Finite Group Databasebeta

← #29601870

Subgroups — #29601870

Order 15616.

1966 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839684C211yesmaximal, characteristic
2C2×C4⋊C4×Dic61C211yesmaximal, characteristic, complemented
3C2×C4⋊C4×Dic61C211yesmaximal, characteristic, complemented
4C2×#16839613C211yesmaximal, characteristic, complemented
5C2×#16839609C211yesmaximal, characteristic
6C2×#16839609C211yesmaximal, characteristic
7C2×#16839609C211yesmaximal, characteristic
8#21444080C211yesmaximal, characteristic, complemented
9#21444073C211yesmaximal, characteristic, complemented
10#21444071C211yesmaximal, characteristic, complemented
11#21444065C211yesmaximal, characteristic
12#21444063C211yesmaximal, characteristic
13#21444061C211yesmaximal, characteristic
14#95×Dic61C211yesmaximal, characteristic, complemented
15C61×#1441C211yesmaximal, characteristic, complemented
16C23×C4×D61C2211yescharacteristic
17C22×C4⋊Dic61C2211yescharacteristic
18C22×C4⋊Dic61C2211yescharacteristic
19C22×#11758196C2211yescharacteristic
20C22×#11758196C2211yescharacteristic
21C22×#11758198C2211yescharacteristic
22C22×#11758198C2211yescharacteristic
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×C4×Dic61C2211yescharacteristic
28C22×C4×Dic61C2211yescharacteristic
29C22×C4×Dic61C2211yescharacteristic
30C22×C4×Dic61C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32C22×C4×Dic61C2211yescharacteristic
33#16839684C418yescomplemented
34C4⋊C4×Dic61—24no—
35C4⋊C4×Dic61—24no—
36#16839613—24no—
37#16839609—24no—
38#16839609—24no—
39#16839609—24no—
40C2×#14519684C2211yescharacteristic
41C2×#14519684C2211yescharacteristic
42C2×#14519684C2211yescharacteristic
43C2×#14519684C2211yescharacteristic
44C2×#14519684C2211yescharacteristic
45C2×#14519684C2211yescharacteristic
46C2×#14519684C2211yescharacteristic
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C22×C4⋊C4×C61C2211yescharacteristic
52C22×C4⋊C4×C61C2211yescharacteristic
53C2×#95×C61C2211yescharacteristic
54C2×#95×C61C2211yescharacteristic
55C2×#95×C61C2211yescharacteristic
56C2×#95×C61C2211yescharacteristic
57C2×#95×C61C2211yescharacteristic
58C24×D61C2311yescharacteristic
59C23×Dic61C2311yescharacteristic
60C23×Dic61C2311yescharacteristic
61C23×Dic61C2311yescharacteristic
62C23×Dic61C2311yescharacteristic
63C23×Dic61C2311yescharacteristic
64C23×Dic61C2311yescharacteristic
65C23×Dic61C2311yescharacteristic
66C22×C4×D61—22no—
67C22×C4×D61—22no—
68C22×C4×D61—22no—
69C22×C4×D61—22no—
70C22×C4×D61—22no—
71C22×C4×D61—22no—
72C22×C4×D61Q814yes—
73C2×C4⋊Dic61—22no—
74C2×C4⋊Dic61—22no—
75C2×C4⋊Dic61—22no—
76C2×C4⋊Dic61—22no—
77C2×C4⋊Dic61—22no—
78C2×C4⋊Dic61C2×C414yescomplemented
79C2×#11758196—22no—
80C2×#11758196—22no—
