Finite Group Databasebeta

← #29840458

Subgroups — #29840458

Order 15616.

2310 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840316C211yesmaximal, characteristic
2#21448823C212yesmaximal
3#21448821C214yesmaximal
4#21448820C212yesmaximal
5#21448778C211yesmaximal, characteristic, complemented
6#21448777C212yesmaximal, complemented
7#21448776C211yesmaximal, characteristic, complemented
8C4⋊C4×Dic122C211yesmaximal, characteristic, complemented
9#21448731C212yesmaximal, complemented
10#21448557C214yesmaximal, complemented
11#21448440C212yesmaximal
12#21448390C212yesmaximal, complemented
13C4×#14519775C212yesmaximal, complemented
14#384×D61C211yesmaximal, characteristic
15#21448173C212yesmaximal
16C4×#14519735C211yesmaximal, characteristic
17Q8×C4⋊C4×C61C211yesmaximal, characteristic, complemented
18#16840316C4116yescomplemented
19C2×#14519776C2211yescharacteristic
20C2×#14519775C2211yescharacteristic
21C2×#14519767C2212yes—
22C2×#14519757C2211yescharacteristic
23C2×#14519755C2212yes—
24C2×#14519753C2211yescharacteristic
25C2×C4×Dic122C2212yes—
26C2×C4×Dic122C2212yes—
27C2×C4×Dic122C2211yescharacteristic
28C2×#14519742C2214yes—
29C2×#14519735C2211yescharacteristic
30C2×#14519735C2211yescharacteristic
31C2×#14519734C2212yes—
32C2×C4⋊C4×D61C2212yes—
33C2×C4⋊C4×D61C2212yes—
34C2×C4⋊C4×D61C2212yes—
35C2×C42×D61C2211yescharacteristic
36#16839669C2212yes—
37#16839667C2212yes—
38#16839666C2214yes—
39#16839660C2212yes—
40#16839659C2214yes—
41#16839658C2214yes—
42#16839657C2214yes—
43#16839657C2214yes—
44#16839657C2214yes—
45#16839657C2214yes—
46#16839648C2214yes—
47#16839646C2214yes—
48#16839645C2214yes—
49#16839643C2214yes—
50#16839633C2214yes—
51#16839633C2214yes—
52#16839632C2211yescharacteristic
53#16839631C2212yes—
54#16839631C2212yes—
55#16839631C2212yes—
56#16839631C2212yes—
57#16839628C2212yes—
58#16839627C2212yes—
59C4⋊C4×Dic61C2211yescharacteristic
60C4⋊C4×Dic61C2212yes—
61C4⋊C4×Dic61C2212yes—
62C4⋊C4×Dic61C2212yes—
63C4⋊C4×Dic61C2211yescharacteristic
64C4⋊C4×Dic61C2212yes—
65C4×#11758196C2214yes—
66C4×#11758196C2214yes—
67C4×C4⋊Dic61C2212yes—
68C4×C4⋊Dic61C2211yescharacteristic
69#16839613C2214yes—
70C4×#11758198C2214yes—
71C4×#11758198C2212yes—
72#16839609C2212yes—
73#16839609C2214yes—
74#16839607C2212yes—
75C42×Dic61C2212yes—
76C2×C4×Q8×C61C2212yes—
77C2×C4×Q8×C61C2211yescharacteristic
78C61×#389C2214yes—
79C61×#389C2212yes—
80C61×#384C2211yescharacteristic
81C61×#384C2212yes—
82C4×C4⋊C4×C61C2211yescharacteristic
83C4×C4⋊C4×C61C2212yes—
84C22×Dic122C2312yes—
85C22×Dic122C2311yescharacteristic
86C22×C4×D61C2311yescharacteristic
87C22×C4×D61C2311yescharacteristic
88C22×C4×D61C2314yes—
89C22×C4×D61C2311yescharacteristic
90#14519776C2×C418yescomplemented
91#14519775C2×C418yescomplemented
92#14519767C2×C4116yescomplemented
