Finite Group Databasebeta

← #29690606

Subgroups — #29690606

Order 15616.

762 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839820C211yesmaximal, characteristic
2#21448443C211yesmaximal, characteristic
3#21448426C211yesmaximal, characteristic
4#21446586C211yesmaximal, characteristic, complemented
5#21446584C211yesmaximal, characteristic, complemented
6#21446576C211yesmaximal, characteristic, complemented
7#21446574C211yesmaximal, characteristic, complemented
8#21446020C211yesmaximal, characteristic
9#21446016C211yesmaximal, characteristic
10#21446007C211yesmaximal, characteristic
11#21445986C211yesmaximal, characteristic, complemented
12#21445977C211yesmaximal, characteristic, complemented
13#21445951C211yesmaximal, characteristic, complemented
14#21445948C211yesmaximal, characteristic, complemented
15C61×#1852C211yesmaximal, characteristic
16C2×#14519736C2211yescharacteristic
17C2×#14519736C2211yescharacteristic
18#16839820C418yescomplemented
19C2×#14519711C2211yescharacteristic
20C2×#14519710C2211yescharacteristic
21C2×#14519710C2211yescharacteristic
22C2×#14519710C2211yescharacteristic
23C2×#14519709C2211yescharacteristic
24C2×#14519708C2211yescharacteristic
25C2×#14519706C2211yescharacteristic
26C2×#14519706C2211yescharacteristic
27C2×C22⋊#92418C2211yescharacteristic
28C2×#14519687C2211yescharacteristic
29C2×C8×Dic61C2211yescharacteristic
30#16839658—21no—
31#16839658—21no—
32#16839656—21no—
33#16839650—21no—
34#16839647—21no—
35#16839645—21no—
36#16839635—21no—
37#16839635—21no—
38#16839631C2211yescharacteristic
39#16839631C2211yescharacteristic
40#16839631C2211yescharacteristic
41#16839627C2211yescharacteristic
42#16839627C2211yescharacteristic
43#16839627C2211yescharacteristic
44#16839622C2211yescharacteristic
45C4⋊C4×Dic61C2211yescharacteristic
46C4⋊C4×Dic61C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53C22×C4⋊C4×C61C2211yescharacteristic
54C2×#107×C61C2211yescharacteristic
55C2×#107×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C61×#380C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C22×#92418C2311yescharacteristic
61C22×#92418C2311yescharacteristic
62#14519736—41no—
63#14519736—41no—
64#14519736C2×C414yes—
65#14519736Q814yes—
66C2×C4⋊Dic61D411yescharacteristic
67C2×C4⋊Dic61D411yescharacteristic
68C2×C4⋊Dic61C2311yescharacteristic
69C2×C4⋊Dic61C2311yescharacteristic
70C2×C4⋊Dic61C2311yescharacteristic
71C2×C4⋊Dic61C2311yescharacteristic
72C2×#11758196—21no—
73C2×#11758196—21no—
74C2×#11758196—21no—
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×C22⋊Dic61—21no—
79C2×C22⋊Dic61—21no—
80C2×C22⋊Dic61D411yescharacteristic
81C2×C22⋊Dic61D411yescharacteristic
82C2×C4×Dic61—21no—
83C2×C4×Dic61—21no—
84C2×C4×Dic61—21no—
85C2×C4×Dic61C2311yescharacteristic
86C2×C4×Dic61C2311yescharacteristic
87#14519711—41no—
88#14519710—41no—
89#14519710—41no—
90#14519710—41no—
91#14519709—41no—
92#14519708—41no—
93#14519706C2×C414yescomplemented
94#14519706C2×C414yescomplemented
95C22⋊#92418C2×C414yes—
96#14519687C2×C414yescomplemented
97C8×Dic61C2×C414yescomplemented
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107C23×C4×C61—21no—
108C23×C4×C61C2311yescharacteristic
109C22×C8×C61C2311yescharacteristic
110C22×C8×C61C2311yescharacteristic
111C2×C4⋊C4×C61—21no—
112C2×C4⋊C4×C61—41no—
113C2×C4⋊C4×C61—41no—
