Finite Group Databasebeta

← #29647342

Subgroups — #29647342

Order 15616.

1046 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840296C211yesmaximal, characteristic
2#21448217C211yesmaximal, characteristic, complemented
3#21444397C214yesmaximal, complemented
4#21444392C212yesmaximal, complemented
5#21444388C212yesmaximal
6#21444306C214yesmaximal, complemented
7C2×C61×#431C211yesmaximal, characteristic, complemented
8#16840296—21no—
9#16840296—21no—
10#16840296—21no—
11#16840296—21no—
12#16840296C412yescomplemented
13#16840296C412yescomplemented
14#16840296C2212yes—
15#16840296C2212yes—
16C2×#14519771—21no—
17C2×#14519769C411yescharacteristic, complemented
18C2×#14519765C411yescharacteristic, complemented
19C2×#14519760—21no—
20C2×#14519756C2211yescharacteristic
21C2×#14519751C2211yescharacteristic
22C2×C4×Dic122C411yescharacteristic, complemented
23C2×C4×D244C411yescharacteristic, complemented
24C2×C4×C22⋊D61—21no—
25C2×#14519734—21no—
26#16839630C2212yescomplemented
27#16839628—21no—
28#16839625—21no—
29#16839622C2212yes—
30C4×C4⋊Dic61—21no—
31C4×C22⋊Dic61—21no—
32#16839608C2212yescomplemented
33#16839500C2218yescomplemented
34#16839497C2218yes—
35C22×C42×C61C2211yescharacteristic
36C61×#431—21no—
37C61×#431—21no—
38C61×#431C2212yescomplemented
39C61×#431C2212yescomplemented
40C2×C4⋊C8×C61—21no—
41C2×C22⋊C8×C61C2212yes—
42C2×C4×C8×C61—21no—
43C22×Dic122C2×C411yescharacteristic
44C22×D244C2×C411yescharacteristic
45C22×C22⋊D61—21no—
46C22×C4×D61—21no—
47#14519771—22no—
48#14519771—22no—
49#14519771—22no—
50#14519771—22no—
51#14519769—21no—
52#14519769—21no—
53#14519769C2×C412yes—
54#14519769C2×C412yes—
55#14519765—21no—
56#14519765—21no—
57#14519765C2×C412yes—
58#14519765C2×C412yes—
59#14519760—22no—
60#14519760—22no—
61#14519760—22no—
62#14519760—22no—
63#14519756—21no—
64#14519756—21no—
65#14519756C2×C412yes—
66#14519756C2312yes—
67#14519751—21no—
68#14519751—21no—
69#14519751C2×C412yes—
70#14519751C2312yes—
71C4×Dic122—21no—
72C4×Dic122—21no—
73C4×Dic122C2×C412yes—
74C4×Dic122C2×C412yes—
75C4×D244—21no—
76C4×D244—21no—
77C4×D244C2×C412yes—
78C4×D244C2×C412yes—
79C4×C22⋊D61—22no—
80C4×C22⋊D61—22no—
81C4×C22⋊D61—22no—
82C4×C22⋊D61—22no—
83#14519734—22no—
84#14519734—22no—
85#14519734—22no—
86#14519734—22no—
87C2×C4⋊Dic61—22no—
88C2×C4⋊Dic61C2×C411yescharacteristic
89C2×C4⋊Dic61C2×C411yescharacteristic
90C2×#11758196—21no—
91C2×#11758196—21no—
92C2×#11758196—21no—
93C2×#11758196—21no—
94C2×C22⋊Dic61—21no—
95C2×C22⋊Dic61—22no—
96C2×#11758198—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×C4×Dic61—21no—
101C2×C4×Dic61—22no—
102#14519684—22no—
103#14519684—22no—
104#14519684—22no—
105#14519684C2314yes—
106C23×C4×C61D411yescharacteristic
107C23×C4×C61D411yescharacteristic
108C23×C4×C61C2311yescharacteristic
109C22×C8×C61—22no—
110C2×C42×C61C2×C411yescharacteristic
111C2×C42×C61C2×C411yescharacteristic
112C2×C42×C61C2×C411yescharacteristic
113C2×C42×C61C2×C411yescharacteristic
114C2×C42×C61D411yescharacteristic
