Finite Group Databasebeta

← #29689455

Subgroups — #29689455

Order 15616.

1474 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D61C211yesmaximal, characteristic
2#21448201C211yesmaximal, characteristic
3#21448200C211yesmaximal, characteristic
4#21446805C211yesmaximal, characteristic, complemented
5#21446804C211yesmaximal, characteristic, complemented
6#21446803C211yesmaximal, characteristic, complemented
7#21446802C214yesmaximal, complemented
8#21445892C214yesmaximal
9C61×#1996C211yesmaximal, characteristic, complemented
10C22×Q8×D61C411yescharacteristic, complemented
11C23×C4×D61C2211yescharacteristic
12C2×#14519757C411yescharacteristic, complemented
13C2×#14519756C2211yescharacteristic
14C2×#14519755C412yescomplemented
15C2×#14519754C2212yes—
16C2×#14519753C411yescharacteristic, complemented
17C22⋊Q8×D61—21no—
18C22⋊Q8×D61—21no—
19C22⋊Q8×D61—21no—
20C22⋊Q8×D61—21no—
21C22⋊Q8×D61—21no—
22C22⋊Q8×D61—21no—
23C22⋊Q8×D61—21no—
24C22⋊Q8×D61—21no—
25C2×#14519735—21no—
26C2×#14519734—21no—
27C2×C4⋊C4×D61C411yescharacteristic, complemented
28C2×C4⋊C4×D61C412yescomplemented
29C2×C22⋊C4×D61C2212yes—
30#16839624—21no—
31#16839624—21no—
32#16839622C2211yescharacteristic
33#16839621—21no—
34#16839620C2212yes—
35#16839619—21no—
36#16839617C2212yes—
37#16839617C2212yes—
38C22⋊C4×Dic61C2212yes—
39C4×#11758198—21no—
40C4×C22⋊Dic61C2211yescharacteristic
41#16839609—21no—
42#16839529C2214yes—
43#16839528C2214yes—
44#16839528C2214yes—
45C2×C22⋊Q8×C61C2211yescharacteristic
46C61×#380C2211yescharacteristic
47C4×C22⋊C4×C61C2211yescharacteristic
48C61×#342C2214yes—
49C24×D61C2311yescharacteristic
50C22×Dic122C2×C412yes—
51C22×Dic122C2×C411yescharacteristic
52C2×Q8×D61—21no—
53C2×Q8×D61—21no—
54C2×Q8×D61—21no—
55C2×Q8×D61—21no—
56C2×Q8×D61—44no—
57C23×Dic61C2311yescharacteristic
58C22×C4×D61—44no—
59C22×C4×D61C2×C411yescharacteristic
60C22×C4×D61C2×C412yes—
61C22×C4×D61C2×C412yes—
62C22×C4×D61C2×C411yescharacteristic
63C22×C4×D61C2×C411yescharacteristic
64C22×C4×D61C2×C411yescharacteristic
65C22×C4×D61D411yescharacteristic
66C22×C4×D61D411yescharacteristic
67C22×C4×D61D411yescharacteristic
68C22×C4×D61D411yescharacteristic
69C22×C4×D61D411yescharacteristic
70C22×C4×D61D411yescharacteristic
71C22×C4×D61D411yescharacteristic
72C22×C4×D61D411yescharacteristic
73#14519757—21no—
74#14519757—21no—
75#14519757—21no—
76#14519757—21no—
77#14519756—21no—
78#14519756—21no—
79#14519756—21no—
80#14519756—21no—
81#14519755—22no—
82#14519755—22no—
83#14519755—22no—
84#14519755—22no—
85#14519754—22no—
86#14519754—22no—
