Finite Group Databasebeta

← #30620137

Subgroups — #30620137

Order 15616.

1474 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840743C211yesmaximal, characteristic, complemented
2C2×#16840741C211yesmaximal, characteristic, complemented
3#21462327C212yesmaximal, complemented
4#21461960C212yesmaximal, complemented
5#21461843C212yesmaximal, complemented
6#21461842C212yesmaximal, complemented
7#21461682C211yesmaximal, characteristic, complemented
8#21461650C211yesmaximal, characteristic, complemented
9#21461648C211yesmaximal, characteristic, complemented
10#21461564C211yesmaximal, characteristic, complemented
11C2×#16840414C211yesmaximal, characteristic
12C2×#14519856C2212yes—
13C2×#14519856C2212yes—
14#16840743—24no—
15#16840741—24no—
16C2×#14519836C2211yescharacteristic
17C2×#14519836C2212yes—
18C2×#14519836C2211yescharacteristic
19C2×#14519836C2211yescharacteristic
20C2×#14519836C2212yes—
21C2×#14519836C2211yescharacteristic
22C2×#14519835C2212yes—
23C2×#14519835C2212yes—
24#16840713—22no—
25#16840711—22no—
26#16840711—22no—
27#16840705C2212yes—
28#16840705C2212yes—
29#16840704C2212yes—
30C4⋊C4×#6923—22no—
31C4×C22⋊#6923C2212yes—
32#16840640C2212yes—
33#16840640C2212yes—
34C22×#11758226C2211yescharacteristic
35C22×#11758222C2211yescharacteristic
36#16840414—22no—
37#16840414—22no—
38#16840414—22no—
39#16840414—22no—
40C2×#14519775C411yescharacteristic, complemented
41C2×#14519762C411yescharacteristic, complemented
42C2×#14519762C2211yescharacteristic
43C2×#14519759C411yescharacteristic, complemented
44C2×#14519759C2211yescharacteristic
45C2×#14519757C411yescharacteristic, complemented
46C2×#14519750C411yescharacteristic, complemented
47C2×#14519750C2211yescharacteristic
48C2×#14519739C2211yescharacteristic
49C2×C4×C22⋊D61C411yescharacteristic, complemented
50C2×C4⋊C4×D61C411yescharacteristic, complemented
51C2×C4⋊C4×D61C2211yescharacteristic
52C2×C22⋊Q8×C61C411yescharacteristic, complemented
53#14519856—24no—
54#14519856—24no—
55#14519856—42no—
56#14519856—42no—
57C2×C4⋊#6923—22no—
58C2×C4⋊#6923—22no—
59C2×C4⋊#6923—22no—
60C2×C22⋊#6923C2312yes—
61C2×C22⋊#6923C2312yes—
62C2×C22⋊#6923C2312yes—
63C2×C22⋊#6923C2312yes—
64C2×C4×#6923—22no—
65C2×C4×#6923—22no—
66C2×C4×#6923—22no—
67#14519836—22no—
68#14519836—22no—
69#14519836—22no—
70#14519836—24no—
71#14519836—42no—
72#14519836D414yescomplemented
73#14519835—24no—
74#14519835—42no—
75(C2×#6923)⋊C4—22no—
76(C2×#6923)⋊C4—22no—
77(C2×#6923)⋊C4—22no—
78(C2×#6923)⋊C4—22no—
79(C2×#6923)⋊C4—22no—
80(C2×#6923)⋊C4—22no—
81C2×#11758226—22no—
82C2×#11758226—22no—
83C2×#11758226—22no—
84C2×#11758226—22no—
85C2×#11758226—42no—
86C2×#11758222—22no—
87C2×#11758222—22no—
88C2×#11758222—22no—
89C2×#11758222—22no—
90C2×#11758222—42no—
91C22×Dic122C2×C411yescharacteristic
