Finite Group Databasebeta

← #29696187

Subgroups — #29696187

Order 15616.

1106 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840470C211yesmaximal, characteristic
2M16×C22⋊D61C211yesmaximal, characteristic
3#21454551C211yesmaximal, characteristic
4#21446806C211yesmaximal, characteristic, complemented
5#21446806C211yesmaximal, characteristic, complemented
6#21446288C211yesmaximal, characteristic, complemented
7#21446284C211yesmaximal, characteristic, complemented
8#21446284C211yesmaximal, characteristic, complemented
9#21445898C211yesmaximal, characteristic, complemented
10#21445897C211yesmaximal, characteristic, complemented
11#21445813C211yesmaximal, characteristic, complemented
12#101×Dic61C211yesmaximal, characteristic, complemented
13C2×#16839530C211yesmaximal, characteristic, complemented
14#343×D61C211yesmaximal, characteristic, complemented
15C61×#1901C211yesmaximal, characteristic, complemented
16C22×#11758194C2211yescharacteristic
17C2×M16×D61C2211yescharacteristic
18C2×M16×D61C2211yescharacteristic
19#16840470—21no—
20#16840470—21no—
21#16840470—21no—
22#16840470—21no—
23#16840470—21no—
24#16840470—21no—
25#16840470—21no—
26#16840470—21no—
27C2×#14519776C2211yescharacteristic
28C2×#14519767C412yes—
29C2×#14519757C412yes—
30C2×#14519754C412yes—
31C2×#14519753C2211yescharacteristic
32C2×Q8×Dic61C2211yescharacteristic
33C2×C4×C22⋊D61C2211yescharacteristic
34C2×#14519737C412yes—
35C22×C4⋊Dic61C2211yescharacteristic
36C2×C4⋊C4×D61C2211yescharacteristic
37#16839838—21no—
38#16839837—21no—
39#16839836—21no—
40#16839833—21no—
41#16839831—21no—
42#16839830—21no—
43C8×C22⋊D61—21no—
44#16839825—21no—
45#16839785C2211yescharacteristic
46#16839785C2211yescharacteristic
47C2×#14519696C2211yescharacteristic
48C2×#14519696C2211yescharacteristic
49#16839726C2211yescharacteristic
50#16839725C2211yescharacteristic
51#16839725C2211yescharacteristic
52M16×Dic61C2211yescharacteristic
53M16×Dic61C2211yescharacteristic
54#16839531C2211yescharacteristic
55#16839531C2211yescharacteristic
56#16839530C2211yescharacteristic
57#16839530C2211yescharacteristic
58#16839530C2211yescharacteristic
59#16839530C2211yescharacteristic
60#16839530C2211yescharacteristic
61#16839530C2211yescharacteristic
62#16839530C2211yescharacteristic
63#16839530C2211yescharacteristic
64C22×M16×C61C2211yescharacteristic
65C2×C22⋊Q8×C61C2211yescharacteristic
66C2×#101×C61C2211yescharacteristic
67C2×#101×C61C2211yescharacteristic
68C61×#407C2211yescharacteristic
69C61×#343C2211yescharacteristic
70C61×#343C2211yescharacteristic
71C22×Dic122C2×C412yes—
72C22×C22⋊D61C2×C411yescharacteristic
73C23×Dic61C2×C412yes—
74C22×C4×D61C2×C412yes—
75C22×C4×D61C2311yescharacteristic
76C2×#11758194—21no—
77C2×#11758194—22no—
78C2×#11758194—41no—
79C2×#11758194C2311yescharacteristic
