Finite Group Databasebeta

← #29645971

Subgroups — #29645971

Order 15616.

1020 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840291C211yesmaximal, characteristic
2#21454449C211yesmaximal, characteristic, complemented
3#431×D61C211yesmaximal, characteristic, complemented
4#21444176C211yesmaximal, characteristic, complemented
5#21444174C211yesmaximal, characteristic, complemented
6#21444171C211yesmaximal, characteristic, complemented
7#21444164C214yesmaximal, complemented
8#21444130C214yesmaximal, complemented
9C61×#1469C211yesmaximal, characteristic, complemented
10#16840291—21no—
11#16840291—21no—
12#16840291—21no—
13#16840291—21no—
14#16840291—21no—
15#16840291—21no—
16#16840291—21no—
17#16840291—21no—
18C2×#14519770C412yes—
19C2×#14519769C2211yescharacteristic
20C2×#14519759C2212yes—
21C2×#14519753C411yescharacteristic
22C2×#14519748C411yescharacteristic
23C2×Q8×Dic61C411yescharacteristic
24C2×D4×Dic61C411yescharacteristic
25C2×#14519737C412yes—
26C2×#14519733C2212yes—
27C2×C42×D61C2211yescharacteristic
28#16839819C2211yescharacteristic
29#16839817—21no—
30#16839815C2211yescharacteristic
31#16839814—21no—
32#16839814—21no—
33#16839813—21no—
34#16839812C2212yes—
35#16839812C2212yes—
36#16839784—21no—
37C4⋊C8×D61—21no—
38#16839724C2212yes—
39C22⋊C8×D61C2212yes—
40#16839714—21no—
41C4×C8×D61—21no—
42#16839487C2214yes—
43#16839487C2214yes—
44#16839486C2214yes—
45C2×#124×C61C2211yescharacteristic
46C61×#432C2211yescharacteristic
47C61×#431C2211yescharacteristic
48C61×#323C2214yes—
49C22×C22⋊D61C2×C412yes—
50C23×Dic61C2×C412yes—
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61C2311yescharacteristic
54C2×#11758189—22no—
55C2×C8×D61—22no—
56#14519770—22no—
57#14519770—22no—
58#14519770—22no—
59#14519770—22no—
60#14519769—21no—
61#14519769—21no—
62#14519769—21no—
63#14519769—21no—
64#14519759—22no—
65#14519759—22no—
66#14519759—22no—
67#14519759—22no—
68#14519753—21no—
69#14519753—21no—
70#14519753—21no—
71#14519753—21no—
72#14519748—21no—
73#14519748—21no—
74#14519748—21no—
75#14519748—21no—
76Q8×Dic61—21no—
77Q8×Dic61—21no—
78Q8×Dic61—21no—
79Q8×Dic61—21no—
80D4×Dic61—21no—
81D4×Dic61—21no—
82D4×Dic61—21no—
83D4×Dic61—21no—
84#14519737—22no—
85#14519737—22no—
86#14519737—22no—
87#14519737—22no—
88#14519733—22no—
89#14519733—22no—
90#14519733—22no—
91#14519733—22no—
92C2×C4⋊Dic61C2×C411yescharacteristic
93C2×C4⋊Dic61C2×C411yescharacteristic
94C2×C4⋊Dic61C2×C412yes—
95C2×#11758196C2×C412yes—
96C2×#11758196C2×C412yes—
97C2×#11758196C2312yes—
98C2×C22⋊Dic61C2×C412yes—
99C2×C22⋊Dic61C2×C412yes—
100C2×#11758198C2×C412yes—
101C2×C4×Dic61C2×C412yes—
102C2×C4×Dic61C2×C411yescharacteristic
103C2×C4×Dic61C2×C411yescharacteristic
104C2×C4×Dic61C2311yescharacteristic
105C42×D61D411yescharacteristic
106C42×D61D411yescharacteristic
107C42×D61D411yescharacteristic
108C42×D61D411yescharacteristic