92C22×D244C2×C411yescharacteristic
93C22×D244C2311yescharacteristic
94C22×D244C2311yescharacteristic
95C22×C22⋊D61C2×C411yescharacteristic
96C22×C22⋊D61C2×C411yescharacteristic
97C22×C22⋊D61C2311yescharacteristic
98C22×C4×D61C2×C411yescharacteristic
99C22×C4×D61C2×C411yescharacteristic
100C22×C4×D61C2×C411yescharacteristic
101C22×C4×D61C2×C411yescharacteristic
102C22×C4×D61C2311yescharacteristic
103C22×C4×D61C2311yescharacteristic
104C22×C4×D61C2311yescharacteristic
105#14519775—22no—
106#14519775—22no—
107#14519762—22no—
108#14519762—22no—
109#14519762—22no—
110#14519762—22no—
111#14519759—22no—
112#14519759—22no—
113#14519759—22no—
114#14519759—22no—
115#14519757—22no—
116#14519757—22no—
117#14519750—22no—
118#14519750—22no—
119#14519750—22no—
120#14519750—22no—
121#14519739—22no—
122#14519739—22no—
123C4×C22⋊D61—21no—
124C4×C22⋊D61—21no—
125C4×C22⋊D61—21no—
126C4×C22⋊D61—21no—
127C2×C4⋊Dic61C2×C411yescharacteristic
128C2×C4⋊Dic61C2×C411yescharacteristic
129C2×#11758196C2×C411yescharacteristic
130C2×#11758196C2×C411yescharacteristic
131C2×#11758196C2×C411yescharacteristic
132C2×#11758196C2×C411yescharacteristic
133C2×#11758196C2×C411yescharacteristic
134C4⋊C4×D61—21no—
135C4⋊C4×D61—21no—
136C4⋊C4×D61—21no—
137C4⋊C4×D61—21no—
138C4⋊C4×D61D412yes—
139C4⋊C4×D61D412yes—
140C4⋊C4×D61D412yes—
141C4⋊C4×D61D412yes—
142C2×C22⋊Dic61C2×C411yescharacteristic
143C2×#11758198C2×C411yescharacteristic
144C2×#11758198C2×C411yescharacteristic
145C2×#11758198C2×C411yescharacteristic
146C2×#11758198C2×C411yescharacteristic
147C2×#11758198C2311yescharacteristic
148C2×C4×Dic61C2×C411yescharacteristic
149C22×Q8×C61C2×C411yescharacteristic
150C23×C4×C61C2×C411yescharacteristic
151C22⋊Q8×C61—22no—
152C22⋊Q8×C61—22no—
153C2×C4⋊C4×C61C2×C411yescharacteristic
154C2×C4⋊C4×C61C2×C411yescharacteristic
155C2×C4⋊C4×C61C2×C411yescharacteristic
156C2×C22⋊C4×C61C2×C411yescharacteristic
157C2×C22⋊C4×C61C2×C411yescharacteristic
158C24×C61C22×C411yescharacteristic
159C23×D61C22×C411yescharacteristic
160C23×D61C22×C411yescharacteristic
161C23×D61C2411yescharacteristic
162C22×#6923—22no—
163C22×#6923—22no—
164C22×#6923—22no—
165C22×#6923—22no—
166C2×Q8×C61—22no—
167C2×Q8×C61—22no—
168C2×Q8×C61—41no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—22no—
172C22×C4×C61—41no—
173C22×C4×C61C22×C411yescharacteristic
174C22×C4×C61C22×C411yescharacteristic
175C22×C4×C61C22×C411yescharacteristic
176C22×C4×C61C22×C411yescharacteristic
177C22×C4×C61C22×C411yescharacteristic
178C22×C4×C61C22×C411yescharacteristic
179C2×C22⋊D61—22no—
180C2×C22⋊D61—21no—
181C2×C22⋊D61—22no—
182C2×C22⋊D61—21no—
183C2×C22⋊D61—22no—
184C2×C22⋊D61—22no—
185C2×C22⋊D61—21no—
186C2×C22⋊D61—21no—
187C2×C22⋊D61—41no—
188C2×C22⋊D61—42no—
189C22×Dic61C22×C411yescharacteristic
190C22×Dic61C22×C411yescharacteristic
