Finite Group Databasebeta

← #29689052

Subgroups — #29689052

Order 15616.

1590 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840275C211yesmaximal, characteristic
2C22×#14519689C211yesmaximal, characteristic, complemented
3#380×D61C211yesmaximal, characteristic, complemented
4#21446247C211yesmaximal, characteristic, complemented
5#21446245C211yesmaximal, characteristic, complemented
6#21446243C211yesmaximal, characteristic, complemented
7#21446135C212yesmaximal, complemented
8#21446123C212yesmaximal, complemented
9#21445912C212yesmaximal, complemented
10#21445758C212yesmaximal, complemented
11C61×#1892C211yesmaximal, characteristic, complemented
12C22×#11758226C2211yescharacteristic
13C23×C4×D61C2211yescharacteristic
14C23×#92418C2211yescharacteristic
15#16840275—24no—
16#16840275C418yescomplemented
17C2×#14519762—21no—
18C2×#14519753C2211yescharacteristic
19C2×#14519752C2211yescharacteristic
20C2×#14519751C2211yescharacteristic
21C2×#14519747—21no—
22C2×#14519739—21no—
23C2×#14519737—21no—
24C2×#14519735C2211yescharacteristic
25C2×C4⋊C4×D61C2212yes—
26C2×C22⋊C4×D61—21no—
27C2×#14519701C2212yescomplemented
28C2×#14519699C2212yescomplemented
29C2×#14519697C2212yescomplemented
30C2×#14519689—24no—
31C2×#14519689C2212yes—
32C2×#14519689C2212yes—
33#16839622C2211yescharacteristic
34#16839621—21no—
35#16839620—21no—
36#16839619C2212yes—
37#95×D61—21no—
38#16839525C2212yescomplemented
39#16839524C2212yescomplemented
40#16839524C2212yescomplemented
41C23×C8×C61C2211yescharacteristic
42C2×C22⋊Q8×C61C2211yescharacteristic
43C2×#103×C61C2212yescomplemented
44C61×#380C2211yescharacteristic
45C61×#340C2212yescomplemented
46C24×D61D411yescharacteristic
47C2×#11758226—22no—
48C2×#11758226—42no—
49C2×#11758226—42no—
50C2×#11758226C2×C414yescomplemented
51C22×D244—21no—
52C22×D244—21no—
53C22×D244C2311yescharacteristic
54C22×C22⋊D61—21no—
55C23×Dic61D411yescharacteristic
56C22×C4×D61—21no—
57C22×C4×D61—22no—
58C22×C4×D61—42no—
59C22×C4×D61—42no—
60C22×C4×D61C2×C414yes—
61C22×C4×D61D411yescharacteristic
62C22×C4×D61D411yescharacteristic
63C22×C4×D61D414yes—
64C22×C4×D61C2311yescharacteristic
65C22×C4×D61C2311yescharacteristic
66C22×#92418—22no—
67C22×#92418—42no—
68C22×#92418C2312yes—
69#14519762—28no—
70#14519753—22no—
71#14519753C2×C414yes—
72#14519752—22no—
73#14519752C2×C414yes—
74#14519751—22no—
75#14519751C2×C414yescomplemented
76#14519747—28no—
77#14519739—28no—
78#14519737—28no—
79#14519735—22no—
80#14519735C2×C414yescomplemented
81C2×C4⋊Dic61C2312yes—
82C2×C4⋊Dic61C2311yescharacteristic
83C2×#11758196—21no—
84C2×#11758196—22no—
85C4⋊C4×D61—42no—
86C4⋊C4×D61—42no—
87C2×C22⋊Dic61—21no—
88C2×#11758198—21no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×#11758198—22no—
93C22⋊C4×D61—44no—
94C2×C4×Dic61—21no—
95#14519701—42no—
96#14519699—42no—
97#14519697—42no—
98#14519689—24no—
99#14519689—24no—
100#14519684—21no—
101#14519684—22no—
102C22×Q8×C61C2311yescharacteristic