81C2×#11758196—22no—
82C2×#11758196—22no—
83C2×#11758196—22no—
84C2×#11758196C2×C414yescomplemented
85C2×#11758198—22no—
86C2×#11758198—22no—
87C2×#11758198—22no—
88C2×#11758198—22no—
89C2×#11758198—22no—
90C2×#11758198—22no—
91C2×#11758198—22no—
92C2×#11758198—22no—
93C2×#11758198—22no—
94C2×#11758198—22no—
95C2×#11758198—22no—
96C2×#11758198—22no—
97C2×#11758198—22no—
98C2×#11758198—22no—
99C2×#11758198—22no—
100C2×#11758198C2×C414yes—
101C2×#11758198C2×C414yes—
102C2×#11758198C2×C414yes—
103C2×C4×Dic61—22no—
104C2×C4×Dic61—22no—
105C2×C4×Dic61—22no—
106C2×C4×Dic61—22no—
107C2×C4×Dic61—22no—
108C2×C4×Dic61—22no—
109C2×C4×Dic61—22no—
110C2×C4×Dic61—22no—
111C2×C4×Dic61—22no—
112C2×C4×Dic61—22no—
113C2×C4×Dic61—22no—
114C2×C4×Dic61—22no—
115C2×C4×Dic61—22no—
116C2×C4×Dic61—22no—
117C2×C4×Dic61—22no—
118C2×C4×Dic61D414yes—
119C2×C4×Dic61D414yes—
120C2×C4×Dic61D414yes—
121#14519684—22no—
122#14519684—22no—
123#14519684—22no—
124#14519684—22no—
125#14519684—22no—
126#14519684—22no—
127#14519684—22no—
128#14519684—22no—
129#14519684—22no—
130#14519684—22no—
131#14519684C2×C414yescomplemented
132C23×C4×C61C2311yescharacteristic
133C23×C4×C61C2311yescharacteristic
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C2×C4⋊C4×C61—22no—
140C2×C4⋊C4×C61—22no—
141C2×C4⋊C4×C61—22no—
142C2×C4⋊C4×C61—22no—
143C2×C4⋊C4×C61—22no—
144C2×C4⋊C4×C61C2×C414yescomplemented
145#95×C61—22no—
146#95×C61—22no—
147#95×C61—22no—
148#95×C61—22no—
149#95×C61—22no—
150C24×C61C2411yescharacteristic
151C23×D61—21no—
152C23×D61—21no—
153C23×D61—21no—
154C23×D61—21no—
155C23×D61—21no—
156C23×D61—21no—
157C23×D61—21no—
158C23×D61—21no—
159C23×D61—21no—
160C23×D61—21no—
161C23×D61—21no—
162C23×D61—21no—
163C23×D61C22×C412yes—
164C23×D61C2×Q812yes—
165C23×D61#4112yes—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—21no—
172C22×C4×C61—21no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61—21no—
201C22×C4×C61—21no—
202C22×C4×C61—21no—
203C22×C4×C61—21no—
204C22×C4×C61C22×C412yes—
205C22×C4×C61C22×C412yes—
206C22×C4×C61C22×C412yes—
207C22×C4×C61C2×D412yes—
208C22×C4×C61C2×D412yes—
209C22×C4×C61C2×D412yes—
210C22×C4×C61C2×Q812yes—
211C22×C4×C61#4112yes—
212C22×C4×C61#4112yes—
213C22×C4×C61#4112yes—
214C22×C4×C61#4112yes—
215C22×Dic61—21no—
216C22×Dic61—21no—
217C22×Dic61—21no—
218C22×Dic61—21no—
219C22×Dic61—21no—
220C22×Dic61—21no—
221C22×Dic61—21no—
222C22×Dic61—21no—
223C22×Dic61—21no—
224C22×Dic61—21no—
225C22×Dic61—21no—
226C22×Dic61—21no—
227C22×Dic61—21no—
228C22×Dic61—21no—
229C22×Dic61—21no—
230C22×Dic61—21no—
231C22×Dic61—21no—
232C22×Dic61—21no—
233C22×Dic61—21no—
234C22×Dic61—21no—
235C22×Dic61—21no—
236C22×Dic61—21no—
237C22×Dic61—21no—
238C22×Dic61—21no—