87#14519754—22no—
88#14519754—22no—
89#14519753—21no—
90#14519753—21no—
91#14519753—21no—
92#14519753—21no—
93#14519735—44no—
94#14519734—44no—
95C2×C4⋊Dic61—21no—
96C2×C4⋊Dic61C2×C411yescharacteristic
97C2×C4⋊Dic61C2×C412yes—
98C2×#11758196—22no—
99C2×#11758196C2×C412yes—
100C2×#11758196C2×C412yes—
101C2×#11758196C2×C412yes—
102C4⋊C4×D61—22no—
103C4⋊C4×D61—22no—
104C4⋊C4×D61—22no—
105C4⋊C4×D61—22no—
106C4⋊C4×D61—21no—
107C4⋊C4×D61—21no—
108C4⋊C4×D61—21no—
109C4⋊C4×D61—21no—
110C2×C22⋊Dic61C2312yes—
111C2×C22⋊Dic61C2312yes—
112C2×C22⋊Dic61C2312yes—
113C2×#11758198—22no—
114C2×#11758198—22no—
115C2×#11758198—22no—
116C2×#11758198—22no—
117C2×#11758198C2×C412yes—
118C2×#11758198C2×C412yes—
119C22⋊C4×D61—22no—
120C22⋊C4×D61—22no—
121C22⋊C4×D61—22no—
122C22⋊C4×D61—22no—
123C2×C4×Dic61—21no—
124C2×C4×Dic61—22no—
125#14519684—21no—
126#14519684—21no—
127#14519684—22no—
128#14519684—22no—
129C22×Q8×C61C2×C411yescharacteristic
130C23×C4×C61C2311yescharacteristic
131C22⋊Q8×C61—21no—
132C22⋊Q8×C61—21no—
133C22⋊Q8×C61—21no—
134C22⋊Q8×C61—21no—
135C2×C4⋊C4×C61—21no—
136C2×C4⋊C4×C61C2×C412yes—
137C2×C4⋊C4×C61C2×C411yescharacteristic
138C2×C22⋊C4×C61C2312yes—
139C2×C22⋊C4×C61C2312yes—
140C2×C22⋊C4×C61C2312yes—
141C2×C42×C61—21no—
142#95×C61—21no—
143#95×C61—21no—
144C24×C61C2411yescharacteristic
145C23×D61—22no—
146C23×D61—22no—
147C23×D61—42no—
148C23×D61—42no—
149C23×D61C22×C411yescharacteristic
150C23×D61C22×C411yescharacteristic
151C23×D61C2×D411yescharacteristic
152C23×D61C2×D411yescharacteristic
153C23×D61C2×D411yescharacteristic
154C23×D61C2×D411yescharacteristic
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—42no—
158C22×C4×C61—22no—
159C22×C4×C61—22no—
160C22×C4×C61—42no—
161C22×C4×C61C22×C411yescharacteristic
162C22×C4×C61C22×C412yes—
163C22×C4×C61C22×C412yes—
164C22×C4×C61C22×C411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D411yescharacteristic
169C22×Dic61—22no—
170C22×Dic61—22no—
171C22×Dic61—42no—
172C22×Dic61C22×C411yescharacteristic
173C22×Dic61C22×C412yes—
174C22×Dic61C22×C412yes—
175C22×Dic61C22×C411yescharacteristic
176C22×Dic61C2×D411yescharacteristic
177C22×Dic61C2×D411yescharacteristic
178C22×Dic61C2×D411yescharacteristic
179C22×Dic61C2×D411yescharacteristic
180Q8×D61—44no—
181Q8×D61—44no—
182Q8×D61—44no—
183Q8×D61—44no—
184C2×C4×D61—24no—
185C2×C4×D61—24no—
186C2×C4×D61—24no—
187C2×C4×D61—22no—
188C2×C4×D61—22no—
189C2×C4×D61—22no—
190C2×C4×D61—22no—
191C2×C4×D61—42no—
192C2×C4×D61—42no—
193C2×C4×D61—42no—
194C2×C4×D61—42no—
195C2×C4×D61—42no—
196C2×C4×D61—42no—
197C2×C4×D61—42no—
