Finite Group Databasebeta

← #29677830

Subgroups — #29677830

Order 15616.

1522 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840238C211yesmaximal, characteristic
2C2×#16839769C211yesmaximal, characteristic
3C2×#103×D61C211yesmaximal, characteristic
4C2×#16839716C211yesmaximal, characteristic
5#21448173C211yesmaximal, characteristic
6#21445652C211yesmaximal, characteristic, complemented
7#21445651C211yesmaximal, characteristic, complemented
8#21445649C211yesmaximal, characteristic, complemented
9#21445648C211yesmaximal, characteristic, complemented
10#103×Dic61C211yesmaximal, characteristic, complemented
11C4×#14519702C211yesmaximal, characteristic, complemented
12#21445638C211yesmaximal, characteristic, complemented
13#21445537C211yesmaximal, characteristic
14#21445534C211yesmaximal, characteristic
15C4×#103×C61C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19#16840238—24no—
20#16840238C418yescomplemented
21C2×Q8×Dic61C2211yescharacteristic
22C2×C4×Dic122—21no—
23C2×C4×Dic122C2211yescharacteristic
24C2×#14519742—21no—
25C2×#14519742C2211yescharacteristic
26C2×#14519735—21no—
27C2×#14519735C2211yescharacteristic
28C2×#14519735C2211yescharacteristic
29C2×#14519734—21no—
30C2×#14519734C2211yescharacteristic
31C2×C4⋊C4×D61C2211yescharacteristic
32#16839769C418yescomplemented
33C2×#14519702C2211yescharacteristic
34C2×#14519702C2211yescharacteristic
35C2×#14519701C2211yescharacteristic
36C2×#14519701C2211yescharacteristic
37C2×#14519700C2211yescharacteristic
38C2×#14519700C2211yescharacteristic
39#103×D61C418yescomplemented
40#16839716—24no—
41C2×#14519688C2211yescharacteristic
42C2×#14519687C2211yescharacteristic
43C2×C8×Dic61C2211yescharacteristic
44C4⋊C4×Dic61C2211yescharacteristic
45C4⋊C4×Dic61C2211yescharacteristic
46C4×#11758196—21no—
47C4×C4⋊Dic61C2211yescharacteristic
48#16839613—21no—
49C4×#11758198—21no—
50#16839609—21no—
51#16839525C2211yescharacteristic
52#16839525C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839524C2211yescharacteristic
56#16839524C2211yescharacteristic
57C2×C4×Q8×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×C4×C8×C61C2211yescharacteristic
61C4×C4⋊C4×C61C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C61×#340C2211yescharacteristic
64C22×Dic122—21no—
65C22×Dic122C2311yescharacteristic
66C2×Q8×D61—22no—
67C2×Q8×D61—22no—
68C2×Q8×D61—22no—
69C2×Q8×D61C2×C414yes—
70C2×Q8×D61C2×C414yes—
71C2×Q8×D61C2×C414yes—
72C22×C4×D61—21no—
73C22×C4×D61—21no—
74C22×C4×D61C2311yescharacteristic
75C2×#11758189—22no—
76C2×#11758189—22no—
77C2×#11758189C2×C414yes—
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80C2×C8×D61—22no—
81C2×C8×D61—22no—
82C2×C8×D61C2×C414yes—
83Q8×Dic61—22no—
84Q8×Dic61C2×C414yescomplemented
85C4×Dic122—22no—
86C4×Dic122—28no—
87C4×Dic122C2×C414yescomplemented