239C22×Dic61—21no—
240C22×Dic61—21no—
241C22×Dic61—21no—
242C22×Dic61—21no—
243C22×Dic61—21no—
244C22×Dic61—21no—
245C22×Dic61—21no—
246C22×Dic61—21no—
247C22×Dic61—21no—
248C22×Dic61—21no—
249C22×Dic61C22×C412yes—
250C22×Dic61C22×C412yes—
251C22×Dic61C22×C412yes—
252C22×Dic61C2×D412yes—
253C22×Dic61C2×D412yes—
254C22×Dic61C2×D412yes—
255C22×Dic61C2×D412yes—
256C22×Dic61C2×D412yes—
257C22×Dic61C2×D412yes—
258C22×Dic61C2×Q812yes—
259C22×Dic61#4112yes—
260C22×Dic61#4112yes—
261C22×Dic61#4112yes—
262C22×Dic61#4112yes—
263C22×Dic61#4112yes—
264C2×C4×D61—28no—
265C2×C4×D61—28no—
266C2×C4×D61—28no—
267C2×C4×D61—44no—
268C2×C4×D61—44no—
269C2×C4×D61—44no—
270C2×C4×D61—44no—
271C4⋊C4×C61—28no—
272C4⋊C4×C61—28no—
273#11758198—28no—
274#11758198—28no—
275#11758198—28no—
276#11758198—28no—
277#11758198—28no—
278#11758198—28no—
279C4⋊Dic61—28no—
280C4⋊Dic61—28no—
281#11758196—28no—
282#11758196—28no—
283C4×Dic61—28no—
284C4×Dic61—28no—
285C4×Dic61—28no—
286C4×Dic61—44no—
287C4×Dic61—44no—
288C4×Dic61—44no—
289C23×C61C23×C411yescharacteristic
290C23×C61C22×D411yescharacteristic
291C23×C61C22×D411yescharacteristic
292C23×C61C22×D411yescharacteristic
293C23×C61C22×Q811yescharacteristic
294C23×C61C2×#4111yescharacteristic
295C23×C61C2×#4111yescharacteristic
296C23×C61C2×#4111yescharacteristic
297C23×C61C2×#4111yescharacteristic
298C23×C61C2×#4111yescharacteristic
299C23×C61C2×#4111yescharacteristic
300C23×C61C2×#4111yescharacteristic
301C23×C61C2×#4111yescharacteristic
302C23×C61C2×#4111yescharacteristic
303C23×C61C2×#4111yescharacteristic
304C22×D61—22no—
305C22×D61—22no—
306C22×D61—22no—
307C22×D61—22no—
308C22×D61—22no—
309C22×D61—22no—
310C22×D61—22no—
311C22×D61—22no—
312C22×D61—22no—
313C22×D61—22no—
314C22×D61—22no—
315C22×D61—22no—
316C22×D61—22no—
317C22×D61—22no—
318C22×D61—22no—
319C22×D61—22no—
320C22×D61—22no—
321C22×D61—22no—
322C22×D61—41no—
323C22×D61—41no—
324C22×D61—41no—
325C22×D61—41no—
326C22×D61—41no—
327C22×D61—41no—
328C22×D61—41no—
329C22×D61—41no—
330C22×D61—41no—
331C22×D61—41no—
332C22×D61—41no—
333C22×D61—41no—
334C22×D61—41no—
335C22×D61—41no—
336C22×D61—41no—
337C22×D61—41no—
338C22×D61C4×Q814yes—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—22no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—22no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—22no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—22no—
357C2×C4×C61—22no—
358C2×C4×C61—22no—
359C2×C4×C61—22no—
360C2×C4×C61—22no—
361C2×C4×C61—22no—
362C2×C4×C61—22no—
363C2×C4×C61—22no—
364C2×C4×C61—22no—
365C2×C4×C61—22no—
366C2×C4×C61—41no—
367C2×C4×C61—41no—
368C2×C4×C61—41no—
369C2×C4×C61—41no—
370C2×C4×C61—41no—
371C2×C4×C61—41no—
372C2×C4×C61—41no—
