2×C22⋊D61—21no—
242C2×C22⋊D61—21no—
243C2×C22⋊D61—21no—
244C2×C22⋊D61—21no—
245C2×C22⋊D61—21no—
246C2×C22⋊D61—21no—
247C2×C22⋊D61—21no—
248C2×C22⋊D61—21no—
249C2×C22⋊D61—21no—
250C2×C22⋊D61—44no—
251C2×C22⋊D61—44no—
252C2×C22⋊D61—42no—
253C2×C22⋊D61—42no—
254C2×C22⋊D61—42no—
255C2×C22⋊D61—42no—
256C2×C22⋊D61C22⋊C411yescharacteristic
257C2×C22⋊D61C22⋊C411yescharacteristic
258C22×Dic61—21no—
259C22×Dic61—21no—
260C22×Dic61—21no—
261C22×Dic61—21no—
262C22×Dic61C2×D411yescharacteristic
263C22×Dic61C2×D411yescharacteristic
264#11758224—42no—
265#11758224—42no—
266#11758224—44no—
267#11758224—44no—
268#11758224—44no—
269D4×D61—22no—
270D4×D61—22no—
271D4×D61—44no—
272D4×D61—42no—
273D4×D61—42no—
274D4×D61—42no—
275D4×D61—42no—
276D4×D61—81no—
277D4×D61—81no—
278#11758222—42no—
279#11758222—42no—
280#11758222—44no—
281C2×D244—21no—
282C2×D244C22⋊C411yescharacteristic
283C2×D244C22×C411yescharacteristic
284C2×C4×D61—21no—
285C2×C4×D61—21no—
286C2×C4×D61—21no—
287C2×C4×D61—81no—
288C2×C4×D61—81no—
289C2×C4×D61C22×C411yescharacteristic
290C2×C4×D61C22×C411yescharacteristic
291C2×C4×D61C2×D411yescharacteristic
292C2×C4×D61C2×D411yescharacteristic
293C2×C4×D61C2×D411yescharacteristic
294C2×C4×D61C2×D411yescharacteristic
295C2×C4×D61C2×D411yescharacteristic
296C2×C4×D61C2×D411yescharacteristic
297C2×C4×D61C2411yescharacteristic
298C2×Dic122—21no—
299C2×Dic122—21no—
300C22⋊#6923—42no—
301C22⋊#6923—42no—
302C22⋊#6923—81no—
303#11758217—81no—
304C2×#92420—21no—
305C2×#92420—21no—
306C2×#92420—21no—
307C2×#92420—21no—
308C2×#92420—81no—
309C4⋊#6923—81no—
310C4×#6923—42no—
311C4×#6923—81no—
312#11758213—81no—
313D61⋊C8—81no—
314C4⋊C4×C61C22⋊C411yescharacteristic
315C4⋊C4×C61C22×C411yescharacteristic
316C22⋊C4×C61—21no—
317C22⋊C4×C61—21no—
318C22⋊C4×C61—21no—
319C22⋊C4×C61C22⋊C411yescharacteristic
320C22⋊C4×C61C22⋊C411yescharacteristic
321C42×C61C22×C411yescharacteristic
322C22⋊Dic61—21no—
323C22⋊Dic61—21no—
324C22⋊Dic61—21no—
325C22⋊Dic61—21no—
326C22⋊Dic61—21no—
327C22⋊Dic61—21no—
328C22⋊Dic61—21no—
329C22⋊Dic61—21no—
330C22⋊Dic61—21no—
331C22⋊Dic61C22⋊C411yescharacteristic
332C22⋊Dic61C22⋊C411yescharacteristic
333#11758198—21no—
334#11758198—21no—
335#11758198—21no—
336#11758198—21no—
337#11758198C22⋊C411yescharacteristic
338#11758198C22⋊C411yescharacteristic
339#11758198C22⋊C411yescharacteristic
340#11758198C22⋊C411yescharacteristic
341C4⋊Dic61—21no—
342C4⋊Dic61—21no—
343C4⋊Dic61—21no—
344C4⋊Dic61C22⋊C411yescharacteristic
345C4⋊Dic61C22×C411yescharacteristic
346C4⋊Dic61C22×C411yescharacteristic