80C2×#11758194C2311yescharacteristic
81C2×#11758194C2311yescharacteristic
82C2×#11758194C2311yescharacteristic
83C2×#11758189—21no—
84C2×#11758189—21no—
85M16×D61—22no—
86M16×D61—22no—
87M16×D61—41no—
88M16×D61—41no—
89C22×#92418—21no—
90C2×C8×D61—21no—
91C2×C8×D61—21no—
92#14519776—21no—
93#14519776—21no—
94#14519776—21no—
95#14519776—21no—
96#14519767—22no—
97#14519767—22no—
98#14519767—22no—
99#14519767—22no—
100#14519757—22no—
101#14519757—22no—
102#14519757—22no—
103#14519757—22no—
104#14519754—22no—
105#14519754—22no—
106#14519754—22no—
107#14519754—22no—
108#14519753—21no—
109#14519753—21no—
110#14519753—21no—
111#14519753—21no—
112Q8×Dic61—21no—
113Q8×Dic61—21no—
114Q8×Dic61—21no—
115Q8×Dic61—21no—
116C4×C22⋊D61D411yescharacteristic
117C4×C22⋊D61D411yescharacteristic
118C4×C22⋊D61D411yescharacteristic
119C4×C22⋊D61D411yescharacteristic
120C4×C22⋊D61D411yescharacteristic
121C4×C22⋊D61D411yescharacteristic
122C4×C22⋊D61D411yescharacteristic
123C4×C22⋊D61D411yescharacteristic
124#14519737—22no—
125#14519737—22no—
126#14519737—22no—
127#14519737—22no—
128C2×C4⋊Dic61—21no—
129C2×C4⋊Dic61—21no—
130C2×C4⋊Dic61—21no—
131C2×C4⋊Dic61—21no—
132C2×C4⋊Dic61C2×C412yes—
133C2×C4⋊Dic61C2×C412yes—
134C2×C4⋊Dic61C2311yescharacteristic
135C2×C4⋊Dic61C2311yescharacteristic
136C2×#11758196C2×C412yes—
137C2×#11758196C2×C412yes—
138C2×#11758196C2×C412yes—
139C2×#11758196C2×C411yescharacteristic
140C4⋊C4×D61—21no—
141C4⋊C4×D61—21no—
142C4⋊C4×D61—21no—
143C4⋊C4×D61—21no—
144C2×C22⋊Dic61C2×C411yescharacteristic
145C2×#11758198C2×C412yes—
146C2×#11758198C2×C411yescharacteristic
147C2×C4×Dic61C2×C412yes—
148C2×C4×Dic61C2311yescharacteristic
149#14519706—21no—
150#14519706—21no—
151#14519706—21no—
152#14519706—21no—
153#14519696—22no—
154#14519696—41no—
155C22⋊#92418—21no—
156C22⋊#92418—21no—
157#14519689—21no—
158#14519689—21no—
159#14519689—21no—
160#14519689—21no—
161#14519687—21no—
162#14519687—21no—
163C8×Dic61—21no—
164C8×Dic61—21no—
165C22×Q8×C61C2311yescharacteristic
166C23×C4×C61C2311yescharacteristic
167C2×M16×C61—21no—
168C2×M16×C61—22no—
169C2×M16×C61—41no—
170C2×M16×C61C2311yescharacteristic
171C2×M16×C61C2311yescharacteristic
172C2×M16×C61C2311yescharacteristic
173C2×M16×C61C2311yescharacteristic
174C22×C8×C61—21no—
175C22⋊Q8×C61—21no—
176C22⋊Q8×C61—21no—
177C22⋊Q8×C61—21no—
178C22⋊Q8×C61—21no—
179C2×C4⋊C4×C61C2×C412yes—
180C2×C4⋊C4×C61C2311yescharacteristic
181C2×C22⋊C4×C61C2×C412yes—
182#101×C61—22no—
183#101×C61—41no—
184C22⋊C8×C61—21no—
185C22⋊C8×C61—21no—
186C24×C61C22×C411yescharacteristic
187C23×D61C22×C411yescharacteristic
188C2×Q8×C61—21no—
189C2×Q8×C61—21no—
190C2×Q8×C61—21no—
191C2×Q8×C61—21no—
192C2×Q8×C61—21no—
193C2×Q8×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61C22×C412yes—