93#14519757C2×C418yes—
94#14519755C2×C4116yes—
95#14519753C2×C418yes—
96C4×Dic122—44no—
97C4×Dic122C2×C4116yescomplemented
98C4×Dic122C2×C418yescomplemented
99#14519742—48no—
100#14519735—24no—
101#14519735Q818yescomplemented
102#14519734C2×C4116yes—
103C2×C4⋊Dic61C2312yes—
104C2×C4⋊Dic61C2312yes—
105C2×C4⋊Dic61C2311yescharacteristic
106C2×C4⋊Dic61C2312yes—
107C2×C4⋊Dic61C2311yescharacteristic
108C2×C4⋊Dic61C2312yes—
109C2×C4⋊Dic61C2311yescharacteristic
110C2×#11758196C2314yes—
111C2×#11758196C2314yes—
112C2×#11758196C2314yes—
113C2×#11758196C2314yes—
114C2×#11758196C2314yes—
115C2×#11758196C2312yes—
116C2×#11758196C2312yes—
117C2×#11758196C2312yes—
118C2×#11758196C2312yes—
119C2×#11758196C2312yes—
120C4⋊C4×D61—28no—
121C4⋊C4×D61—44no—
122C4⋊C4×D61—44no—
123C2×#11758198C2312yes—
124C2×#11758198C2312yes—
125C2×#11758198C2312yes—
126C2×#11758198C2312yes—
127C2×C4×Dic61C2312yes—
128C2×C4×Dic61C2312yes—
129C2×C4×Dic61C2312yes—
130C2×C4×Dic61C2312yes—
131C2×C4×Dic61C2314yes—
132C2×C4×Dic61C2314yes—
133C2×C4×Dic61C2314yes—
134C2×C4×Dic61C2311yescharacteristic
135C2×C4×Dic61C2311yescharacteristic
136C2×C4×Dic61C2311yescharacteristic
137C2×C4×Dic61C2312yes—
138C2×C4×Dic61C2312yes—
139C42×D61C2×C418yes—
140#14519684C2312yes—
141#14519684C2312yes—
142#14519684C2312yes—
143#14519684C2314yes—
144#14519684C2314yes—
145#14519684C2314yes—
146#14519684C2314yes—
147#14519684C2314yes—
148#14519684C2314yes—
149#14519684C2314yes—
150C22×Q8×C61C2311yescharacteristic
151C4×Q8×C61—44no—
152C4×Q8×C61C2×C418yescomplemented
153C2×C4⋊C4×C61C2312yes—
154C2×C4⋊C4×C61C2312yes—
155C2×C4⋊C4×C61C2311yescharacteristic
156C2×C4⋊C4×C61C2312yes—
157C2×C4⋊C4×C61C2314yes—
158C2×C4⋊C4×C61C2314yes—
159C2×C4⋊C4×C61C2312yes—
160C2×C4⋊C4×C61C2311yescharacteristic
161C2×C4⋊C4×C61C2311yescharacteristic
162C2×C42×C61C2312yes—
163C2×C42×C61C2314yes—
164C2×C42×C61C2311yescharacteristic
165C2×C42×C61C2312yes—
166#95×C61C2312yes—
167#95×C61C2314yes—
168C23×D61C2411yescharacteristic
169C2×Q8×C61—22no—
170C2×Q8×C61—22no—
171C2×Q8×C61C22×C414yes—
172C22×C4×C61C2414yes—
173C22×C4×C61C2412yes—
174C22×C4×C61C2411yescharacteristic
175C22×C4×C61C2412yes—
176C22×C4×C61C2412yes—
177C22×C4×C61C2412yes—
178C22×C4×C61C2411yescharacteristic
179C22×C4×C61C2411yescharacteristic
180C22×Dic61C2414yes—
181C22×Dic61C2412yes—
182C22×Dic61C2411yescharacteristic
183C22×Dic61C2412yes—
184C22×Dic61C2412yes—
185C22×Dic61C2412yes—
186C22×Dic61C2411yescharacteristic
187C22×Dic61C2411yescharacteristic
188C2×C4×D61—22no—
189C2×C4×D61—22no—
190C2×C4×D61—22no—
191C2×C4×D61—22no—
192C2×C4×D61—28no—
193C2×C4×D61—44no—
194C2×C4×D61—44no—
195C2×C4×D61C22×C414yes—
196C2×C4×D61C22×C414yes—
197C2×C4×D61C22×C414yes—
198C2×C4×D61C2×Q814yes—
199C2×C4×D61#4114yes—
200C2×Dic122—22no—