88#14519742—28no—
89#14519742—22no—
90#14519742C2×C414yescomplemented
91#14519735—22no—
92#14519735—22no—
93#14519735—28no—
94#14519735C2×C414yes—
95#14519735C2×C414yes—
96#14519734—28no—
97#14519734C2×C414yes—
98#14519734D414yes—
99C2×C4⋊Dic61—21no—
100C2×C4⋊Dic61C2311yescharacteristic
101C2×C4⋊Dic61C2311yescharacteristic
102C2×C4⋊Dic61C2311yescharacteristic
103C2×#11758196—21no—
104C2×#11758196—21no—
105C2×#11758196—21no—
106C2×#11758196D411yescharacteristic
107C2×#11758196D411yescharacteristic
108C4⋊C4×D61—22no—
109C4⋊C4×D61C2×C414yes—
110C2×#11758198—21no—
111C2×#11758198—21no—
112C2×#11758198D411yescharacteristic
113C2×#11758198D411yescharacteristic
114C2×C4×Dic61—21no—
115C2×C4×Dic61—21no—
116C2×C4×Dic61—21no—
117C2×C4×Dic61—21no—
118C2×C4×Dic61—21no—
119C2×C4×Dic61—21no—
120C2×C4×Dic61—21no—
121C2×C4×Dic61—21no—
122C2×C4×Dic61C2311yescharacteristic
123#14519702C2×C414yes—
124#14519702C2×C414yescomplemented
125#14519701C2×C414yes—
126#14519701C2×C414yescomplemented
127#14519700C2×C414yes—
128#14519700C2×C414yescomplemented
129#14519688—22no—
130#14519687—22no—
131C8×Dic61—22no—
132#14519684—21no—
133#14519684—21no—
134#14519684—21no—
135C22×Q8×C61C2311yescharacteristic
136C22×C8×C61C2311yescharacteristic
137C22×C8×C61C2311yescharacteristic
138C4×Q8×C61—22no—
139C4×Q8×C61C2×C414yescomplemented
140C2×C4⋊C4×C61—21no—
141C2×C4⋊C4×C61C2311yescharacteristic
142C2×C4⋊C4×C61C2311yescharacteristic
143C2×C4⋊C4×C61C2311yescharacteristic
144C2×C42×C61—21no—
145C2×C42×C61—21no—
146C2×C42×C61C2311yescharacteristic
147#103×C61C2×C414yes—
148#103×C61C2×C414yescomplemented
149C4×C8×C61—22no—
150#95×C61—21no—
151C23×D61C2×D411yescharacteristic
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61C22×C412yes—
156C2×Q8×C61C22×C412yes—
157C2×Q8×C61C22×C412yes—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61C2×D411yescharacteristic
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2411yescharacteristic
165C22×Dic61—21no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61C2×D411yescharacteristic
170C22×Dic61C2×D411yescharacteristic
171C22×Dic61C2×D411yescharacteristic
172Q8×D61—28no—
173Q8×D61—28no—
174Q8×D61—28no—
175Q8×D61C42116yescomplemented
176C2×C4×D61—24no—
177C2×C4×D61—24no—
178C2×C4×D61—24no—
179C2×C4×D61—24no—
180C2×C4×D61—81no—
181C2×C4×D61—81no—
182C2×C4×D61C22×C412yes—
183C2×C4×D61C22×C412yes—
184C2×C4×D61C22×C412yes—
185C2×C4×D61C2×D412yes—
186C2×C4×D61#4112yes—
187C2×C4×D61#4112yes—
188C2×Dic122—21no—
189C2×Dic122—21no—
190C2×Dic122—21no—
191C2×Dic122—24no—
192C2×Dic122—24no—
193C2×Dic122—24no—
194C2×Dic122C22×C412yes—
195C2×Dic122C22×C412yes—
196C2×Dic122C22×C412yes—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61C22×C412yes—
202C2×C8×C61C22×C412yes—
203C4⋊C4×C61—24no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61C22×C412yes—