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C4⋊C4×C61C2311yescharacteristic
117C2×C4⋊C4×C61C2311yescharacteristic
118C2×C22⋊C4×C61—21no—
119#107×C61—41no—
120#107×C61—41no—
121C22⋊C8×C61C2×C414yes—
122#95×C61—21no—
123C24×C61C2×D411yescharacteristic
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—21no—
132C22×C4×C61—42no—
133C22×C4×C61—81no—
134C22×C4×C61—81no—
135C22×C4×C61C22×C412yes—
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×Q812yes—
138C22×C4×C61C2411yescharacteristic
139C22×Dic61—21no—
140C22×Dic61—21no—
141C22×Dic61—21no—
142C22×Dic61—21no—
143C22×Dic61C2×D411yescharacteristic
144C22×Dic61C2×D411yescharacteristic
145C22×Dic61C2×D411yescharacteristic
146C22×Dic61C2×D411yescharacteristic
147C2×C8×C61—21no—
148C2×C8×C61—21no—
149C2×C8×C61—21no—
150C2×C8×C61—21no—
151C2×C8×C61C22×C412yes—
152C2×C8×C61C22×C412yes—
153C4⋊C4×C61—21no—
154C4⋊C4×C61—21no—
155C4⋊C4×C61—21no—
156C4⋊C4×C61—21no—
157C4⋊C4×C61—21no—
158C4⋊C4×C61—21no—
159C4⋊C4×C61—21no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—42no—
162C22⋊C4×C61—81no—
163C22⋊Dic61—42no—
164C22⋊Dic61—81no—
165C22⋊Dic61C4⋊C414yes—
166C22⋊Dic61C4⋊C414yes—
167C4⋊Dic61—21no—
168C4⋊Dic61—21no—
169C4⋊Dic61—21no—
170C4⋊Dic61—21no—
171C4⋊Dic61—21no—
172C4⋊Dic61—21no—
173C4⋊Dic61—21no—
174C4⋊Dic61—21no—
175C4⋊Dic61C4⋊C414yes—
176C4⋊Dic61C4⋊C414yes—
177#11758196—81no—
178#11758196—81no—
179#11758196—81no—
180#11758196—81no—
181#11758196—81no—
182#11758196—81no—
183C4×Dic61—42no—
184C4×Dic61—81no—
185C4×Dic61—81no—
186C4×Dic61C22×C412yes—
187C4×Dic61C22×C412yes—
188C4×Dic61C2×Q812yes—
189C4×Dic61C2×Q812yes—
190C2×#92418—21no—
191C2×#92418—21no—
192C2×#92418—21no—
193C2×#92418—21no—
194C2×#92418C22×C412yes—
195C2×#92418C22×C412yes—
196C23×C61—21no—
197C23×C61—21no—
198C23×C61—21no—
199C23×C61—21no—
200C23×C61—21no—
201C23×C61—21no—
202C23×C61C2×C4⋊C412yes—
203C23×C61C22×D411yescharacteristic
204C2×C4×C61—21no—
205C2×C4×C61—21no—
206C2×C4×C61—22no—
207C2×C4×C61—22no—
208C2×C4×C61—22no—
209C2×C4×C61—22no—
210C2×C4×C61—41no—
211C2×C4×C61—41no—
212C2×C4×C61—41no—
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—84no—
223C2×C4×C61C2×C4⋊C412yes—
224C2×C4×C61C23×C411yescharacteristic
225C2×C4×C61C22×Q811yescharacteristic
226C2×C4×C61H(5,𝔽2)11yescharacteristic
227C2×C4×C61H(5,𝔽2)11yescharacteristic
228C2×C4×C612−1+411yescharacteristic
229C2×C4×C612−1+411yescharacteristic
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—41no—
239C2×Dic61—41no—
240C2×Dic61—41no—
241C2×Dic61—41no—
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×Dic61C2×C4⋊C412yes—
251C2×Dic61C2×C4⋊C412yes—
252C2×Dic61C2×C4⋊C412yes—
253C2×Dic61C2×C4⋊C412yes—
254C8×C61—22no—
255C8×C61—22no—
256#92418—22no—
257#92418—22no—
258#21991—611nomaximal, Sylow
259C22×C61—22no—
260C22×C61—22no—
261C22×C61—22no—
262C22×C61—41no—
263C22×C61—41no—
264C22×C61—41no—
265C22×C61—41no—
266C22×C61C22×C4⋊C411yescharacteristic
267C22×C61#53511yescharacteristic
268C22×C61#53611yescharacteristic
269C22×C61#57611yescharacteristic
270C22×C61#57611yescharacteristic
271C22×C61#57811yescharacteristic
272C22×C61#57811yescharacteristic
273C4×C61—22no—
274C4×C61—81no—
275C4×C61—81no—
276C4×C61—81no—
277C4×C61—81no—
278C4×C61#52011yescharacteristic
279C4×C61#52011yescharacteristic
280C4×C61#54411yescharacteristic