201C2×Dic122—22no—
202C2×Dic122—24no—
203C2×Dic122—24no—
204C2×Dic122C22×C418yes—
205C2×Dic122C22×C414yes—
206C4⋊C4×C61—24no—
207C4⋊C4×C61—22no—
208C4⋊C4×C61—24no—
209C4⋊C4×C61—44no—
210C4⋊C4×C61—42no—
211C4⋊C4×C61—44no—
212C4⋊C4×C61C22×C418yes—
213C4⋊C4×C61C22×C414yes—
214C4⋊C4×C61C2×Q814yes—
215C42×C61—24no—
216C42×C61—44no—
217C42×C61C22×C414yes—
218C42×C61C22×C418yes—
219#11758198—24no—
220#11758198C22×C418yes—
221#11758198C22×C418yes—
222#11758198C2×Q818yes—
223C4⋊Dic61—24no—
224C4⋊Dic61—22no—
225C4⋊Dic61—24no—
226C4⋊Dic61—42no—
227C4⋊Dic61C22×C414yes—
228C4⋊Dic61C22×C418yes—
229C4⋊Dic61C2×Q814yes—
230#11758196—28no—
231#11758196—28no—
232#11758196—44no—
233#11758196—44no—
234#11758196—44no—
235#11758196C22×C418yes—
236#11758196C22×C418yes—
237#11758196C22×C418yes—
238#11758196C22×C418yes—
239#11758196C22×C418yes—
240C4×Dic61—24no—
241C4×Dic61—24no—
242C4×Dic61—24no—
243C4×Dic61—24no—
244C4×Dic61—44no—
245C4×Dic61—44no—
246C4×Dic61—44no—
247C4×Dic61C22×C414yes—
248C4×Dic61C22×C414yes—
249C4×Dic61C22×C414yes—
250C4×Dic61C22×C418yes—
251C4×Dic61C2×Q818yes—
252C23×C61C2511yescharacteristic
253C22×D61—21no—
254C22×D61—21no—
255C22×D61—21no—
256C22×D61—21no—
257C22×D61C23×C412yes—
258C22×D61C22×Q812yes—
259C22×D61C2×#4112yes—
260Q8×C61—28no—
261C2×C4×C61—22no—
262C2×C4×C61—22no—
263C2×C4×C61—21no—
264C2×C4×C61—22no—
265C2×C4×C61—22no—
266C2×C4×C61—22no—
267C2×C4×C61—21no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—24no—
271C2×C4×C61—22no—
272C2×C4×C61—24no—
273C2×C4×C61—22no—
274C2×C4×C61—24no—
275C2×C4×C61C23×C412yes—
276C2×C4×C61C23×C414yes—
277C2×C4×C61C23×C414yes—
278C2×C4×C61C23×C412yes—
279C2×C4×C61C23×C412yes—
280C2×C4×C61C22×Q814yes—
281C2×C4×C61C22×Q812yes—
282C2×C4×C61C2×#4112yes—
283C2×C4×C61H(5,𝔽2)12yes—
284C2×C4×C612−1+412yes—
285C2×Dic61—22no—
286C2×Dic61—22no—
287C2×Dic61—22no—
288C2×Dic61—21no—
289C2×Dic61—22no—
290C2×Dic61—22no—
291C2×Dic61—22no—
292C2×Dic61—21no—
293C2×Dic61—22no—
294C2×Dic61—24no—
295C2×Dic61—24no—
296C2×Dic61—24no—
297C2×Dic61—22no—
298C2×Dic61—22no—
299C2×Dic61C23×C412yes—
300C2×Dic61C23×C414yes—
301C2×Dic61C23×C414yes—
302C2×Dic61C23×C412yes—
303C2×Dic61C23×C412yes—
304C2×Dic61C22×Q814yes—
305C2×Dic61C22×Q812yes—
306C2×Dic61C2×#4112yes—
307C2×Dic61H(5,𝔽2)12yes—
308C2×Dic612−1+412yes—
309C4×D61—28no—
310C4×D61—28no—
311C4×D61—88no—
312C4×D61C4×Q8116yescomplemented
313Dic122—28no—
314Dic122—216no—
315#34214—611nomaximal, Sylow
316C22×C61C24×C411yescharacteristic
317C22×C61C23×Q811yescharacteristic
318C22×C61C22×#4111yescharacteristic
319C22×C61C2×H(5,𝔽2)11yescharacteristic
320C22×C61C2×H(5,𝔽2)11yescharacteristic
321C22×C61C2×2−1+411yescharacteristic
322C22×C61C2×2−1+411yescharacteristic
323C2×D61—22no—
324C2×D61—22no—
325C2×D61—22no—
326C2×D61—22no—
327C2×D61—22no—
328C2×D61—22no—