109C42×D61D411yescharacteristic
110C42×D61D411yescharacteristic
111C42×D61D411yescharacteristic
112C42×D61D411yescharacteristic
113C4⋊#92418—21no—
114C4⋊#92418—21no—
115#14519706—22no—
116#14519706—22no—
117C22⋊#92418C2312yes—
118C22⋊#92418C2312yes—
119#14519689—22no—
120#14519689—22no—
121#14519688—21no—
122C4×#92418—21no—
123C8×Dic61—22no—
124C8×Dic61—22no—
125C22×Q8×C61C2×C411yescharacteristic
126C22×D4×C61C2×C411yescharacteristic
127#124×C61—21no—
128#124×C61—21no—
129#124×C61—21no—
130#124×C61—21no—
131C2×C22⋊C4×C61C2×C412yes—
132C2×C22⋊C4×C61C2312yes—
133C2×C42×C61C2311yescharacteristic
134C4⋊C8×C61—21no—
135C4⋊C8×C61—21no—
136C22⋊C8×C61C2312yes—
137C22⋊C8×C61C2312yes—
138#97×C61—21no—
139C4×C8×C61—21no—
140C24×C61C22×C412yes—
141C23×D61C22×C411yescharacteristic
142C2×Q8×C61—21no—
143C2×Q8×C61—21no—
144C2×Q8×C61—42no—
145C2×D4×C61—21no—
146C2×D4×C61—21no—
147C2×D4×C61—42no—
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C22×C412yes—
151C22×C4×C61C2411yescharacteristic
152C2×C22⋊D61—22no—
153C2×C22⋊D61—22no—
154C2×C22⋊D61—44no—
155C22×Dic61—22no—
156C22×Dic61—22no—
157C22×Dic61—28no—
158C22×Dic61C22×C412yes—
159C22×Dic61C22×C412yes—
160C22×Dic61C22×C411yescharacteristic
161C22×Dic61C22×C411yescharacteristic
162C22×Dic61C22×C411yescharacteristic
163C2×C4×D61—24no—
164C2×C4×D61—42no—
165C2×C4×D61—42no—
166C2×C4×D61C22⋊C411yescharacteristic
167C2×C4×D61C22⋊C411yescharacteristic
168C2×C4×D61C22⋊C411yescharacteristic
169C2×C4×D61C22⋊C411yescharacteristic
170C2×C4×D61C22⋊C411yescharacteristic
171C2×C4×D61C22⋊C411yescharacteristic
172C2×C4×D61C22⋊C411yescharacteristic
173C2×C4×D61C22⋊C411yescharacteristic
174C2×C4×D61C2×D411yescharacteristic
175C2×C4×D61C2×D411yescharacteristic
176C2×C4×D61C2×D411yescharacteristic
177C2×C4×D61C2×D411yescharacteristic
178C2×C8×C61—22no—
179C2×C8×C61—22no—
180C22⋊C4×C61—22no—
181C22⋊C4×C61—22no—
182C22⋊C4×C61—22no—
183C22⋊C4×C61—22no—
184C42×C61C2×D411yescharacteristic
185C42×C61C2×D411yescharacteristic
186C42×C61C2×D411yescharacteristic
187C42×C61C2×D411yescharacteristic
188C22⋊Dic61—22no—
189C22⋊Dic61—22no—
190C22⋊Dic61—22no—
191C22⋊Dic61—22no—
192#11758198—22no—
193#11758198—22no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—22no—
199C4⋊Dic61—22no—
200#11758196—22no—
201#11758196—22no—
202#11758196—22no—
203#11758196—22no—
204#11758196—22no—
205#11758196—22no—
206C4×Dic61—22no—
207C4×Dic61—22no—
208C4×Dic61C22⋊C411yescharacteristic
209C4×Dic61C22⋊C411yescharacteristic
210C4×Dic61C22⋊C411yescharacteristic
211C4×Dic61C22⋊C411yescharacteristic
212C4×Dic61C22⋊C411yescharacteristic
213C4×Dic61C22⋊C411yescharacteristic
214C4×Dic61C22⋊C411yescharacteristic
215C4×Dic61C22⋊C411yescharacteristic
216C4×Dic61C2×D411yescharacteristic
217C4×Dic61C2×D411yescharacteristic
218C4×Dic61C2×D411yescharacteristic
219C4×Dic61C2×D411yescharacteristic
220C2×#92418—22no—
221C2×#92418—22no—