191C22×Dic61C22×C411yescharacteristic
192C22×Dic61C22×C411yescharacteristic
193C22×Dic61C22×C411yescharacteristic
194#11758226—44no—
195#11758226—44no—
196#11758226—44no—
197#11758226—44no—
198#11758222—44no—
199#11758222—44no—
200#11758222—44no—
201#11758222—44no—
202C2×D244—22no—
203C2×D244—22no—
204C2×D244—22no—
205C2×D244—21no—
206C2×D244—22no—
207C2×D244—21no—
208C2×D244—22no—
209C2×D244—22no—
210C2×D244—41no—
211C2×D244C2×D412yes—
212C2×D244#4112yes—
213C2×C4×D61—21no—
214C2×C4×D61—21no—
215C2×C4×D61—21no—
216C2×C4×D61—21no—
217C2×C4×D61—22no—
218C2×C4×D61—22no—
219C2×C4×D61—22no—
220C2×C4×D61—22no—
221C2×C4×D61—21no—
222C2×C4×D61—21no—
223C2×C4×D61—22no—
224C2×C4×D61—21no—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—21no—
230C2×C4×D61—42no—
231C2×C4×D61—41no—
232C2×C4×D61—41no—
233C2×C4×D61—41no—
234C2×C4×D61—42no—
235C2×C4×D61C2×D412yes—
236C2×C4×D61C2×D412yes—
237C2×C4×D61C2×D412yes—
238C2×C4×D61C2×D412yes—
239C2×C4×D61C2×D412yes—
240C2×C4×D61C2×D412yes—
241C2×Dic122—22no—
242C2×Dic122—22no—
243C2×Dic122—41no—
244C22⋊#6923—22no—
245C22⋊#6923—22no—
246C22⋊#6923—22no—
247C22⋊#6923—22no—
248C22⋊#6923—22no—
249C22⋊#6923—22no—
250C22⋊#6923—22no—
251C22⋊#6923C2×D414yes—
252C4⋊#6923—44no—
253C4⋊#6923—44no—
254C4⋊#6923—44no—
255C4×#6923—44no—
256C4×#6923—44no—
257C4×#6923—44no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61—21no—
260C4⋊C4×C61—22no—
261C4⋊C4×C61C22⋊C412yes—
262C4⋊C4×C61C22⋊C412yes—
263C22⋊C4×C61—22no—
264C22⋊C4×C61—22no—
265C22⋊Dic61—21no—
266C22⋊Dic61—21no—
267#11758198—22no—
268#11758198—21no—
269#11758198—21no—
270#11758198—22no—
271#11758198—22no—
272#11758198—22no—
273C4⋊Dic61—21no—
274C4⋊Dic61—21no—
275C4⋊Dic61C22⋊C412yes—
276C4⋊Dic61C22⋊C412yes—
277#11758196—22no—
278#11758196—21no—
279#11758196—21no—
280#11758196—22no—
281#11758196C22⋊C411yescharacteristic
282#11758196C22⋊C411yescharacteristic
283#11758196C22⋊C411yescharacteristic
284#11758196C22⋊C411yescharacteristic
285#11758196C22⋊C412yes—
286#11758196C22⋊C412yes—
287C4×Dic61—21no—
288C4×Dic61—21no—
289C23×C61—21no—
290C23×C61—21no—
291C23×C61—21no—
292C23×C61—41no—
293C23×C61—41no—
294C23×C61C23×C411yescharacteristic
295C22×D61—21no—
296C22×D61—21no—
297C22×D61—21no—
298C22×D61—21no—
299C22×D61—21no—
300C22×D61—41no—
301C22×D61—41no—
302C22×D61—41no—
303C22×D61—41no—
304C22×D61—41no—
305C22×D61—41no—
306C22×D61C4×D412yes—
307C22×D61C22×D412yes—
308C22×D61C22×D411yescharacteristic
309C22×D61C2×#4111yescharacteristic
310C22×D61H(5,𝔽2)12yes—
311C2×#6923—24no—
312C2×#6923—42no—
313C2×#6923—42no—
314C2×#6923—42no—
315C2×#6923—42no—
316C2×#6923—42no—
317C2×#6923—42no—
318C2×#6923—42no—
319C2×#6923—42no—
320C2×#6923—42no—
321C2×#6923—42no—
322C2×#6923—42no—
323Q8×C61—44no—
