Finite Group Databasebeta

← #29696331

Subgroups — #29696331

Order 15616.

1258 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839834C211yesmaximal, characteristic, complemented
2D4×C4⋊Dic61C211yesmaximal, characteristic, complemented
3#21446789C211yesmaximal, characteristic, complemented
4#21446777C211yesmaximal, characteristic, complemented
5#21446258C211yesmaximal, characteristic, complemented
6#21446248C211yesmaximal, characteristic, complemented
7#21446137C211yesmaximal, characteristic, complemented
8#21446137C211yesmaximal, characteristic, complemented
9#21445914C211yesmaximal, characteristic, complemented
10#21445909C211yesmaximal, characteristic, complemented
11#21445819C211yesmaximal, characteristic, complemented
12#21445644C211yesmaximal, characteristic, complemented
13#21445540C211yesmaximal, characteristic, complemented
14C2×#16839524C211yesmaximal, characteristic, complemented
15C2×C61×#553C211yesmaximal, characteristic
16C22×#11758194C2211yescharacteristic
17C23×#92418C2211yescharacteristic
18C2×D4×Dic61—21no—
19C22×C4⋊Dic61C2211yescharacteristic
20C22×C4⋊Dic61C2211yescharacteristic
21#16839834—24no—
22C2×C4⋊#92418C2211yescharacteristic
23C2×#14519698C2211yescharacteristic
24C2×#14519698C2211yescharacteristic
25C2×#14519698C2211yescharacteristic
26C2×#14519698C2211yescharacteristic
27C2×C22⋊#92418C2211yescharacteristic
28C2×C22⋊#92418C2211yescharacteristic
29C2×#14519688C2211yescharacteristic
30#16839661—21no—
31#16839637—21no—
32#16839637—21no—
33#16839632C2211yescharacteristic
34#16839622C2211yescharacteristic
35#16839622C2211yescharacteristic
36C4×C4⋊Dic61C2211yescharacteristic
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×#553—24no—
50C61×#553C418yescomplemented
51C2×#126×C61—21no—
52C2×#125×C61C2211yescharacteristic
53C2×#123×C61—21no—
54C2×#121×C61—21no—
55C2×#121×C61C2211yescharacteristic
56C2×#121×C61C2211yescharacteristic
57C2×C4×D4×C61—21no—
58C2×C4×D4×C61C2211yescharacteristic
59C2×C4×D4×C61C2211yescharacteristic
60C2×#117×C61C2211yescharacteristic
61C22×C4⋊C4×C61C2211yescharacteristic
62C23×Dic61—21no—
63C23×Dic61—21no—
64C2×#11758194—22no—
65C2×#11758194—22no—
66C2×#11758194—41no—
67C22×#92418—22no—
68C22×#92418—22no—
69C22×#92418—41no—
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74D4×Dic61—44no—
75C2×C4⋊Dic61—22no—
76C2×C4⋊Dic61—22no—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61—21no—
79C2×C4⋊Dic61—21no—
80C2×C4⋊Dic61—21no—
81C2×C4⋊Dic61—41no—
82C2×C4⋊Dic61—41no—
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C4⋊Dic61C2311yescharacteristic
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61—21no—
89C2×C4×Dic61—21no—
90C4⋊#92418—22no—
91#14519698—22no—
92#14519698—22no—
93#14519698—41no—
94#14519698—41no—
95C22⋊#92418—22no—
96C22⋊#92418—22no—
97#14519688—22no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101C22×D4×C61—21no—
102C22×D4×C61—21no—
103C22×D4×C61D411yescharacteristic
104C22×D4×C61C2311yescharacteristic
105C23×C4×C61—21no—
106C23×C4×C61—21no—
107C23×C4×C61C2311yescharacteristic
108C23×C4×C61C2311yescharacteristic
109#126×C61—28no—
110#125×C61—22no—
111#125×C61C2×C414yescomplemented
