Finite Group Databasebeta

← #29696316

Subgroups — #29696316

Order 15616.

1194 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839834C211yesmaximal, characteristic, complemented
2#21448748C211yesmaximal, characteristic, complemented
3#21446793C211yesmaximal, characteristic, complemented
4#21446772C211yesmaximal, characteristic, complemented
5#21446258C211yesmaximal, characteristic, complemented
6#21446248C211yesmaximal, characteristic, complemented
7#21446142C211yesmaximal, characteristic, complemented
8#21446137C211yesmaximal, characteristic, complemented
9#21445914C211yesmaximal, characteristic, complemented
10#21445914C211yesmaximal, characteristic, complemented
11#21445829C211yesmaximal, characteristic, complemented
12#21445644C211yesmaximal, characteristic, complemented
13#21445540C211yesmaximal, characteristic, complemented
14#21445535C211yesmaximal, characteristic, complemented
15C2×C61×#555C211yesmaximal, characteristic
16C22×#11758194C2211yescharacteristic
17C23×#92418C2211yescharacteristic
18C2×#14519736C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20#16839834—24no—
21C2×C4⋊#92418C2211yescharacteristic
22C2×#14519698C2211yescharacteristic
23C2×#14519698C2211yescharacteristic
24C2×#14519698C2211yescharacteristic
25C2×#14519698C2211yescharacteristic
26C2×C22⋊#92418C2211yescharacteristic
27C2×C22⋊#92418C2211yescharacteristic
28C2×#14519688C2211yescharacteristic
29#16839655—21no—
30#16839648—21no—
31#16839642—21no—
32#16839628C2211yescharacteristic
33#16839622C2211yescharacteristic
34#16839622C2211yescharacteristic
35C4×C4⋊Dic61C2211yescharacteristic
36C22⋊C4×Dic61—21no—
37#16839524C2211yescharacteristic
38#16839524C2211yescharacteristic
39#16839524C2211yescharacteristic
40#16839524C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49C61×#555—24no—
50C61×#555C418yescomplemented
51C2×C4⋊Q8×C61C2211yescharacteristic
52C2×#124×C61—21no—
53C2×#124×C61—21no—
54C2×#121×C61—21no—
55C2×#121×C61C2211yescharacteristic
56C2×#121×C61C2211yescharacteristic
57C2×C4×D4×C61C2211yescharacteristic
58C2×C4×D4×C61C2211yescharacteristic
59C2×#117×C61—21no—
60C2×#117×C61C2211yescharacteristic
61C2×#117×C61C2211yescharacteristic
62C23×Dic61—21no—
63C2×#11758194—22no—
64C2×#11758194—22no—
65C2×#11758194—41no—
66C22×#92418—22no—
67C22×#92418—22no—
68C22×#92418—41no—
69C22×#92418C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73#14519736—22no—
74#14519736—41no—
75C2×C4⋊Dic61—22no—
76C2×C4⋊Dic61—21no—
77C2×C4⋊Dic61—41no—
78C2×C4⋊Dic61C2311yescharacteristic
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C22⋊Dic61—21no—
83C2×C22⋊Dic61—21no—
84C2×C22⋊Dic61—21no—
85C2×C4×Dic61—21no—
86C2×C4×Dic61—21no—
87C4⋊#92418—22no—
88#14519698—22no—
89#14519698—22no—
90#14519698—41no—
91#14519698—41no—
92C22⋊#92418—22no—
93C22⋊#92418—22no—
94#14519688—22no—
95#14519684—21no—
96#14519684—21no—
97#14519684—21no—
98#14519684—21no—
99#14519684—21no—
100C22×Q8×C61—21no—
101C22×D4×C61—21no—
102C22×D4×C61—21no—
103C22×D4×C61D411yescharacteristic
104C22×D4×C61C2311yescharacteristic
105C23×C4×C61—21no—