373C2×C4×C61—41no—
374C2×C4×C61—41no—
375C2×C4×C61—41no—
376C2×C4×C61—41no—
377C2×C4×C61—41no—
378C2×C4×C61—41no—
379C2×C4×C61—41no—
380C2×C4×C61—41no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
383C2×C4×C61—41no—
384C2×C4×C61—41no—
385C2×C4×C61—41no—
386C2×C4×C61C4×D414yes—
387C2×C4×C61C4×D414yes—
388C2×Dic61—22no—
389C2×Dic61—22no—
390C2×Dic61—22no—
391C2×Dic61—22no—
392C2×Dic61—22no—
393C2×Dic61—22no—
394C2×Dic61—22no—
395C2×Dic61—22no—
396C2×Dic61—22no—
397C2×Dic61—22no—
398C2×Dic61—22no—
399C2×Dic61—22no—
400C2×Dic61—22no—
401C2×Dic61—22no—
402C2×Dic61—22no—
403C2×Dic61—22no—
404C2×Dic61—22no—
405C2×Dic61—22no—
406C2×Dic61—22no—
407C2×Dic61—22no—
408C2×Dic61—22no—
409C2×Dic61—41no—
410C2×Dic61—41no—
411C2×Dic61—41no—
412C2×Dic61—41no—
413C2×Dic61—41no—
414C2×Dic61—41no—
415C2×Dic61—41no—
416C2×Dic61—41no—
417C2×Dic61—41no—
418C2×Dic61—41no—
419C2×Dic61—41no—
420C2×Dic61—41no—
421C2×Dic61—41no—
422C2×Dic61—41no—
423C2×Dic61—41no—
424C2×Dic61—41no—
425C2×Dic61—41no—
426C2×Dic61—41no—
427C2×Dic61—41no—
428C2×Dic61—41no—
429C2×Dic61C4×D414yes—
430C2×Dic61#12114yes—
431C2×Dic61#12114yes—
432C2×Dic61#12114yes—
433C2×Dic61C22⋊Q814yes—
434C2×Dic61C22⋊Q814yes—
435C2×Dic61C22⋊Q814yes—
436C2×Dic61#12614yes—
437C4×D61—416no—
438C4×#396—611nomaximal, Sylow
439C22×C61C2×C4×D411yescharacteristic
440C22×C61C2×C4×D411yescharacteristic
441C22×C61C2×C4×D411yescharacteristic
442C22×C61C2×C4×Q811yescharacteristic
443C22×C61C4×#4111yescharacteristic
444C22×C61C4×#4111yescharacteristic
445C22×C61C4×#4111yescharacteristic
446C22×C61C2×#12111yescharacteristic
447C22×C61C2×#12111yescharacteristic
448C22×C61C2×#12111yescharacteristic
449C22×C61C2×C22⋊Q811yescharacteristic
450C22×C61C2×C22⋊Q811yescharacteristic
451C22×C61C2×C22⋊Q811yescharacteristic
452C22×C61#52511yescharacteristic
453C22×C61#52511yescharacteristic
454C22×C61#52511yescharacteristic
455C22×C61#52511yescharacteristic
456C22×C61#52511yescharacteristic
457C22×C61#52511yescharacteristic
458C22×C61C2×#12611yescharacteristic
459C22×C61#52911yescharacteristic
460C22×C61#52911yescharacteristic
461C22×C61#52911yescharacteristic
462C22×C61#52911yescharacteristic
463C22×C61#52911yescharacteristic
464C22×C61#52911yescharacteristic
465C22×C61#52911yescharacteristic
466C22×C61#52911yescharacteristic
467C22×C61#52911yescharacteristic
468C22×C61#53211yescharacteristic
469C22×C61#53211yescharacteristic
470C22×C61#53211yescharacteristic
471C22×C61#53311yescharacteristic
472C22×C61#53311yescharacteristic
473C22×C61#53311yescharacteristic
474C2×D61—24no—
475C2×D61—24no—
476C2×D61—24no—
477C2×D61—42no—
478C2×D61—42no—
479C2×D61—42no—
480C2×D61—42no—
481C2×D61—42no—
482C2×D61—42no—
483C2×D61—42no—