347C4⋊Dic61C22×C411yescharacteristic
348#11758196—21no—
349#11758196—21no—
350#11758196—21no—
351#11758196C22⋊C411yescharacteristic
352#11758196C22⋊C411yescharacteristic
353C4×Dic61C22×C411yescharacteristic
354C4×Dic61C2×D411yescharacteristic
355C4×Dic61C2×D411yescharacteristic
356C23×C61—21no—
357C23×C61—21no—
358C23×C61—21no—
359C23×C61—42no—
360C23×C61—42no—
361C23×C61—81no—
362C23×C61—81no—
363C23×C61—81no—
364C23×C61—81no—
365C23×C61C2×C22⋊C411yescharacteristic
366C23×C61C2×C22⋊C411yescharacteristic
367C22×D61—21no—
368C22×D61—21no—
369C22×D61—21no—
370C22×D61—41no—
371C22×D61—41no—
372C22×D61—41no—
373C22×D61—41no—
374C22×D61—42no—
375C22×D61—42no—
376C22×D61—81no—
377C22×D61—81no—
378C22×D61—81no—
379C22×D61—81no—
380C22×D61C2×C22⋊C411yescharacteristic
381C22×D61C2×C22⋊C411yescharacteristic
382C22×D61AGL(1,ℤ/8)12yes—
383C22×D61AGL(1,ℤ/8)12yes—
384C22×D61C22×D411yescharacteristic
385C2×#6923—22no—
386C2×#6923—41no—
387C2×#6923—41no—
388C2×#6923—41no—
389C2×#6923—41no—
390C2×#6923—41no—
391C2×#6923—41no—
392C2×#6923—41no—
393C2×#6923—41no—
394C2×#6923—41no—
395C2×#6923—41no—
396C2×#6923—41no—
397C2×#6923—84no—
398D4×C61—22no—
399D4×C61—41no—
400D4×C61—41no—
401D4×C61—41no—
402D4×C61—42no—
403D4×C61—42no—
404D4×C61—42no—
405D4×C61—81no—
406D4×C61—81no—
407D4×C61—81no—
408C2×C4×C61—21no—
409C2×C4×C61—41no—
410C2×C4×C61—41no—
411C2×C4×C61—42no—
412C2×C4×C61C2×C22⋊C411yescharacteristic
413C2×C4×C61C2×C22⋊C411yescharacteristic
414C2×C4×C61C2×C22⋊C411yescharacteristic
415C2×C4×C61C2×C22⋊C411yescharacteristic
416C2×C4×C61C23×C411yescharacteristic
417C22⋊D61—22no—
418C22⋊D61—22no—
419C22⋊D61—42no—
420C22⋊D61—42no—
421C22⋊D61—42no—
422C22⋊D61—42no—
423C22⋊D61—42no—
424C22⋊D61—41no—
425C22⋊D61—41no—
426C22⋊D61—41no—
427C22⋊D61—41no—
428C22⋊D61—41no—
429C22⋊D61—41no—
430C22⋊D61—42no—
431C22⋊D61—42no—
432C22⋊D61—81no—
433C22⋊D61—81no—
434C22⋊D61—81no—
435C2×Dic61—21no—
436C2×Dic61—21no—
437C2×Dic61—21no—
438C2×Dic61—41no—
439C2×Dic61—41no—
440C2×Dic61—42no—
441C2×Dic61—42no—
442C2×Dic61—42no—
443C2×Dic61—42no—
444C2×Dic61C2×C22⋊C411yescharacteristic
445C2×Dic61C2×C22⋊C411yescharacteristic
446C2×Dic61C2×C22⋊C411yescharacteristic
447C2×Dic61C2×C22⋊C411yescharacteristic
448C2×Dic61C22×D411yescharacteristic
449D244—22no—
450D244—41no—
451D244—41no—
452D244—41no—
453C4×D61—21no—
454C4×D61—21no—
455C4×D61—41no—
456C4×D61—41no—
457C4×D61—41no—
458C4×D61—41no—
459C4×D61—41no—
460C4×D61—41no—
461C4×D61—41no—
462C4×D61—41no—
463C4×D61—42no—
464C4×D61—42no—
465C4×D61—42no—
466Dic122—42no—
467Dic122—42no—