115C2×C42×C61D411yescharacteristic
116C2×C42×C61D411yescharacteristic
117C2×C42×C61D411yescharacteristic
118C2×C42×C61D411yescharacteristic
119C2×C42×C61D411yescharacteristic
120C2×C42×C61C2311yescharacteristic
121C2×C42×C61C2311yescharacteristic
122C4⋊C8×C61—22no—
123C4⋊C8×C61—22no—
124C22⋊C8×C61—22no—
125C22⋊C8×C61C2314yes—
126C4×C8×C61—22no—
127C4×C8×C61—22no—
128C24×C61C2×D411yescharacteristic
129C23×D61—21no—
130C22×C4×C61—24no—
131C22×C4×C61—42no—
132C22×C4×C61—42no—
133C22×C4×C61C22⋊C411yescharacteristic
134C22×C4×C61C22⋊C411yescharacteristic
135C22×C4×C61C22⋊C411yescharacteristic
136C22×C4×C61C22⋊C411yescharacteristic
137C22×C4×C61C22⋊C411yescharacteristic
138C22×C4×C61C22⋊C411yescharacteristic
139C22×C4×C61C22⋊C411yescharacteristic
140C22×C4×C61C22⋊C411yescharacteristic
141C22×C4×C61C22×C411yescharacteristic
142C22×C4×C61C22×C411yescharacteristic
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2411yescharacteristic
151C2×C22⋊D61—22no—
152C2×C22⋊D61—22no—
153C2×C22⋊D61—44no—
154C22×Dic61—21no—
155C22×Dic61—21no—
156C22×Dic61—21no—
157C22×Dic61—24no—
158C2×D244—21no—
159C2×D244—42no—
160C2×D244C22×C412yes—
161C2×C4×D61—22no—
162C2×C4×D61—22no—
163C2×C4×D61—44no—
164C2×Dic122—21no—
165C2×Dic122—42no—
166C2×Dic122C22×C412yes—
167C2×C8×C61—24no—
168C2×C8×C61—44no—
169C42×C61C22⋊C411yescharacteristic
170C42×C61C22⋊C411yescharacteristic
171C42×C61C22⋊C411yescharacteristic
172C42×C61C22⋊C411yescharacteristic
173C42×C61C22⋊C411yescharacteristic
174C42×C61C22⋊C411yescharacteristic
175C42×C61C22⋊C411yescharacteristic
176C42×C61C22⋊C411yescharacteristic
177C42×C61C22×C411yescharacteristic
178C42×C61C22×C411yescharacteristic
179C42×C61C22×C411yescharacteristic
180C42×C61C22×C411yescharacteristic
181C42×C61C2×D411yescharacteristic
182C42×C61C2×D411yescharacteristic
183C42×C61C2×D411yescharacteristic
184C42×C61C2×D411yescharacteristic
185C22⋊Dic61—22no—
186C22⋊Dic61—22no—
187C22⋊Dic61—44no—
188#11758198—22no—
189#11758198—22no—
190#11758198—22no—
191#11758198—22no—
192#11758198—22no—
193#11758198—22no—
194#11758198—22no—
195#11758198—22no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—44no—
199C4⋊Dic61C22×C412yes—
200C4⋊Dic61C22×C412yes—
201#11758196—22no—
202#11758196—22no—
203#11758196—22no—
204#11758196—22no—
205#11758196—22no—
206#11758196—22no—
207#11758196—22no—
208#11758196—22no—
209C4×Dic61—22no—
210C4×Dic61—22no—
211C4×Dic61—44no—
212C23×C61—41no—
213C23×C61—41no—
214C23×C61C2×C22⋊C411yescharacteristic
215C23×C61C2×C22⋊C411yescharacteristic
216C23×C61#13514yes—
217C23×C61C22×D411yescharacteristic
218C22×D61—22no—
219C22×D61—42no—
220C22×D61—42no—
221C22×D61—42no—
222C2×C4×C61—22no—
223C2×C4×C61—22no—
224C2×C4×C61—22no—
225C2×C4×C61—22no—
226C2×C4×C61—22no—
227C2×C4×C61—22no—
228C2×C4×C61—22no—
229C2×C4×C61—22no—
230C2×C4×C61—22no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—22no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61—41no—
240C2×C4×C61C2×C22⋊C411yescharacteristic