103C23×C4×C61C2311yescharacteristic
104C22×C8×C61—22no—
105C22×C8×C61—42no—
106C22×C8×C61C2312yes—
107C22⋊Q8×C61—22no—
108C22⋊Q8×C61C2×C414yescomplemented
109C2×C4⋊C4×C61—21no—
110C2×C4⋊C4×C61C2312yes—
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C22⋊C4×C61—21no—
113C2×C22⋊C4×C61—21no—
114#103×C61—42no—
115#95×C61—21no—
116C24×C61C2×D411yescharacteristic
117C23×D61—22no—
118C23×D61—22no—
119C23×D61—24no—
120C23×D61—21no—
121C23×D61—42no—
122C23×D61C22⋊C414yes—
123C23×D61C2×D411yescharacteristic
124C23×D61C2×D411yescharacteristic
125C2×Q8×C61—21no—
126C2×Q8×C61—22no—
127C2×Q8×C61—22no—
128C2×Q8×C61C22×C412yes—
129C22×C4×C61—22no—
130C22×C4×C61—22no—
131C22×C4×C61—21no—
132C22×C4×C61—21no—
133C22×C4×C61—22no—
134C22×C4×C61C22×C412yes—
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D412yes—
137C22×C4×C61C2411yescharacteristic
138C2×C22⋊D61—24no—
139C2×C22⋊D61—42no—
140C2×C22⋊D61—42no—
141C22×Dic61—21no—
142C22×Dic61—22no—
143C22×Dic61—42no—
144C22×Dic61C22⋊C414yes—
145C22×Dic61C2×D411yescharacteristic
146C22×Dic61C2×D411yescharacteristic
147#11758226—48no—
148#11758226—44no—
149#11758226—44no—
150C2×D244—22no—
151C2×D244—22no—
152C2×D244—24no—
153C2×D244—24no—
154C2×D244—21no—
155C2×D244—44no—
156C2×D244—44no—
157C2×D244C22×C412yes—
158C2×C4×D61—22no—
159C2×C4×D61—22no—
160C2×C4×D61—22no—
161C2×C4×D61—22no—
162C2×C4×D61—24no—
163C2×C4×D61—48no—
164C2×C4×D61—44no—
165C2×C4×D61—44no—
166C2×C4×D61—42no—
167C2×C4×D61—42no—
168C2×C4×D61—44no—
169C2×C4×D61—44no—
170C2×C4×D61—44no—
171C2×C4×D61—44no—
172C2×C4×D61C22⋊C414yes—
173C2×C4×D61C22⋊C414yes—
174C2×C4×D61C22×C412yes—
175C2×C4×D61C22×C412yes—
176C2×C4×D61C2×D412yes—
177C2×C4×D61C2×D412yes—
178C2×C8×C61—22no—
179C2×C8×C61—22no—
180C2×C8×C61—22no—
181C2×C8×C61—44no—
182C4⋊C4×C61—24no—
183C4⋊C4×C61—21no—
184C4⋊C4×C61—22no—
185C4⋊C4×C61—22no—
186C4⋊C4×C61C22×C412yes—
187C22⋊C4×C61—24no—
188C22⋊C4×C61—42no—
189C22⋊Dic61—42no—
190#11758198—24no—
191#11758198—24no—
192#11758198—24no—
193#11758198—24no—
194#11758198—44no—
195C4⋊Dic61—21no—
196C4⋊Dic61—22no—
197C4⋊Dic61—22no—
198C4⋊Dic61C22×C412yes—
199#11758196—24no—
200#11758196—44no—
201C4×Dic61—24no—
202C2×#92418—22no—
203C2×#92418—22no—
204C2×#92418—22no—
205C2×#92418—44no—
206C23×C61—22no—
207C23×C61—22no—
208C23×C61C2×C22⋊C412yes—
209C23×C61AGL(1,ℤ/8)12yes—
210C23×C61#13712yes—
211C23×C61C22×D411yescharacteristic
212C22×D61—22no—
213C22×D61—21no—
214C22×D61—21no—
215C22×D61—22no—
216C22×D61—22no—
217C22×D61—21no—
218C22×D61—21no—
219C22×D61—28no—
220C22×D61—28no—
221C22×D61—22no—
222C22×D61—44no—
223C22×D61—48no—
224C22×D61—48no—
225C22×D61—42no—
226C22×D61—42no—
227C22×D61—41no—
228C22×D61—41no—
229C22×D61C2×C22⋊C412yes—
230C22×D61C2×C22⋊C412yes—
231C22×D61#13514yes—
232Q8×C61—24no—
233Q8×C61—41no—
234Q8×C61—41no—
235C2×C4×C61—22no—
236C2×C4×C61—24no—
237C2×C4×C61—22no—
238C2×C4×C61—22no—
239C2×C4×C61—22no—
240C2×C4×C61—22no—
241C2×C4×C61—42no—
242C2×C4×C61—42no—