468#92420—41no—
469#92420—41no—
470#92420—41no—
471#92420—41no—
472#17620—611nomaximal, Sylow
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×C61—41no—
482C22×C61—41no—
483C22×C61—41no—
484C22×C61—41no—
485C22×C61—41no—
486C22×C61—41no—
487C22×C61—162no—
488C22×C61—162no—
489C22×C61#41812yes—
490C22×C61C22×C22⋊C411yescharacteristic
491C2×D61—21no—
492C2×D61—21no—
493C2×D61—21no—
494C2×D61—21no—
495C2×D61—21no—
496C2×D61—21no—
497C2×D61—21no—
498C2×D61—42no—
499C2×D61—42no—
500C2×D61—41no—
501C2×D61—41no—
502C2×D61—41no—
503C2×D61—81no—
504C2×D61—81no—
505C2×D61—162no—
506C2×D61—162no—
507C2×D61#41812yes—
508C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
509C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
510#6923—42no—
511#6923—81no—
512#6923—81no—
513#6923—81no—
514C4×C61—21no—
515C4×C61—21no—
516C4×C61—21no—
517C4×C61—21no—
518C4×C61—21no—
519C4×C61—41no—
520Dic61—21no—
521Dic61—21no—
522Dic61—21no—
523Dic61—21no—
524Dic61—21no—
525Dic61—41no—
526Dic61—41no—
527Dic61—41no—
528#3496—611no—
529#2973—611no—
530#2353—611no—
531#1519—611no—
532#1519—611no—
533#1514—611no—
534#1514—611no—
535#1510—611no—
536#1510—611no—
537#1507—611no—
538#1507—611no—
539#1505—611no—
540#1505—611no—
541C2×#327—611no—
542C2×#327—611no—
543C2×C61—22no—
544C2×C61—41no—
545C2×C61—81no—
546C2×C61—81no—
547C2×C61—81no—
548C2×C61#288311yescharacteristic
549C2×C61C2×#41811yescharacteristic
550C2×C61#290111yescharacteristic
551D61—21no—
552D61—21no—
553D61—22no—
554D61—41no—
555D61—81no—
556C2×H(5,𝔽2)—1221no—
557#547—611no—
558#547—611no—
559#547—611no—
560#547—611no—
561#546—1221no—
562#546—1221no—
563#546—1221no—
564#546—1221no—
565D42—611no—
566D42—611no—
567D42—611no—
568D42#692311yescharacteristic, complemented
569#537—1221no—
570#534—1221no—
571#534—1221no—
572#532—611no—
573#532—611no—
574C2×#121—611no—
575C2×#121—611no—
576C2×#121—611no—
577C2×#121—611no—
578C2×C4×D4—611no—
579#435—1221no—
580#435—1221no—
581#435—1221no—
582#435—1221no—
583#432—611no—
584#432—611no—
585#407—611no—
586#407—611no—
587C2×C22⋊C8—611no—
588C2×C22⋊C8—611no—
589#388—1221no—
590#387—1221no—
591#386—1221no—
592#383—611no—
593#381—611no—
594#380—611no—
595C4×C22⋊C4—611no—
596C4×C22⋊C4—1221no—
597#376—611no—
598C2×#95—611no—
599#327—611no—
600#327—611no—
601#327—611no—
602#327—611no—
603#327—611no—
604#327—611no—
605#327—611no—
606#327—611no—
607#327—611no—
608#327—611no—
609#327—611no—
610#327—611no—
611#327—611no—
612#327—611no—
613#327—611no—
614#327—611no—
615C61#1762011yescharacteristic, complemented, Sylow
