Finite Group Databasebeta

← #29737672

Subgroups — #29737672

Order 15616.

774 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448694C211yesmaximal, characteristic
2#21447376C211yesmaximal, characteristic, complemented
3#21447320C211yesmaximal, characteristic, complemented
4#21447320C211yesmaximal, characteristic, complemented
5#21447149C211yesmaximal, characteristic, complemented
6#21446772C211yesmaximal, characteristic, complemented
7#21446580C211yesmaximal, characteristic, complemented
8#21446394C211yesmaximal, characteristic, complemented
9#21446394C211yesmaximal, characteristic, complemented
10#21446012C211yesmaximal, characteristic
11#21445999C211yesmaximal, characteristic
12#21445907C211yesmaximal, characteristic
13#21445842C211yesmaximal, characteristic
14C2×#16839524C211yesmaximal, characteristic
15C61×#2440C211yesmaximal, characteristic
16C23×#92418C2211yescharacteristic
17C22×C4⋊Dic61C2211yescharacteristic
18C2×#14519708C2211yescharacteristic
19C2×#14519708C2211yescharacteristic
20C2×#14519708C2211yescharacteristic
21C2×#14519708C2211yescharacteristic
22C2×C4⋊#92418C2211yescharacteristic
23C2×C4⋊#92418C2211yescharacteristic
24C2×C22⋊#92418C2211yescharacteristic
25#16839660C2211yescharacteristic
26#16839660C2211yescharacteristic
27#16839645—21no—
28#16839645—21no—
29#16839622C2211yescharacteristic
30#16839620—21no—
31C4×C4⋊Dic61C2211yescharacteristic
32C4×C4⋊Dic61C2211yescharacteristic
33C22⋊C4×Dic61—21no—
34#16839524C2211yescharacteristic
35#16839524C2211yescharacteristic
36#16839524C2211yescharacteristic
37#16839524C2211yescharacteristic
38#16839524C2211yescharacteristic
39#16839524C2211yescharacteristic
40#16839524C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48C2×C4⋊Q8×C61C2211yescharacteristic
49C2×C22⋊Q8×C61—21no—
50C22×C4⋊C4×C61C2211yescharacteristic
51C61×#398—21no—
52C61×#395—21no—
53C61×#389C2211yescharacteristic
54C61×#389C2211yescharacteristic
55C61×#385—21no—
56C61×#384C2211yescharacteristic
57C61×#380C2211yescharacteristic
58C4×C22⋊C4×C61C2211yescharacteristic
59C23×Dic61—21no—
60C22×#92418—22no—
61C22×#92418—22no—
62C22×#92418—41no—
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C2×C4⋊Dic61—21no—
68C2×C4⋊Dic61—22no—
69C2×C4⋊Dic61Q814yescomplemented
70C2×C4⋊Dic61C2311yescharacteristic
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×#11758196—21no—
75C2×#11758196—21no—
76C2×C22⋊Dic61—21no—
77C2×C4×Dic61—21no—
78C2×C4×Dic61—21no—
79#14519708—22no—
80#14519708—22no—
81#14519708—41no—
82#14519708—41no—
83C4⋊#92418—22no—
84C4⋊#92418—41no—
85C22⋊#92418—22no—
86#14519684—21no—
87#14519684—21no—
88#14519684—21no—
89#14519684—21no—
90#14519684—21no—
91C22×Q8×C61—21no—
92C23×C4×C61—21no—
93C23×C4×C61C2311yescharacteristic
94C4⋊Q8×C61—22no—
95C4⋊Q8×C61—41no—
96C22⋊Q8×C61—44no—
97C2×C4⋊C4×C61—22no—
98C2×C4⋊C4×C61—21no—
99C2×C4⋊C4×C61—21no—
100C2×C4⋊C4×C61—21no—
101C2×C4⋊C4×C61—21no—
102C2×C4⋊C4×C61—21no—
103C2×C4⋊C4×C61—21no—
104C2×C4⋊C4×C61—41no—
105C2×C4⋊C4×C61C2311yescharacteristic
106C2×C4⋊C4×C61C2311yescharacteristic
107C2×C4⋊C4×C61C2311yescharacteristic
108C2×C4⋊C4×C61C2311yescharacteristic
109C2×C22⋊C4×C61—21no—
110C2×C22⋊C4×C61D411yescharacteristic
111C2×C22⋊C4×C61D411yescharacteristic