243C2×C4×C61—42no—
244C2×C4×C61—42no—
245C2×C4×C61—42no—
246C2×C4×C61C2×C22⋊C412yes—
247C2×C4×C61C23×C411yescharacteristic
248C2×C4×C61C22×D411yescharacteristic
249C2×C4×C61H(5,𝔽2)12yes—
250C2×C4×C61H(5,𝔽2)12yes—
251C22⋊D61—48no—
252C2×Dic61—22no—
253C2×Dic61—22no—
254C2×Dic61—22no—
255C2×Dic61—44no—
256C2×Dic61—41no—
257C2×Dic61—41no—
258C2×Dic61—42no—
259C2×Dic61—42no—
260C2×Dic61—42no—
261C2×Dic61C2×C22⋊C412yes—
262C2×Dic61C2×C22⋊C412yes—
263D244—24no—
264D244—48no—
265D244—48no—
266D244—41no—
267D244—41no—
268C4×D61—24no—
269C4×D61—24no—
270C4×D61—22no—
271C4×D61—22no—
272C4×D61—22no—
273C4×D61—22no—
274C4×D61—44no—
275C4×D61—44no—
276C4×D61—48no—
277C4×D61—88no—
278C8×C61—42no—
279#92418—42no—
280#21763—611nomaximal, Sylow
281C22×C61—22no—
282C22×C61—22no—
283C22×C61—24no—
284C22×C61—24no—
285C22×C61#41714yes—
286C22×C61C22×C22⋊C411yescharacteristic
287C22×C61#53412yes—
288C22×C61C2×#13512yes—
289C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
290C22×C61C2×#13711yescharacteristic
291C2×D61—22no—
292C2×D61—22no—
293C2×D61—24no—
294C2×D61—24no—
295C2×D61—22no—
296C2×D61—22no—
297C2×D61—22no—
298C2×D61—416no—
299C2×D61—42no—
300C2×D61—42no—
301C2×D61—42no—
302C2×D61—42no—
303C2×D61—42no—
304C2×D61—82no—
305C2×D61—82no—
306C2×D61#41614yes—
307C4×C61—22no—
308C4×C61—42no—
309C4×C61—42no—
310C4×C61—82no—
311C4×C61#51812yes—
312C4×C61#53411yescharacteristic
313C4×C61#53411yescharacteristic
314Dic61—22no—
315Dic61—22no—
316Dic61—42no—
317Dic61—82no—
318C2×#525—611no—
319C22×C22⋊C8—611no—
320C2×#380—611no—
321#1893—611no—
322#1893—611no—
323#1892—611no—
324#1892D6111yescharacteristic, complemented
325#1874—612no—
326#1872—612no—
327#1825—612no—
328#1788—612no—
329C2×C61—24no—
330C2×C61#230811yescharacteristic
331C2×C61C2×#41611yescharacteristic
332C2×C61C2×#41711yescharacteristic
333C2×C61#318812yes—
334C2×C61#319012yes—
335D61—24no—
336D61—42no—
337D61—82no—
338C22×#41—611no—
339C24×C4—611no—
340C23×C8—611no—
341C23×C8C2×D6111yescharacteristic
342#525—618no—
343#525—1224no—
344C2×#123—1221no—
345C2×C22⋊Q8—611no—
346C2×C22⋊Q8C2×D6111yescharacteristic
347C2×#121—611no—
348C2×#121—611no—
349C2×#120—1221no—
350C2×C4×D4—1221no—
351C2×C4×D4—1221no—
352C2×#117—611no—
353C22×C4⋊C4—612no—
354C22×C22⋊C4—1221no—
355C2×#103—612no—
356C2×#103C2×D6112yescomplemented
357C2×#102—612no—
358C2×#102—612no—
359C2×C22⋊C8—612no—
360C2×C22⋊C8—612no—
361C2×C22⋊C8—1224no—
362#380—611no—
363#380—612no—
364#380—1221no—
365#380—1221no—
366#380C2×D6111yescharacteristic
367C2×#95—1221no—
368#340—612no—
369#340—612no—
370#340—612no—
371#340C2×D6112yescomplemented
372C61#2176311yescharacteristic, complemented, Sylow
373C25—611no—
374C2×#41—614no—
375C2×#41—1222no—
376C2×#41—2442no—
377C2×#41—2442no—
378C22×Q8C22×D6111yescharacteristic
379C22×D4—611no—
380C22×D4—1221no—
381C22×D4—1221no—
382C22×D4—1221no—
383C23×C4—611no—
384C23×C4—611no—
385C23×C4—611no—
386C23×C4—614no—
387C23×C4—611no—