616H(5,𝔽2)—2444no—
617H(5,𝔽2)—2444no—
618C2×#41—1221no—
619C2×#41—1221no—
620C2×#41—1221no—
621C2×#41—1221no—
622C2×#41—1221no—
623C2×#41—1221no—
624C22×D4—21no—
625C22×D4—611no—
626C22×D4—611no—
627C22×D4—611no—
628C22×D4—1221no—
629C22×D4—1221no—
630C22×D4—1221no—
631C22×D4—1221no—
632C22×D4—1221no—
633C22×D4—1221no—
634C22×D4—1221no—
635C22×D4C2×#692311yescharacteristic
636C22×D4C2×#692311yescharacteristic, complemented
637C23×C4—611no—
638C23×C4—611no—
639C23×C4—1221no—
640C2×M16—1221no—
641C2×M16—1221no—
642C22×C8—1221no—
643C22×C8—1221no—
644C4⋊Q8—611no—
645C4⋊Q8—611no—
646#127—611no—
647#127C2×#692311yescharacteristic, complemented
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—
658C22⋊Q8—1221no—
659C22⋊Q8—1221no—
660C22⋊Q8—1221no—
661C22⋊Q8—1221no—
662#121—21no—
663#121—611no—
664#121—611no—
665#121—611no—
666#121—611no—
667#121—611no—
668#121—611no—
669#121—611no—
670#121—611no—
671#121—611no—
672#121—611no—
673#121—1221no—
674#121—1221no—
675#121—1221no—
676#121—1221no—
677#121—1221no—
678#121—1221no—
679#121—1221no—
680#121—1221no—
681#121—1221no—
682#121—1221no—
683#121—1221no—
684#121—1221no—
685#121—1221no—
686#121C2×#692311yescharacteristic
687#121C2×#692311yescharacteristic, complemented
688#120—21no—
689#120—21no—
690#120—1221no—
691#120—1221no—
692#120—1221no—
693#120—1221no—
694#120—1221no—
695#120—1221no—
696C4×D4—611no—
697C4×D4—611no—
698C4×D4—611no—
699C4×D4—611no—
700C4×D4—611no—
701C4×D4—611no—
702C4×D4—611no—
703C4×D4—611no—
704C4×D4—611no—
705C4×D4—611no—
706C4×D4—1221no—
707C4×D4—1221no—
708C4×D4C2×#692311yescharacteristic
709C4×D4C2×#692311yescharacteristic, complemented
710C2×C4⋊C4—611no—
711C2×C4⋊C4—611no—
712C2×C4⋊C4—611no—
713C2×C4⋊C4—611no—
714C2×C4⋊C4—611no—
715C2×C4⋊C4—1221no—
716C2×C22⋊C4—611no—
717C2×C22⋊C4—611no—
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×C22⋊C4—1221no—
725C2×C42—611no—
726C2×C42—1221no—
727C2×C42—1221no—
728C4⋊C8—1221no—
729C4⋊C8—1221no—
730C22⋊C8—611no—
731C22⋊C8—611no—
732C22⋊C8—611no—
733C22⋊C8—611no—
734C22⋊C8—1221no—
735C22⋊C8—1221no—
736C22⋊C8—1221no—
737C22⋊C8—1221no—
738#97—1221no—
739#97—1221no—
740#95—611no—
741#95—611no—
742#95—611no—
743#95—611no—
744#95—1221no—
745#95—1221no—
746#95—1221no—
747#95—1221no—
748#95—1221no—
749C24—21no—
750C24—21no—
751C24—611no—
752C24—611no—
753C24—1221no—
754C24—1221no—
755#41—2442no—
756#41—2442no—
757#41—2444no—
758#41—2442no—
759#41—2442no—
760#41—2444no—
761#41—2444no—
762#41—2444no—
763C2×Q8—1221no—
764C2×Q8—1221no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—44no—