106C23×C4×C61C2311yescharacteristic
107C23×C4×C61C2311yescharacteristic
108C4⋊Q8×C61—22no—
109C4⋊Q8×C61C2×C414yescomplemented
110#124×C61—28no—
111#124×C61—28no—
112#121×C61—28no—
113#121×C61—22no—
114#121×C61—22no—
115#121×C61C2×C414yes—
116#121×C61C2×C414yescomplemented
117C4×D4×C61—22no—
118C4×D4×C61C2×C414yes—
119C4×D4×C61C2×C414yescomplemented
120C4×D4×C61D414yes—
121#117×C61—22no—
122#117×C61—22no—
123#117×C61—28no—
124#117×C61C2×C414yes—
125#117×C61C2×C414yescomplemented
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61D411yescharacteristic
128C2×C4⋊C4×C61C2311yescharacteristic
129C2×C4⋊C4×C61C2311yescharacteristic
130C2×C4⋊C4×C61C2311yescharacteristic
131C2×C22⋊C4×C61—21no—
132C2×C22⋊C4×C61—21no—
133C2×C22⋊C4×C61—21no—
134C2×C22⋊C4×C61—21no—
135C2×C22⋊C4×C61—21no—
136C2×C22⋊C4×C61D411yescharacteristic
137C2×C22⋊C4×C61D411yescharacteristic
138C2×C42×C61—21no—
139C2×C42×C61—21no—
140C2×C42×C61C2311yescharacteristic
141C24×C61—21no—
142C24×C61C2×D411yescharacteristic
143C24×C61C2×D411yescharacteristic
144C2×Q8×C61—24no—
145C2×Q8×C61—81no—
146C2×Q8×C61—81no—
147C2×D4×C61—24no—
148C2×D4×C61—24no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—41no—
155C2×D4×C61—41no—
156C2×D4×C61—81no—
157C2×D4×C61—81no—
158C2×D4×C61—81no—
159C2×D4×C61—81no—
160C2×D4×C61C22⋊C414yes—
161C2×D4×C61C22×C412yes—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
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—24no—
174C22×C4×C61—42no—
175C22×C4×C61—42no—
176C22×C4×C61C22×C412yes—
177C22×C4×C61C22×C412yes—
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2×D412yes—
183C22×C4×C61C2×D412yes—
184C22×C4×C61C2411yescharacteristic
185C22×Dic61—21no—
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61—42no—
190C22×Dic61—42no—
191C22×Dic61—81no—
192C4⋊C4×C61—24no—
193C4⋊C4×C61—21no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61—21no—
196C4⋊C4×C61C22⋊C414yes—
197C4⋊C4×C61C22×C412yes—
198C4⋊C4×C61C22×C412yes—
199C4⋊C4×C61C22×C412yes—
200C22⋊C4×C61—24no—
201C22⋊C4×C61—24no—
202C22⋊C4×C61—24no—
203C22⋊C4×C61—24no—
204C22⋊C4×C61—24no—
205C22⋊C4×C61C22⋊C414yes—
206C22⋊C4×C61C22⋊C414yes—
207C42×C61—24no—
208C42×C61—24no—
209C42×C61C22×C412yes—
210C42×C61C2×D412yes—
211C22⋊Dic61—42no—
212C22⋊Dic61—42no—
213C22⋊Dic61—81no—
214C4⋊Dic61—21no—
215C4⋊Dic61—21no—
216C4⋊Dic61—21no—
217C4⋊Dic61—21no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—42no—
222C4⋊Dic61#4112yes—
223C4×Dic61—42no—
224C4×Dic61—81no—
225#11758194—44no—
226C2×#92418—21no—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—44no—
238C2×#92418#4112yes—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—22no—
252C23×C61—41no—
253C23×C61—41no—
254C23×C61—41no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61C2×C22⋊C412yes—
259C23×C61C2×C22⋊C412yes—
260C23×C61C22×D411yescharacteristic
261Q8×C61—84no—
262D4×C61—22no—
263D4×C61—22no—
264D4×C61—44no—
265D4×C61—41no—
266D4×C61—41no—
267D4×C61—84no—
268D4×C61—84no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—48no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61C2×C22⋊C412yes—