112#123×C61—28no—
113#121×C61—28no—
114#121×C61—22no—
115#121×C61—22no—
116#121×C61C2×C414yescomplemented
117#121×C61C2×C414yescomplemented
118C4×D4×C61—28no—
119C4×D4×C61—22no—
120C4×D4×C61C2×C414yes—
121C4×D4×C61C2×C414yescomplemented
122C4×D4×C61D414yes—
123#117×C61—22no—
124#117×C61C2×C414yescomplemented
125C2×C4⋊C4×C61—22no—
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61—21no—
128C2×C4⋊C4×C61—21no—
129C2×C4⋊C4×C61C2×C414yescomplemented
130C2×C4⋊C4×C61D411yescharacteristic
131C2×C4⋊C4×C61C2311yescharacteristic
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C22⋊C4×C61—21no—
135C2×C22⋊C4×C61—21no—
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61—21no—
138C2×C22⋊C4×C61D411yescharacteristic
139C2×C22⋊C4×C61D411yescharacteristic
140C2×C42×C61—21no—
141C2×C42×C61C2311yescharacteristic
142C24×C61—21no—
143C24×C61C2×D411yescharacteristic
144C24×C61C2×D411yescharacteristic
145C2×D4×C61—22no—
146C2×D4×C61—22no—
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—42no—
155C2×D4×C61—42no—
156C2×D4×C61—81no—
157C2×D4×C61—81no—
158C2×D4×C61C22⋊C414yes—
159C2×D4×C61C22×C412yes—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
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—24no—
172C22×C4×C61—24no—
173C22×C4×C61—81no—
174C22×C4×C61—81no—
175C22×C4×C61—81no—
176C22×C4×C61—81no—
177C22×C4×C61C22×C412yes—
178C22×C4×C61C22×C412yes—
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D412yes—
184C22×C4×C61C2×D412yes—
185C22×C4×C61C2411yescharacteristic
186C22×Dic61—21no—
187C22×Dic61—21no—
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61—42no—
191C22×Dic61—42no—
192C22×Dic61—42no—
193C22×Dic61—42no—
194C22×Dic61—81no—
195C22×Dic61—81no—
196C4⋊C4×C61—24no—
197C4⋊C4×C61—24no—
198C4⋊C4×C61—24no—
199C4⋊C4×C61—21no—
200C4⋊C4×C61—21no—
201C4⋊C4×C61—21no—
202C4⋊C4×C61C22⋊C414yes—
203C4⋊C4×C61C22×C412yes—
204C4⋊C4×C61C22×C412yes—
205C4⋊C4×C61C22×C412yes—
206C22⋊C4×C61—24no—
207C22⋊C4×C61—24no—
208C22⋊C4×C61—24no—
209C22⋊C4×C61—24no—
210C22⋊C4×C61C22⋊C414yes—
211C22⋊C4×C61C22⋊C414yes—
212C42×C61—24no—
213C42×C61C22×C412yes—
214C42×C61C2×D412yes—
215C22⋊Dic61—42no—
216C22⋊Dic61—42no—
217C4⋊Dic61—21no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—21no—
223C4⋊Dic61—21no—
224C4⋊Dic61—42no—
225C4⋊Dic61—42no—
226C4⋊Dic61—42no—
227C4⋊Dic61—81no—
228C4⋊Dic61#4112yes—
229C4×Dic61—42no—
230#11758194—44no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—44no—
243C2×#92418#4112yes—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—22no—
255C23×C61—41no—
256C23×C61—41no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61C2×C22⋊C412yes—
262C23×C61C2×C22⋊C412yes—
263C23×C61AGL(1,ℤ/8)12yes—
264C23×C61#13712yes—
265C23×C61C22×D411yescharacteristic
266D4×C61—28no—
267D4×C61—22no—
268D4×C61—22no—
269D4×C61—48no—
270D4×C61—41no—
271D4×C61—41no—
272D4×C61—84no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
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—22no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—84no—
299C2×C4×C61—84no—
300C2×C4×C61C2×C22⋊C412yes—
301C2×C4×C61C2×C22⋊C412yes—
302C2×C4×C61C2×C22⋊C412yes—