198C2×C4×D61—42no—
199C2×C4×D61—42no—
200C2×C4×D61—44no—
201C2×C4×D61—44no—
202C2×C4×D61C22⋊C411yescharacteristic
203C2×C4×D61C22⋊C411yescharacteristic
204C2×C4×D61C22⋊C411yescharacteristic
205C2×C4×D61C22⋊C411yescharacteristic
206C2×C4×D61C22⋊C411yescharacteristic
207C2×C4×D61C22⋊C411yescharacteristic
208C2×C4×D61C22⋊C411yescharacteristic
209C2×C4×D61C22⋊C411yescharacteristic
210C2×C4×D61C22⋊C411yescharacteristic
211C2×C4×D61C22⋊C411yescharacteristic
212C2×C4×D61C22⋊C411yescharacteristic
213C2×C4×D61C22⋊C411yescharacteristic
214C2×C4×D61C22⋊C411yescharacteristic
215C2×C4×D61C22⋊C411yescharacteristic
216C2×C4×D61C22⋊C411yescharacteristic
217C2×C4×D61C22⋊C411yescharacteristic
218C2×Dic122—21no—
219C2×Dic122—21no—
220C2×Dic122—22no—
221C2×Dic122—22no—
222C2×Dic122—44no—
223C2×Dic122—42no—
224C4⋊C4×C61—22no—
225C4⋊C4×C61—22no—
226C4⋊C4×C61—21no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—42no—
229C22⋊C4×C61—22no—
230C22⋊C4×C61—22no—
231C22⋊C4×C61—22no—
232C22⋊C4×C61—24no—
233C22⋊C4×C61—22no—
234C42×C61—42no—
235C22⋊Dic61—22no—
236C22⋊Dic61—22no—
237C22⋊Dic61—22no—
238C22⋊Dic61—22no—
239C22⋊Dic61—24no—
240#11758198—22no—
241#11758198—22no—
242#11758198—22no—
243#11758198—22no—
244#11758198—44no—
245#11758198—44no—
246#11758198—44no—
247#11758198—44no—
248C4⋊Dic61—21no—
249C4⋊Dic61—21no—
250C4⋊Dic61—22no—
251C4⋊Dic61—22no—
252C4⋊Dic61—42no—
253#11758196—22no—
254#11758196—22no—
255#11758196—22no—
256#11758196—22no—
257#11758196—22no—
258#11758196—22no—
259#11758196—44no—
260C4×Dic61—44no—
261C4×Dic61—42no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61C23×C411yescharacteristic
265C23×C61C22×D411yescharacteristic
266C23×C61C22×D411yescharacteristic
267C23×C612−1+412yes—
268C23×C612−1+412yes—
269C22×D61—22no—
270C22×D61—22no—
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—21no—
274C22×D61—21no—
275C22×D61—22no—
276C22×D61—22no—
277C22×D61—21no—
278C22×D61—21no—
279C22×D61—22no—
280C22×D61—22no—
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—41no—
284C22×D61—41no—
285C22×D61—41no—
286C22×D61—41no—
287C22×D61—41no—
288C22×D61—41no—
289C22×D61—48no—
290C22×D61—48no—
291C22×D61C2×C22⋊C411yescharacteristic
292C22×D61C2×C22⋊C411yescharacteristic
293C22×D61C2×C22⋊C411yescharacteristic
294C22×D61C2×C22⋊C411yescharacteristic
295Q8×C61—42no—
296Q8×C61—42no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—42no—
306C2×C4×C61—42no—
307C2×C4×C61—42no—
308C2×C4×C61—42no—
309C2×C4×C61—42no—
310C2×C4×C61—42no—
311C2×C4×C61—42no—
312C2×C4×C61—42no—
313C2×C4×C61C2×C22⋊C411yescharacteristic