388C23×C4—611no—
389C23×C4—614no—
390C23×C4—1221no—
391C23×C4—1222no—
392C23×C4—2442no—
393C23×C4—2442no—
394C23×C4C22×D6111yescharacteristic
395C22×C8—22no—
396C22×C8—42no—
397C22×C8—612no—
398C22×C8—1222no—
399C22×C8—2442no—
400C22×C8C22×D6112yes—
401#123—1228no—
402C22⋊Q8—22no—
403C22⋊Q8—614no—
404C22⋊Q8—1222no—
405C22⋊Q8C4×D6114yescomplemented
406#121—614no—
407#121—614no—
408#121—1222no—
409#121—1222no—
410#120—1228no—
411C4×D4—1228no—
412C4×D4—1228no—
413#117—614no—
414#117—1222no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—611no—
417C2×C4⋊C4—612no—
418C2×C4⋊C4—1221no—
419C2×C4⋊C4—1222no—
420C2×C4⋊C4—2442no—
421C2×C4⋊C4—2442no—
422C2×C4⋊C4C22×D6112yes—
423C2×C4⋊C4C22×D6111yescharacteristic
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—1221no—
427C2×C22⋊C4—1221no—
428C2×C22⋊C4—1221no—
429C2×C22⋊C4—1221no—
430C2×C22⋊C4—1222no—
431C2×C22⋊C4—1221no—
432C2×C22⋊C4—2444no—
433C2×C42—1221no—
434#103—42no—
435#103—2442no—
436#102—2442no—
437#102—2442no—
438C22⋊C8—1224no—
439C22⋊C8—1224no—
440#95—21no—
441#95—1222no—
442#95—1221no—
443C24—611no—
444C24—611no—
445C24—614no—
446C24—1224no—
447C24—1222no—
448C24—1222no—
449C24—1221no—
450C24—2442no—
451C24D4×D6111yescharacteristic
452#41—2448no—
453#41—2444no—
454#41—2444no—
455C2×Q8—21no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8C2×C4×D6112yes—
459C2×D4—612no—
460C2×D4—1224no—
461C2×D4—1224no—
462C2×D4—1224no—
463C2×D4—1221no—
464C2×D4—1222no—
465C2×D4—1222no—
466C2×D4—2444no—
467C2×D4—2444no—
468C2×D4—2442no—
469C2×D4—2442no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—611no—
476C22×C4—611no—
477C22×C4—614no—
478C22×C4—612no—
479C22×C4—612no—
480C22×C4—612no—
481C22×C4—612no—
482C22×C4—614no—
483C22×C4—614no—
484C22×C4—1224no—
485C22×C4—1222no—
486C22×C4—1222no—
487C22×C4—1222no—
488C22×C4—1222no—
489C22×C4—1221no—
490C22×C4—1222no—
491C22×C4—2448no—
492C22×C4—2444no—
493C22×C4—2444no—
494C22×C4—2442no—
495C22×C4—2442no—
496C22×C4—2444no—
497C22×C4—2444no—
498C22×C4—2444no—
499C22×C4—2444no—
500C22×C4—2442no—
501C22×C4C2×C4×D6112yes—
502C22×C4D4×D6112yes—
503C22×C4D4×D6111yescharacteristic
504C22×C4C23×D6111yescharacteristic
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—44no—
509C2×C8—1222no—
510C2×C8—1222no—
511C2×C8—1222no—
512C2×C8—2444no—
513C4⋊C4—21no—
514C4⋊C4—24no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—612no—
518C4⋊C4—1224no—
519C4⋊C4—1221no—
520C4⋊C4—1222no—
521C4⋊C4—1222no—
522C4⋊C4—2444no—
523C4⋊C4C2×C4×D6112yes—
524C22⋊C4—24no—
525C22⋊C4—42no—
526C22⋊C4—1224no—
527C22⋊C4—1224no—
528C22⋊C4—1224no—
529C22⋊C4—1224no—
530C22⋊C4—2444no—
531C22⋊C4—2442no—
532C42—1224no—
533C23—22no—
534C23—22no—
535C23—612no—
536C23—614no—
537C23—612no—
538C23—1228no—
539C23—1221no—
540C23—1221no—
541C23—1222no—
542C23—1228no—
543C23—1222no—
544C23—1221no—
545C23—1221no—
546C23—1222no—
547C23—1222no—
548C23—2444no—
549C23—2448no—
550C23—2448no—
551C23—2442no—
552C23—2441no—