324C2×C4×C61—21no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61—21no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—41no—
335C2×C4×C61—42no—
336C2×C4×C61—42no—
337C2×C4×C61—41no—
338C2×C4×C61C2×C22⋊C412yes—
339C2×C4×C61C2×C22⋊C411yescharacteristic
340C2×C4×C61C2×C22⋊C411yescharacteristic
341C2×C4×C61C2×C22⋊C412yes—
342C2×C4×C61C4×D412yes—
343C22⋊D61—44no—
344C22⋊D61—42no—
345C22⋊D61—42no—
346C22⋊D61—42no—
347C22⋊D61—42no—
348C2×Dic61—21no—
349C2×Dic61—21no—
350C2×Dic61—21no—
351C2×Dic61—21no—
352C2×Dic61—22no—
353C2×Dic61—21no—
354C2×Dic61—21no—
355C2×Dic61—21no—
356C2×Dic61—21no—
357C2×Dic61—41no—
358C2×Dic61C2×C22⋊C411yescharacteristic
359C2×Dic61C2×C22⋊C412yes—
360C2×Dic61C2×C22⋊C411yescharacteristic
361C2×Dic61C2×C22⋊C411yescharacteristic
362C2×Dic61C2×C22⋊C411yescharacteristic
363D244—24no—
364D244—24no—
365D244—44no—
366D244—42no—
367D244—42no—
368C4×D61—22no—
369C4×D61—22no—
370C4×D61—22no—
371C4×D61—22no—
372C4×D61—22no—
373C4×D61—22no—
374C4×D61—22no—
375C4×D61—22no—
376C4×D61—24no—
377C4×D61—42no—
378C4×D61—42no—
379C4×D61—42no—
380C4×D61—42no—
381C4×D61—42no—
382C4×D61—42no—
383C4×D61—42no—
384C4×D61—42no—
385C4×D61—42no—
386Dic122—44no—
387#22406—611nomaximal, Sylow
388C22×C61—21no—
389C22×C61—21no—
390C22×C61—41no—
391C22×C61—41no—
392C22×C61—41no—
393C22×C61—81no—
394C22×C61—81no—
395C22×C61C22×C22⋊C411yescharacteristic
396C22×C61C2×C4×D411yescharacteristic
397C22×C61#51811yescharacteristic
398C2×D61—22no—
399C2×D61—22no—
400C2×D61—22no—
401C2×D61—41no—
402C2×D61—41no—
403C2×D61—42no—
404C2×D61—42no—
405C2×D61—41no—
406C2×D61—41no—
407C2×D61—42no—
408C2×D61—41no—
409C2×D61—41no—
410C2×D61—41no—
411C2×D61—81no—
412C2×D61—81no—
413C2×D61D4212yes—
414C2×D61#54612yes—
415#6923—44no—
416#6923—82no—
417#6923—82no—
418#6923—82no—
419C4×C61—22no—
420C4×C61—21no—
421C4×C61—21no—
422C4×C61—22no—
423C4×C61—22no—
424C4×C61—41no—
425C4×C61—41no—
426Dic61—22no—
427Dic61—21no—
428Dic61—21no—
429Dic61—21no—
430Dic61—41no—
431Dic61—41no—
432Dic61#41012yescomplemented
433C2×#547—611no—
434C2×#410—611no—
435C2×#410—611no—
436#2344—612no—
437#1964—612no—
438#1899—612no—
439#1899—612no—
440#1799—611no—
441#1782—611no—
442#1782—611no—
443C4×#99—611no—
444C2×C61—21no—
445C2×C61—21no—
446C2×C61—81no—
447C2×C61D4×C22⋊C411yescharacteristic
448C2×C61C2×#41011yescharacteristic
449C2×C61#288411yescharacteristic
450D61—22no—
451D61—22no—
452D61—42no—
453D61—81no—
454C22×#41—611no—
455C22×#41—611no—
456#547—1222no—
457#547—1222no—
458#547—1222no—
459#547—1222no—
460C2×C4⋊Q8—611no—
461C2×#123—611no—
462C2×#123—611no—
463C2×#123—611no—
464C2×#123—611no—
465C2×C22⋊Q8—611no—
466C2×C22⋊Q8#692311yescharacteristic, complemented
467C2×#121—611no—
468C2×#121—611no—
469C2×C4×D4—611no—
470C2×C4×D4—611no—
471C2×#117—612no—
472C2×#117—612no—
473C22×C4⋊C4—611no—