199C22×C4×C61C22×C411yescharacteristic
200C22×C4×C61C22×C412yes—
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2×D411yescharacteristic
203C22×C4×C61C2×D411yescharacteristic
204C22×C4×C61C2×D411yescharacteristic
205C22×C4×C61C2411yescharacteristic
206C2×C22⋊D61—24no—
207C2×C22⋊D61C22⋊C411yescharacteristic
208C2×C22⋊D61C22⋊C411yescharacteristic
209C2×C22⋊D61C22⋊C411yescharacteristic
210C2×C22⋊D61C22⋊C411yescharacteristic
211C22×Dic61—22no—
212C22×Dic61—22no—
213C22×Dic61—82no—
214C22×Dic61C22×C411yescharacteristic
215C22×Dic61C22×C411yescharacteristic
216C22×Dic61C22×C412yes—
217C22×Dic61C22×C412yes—
218C22×Dic61C22×C411yescharacteristic
219C2×C4×D61—21no—
220C2×C4×D61—21no—
221C2×C4×D61—21no—
222C2×C4×D61—21no—
223C2×C4×D61—22no—
224C2×C4×D61—22no—
225C2×C4×D61—82no—
226C2×C4×D61C2×D411yescharacteristic
227C2×C4×D61C2×D411yescharacteristic
228C2×C4×D61C2×D411yescharacteristic
229C2×C4×D61C2×D411yescharacteristic
230C2×Dic122—22no—
231C2×Dic122—22no—
232C2×Dic122—82no—
233M16×C61—21no—
234M16×C61—21no—
235M16×C61—21no—
236M16×C61—21no—
237M16×C61—21no—
238M16×C61—21no—
239M16×C61—21no—
240M16×C61—42no—
241M16×C61#4112yes—
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61—42no—
247C4⋊C4×C61—22no—
248C4⋊C4×C61—22no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C22⋊C4×C61—22no—
252C22⋊C4×C61—22no—
253C22⋊Dic61C22⋊C411yescharacteristic
254C22⋊Dic61C22⋊C411yescharacteristic
255C22⋊Dic61C22⋊C411yescharacteristic
256C22⋊Dic61C22⋊C411yescharacteristic
257#11758198—22no—
258#11758198—22no—
259#11758198C22⋊C411yescharacteristic
260#11758198C22⋊C411yescharacteristic
261#11758198C22⋊C411yescharacteristic
262#11758198C22⋊C411yescharacteristic
263C4⋊Dic61—22no—
264C4⋊Dic61—22no—
265C4⋊Dic61—21no—
266C4⋊Dic61—21no—
267C4⋊Dic61—21no—
268C4⋊Dic61—21no—
269C4⋊Dic61—22no—
270C4⋊Dic61—22no—
271#11758196—22no—
272#11758196—22no—
273#11758196—22no—
274#11758196—22no—
275#11758196—22no—
276#11758196—22no—
277#11758196C22⋊C411yescharacteristic
278#11758196C22⋊C411yescharacteristic
279#11758196C22⋊C411yescharacteristic
280#11758196C22⋊C411yescharacteristic
281C4×Dic61—22no—
282C4×Dic61—22no—
283C4×Dic61C2×D411yescharacteristic
284C4×Dic61C2×D411yescharacteristic
285C4×Dic61C2×D411yescharacteristic
286C4×Dic61C2×D411yescharacteristic
287#11758194—21no—
288#11758194—21no—
289#11758194—21no—
290#11758194—21no—
291#11758194—21no—
292#11758194—21no—
293#11758194—21no—
294#11758194—42no—
295#11758194#4112yes—
296C2×#92418—21no—
297C2×#92418—21no—
298C2×#92418—21no—
299C2×#92418—21no—
300C2×#92418—42no—
301#11758189—42no—
302#11758189—42no—
303C8×D61—42no—
304C8×D61—42no—
305C23×C61—21no—
306C23×C61—21no—
307C23×C61—22no—
308C23×C61—41no—
309C23×C61C2×C22⋊C411yescharacteristic
310C23×C61C2×C22⋊C411yescharacteristic