296C2×C4×C61C2×C22⋊C412yes—
297C2×C4×C61C2×C22⋊C412yes—
298C2×C4×C61C2×C22⋊C412yes—
299C2×C4×C61C23×C411yescharacteristic
300C2×C4×C61C22×D411yescharacteristic
301C2×C4×C61C2×#4111yescharacteristic
302C2×C4×C61C2×#4111yescharacteristic
303C2×C4×C61H(5,𝔽2)11yescharacteristic
304C2×C4×C612−1+411yescharacteristic
305C2×Dic61—22no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—84no—
318#92418—22no—
319#92418—41no—
320#92418—41no—
321#92418—41no—
322#22492—611nomaximal, Sylow
323C22×C61—22no—
324C22×C61—22no—
325C22×C61—22no—
326C22×C61—22no—
327C22×C61—22no—
328C22×C61—22no—
329C22×C61—41no—
330C22×C61—41no—
331C22×C61—41no—
332C22×C61—41no—
333C22×C61—41no—
334C22×C61—41no—
335C22×C61—41no—
336C22×C61—41no—
337C22×C61—42no—
338C22×C61—42no—
339C22×C61—42no—
340C22×C61—81no—
341C22×C61—81no—
342C22×C61—81no—
343C22×C61—81no—
344C22×C61C22×C22⋊C411yescharacteristic
345C22×C61#54611yescharacteristic
346C22×C61#54711yescharacteristic
347C22×C61#57511yescharacteristic
348C22×C61#57511yescharacteristic
349C22×C61#57611yescharacteristic
350C22×C61#57711yescharacteristic
351C4×C61—22no—
352C4×C61—22no—
353C4×C61—22no—
354C4×C61—22no—
355C4×C61—42no—
356C4×C61—42no—
357C4×C61—42no—
358C4×C61C4×#4111yescharacteristic
359C4×C61#52011yescharacteristic
360C4×C61#54611yescharacteristic
361C4×C61#54711yescharacteristic
362Dic61—42no—
363Dic61—81no—
364Dic61—81no—
365Dic61—81no—
366C2×#555D6111yescharacteristic
367C2×#435—611no—
368#2352—611no—
369#1993—611no—
370#1988—611no—
371#1895—611no—
372#1893—611no—
373#1875—611no—
374#1874—611no—
375#1825—611no—
376#1825—611no—
377#1804—611no—
378#1762—611no—
379#1736—611no—
380#1735—611no—
381C2×C61—42no—
382C2×C61—42no—
383C2×C61—82no—
384C2×C61#233911yescharacteristic
385C2×C61#289611yescharacteristic
386C2×C61#289711yescharacteristic
387C2×C61#331911yescharacteristic
388C2×C61#332111yescharacteristic
389C2×C61#334711yescharacteristic
390C2×C61#334811yescharacteristic
391C22×M16—611no—
392C23×C8—611no—
393#555—24no—
394#555Dic6118yescomplemented
395C2×C4⋊Q8C2×D6111yescharacteristic
396C2×#124—21no—
397C2×#124—21no—
398C2×#121—21no—
399C2×#121C2×D6111yescharacteristic
400C2×#121C2×D6111yescharacteristic
401C2×C4×D4C2×D6111yescharacteristic
402C2×C4×D4C2×D6111yescharacteristic
403C2×#117—21no—
404C2×#117—611no—
405C2×#117C2×D6111yescharacteristic
406C2×#117C2×D6111yescharacteristic
407C22×C4⋊C4—611no—
408#435—1224no—
409C2×C4⋊C8—611no—
410C2×#102—611no—
411C2×#102—611no—
412C2×#102—611no—
413C2×#102—611no—
414C2×C22⋊C8—611no—
415C2×C22⋊C8—611no—
416C2×#97—611no—
417#388—1221no—
418#387—1221no—
419#386—1221no—
420#382—611no—
421#380—611no—
422#380—611no—
423C4×C4⋊C4—611no—
424C4×C22⋊C4—1221no—
425#340—611no—
426#340—611no—
427#340—611no—
428#340—611no—
429#340—611no—
430#340—611no—
431#340—611no—
432#340—611no—
433#340—611no—
434#340—611no—
435#340—611no—
436#340—611no—
437C61#2249211yescharacteristic, complemented, Sylow
438C22×Q8—21no—
439C22×D4—21no—
440C22×D4—21no—
441C22×D4C22⋊D6111yescharacteristic
442C22×D4C22×D6111yescharacteristic
443C23×C4—21no—