303C2×C4×C61C2×C22⋊C412yes—
304C2×C4×C61C23×C411yescharacteristic
305C2×C4×C61C22×D411yescharacteristic
306C2×C4×C61C2×#4111yescharacteristic
307C2×C4×C61C2×#4111yescharacteristic
308C2×C4×C61H(5,𝔽2)11yescharacteristic
309C2×C4×C612−1+411yescharacteristic
310C2×Dic61—22no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—41no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—84no—
323C2×Dic61—84no—
324#92418—22no—
325#92418—41no—
326#92418—41no—
327#92418—41no—
328#22493—611nomaximal, Sylow
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—22no—
332C22×C61—22no—
333C22×C61—22no—
334C22×C61—22no—
335C22×C61—22no—
336C22×C61—22no—
337C22×C61—22no—
338C22×C61—41no—
339C22×C61—41no—
340C22×C61—41no—
341C22×C61—41no—
342C22×C61—42no—
343C22×C61—42no—
344C22×C61—42no—
345C22×C61—81no—
346C22×C61—81no—
347C22×C61—81no—
348C22×C61—81no—
349C22×C61#41714yes—
350C22×C61C22×C22⋊C411yescharacteristic
351C22×C61#54611yescharacteristic
352C22×C61#54711yescharacteristic
353C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
354C22×C61C2×#13711yescharacteristic
355C22×C61#57611yescharacteristic
356C22×C61#57711yescharacteristic
357C4×C61—22no—
358C4×C61—22no—
359C4×C61—22no—
360C4×C61—22no—
361C4×C61—42no—
362C4×C61—42no—
363C4×C61—42no—
364C4×C61C4×#4111yescharacteristic
365C4×C61#52011yescharacteristic
366C4×C61#54611yescharacteristic
367C4×C61#54711yescharacteristic
368Dic61—42no—
369Dic61—81no—
370Dic61—81no—
371Dic61—81no—
372C2×#553D6111yescharacteristic
373C2×#435—611no—
374D4×C4⋊C4—611no—
375#1992—611no—
376#1989—611no—
377#1895—611no—
378#1893—611no—
379#1874—611no—
380#1874—611no—
381#1825—611no—
382#1824—611no—
383#1802—611no—
384#1762—611no—
385#1736—611no—
386C2×#340—611no—
387C2×C61—24no—
388C2×C61—42no—
389C2×C61—82no—
390C2×C61#233911yescharacteristic
391C2×C61C2×#41711yescharacteristic
392C2×C61#289711yescharacteristic
393C2×C61#331811yescharacteristic
394C2×C61#332011yescharacteristic
395C2×C61#334511yescharacteristic
396C2×C61#334611yescharacteristic
397C22×M16—611no—
398C23×C8—611no—
399#553—24no—
400#553Dic6118yescomplemented
401C2×#126—21no—
402C2×#125C2×D6111yescharacteristic
403C2×#123—21no—
404C2×#121—21no—
405C2×#121C2×D6111yescharacteristic
406C2×#121C2×D6111yescharacteristic
407C2×C4×D4—21no—
408C2×C4×D4—1221no—
409C2×C4×D4C2×D6111yescharacteristic
410C2×C4×D4C2×D6111yescharacteristic
411C2×#117C2×D6111yescharacteristic
412C22×C4⋊C4—611no—
413C22×C4⋊C4—611no—
414C22×C4⋊C4C2×D6111yescharacteristic
415#435—1224no—
416C2×C4⋊C8—611no—
417C2×#102—611no—
418C2×#102—611no—
419C2×#102—611no—
420C2×#102—611no—
421C2×C22⋊C8—611no—
422C2×C22⋊C8—611no—
423C2×#97—611no—
424#389—1221no—
425#385—1221no—
426#385—1221no—
427#384—611no—
428#380—611no—
429#380—611no—
430C4×C4⋊C4—611no—
431#340—611no—
432#340—611no—
433#340—611no—
434#340—611no—
435#340—611no—
436#340—611no—
437#340—611no—
438#340—611no—
439#340—611no—
440#340—611no—
441#340—611no—
442#340—611no—
443C61#2249311yescharacteristic, complemented, Sylow
444C22×D4—21no—
445C22×D4—21no—
446C22×D4C22⋊D6111yescharacteristic
447C22×D4C22×D6111yescharacteristic
448C23×C4—21no—
449C23×C4—21no—