484C2×D61—42no—
485C2×D61—42no—
486C2×D61—42no—
487C2×D61—42no—
488C2×D61—42no—
489C4×C61—24no—
490C4×C61—24no—
491C4×C61—42no—
492C4×C61—42no—
493C4×C61—42no—
494C4×C61—42no—
495C4×C61—42no—
496Dic61—24no—
497Dic61—42no—
498Dic61—42no—
499Dic61—42no—
500Dic61—42no—
501Dic61—42no—
502Dic61#39618yescomplemented
503C2×#396—611no—
504C2×C4×C4⋊C4—611no—
505C2×C4×C4⋊C4—611no—
506C2×C4×C4⋊C4—611no—
507C2×C4×C22⋊C4—611no—
508C2×C4×C22⋊C4—611no—
509C2×C4×C22⋊C4—611no—
510#1443—611no—
511#1441—611no—
512#1441—611no—
513#1441D6111yescharacteristic, complemented
514#1439—611no—
515#1439—611no—
516#1439—611no—
517C4×#95—611no—
518C2×C61C4×#12111yescharacteristic
519C2×C61C4×#12111yescharacteristic
520C2×C61C4×#12111yescharacteristic
521C2×C61C4×C22⋊Q811yescharacteristic
522C2×C61C4×C22⋊Q811yescharacteristic
523C2×C61C4×C22⋊Q811yescharacteristic
524C2×C61C4×#12611yescharacteristic
525C2×C61C2×#39611yescharacteristic
526C2×C61#239211yescharacteristic
527C2×C61#239211yescharacteristic
528C2×C61#239211yescharacteristic
529C2×C61#239611yescharacteristic
530C2×C61#239611yescharacteristic
531C2×C61#239611yescharacteristic
532C2×C61#240111yescharacteristic
533D61—44no—
534C24×C4—611no—
535C22×C4⋊C4—611no—
536C22×C4⋊C4—611no—
537C22×C4⋊C4—611no—
538C22×C4⋊C4—611no—
539C22×C4⋊C4C2×D6111yescharacteristic
540C22×C4⋊C4C2×D6111yescharacteristic
541C22×C22⋊C4—611no—
542C22×C22⋊C4—611no—
543C22×C22⋊C4—611no—
544C22×C22⋊C4—611no—
545C22×C22⋊C4—611no—
546C22×C22⋊C4—611no—
547C22×C42—611no—
548C22×C42—611no—
549C22×C42—611no—
550C22×C42—611no—
551C22×C42—611no—
552C22×C42—611no—
553#396—618no—
554C4×C4⋊C4—1224no—
555C4×C4⋊C4—1224no—
556C4×C4⋊C4—1224no—
557C4×C22⋊C4—1224no—
558C4×C22⋊C4—1224no—
559C4×C22⋊C4—1224no—
560C2×#95—611no—
561C2×#95—611no—
562C2×#95—611no—
563C2×#95—611no—
564C2×#95—611no—
565C2×#95—611no—
566C2×#95—611no—
567C2×#95—611no—
568C2×#95—611no—
569C2×#95—611no—
570C2×#95—611no—
571C2×#95C2×D6111yescharacteristic
572C2×#95C2×D6111yescharacteristic
573C2×#95C2×D6111yescharacteristic
574C2×#95C2×D6111yescharacteristic
575C2×#95C2×D6111yescharacteristic
576C61C4×#39611yescharacteristic, complemented, Sylow
577C25—611no—
578C23×C4—611no—
579C23×C4—611no—
580C23×C4—611no—
581C23×C4—611no—
582C23×C4—611no—
583C23×C4—611no—
584C23×C4—611no—
585C23×C4—614no—
586C23×C4—1222no—
587C23×C4—1222no—
588C23×C4—1222no—
589C23×C4—1222no—
590C23×C4—1222no—
591C23×C4—1222no—
592C23×C4C22×D6111yescharacteristic
593C23×C4C22×D6111yescharacteristic
594C23×C4C22×D6111yescharacteristic
595C23×C4C22×D6111yescharacteristic
596C23×C4C22×D6111yescharacteristic
597C23×C4C22×D6111yescharacteristic
598C23×C4C22×D6111yescharacteristic
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—614no—