329C2×D61C2×C4×Q814yes—
330C4×C61—24no—
331C4×C61—22no—
332C4×C61—24no—
333C4×C61—24no—
334C4×C61—44no—
335C4×C61—42no—
336C4×C61C2×C4×Q814yes—
337C4×C61#52014yes—
338Dic61—24no—
339Dic61—24no—
340Dic61—22no—
341Dic61—24no—
342Dic61—44no—
343Dic61—42no—
344Dic61C2×C4×Q814yes—
345Dic61#52014yes—
346C2×#533—611no—
347#2360—614no—
348#2360—612no—
349#2360—612no—
350#2355—611no—
351#2355—612no—
352#2355—611no—
353Q8×C4⋊C4—612no—
354Q8×C4⋊C4—611no—
355Q8×C4⋊C4D6111yescharacteristic, complemented
356#2330—614no—
357#2317—612no—
358C4×C4⋊Q8—612no—
359C4×C4⋊Q8—612no—
360C2×#384—611no—
361#2274—612no—
362C4×#117—611no—
363C2×C61C22×C4×Q811yescharacteristic
364C2×C61C2×#52011yescharacteristic
365C2×C61C2×#52011yescharacteristic
366C2×C61#350311yescharacteristic
367C2×C61#350311yescharacteristic
368C2×C61#350811yescharacteristic
369C2×C61#350911yescharacteristic
370D61—24no—
371#533—6116no—
372C2×C4⋊Q8—611no—
373C2×C4⋊Q8—611no—
374C2×#125—612no—
375C2×C22⋊Q8—611no—
376C2×C22⋊Q8—612no—
377C2×C22⋊Q8—611no—
378C2×C4×Q8—614no—
379C2×C4×Q8—611no—
380C2×C4×Q8—612no—
381C2×C4×Q8—612no—
382C2×C4×Q8C2×D6112yes—
383C2×C4×Q8C2×D6111yescharacteristic
384C2×#117—611no—
385C2×#117—611no—
386C2×#117—612no—
387C22×C4⋊C4—612no—
388C22×C4⋊C4—612no—
389C22×C4⋊C4—612no—
390C22×C42—611no—
391#391—612no—
392#391—612no—
393#391—614no—
394#389—614no—
395#389—614no—
396#389—614no—
397#389—614no—
398#389—614no—
399#389—612no—
400#389—614no—
401#389C2×D6112yes—
402#389C2×D6114yes—
403#387—614no—
404#387—614no—
405#387—614no—
406#387—614no—
407#385—614no—
408#385—614no—
409#384—612no—
410#384—612no—
411#384—612no—
412#384—612no—
413#384—611no—
414#384C2×D6112yes—
415#384C2×D6111yescharacteristic
416#382—612no—
417#382—612no—
418C4×C4⋊C4—612no—
419C4×C4⋊C4—612no—
420C4×C4⋊C4—611no—
421C4×C4⋊C4—612no—
422C4×C4⋊C4—612no—
423C4×C4⋊C4—611no—
424C4×C4⋊C4—614no—
425C4×C4⋊C4—614no—
426C4×C4⋊C4—612no—
427C4×C4⋊C4—611no—
428C4×C4⋊C4—614no—
429C4×C4⋊C4C2×D6111yescharacteristic
430C4×C4⋊C4C2×D6112yes—
431C4×C22⋊C4—612no—
432C4×C22⋊C4—614no—
433C4×C22⋊C4—612no—
434C4×C22⋊C4—614no—
435#376—612no—
436C43—612no—
437C61#3421411yescharacteristic, complemented, Sylow
438C22×Q8—612no—
439C22×Q8—611no—
440C22×Q8C22×D6111yescharacteristic
441C23×C4—611no—
442C23×C4—611no—
443C23×C4—611no—
444C23×C4—614no—
445C4⋊Q8—618no—
446C4⋊Q8—618no—
447#125—6116no—
448C22⋊Q8—618no—
449C22⋊Q8—6116no—
450C22⋊Q8—618no—
451C4×Q8—44no—
452C4×Q8—6116no—
453C4×Q8—618no—
454C4×Q8—2444no—
455C4×Q8—2448no—
456C4×Q8C4×D6118yescomplemented
457#117—618no—
458#117—6116no—
459#117—1224no—
460C2×C4⋊C4—612no—
461C2×C4⋊C4—612no—
462C2×C4⋊C4—611no—
463C2×C4⋊C4—612no—
464C2×C4⋊C4—612no—
465C2×C4⋊C4—612no—
466C2×C4⋊C4—612no—
467C2×C4⋊C4—611no—
468C2×C4⋊C4—614no—
469C2×C4⋊C4—612no—
470C2×C4⋊C4—612no—