474C22×C4⋊C4—611no—
475#410—1224no—
476#410—1224no—
477C2×#99—611no—
478C2×#99—611no—
479C2×#99—611no—
480C2×#99—612no—
481C2×#99—612no—
482C2×#99—611no—
483C2×#99—612no—
484C2×#99—612no—
485#389—1222no—
486#387—1222no—
487#387—1222no—
488#381—612no—
489#381—612no—
490#380—612no—
491C4×C4⋊C4—1222no—
492C4×C22⋊C4—612no—
493#342—612no—
494#342—612no—
495C61#2240611yescharacteristic, complemented, Sylow
496C2×#41—1222no—
497C2×#41—1222no—
498C2×#41—1222no—
499C2×#41—1222no—
500C2×#41—1222no—
501C2×#41—1222no—
502C2×#41—1222no—
503C2×#41—1222no—
504C2×#41—2442no—
505C2×#41—2442no—
506C22×Q8—611no—
507C22×Q8C2×#692311yescharacteristic
508C22×D4—611no—
509C22×D4—611no—
510C22×D4—611no—
511C22×D4—611no—
512C22×D4—611no—
513C22×D4—611no—
514C23×C4—611no—
515C23×C4—611no—
516C23×C4—611no—
517C23×C4—611no—
518C23×C4—611no—
519C23×C4—611no—
520C23×C4—611no—
521C23×C4C2×#692311yescharacteristic
522C4⋊Q8—1222no—
523C4⋊Q8—1222no—
524#123—1222no—
525#123—1222no—
526#123—1222no—
527#123—1222no—
528#123—1222no—
529#123—1222no—
530#123—1222no—
531#123—1222no—
532C22⋊Q8—22no—
533C22⋊Q8—22no—
534C22⋊Q8—1222no—
535C22⋊Q8—1222no—
536#121—1222no—
537#121—1222no—
538#121—1222no—
539#121—1222no—
540C4×D4—1222no—
541C4×D4—1222no—
542C4×D4—1221no—
543C4×D4—1221no—
544C4×D4—1221no—
545C4×D4—1221no—
546#117—1224no—
547#117—1224no—
548#117—2442no—
549#117—2442no—
550C2×C4⋊C4—611no—
551C2×C4⋊C4—611no—
552C2×C4⋊C4—611no—
553C2×C4⋊C4—612no—
554C2×C4⋊C4—612no—
555C2×C4⋊C4—612no—
556C2×C4⋊C4—612no—
557C2×C4⋊C4—611no—
558C2×C4⋊C4—611no—
559C2×C4⋊C4—611no—
560C2×C4⋊C4—611no—
561C2×C4⋊C4—1221no—
562C2×C4⋊C4—1221no—
563C2×C4⋊C4—1221no—
564C2×C4⋊C4—1221no—
565C2×C4⋊C4—1222no—
566C2×C4⋊C4—1222no—
567C2×C4⋊C4—1222no—
568C2×C4⋊C4C2×#692311yescharacteristic
569C2×C4⋊C4C2×#692311yescharacteristic
570C2×C4⋊C4C2×#692311yescharacteristic
571C2×C22⋊C4—612no—
572C2×C22⋊C4—611no—
573C2×C22⋊C4—611no—
574C2×C22⋊C4—611no—
575C2×C22⋊C4—611no—
576C2×C22⋊C4—611no—
577C2×C22⋊C4—611no—
578C2×C22⋊C4—612no—
579C2×C22⋊C4—612no—
580C2×C22⋊C4—612no—
581C2×C22⋊C4C2×#692311yescharacteristic
582C2×C22⋊C4C2×#692311yescharacteristic
583C2×C42—611no—
584C2×C42—1222no—
585C2×C42—1222no—
586C2×C42—1222no—
587#99—614no—
588#99—1224no—
589#99—1224no—
590#99—1222no—
591#99—1222no—
592#99—1222no—
593#99—2442no—
594#99—2442no—
595#95—1222no—
596#95—1222no—
597#95—1222no—
598#95—1222no—
599#95—1222no—
600#95—1222no—
601C24—611no—
602C24—611no—
603C24—611no—
604C24C22×#692311yescharacteristic
605#41—2444no—
606#41—2444no—
607#41—2444no—
608#41—2444no—
609#41—2444no—
610#41—2444no—
611#41—2444no—
612#41—2444no—
613C2×Q8—22no—
614C2×Q8—22no—
615C2×Q8—41no—
616C2×Q8—1222no—
617C2×Q8—1222no—
618C2×Q8—2441no—
619C2×D4—612no—
620C2×D4—612no—
621C2×D4—1222no—
622C2×D4—1222no—
623C2×D4—1221no—
624C2×D4—1222no—
