Finite Group Databasebeta

← #29680974

Subgroups — #29680974

Order 15616.

1446 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D61C211yesmaximal, characteristic
2C2×#16839803C211yesmaximal, characteristic
3C2×#16839769C211yesmaximal, characteristic
4C2×#16839769C211yesmaximal, characteristic
5#21448300C211yesmaximal, characteristic
6#21446090C211yesmaximal, characteristic, complemented
7#21446089C211yesmaximal, characteristic, complemented
8#21446088C211yesmaximal, characteristic, complemented
9#21446087C211yesmaximal, characteristic, complemented
10#21446072C211yesmaximal, characteristic, complemented
11#21446071C211yesmaximal, characteristic, complemented
12#21446070C211yesmaximal, characteristic, complemented
13#21445537C211yesmaximal, characteristic
14#21445511C211yesmaximal, characteristic
15C61×#1863C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C2×Q8×Dic61C2211yescharacteristic
20C2×C4×Dic122—21no—
21C2×C4×Dic122C2211yescharacteristic
22C2×#14519742—21no—
23C2×#14519742C2211yescharacteristic
24C4×Q8×D61—24no—
25C4×Q8×D61—24no—
26C2×#14519735C2211yescharacteristic
27C2×#14519735C2211yescharacteristic
28C2×C4⋊C4×D61—21no—
29C2×C4⋊C4×D61C2211yescharacteristic
30C2×C42×D61—21no—
31C2×C42×D61C2211yescharacteristic
32#16839803—24no—
33C2×#14519710C2211yescharacteristic
34C2×#14519709C2211yescharacteristic
35C2×#14519708C2211yescharacteristic
36#16839769—24no—
37#16839769C418yescomplemented
38C2×#14519702C2211yescharacteristic
39C2×#14519702C2211yescharacteristic
40C2×#14519701C2211yescharacteristic
41C2×#14519701C2211yescharacteristic
42C2×#14519700C2211yescharacteristic
43C2×#14519700C2211yescharacteristic
44#16839661C2211yescharacteristic
45#16839660C2211yescharacteristic
46#16839658C2211yescharacteristic
47#16839636—21no—
48#16839633—21no—
49C4⋊C4×Dic61—21no—
50#16839613—21no—
51#16839525C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839517C2211yescharacteristic
55#16839516C2211yescharacteristic
56#16839516C2211yescharacteristic
57C2×C4×Q8×C61C2211yescharacteristic
58C2×#107×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#103×C61C2211yescharacteristic
61C61×#389C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C61×#336C2211yescharacteristic
64C22×Dic122—21no—
65C22×Dic122C2311yescharacteristic
66C2×Q8×D61—22no—
67C2×Q8×D61—22no—
68C2×Q8×D61—22no—
69C2×Q8×D61C2×C414yes—
70C2×Q8×D61D414yes—
71C2×Q8×D61Q814yes—
72C22×C4×D61—21no—
73C22×C4×D61—21no—
74C22×C4×D61D411yescharacteristic
75C22×C4×D61D411yescharacteristic
76C22×C4×D61C2311yescharacteristic
77C2×#11758189—22no—
78C2×#11758189—22no—
79C2×#11758189—22no—
80C2×#11758189—22no—
81C2×#11758189—22no—
82C2×#11758189C2×C414yes—
83C22×#92418C2311yescharacteristic
84C22×#92418C2311yescharacteristic
85Q8×Dic61—22no—
86Q8×Dic61—22no—
87C4×Dic122—28no—
88C4×Dic122—22no—
89C4×Dic122—22no—
90#14519742—28no—
91#14519742—22no—
92#14519742—22no—
93#14519735—22no—
94#14519735—22no—
95#14519735—22no—
96#14519735C2×C414yes—
97C2×C4⋊Dic61—21no—
98C2×C4⋊Dic61—21no—
99C2×C4⋊Dic61C2311yescharacteristic
100C2×C4⋊Dic61C2311yescharacteristic
101C2×C4⋊Dic61C2311yescharacteristic
102C2×#11758196—21no—
103C2×#11758196—21no—
104C2×#11758196—21no—