112C2×C42×C61C2311yescharacteristic
113C2×C42×C61C2311yescharacteristic
114#95×C61—21no—
115#95×C61—21no—
116#95×C61—21no—
117#95×C61D411yescharacteristic
118#95×C61D411yescharacteristic
119C24×C61C2×D411yescharacteristic
120C2×Q8×C61—42no—
121C2×Q8×C61—42no—
122C2×Q8×C61—81no—
123C22×C4×C61—21no—
124C22×C4×C61—21no—
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61—42no—
132C22×C4×C61—42no—
133C22×C4×C61—81no—
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2×Q812yes—
140C22×C4×C61#4112yes—
141C22×C4×C61C2411yescharacteristic
142C22×Dic61—21no—
143C22×Dic61—21no—
144C22×Dic61—24no—
145C22×Dic61—21no—
146C22×Dic61—21no—
147C22×Dic61—81no—
148C22×Dic61—81no—
149C4⋊C4×C61—21no—
150C4⋊C4×C61—21no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—21no—
153C4⋊C4×C61—21no—
154C4⋊C4×C61—21no—
155C4⋊C4×C61—21no—
156C4⋊C4×C61—42no—
157C4⋊C4×C61—42no—
158C4⋊C4×C61—42no—
159C4⋊C4×C61—42no—
160C4⋊C4×C61—42no—
161C4⋊C4×C61—81no—
162C4⋊C4×C61#4112yes—
163C22⋊C4×C61—22no—
164C22⋊C4×C61—42no—
165C22⋊C4×C61SD1614yes—
166C42×C61—21no—
167C42×C61—21no—
168C42×C61—21no—
169C42×C61—21no—
170C22⋊Dic61—42no—
171C4⋊Dic61—24no—
172C4⋊Dic61—21no—
173C4⋊Dic61—21no—
174C4⋊Dic61—21no—
175C4⋊Dic61—21no—
176C4⋊Dic61—21no—
177C4⋊Dic61—21no—
178C4⋊Dic61C2×Q812yes—
179C4⋊Dic61C2×Q812yes—
180#11758196—81no—
181#11758196—81no—
182C4×Dic61—81no—
183C4×Dic61—81no—
184C2×#92418—21no—
185C2×#92418—21no—
186C2×#92418—21no—
187C2×#92418—21no—
188C2×#92418—21no—
189C2×#92418—21no—
190C2×#92418—21no—
191C2×#92418—21no—
192C2×#92418—21no—
193C2×#92418—21no—
194C2×#92418—21no—
195C2×#92418—44no—
196C2×#92418#4112yes—
197C23×C61—21no—
198C23×C61—21no—
199C23×C61—21no—
200C23×C61—21no—
201C23×C61C22⋊Q812yes—
202C23×C61C2×SD1612yes—
203C23×C61#13712yes—
204C23×C61C22×D411yescharacteristic
205Q8×C61—84no—
206C2×C4×C61—21no—
207C2×C4×C61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—22no—
213C2×C4×C61—22no—
214C2×C4×C61—22no—
215C2×C4×C61—22no—
216C2×C4×C61—21no—
217C2×C4×C61—22no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—84no—
235C2×C4×C61C22⋊Q812yes—
236C2×C4×C61C2×SD1612yes—
237C2×C4×C61C2×SD1612yes—
238C2×C4×C61C22×Q811yescharacteristic
239C2×C4×C61C2×#4111yescharacteristic
240C2×C4×C61C2×#4111yescharacteristic
241C2×C4×C61C2×#4111yescharacteristic
242C2×C4×C61H(5,𝔽2)11yescharacteristic
243C2×C4×C612−1+411yescharacteristic
244C2×Dic61—22no—
245C2×Dic61—22no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254C2×Dic61—41no—
255C2×Dic61—41no—
256C2×Dic61—84no—
257#92418—22no—
258#92418—41no—
259#92418—41no—
260#92418—41no—
261#25992—611nomaximal, Sylow
262C22×C61—22no—
263C22×C61—22no—
264C22×C61—22no—
265C22×C61—22no—
266C22×C61—22no—
267C22×C61—22no—
268C22×C61#47514yes—
269C22×C61C2×C22⋊Q811yescharacteristic
270C22×C61#54611yescharacteristic
271C22×C61#54711yescharacteristic
272C22×C61C22×SD1611yescharacteristic
273C22×C61C2×#13711yescharacteristic
274C22×C61#57611yescharacteristic
275C22×C61#57711yescharacteristic
276C4×C61—22no—
277C4×C61—22no—
278C4×C61—22no—
279C4×C61—41no—
280C4×C61—42no—
281C4×C61—41no—
282C4×C61—81no—
283C4×C61—81no—
284C4×C61—81no—
285C4×C61#53311yescharacteristic
286C4×C61#54411yescharacteristic
287C4×C61#55111yescharacteristic