625C2×D4—1222no—
626C2×D4—1222no—
627C2×D4—1221no—
628C2×D4—1221no—
629C2×D4—1221no—
630C2×D4—1222no—
631C2×D4—1221no—
632C2×D4—1222no—
633C2×D4—1222no—
634C2×D4—1222no—
635C2×D4—1221no—
636C2×D4—1222no—
637C2×D4—2441no—
638C2×D4—2441no—
639C2×D4—2442no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—41no—
644C22×C4—611no—
645C22×C4—611no—
646C22×C4—611no—
647C22×C4—612no—
648C22×C4—612no—
649C22×C4—612no—
650C22×C4—612no—
651C22×C4—612no—
652C22×C4—612no—
653C22×C4—611no—
654C22×C4—611no—
655C22×C4—1221no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—1221no—
659C22×C4—1221no—
660C22×C4—1221no—
661C22×C4—1221no—
662C22×C4—1221no—
663C22×C4—1222no—
664C22×C4—1222no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—1222no—
668C22×C4—1222no—
669C22×C4—1222no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1222no—
673C22×C4—1222no—
674C22×C4—1222no—
675C22×C4—1222no—
676C22×C4—2441no—
677C22×C4—2441no—
678C22×C4—2441no—
679C22×C4—2442no—
680C22×C4—2442no—
681C22×C4C22×#692311yescharacteristic
682C22×C4C22×#692311yescharacteristic
683C22×C4C22×#692311yescharacteristic
684C22×C4C22×#692311yescharacteristic
685C22×C4C22×#692311yescharacteristic
686C22×C4C22×#692311yescharacteristic
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—22no—
690C4⋊C4—611no—
691C4⋊C4—611no—
692C4⋊C4—611no—
693C4⋊C4—611no—
694C4⋊C4—612no—
695C4⋊C4—612no—
696C4⋊C4—612no—
697C4⋊C4—612no—
698C4⋊C4—1221no—
699C4⋊C4—1221no—
700C4⋊C4—1221no—
701C4⋊C4—1221no—
702C4⋊C4—1222no—
703C4⋊C4—1222no—
704C4⋊C4—2444no—
705C4⋊C4—2444no—
706C4⋊C4—2444no—
707C4⋊C4C22⋊#692312yes—
708C4⋊C4C22⋊#692312yes—
709C22⋊C4—22no—
710C22⋊C4—22no—
711C22⋊C4—614no—
712C22⋊C4—1222no—
713C22⋊C4—1222no—
714C22⋊C4—1221no—
715C22⋊C4—1221no—
716C22⋊C4—1222no—
717C22⋊C4—1222no—
718C22⋊C4—1221no—
719C22⋊C4—1221no—
720C22⋊C4—1222no—
721C22⋊C4—1222no—
722C22⋊C4—1222no—
723C22⋊C4—1222no—
724C22⋊C4—1222no—
725C22⋊C4—1222no—
726C22⋊C4—1222no—
727C42—1221no—
728C42—1221no—
729C42—2444no—
730C42—2444no—
731C42—2444no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—41no—
736C23—41no—
737C23—612no—
738C23—611no—
739C23—611no—
740C23—612no—
741C23—612no—
742C23—1221no—
743C23—1221no—
744C23—1221no—
745C23—1221no—
746C23—1221no—
747C23—2441no—
748C23—2441no—
749C23—2441no—
750C23—2441no—
751C23—2441no—
752C23—2441no—
753C23C23×#692311yescharacteristic
754Q8—44no—
755Q8—2444no—
756D4—1224no—
757D4—1224no—
758D4—2444no—
759D4—2442no—
760D4—2442no—
761D4—2442no—
762D4—2444no—
763D4—2442no—
764D4—2442no—
765D4—2442no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—41no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—41no—
780C2×C4—611no—
781C2×C4—611no—
782C2×C4—611no—
783C2×C4—611no—
784C2×C4—612no—
785C2×C4—1224no—
786C2×C4—1222no—
787C2×C4—1222no—
788C2×C4—1222no—