311C23×C61C23×C411yescharacteristic
312C22×D61—21no—
313C22×D61—21no—
314C22×D61—22no—
315C22×D61—41no—
316C22×D61C2×C22⋊C411yescharacteristic
317C22×D61C2×C22⋊C411yescharacteristic
318Q8×C61—41no—
319Q8×C61—41no—
320Q8×C61—41no—
321Q8×C61—41no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
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—22no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—42no—
337C2×C4×C61C2×C22⋊C411yescharacteristic
338C2×C4×C61C2×C22⋊C411yescharacteristic
339C2×C4×C61C22×D411yescharacteristic
340C2×C4×C61C22×D411yescharacteristic
341C2×C4×C61C2×#4111yescharacteristic
342C2×C4×C61C2×#4111yescharacteristic
343C2×C4×C61H(5,𝔽2)11yescharacteristic
344C2×C4×C612−1+411yescharacteristic
345C22⋊D61—22no—
346C22⋊D61—22no—
347C22⋊D61—22no—
348C22⋊D61#10114yescomplemented
349C2×Dic61—21no—
350C2×Dic61—21no—
351C2×Dic61—22no—
352C2×Dic61—22no—
353C2×Dic61—22no—
354C2×Dic61—41no—
355C2×Dic61—42no—
356C2×Dic61—42no—
357C2×Dic61—82no—
358C2×Dic61—82no—
359C2×Dic61C2×C22⋊C411yescharacteristic
360C2×Dic61C2×C22⋊C411yescharacteristic
361C2×Dic61C2×C22⋊C411yescharacteristic
362C2×Dic61C2×C22⋊C411yescharacteristic
363C2×Dic61C2×C22⋊C411yescharacteristic
364C2×Dic61C2×C22⋊C411yescharacteristic
365C4×D61—21no—
366C4×D61—21no—
367C4×D61—21no—
368C4×D61—21no—
369C4×D61—21no—
370C4×D61—21no—
371C4×D61—21no—
372C4×D61—21no—
373C4×D61—82no—
374C4×D61—82no—
375Dic122—82no—
376Dic122—82no—
377C8×C61—22no—
378C8×C61—41no—
379C8×C61—41no—
380C8×C61—41no—
381#92418—22no—
382#92418—41no—
383#92418—41no—
384#92418—41no—
385#22481—611nomaximal, Sylow
386C22×C61—21no—
387C22×C61—21no—
388C22×C61—21no—
389C22×C61—21no—
390C22×C61—21no—
391C22×C61—21no—
392C22×C61—21no—
393C22×C61—42no—
394C22×C61—42no—
395C22×C61C2×#10112yes—
396C22×C61C22×C22⋊C411yescharacteristic
397C22×C61C4×#4111yescharacteristic
398C22×C61#52011yescharacteristic
399C2×D61—21no—
400C2×D61—21no—
401C2×D61—21no—
402C2×D61—21no—
403C2×D61—21no—
404C2×D61—42no—
405C2×D61—42no—
406C2×D61C2×#10112yes—
407C4×C61—21no—
408C4×C61—21no—
409C4×C61—42no—
410C4×C61—42no—
411C4×C61#54611yescharacteristic
412C4×C61#54611yescharacteristic
413C4×C61#54711yescharacteristic
414C4×C61#54711yescharacteristic
415Dic61—21no—
416Dic61—21no—
417Dic61—21no—
418Dic61—21no—
419Dic61—21no—
420Dic61—42no—
421Dic61—42no—
422Dic61C2×#10112yes—
423C2×#554—611no—
424D4×M16—611no—
425D4×M16—611no—
426#1997—611no—
427#1997—611no—
428#1901—611no—
429#1901—611no—
430#1901—611no—
431#1901D6111yescharacteristic, complemented
432#1821—611no—
433#1821—611no—
434#1801—611no—
435C4×#101—611no—
436C2×#343—611no—
437C2×#343—611no—
438C2×C61—21no—
439C2×C61—21no—
440C2×C61—22no—
441C2×C61—41no—
442C2×C61#233911yescharacteristic
443C2×C61C22×#10111yescharacteristic
444C2×C61#288811yescharacteristic