314C2×C4×C61C2×C22⋊C411yescharacteristic
315C2×C4×C61C2×C22⋊C411yescharacteristic
316C2×C4×C61C2×C22⋊C411yescharacteristic
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—42no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329C2×Dic61—42no—
330C2×Dic61—42no—
331C2×Dic61—42no—
332C2×Dic61—42no—
333C2×Dic61C2×C22⋊C411yescharacteristic
334C2×Dic61C2×C22⋊C411yescharacteristic
335C2×Dic61C2×C22⋊C411yescharacteristic
336C2×Dic61C2×C22⋊C411yescharacteristic
337C4×D61—22no—
338C4×D61—22no—
339C4×D61—22no—
340C4×D61—22no—
341C4×D61—22no—
342C4×D61—22no—
343C4×D61—22no—
344C4×D61—22no—
345C4×D61—22no—
346C4×D61—41no—
347C4×D61—41no—
348C4×D61—41no—
349C4×D61—41no—
350C4×D61—41no—
351C4×D61—41no—
352C4×D61—44no—
353C4×D61—44no—
354C4×D61—44no—
355C4×D61—44no—
356C4×D61#9914yes—
357Dic122—44no—
358Dic122—42no—
359Dic122—42no—
360Dic122—44no—
361#21825—611nomaximal, Sylow
362C22×C61—21no—
363C22×C61—21no—
364C22×C61—21no—
365C22×C61—21no—
366C22×C61—21no—
367C22×C61—21no—
368C22×C61—42no—
369C22×C61—42no—
370C22×C61C22×C22⋊C411yescharacteristic
371C22×C61#51912yes—
372C22×C61#53611yescharacteristic
373C22×C61#53612yes—
374C22×C61#53611yescharacteristic
375C2×D61—28no—
376C2×D61—21no—
377C2×D61—21no—
378C2×D61—21no—
379C2×D61—21no—
380C2×D61—21no—
381C2×D61—21no—
382C2×D61—21no—
383C2×D61—21no—
384C2×D61—21no—
385C2×D61—21no—
386C2×D61—42no—
387C2×D61—44no—
388C2×D61—42no—
389C2×D61—42no—
390C2×D61—44no—
391C2×D61—42no—
392C2×D61—44no—
393C2×D61C2×#9912yes—
394C2×D61#41012yes—
395C4×C61—21no—
396C4×C61—21no—
397C4×C61—21no—
398C4×C61—42no—
399C4×C61—42no—
400C4×C61—82no—
401C4×C61—82no—
402C4×C61C2×#9912yes—
403Dic61—21no—
404Dic61—21no—
405Dic61—21no—
406Dic61—42no—
407Dic61—42no—
408Dic61—82no—
409Dic61—82no—
410Dic61C2×#9912yes—
411C22×C22⋊Q8—611no—
412#2280—611no—
413#2280—611no—
414#1996—611no—
415#1996—611no—
416#1996—614no—
417#1996—611no—
418#1996D6111yescharacteristic, complemented
419#1819—614no—
420C2×C61—21no—
421C2×C61—22no—
422C2×C61—21no—
423C2×C61—22no—
424C2×C61#231011yescharacteristic
425C2×C61C22×#9911yescharacteristic
426C2×C61C2×#41011yescharacteristic
427D61—22no—
428D61—22no—
429D61—41no—
430D61—41no—
431C23×Q8—611no—
432C24×C4—611no—
433C2×C22⋊Q8—611no—
434C2×C22⋊Q8—611no—
435C2×C22⋊Q8—612no—
436C2×C22⋊Q8—611no—
437C2×C22⋊Q8—612no—
438C2×C22⋊Q8—1221no—
439C2×C22⋊Q8—1221no—
440C2×C22⋊Q8—1221no—
441C2×C22⋊Q8—1221no—
442C2×C22⋊Q8—1221no—
443C2×C22⋊Q8—1221no—
444C2×C22⋊Q8—1221no—
445C2×C22⋊Q8—1221no—
446C2×C22⋊Q8C2×D6111yescharacteristic
447C2×#117—1221no—