471C2×C4⋊C4—614no—
472C2×C4⋊C4—611no—
473C2×C4⋊C4—614no—
474C2×C4⋊C4—612no—
475C2×C4⋊C4—614no—
476C2×C4⋊C4—614no—
477C2×C4⋊C4—1228no—
478C2×C4⋊C4—2444no—
479C2×C4⋊C4—2444no—
480C2×C4⋊C4C22×D6112yes—
481C2×C4⋊C4C22×D6112yes—
482C2×C4⋊C4C22×D6111yescharacteristic
483C2×C4⋊C4C22×D6112yes—
484C2×C4⋊C4C22×D6114yes—
485C2×C4⋊C4C22×D6114yes—
486C2×C4⋊C4C22×D6112yes—
487C2×C4⋊C4C22×D6111yescharacteristic
488C2×C4⋊C4C22×D6111yescharacteristic
489C2×C22⋊C4—612no—
490C2×C22⋊C4—612no—
491C2×C22⋊C4—612no—
492C2×C22⋊C4—612no—
493C2×C42—612no—
494C2×C42—612no—
495C2×C42—611no—
496C2×C42—611no—
497C2×C42—611no—
498C2×C42—618no—
499C2×C42—612no—
500C2×C42—612no—
501C2×C42—612no—
502C2×C42—612no—
503C2×C42—614no—
504C2×C42—614no—
505C2×C42—614no—
506C2×C42C22×D6112yes—
507C2×C42C22×D6114yes—
508C2×C42C22×D6112yes—
509C2×C42C22×D6111yescharacteristic
510#95—612no—
511#95—612no—
512#95—612no—
513#95—614no—
514#95—614no—
515#95—614no—
516#95—614no—
517#95—614no—
518#95—614no—
519#95—614no—
520#95C22×D6112yes—
521#95C22×D6114yes—
522C24—611no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—618no—
526C2×Q8—614no—
527C2×Q8—1224no—
528C2×Q8—1224no—
529C2×Q8—1222no—
530C2×Q8—1222no—
531C2×Q8C2×C4×D6114yes—
532C22×C4—611no—
533C22×C4—611no—
534C22×C4—614no—
535C22×C4—614no—
536C22×C4—614no—
537C22×C4—612no—
538C22×C4—612no—
539C22×C4—612no—
540C22×C4—611no—
541C22×C4—614no—
542C22×C4—614no—
543C22×C4—612no—
544C22×C4—614no—
545C22×C4—1222no—
546C22×C4—1222no—
547C22×C4—1228no—
548C22×C4—1222no—
549C22×C4—1222no—
550C22×C4—2444no—
551C22×C4—2444no—
552C22×C4C23×D6114yes—
553C22×C4C23×D6112yes—
554C22×C4C23×D6112yes—
555C22×C4C23×D6112yes—
556C22×C4C23×D6111yescharacteristic
557C22×C4C23×D6112yes—
558C22×C4C23×D6111yescharacteristic
559C22×C4C23×D6111yescharacteristic
560C4⋊C4—24no—
561C4⋊C4—22no—
562C4⋊C4—24no—
563C4⋊C4—42no—
564C4⋊C4—44no—
565C4⋊C4—44no—
566C4⋊C4—618no—
567C4⋊C4—618no—
568C4⋊C4—618no—
569C4⋊C4—618no—
570C4⋊C4—618no—
571C4⋊C4—618no—
572C4⋊C4—614no—
573C4⋊C4—614no—
574C4⋊C4—1228no—
575C4⋊C4—1228no—
576C4⋊C4—1224no—
577C4⋊C4—1222no—
578C4⋊C4—1224no—
579C4⋊C4—2444no—
580C4⋊C4—2442no—
581C4⋊C4—2444no—
582C4⋊C4—2444no—
583C4⋊C4C2×C4×D6118yes—
584C4⋊C4C2×C4×D6114yes—
585C4⋊C4Q8×D6114yes—
586C22⋊C4—618no—
587C22⋊C4—618no—
588C22⋊C4—618no—
589C22⋊C4—1224no—
590C42—24no—
591C42—44no—
592C42—614no—
593C42—614no—
594C42—614no—
595C42—618no—
596C42—618no—
597C42—1224no—
598C42—1224no—
599C42—1224no—
600C42—1224no—
601C42—2444no—
602C42—2444no—
603C42—2444no—
604C42C2×C4×D6114yes—
605C42C2×C4×D6118yes—
606C23—612no—
607C23—612no—
608C23—612no—
609C23—1221no—
610C23—1221no—
611C23—1221no—
612C23—1221no—
613C23C24×D6111yescharacteristic
614Q8—28no—
615Q8—12216no—
616Q8—1228no—
617C2×C4—22no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—24no—