241C2×C4×C61C2×C22⋊C411yescharacteristic
242C2×C4×C61C2×C22⋊C411yescharacteristic
243C2×C4×C61C2×C22⋊C411yescharacteristic
244C2×C4×C61C2×C22⋊C411yescharacteristic
245C2×C4×C61C2×C22⋊C411yescharacteristic
246C2×C4×C61C2×C22⋊C411yescharacteristic
247C2×C4×C61C2×C22⋊C411yescharacteristic
248C2×C4×C61C2×C22⋊C411yescharacteristic
249C2×C4×C61C2×C22⋊C411yescharacteristic
250C2×C4×C61C23×C411yescharacteristic
251C2×C4×C61C22×D411yescharacteristic
252C22⋊D61—44no—
253C22⋊D61—44no—
254C2×Dic61—22no—
255C2×Dic61—22no—
256C2×Dic61—22no—
257C2×Dic61—42no—
258C2×Dic61—42no—
259C2×Dic61—42no—
260C2×Dic61—44no—
261C2×Dic61—44no—
262C2×Dic61—44no—
263D244—42no—
264D244—42no—
265C4×D61—44no—
266C4×D61—44no—
267Dic122—42no—
268Dic122—42no—
269C8×C61—44no—
270#17567—611nomaximal, Sylow
271C22×C61—21no—
272C22×C61—21no—
273C22×C61—21no—
274C22×C61—21no—
275C22×C61—21no—
276C22×C61—21no—
277C22×C61—44no—
278C22×C61#41612yes—
279C22×C61#41612yes—
280C22×C61C22×C22⋊C411yescharacteristic
281C22×C61C2×#13512yes—
282C2×D61—42no—
283C2×D61—42no—
284C2×D61—42no—
285C2×D61—84no—
286C4×C61—21no—
287C4×C61—21no—
288C4×C61—21no—
289C4×C61—21no—
290C4×C61—21no—
291C4×C61—21no—
292C4×C61—21no—
293C4×C61—21no—
294C4×C61—21no—
295C4×C61—21no—
296C4×C61#41012yes—
297C4×C61#42112yes—
298Dic61—42no—
299Dic61—42no—
300Dic61—42no—
301Dic61—84no—
302C2×#529—611no—
303C2×#431D6111yescharacteristic, complemented
304#2283—611no—
305#1521—614no—
306#1520—612no—
307#1519—612no—
308#1500—614no—
309C2×C61—22no—
310C2×C61—22no—
311C2×C61—22no—
312C2×C61C2×#41011yescharacteristic
313C2×C61C2×#41611yescharacteristic
314C2×C61C2×#42111yescharacteristic
315D61—82no—
316#529—612no—
317#529—612no—
318#529—612no—
319#529—612no—
320#529—1221no—
321#529—1221no—
322#529—1221no—
323#529—1221no—
324C2×#126—1221no—
325C2×#125—611no—
326C2×#124—611no—
327C2×#123—1221no—
328C2×C22⋊Q8—611no—
329C2×#121—611no—
330C2×C4×Q8—611no—
331C2×C4×D4—611no—
332C2×C4×D4—1221no—
333C2×#117—1221no—
334C22×C42C2×D6111yescharacteristic
335#431—21no—
336#431—21no—
337#431C2×D6112yescomplemented
338#431C2×D6112yescomplemented
339C2×C4⋊C8—21no—
340C2×C22⋊C8C2×D6112yes—
341C2×C4×C8—21no—
342#383—612no—
343#382—1221no—
344#381—1221no—
345#380—612no—
346C4×C4⋊C4—1221no—
347C4×C22⋊C4—1221no—
348#376—612no—
349#328—618no—
350#327—618no—
351C61#1756711yescharacteristic, complemented, Sylow
352C22×Q8—611no—
353C22×D4—611no—
354C22×D4—1221no—
355C23×C4—1221no—
356C23×C4D24411yescharacteristic
357C23×C4D24411yescharacteristic
358C23×C4C22×D6111yescharacteristic
359C22×C8—22no—
360#126—1222no—
361#126—1222no—
362#126—1222no—
363#126—1222no—
364#125—612no—
365#125—612no—
366#125—1221no—
367#125—1221no—
368#124—612no—
369#124—612no—
370#124—1221no—
371#124—1221no—
372#123—1222no—
373#123—1222no—
374#123—1222no—
375#123—1222no—
376C22⋊Q8—612no—
377C22⋊Q8—612no—
378C22⋊Q8—1221no—
379C22⋊Q8—1221no—
380#121—612no—
381#121—612no—
382#121—1221no—
383#121—1221no—
384C4×Q8—612no—
385C4×Q8—612no—
386C4×Q8—1221no—