208C4⋊C4×C61C22×C412yes—
209C4⋊C4×C61C22×C412yes—
210C42×C61—24no—
211C42×C61—81no—
212C42×C61C22×C412yes—
213C42×C61C2×D412yes—
214#11758198—24no—
215#11758198—24no—
216#11758198C22⋊C414yes—
217#11758198C22⋊C414yes—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—24no—
222C4⋊Dic61C22×C412yes—
223C4⋊Dic61C22×C412yes—
224C4⋊Dic61C22×C412yes—
225#11758196—24no—
226#11758196—24no—
227#11758196—24no—
228#11758196C22⋊C414yes—
229#11758196C22⋊C414yes—
230C4×Dic61—24no—
231C4×Dic61—24no—
232C4×Dic61—24no—
233C4×Dic61—24no—
234C4×Dic61—24no—
235C4×Dic61—81no—
236C4×Dic61—81no—
237C4×Dic61—81no—
238C4×Dic61C22×C412yes—
239C4×Dic61C2×D412yes—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418C22×C412yes—
245C2×#92418C22×C412yes—
246#11758189—28no—
247C8×D61—28no—
248C23×C61C22×D411yescharacteristic
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—21no—
252C22×D61—21no—
253C22×D61C2×C22⋊C412yes—
254C22×D61C4×D412yes—
255C22×D61C4×D412yes—
256Q8×C61—22no—
257Q8×C61—22no—
258Q8×C61—22no—
259Q8×C61C2×C4214yes—
260C2×C4×C61—22no—
261C2×C4×C61—22no—
262C2×C4×C61—22no—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—41no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61—41no—
274C2×C4×C61—41no—
275C2×C4×C61—41no—
276C2×C4×C61C2×C22⋊C412yes—
277C2×C4×C61C2×C22⋊C412yes—
278C2×C4×C61C23×C411yescharacteristic
279C2×C4×C61C23×C411yescharacteristic
280C2×C4×C61C23×C411yescharacteristic
281C2×C4×C61C22×D411yescharacteristic
282C2×C4×C61C2×#4111yescharacteristic
283C2×C4×C61C2×#4111yescharacteristic
284C2×Dic61—22no—
285C2×Dic61—22no—
286C2×Dic61—22no—
287C2×Dic61—21no—
288C2×Dic61—21no—
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61—22no—
292C2×Dic61—22no—
293C2×Dic61—22no—
294C2×Dic61—41no—
295C2×Dic61—41no—
296C2×Dic61—41no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61C2×C22⋊C412yes—
301C2×Dic61C2×C22⋊C412yes—
302C2×Dic61C2×C22⋊C412yes—
303C2×Dic61C4×D412yes—
304C2×Dic61C4×D412yes—
305C4×D61—216no—
306C4×D61—84no—
307C4×D61C2×C4214yes—
308C4×D61#11714yes—
309C4×D61C4×D414yes—
310C4×D61C4×D414yes—
311Dic122—22no—
312Dic122—22no—
313Dic122—22no—
314Dic122—216no—
315Dic122C2×C4214yes—
316C8×C61—22no—
317C8×C61—22no—
318#92418—22no—
319#92418—22no—
320#20417—611nomaximal, Sylow
321C22×C61C22×C22⋊C411yescharacteristic
322C22×C61C2×C4×D411yescharacteristic
323C22×C61C2×C4×D411yescharacteristic
324C22×C61#57711yescharacteristic
325C22×C61#57711yescharacteristic
326C22×C61#57811yescharacteristic
327C22×C61#57811yescharacteristic
328C2×D61—22no—
329C2×D61—22no—
330C2×D61—22no—
331C2×D61—22no—
332C2×D61—22no—
333C2×D61—22no—
334C2×D61C4×C22⋊C414yes—
335C4×C61—22no—
336C4×C61—22no—
337C4×C61—24no—
338C4×C61—42no—
339C4×C61—42no—
340C4×C61—42no—
341C4×C61C22×C4211yescharacteristic
342C4×C61C2×#11711yescharacteristic