772C2×D4—81no—
773C2×D4—81no—
774C2×D4—611no—
775C2×D4—611no—
776C2×D4—611no—
777C2×D4—611no—
778C2×D4—1221no—
779C2×D4—1221no—
780C2×D4—1221no—
781C2×D4—1221no—
782C2×D4—1221no—
783C2×D4—1222no—
784C2×D4—1222no—
785C2×D4—1221no—
786C2×D4—1221no—
787C2×D4—1221no—
788C2×D4—1221no—
789C2×D4—1221no—
790C2×D4—1221no—
791C2×D4—1221no—
792C2×D4—1221no—
793C2×D4—1221no—
794C2×D4—4881no—
795C2×D4—4881no—
796C2×D4—2444no—
797C2×D4—2442no—
798C2×D4—2442no—
799C2×D4—2442no—
800C2×D4—2442no—
801C2×D4—2444no—
802C2×D4—2444no—
803C2×D4—2442no—
804C2×D4—2442no—
805C2×D4—2442no—
806C2×D4—2442no—
807C2×D4C22⋊#692311yescharacteristic
808C2×D4C22×#692311yescharacteristic
809C2×D4C22×#692311yescharacteristic
810C2×D4C22×#692311yescharacteristic
811C22×C4—21no—
812C22×C4—611no—
813C22×C4—611no—
814C22×C4—611no—
815C22×C4—611no—
816C22×C4—611no—
817C22×C4—611no—
818C22×C4—611no—
819C22×C4—611no—
820C22×C4—611no—
821C22×C4—611no—
822C22×C4—611no—
823C22×C4—1221no—
824C22×C4—1221no—
825C22×C4—1221no—
826C22×C4—1221no—
827C22×C4—1221no—
828C22×C4—1221no—
829C22×C4—1221no—
830C22×C4—1221no—
831C22×C4—1221no—
832C22×C4—1221no—
833C22×C4—1221no—
834C22×C4—4881no—
835C22×C4—4881no—
836C22×C4—4881no—
837C22×C4—2442no—
838C22×C4—2442no—
839C22×C4C22×#692311yescharacteristic
840C22×C4C22×#692311yescharacteristic
841M16—4881no—
842M16—4881no—
843C2×C8—1221no—
844C2×C8—1221no—
845C2×C8—1221no—
846C2×C8—1221no—
847C2×C8—4881no—
848C2×C8—4881no—
849C4⋊C4—611no—
850C4⋊C4—611no—
851C4⋊C4—611no—
852C4⋊C4—611no—
853C4⋊C4—611no—
854C4⋊C4—611no—
855C4⋊C4—1221no—
856C4⋊C4—1221no—
857C4⋊C4—1221no—
858C4⋊C4—1221no—
859C4⋊C4—1221no—
860C4⋊C4—1221no—
861C4⋊C4—4881no—
862C4⋊C4C22⋊#692311yescharacteristic
863C4⋊C4C22×#692311yescharacteristic
864C22⋊C4—21no—
865C22⋊C4—21no—
866C22⋊C4—21no—
867C22⋊C4—611no—
868C22⋊C4—611no—
869C22⋊C4—611no—
870C22⋊C4—611no—
871C22⋊C4—611no—
872C22⋊C4—611no—
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—1221no—
886C22⋊C4—4881no—
887C22⋊C4—2442no—
888C22⋊C4—2442no—
889C22⋊C4C22⋊#692311yescharacteristic
890C22⋊C4C22⋊#692311yescharacteristic
891C42—611no—
892C42—611no—
893C42—611no—
894C42—4881no—
895C42—2442no—
896C42C22×#692311yescharacteristic
897C23—21no—
898C23—21no—
899C23—21no—
900C23—42no—
901C23—42no—
902C23—81no—
903C23—81no—
904C23—81no—
905C23—81no—
906C23—611no—
907C23—611no—
908C23—612no—
909C23—612no—
910C23—611no—
911C23—1221no—
912C23—1221no—
913C23—1221no—
914C23—4881no—
915C23—4881no—
916C23—4881no—
917C23—4881no—
918C23—2441no—
919C23—2441no—
920C23—2441no—
921C23—2441no—