222#11758189—44no—
223C8×D61—44no—
224C23×C61—22no—
225C23×C61—24no—
226C23×C61—42no—
227C23×C61—42no—
228C23×C61C23×C411yescharacteristic
229C22×D61—22no—
230C22×D61—22no—
231C22×D61—41no—
232C22×D61C2×C22⋊C411yescharacteristic
233C22×D61C2×C22⋊C411yescharacteristic
234Q8×C61—42no—
235Q8×C61—42no—
236D4×C61—42no—
237D4×C61—42no—
238C2×C4×C61—22no—
239C2×C4×C61—22no—
240C2×C4×C61—22no—
241C2×C4×C61—41no—
242C2×C4×C61—42no—
243C2×C4×C61C2×C22⋊C411yescharacteristic
244C2×C4×C61C2×C22⋊C411yescharacteristic
245C2×C4×C61C2×C22⋊C411yescharacteristic
246C2×C4×C61C2×C22⋊C411yescharacteristic
247C2×C4×C61C22×D411yescharacteristic
248C2×C4×C61C22×D411yescharacteristic
249C22⋊D61—44no—
250C22⋊D61—44no—
251C2×Dic61—22no—
252C2×Dic61—22no—
253C2×Dic61—24no—
254C2×Dic61—41no—
255C2×Dic61—41no—
256C2×Dic61—44no—
257C2×Dic61—44no—
258C2×Dic61—42no—
259C2×Dic61C2×C22⋊C411yescharacteristic
260C2×Dic61C2×C22⋊C411yescharacteristic
261C2×Dic61C2×C22⋊C411yescharacteristic
262C2×Dic61C2×C22⋊C411yescharacteristic
263C2×Dic61C2×C22⋊C411yescharacteristic
264C2×Dic61C2×C22⋊C411yescharacteristic
265C2×Dic61#13114yes—
266C4×D61—22no—
267C4×D61—22no—
268C4×D61—22no—
269C4×D61—22no—
270C4×D61—22no—
271C4×D61—22no—
272C4×D61—22no—
273C4×D61—22no—
274C4×D61—41no—
275C4×D61—41no—
276C4×D61—41no—
277C4×D61—41no—
278C8×C61—42no—
279C8×C61—42no—
280#92418—42no—
281#92418—42no—
282#17376—611nomaximal, Sylow
283C22×C61—21no—
284C22×C61—21no—
285C22×C61—42no—
286C22×C61—42no—
287C22×C61—42no—
288C22×C61—84no—
289C22×C61C22×C22⋊C411yescharacteristic
290C22×C61C2×#13112yes—
291C2×D61—21no—
292C2×D61—21no—
293C2×D61—21no—
294C2×D61—21no—
295C2×D61—21no—
296C2×D61—44no—
297C2×D61#41012yes—
298C4×C61—21no—
299C4×C61—21no—
300C4×C61—21no—
301C4×C61—21no—
302C4×C61—21no—
303C4×C61—42no—
304C4×C61#41312yes—
305Dic61—21no—
306Dic61—21no—
307Dic61—21no—
308Dic61—21no—
309Dic61—42no—
310Dic61—42no—
311Dic61#40812yes—
312Dic61#40812yes—
313C2×#529—611no—
314#2920—611no—
315C2×#431—611no—
316#1470—611no—
317#1470—611no—
318#1469—611no—
319#1469D6111yescharacteristic, complemented
320#1468—614no—
321#1458—614no—
322C2×C61—22no—
323C2×C61—82no—
324C2×C61C2×#40811yescharacteristic
325C2×C61C2×#41011yescharacteristic
326C2×C61C2×#41311yescharacteristic
327D61—22no—
328D61—41no—
329#529—1221no—
330#529—1221no—
331#529—1221no—
332#529—1221no—
333#529—1221no—
334#529—1221no—
335#529—1221no—
336#529—1221no—
337C2×#126—612no—
338C2×#125—611no—
339C2×#124C2×D6111yescharacteristic
340C2×#123—612no—
341C2×C22⋊Q8—611no—
342C2×#121—611no—
343C2×C4×Q8—611no—
344C2×C4×D4—611no—
345C2×C4×D4—612no—
346C2×#117—612no—
347C22×C42—611no—
348#432—611no—
349#432—1221no—
350#432C2×D6111yescharacteristic
351#431—611no—
352#431—612no—
353#431—612no—
354#431—1221no—
355#431—1221no—
356#431—1221no—
357#431C2×D6111yescharacteristic
358#423—1221no—
359C2×C4⋊C8—1221no—
360#407—612no—
