Finite Group Databasebeta

← #29737678

Subgroups — #29737678

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#21449522C211yesmaximal, characteristic
2#21448696C211yesmaximal, characteristic
3#21447380C211yesmaximal, characteristic, complemented
4#21447322C211yesmaximal, characteristic, complemented
5#21447319C211yesmaximal, characteristic, complemented
6#21447151C211yesmaximal, characteristic, complemented
7#21446769C211yesmaximal, characteristic, complemented
8#21446581C211yesmaximal, characteristic, complemented
9#21446400C211yesmaximal, characteristic, complemented
10#21446396C211yesmaximal, characteristic, complemented
11#21446014C211yesmaximal, characteristic
12#21445996C211yesmaximal, characteristic
13#21445842C211yesmaximal, characteristic
14C2×#16839524C211yesmaximal, characteristic
15C61×#1824C211yesmaximal, characteristic
16C23×#92418C2211yescharacteristic
17C2×#14519776C2211yescharacteristic
18C2×#14519754—21no—
19C22×C4⋊Dic61C2211yescharacteristic
20C2×#14519709C2211yescharacteristic
21C2×#14519709C2211yescharacteristic
22C2×#14519708C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
24C2×#14519706C2211yescharacteristic
25C2×#14519706C2211yescharacteristic
26#16839696—21no—
27#16839683—21no—
28#16839661C2211yescharacteristic
29#16839661C2211yescharacteristic
30#16839661C2211yescharacteristic
31#16839658C2211yescharacteristic
32#16839648—21no—
33#16839648—21no—
34#16839634—21no—
35#16839631C2211yescharacteristic
36#16839622—21no—
37#16839622C2211yescharacteristic
38C4⋊C4×Dic61C2211yescharacteristic
39C4⋊C4×Dic61C2211yescharacteristic
40C4×C22⋊Dic61—21no—
41C4×C22⋊Dic61C2211yescharacteristic
42#16839525C2211yescharacteristic
43#16839525C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839516C2211yescharacteristic
51#16839516C2211yescharacteristic
52C22×C4⋊C4×C61C2211yescharacteristic
53C2×C22⋊C8×C61C2211yescharacteristic
54C61×#380C2211yescharacteristic
55C61×#340C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C22×Dic122—21no—
60C23×Dic61—21no—
61C22×#92418—22no—
62C22×#92418—22no—
63C22×#92418—41no—
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66#14519776—22no—
67#14519776—41no—
68#14519754—44no—
69C2×C4⋊Dic61—22no—
70C2×C4⋊Dic61—21no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61—41no—
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×C4⋊Dic61C2311yescharacteristic
79C2×#11758196—21no—
80C2×#11758196—21no—
81C2×#11758196—21no—
82C2×#11758196—21no—
83C2×C22⋊Dic61—21no—
84C2×C22⋊Dic61D411yescharacteristic
85C2×C22⋊Dic61D411yescharacteristic
86C2×C4×Dic61—21no—
87C2×C4×Dic61—21no—
88C2×C4×Dic61C2311yescharacteristic
89C2×C4×Dic61C2311yescharacteristic
90#14519709—22no—
91#14519709—41no—
92#14519708—22no—
93#14519708—41no—
94#14519706—22no—
95#14519706—41no—
96#14519684—21no—
97#14519684—21no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684D411yescharacteristic
104#14519684D411yescharacteristic
105C23×C4×C61—21no—
106C23×C4×C61C2311yescharacteristic
107C22×C8×C61C2311yescharacteristic
108C22×C8×C61C2311yescharacteristic
109C2×C4⋊C4×C61—21no—
110C2×C4⋊C4×C61—22no—
111C2×C4⋊C4×C61Q814yescomplemented
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C22⋊C4×C61—21no—
117C22⋊C8×C61—22no—
118#95×C61—21no—
119C24×C61C2×D411yescharacteristic
120C22×C4×C61—21no—
121C22×C4×C61—21no—
122C22×C4×C61—21no—
123C22×C4×C61—21no—
124C22×C4×C61—21no—
125C22×C4×C61—21no—
126C22×C4×C61—24no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—81no—
130C22×C4×C61—81no—
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61C2×Q812yes—
133C22×C4×C61#4112yes—
134C22×C4×C61C2411yescharacteristic
135C22×Dic61—21no—
136C22×Dic61—21no—
137C22×Dic61—21no—
138C22×Dic61—21no—
139C22×Dic61—42no—
140C22×Dic61—42no—
141C22×Dic61—81no—
142C22×Dic61C2×D411yescharacteristic
143C22×Dic61C2×D411yescharacteristic
144C22×Dic61C2×D411yescharacteristic
145C22×Dic61C2×D411yescharacteristic
146C2×Dic122—42no—