605C2×C4⋊C4—614no—
606C2×C4⋊C4—1222no—
607C2×C4⋊C4—1222no—
608C2×C4⋊C4—1222no—
609C2×C4⋊C4—1222no—
610C2×C4⋊C4—1222no—
611C2×C4⋊C4—1222no—
612C2×C4⋊C4—1222no—
613C2×C4⋊C4—1222no—
614C2×C4⋊C4—1222no—
615C2×C4⋊C4—1222no—
616C2×C4⋊C4C4×D6114yescomplemented
617C2×C22⋊C4—614no—
618C2×C22⋊C4—614no—
619C2×C22⋊C4—614no—
620C2×C22⋊C4—1222no—
621C2×C22⋊C4—1222no—
622C2×C22⋊C4—1222no—
623C2×C22⋊C4—1222no—
624C2×C22⋊C4—1222no—
625C2×C22⋊C4—1222no—
626C2×C22⋊C4—1222no—
627C2×C22⋊C4—1222no—
628C2×C22⋊C4—1222no—
629C2×C22⋊C4—1222no—
630C2×C22⋊C4—1222no—
631C2×C22⋊C4—1222no—
632C2×C22⋊C4—1222no—
633C2×C22⋊C4—1222no—
634C2×C22⋊C4—1222no—
635C2×C42—614no—
636C2×C42—614no—
637C2×C42—614no—
638C2×C42—1222no—
639C2×C42—1222no—
640C2×C42—1222no—
641C2×C42—1222no—
642C2×C42—1222no—
643C2×C42—1222no—
644C2×C42—1222no—
645C2×C42—1222no—
646C2×C42—1222no—
647C2×C42—1222no—
648C2×C42—1222no—
649C2×C42—1222no—
650C2×C42—1222no—
651C2×C42—1222no—
652C2×C42—1222no—
653#95—22no—
654#95—22no—
655#95—22no—
656#95—22no—
657#95—22no—
658#95—614no—
659#95—1222no—
660#95—1222no—
661#95—1222no—
662#95—1222no—
663#95—1222no—
664#95—1222no—
665#95—1222no—
666#95—1222no—
667#95—1222no—
668#95—1222no—
669C24—612no—
670C24—612no—
671C24—612no—
672C24—1221no—
673C24—1221no—
674C24—1221no—
675C24—1221no—
676C24—1221no—
677C24—1221no—
678C24—1221no—
679C24—1221no—
680C24—1221no—
681C24—1221no—
682C24—1221no—
683C24—1221no—
684C24C23×D6111yescharacteristic
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—612no—
724C22×C4—612no—
725C22×C4—612no—
726C22×C4—612no—
727C22×C4—612no—
728C22×C4—612no—
729C22×C4—612no—
730C22×C4—612no—
731C22×C4—612no—
732C22×C4—612no—
733C22×C4—612no—
734C22×C4—612no—
735C22×C4—612no—
736C22×C4—612no—
737C22×C4—612no—
738C22×C4—1228no—
739C22×C4—1228no—
740C22×C4—1228no—
741C22×C4—1221no—
742C22×C4—1221no—
743C22×C4—1221no—
744C22×C4—1221no—
745C22×C4—1221no—
746C22×C4—1221no—
747C22×C4—1221no—
748C22×C4—1221no—
749C22×C4—1221no—
750C22×C4—1221no—
751C22×C4—1221no—
752C22×C4—1221no—
753C22×C4—1221no—
754C22×C4—1221no—
755C22×C4—1221no—
756C22×C4—1221no—
757C22×C4—1221no—
758C22×C4—1221no—
759C22×C4—1221no—
760C22×C4—1221no—
761C22×C4—1221no—
762C22×C4—1221no—
763C22×C4—1221no—
764C22×C4—1221no—
765C22×C4—1221no—
766C22×C4—1221no—
767C22×C4—1221no—
768C22×C4—1221no—
769C22×C4—1221no—
770C22×C4—1221no—
771C22×C4—1221no—
772C22×C4—1221no—
773C22×C4—1221no—
774C22×C4—1221no—
775C22×C4—2444no—
776C22×C4—2444no—
777C22×C4—2444no—
778C22×C4—2444no—
779C22×C4C2×C4×D6112yes—
780C22×C4C2×C4×D6112yes—
781C22×C4C2×C4×D6112yes—
782C22×C4D4×D6112yes—
783C22×C4D4×D6112yes—
784C22×C4D4×D6112yes—
785C22×C4#1175822412yes—
786C22×C4#1175822412yes—
787C22×C4Q8×D6112yes—