450C23×C4—1221no—
451C23×C4—1221no—
452C23×C4C22×D6111yescharacteristic
453C23×C4C22×D6111yescharacteristic
454C2×M16—1222no—
455C2×M16—1222no—
456C2×M16—2441no—
457C22×C8—611no—
458C22×C8—611no—
459C22×C8—611no—
460C22×C8—611no—
461C22×C8—1222no—
462C22×C8—1222no—
463C22×C8—2441no—
464#126—28no—
465#125—22no—
466#125C2×Dic6114yescomplemented
467#123—28no—
468#121—28no—
469#121—22no—
470#121—22no—
471#121C2×Dic6114yescomplemented
472#121C2×Dic6114yescomplemented
473C4×D4—28no—
474C4×D4—22no—
475C4×D4—2444no—
476C4×D4C2×Dic6114yes—
477C4×D4C2×Dic6114yescomplemented
478C4×D4C22⋊D6114yes—
479#117—22no—
480#117C2×Dic6114yescomplemented
481C2×C4⋊C4—21no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4—611no—
487C2×C4⋊C4—611no—
488C2×C4⋊C4—611no—
489C2×C4⋊C4—1222no—
490C2×C4⋊C4—1222no—
491C2×C4⋊C4—1221no—
492C2×C4⋊C4—1221no—
493C2×C4⋊C4—1221no—
494C2×C4⋊C4—1221no—
495C2×C4⋊C4—2441no—
496C2×C4⋊C4—2441no—
497C2×C4⋊C4C2×Dic6114yescomplemented
498C2×C4⋊C4C22⋊D6111yescharacteristic
499C2×C4⋊C4C22×D6111yescharacteristic
500C2×C4⋊C4C22×D6111yescharacteristic
501C2×C4⋊C4C22×D6111yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—1221no—
507C2×C22⋊C4—1221no—
508C2×C22⋊C4C22⋊D6111yescharacteristic
509C2×C22⋊C4C22⋊D6111yescharacteristic
510C2×C42—21no—
511C2×C42—1221no—
512C2×C42C22×D6111yescharacteristic
513C4⋊C8—1222no—
514#102—1222no—
515#102—1222no—
516#102—2441no—
517#102—2441no—
518C22⋊C8—1222no—
519C22⋊C8—1222no—
520#97—1222no—
521#95—1221no—
522#95—1221no—
523#95—1221no—
524C24—21no—
525C24C2×C22⋊D6111yescharacteristic
526C24C2×C22⋊D6111yescharacteristic
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—24no—
530C2×D4—24no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—42no—
537C2×D4—42no—
538C2×D4—81no—
539C2×D4—81no—
540C2×D4C22⋊Dic6114yes—
541C2×D4C22×Dic6112yes—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—81no—
556C22×C4—81no—
557C22×C4—81no—
558C22×C4—81no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—1221no—
563C22×C4—4881no—
564C22×C4—4881no—
565C22×C4—2442no—
566C22×C4—2442no—
567C22×C4—2442no—
568C22×C4—2442no—
569C22×C4C22×Dic6112yes—
570C22×C4C22×Dic6112yes—
571C22×C4C2×C22⋊D6112yes—
572C22×C4C2×C22⋊D6112yes—
573C22×C4C2×C22⋊D6111yescharacteristic
574C22×C4C2×C22⋊D6111yescharacteristic
575C22×C4C2×C22⋊D6111yescharacteristic
576C22×C4C2×C22⋊D6111yescharacteristic
577C22×C4C23×D6111yescharacteristic
578M16—2444no—
579C2×C8—612no—
580C2×C8—1221no—
581C2×C8—1221no—
582C2×C8—1221no—
583C2×C8—1221no—
584C2×C8—1221no—
585C2×C8—1221no—
586C2×C8—1221no—
587C2×C8—1221no—
588C2×C8—1221no—
589C2×C8—1221no—
590C2×C8—1221no—
591C2×C8—2444no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—612no—
599C4⋊C4—1221no—
600C4⋊C4—1221no—
601C4⋊C4—1221no—
602C4⋊C4—1221no—
603C4⋊C4—1221no—
604C4⋊C4—1221no—
605C4⋊C4—1221no—
606C4⋊C4—4881no—
607C4⋊C4—2442no—
608C4⋊C4—2442no—
609C4⋊C4—2442no—
610C4⋊C4C22⋊Dic6114yes—
611C4⋊C4C22×Dic6112yes—
612C4⋊C4C22×Dic6112yes—
613C4⋊C4C22×Dic6112yes—
614C22⋊C4—24no—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—2442no—
619C22⋊C4—2442no—
620C22⋊C4C22⋊Dic6114yes—
621C22⋊C4C22⋊Dic6114yes—
622C42—24no—