387C4×Q8—1221no—
388C4×D4—612no—
389C4×D4—612no—
390C4×D4—1222no—
391C4×D4—1222no—
392C4×D4—1222no—
393C4×D4—1222no—
394C4×D4—1221no—
395C4×D4—1221no—
396#117—1222no—
397#117—1222no—
398#117—1222no—
399#117—1222no—
400C2×C4⋊C4—611no—
401C2×C4⋊C4—611no—
402C2×C4⋊C4—1221no—
403C2×C4⋊C4—1221no—
404C2×C4⋊C4—1221no—
405C2×C4⋊C4—1221no—
406C2×C4⋊C4—1222no—
407C2×C22⋊C4—1221no—
408C2×C22⋊C4—1221no—
409C2×C22⋊C4—1221no—
410C2×C22⋊C4—1221no—
411C2×C22⋊C4—1221no—
412C2×C22⋊C4—1222no—
413C2×C42—1221no—
414C2×C42—1222no—
415C2×C42C4×D6111yescharacteristic
416C2×C42C4×D6111yescharacteristic
417C2×C42C4×D6111yescharacteristic
418C2×C42C4×D6111yescharacteristic
419C2×C42D24411yescharacteristic
420C2×C42D24411yescharacteristic
421C2×C42C22⋊D6111yescharacteristic
422C2×C42C22⋊D6111yescharacteristic
423C2×C42C22⋊D6111yescharacteristic
424C2×C42C22⋊D6111yescharacteristic
425C2×C42C22×D6111yescharacteristic
426C2×C42C22×D6111yescharacteristic
427C4⋊C8—22no—
428C4⋊C8—22no—
429C22⋊C8—22no—
430C22⋊C8C22×D6114yes—
431C4×C8—22no—
432C4×C8—22no—
433#95—614no—
434#95—1222no—
435#95—1222no—
436#95—1222no—
437C24—1221no—
438C24C2×D24411yescharacteristic
439C2×Q8—612no—
440C2×Q8—1221no—
441C2×Q8—2442no—
442C2×D4—612no—
443C2×D4—1222no—
444C2×D4—1222no—
445C2×D4—1221no—
446C2×D4—2442no—
447C2×D4—2444no—
448C22×C4—24no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—1221no—
452C22×C4—1221no—
453C22×C4—1221no—
454C22×C4—1222no—
455C22×C4—1222no—
456C22×C4—1224no—
457C22×C4—2444no—
458C22×C4#1175819811yescharacteristic
459C22×C4#1175819811yescharacteristic
460C22×C4#1175819811yescharacteristic
461C22×C4#1175819811yescharacteristic
462C22×C4#1175819811yescharacteristic
463C22×C4#1175819811yescharacteristic
464C22×C4#1175819811yescharacteristic
465C22×C4#1175819811yescharacteristic
466C22×C4C2×C4×D6111yescharacteristic
467C22×C4C2×C4×D6111yescharacteristic
468C22×C4C2×D24411yescharacteristic
469C22×C4C2×D24411yescharacteristic
470C22×C4C2×D24411yescharacteristic
471C22×C4C2×D24411yescharacteristic
472C22×C4C2×D24411yescharacteristic
473C22×C4C2×C22⋊D6111yescharacteristic
474C22×C4C2×C22⋊D6111yescharacteristic
475C22×C4C23×D6111yescharacteristic
476C2×C8—24no—
477C2×C8—44no—
478C4⋊C4—612no—
479C4⋊C4—612no—
480C4⋊C4—1222no—
481C4⋊C4—1221no—
482C4⋊C4—1221no—
483C4⋊C4—1222no—
484C4⋊C4—1222no—
485C4⋊C4—1222no—
486C4⋊C4—1222no—
487C4⋊C4—1222no—
488C4⋊C4—1222no—
489C4⋊C4—1222no—
490C4⋊C4—2444no—
491C22⋊C4—1222no—
492C22⋊C4—1222no—
493C22⋊C4—1222no—
494C22⋊C4—1222no—
495C22⋊C4—1222no—
496C22⋊C4—1222no—
497C22⋊C4—1222no—
498C22⋊C4—1222no—
499C22⋊C4—1222no—
500C22⋊C4—1222no—
501C22⋊C4—2444no—
502C42—1222no—
503C42—1222no—
504C42—2444no—
505C42#1175819811yescharacteristic
506C42#1175819811yescharacteristic
507C42#1175819811yescharacteristic
508C42#1175819811yescharacteristic
509C42#1175819811yescharacteristic
510C42#1175819811yescharacteristic
511C42#1175819811yescharacteristic
512C42#1175819811yescharacteristic
513C42C2×C4×D6111yescharacteristic