445D61—22no—
446D61—41no—
447C22×M16—611no—
448C22×M16—611no—
449C22×M16—611no—
450C22×M16C2×D6111yescharacteristic
451#554—1221no—
452#554—1221no—
453#554—1221no—
454#554—1221no—
455#554—1221no—
456#554—1221no—
457#554—1221no—
458#554—1221no—
459C2×C4⋊Q8—611no—
460C2×#125—612no—
461C2×C22⋊Q8—611no—
462C2×C22⋊Q8—612no—
463C2×C22⋊Q8—612no—
464C2×C22⋊Q8C2×D6111yescharacteristic
465C2×C4×Q8—611no—
466C2×C4×D4—611no—
467C2×C4×D4—612no—
468C22×C4⋊C4—611no—
469C22×C4⋊C4—611no—
470#436—1221no—
471#436—1221no—
472#435—1221no—
473#435—1221no—
474#435—1221no—
475#435—1221no—
476C8×D4—1221no—
477C8×D4—1221no—
478#423—611no—
479#423—611no—
480C2×#101—611no—
481C2×#101—611no—
482C2×#101C2×D6111yescharacteristic
483C2×#101C2×D6111yescharacteristic
484#407—611no—
485#407—611no—
486#407—611no—
487#407C2×D6111yescharacteristic
488C4×M16—611no—
489C4×M16—611no—
490#343—611no—
491#343—611no—
492#343—611no—
493#343—611no—
494#343—611no—
495#343—611no—
496#343—611no—
497#343—611no—
498#343—611no—
499#343—611no—
500#343C2×D6111yescharacteristic
501#343C2×D6111yescharacteristic
502C61#2248111yescharacteristic, complemented, Sylow
503C22×Q8—612no—
504C22×Q8C22×D6111yescharacteristic
505C22×D4—611no—
506C23×C4—611no—
507C23×C4—612no—
508C23×C4—612no—
509C23×C4C22×D6111yescharacteristic
510C2×M16—21no—
511C2×M16—22no—
512C2×M16—41no—
513C2×M16—611no—
514C2×M16—611no—
515C2×M16—611no—
516C2×M16—611no—
517C2×M16—1221no—
518C2×M16—1221no—
519C2×M16—1221no—
520C2×M16—1222no—
521C2×M16—1222no—
522C2×M16—1222no—
523C2×M16—2441no—
524C2×M16—2441no—
525C2×M16—2441no—
526C2×M16C22×D6111yescharacteristic
527C2×M16C22×D6111yescharacteristic
528C2×M16C22×D6111yescharacteristic
529C2×M16C22×D6111yescharacteristic
530C22×C8—21no—
531C22×C8—1221no—
532C22×C8—1221no—
533C22×C8—1221no—
534C4⋊Q8—1221no—
535C4⋊Q8—1221no—
536C4⋊Q8—1221no—
537C4⋊Q8—1221no—
538#125—1222no—
539#125—1222no—
540#125—1222no—
541#125—1222no—
542C22⋊Q8—21no—
543C22⋊Q8—21no—
544C22⋊Q8—21no—
545C22⋊Q8—21no—
546C22⋊Q8—1222no—
547C22⋊Q8—1222no—
548C22⋊Q8—1222no—
549C22⋊Q8—1222no—
550C22⋊Q8—1222no—
551C22⋊Q8—1222no—
552C22⋊Q8—1222no—
553C22⋊Q8—1222no—
554C22⋊Q8—1221no—
555C22⋊Q8—1221no—
556C22⋊Q8—1221no—
557C22⋊Q8—1221no—
558C4×Q8—1221no—
559C4×Q8—1221no—
560C4×Q8—1221no—
561C4×Q8—1221no—
562C4×D4—611no—
563C4×D4—611no—
564C4×D4—611no—
565C4×D4—611no—
566C4×D4—611no—
567C4×D4—611no—
568C4×D4—611no—
569C4×D4—611no—
570C4×D4—1222no—
571C4×D4—1222no—
572C4×D4—1222no—
573C4×D4—1222no—
574C2×C4⋊C4—611no—
575C2×C4⋊C4—612no—
576C2×C4⋊C4—612no—
577C2×C4⋊C4—612no—
578C2×C4⋊C4—612no—
579C2×C4⋊C4—612no—
580C2×C4⋊C4—611no—
581C2×C4⋊C4—611no—
582C2×C4⋊C4—1221no—
583C2×C4⋊C4—1221no—
584C2×C4⋊C4—1221no—
585C2×C4⋊C4—1221no—
586C2×C4⋊C4—1221no—
587C2×C4⋊C4—1221no—
588C2×C4⋊C4—1221no—
589C2×C4⋊C4—1221no—