343C4×C61C2×C4×D411yescharacteristic
344C4×C61C2×C4×D411yescharacteristic
345Dic61—22no—
346Dic61—22no—
347Dic61—24no—
348Dic61—42no—
349Dic61—42no—
350Dic61—42no—
351Dic61C4×C22⋊C414yes—
352C2×#519—611no—
353C2×#419—611no—
354C22×#103—611no—
355C2×#405—611no—
356#2274—611no—
357#1763—611no—
358#1763—611no—
359#1763—611no—
360#1763—611no—
361C4×#103—611no—
362C4×#103—611no—
363C4×#103—611no—
364C4×#103D6111yescharacteristic, complemented
365#1736—611no—
366#1735—611no—
367C2×C61C2×C4×C22⋊C411yescharacteristic
368C2×C61#289811yescharacteristic
369C2×C61#289811yescharacteristic
370C2×C61#294711yescharacteristic
371C2×C61#294711yescharacteristic
372C2×C61#294911yescharacteristic
373C2×C61#295011yescharacteristic
374D61—24no—
375C23×Q8—611no—
376C22×M16—611no—
377C23×C8—611no—
378#519—618no—
379#519—1224no—
380C2×C4×Q8—611no—
381C2×C4×Q8—611no—
382C2×C4×Q8—611no—
383C2×C4×Q8—1221no—
384C2×C4×Q8—1221no—
385C2×C4×Q8C2×D6111yescharacteristic
386C2×#117—611no—
387C2×#117—611no—
388C2×#117—611no—
389C2×#117—1221no—
390C2×#117—1221no—
391C22×C4⋊C4—611no—
392#419—618no—
393C2×#103—611no—
394C2×#103—611no—
395C2×#103—611no—
396C2×#103—611no—
397C2×#103—611no—
398C2×#103—611no—
399C2×#103—618no—
400C2×#103C2×D6111yescharacteristic
401C2×#103C2×D6111yescharacteristic
402#405—1224no—
403C2×#97—611no—
404C2×#97—611no—
405C2×C4×C8—611no—
406C2×C4×C8C2×D6111yescharacteristic
407C4×C4⋊C4—611no—
408C4×C4⋊C4—611no—
409C4×C4⋊C4—611no—
410C4×C4⋊C4—1221no—
411C4×C4⋊C4—1221no—
412C4×C4⋊C4C2×D6111yescharacteristic
413C4×C22⋊C4—1221no—
414C4×C22⋊C4—1221no—
415#340—611no—
416#340—611no—
417#340—611no—
418#340—611no—
419#340—611no—
420#340—611no—
421#340C2×D6111yescharacteristic
422#340C2×D6111yescharacteristic
423C61#2041711yescharacteristic, complemented, Sylow
424C22×Q8—614no—
425C22×Q8—614no—
426C22×Q8—614no—
427C22×Q8—611no—
428C22×Q8—1221no—
429C22×Q8—1222no—
430C22×Q8—1222no—
431C22×Q8—1222no—
432C22×Q8C22×D6111yescharacteristic
433C23×C4—611no—
434C23×C4—1221no—
435C23×C4—1221no—
436C2×M16—614no—
437C2×M16—1222no—
438C2×M16—1222no—
439C22×C8—611no—
440C22×C8—611no—
441C22×C8—614no—
442C22×C8—1222no—
443C22×C8—1222no—
444C22×C8C22×D6111yescharacteristic
445C22×C8C22×D6111yescharacteristic
446C4×Q8—22no—
447C4×Q8—614no—
448C4×Q8—614no—
449C4×Q8—614no—
450C4×Q8—1228no—
451C4×Q8—1222no—
452C4×Q8—1222no—
453C4×Q8—1228no—
454C4×Q8—1222no—
455C4×Q8C4×D6114yescomplemented
456#117—614no—
457#117—614no—
458#117—614no—
459#117—614no—
460#117—1228no—
461#117—1228no—
462#117—1222no—
463#117—1222no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—611no—
466C2×C4⋊C4—611no—
467C2×C4⋊C4—611no—
468C2×C4⋊C4—611no—
469C2×C4⋊C4—611no—
470C2×C4⋊C4—614no—
471C2×C4⋊C4—1222no—
472C2×C4⋊C4—1221no—
473C2×C4⋊C4—1221no—
474C2×C4⋊C4—1221no—
475C2×C4⋊C4—1221no—