922C23—2442no—
923C23—2442no—
924C23C2×C22⋊#692311yescharacteristic
925C23C2×C22⋊#692311yescharacteristic
926Q8—2442no—
927Q8—2442no—
928D4—22no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—42no—
933D4—42no—
934D4—42no—
935D4—81no—
936D4—81no—
937D4—81no—
938D4—1222no—
939D4—1222no—
940D4—1222no—
941D4—4881no—
942D4—4881no—
943D4—4881no—
944D4—2441no—
945D4—2441no—
946D4—2441no—
947D4—2442no—
948D4—2442no—
949D4—2441no—
950D4—2441no—
951D4—2442no—
952D4—2441no—
953D4—2441no—
954D4—2441no—
955D4—2441no—
956D4—2442no—
957D4—2442no—
958D4—2442no—
959D4—2442no—
960C2×C4—21no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—42no—
964C2×C4—611no—
965C2×C4—611no—
966C2×C4—611no—
967C2×C4—611no—
968C2×C4—611no—
969C2×C4—1221no—
970C2×C4—1221no—
971C2×C4—1222no—
972C2×C4—1221no—
973C2×C4—1221no—
974C2×C4—1221no—
975C2×C4—4884no—
976C2×C4—2441no—
977C2×C4—2441no—
978C2×C4—2441no—
979C2×C4—2441no—
980C2×C4—2441no—
981C2×C4—2441no—
982C2×C4—2441no—
983C2×C4—2441no—
984C2×C4—2442no—
985C2×C4—2442no—
986C2×C4—2442no—
987C2×C4—2441no—
988C2×C4—2441no—
989C2×C4—2442no—
990C2×C4—2442no—
991C2×C4—2441no—
992C2×C4—2441no—
993C2×C4—2441no—
994C2×C4—2441no—
995C2×C4—2441no—
996C2×C4—2441no—
997C2×C4—2441no—
998C2×C4—2441no—
999C2×C4—2441no—
1000C2×C4—2442no—
1001C2×C4—2441no—
1002C2×C4—2441no—
1003C2×C4—2442no—
1004C2×C4C2×C22⋊#692311yescharacteristic
1005C2×C4C2×C22⋊#692311yescharacteristic
1006C2×C4C2×C22⋊#692311yescharacteristic
1007C2×C4C2×C22⋊#692311yescharacteristic
1008C2×C4C23×#692311yescharacteristic
1009C8—2441no—
1010C8—2441no—
1011C8—2441no—
1012C8—2441no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—21no—
1017C22—21no—
1018C22—41no—
1019C22—41no—
1020C22—41no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—41no—
1026C22—41no—
1027C22—162no—
1028C22—162no—
1029C22—611no—
1030C22—611no—
1031C22—612no—
1032C22—1221no—
1033C22—1221no—
1034C22—1221no—
1035C22—1221no—
1036C22—1221no—
1037C22—1221no—
1038C22—1221no—
1039C22—9762no—
1040C22—9762no—
1041C22—4881no—
1042C22—4881no—
1043C22—2442no—
1044C22—2442no—
1045C22—2441no—
1046C22—2441no—
1047C22—2441no—
1048C22#1684075412yes—
1049C22C22×C22⋊#692311yescharacteristic
1050C4—21no—
1051C4—21no—
1052C4—21no—
1053C4—21no—
1054C4—21no—
1055C4—41no—
1056C4—1221no—
1057C4—1221no—
1058C4—1221no—
1059C4—1221no—
1060C4—1221no—
1061C4—4881no—
1062C4—4881no—
1063C4—4881no—
1064C4—2442no—
1065C4—2441no—
1066C4—2441no—
1067C4—2441no—
1068C2—22no—
1069C2—41no—
1070C2—81no—
1071C2—81no—
1072C2—81no—
1073C2—1221no—
1074C2—1221no—
1075C2—1222no—