514C42C2×C4×D6111yescharacteristic
515C42C2×C4×D6111yescharacteristic
516C42C2×C4×D6111yescharacteristic
517C42C2×C22⋊D6111yescharacteristic
518C42C2×C22⋊D6111yescharacteristic
519C42C2×C22⋊D6111yescharacteristic
520C42C2×C22⋊D6111yescharacteristic
521C23—41no—
522C23—41no—
523C23—1222no—
524C23—2442no—
525C23—2442no—
526C23—2442no—
527C23C2×#1175819811yescharacteristic
528C23C2×#1175819811yescharacteristic
529C23#1451979914yes—
530C23C22×D24411yescharacteristic
531Q8—2442no—
532Q8—2442no—
533D4—2442no—
534D4—2444no—
535D4—2444no—
536D4—2442no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—1222no—
556C2×C4—1222no—
557C2×C4—1222no—
558C2×C4—2444no—
559C2×C4—2444no—
560C2×C4—2444no—
561C2×C4—2444no—
562C2×C4—2442no—
563C2×C4—2442no—
564C2×C4—2442no—
565C2×C4—2444no—
566C2×C4C2×#1175819811yescharacteristic
567C2×C4C2×#1175819811yescharacteristic
568C2×C4C2×#1175819811yescharacteristic
569C2×C4C2×#1175819811yescharacteristic
570C2×C4C2×#1175819811yescharacteristic
571C2×C4C2×#1175819811yescharacteristic
572C2×C4C2×#1175819811yescharacteristic
573C2×C4C2×#1175819811yescharacteristic
574C2×C4C2×#1175819811yescharacteristic
575C2×C4C2×#1175819811yescharacteristic
576C2×C4C22×C4×D6111yescharacteristic
577C2×C4C22×C22⋊D6111yescharacteristic
578C8—44no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—44no—
586C22—4884no—
587C22—2442no—
588C22—2442no—
589C22—2442no—
590C22#1683975912yes—
591C22#1683975912yes—
592C22C22×#1175819811yescharacteristic
593C22C2×#1451979912yes—
594C4—21no—
595C4—21no—
596C4—21no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—21no—
601C4—21no—
602C4—21no—
603C4—21no—
604C4—4884no—
605C4—2442no—
606C4—2442no—
607C4—2442no—
608C4#1683973512yes—
609C4#1683977812yes—
610C2—22no—
611C2—22no—
612C2—22no—
613C2—4882no—
614C2C2×#1683973511yescharacteristic
615C2C2×#1683975911yescharacteristic
616C2C2×#1683977811yescharacteristic
subgroupG/H
centerC2×C4C2×#11758198
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#431C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519751C22
cosocleC22×C4×C61C24
hypercenterC2×#431D61
hypocenterC61#17567
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C2×#431

Complements

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

NH ≅ G/Ntype
2. #21448217C2semidirect
3. #21444397C2semidirect
4. #21444392C2semidirect
6. #21444306C2semidirect
7. C2×C61×#431C2semidirect
12. #16840296C4semidirect
13. #16840296C4semidirect
17. C2×#14519769C4semidirect
18. C2×#14519765C4semidirect
22. C2×C4×Dic122C4semidirect
23. C2×C4×D244C4semidirect
26. #16839630C22semidirect
32. #16839608C22semidirect
33. #16839500C22semidirect
38. C61×#431C22semidirect
39. C61×#431C22semidirect
303. C2×#431D61semidirect
337. #431C2×D61semidirect
338. #431C2×D61semidirect
351. C61#17567semidirect

Maximal subgroups

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

subgroupindex
C2×#168402962
#214482172
#214443972
#214443922
#214443882
#214443062
C2×C61×#4312
#1756761