361C2×C22⋊C8—612no—
362C4×M16—1221no—
363C2×C4×C8—1221no—
364#324—614no—
365#324—614no—
366#323—614no—
367#323C2×D6114yes—
368C61#1737611yescharacteristic, complemented, Sylow
369C22×Q8C4×D6111yescharacteristic
370C22×D4—612no—
371C22×D4C4×D6111yescharacteristic
372C23×C4—611no—
373C23×C4—611no—
374C23×C4—611no—
375C23×C4—612no—
376C2×M16—1222no—
377C22×C8—1222no—
378#126—1222no—
379#126—1222no—
380#126—1222no—
381#126—1222no—
382#125—1221no—
383#125—1221no—
384#125—1221no—
385#125—1221no—
386#124—21no—
387#124—21no—
388#124—21no—
389#124—21no—
390#123—1222no—
391#123—1222no—
392#123—1222no—
393#123—1222no—
394C22⋊Q8—1221no—
395C22⋊Q8—1221no—
396C22⋊Q8—1221no—
397C22⋊Q8—1221no—
398#121—1221no—
399#121—1221no—
400#121—1221no—
401#121—1221no—
402C4×Q8—1221no—
403C4×Q8—1221no—
404C4×Q8—1221no—
405C4×Q8—1221no—
406C4×D4—1221no—
407C4×D4—1221no—
408C4×D4—1221no—
409C4×D4—1221no—
410C4×D4—1222no—
411C4×D4—1222no—
412C4×D4—1222no—
413C4×D4—1222no—
414#117—1222no—
415#117—1222no—
416#117—1222no—
417#117—1222no—
418C2×C4⋊C4—612no—
419C2×C4⋊C4—611no—
420C2×C4⋊C4—612no—
421C2×C4⋊C4—611no—
422C2×C4⋊C4—612no—
423C2×C4⋊C4—612no—
424C2×C22⋊C4—612no—
425C2×C22⋊C4—612no—
426C2×C22⋊C4—612no—
427C2×C22⋊C4C4×D6112yes—
428C2×C22⋊C4C22×D6112yes—
429C2×C42—611no—
430C2×C42—611no—
431C2×C42—611no—
432C2×C42—611no—
433C2×C42—611no—
434C2×C42—611no—
435C2×C42—611no—
436C2×C42—611no—
437C2×C42—611no—
438C2×C42—611no—
439C2×C42—611no—
440C2×C42—612no—
441C2×C42C22×D6111yescharacteristic
442C4⋊C8—21no—
443C4⋊C8—21no—
444C4⋊C8—1222no—
445C4⋊C8—1222no—
446C4⋊C8—1221no—
447C4⋊C8—1221no—
448C22⋊C8—612no—
449C22⋊C8—612no—
450C22⋊C8—1222no—
451C22⋊C8—1222no—
452C22⋊C8C22×D6112yes—
453C22⋊C8C22×D6112yes—
454#97—21no—
455#97—1221no—
456C4×C8—21no—
457C4×C8—1222no—
458C4×C8—1222no—
459C4×C8—1221no—
460C24—611no—
461C24C2×C4×D6112yes—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—42no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—42no—
468C2×D4—1222no—
469C2×D4—1222no—
470C2×D4—2444no—
471C22×C4—611no—
472C22×C4—611no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—611no—
476C22×C4—611no—
477C22×C4—611no—
478C22×C4—611no—
479C22×C4—611no—
480C22×C4—611no—
481C22×C4—611no—
482C22×C4—611no—
483C22×C4—611no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—612no—
487C22×C4—612no—
488C22×C4—1224no—
489C22×C4—1222no—
490C22×C4—1222no—
491C22×C4—1228no—
492C22×C4—2442no—
493C22×C4—2442no—
494C22×C4C2×C4×D6111yescharacteristic
495C22×C4C2×C4×D6111yescharacteristic
496C22×C4C2×C4×D6112yes—
497C22×C4C23×D6111yescharacteristic
498M16—2444no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—1222no—
502C2×C8—1222no—
503C2×C8—2444no—
504C4⋊C4—1222no—
505C4⋊C4—1222no—
506C4⋊C4—1222no—
507C4⋊C4—1222no—
508C4⋊C4—1222no—
509C4⋊C4—1222no—
510C4⋊C4—1222no—
511C4⋊C4—1222no—
512C4⋊C4—1221no—
513C4⋊C4—1221no—
514C4⋊C4—1221no—