281C4×C61#54411yescharacteristic
282Dic61—22no—
283Dic61—22no—
284Dic61—22no—
285Dic61—22no—
286Dic61—81no—
287Dic61—81no—
288Dic61—81no—
289Dic61—81no—
290C2×#433—611no—
291#2317—611no—
292#2314—611no—
293#1949—611no—
294#1949—611no—
295#1947—611no—
296#1947—611no—
297#1854—611no—
298#1854—611no—
299#1852—611no—
300#1852D6111yescharacteristic
301#1847—611no—
302#1845—611no—
303#1836—611no—
304#1835—611no—
305C2×C61—42no—
306C2×C61#231711yescharacteristic
307C2×C61#291311yescharacteristic
308C2×C61#291311yescharacteristic
309C2×C61#322011yescharacteristic
310C2×C61#322311yescharacteristic
311C2×C61#324311yescharacteristic
312C2×C61#324311yescharacteristic
313C2×#117—611no—
314C2×#117—611no—
315C22×C4⋊C4C2×D6111yescharacteristic
316#433—618no—
317C2×#107—611no—
318C2×#107—611no—
319C2×#107—611no—
320C2×#107—611no—
321C2×#107C2×D6111yescharacteristic
322C2×#107C2×D6111yescharacteristic
323C2×#106—611no—
324C2×#106—611no—
325C2×C4⋊C8—611no—
326C2×C4⋊C8—611no—
327C2×C22⋊C8—611no—
328C2×C22⋊C8C2×D6111yescharacteristic
329C2×#97—611no—
330C2×C4×C8—611no—
331#389—1221no—
332#389—1221no—
333#388—1221no—
334#388—1221no—
335#387—1221no—
336#387—1221no—
337#385—1221no—
338#385—1221no—
339#384—611no—
340#384—611no—
341#384—611no—
342#382—611no—
343#382—611no—
344#382—611no—
345#380—611no—
346#380C2×D6111yescharacteristic
347C4×C4⋊C4—611no—
348C4×C4⋊C4—611no—
349#340—611no—
350#340—611no—
351#340—611no—
352#340—611no—
353#340—611no—
354#340—611no—
355#340C2×D6111yescharacteristic
356#340C2×D6111yescharacteristic
357C61#2199111yescharacteristic, complemented, Sylow
358C23×C4—21no—
359C23×C4C22×D6111yescharacteristic
360C22×C8—611no—
361C22×C8—611no—
362C22×C8C22×D6111yescharacteristic
363C22×C8C22×D6111yescharacteristic
364#117—614no—
365#117—614no—
366#117—2441no—
367#117—2441no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—41no—
370C2×C4⋊C4—41no—
371C2×C4⋊C4—611no—
372C2×C4⋊C4—611no—
373C2×C4⋊C4—611no—
374C2×C4⋊C4—611no—
375C2×C4⋊C4—611no—
376C2×C4⋊C4—611no—
377C2×C4⋊C4—1221no—
378C2×C4⋊C4—1221no—
379C2×C4⋊C4—1221no—
380C2×C4⋊C4—1221no—
381C2×C4⋊C4—1221no—
382C2×C4⋊C4—1221no—
383C2×C4⋊C4C22×D6111yescharacteristic
384C2×C4⋊C4C22×D6111yescharacteristic
385C2×C4⋊C4C22×D6111yescharacteristic
386C2×C4⋊C4C22×D6111yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—611no—
389C2×C22⋊C4—611no—
390C2×C22⋊C4—1221no—
391C2×C22⋊C4—1221no—
392C2×C42—611no—
393C2×C42—611no—
394C2×C42—1221no—
395C2×C42—1221no—
396C2×C42—1221no—
397#107—41no—
398#107—41no—
399#107—2441no—
400#107—2441no—
401#107—2441no—
402#107—2441no—
403#106—2441no—
404#106—2441no—
405C4⋊C8—614no—
406C4⋊C8—614no—
407C22⋊C8—614no—
408C22⋊C8C4×D6114yes—
409#97—614no—
410C4×C8—614no—
411#95—21no—
412#95—1221no—
413#95—1221no—
414#95—1221no—
415#95—1221no—
416#95—1221no—
417#95—1221no—
418#95—1221no—
419#95—1221no—
420#95—1221no—
421C24D4×D6111yescharacteristic
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—42no—
431C22×C4—81no—
432C22×C4—81no—
433C22×C4—611no—
434C22×C4—611no—
435C22×C4—611no—
436C22×C4—611no—
437C22×C4—1221no—
438C22×C4—1221no—
439C22×C4—1221no—
440C22×C4—1221no—
441C22×C4C2×C4×D6112yes—
442C22×C4D4×D6111yescharacteristic
443C22×C4Q8×D6112yes—
444C22×C4C23×D6111yescharacteristic
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—612no—
450C2×C8—612no—