105C2×#11758196—21no—
106C2×#11758196—21no—
107C4⋊C4×D61—28no—
108C4⋊C4×D61—22no—
109C4⋊C4×D61D414yes—
110C2×#11758198—21no—
111C2×#11758198—21no—
112C2×C4×Dic61—21no—
113C2×C4×Dic61—21no—
114C2×C4×Dic61—21no—
115C2×C4×Dic61—21no—
116C2×C4×Dic61—21no—
117C2×C4×Dic61D411yescharacteristic
118C2×C4×Dic61D411yescharacteristic
119C2×C4×Dic61C2311yescharacteristic
120C42×D61—28no—
121C42×D61—22no—
122C42×D61—22no—
123#14519710—22no—
124#14519709—22no—
125#14519708—22no—
126#14519702—22no—
127#14519702C2×C414yescomplemented
128#14519701—22no—
129#14519701C2×C414yescomplemented
130#14519700—22no—
131#14519700C2×C414yescomplemented
132#14519684—21no—
133#14519684—21no—
134#14519684—21no—
135C22×Q8×C61C2311yescharacteristic
136C22×C8×C61C2311yescharacteristic
137C22×C8×C61C2311yescharacteristic
138C4×Q8×C61—22no—
139C4×Q8×C61—22no—
140C2×C4⋊C4×C61—21no—
141C2×C4⋊C4×C61—21no—
142C2×C4⋊C4×C61C2311yescharacteristic
143C2×C4⋊C4×C61C2311yescharacteristic
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C42×C61—21no—
146C2×C42×C61C2311yescharacteristic
147#107×C61—22no—
148#103×C61—22no—
149#103×C61C2×C414yescomplemented
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×C61C2×D412yes—
157C2×Q8×C61C2×Q812yes—
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×D61C4⋊C4116yescomplemented
176C2×C4×D61—24no—
177C2×C4×D61—24no—
178C2×C4×D61—22no—
179C2×C4×D61—24no—
180C2×C4×D61—22no—
181C2×C4×D61—22no—
182C2×C4×D61—24no—
183C2×C4×D61—22no—
184C2×C4×D61—41no—
185C2×C4×D61—41no—
186C2×C4×D61—42no—
187C2×C4×D61—42no—
188C2×C4×D61C22×C412yes—
189C2×C4×D61C2×D412yes—
190C2×C4×D61C2×D412yes—
191C2×C4×D61C2×Q812yes—
192C2×C4×D61#4112yes—
193C2×C4×D61#4112yes—
194C2×Dic122—21no—
195C2×Dic122—21no—
196C2×Dic122—21no—
197C2×Dic122—24no—
198C2×Dic122—24no—
199C2×Dic122—24no—
200C2×Dic122C22×C412yes—
201C2×Dic122C2×D412yes—
202C2×Dic122C2×Q812yes—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61C22×C412yes—
209C4⋊C4×C61—24no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61—21no—
212C4⋊C4×C61—21no—
213C4⋊C4×C61—21no—
214C4⋊C4×C61—42no—
215C4⋊C4×C61C22×C412yes—
216C4⋊C4×C61C2×D412yes—
217C42×C61—24no—
218C42×C61—21no—
219C42×C61—21no—
220#11758198—24no—
221#11758198—42no—
222C4⋊Dic61—24no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—42no—
228C4⋊Dic61C22×C412yes—
229C4⋊Dic61C2×D412yes—
230#11758196—24no—
231#11758196—24no—
232#11758196—24no—
233#11758196—42no—
234#11758196—42no—
235C4×Dic61—24no—
236C4×Dic61—24no—
237C4×Dic61—24no—
238C4×Dic61—21no—
239C4×Dic61—21no—
240C4×Dic61—24no—
241C4×Dic61—22no—
242C4×Dic61—22no—
243C4×Dic61—42no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418C22×C412yes—
250#11758189—28no—
251#11758189—44no—
252C23×C61C22×D411yescharacteristic
253C22×D61—21no—
254C22×D61—21no—
255C22×D61—21no—
256C22×D61—21no—
257C22×D61C4×D412yes—
258C22×D61#12012yes—
259C22×D61C22⋊Q812yes—
260Q8×C61—22no—
261Q8×C61—22no—
262Q8×C61—22no—
263Q8×C61C2×C4⋊C414yes—
264C2×C4×C61—22no—
265C2×C4×C61—21no—
266C2×C4×C61—22no—
267C2×C4×C61—22no—
268C2×C4×C61—21no—
269C2×C4×C61—22no—
270C2×C4×C61—21no—
271C2×C4×C61—22no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—41no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61#13712yes—