448C2×#117—1221no—
449C22×C4⋊C4—611no—
450C22×C4⋊C4—612no—
451C22×C22⋊C4—612no—
452#381—1221no—
453#381—1221no—
454#380—611no—
455#380—612no—
456#380—1221no—
457#380—1221no—
458#380C2×D6111yescharacteristic
459#379—612no—
460#379—612no—
461C4×C22⋊C4—611no—
462C4×C22⋊C4—612no—
463C4×C22⋊C4—1221no—
464C4×C22⋊C4—1221no—
465C4×C22⋊C4C2×D6111yescharacteristic
466#342—614no—
467#342—614no—
468#342—614no—
469#342C2×D6114yes—
470C61#2182511yescharacteristic, complemented, Sylow
471C25—611no—
472C22×Q8—612no—
473C22×Q8—611no—
474C22×Q8—1221no—
475C22×Q8—1221no—
476C22×Q8—1221no—
477C22×Q8—1221no—
478C22×Q8—2444no—
479C22×Q8C4×D6111yescharacteristic
480C23×C4—611no—
481C23×C4—611no—
482C23×C4—611no—
483C23×C4—611no—
484C23×C4—611no—
485C23×C4—611no—
486C23×C4—611no—
487C23×C4—611no—
488C23×C4—611no—
489C23×C4—611no—
490C23×C4—611no—
491C23×C4—611no—
492C23×C4—611no—
493C23×C4—612no—
494C23×C4—612no—
495C23×C4—2444no—
496C23×C4C22×D6111yescharacteristic
497C22⋊Q8—21no—
498C22⋊Q8—21no—
499C22⋊Q8—21no—
500C22⋊Q8—21no—
501C22⋊Q8—1222no—
502C22⋊Q8—1222no—
503C22⋊Q8—1222no—
504C22⋊Q8—1222no—
505C22⋊Q8—1222no—
506C22⋊Q8—1222no—
507C22⋊Q8—1222no—
508C22⋊Q8—1222no—
509C22⋊Q8—1221no—
510C22⋊Q8—1221no—
511C22⋊Q8—1221no—
512C22⋊Q8—1221no—
513C22⋊Q8—1221no—
514C22⋊Q8—1221no—
515C22⋊Q8—1221no—
516C22⋊Q8—1221no—
517C22⋊Q8—1221no—
518C22⋊Q8—1221no—
519C22⋊Q8—1221no—
520C22⋊Q8—1221no—
521#117—2444no—
522#117—2444no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—612no—
525C2×C4⋊C4—612no—
526C2×C4⋊C4—612no—
527C2×C4⋊C4—612no—
528C2×C4⋊C4—611no—
529C2×C4⋊C4—1221no—
530C2×C4⋊C4—1221no—
531C2×C4⋊C4—1221no—
532C2×C4⋊C4—1221no—
533C2×C4⋊C4—1222no—
534C2×C4⋊C4—1222no—
535C2×C4⋊C4—1222no—
536C2×C4⋊C4—1222no—
537C2×C4⋊C4—1222no—
538C2×C4⋊C4—1221no—
539C2×C4⋊C4C4×D6111yescharacteristic
540C2×C4⋊C4C4×D6112yes—
541C2×C22⋊C4—612no—
542C2×C22⋊C4—612no—
543C2×C22⋊C4—612no—
544C2×C22⋊C4—612no—
545C2×C22⋊C4—612no—
546C2×C22⋊C4—1222no—
547C2×C22⋊C4—1222no—
548C2×C22⋊C4—1222no—
549C2×C22⋊C4—1222no—
550C2×C22⋊C4—1222no—
551C2×C22⋊C4—1222no—
552C2×C22⋊C4—1222no—
553C2×C22⋊C4—1222no—
554C2×C22⋊C4C22×D6112yes—
555C2×C22⋊C4C22×D6112yes—
556C2×C22⋊C4C22×D6112yes—
557C2×C42—21no—
558C2×C42—1222no—
559C2×C42—1221no—
560#95—21no—
561#95—21no—
562#95—1222no—
563#95—1222no—
564#95—1221no—
565#95—1221no—
566C24—611no—
567C24—611no—
568C24—611no—
569C24—611no—
570C24—611no—
571C24—611no—
572C24—1222no—
573C24—1222no—
574C24—2442no—
575C24—2442no—
576C24C23×D6111yescharacteristic
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—42no—
580C2×Q8—1222no—