288C4×C61#55211yescharacteristic
289Dic61—42no—
290Dic61—42no—
291Dic61—81no—
292Dic61—81no—
293#2440D6111yescharacteristic
294#2345—611no—
295#2099—611no—
296#2088—611no—
297#2088—611no—
298#2058—611no—
299#1988—611no—
300#1948—611no—
301#1919—611no—
302#1919—611no—
303#1853—611no—
304#1850—611no—
305#1824—611no—
306#1807—611no—
307C2×#340—611no—
308C2×C61—24no—
309C2×C61#243811yescharacteristic
310C2×C61C2×#47511yescharacteristic
311C2×C61#308111yescharacteristic
312C2×C61#329511yescharacteristic
313C2×C61#332011yescharacteristic
314C2×C61#333511yescharacteristic
315C2×C61#334611yescharacteristic
316C23×C8—611no—
317C2×C4⋊Q8C2×D6111yescharacteristic
318C2×C22⋊Q8—21no—
319C22×C4⋊C4—611no—
320C22×C4⋊C4C2×D6111yescharacteristic
321C2×#106—611no—
322C2×#106—611no—
323C2×#106—611no—
324C2×#106—611no—
325C2×C4⋊C8—611no—
326C2×C4⋊C8—611no—
327C2×C22⋊C8—611no—
328#398—21no—
329#395—21no—
330#389—611no—
331#389—611no—
332#389C2×D6111yescharacteristic
333#389C2×D6111yescharacteristic
334#387—1221no—
335#387—1221no—
336#385—21no—
337#384C2×D6111yescharacteristic
338#380—611no—
339#380—1221no—
340#380C2×D6111yescharacteristic
341C4×C4⋊C4—611no—
342C4×C4⋊C4—611no—
343C4×C22⋊C4—1221no—
344C4×C22⋊C4C2×D6111yescharacteristic
345#340—611no—
346#340—611no—
347#340—611no—
348#340—611no—
349#340—611no—
350#340—611no—
351#340—611no—
352#340—611no—
353#340—611no—
354#340—611no—
355#340—611no—
356#340—611no—
357#336—611no—
358#336—611no—
359C61#2599211yescharacteristic, complemented, Sylow
360C22×Q8—21no—
361C23×C4—21no—
362C23×C4—1221no—
363C23×C4C22×D6111yescharacteristic
364C22×C8—611no—
365C22×C8—611no—
366C22×C8—611no—
367C22×C8—611no—
368C22×C8—1222no—
369C22×C8—1222no—
370C22×C8—2441no—
371C4⋊Q8—22no—
372C4⋊Q8—41no—
373C22⋊Q8—44no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—41no—
382C2×C4⋊C4—614no—
383C2×C4⋊C4—611no—
384C2×C4⋊C4—611no—
385C2×C4⋊C4—611no—
386C2×C4⋊C4—611no—
387C2×C4⋊C4—1222no—
388C2×C4⋊C4—1221no—
389C2×C4⋊C4—1221no—
390C2×C4⋊C4—1221no—
391C2×C4⋊C4C22×D6111yescharacteristic
392C2×C4⋊C4C22×D6111yescharacteristic
393C2×C4⋊C4C22×D6111yescharacteristic
394C2×C4⋊C4C22×D6111yescharacteristic
395C2×C22⋊C4—21no—
396C2×C22⋊C4—1221no—
397C2×C22⋊C4C22⋊D6111yescharacteristic
398C2×C22⋊C4C22⋊D6111yescharacteristic
399C2×C42—1221no—
400C2×C42—1221no—
401C2×C42C22×D6111yescharacteristic
402C2×C42C22×D6111yescharacteristic
403#106—1222no—
404#106—1222no—
405#106—2441no—
406#106—2441no—
407C4⋊C8—1222no—
408C4⋊C8—2441no—
409C22⋊C8—1222no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—1221no—
414#95—1221no—
415#95—1221no—
416#95—1221no—
417#95—1221no—
418#95C22⋊D6111yescharacteristic
419#95C22⋊D6111yescharacteristic
420C24C2×C22⋊D6111yescharacteristic
421C2×Q8—42no—
422C2×Q8—42no—
423C2×Q8—81no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—81no—
435C22×C4—1224no—
436C22×C4—1221no—
437C22×C4—1221no—
438C22×C4—1221no—
439C22×C4—1221no—
440C22×C4—4881no—
441C22×C4—4881no—
442C22×C4Q8×D6112yes—
443C22×C4#1175822612yes—
444C22×C4C2×C22⋊D6111yescharacteristic
445C22×C4C2×C22⋊D6111yescharacteristic
446C22×C4C2×C22⋊D6111yescharacteristic
447C22×C4C2×C22⋊D6111yescharacteristic
448C22×C4C2×C22⋊D6111yescharacteristic
449C22×C4C23×D6111yescharacteristic