789C2×C4—1222no—
790C2×C4—1222no—
791C2×C4—1222no—
792C2×C4—1222no—
793C2×C4—1222no—
794C2×C4—1222no—
795C2×C4—1221no—
796C2×C4—1221no—
797C2×C4—1221no—
798C2×C4—1221no—
799C2×C4—1224no—
800C2×C4—1221no—
801C2×C4—1221no—
802C2×C4—1221no—
803C2×C4—1221no—
804C2×C4—2442no—
805C2×C4—2442no—
806C2×C4—2442no—
807C2×C4—2442no—
808C2×C4—2442no—
809C2×C4—2442no—
810C2×C4—2442no—
811C2×C4—2442no—
812C2×C4—2442no—
813C2×C4—2442no—
814C2×C4—2442no—
815C2×C4—2442no—
816C2×C4—2442no—
817C2×C4—2442no—
818C2×C4—2442no—
819C2×C4—2442no—
820C2×C4—2442no—
821C2×C4—2442no—
822C2×C4—2442no—
823C2×C4—2442no—
824C2×C4—2441no—
825C2×C4C2×C22⋊#692312yes—
826C2×C4C2×C22⋊#692312yes—
827C2×C4C2×C22⋊#692311yescharacteristic
828C2×C4C2×C22⋊#692311yescharacteristic
829C2×C4D4×#692312yes—
830C22—21no—
831C22—21no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—81no—
836C22—81no—
837C22—612no—
838C22—612no—
839C22—1222no—
840C22—1222no—
841C22—1222no—
842C22—4881no—
843C22—4881no—
844C22—2441no—
845C22—2441no—
846C22—2442no—
847C22—2442no—
848C22—2442no—
849C22—2441no—
850C22—2441no—
851C22—2441no—
852C22—2441no—
853C22—2441no—
854C22C22×C22⋊#692311yescharacteristic
855C22C2×D4×#692311yescharacteristic
856C22#1684082911yescharacteristic
857C4—21no—
858C4—21no—
859C4—22no—
860C4—22no—
861C4—22no—
862C4—41no—
863C4—41no—
864C4—612no—
865C4—1221no—
866C4—1221no—
867C4—1222no—
868C4—1221no—
869C4—4882no—
870C4—4882no—
871C4—4882no—
872C4—2444no—
873C4—2441no—
874C4—2441no—
875C2—21no—
876C2—21no—
877C2—81no—
878C2—1222no—
879C2—1222no—
880C2—4881no—
881C2—2442no—
882C2D4×C22⋊#692311yescharacteristic
883C2D61⋊#41011yescharacteristic
884C2#2146242011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×C22⋊Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840414C2
cosocleC23×D61C24
hypercenterC2×C22⋊Q8#6923
hypocenterC61#22406
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4⋊C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#16840743C2semidirect
2. C2×#16840741C2semidirect
3. #21462327C2semidirect
4. #21461960C2semidirect
5. #21461843C2semidirect
6. #21461842C2semidirect
7. #21461682C2semidirect
8. #21461650C2semidirect
9. #21461648C2semidirect
10. #21461564C2semidirect
40. C2×#14519775C4semidirect
41. C2×#14519762C4semidirect
43. C2×#14519759C4semidirect
45. C2×#14519757C4semidirect
46. C2×#14519750C4semidirect
49. C2×C4×C22⋊D61C4semidirect
50. C2×C4⋊C4×D61C4semidirect
52. C2×C22⋊Q8×C61C4semidirect
72. #14519836D4semidirect
432. Dic61#410semidirect
466. C2×C22⋊Q8#6923semidirect
495. C61#22406semidirect

Maximal subgroups

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

subgroupindex
C2×#168407432
C2×#168407412
#214623272
#214619602
#214618432
#214618422
#214616822
#214616502
#214616482
#214615642
C2×#168404142
#2240661