282C2×C4×C61C23×C411yescharacteristic
283C2×C4×C61C22×D411yescharacteristic
284C2×C4×C61C22×D411yescharacteristic
285C2×C4×C61C22×Q811yescharacteristic
286C2×C4×C61C2×#4111yescharacteristic
287C2×C4×C61C2×#4111yescharacteristic
288C2×Dic61—22no—
289C2×Dic61—21no—
290C2×Dic61—22no—
291C2×Dic61—22no—
292C2×Dic61—21no—
293C2×Dic61—22no—
294C2×Dic61—21no—
295C2×Dic61—22no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61C4×D412yes—
306C2×Dic61#12012yes—
307C2×Dic61C22⋊Q812yes—
308C2×Dic61#13712yes—
309C4×D61—28no—
310C4×D61—216no—
311C4×D61—44no—
312C4×D61—48no—
313C4×D61C2×C4⋊C414yes—
314C4×D61C4×D414yes—
315C4×D61C22⋊Q814yes—
316C4×D61#12314yes—
317Dic122—22no—
318Dic122—22no—
319Dic122—22no—
320Dic122—216no—
321Dic122C2×C4⋊C414yes—
322C8×C61—22no—
323C8×C61—41no—
324#92418—22no—
325#92418—41no—
326#20874—611nomaximal, Sylow
327C22×C61C2×C4×D411yescharacteristic
328C22×C61C2×#12011yescharacteristic
329C22×C61C2×C22⋊Q811yescharacteristic
330C22×C61C2×#13711yescharacteristic
331C22×C61C2×#13711yescharacteristic
332C22×C61#57511yescharacteristic
333C22×C61#57511yescharacteristic
334C2×D61—22no—
335C2×D61—22no—
336C2×D61—22no—
337C2×D61—22no—
338C2×D61—22no—
339C2×D61—22no—
340C2×D61#38514yes—
341C4×C61—22no—
342C4×C61—24no—
343C4×C61—42no—
344C4×C61—41no—
345C4×C61—42no—
346C4×C61—81no—
347C4×C61C22×C4⋊C411yescharacteristic
348C4×C61C2×C4×D411yescharacteristic
349C4×C61C2×C22⋊Q811yescharacteristic
350C4×C61C2×#12311yescharacteristic
351Dic61—22no—
352Dic61—24no—
353Dic61—42no—
354Dic61—41no—
355Dic61—42no—
356Dic61—81no—
357Dic61#38514yes—
358C22×C4×Q8—611no—
359C2×#428—611no—
360C2×#419—611no—
361C2×#419—611no—
362#2296—611no—
363#1865—611no—
364#1865—611no—
365#1865—611no—
366#1865—611no—
367#1863—611no—
368#1863—611no—
369#1863—611no—
370#1863D6111yescharacteristic, complemented
371#1736—611no—
372#1728—611no—
373C2×C61C2×#38511yescharacteristic
374C2×C61C4×#13711yescharacteristic
375C2×C61C4×#13711yescharacteristic
376C2×C61#300411yescharacteristic
377C2×C61#300511yescharacteristic
378C2×C61#307811yescharacteristic
379C2×C61#307811yescharacteristic
380D61—24no—
381C23×Q8—611no—
382C22×M16—611no—
383C22×M16—611no—
384C2×C4×Q8—611no—
385C2×C4×Q8—611no—
386C2×C4×Q8—611no—
387C2×C4×Q8—1221no—
388C2×C4×Q8—1221no—
389C2×C4×Q8—1224no—
390C2×C4×Q8—1224no—
391C2×C4×Q8C2×D6111yescharacteristic
392C2×#117—611no—
393C2×#117—611no—
394C22×C4⋊C4—611no—
395C22×C4⋊C4—1221no—
396C22×C42—611no—
397C22×C42—1221no—
398#428—1224no—
399C2×#107—611no—
400C2×#107C2×D6111yescharacteristic
401C2×#106—611no—
402C2×#106—611no—
403#419—618no—
404#419—1224no—
405C2×#103—611no—
406C2×#103—611no—
407C2×#103—611no—
408C2×#103—611no—
409C2×#103—611no—
410C2×#103—611no—
411C2×#103C2×D6111yescharacteristic
412C2×#103C2×D6111yescharacteristic
413#389—611no—
414#389—611no—
415#389—611no—
416#389C2×D6111yescharacteristic
417#385—1221no—
418#385—1221no—
419C4×C4⋊C4—1221no—
420C4×C4⋊C4—1221no—
421#340—611no—
422#340—611no—
423#340—611no—
424#340C2×D6111yescharacteristic
425#336—611no—
426#336—611no—
427#336—611no—
428#336C2×D6111yescharacteristic
429C61#2087411yescharacteristic, complemented, Sylow
430C22×Q8—614no—
431C22×Q8—614no—