515C4⋊C4—1221no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—1222no—
521C22⋊C4—1222no—
522C22⋊C4—1222no—
523C22⋊C4—1222no—
524C22⋊C4—1222no—
525C22⋊C4—1222no—
526C42—611no—
527C42—611no—
528C42—611no—
529C42—611no—
530C42—611no—
531C42—611no—
532C42—611no—
533C42—611no—
534C42—611no—
535C42—611no—
536C42—611no—
537C42—611no—
538C42—1222no—
539C42—1222no—
540C42D4×D6111yescharacteristic
541C42D4×D6111yescharacteristic
542C42D4×D6111yescharacteristic
543C42D4×D6111yescharacteristic
544C23—22no—
545C23—24no—
546C23—42no—
547C23—42no—
548C23—611no—
549C23—611no—
550C23—1222no—
551C23—1222no—
552C23—2441no—
553C23C22×C4×D6111yescharacteristic
554Q8—42no—
555Q8—42no—
556D4—42no—
557D4—42no—
558D4—2444no—
559D4—2444no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—611no—
566C2×C4—611no—
567C2×C4—614no—
568C2×C4—611no—
569C2×C4—611no—
570C2×C4—611no—
571C2×C4—611no—
572C2×C4—1222no—
573C2×C4—1222no—
574C2×C4—1222no—
575C2×C4—1222no—
576C2×C4—1222no—
577C2×C4—1222no—
578C2×C4—1222no—
579C2×C4—1222no—
580C2×C4—1222no—
581C2×C4—1222no—
582C2×C4—1224no—
583C2×C4—2441no—
584C2×C4—2441no—
585C2×C4—2441no—
586C2×C4—2441no—
587C2×C4—2444no—
588C2×C4—2444no—
589C2×C4—2441no—
590C2×C4—2441no—
591C2×C4—2442no—
592C2×C4C22⋊C4×D6111yescharacteristic
593C2×C4C22⋊C4×D6111yescharacteristic
594C2×C4C22⋊C4×D6111yescharacteristic
595C2×C4C22⋊C4×D6111yescharacteristic
596C2×C4C2×D4×D6111yescharacteristic
597C2×C4C2×D4×D6111yescharacteristic
598C8—42no—
599C8—42no—
600C8—2442no—
601C8—2442no—
602C22—21no—
603C22—21no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—84no—
608C22—612no—
609C22—1221no—
610C22—1221no—
611C22—1221no—
612C22—1221no—
613C22—1221no—
614C22—2444no—
615C22C2×C22⋊C4×D6111yescharacteristic
616C22#131×D6112yes—
617C4—21no—
618C4—21no—
619C4—21no—
620C4—21no—
621C4—21no—
622C4—42no—
623C4—612no—
624C4—612no—
625C4—1221no—
626C4—1221no—
627C4—1221no—
628C4—1221no—
629C4—2442no—
630C4—2442no—
631C4#1683974312yes—
632C2—22no—
633C2—82no—
634C2—1222no—
635C2—2441no—
636C2#408×D6111yescharacteristic
637C2#410×D6111yescharacteristic
638C2C2×#1683974311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1469C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519748C4
cosocleC22×C4×C61C24
hypercenter#1469D61
hypocenterC61#17376
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1469

Complements

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

NH ≅ G/Ntype
2. #21454449C2semidirect
3. #431×D61C2semidirect
4. #21444176C2semidirect
5. #21444174C2semidirect
6. #21444171C2semidirect
7. #21444164C2semidirect
8. #21444130C2semidirect
9. C61×#1469C2semidirect
319. #1469D61semidirect
368. C61#17376semidirect

Maximal subgroups

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

subgroupindex
C2×#168402912
#214544492
#431×D612
#214441762
#214441742
#214441712
#214441642
#214441302
C61×#14692
#1737661