623C42—2442no—
624C42C22×Dic6112yes—
625C42C2×C22⋊D6112yes—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—22no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23C2×C22⋊Dic6112yes—
644C23C2×C22⋊Dic6112yes—
645C23#1451980212yes—
646C23#1451980712yes—
647C23C22×C22⋊D6111yescharacteristic
648D4—28no—
649D4—22no—
650D4—22no—
651D4—48no—
652D4—41no—
653D4—41no—
654D4—84no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—84no—
681C2×C4—84no—
682C2×C4—1222no—
683C2×C4—4884no—
684C2×C4—4884no—
685C2×C4—2441no—
686C2×C4—2441no—
687C2×C4—2441no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4—2441no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4C2×C22⋊Dic6112yes—
697C2×C4C2×C22⋊Dic6112yes—
698C2×C4C2×C22⋊Dic6112yes—
699C2×C4C2×C22⋊Dic6112yes—
700C2×C4C23×Dic6111yescharacteristic
701C2×C4C22×C22⋊D6111yescharacteristic
702C2×C4#41×D6111yescharacteristic
703C2×C4#41×D6111yescharacteristic
704C2×C4#1451982311yescharacteristic
705C2×C4#1451982411yescharacteristic
706C8—1222no—
707C8—2441no—
708C8—2441no—
709C8—2441no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22#1683976314yes—
731C22C22×C22⋊Dic6111yescharacteristic
732C22#1684040011yescharacteristic
733C22#1684041111yescharacteristic
734C22C2×#1451980211yescharacteristic
735C22C2×#1451980711yescharacteristic
736C22#1684056511yescharacteristic
737C22#1684057311yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—22no—
742C4—42no—
743C4—42no—
744C4—42no—
745C4—4881no—
746C4—4881no—
747C4—4881no—
748C4—2442no—
749C4#41×Dic6111yescharacteristic
750C4#1684024511yescharacteristic
751C4#1684040011yescharacteristic
752C4#1684041111yescharacteristic
753C2—24no—
754C2—42no—
755C2—82no—
756C2#2144864911yescharacteristic
757C2C2×#1683976311yescharacteristic
758C2#2145434511yescharacteristic
759C2#2145795411yescharacteristic
760C2#2145798411yescharacteristic
761C2#2145828311yescharacteristic
762C2#2145830411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
Fitting, prime radicalC2×C61×#553C2
socleC23×C61C22×D4
cosocleC22×C4×C61C24
hypercenterC2×#553D61
hypocenterC61#22493
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#16839834C2semidirect
2. D4×C4⋊Dic61C2semidirect
3. #21446789C2semidirect
4. #21446777C2semidirect
5. #21446258C2semidirect
6. #21446248C2semidirect
7. #21446137C2semidirect
8. #21446137C2semidirect
9. #21445914C2semidirect
10. #21445909C2semidirect
11. #21445819C2semidirect
12. #21445644C2semidirect
13. #21445540C2semidirect
14. C2×#16839524C2semidirect
50. C61×#553C4semidirect
111. #125×C61C2×C4semidirect
116. #121×C61C2×C4semidirect
117. #121×C61C2×C4semidirect
121. C4×D4×C61C2×C4semidirect
124. #117×C61C2×C4semidirect
129. C2×C4⋊C4×C61C2×C4semidirect
400. #553Dic61semidirect
443. C61#22493semidirect
466. #125C2×Dic61semidirect
471. #121C2×Dic61semidirect
472. #121C2×Dic61semidirect
477. C4×D4C2×Dic61semidirect
480. #117C2×Dic61semidirect
497. C2×C4⋊C4C2×Dic61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398342
D4×C4⋊Dic612
#214467892
#214467772
#214462582
#214462482
#214461372
#214459142
#214459092
#214458192
#214456442
#214455402
C2×#168395242
C2×C61×#5532
#2249361