627C2×C4—22no—
628C2×C4—24no—
629C2×C4—22no—
630C2×C4—24no—
631C2×C4—612no—
632C2×C4—612no—
633C2×C4—612no—
634C2×C4—612no—
635C2×C4—612no—
636C2×C4—612no—
637C2×C4—6116no—
638C2×C4—612no—
639C2×C4—614no—
640C2×C4—614no—
641C2×C4—614no—
642C2×C4—1228no—
643C2×C4—1222no—
644C2×C4—1222no—
645C2×C4—1222no—
646C2×C4—1221no—
647C2×C4—1222no—
648C2×C4—1222no—
649C2×C4—1221no—
650C2×C4—1222no—
651C2×C4—1228no—
652C2×C4—1222no—
653C2×C4—1224no—
654C2×C4—1224no—
655C2×C4—1224no—
656C2×C4—1222no—
657C2×C4—1222no—
658C2×C4—4888no—
659C2×C4C22×C4×D6112yes—
660C2×C4C22×C4×D6114yes—
661C2×C4C22×C4×D6114yes—
662C2×C4C22×C4×D6112yes—
663C2×C4C22×C4×D6112yes—
664C2×C4C2×Q8×D6114yes—
665C2×C4C2×Q8×D6112yes—
666C2×C4#41×D6112yes—
667C2×C4#1451982212yes—
668C2×C4#1451982512yes—
669C22—614no—
670C22—1222no—
671C22—1222no—
672C22—1222no—
673C22—1222no—
674C22—1222no—
675C22—1222no—
676C22C23×C4×D6111yescharacteristic
677C22C22×Q8×D6111yescharacteristic
678C22C2×#41×D6111yescharacteristic
679C22H(5,𝔽2)×D6111yescharacteristic
680C22C2×#1451982211yescharacteristic
681C222−1+4×D6111yescharacteristic
682C22C2×#1451982511yescharacteristic
683C4—22no—
684C4—24no—
685C4—24no—
686C4—24no—
687C4—42no—
688C4—44no—
689C4—614no—
690C4—614no—
691C4—1224no—
692C4—1222no—
693C4—1224no—
694C4—1224no—
695C4—2444no—
696C4—2442no—
697C4C4×Q8×D6114yes—
698C4#1684024314yes—
699C2—1224no—
700C2C2×C4×Q8×D6111yescharacteristic
701C2#520×D6111yescharacteristic
702C2C2×#1684024311yescharacteristic
703C2#2145963011yescharacteristic
704C2#2145963711yescharacteristic
705C2#2145968911yescharacteristic
706C2#2145970211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D61
commutatorC22×C61C24×C4
FittingQ8×C4⋊C4×C61C2
socle, cosocleC23×C61C25
prime radicalC23×D61C24
hypercenterQ8×C4⋊C4D61
hypocenterC61#34214
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ Q8×C4⋊C4

Complements

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

NH ≅ G/Ntype
5. #21448778C2semidirect
6. #21448777C2semidirect
7. #21448776C2semidirect
8. C4⋊C4×Dic122C2semidirect
9. #21448731C2semidirect
10. #21448557C2semidirect
12. #21448390C2semidirect
13. C4×#14519775C2semidirect
17. Q8×C4⋊C4×C61C2semidirect
18. #16840316C4semidirect
90. #14519776C2×C4semidirect
91. #14519775C2×C4semidirect
92. #14519767C2×C4semidirect
97. C4×Dic122C2×C4semidirect
98. C4×Dic122C2×C4semidirect
101. #14519735Q8semidirect
152. C4×Q8×C61C2×C4semidirect
312. C4×D61C4×Q8semidirect
355. Q8×C4⋊C4D61semidirect
437. C61#34214semidirect
456. C4×Q8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168403162
#214488232
#214488212
#214488202
#214487782
#214487772
#214487762
C4⋊C4×Dic1222
#214487312
#214485572
#214484402
#214483902
C4×#145197752
#384×D612
#214481732
C4×#145197352
Q8×C4⋊C4×C612
#3421461