553C23—2441no—
554C23—2442no—
555C23C22⋊C4×D6112yes—
556C23#1451980412yes—
557C23#1451980912yes—
558C23C2×D4×D6111yescharacteristic
559Q8—24no—
560Q8—41no—
561Q8—41no—
562D4—1224no—
563D4—2448no—
564D4—2448no—
565D4—2448no—
566D4—2441no—
567D4—2441no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—612no—
580C2×C4—612no—
581C2×C4—1222no—
582C2×C4—1222no—
583C2×C4—1224no—
584C2×C4—1224no—
585C2×C4—1222no—
586C2×C4—1222no—
587C2×C4—1222no—
588C2×C4—1222no—
589C2×C4—1222no—
590C2×C4—4888no—
591C2×C4—2444no—
592C2×C4—2444no—
593C2×C4—2448no—
594C2×C4—2444no—
595C2×C4—2442no—
596C2×C4—2442no—
597C2×C4—2442no—
598C2×C4—2441no—
599C2×C4—2441no—
600C2×C4C22⋊C4×D6112yes—
601C2×C4C22×C4×D6111yescharacteristic
602C2×C4C2×D4×D6111yescharacteristic
603C2×C4#1451982212yes—
604C2×C4#1451982312yes—
605C8—42no—
606C8—2442no—
607C22—22no—
608C22—24no—
609C22—24no—
610C22—22no—
611C22—614no—
612C22—1222no—
613C22—1224no—
614C22—1224no—
615C22—1222no—
616C22—1222no—
617C22—1222no—
618C22—1222no—
619C22—4882no—
620C22—4882no—
621C22—24416no—
622C22—2442no—
623C22—2442no—
624C22—2442no—
625C22—2442no—
626C22—2442no—
627C22#1683976214yes—
628C22C2×C22⋊C4×D6111yescharacteristic
629C22#1684032012yes—
630C22#135×D6112yes—
631C22C2×#1451980411yescharacteristic
632C22C2×#1451980911yescharacteristic
633C4—22no—
634C4—42no—
635C4—42no—
636C4—82no—
637C4—1222no—
638C4—1222no—
639C4—4882no—
640C4—2442no—
641C4#1684023412yes—
642C4#1684032211yescharacteristic
643C4#1684032311yescharacteristic
644C2—24no—
645C2—1224no—
646C2—4882no—
647C2—2442no—
648C2#2144839311yescharacteristic
649C2#416×D6111yescharacteristic
650C2C2×#1683976211yescharacteristic
651C2#2145658512yes—
652C2#2145660112yes—
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1892C2
socleC23×C61C22×D4
prime radicalC2×#16840275C2
cosocleC22×C4×C61C24
hypercenter#1892D61
hypocenterC61#21763
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1892

Complements

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

NH ≅ G/Ntype
2. C22×#14519689C2semidirect
3. #380×D61C2semidirect
4. #21446247C2semidirect
5. #21446245C2semidirect
6. #21446243C2semidirect
7. #21446135C2semidirect
8. #21446123C2semidirect
9. #21445912C2semidirect
10. #21445758C2semidirect
11. C61×#1892C2semidirect
16. #16840275C4semidirect
27. C2×#14519701C22semidirect
28. C2×#14519699C22semidirect
29. C2×#14519697C22semidirect
38. #16839525C22semidirect
39. #16839524C22semidirect
40. #16839524C22semidirect
43. C2×#103×C61C22semidirect
45. C61×#340C22semidirect
50. C2×#11758226C2×C4semidirect
75. #14519751C2×C4semidirect
80. #14519735C2×C4semidirect
108. C22⋊Q8×C61C2×C4semidirect
324. #1892D61semidirect
356. C2×#103C2×D61semidirect
371. #340C2×D61semidirect
372. C61#21763semidirect
405. C22⋊Q8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402752
C22×#145196892
#380×D612
#214462472
#214462452
#214462432
#214461352
#214461232
#214459122
#214457582
C61×#18922
#2176361