581C2×Q8—1222no—
582C2×Q8—1221no—
583C2×Q8—1221no—
584C2×Q8—2442no—
585C2×Q8—2444no—
586C2×Q8—2444no—
587C2×Q8—2444no—
588C2×Q8—2444no—
589C2×Q8—2444no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—42no—
593C22×C4—611no—
594C22×C4—611no—
595C22×C4—611no—
596C22×C4—611no—
597C22×C4—611no—
598C22×C4—611no—
599C22×C4—611no—
600C22×C4—611no—
601C22×C4—611no—
602C22×C4—611no—
603C22×C4—611no—
604C22×C4—611no—
605C22×C4—611no—
606C22×C4—611no—
607C22×C4—611no—
608C22×C4—611no—
609C22×C4—611no—
610C22×C4—611no—
611C22×C4—611no—
612C22×C4—611no—
613C22×C4—611no—
614C22×C4—611no—
615C22×C4—612no—
616C22×C4—612no—
617C22×C4—1224no—
618C22×C4—1224no—
619C22×C4—1224no—
620C22×C4—1222no—
621C22×C4—1222no—
622C22×C4—1222no—
623C22×C4—1222no—
624C22×C4—1222no—
625C22×C4—1222no—
626C22×C4—2442no—
627C22×C4—2442no—
628C22×C4—2442no—
629C22×C4—2442no—
630C22×C4—2442no—
631C22×C4—2442no—
632C22×C4—2442no—
633C22×C4—2442no—
634C22×C4—2442no—
635C22×C4—2444no—
636C22×C4—2444no—
637C22×C4—2442no—
638C22×C4C2×C4×D6111yescharacteristic
639C22×C4C2×C4×D6112yes—
640C22×C4C2×C4×D6112yes—
641C22×C4C2×C4×D6111yescharacteristic
642C22×C4D4×D6111yescharacteristic
643C22×C4D4×D6111yescharacteristic
644C22×C4D4×D6111yescharacteristic
645C22×C4D4×D6111yescharacteristic
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—42no—
651C4⋊C4—1222no—
652C4⋊C4—1222no—
653C4⋊C4—1222no—
654C4⋊C4—1222no—
655C4⋊C4—1222no—
656C4⋊C4—1222no—
657C4⋊C4—1222no—
658C4⋊C4—1222no—
659C4⋊C4—1221no—
660C4⋊C4—1221no—
661C4⋊C4—2442no—
662C4⋊C4—2444no—
663C22⋊C4—22no—
664C22⋊C4—22no—
665C22⋊C4—24no—
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—1222no—
669C22⋊C4—1222no—
670C22⋊C4—1222no—
671C22⋊C4—1222no—
672C22⋊C4—1222no—
673C22⋊C4—1222no—
674C22⋊C4—1222no—
675C22⋊C4—1222no—
676C22⋊C4—1224no—
677C22⋊C4—2444no—
678C22⋊C4—2444no—
679C22⋊C4—2444no—
680C22⋊C4—2444no—
681C42—42no—
682C42—2442no—
683C42—2444no—
684C23—41no—
685C23—41no—
686C23—611no—
687C23—611no—
688C23—611no—
689C23—611no—
690C23—1222no—
691C23—1222no—
692C23—1222no—
693C23—1222no—
694C23—1222no—
695C23—1222no—
696C23—1222no—
697C23—1222no—
698C23—1221no—
699C23—1221no—
700C23—1222no—
701C23—1222no—
702C23—1221no—
703C23—1221no—
704C23—2441no—
705C23—2441no—
706C23—2441no—
707C23—2441no—
708C23—2441no—
709C23—2441no—
710C23—2448no—
711C23—2448no—
712C23C22×C4×D6111yescharacteristic
713C23C2×D4×D6111yescharacteristic
714C23C2×D4×D6111yescharacteristic
715C23#1451982412yes—
716C23#1451982512yes—
717Q8—42no—
718Q8—42no—
719Q8—2442no—
720Q8—2444no—
721Q8—2444no—