451C2×C8—1221no—
452C2×C8—1221no—
453C2×C8—1221no—
454C2×C8—1221no—
455C2×C8C2×C4×D6112yes—
456C2×C8C2×C4×D6112yes—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—42no—
466C4⋊C4—614no—
467C4⋊C4—614no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4—1221no—
473C4⋊C4—1221no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C4⋊C4—4881no—
477C4⋊C4—4881no—
478C4⋊C4—4881no—
479C4⋊C4—4881no—
480C4⋊C4—4881no—
481C4⋊C4—4881no—
482C22⋊C4—81no—
483C22⋊C4—614no—
484C22⋊C4—614no—
485C22⋊C4—4881no—
486C22⋊C4—2442no—
487C42—612no—
488C42—612no—
489C42—612no—
490C42—612no—
491C42—4881no—
492C42—4881no—
493C42—2442no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23C4⋊C4×D6112yes—
501C23C2×D4×D6111yescharacteristic
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—84no—
521C2×C4—612no—
522C2×C4—612no—
523C2×C4—612no—
524C2×C4—612no—
525C2×C4—1221no—
526C2×C4—1221no—
527C2×C4—1221no—
528C2×C4—1221no—
529C2×C4—1221no—
530C2×C4—1221no—
531C2×C4—1221no—
532C2×C4—1221no—
533C2×C4—2441no—
534C2×C4—2441no—
535C2×C4—2441no—
536C2×C4—2441no—
537C2×C4—2441no—
538C2×C4—2441no—
539C2×C4—2441no—
540C2×C4—2441no—
541C2×C4—2441no—
542C2×C4—2441no—
543C2×C4—2441no—
544C2×C4—2441no—
545C2×C4C4⋊C4×D6112yes—
546C2×C4C22×C4×D6111yescharacteristic
547C2×C4C2×Q8×D6111yescharacteristic
548C2×C4#1451982211yescharacteristic
549C2×C4#1451982211yescharacteristic
550C2×C4#1451982411yescharacteristic
551C2×C4#1451982411yescharacteristic
552C8—22no—
553C8—22no—
554C8—1222no—
555C8—1222no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22C2×C4⋊C4×D6111yescharacteristic
564C22#1684032711yescharacteristic
565C22#1684033411yescharacteristic
566C22#1684056311yescharacteristic
567C22#1684056611yescharacteristic
568C22#1684057511yescharacteristic
569C22#1684057811yescharacteristic
570C4—22no—
571C4—81no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4—1222no—
576C4—1222no—
577C4—1222no—
578C4—1222no—
579C4—4881no—
580C4—4881no—
581C4—4881no—
582C4—4881no—
583C4#1684024111yescharacteristic
584C4#1684024111yescharacteristic
585C4#1684039111yescharacteristic
586C4#1684039111yescharacteristic
587C2—42no—
588C2#2144843811yescharacteristic
589C2#2145441511yescharacteristic
590C2#2145441811yescharacteristic
591C2#2145686511yescharacteristic
592C2#2145689811yescharacteristic
593C2#2145709811yescharacteristic
594C2#2145710611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1852C2
socleC23×C61C22×D4
prime radicalC24×C61C2×D4
cosocleC22×C4×C61C24
hypercenter#1852D61
hypocenterC61#21991
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1852

Complements

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

NH ≅ G/Ntype
4. #21446586C2semidirect
5. #21446584C2semidirect
6. #21446576C2semidirect
7. #21446574C2semidirect
11. #21445986C2semidirect
12. #21445977C2semidirect
13. #21445951C2semidirect
14. #21445948C2semidirect
18. #16839820C4semidirect
93. #14519706C2×C4semidirect
94. #14519706C2×C4semidirect
96. #14519687C2×C4semidirect
97. C8×Dic61C2×C4semidirect
357. C61#21991semidirect

Maximal subgroups

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

subgroupindex
C2×#168398202
#214484432
#214484262
#214465862
#214465842
#214465762
#214465742
#214460202
#214460162
#214460072
#214459862
#214459772
#214459512
#214459482
C61×#18522
#2199161