476C2×C4⋊C4C22×D6111yescharacteristic
477C2×C4⋊C4C22×D6111yescharacteristic
478C2×C4⋊C4C22×D6111yescharacteristic
479C2×C22⋊C4—611no—
480C2×C22⋊C4—611no—
481C2×C22⋊C4—1221no—
482C2×C22⋊C4—1221no—
483C2×C42—21no—
484C2×C42—21no—
485C2×C42—611no—
486C2×C42—1221no—
487C2×C42—1221no—
488C2×C42—1221no—
489C2×C42—1221no—
490C2×C42—1221no—
491C2×C42—1221no—
492C2×C42—1221no—
493C2×C42—1221no—
494C2×C42C22×D6111yescharacteristic
495#103—614no—
496#103—614no—
497#103—614no—
498#103—614no—
499#103—614no—
500#103—614no—
501#103C4×D6114yes—
502#103C4×D6114yescomplemented
503#97—1222no—
504#97—1222no—
505C4×C8—22no—
506C4×C8—1222no—
507#95—21no—
508#95—1221no—
509#95—1221no—
510#95—1221no—
511C24—611no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—6116no—
516C2×Q8—612no—
517C2×Q8—612no—
518C2×Q8—612no—
519C2×Q8—1224no—
520C2×Q8—1224no—
521C2×Q8—1224no—
522C2×Q8—1228no—
523C2×Q8—1228no—
524C2×Q8—1228no—
525C2×Q8—1221no—
526C2×Q8—1221no—
527C2×Q8—1221no—
528C2×Q8C2×C4×D6112yes—
529C2×Q8C2×C4×D6112yes—
530C2×Q8C2×C4×D6112yes—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—611no—
536C22×C4—612no—
537C22×C4—612no—
538C22×C4—612no—
539C22×C4—612no—
540C22×C4—612no—
541C22×C4—612no—
542C22×C4—611no—
543C22×C4—611no—
544C22×C4—1224no—
545C22×C4—1224no—
546C22×C4—1224no—
547C22×C4—1224no—
548C22×C4—1221no—
549C22×C4—1221no—
550C22×C4—1221no—
551C22×C4—1221no—
552C22×C4—4881no—
553C22×C4—4881no—
554C22×C4D4×D6111yescharacteristic
555C22×C4D4×D6111yescharacteristic
556C22×C4C23×D6111yescharacteristic
557M16—1228no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—612no—
563C2×C8—612no—
564C2×C8—1228no—
565C2×C8—1221no—
566C2×C8—1221no—
567C2×C8—1221no—
568C2×C8—1221no—
569C2×C8C2×C4×D6112yes—
570C2×C8C2×C4×D6112yes—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—24no—
575C4⋊C4—614no—
576C4⋊C4—614no—
577C4⋊C4—612no—
578C4⋊C4—612no—
579C4⋊C4—612no—
580C4⋊C4—1224no—
581C4⋊C4—1224no—
582C4⋊C4—1224no—
583C4⋊C4—1221no—
584C4⋊C4—1221no—
585C4⋊C4—1221no—
586C4⋊C4—1224no—
587C4⋊C4C2×C4×D6112yes—
588C4⋊C4C2×C4×D6112yes—
589C4⋊C4C2×C4×D6112yes—
590C22⋊C4—614no—
591C22⋊C4—614no—
592C22⋊C4—1224no—
593C22⋊C4—1224no—
594C42—24no—
595C42—81no—
596C42—612no—
597C42—612no—
598C42—1224no—
599C42—1224no—
600C42—1224no—
601C42—1224no—
602C42—1224no—
603C42—4881no—
604C42—4881no—
605C42—4881no—
606C42C2×C4×D6112yes—
607C42D4×D6112yes—
608C23—612no—
609C23—612no—
610C23—612no—
611C23—1221no—
612C23—1221no—
613C23—1221no—
614C23—1221no—
615C23C2×D4×D6111yescharacteristic
616Q8—22no—
617Q8—22no—
618Q8—22no—
619Q8—614no—
620Q8—12216no—
621Q8—1222no—
622Q8—1222no—
623Q8—1222no—
624Q8C42×D6114yes—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—612no—
642C2×C4—612no—
643C2×C4—612no—
644C2×C4—614no—
645C2×C4—614no—
646C2×C4—614no—
647C2×C4—614no—
648C2×C4—612no—