444C23×C4—1221no—
445C23×C4C22×D6111yescharacteristic
446C23×C4C22×D6111yescharacteristic
447C2×M16—1222no—
448C2×M16—1222no—
449C2×M16—2441no—
450C22×C8—611no—
451C22×C8—611no—
452C22×C8—611no—
453C22×C8—611no—
454C22×C8—1222no—
455C22×C8—1222no—
456C22×C8—2441no—
457C4⋊Q8—22no—
458C4⋊Q8C2×Dic6114yescomplemented
459#124—28no—
460#124—28no—
461#121—28no—
462#121—22no—
463#121—22no—
464#121C2×Dic6114yes—
465#121C2×Dic6114yescomplemented
466C4×D4—22no—
467C4×D4C2×Dic6114yes—
468C4×D4C2×Dic6114yescomplemented
469C4×D4C22⋊D6114yes—
470#117—22no—
471#117—22no—
472#117—28no—
473#117—1222no—
474#117—2441no—
475#117C2×Dic6114yes—
476#117C2×Dic6114yescomplemented
477C2×C4⋊C4—21no—
478C2×C4⋊C4—611no—
479C2×C4⋊C4—611no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4—1222no—
483C2×C4⋊C4—1221no—
484C2×C4⋊C4—2441no—
485C2×C4⋊C4C22⋊D6111yescharacteristic
486C2×C4⋊C4C22×D6111yescharacteristic
487C2×C4⋊C4C22×D6111yescharacteristic
488C2×C4⋊C4C22×D6111yescharacteristic
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—1221no—
495C2×C22⋊C4—1221no—
496C2×C22⋊C4—1221no—
497C2×C22⋊C4C22⋊D6111yescharacteristic
498C2×C22⋊C4C22⋊D6111yescharacteristic
499C2×C42—21no—
500C2×C42—21no—
501C2×C42—1221no—
502C2×C42—1221no—
503C2×C42C22×D6111yescharacteristic
504C4⋊C8—1222no—
505#102—1222no—
506#102—1222no—
507#102—2441no—
508#102—2441no—
509C22⋊C8—1222no—
510C22⋊C8—1222no—
511#97—1222no—
512#95—1221no—
513#95—1221no—
514#95—1221no—
515#95—1221no—
516#95—1221no—
517C24—21no—
518C24C2×C22⋊D6111yescharacteristic
519C24C2×C22⋊D6111yescharacteristic
520C2×Q8—24no—
521C2×Q8—81no—
522C2×Q8—81no—
523C2×D4—24no—
524C2×D4—24no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—41no—
531C2×D4—41no—
532C2×D4—81no—
533C2×D4—81no—
534C2×D4—81no—
535C2×D4—81no—
536C2×D4C22⋊Dic6114yes—
537C2×D4C22×Dic6112yes—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—24no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—1221no—
553C22×C4—1221no—
554C22×C4—1221no—
555C22×C4—1221no—
556C22×C4—4881no—
557C22×C4—2442no—
558C22×C4—2442no—
559C22×C4C22×Dic6112yes—
560C22×C4C22×Dic6112yes—
561C22×C4C2×C22⋊D6112yes—
562C22×C4C2×C22⋊D6112yes—
563C22×C4C2×C22⋊D6111yescharacteristic
564C22×C4C2×C22⋊D6111yescharacteristic
565C22×C4C2×C22⋊D6111yescharacteristic
566C22×C4C2×C22⋊D6111yescharacteristic
567C22×C4C23×D6111yescharacteristic
568M16—2444no—
569C2×C8—612no—
570C2×C8—1221no—
571C2×C8—1221no—
572C2×C8—1221no—
573C2×C8—1221no—
574C2×C8—1221no—
575C2×C8—1221no—
576C2×C8—1221no—
577C2×C8—1221no—
578C2×C8—1221no—
579C2×C8—1221no—
580C2×C8—1221no—
581C2×C8—2444no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—24no—
586C4⋊C4—612no—
587C4⋊C4—1221no—
588C4⋊C4—1221no—
589C4⋊C4—1221no—
590C4⋊C4—1221no—
591C4⋊C4—1221no—
592C4⋊C4—1221no—
593C4⋊C4—1221no—
594C4⋊C4—2442no—
595C4⋊C4C22⋊Dic6114yes—
596C4⋊C4C22×Dic6112yes—
597C4⋊C4C22×Dic6112yes—
598C4⋊C4C22×Dic6112yes—
599C22⋊C4—24no—
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—24no—
603C22⋊C4—24no—
604C22⋊C4—4881no—
605C22⋊C4—2442no—
606C22⋊C4—2442no—
607C22⋊C4C22⋊Dic6114yes—