590C2×C4⋊C4C4×D6112yes—
591C2×C4⋊C4C22×D6111yescharacteristic
592C2×C22⋊C4—611no—
593C2×C22⋊C4—611no—
594C2×C22⋊C4—612no—
595C2×C22⋊C4C4×D6112yes—
596C2×C42—611no—
597C2×C42—612no—
598C4⋊C8—1221no—
599C4⋊C8—1221no—
600C4⋊C8—1221no—
601C4⋊C8—1221no—
602#101—22no—
603#101—41no—
604#101—1222no—
605#101—2441no—
606C22⋊C8—21no—
607C22⋊C8—21no—
608C22⋊C8—1221no—
609C22⋊C8—1221no—
610C22⋊C8—1221no—
611C22⋊C8—1221no—
612C22⋊C8—1221no—
613C22⋊C8—1221no—
614#97—1221no—
615#97—1221no—
616C4×C8—1221no—
617C4×C8—1221no—
618C24—611no—
619C24C2×C4×D6111yescharacteristic
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8—21no—
626C2×Q8—1222no—
627C2×Q8—1222no—
628C2×Q8—4882no—
629C2×D4—611no—
630C2×D4—611no—
631C2×D4—611no—
632C2×D4—611no—
633C2×D4—1224no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—611no—
639C22×C4—611no—
640C22×C4—611no—
641C22×C4—611no—
642C22×C4—611no—
643C22×C4—611no—
644C22×C4—611no—
645C22×C4—612no—
646C22×C4—612no—
647C22×C4—1222no—
648C22×C4—1222no—
649C22×C4—1221no—
650C22×C4—1221no—
651C22×C4—1221no—
652C22×C4—1221no—
653C22×C4—1222no—
654C22×C4—1222no—
655C22×C4—4882no—
656C22×C4—4882no—
657C22×C4C2×C4×D6112yes—
658C22×C4C2×C4×D6111yescharacteristic
659C22×C4C2×C4×D6112yes—
660C22×C4D4×D6111yescharacteristic
661C22×C4D4×D6111yescharacteristic
662C22×C4D4×D6111yescharacteristic
663C22×C4D4×D6111yescharacteristic
664C22×C4C23×D6111yescharacteristic
665M16—21no—
666M16—21no—
667M16—21no—
668M16—21no—
669M16—21no—
670M16—21no—
671M16—21no—
672M16—42no—
673M16—612no—
674M16—1221no—
675M16—1221no—
676M16—1221no—
677M16—1221no—
678M16—1221no—
679M16—1221no—
680M16—1221no—
681M16—2442no—
682M16—2442no—
683M16—2442no—
684M16#1175822412yes—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—42no—
690C2×C8—1221no—
691C2×C8—1221no—
692C2×C8—1221no—
693C2×C8—1221no—
694C2×C8—2442no—
695C2×C8—2442no—
696C2×C8—2442no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—22no—
700C4⋊C4—22no—
701C4⋊C4—611no—
702C4⋊C4—611no—
703C4⋊C4—611no—
704C4⋊C4—611no—
705C4⋊C4—1222no—
706C4⋊C4—1222no—
707C4⋊C4—1222no—
708C4⋊C4—1222no—
709C4⋊C4—1222no—
710C4⋊C4—1222no—
711C4⋊C4—1222no—
712C4⋊C4—1222no—
713C4⋊C4—1221no—
714C4⋊C4—1221no—
715C4⋊C4—1221no—
716C4⋊C4—1221no—
717C4⋊C4—1222no—
718C4⋊C4—1222no—
719C22⋊C4—22no—
720C22⋊C4—22no—
721C22⋊C4—611no—
722C22⋊C4—611no—
723C22⋊C4—611no—
724C22⋊C4—611no—
725C22⋊C4—611no—
726C22⋊C4—611no—
727C22⋊C4—611no—
728C22⋊C4—611no—
729C22⋊C4—1222no—
730C22⋊C4—1222no—
731C42—611no—
732C42—611no—
733C42—611no—
734C42—611no—
735C42—1222no—
736C42—1222no—
737C23—21no—
738C23—21no—
739C23—22no—
740C23—41no—
741C23—611no—
742C23—611no—
743C23—1222no—
744C23—1221no—
745C23—1221no—
746C23—2441no—
747C23C22⋊C4×D6111yescharacteristic
748C23C22⋊C4×D6111yescharacteristic
749C23C22×C4×D6111yescharacteristic