649C2×C4—612no—
650C2×C4—12216no—
651C2×C4—1222no—
652C2×C4—1222no—
653C2×C4—1222no—
654C2×C4—1221no—
655C2×C4—1221no—
656C2×C4—1221no—
657C2×C4—1221no—
658C2×C4—1222no—
659C2×C4—1222no—
660C2×C4—1222no—
661C2×C4—4884no—
662C2×C4—2441no—
663C2×C4—2441no—
664C2×C4—2441no—
665C2×C4—2441no—
666C2×C4—2441no—
667C2×C4—2441no—
668C2×C4C22⋊C4×D6112yes—
669C2×C4C22⋊C4×D6112yes—
670C2×C4C22×C4×D6111yescharacteristic
671C2×C4C22×C4×D6111yescharacteristic
672C2×C4C22×C4×D6111yescharacteristic
673C2×C4C2×D4×D6111yescharacteristic
674C2×C4#41×D6111yescharacteristic
675C2×C4#41×D6111yescharacteristic
676C8—22no—
677C8—22no—
678C8—1222no—
679C8—1222no—
680C22—614no—
681C22—1222no—
682C22—1222no—
683C22—1222no—
684C22—1222no—
685C22—1222no—
686C22—1222no—
687C22C2×C22⋊C4×D6111yescharacteristic
688C22C4×D4×D6111yescharacteristic
689C22C4×D4×D6111yescharacteristic
690C22#1684056811yescharacteristic
691C22#1684056911yescharacteristic
692C22#1684057511yescharacteristic
693C22#1684057611yescharacteristic
694C4—22no—
695C4—22no—
696C4—24no—
697C4—42no—
698C4—42no—
699C4—42no—
700C4—614no—
701C4—1222no—
702C4—1222no—
703C4—1224no—
704C4—2442no—
705C4—2442no—
706C4—2442no—
707C4C2×C42×D6111yescharacteristic
708C4#117×D6111yescharacteristic
709C4C4×D4×D6111yescharacteristic
710C4C4×D4×D6111yescharacteristic
711C2—1224no—
712C2C4×C22⋊C4×D6111yescharacteristic
713C2#2145434711yescharacteristic
714C2#2145434811yescharacteristic
715C2#2145465511yescharacteristic
716C2#2145465711yescharacteristic
717C2#2145467311yescharacteristic
718C2#2145468211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC4×C61C22×C42
FrattiniC22×C4C23×D61
FittingC4×#103×C61C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
cosocleC22×C4×C61C24
hypercenterC4×#103D61
hypocenterC61#20417
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#103

Complements

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

NH ≅ G/Ntype
6. #21445652C2semidirect
7. #21445651C2semidirect
8. #21445649C2semidirect
9. #21445648C2semidirect
10. #103×Dic61C2semidirect
11. C4×#14519702C2semidirect
12. #21445638C2semidirect
15. C4×#103×C61C2semidirect
20. #16840238C4semidirect
32. #16839769C4semidirect
39. #103×D61C4semidirect
84. Q8×Dic61C2×C4semidirect
87. C4×Dic122C2×C4semidirect
90. #14519742C2×C4semidirect
124. #14519702C2×C4semidirect
126. #14519701C2×C4semidirect
128. #14519700C2×C4semidirect
139. C4×Q8×C61C2×C4semidirect
148. #103×C61C2×C4semidirect
175. Q8×D61C42semidirect
364. C4×#103D61semidirect
423. C61#20417semidirect
455. C4×Q8C4×D61semidirect
502. #103C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402382
C2×#168397692
C2×#103×D612
C2×#168397162
#214481732
#214456522
#214456512
#214456492
#214456482
#103×Dic612
C4×#145197022
#214456382
#214455372
#214455342
C4×#103×C612
#2041761