432C22×Q8—614no—
433C22×Q8—611no—
434C22×Q8—1221no—
435C22×Q8—1222no—
436C22×Q8—1222no—
437C22×Q8—1222no—
438C22×Q8C22×D6111yescharacteristic
439C23×C4—611no—
440C23×C4—611no—
441C23×C4—611no—
442C23×C4—1221no—
443C23×C4—1221no—
444C2×M16—614no—
445C2×M16—1222no—
446C2×M16—1222no—
447C2×M16—1222no—
448C2×M16—1222no—
449C2×M16—1222no—
450C22×C8—611no—
451C22×C8—611no—
452C22×C8C22×D6111yescharacteristic
453C22×C8C22×D6111yescharacteristic
454C4×Q8—22no—
455C4×Q8—22no—
456C4×Q8—1222no—
457C4×Q8—1222no—
458C4×Q8—1228no—
459C4×Q8—1222no—
460C4×Q8—1228no—
461C4×Q8—1222no—
462C4×Q8—1222no—
463C4×Q8—1222no—
464#117—614no—
465#117—1222no—
466#117—1222no—
467#117—1222no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—611no—
471C2×C4⋊C4—611no—
472C2×C4⋊C4—614no—
473C2×C4⋊C4—611no—
474C2×C4⋊C4—1222no—
475C2×C4⋊C4—1228no—
476C2×C4⋊C4—1221no—
477C2×C4⋊C4—1221no—
478C2×C4⋊C4—1221no—
479C2×C4⋊C4—1221no—
480C2×C4⋊C4—1221no—
481C2×C4⋊C4—1221no—
482C2×C4⋊C4—1221no—
483C2×C4⋊C4C22×D6111yescharacteristic
484C2×C4⋊C4C22×D6111yescharacteristic
485C2×C4⋊C4C22×D6111yescharacteristic
486C2×C22⋊C4—1221no—
487C2×C22⋊C4—1221no—
488C2×C42—21no—
489C2×C42—611no—
490C2×C42—611no—
491C2×C42—611no—
492C2×C42—1222no—
493C2×C42—1222no—
494C2×C42—1228no—
495C2×C42—1221no—
496C2×C42—1221no—
497C2×C42—1221no—
498C2×C42—1221no—
499C2×C42—1221no—
500C2×C42C22×D6111yescharacteristic
501#107—22no—
502#107—1222no—
503#106—1222no—
504#106—1222no—
505#103—22no—
506#103—614no—
507#103—614no—
508#103—614no—
509#103—1222no—
510#103—1222no—
511#103—1222no—
512#103C4×D6114yescomplemented
513#95—21no—
514#95—1221no—
515#95—1221no—
516#95—1221no—
517C24—611no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—6116no—
522C2×Q8—612no—
523C2×Q8—612no—
524C2×Q8—612no—
525C2×Q8—1224no—
526C2×Q8—1224no—
527C2×Q8—1224no—
528C2×Q8—1228no—
529C2×Q8—1228no—
530C2×Q8—1228no—
531C2×Q8—1221no—
532C2×Q8—1221no—
533C2×Q8—1221no—
534C2×Q8C2×C4×D6112yes—
535C2×Q8D4×D6112yes—
536C2×Q8Q8×D6112yes—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—611no—
542C22×C4—612no—
543C22×C4—612no—
544C22×C4—612no—
545C22×C4—612no—
546C22×C4—612no—
547C22×C4—612no—
548C22×C4—611no—
549C22×C4—611no—
550C22×C4—1222no—
551C22×C4—1222no—
552C22×C4—1224no—
553C22×C4—1224no—
554C22×C4—1224no—
555C22×C4—1224no—
556C22×C4—1222no—
557C22×C4—1221no—
558C22×C4—1222no—
559C22×C4—1221no—
560C22×C4—1221no—
561C22×C4—1221no—
562C22×C4—2441no—
563C22×C4—2441no—
564C22×C4—2442no—
565C22×C4—2442no—
566C22×C4D4×D6111yescharacteristic
567C22×C4D4×D6111yescharacteristic
568C22×C4C23×D6111yescharacteristic
569M16—1228no—
570M16—2444no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—612no—
577C2×C8—1221no—
578C2×C8—1221no—
579C2×C8—1221no—
580C2×C8—1221no—
581C2×C8—1221no—
582C2×C8C2×C4×D6112yes—
583C4⋊C4—24no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—42no—
589C4⋊C4—612no—
590C4⋊C4—612no—
591C4⋊C4—1224no—
592C4⋊C4—1224no—
593C4⋊C4—1224no—
594C4⋊C4—1224no—
595C4⋊C4—1221no—
596C4⋊C4—1221no—
597C4⋊C4—1221no—
598C4⋊C4—1221no—
599C4⋊C4—2442no—
600C4⋊C4—2442no—
601C4⋊C4—2442no—
602C4⋊C4C2×C4×D6112yes—
603C4⋊C4D4×D6112yes—
604C22⋊C4—1224no—
605C22⋊C4—2442no—
606C42—24no—
607C42—21no—
608C42—21no—
609C42—1222no—