722Q8—2442no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—611no—
740C2×C4—614no—
741C2×C4—611no—
742C2×C4—611no—
743C2×C4—611no—
744C2×C4—1222no—
745C2×C4—1222no—
746C2×C4—1222no—
747C2×C4—1222no—
748C2×C4—1222no—
749C2×C4—1222no—
750C2×C4—1222no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1222no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—1222no—
758C2×C4—2441no—
759C2×C4—2441no—
760C2×C4—2441no—
761C2×C4—2441no—
762C2×C4—2441no—
763C2×C4—2441no—
764C2×C4—2444no—
765C2×C4—2444no—
766C2×C4—2444no—
767C2×C4—2444no—
768C2×C4—2441no—
769C2×C4—2441no—
770C2×C4—2441no—
771C2×C4—2442no—
772C2×C4—2442no—
773C2×C4—2442no—
774C2×C4—2442no—
775C2×C4—2442no—
776C2×C4—2442no—
777C2×C4—2442no—
778C2×C4—2442no—
779C2×C4C22⋊C4×D6111yescharacteristic
780C2×C4C22⋊C4×D6111yescharacteristic
781C2×C4C22⋊C4×D6111yescharacteristic
782C2×C4C22⋊C4×D6111yescharacteristic
783C22—21no—
784C22—21no—
785C22—21no—
786C22—21no—
787C22—21no—
788C22—21no—
789C22—42no—
790C22—42no—
791C22—612no—
792C22—612no—
793C22—1228no—
794C22—1221no—
795C22—1221no—
796C22—1221no—
797C22—1221no—
798C22—1221no—
799C22—1221no—
800C22—1221no—
801C22—1221no—
802C22—1221no—
803C22—1221no—
804C22—2442no—
805C22—2442no—
806C22—2444no—
807C22—2444no—
808C22—2442no—
809C22—2442no—
810C22—2444no—
811C22C2×C22⋊C4×D6111yescharacteristic
812C22#1684023812yes—
813C22#1684033211yescharacteristic
814C22#1684033512yes—
815C22#1684033711yescharacteristic
816C4—21no—
817C4—21no—
818C4—21no—
819C4—42no—
820C4—42no—
821C4—82no—
822C4—82no—
823C4—612no—
824C4—1221no—
825C4—1221no—
826C4—1221no—
827C4—4882no—
828C4—4882no—
829C4—2442no—
830C4—2442no—
831C4#99×D6112yes—
832C2—21no—
833C2—22no—
834C2—21no—
835C2—22no—
836C2—1222no—
837C2—1222no—
838C2—2441no—
839C2—2441no—
840C2#2144840211yescharacteristic
841C2C2×#99×D6111yescharacteristic
842C2#410×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1996C2
socleC22×C61C22×C22⋊C4
prime radicalC24×D61C23
cosocleC24×C61C24
hypercenter#1996D61
hypocenterC61#21825
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
4. #21446805C2semidirect
5. #21446804C2semidirect
6. #21446803C2semidirect
7. #21446802C2semidirect
9. C61×#1996C2semidirect
10. C22×Q8×D61C4semidirect
12. C2×#14519757C4semidirect
14. C2×#14519755C4semidirect
16. C2×#14519753C4semidirect
27. C2×C4⋊C4×D61C4semidirect
28. C2×C4⋊C4×D61C4semidirect
418. #1996D61semidirect
470. C61#21825semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D612
#214482012
#214482002
#214468052
#214468042
#214468032
#214468022
#214458922
C61×#19962
#2182561