608C22⋊C4C22⋊Dic6114yes—
609C42—24no—
610C42—24no—
611C42—4881no—
612C42—2442no—
613C42C22×Dic6112yes—
614C42C2×C22⋊D6112yes—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—22no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23C2×C22⋊Dic6112yes—
635C23C2×C22⋊Dic6112yes—
636C23C22×C22⋊D6111yescharacteristic
637Q8—84no—
638D4—22no—
639D4—22no—
640D4—44no—
641D4—41no—
642D4—41no—
643D4—84no—
644D4—84no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—48no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—1222no—
672C2×C4—4884no—
673C2×C4—2441no—
674C2×C4—2441no—
675C2×C4—2441no—
676C2×C4—2441no—
677C2×C4—2441no—
678C2×C4—2441no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4—2441no—
684C2×C4C2×C22⋊Dic6112yes—
685C2×C4C2×C22⋊Dic6112yes—
686C2×C4C2×C22⋊Dic6112yes—
687C2×C4C2×C22⋊Dic6112yes—
688C2×C4C23×Dic6111yescharacteristic
689C2×C4C22×C22⋊D6111yescharacteristic
690C2×C4#41×D6111yescharacteristic
691C2×C4#41×D6111yescharacteristic
692C2×C4#1451982311yescharacteristic
693C2×C4#1451982411yescharacteristic
694C8—1222no—
695C8—2441no—
696C8—2441no—
697C8—2441no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—42no—
713C22—42no—
714C22—42no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22C22×C22⋊Dic6111yescharacteristic
720C22#1684040011yescharacteristic
721C22#1684041111yescharacteristic
722C22#1684056011yescharacteristic
723C22#1684056011yescharacteristic
724C22#1684056511yescharacteristic
725C22#1684057311yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—4881no—
734C4—4881no—
735C4—4881no—
736C4—2442no—
737C4#41×Dic6111yescharacteristic
738C4#1684024511yescharacteristic
739C4#1684040011yescharacteristic
740C4#1684041111yescharacteristic
741C2—42no—
742C2—42no—
743C2—82no—
744C2#2144864911yescharacteristic
745C2#2145433811yescharacteristic
746C2#2145434511yescharacteristic
747C2#2145796911yescharacteristic
748C2#2145799911yescharacteristic
749C2#2145831911yescharacteristic
750C2#2145833411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
Fitting, prime radicalC2×C61×#555C2
socleC23×C61C22×D4
cosocleC22×C4×C61C24
hypercenterC2×#555D61
hypocenterC61#22492
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
1. C2×#16839834C2semidirect
2. #21448748C2semidirect
3. #21446793C2semidirect
4. #21446772C2semidirect
5. #21446258C2semidirect
6. #21446248C2semidirect
7. #21446142C2semidirect
8. #21446137C2semidirect
9. #21445914C2semidirect
10. #21445914C2semidirect
11. #21445829C2semidirect
12. #21445644C2semidirect
13. #21445540C2semidirect
14. #21445535C2semidirect
50. C61×#555C4semidirect
109. C4⋊Q8×C61C2×C4semidirect
116. #121×C61C2×C4semidirect
119. C4×D4×C61C2×C4semidirect
125. #117×C61C2×C4semidirect
394. #555Dic61semidirect
437. C61#22492semidirect
458. C4⋊Q8C2×Dic61semidirect
465. #121C2×Dic61semidirect
468. C4×D4C2×Dic61semidirect
476. #117C2×Dic61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398342
#214487482
#214467932
#214467722
#214462582
#214462482
#214461422
#214461372
#214459142
#214458292
#214456442
#214455402
#214455352
C2×C61×#5552
#2249261