610C42—1222no—
611C42—1224no—
612C42—1224no—
613C42—1224no—
614C42—1224no—
615C42—1221no—
616C42—1221no—
617C42—2442no—
618C23—612no—
619C23—612no—
620C23—612no—
621C23—1221no—
622C23—1221no—
623C23—1221no—
624C23—1221no—
625C23C2×D4×D6111yescharacteristic
626Q8—22no—
627Q8—22no—
628Q8—22no—
629Q8—614no—
630Q8—12216no—
631Q8—1222no—
632Q8—1222no—
633Q8—1222no—
634Q8C4⋊C4×D6114yes—
635C2×C4—22no—
636C2×C4—21no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—21no—
640C2×C4—22no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—612no—
653C2×C4—612no—
654C2×C4—612no—
655C2×C4—614no—
656C2×C4—614no—
657C2×C4—614no—
658C2×C4—614no—
659C2×C4—612no—
660C2×C4—12216no—
661C2×C4—1228no—
662C2×C4—1222no—
663C2×C4—1221no—
664C2×C4—1222no—
665C2×C4—1222no—
666C2×C4—1221no—
667C2×C4—1222no—
668C2×C4—1222no—
669C2×C4—1221no—
670C2×C4—1221no—
671C2×C4—1221no—
672C2×C4—2444no—
673C2×C4—2448no—
674C2×C4—2441no—
675C2×C4—2441no—
676C2×C4—2441no—
677C2×C4—2441no—
678C2×C4—2441no—
679C2×C4—2441no—
680C2×C4—2441no—
681C2×C4#1451980912yes—
682C2×C4C22×C4×D6111yescharacteristic
683C2×C4C2×D4×D6111yescharacteristic
684C2×C4C2×D4×D6111yescharacteristic
685C2×C4C2×Q8×D6111yescharacteristic
686C2×C4#41×D6111yescharacteristic
687C2×C4#41×D6111yescharacteristic
688C8—22no—
689C8—41no—
690C8—1222no—
691C8—2441no—
692C22—614no—
693C22—1222no—
694C22—1222no—
695C22—1222no—
696C22—1222no—
697C22—1222no—
698C22—1222no—
699C22C4×D4×D6111yescharacteristic
700C22#120×D6111yescharacteristic
701C22C22⋊Q8×D6111yescharacteristic
702C22#137×D6111yescharacteristic
703C22C2×#1451980911yescharacteristic
704C22#1684055811yescharacteristic
705C22#1684055911yescharacteristic
706C4—24no—
707C4—22no—
708C4—42no—
709C4—41no—
710C4—42no—
711C4—81no—
712C4—614no—
713C4—1224no—
714C4—1222no—
715C4—4881no—
716C4—2442no—
717C4—2441no—
718C4—2442no—
719C4C2×C4⋊C4×D6111yescharacteristic
720C4C4×D4×D6111yescharacteristic
721C4C22⋊Q8×D6111yescharacteristic
722C4#123×D6111yescharacteristic
723C2—1224no—
724C2#385×D6111yescharacteristic
725C2C4×#1451980911yescharacteristic
726C2#2145464111yescharacteristic
727C2#2145505411yescharacteristic
728C2#2145505711yescharacteristic
729C2#2145562211yescharacteristic
730C2#2145562511yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1863C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
cosocleC22×C4×C61C24
hypercenter#1863D61
hypocenterC61#20874
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1863

Complements

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

NH ≅ G/Ntype
6. #21446090C2semidirect
7. #21446089C2semidirect
8. #21446088C2semidirect
9. #21446087C2semidirect
10. #21446072C2semidirect
11. #21446071C2semidirect
12. #21446070C2semidirect
15. C61×#1863C2semidirect
37. #16839769C4semidirect
127. #14519702C2×C4semidirect
129. #14519701C2×C4semidirect
131. #14519700C2×C4semidirect
149. #103×C61C2×C4semidirect
175. Q8×D61C4⋊C4semidirect
370. #1863D61semidirect
429. C61#20874semidirect
512. #103C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D612
C2×#168398032
C2×#168397692
#214483002
#214460902
#214460892
#214460882
#214460872
#214460722
#214460712
#214460702
#214455372
#214455112
C61×#18632
#2087461