788C22×C4#1175822612yes—
789C22×C4#1175822612yes—
790C4⋊C4—28no—
791C4⋊C4—28no—
792C4⋊C4—1228no—
793C4⋊C4—1228no—
794C4⋊C4—1228no—
795C4⋊C4—1228no—
796C22⋊C4—1228no—
797C22⋊C4—1228no—
798C22⋊C4—1228no—
799C22⋊C4—1228no—
800C22⋊C4—1228no—
801C22⋊C4—1228no—
802C42—1228no—
803C42—1228no—
804C42—1228no—
805C42—2444no—
806C42—2444no—
807C42—2444no—
808C23—614no—
809C23—1222no—
810C23—1222no—
811C23—1222no—
812C23—1222no—
813C23—1222no—
814C23—1222no—
815C23—1222no—
816C23—1222no—
817C23—1222no—
818C23—1222no—
819C23—1222no—
820C23—1222no—
821C23—1222no—
822C23—1222no—
823C23—1222no—
824C23—1222no—
825C23—1222no—
826C23—1222no—
827C23—2441no—
828C23—2441no—
829C23—2441no—
830C23—2441no—
831C23—2441no—
832C23—2441no—
833C23—2441no—
834C23—2441no—
835C23—2441no—
836C23—2441no—
837C23—2441no—
838C23—2441no—
839C23—2441no—
840C23—2441no—
841C23—2441no—
842C23—2441no—
843C23C22×C4×D6111yescharacteristic
844C23C2×D4×D6111yescharacteristic
845C23C2×D4×D6111yescharacteristic
846C23C2×D4×D6111yescharacteristic
847C23C2×Q8×D6111yescharacteristic
848C23#41×D6111yescharacteristic
849C23#41×D6111yescharacteristic
850C23#41×D6111yescharacteristic
851C23#41×D6111yescharacteristic
852C23#41×D6111yescharacteristic
853C23#41×D6111yescharacteristic
854C23C2×#1175822411yescharacteristic
855C23C2×#1175822411yescharacteristic
856C23C2×#1175822611yescharacteristic
857C23C2×#1175822611yescharacteristic
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—614no—
906C2×C4—614no—
907C2×C4—614no—
908C2×C4—614no—
909C2×C4—614no—
910C2×C4—614no—
911C2×C4—614no—
912C2×C4—614no—
913C2×C4—1222no—
914C2×C4—1222no—
915C2×C4—1222no—
916C2×C4—1222no—
917C2×C4—1222no—
918C2×C4—1222no—
919C2×C4—1222no—
920C2×C4—1222no—
921C2×C4—1222no—
922C2×C4—1222no—
923C2×C4—1222no—
924C2×C4—1222no—
925C2×C4—1222no—
926C2×C4—1222no—
927C2×C4—1222no—
928C2×C4—1222no—
929C2×C4—1222no—
930C2×C4—1222no—
931C2×C4—1222no—
932C2×C4—1222no—
933C2×C4—1222no—
934C2×C4—24416no—
935C2×C4—2441no—
936C2×C4—2441no—
937C2×C4—2441no—
938C2×C4—2441no—
939C2×C4—2441no—
940C2×C4—2441no—
941C2×C4—2441no—
942C2×C4—2441no—
943C2×C4—2441no—
944C2×C4—2441no—
945C2×C4—2441no—
946C2×C4—2441no—
947C2×C4—2441no—
948C2×C4—2441no—
949C2×C4—2441no—
950C2×C4—2441no—
951C2×C4—2441no—
952C2×C4—2441no—
953C2×C4—2441no—
954C2×C4—2441no—
955C2×C4#1451973714yes—
956C2×C4#1451973914yes—
957C22—1224no—
958C22—1224no—
959C22—1224no—
960C22—2442no—
961C22—2442no—
962C22—2442no—
963C22—2442no—
964C22—2442no—
965C22—2442no—
966C22—2442no—
967C22—2442no—
968C22—2442no—
969C22—2442no—
970C22—2442no—
971C22—2442no—
972C22C4×D4×D6111yescharacteristic
973C22C2×#1451973711yescharacteristic
974C22C2×#1451973911yescharacteristic