450C2×C8—612no—
451C2×C8—1221no—
452C2×C8—1221no—
453C2×C8—1221no—
454C2×C8—1221no—
455C2×C8—1221no—
456C2×C8—1221no—
457C2×C8—1221no—
458C2×C8—1221no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8—1221no—
462C2×C8—2444no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—42no—
471C4⋊C4—42no—
472C4⋊C4—42no—
473C4⋊C4—42no—
474C4⋊C4—42no—
475C4⋊C4—81no—
476C4⋊C4—612no—
477C4⋊C4—612no—
478C4⋊C4—1221no—
479C4⋊C4—1221no—
480C4⋊C4—1224no—
481C4⋊C4—1221no—
482C4⋊C4—1221no—
483C4⋊C4—1221no—
484C4⋊C4—1221no—
485C4⋊C4—4881no—
486C4⋊C4—4881no—
487C4⋊C4#1175822412yes—
488C22⋊C4—22no—
489C22⋊C4—42no—
490C22⋊C4—2442no—
491C22⋊C4#1175820014yes—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—4881no—
497C42—4881no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23—21no—
502C23#1451975312yes—
503C23C2×#1175820012yes—
504C23#1451980812yes—
505C23C22×C22⋊D6111yescharacteristic
506Q8—84no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—84no—
536C2×C4—1222no—
537C2×C4—1222no—
538C2×C4—4884no—
539C2×C4—2441no—
540C2×C4—2441no—
541C2×C4—2441no—
542C2×C4—2441no—
543C2×C4—2441no—
544C2×C4—2441no—
545C2×C4—2441no—
546C2×C4—2441no—
547C2×C4—2441no—
548C2×C4—2441no—
549C2×C4#1451975312yes—
550C2×C4C2×#1175820012yes—
551C2×C4C2×#1175820012yes—
552C2×C4C2×Q8×D6111yescharacteristic
553C2×C4#41×D6111yescharacteristic
554C2×C4C2×#1175822411yescharacteristic
555C2×C4C2×#1175822611yescharacteristic
556C2×C4#1451982211yescharacteristic
557C2×C4#1451982411yescharacteristic
558C8—1222no—
559C8—2441no—
560C8—2441no—
561C8—2441no—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22#1684004414yes—
569C22C2×#1451975311yescharacteristic
570C22#1684040611yescharacteristic
571C22#1684041111yescharacteristic
572C22C22×#1175820011yescharacteristic
573C22C2×#1451980811yescharacteristic
574C22#1684056511yescharacteristic
575C22#1684057011yescharacteristic
576C4—22no—
577C4—22no—
578C4—22no—
579C4—41no—
580C4—41no—
581C4—42no—
582C4—81no—
583C4—81no—
584C4—81no—
585C4—4881no—
586C4—4881no—
587C4—2442no—
588C4—2442no—
589C4#1684031411yescharacteristic
590C4#1684039111yescharacteristic
591C4#1684043911yescharacteristic
592C4#1684045411yescharacteristic
593C2—24no—
594C2#2144949111yescharacteristic
595C2C2×#1684004411yescharacteristic
596C2#2145564411yescharacteristic
597C2#2145764311yescharacteristic
598C2#2145799011yescharacteristic
599C2#2145817611yescharacteristic
600C2#2145829811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2440C2
socleC23×C61C22×D4
prime radicalC24×C61C2×D4
hypercenter#2440D61
hypocenterC61#25992
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2440

Complements

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

NH ≅ G/Ntype
2. #21447376C2semidirect
3. #21447320C2semidirect
4. #21447320C2semidirect
5. #21447149C2semidirect
6. #21446772C2semidirect
7. #21446580C2semidirect
8. #21446394C2semidirect
9. #21446394C2semidirect
69. C2×C4⋊Dic61Q8semidirect
359. C61#25992semidirect

Maximal subgroups

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

subgroupindex
#214486942
#214473762
#214473202
#214471492
#214467722
#214465802
#214463942
#214460122
#214459992
#214459072
#214458422
C2×#168395242
C61×#24402
#2599261