147C2×Dic122—42no—
148C2×Dic122—81no—
149C2×C8×C61—21no—
150C2×C8×C61—21no—
151C2×C8×C61—21no—
152C2×C8×C61—21no—
153C2×C8×C61—21no—
154C2×C8×C61—21no—
155C4⋊C4×C61—24no—
156C4⋊C4×C61—21no—
157C4⋊C4×C61—21no—
158C4⋊C4×C61—21no—
159C4⋊C4×C61—21no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61C2×Q812yes—
163C4⋊C4×C61C2×Q812yes—
164C22⋊C4×C61—42no—
165C22⋊Dic61—22no—
166C22⋊Dic61—42no—
167C22⋊Dic61SD1614yes—
168C4⋊Dic61—21no—
169C4⋊Dic61—21no—
170C4⋊Dic61—21no—
171C4⋊Dic61—21no—
172C4⋊Dic61—21no—
173C4⋊Dic61—21no—
174C4⋊Dic61—21no—
175C4⋊Dic61—42no—
176C4⋊Dic61—42no—
177C4⋊Dic61—81no—
178C4⋊Dic61—81no—
179C4⋊Dic61#4112yes—
180#11758196—42no—
181#11758196—42no—
182#11758196—42no—
183#11758196—81no—
184C4×Dic61—21no—
185C4×Dic61—21no—
186C4×Dic61—21no—
187C4×Dic61—21no—
188C4×Dic61—81no—
189C4×Dic61—81no—
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
205C2×C4×C61—21no—
206C2×C4×C61—21no—
207C2×C4×C61—22no—
208C2×C4×C61—22no—
209C2×C4×C61—22no—
210C2×C4×C61—22no—
211C2×C4×C61—22no—
212C2×C4×C61—22no—
213C2×C4×C61—41no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—84no—
224C2×C4×C61C22⋊Q812yes—
225C2×C4×C61C22×Q811yescharacteristic
226C2×C4×C61C2×#4111yescharacteristic
227C2×C4×C61C2×#4111yescharacteristic
228C2×C4×C61C2×#4111yescharacteristic
229C2×C4×C61H(5,𝔽2)11yescharacteristic
230C2×C4×C612−1+411yescharacteristic
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—22no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61—21no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C2×Dic61—84no—
254C2×Dic61C2×SD1612yes—
255C2×Dic61C2×SD1612yes—
256Dic122—84no—
257C8×C61—41no—
258C8×C61—41no—
259#92418—22no—
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—42no—
278C4×C61—42no—
279C4×C61—81no—
280C4×C61—81no—
281C4×C61#53311yescharacteristic
282C4×C61#54411yescharacteristic
283C4×C61#55111yescharacteristic
284C4×C61#55211yescharacteristic
285Dic61—22no—
286Dic61—22no—
287Dic61—41no—
288Dic61—42no—
289Dic61—41no—
290Dic61—81no—
291Dic61—81no—
292Dic61—81no—
293#2440—611no—
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#1824D6111yescharacteristic
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⋊Q8—611no—
318C2×C22⋊Q8—1221no—
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⋊C8C2×D6111yescharacteristic
328#398—1221no—
329#395—1221no—
330#389—611no—
331#389—611no—
332#389—611no—
333#389—611no—
334#387—1221no—
335#387—1221no—
336#385—1221no—
337#384—611no—
338#380—611no—
339#380—1221no—
340#380C2×D6111yescharacteristic
341C4×C4⋊C4—611no—
342C4×C4⋊C4—611no—
343C4×C22⋊C4—611no—
344C4×C22⋊C4—1221no—
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#340C2×D6111yescharacteristic
354#340C2×D6111yescharacteristic
355#340C2×D6111yescharacteristic
356#340C2×D6111yescharacteristic
357#336—611no—
358#336—611no—
359C61#2599211yescharacteristic, complemented, Sylow
360C22×Q8—1221no—
361C23×C4—21no—
362C23×C4—1221no—
363C23×C4C22×D6111yescharacteristic
364C22×C8—611no—
365C22×C8—611no—
366C22×C8—1222no—
367C22×C8—1222no—
368C22×C8—2441no—
369C22×C8C22×D6111yescharacteristic
370C22×C8C22×D6111yescharacteristic
371C4⋊Q8—1222no—
372C4⋊Q8—2441no—
373C22⋊Q8—2444no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—611no—
377C2×C4⋊C4—611no—
378C2×C4⋊C4—611no—
379C2×C4⋊C4—611no—
380C2×C4⋊C4—1222no—
381C2×C4⋊C4—1221no—
382C2×C4⋊C4—1221no—
383C2×C4⋊C4—1221no—
384C2×C4⋊C4—1221no—
385C2×C4⋊C4—1221no—
386C2×C4⋊C4—1221no—
387C2×C4⋊C4—1221no—
388C2×C4⋊C4—1221no—
389C2×C4⋊C4—2441no—
390C2×C4⋊C4Dic12214yescomplemented
391C2×C4⋊C4C22×D6111yescharacteristic
392C2×C4⋊C4C22×D6111yescharacteristic
393C2×C4⋊C4C22×D6111yescharacteristic
394C2×C4⋊C4C22×D6111yescharacteristic
395C2×C22⋊C4—21no—
396C2×C22⋊C4—611no—
397C2×C22⋊C4—611no—
398C2×C22⋊C4—1221no—
399C2×C42—611no—
400C2×C42—611no—
401C2×C42—1221no—
402C2×C42—1221no—
403#106—1222no—
404#106—1222no—
405#106—2441no—
406#106—2441no—
407C4⋊C8—1222no—
408C4⋊C8—2441no—