975C22C4×Q8×D6111yescharacteristic
976C22C4×#1175822411yescharacteristic
977C22#1684023011yescharacteristic
978C22C4×#1175822611yescharacteristic
979C22#121×D6111yescharacteristic
980C22#121×D6111yescharacteristic
981C22#121×D6111yescharacteristic
982C22C22⋊Q8×D6111yescharacteristic
983C22C22⋊Q8×D6111yescharacteristic
984C22C22⋊Q8×D6111yescharacteristic
985C22#1684026811yescharacteristic
986C22#1684027011yescharacteristic
987C22#1684027211yescharacteristic
988C22#1684027511yescharacteristic
989C22#1684027511yescharacteristic
990C22#1684027511yescharacteristic
991C22#126×D6111yescharacteristic
992C22#1684028911yescharacteristic
993C22#1684028911yescharacteristic
994C22#1684029111yescharacteristic
995C22#1684029511yescharacteristic
996C22#1684029711yescharacteristic
997C22#1684029711yescharacteristic
998C22#1684029711yescharacteristic
999C22#1684029811yescharacteristic
1000C22#1684029811yescharacteristic
1001C22#1684030711yescharacteristic
1002C22#1684030711yescharacteristic
1003C22#1684031311yescharacteristic
1004C22#1684031711yescharacteristic
1005C22#1684031711yescharacteristic
1006C22#1684031811yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—42no—
1010C4—42no—
1011C4—42no—
1012C4—42no—
1013C4—42no—
1014C4—618no—
1015C4—1224no—
1016C4—2442no—
1017C4—2442no—
1018C4—2442no—
1019C4—2442no—
1020C4—2442no—
1021C2—2444no—
1022C2#2144832511yescharacteristic
1023C2#2144832711yescharacteristic
1024C2#2144832911yescharacteristic
1025C2#2144834911yescharacteristic
1026C2#2144835311yescharacteristic
1027C2#2144835711yescharacteristic
1028C2#2144836911yescharacteristic
1029C2#396×D6111yescharacteristic
1030C2#2144906011yescharacteristic
1031C2#2144906211yescharacteristic
1032C2#2144906411yescharacteristic
1033C2#2144909011yescharacteristic
1034C2#2144909611yescharacteristic
1035C2#2144909611yescharacteristic
1036C2#2144911811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1441C2
socle, cosocleC24×C61C24
prime radicalC24×D61C23
hypercenter#1441D61
hypocenterC61C4×#396
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×Dic61C2semidirect
3. C2×C4⋊C4×Dic61C2semidirect
4. C2×#16839613C2semidirect
8. #21444080C2semidirect
9. #21444073C2semidirect
10. #21444071C2semidirect
14. #95×Dic61C2semidirect
15. C61×#1441C2semidirect
33. #16839684C4semidirect
78. C2×C4⋊Dic61C2×C4semidirect
84. C2×#11758196C2×C4semidirect
131. #14519684C2×C4semidirect
144. C2×C4⋊C4×C61C2×C4semidirect
502. Dic61#396semidirect
513. #1441D61semidirect
576. C61C4×#396semidirect
616. C2×C4⋊C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168396842
C2×C4⋊C4×Dic612
C2×#168396132
C2×#168396092
#214440802
#214440732
#214440712
#214440652
#214440632
#214440612
#95×Dic612
C61×#14412
C4×#39661