750Q8—41no—
751Q8—41no—
752Q8—41no—
753Q8—41no—
754Q8—4882no—
755Q8—4882no—
756D4—614no—
757D4—1222no—
758D4—1222no—
759D4—1222no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—42no—
775C2×C4—611no—
776C2×C4—611no—
777C2×C4—611no—
778C2×C4—611no—
779C2×C4—611no—
780C2×C4—611no—
781C2×C4—1222no—
782C2×C4—1221no—
783C2×C4—1221no—
784C2×C4—1221no—
785C2×C4—1221no—
786C2×C4—1221no—
787C2×C4—1221no—
788C2×C4—1221no—
789C2×C4—1221no—
790C2×C4—1221no—
791C2×C4—1221no—
792C2×C4—1222no—
793C2×C4—1222no—
794C2×C4—4882no—
795C2×C4—4882no—
796C2×C4—4882no—
797C2×C4—4882no—
798C2×C4—2441no—
799C2×C4—2442no—
800C2×C4—2442no—
801C2×C4C22⋊C4×D6111yescharacteristic
802C2×C4C22⋊C4×D6111yescharacteristic
803C2×C4C2×D4×D6111yescharacteristic
804C2×C4C2×D4×D6111yescharacteristic
805C2×C4#41×D6111yescharacteristic
806C2×C4C2×#1175822411yescharacteristic
807C2×C4#1451982211yescharacteristic
808C2×C4#1451982411yescharacteristic
809C8—22no—
810C8—41no—
811C8—41no—
812C8—41no—
813C8—1222no—
814C8—2441no—
815C8—2441no—
816C8—2441no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—42no—
825C22—42no—
826C22—612no—
827C22—1221no—
828C22—1221no—
829C22—1221no—
830C22—1221no—
831C22—1221no—
832C22—2442no—
833C22—2442no—
834C22#101×D6112yes—
835C22C2×C22⋊C4×D6111yescharacteristic
836C22C4×#1175822411yescharacteristic
837C22#1684024111yescharacteristic
838C4—21no—
839C4—21no—
840C4—42no—
841C4—42no—
842C4—612no—
843C4—1221no—
844C4—1221no—
845C4—1221no—
846C4—1221no—
847C4—1221no—
848C4—2442no—
849C4—2442no—
850C4#1684039911yescharacteristic
851C4#1684040111yescharacteristic
852C4#1684041011yescharacteristic
853C4#1684041211yescharacteristic
854C2—21no—
855C2—21no—
856C2—22no—
857C2—41no—
858C2—1222no—
859C2—2441no—
860C2#2144864511yescharacteristic
861C2C2×#101×D6111yescharacteristic
862C2#2145429611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1901C2
socleC22×C61C22×C22⋊C4
prime radicalC22×C22⋊D61C2×C4
cosocleC22×C4×C61C24
hypercenter#1901D61
hypocenterC61#22481
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1901

Complements

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

NH ≅ G/Ntype
4. #21446806C2semidirect
5. #21446806C2semidirect
6. #21446288C2semidirect
7. #21446284C2semidirect
8. #21446284C2semidirect
9. #21445898C2semidirect
10. #21445897C2semidirect
11. #21445813C2semidirect
12. #101×Dic61C2semidirect
13. C2×#16839530C2semidirect
14. #343×D61C2semidirect
15. C61×#1901C2semidirect
348. C22⋊D61#101semidirect
431. #1901D61semidirect
502. C61#22481semidirect

Maximal subgroups

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

subgroupindex
C2×#168404702
M16×C22⋊D612
#214545512
#214468062
#214462882
#214462842
#214458982
#214458972
#214458132
#101×Dic612
C2×#168395302
#343×D612
C61×#19012
#2248161