409C22⋊C8—22no—
410#95—21no—
411#95—611no—
412#95—611no—
413#95—1221no—
414#95—1221no—
415#95—1221no—
416#95—1221no—
417#95—1221no—
418#95—1221no—
419#95—1221no—
420C24D4×D6111yescharacteristic
421C2×Q8—4881no—
422C2×Q8—2442no—
423C2×Q8—2442no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—24no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—81no—
434C22×C4—81no—
435C22×C4—611no—
436C22×C4—611no—
437C22×C4—611no—
438C22×C4—611no—
439C22×C4—1221no—
440C22×C4—1221no—
441C22×C4—1221no—
442C22×C4—1221no—
443C22×C4—4881no—
444C22×C4—2442no—
445C22×C4—2442no—
446C22×C4C2×Dic12212yes—
447C22×C4D4×D6111yescharacteristic
448C22×C4#1175822412yes—
449C22×C4C23×D6111yescharacteristic
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—612no—
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—24no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—612no—
471C4⋊C4—1221no—
472C4⋊C4—1221no—
473C4⋊C4—1221no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C4⋊C4—1221no—
477C4⋊C4—1221no—
478C4⋊C4—4881no—
479C4⋊C4—4881no—
480C4⋊C4—4881no—
481C4⋊C4—2442no—
482C4⋊C4—2442no—
483C4⋊C4—2442no—
484C4⋊C4—2442no—
485C4⋊C4—2442no—
486C4⋊C4C2×Dic12212yes—
487C4⋊C4C2×Dic12212yes—
488C22⋊C4—42no—
489C22⋊C4—614no—
490C22⋊C4—1222no—
491C22⋊C4—2442no—
492C42—1221no—
493C42—1221no—
494C42—1221no—
495C42—1221no—
496C42—4881no—
497C42—4881no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23—21no—
502C23#1451975412yes—
503C23SD16×D6112yes—
504C23#1451980912yes—
505C23C2×D4×D6111yescharacteristic
506Q8—4884no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—84no—
526C2×C4—612no—
527C2×C4—612no—
528C2×C4—1221no—
529C2×C4—1221no—
530C2×C4—1221no—
531C2×C4—1221no—
532C2×C4—1221no—
533C2×C4—1221no—
534C2×C4—1221no—
535C2×C4—1221no—
536C2×C4—1221no—
537C2×C4—1222no—
538C2×C4—1221no—
539C2×C4—4884no—
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—2441no—
550C2×C4—2441no—
551C2×C4#1451975412yes—
552C2×C4C22×Dic12211yescharacteristic
553C2×C4#41×D6111yescharacteristic
554C2×C4#41×D6111yescharacteristic
555C2×C4C2×#1175822411yescharacteristic
556C2×C4#1451982311yescharacteristic
557C2×C4#1451982411yescharacteristic
558C8—41no—
559C8—41no—
560C8—1222no—
561C8—2441no—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22#1684004514yes—
569C22C2×#1451975411yescharacteristic
570C22#1684040411yescharacteristic
571C22#1684041011yescharacteristic
572C22C2×SD16×D6111yescharacteristic
573C22C2×#1451980911yescharacteristic
574C22#1684056611yescharacteristic
575C22#1684057211yescharacteristic
576C4—22no—
577C4—42no—
578C4—42no—
579C4—81no—
580C4—81no—
581C4—1222no—
582C4—1222no—
583C4—4881no—
584C4—4881no—
585C4—4881no—
586C4—2441no—
587C4—2441no—
588C4—2442no—
589C4#1684031511yescharacteristic
590C4#1684039011yescharacteristic
591C4#1684043511yescharacteristic
592C4#1684044911yescharacteristic
593C2—24no—
594C2#2144949711yescharacteristic
595C2C2×#1684004511yescharacteristic
596C2#2145565211yescharacteristic
597C2#2145764111yescharacteristic
598C2#2145798811yescharacteristic
599C2#2145817411yescharacteristic
600C2#2145830811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1824C2
socleC23×C61C22×D4
prime radicalC24×C61C2×D4
hypercenter#1824D61
hypocenterC61#25992
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1824

Complements

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

NH ≅ G/Ntype
3. #21447380C2semidirect
4. #21447322C2semidirect
5. #21447319C2semidirect
6. #21447151C2semidirect
7. #21446769C2semidirect
8. #21446581C2semidirect
9. #21446400C2semidirect
10. #21446396C2semidirect
111. C2×C4⋊C4×C61Q8semidirect
359. C61#25992semidirect
390. C2×C4⋊C4Dic122semidirect

Maximal subgroups

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

subgroupindex
#214495222
#214486962
#214473802
#214473222
#214473192
#214471512
#214467692
#214465812
#214464002
#214463962
#214460142
#214459962
#214458422
C2×#168395242
C61×#18242
#2599261