1076C2—4881no—
1077C2—2441no—
1078C2#2146241811yescharacteristic
1079C2C2×#1684075411yescharacteristic
1080C2#2146244911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingD42×C61C4
socleC22×C61C22×C22⋊C4
prime radical#21459575C2
cosocleC2×C4×D61C24
hypercenterD42#6923
hypocenterC61#17620
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #21462671C2semidirect
2. #21462336C2semidirect
3. #21461255C2semidirect
4. #21461254C2semidirect
5. #21461239C2semidirect
6. #21461238C2semidirect
7. #21461225C2semidirect
8. #21461224C2semidirect
9. #21461215C2semidirect
10. #21461214C2semidirect
11. #21461209C2semidirect
12. #21461208C2semidirect
13. D61⋊#327C2semidirect
14. C2×#16840613C2semidirect
20. #16840785C22semidirect
21. #16840784C22semidirect
22. #16840734C22semidirect
23. #16840733C22semidirect
24. C2×#14519834C22semidirect
25. D61⋊(C22⋊C8)C22semidirect
29. #16840707C22semidirect
30. #16840705C22semidirect
31. #16840704C22semidirect
33. C4×C22⋊#6923C22semidirect
34. #16840698C22semidirect
35. C2×(C2×#6923)⋊C4C22semidirect
36. #16840614C22semidirect
37. #16840614C22semidirect
38. #16840614C22semidirect
39. #16840614C22semidirect
40. #16840613C22semidirect
41. #16840613C22semidirect
42. #16840613C22semidirect
43. #16840613C22semidirect
44. #16840613C22semidirect
45. #16840613C22semidirect
46. #16840613C22semidirect
47. #16840613C22semidirect
48. #16840613C22semidirect
49. #16840613C22semidirect
50. #16840613C22semidirect
51. #16840613C22semidirect
53. #16840417C4semidirect
54. #16840416C4semidirect
55. #16840412C4semidirect
56. #16840412C4semidirect
61. #16840397C4semidirect
62. D4×C22⋊D61C4semidirect
63. D4×C22⋊D61C4semidirect
74. D42×C61C4semidirect
123. C2×D4×D61C2×C4semidirect
127. #14519777C2×C4semidirect
128. #14519776C2×C4semidirect
129. #14519773C2×C4semidirect
146. #14519751C2×C4semidirect
162. #14519748C2×C4semidirect
163. #14519748C2×C4semidirect
174. C4×D244C2×C4semidirect
176. D4×Dic61C2×C4semidirect
177. D4×Dic61C2×C4semidirect
186. C2×C4⋊Dic61C2×C4semidirect
188. C4⋊C4×D61C2×C4semidirect
199. C22×D4×C61C2×C4semidirect
200. #127×C61C2×C4semidirect
203. #121×C61C2×C4semidirect
207. C4×D4×C61C2×C4semidirect
568. D42#6923semidirect
615. C61#17620semidirect
636. C22×D4C2×#6923semidirect
647. #127C2×#6923semidirect
687. #121C2×#6923semidirect
709. C4×D4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214626712
#214623362
#214612552
#214612542
#214612392
#214612382
#214612252
#214612242
#214612152
#214612142
#214612092
#214612082
D61⋊#3272
C2×#168406132
#214595752
#1762061