Finite Group Databasebeta

← #29690555

Subgroups — #29690555

Order 15616.

806 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839812C211yesmaximal, characteristic
2#21448222C211yesmaximal, characteristic
3#21448214C211yesmaximal, characteristic
4#21446581C211yesmaximal, characteristic, complemented
5#21446579C211yesmaximal, characteristic, complemented
6#21446576C211yesmaximal, characteristic, complemented
7#21446574C211yesmaximal, characteristic, complemented
8#21446020C211yesmaximal, characteristic
9#21446018C211yesmaximal, characteristic
10#21446016C211yesmaximal, characteristic
11#21445982C211yesmaximal, characteristic, complemented
12#21445980C211yesmaximal, characteristic, complemented
13#21445948C211yesmaximal, characteristic, complemented
14#21445948C211yesmaximal, characteristic, complemented
15C61×#1854C211yesmaximal, characteristic
16C2×#14519736C2211yescharacteristic
17C22×C4×Dic61C2211yescharacteristic
18#16839812C418yescomplemented
19C2×#14519711C2211yescharacteristic
20C2×#14519710C2211yescharacteristic
21C2×#14519710C2211yescharacteristic
22C2×#14519709C2211yescharacteristic
23C2×#14519708C2211yescharacteristic
24C2×#14519708C2211yescharacteristic
25C2×#14519706C2211yescharacteristic
26C2×#14519706C2211yescharacteristic
27C2×C22⋊#92418C2211yescharacteristic
28C2×C8×Dic61C2211yescharacteristic
29C2×C8×Dic61C2211yescharacteristic
30#16839631C2211yescharacteristic
31#16839631C2211yescharacteristic
32#16839629—21no—
33#16839627C2211yescharacteristic
34#16839627C2211yescharacteristic
35#16839627C2211yescharacteristic
36#16839627C2211yescharacteristic
37#16839623—21no—
38#16839622C2211yescharacteristic
39#16839620—21no—
40#16839620—21no—
41C4⋊C4×Dic61C2211yescharacteristic
42C4⋊C4×Dic61C2211yescharacteristic
43C4×#11758196—21no—
44C4×#11758196—21no—
45C22⋊C4×Dic61—21no—
46#16839607—21no—
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53C2×#117×C61C2211yescharacteristic
54C2×#107×C61C2211yescharacteristic
55C2×#106×C61C2211yescharacteristic
56C2×C22⋊C8×C61C2211yescharacteristic
57C61×#380C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C23×Dic61D411yescharacteristic
61C23×Dic61D411yescharacteristic
62C22×#92418C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64#14519736—41no—
65#14519736—41no—
66C2×C4⋊Dic61C2311yescharacteristic
67C2×C4⋊Dic61C2311yescharacteristic
68C2×C4⋊Dic61C2311yescharacteristic
69C2×C4⋊Dic61C2311yescharacteristic
70C2×#11758196—21no—
71C2×#11758196—21no—
72C2×#11758196—21no—
73C2×#11758196—21no—
74C2×C22⋊Dic61—21no—
75C2×C22⋊Dic61—21no—
76C2×C4×Dic61—21no—
77C2×C4×Dic61—21no—
78C2×C4×Dic61—21no—
79C2×C4×Dic61C2×C414yes—
80C2×C4×Dic61D411yescharacteristic
81C2×C4×Dic61D411yescharacteristic
82C2×C4×Dic61Q814yes—
83C2×C4×Dic61C2311yescharacteristic
84C2×C4×Dic61C2311yescharacteristic
85#14519711—41no—
86#14519710—41no—
87#14519710—41no—
88#14519709—41no—
89#14519708—41no—
90#14519708—41no—
91#14519706C2×C414yes—
92#14519706C2×C414yes—
93C22⋊#92418C2×C414yes—
94C8×Dic61C2×C414yes—
95C8×Dic61C2×C414yes—
96#14519684—21no—
97#14519684—21no—
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×C61C2311yescharacteristic
108C22×C8×C61C2311yescharacteristic
109C22×C8×C61C2311yescharacteristic
110#117×C61—41no—
111#117×C61—41no—
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C4⋊C4×C61C2311yescharacteristic
115C2×C4⋊C4×C61C2311yescharacteristic
116C2×C22⋊C4×C61—21no—
117C2×C22⋊C4×C61—21no—
118C2×C42×C61—21no—
119#107×C61—41no—
120#106×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×C61C22×C412yes—
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2×Q812yes—
135C22×C4×C61C2411yescharacteristic
136C22×Dic61—22no—
137C22×Dic61—22no—
138C22×Dic61—21no—
139C22×Dic61—21no—
140C22×Dic61—21no—
141C22×Dic61—21no—
142C22×Dic61—41no—
143C22×Dic61—41no—
144C22×Dic61C4⋊C414yes—
145C22×Dic61C4⋊C414yes—
146C22×Dic61C2×D411yescharacteristic
147C22×Dic61C2×D411yescharacteristic
148C22×Dic61C2×D411yescharacteristic
149C22×Dic61C2×D411yescharacteristic
150C2×C8×C61—21no—
151C2×C8×C61—21no—
152C2×C8×C61—21no—
153C2×C8×C61—21no—
154C2×C8×C61C22×C412yes—
155C2×C8×C61C22×C412yes—
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×C61—21no—
163C4⋊C4×C61—21no—
164C22⋊C4×C61—42no—
165C22⋊C4×C61—42no—
166C42×C61—42no—
167C22⋊Dic61—42no—
168C22⋊Dic61—42no—
169C4⋊Dic61—21no—
170C4⋊Dic61—21no—
171C4⋊Dic61—21no—
172C4⋊Dic61—21no—
173C4⋊Dic61—21no—
174C4⋊Dic61—21no—
175C4⋊Dic61—21no—
176C4⋊Dic61—21no—
177#11758196—42no—
178#11758196—42no—
179#11758196—42no—
180#11758196—42no—
181C4×Dic61—42no—
182C4×Dic61—42no—
183C4×Dic61—42no—
184C4×Dic61C4⋊C414yes—
185C4×Dic61C4⋊C414yes—
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×C61C2×C4⋊C412yes—
223C2×C4×C61C23×C411yescharacteristic
224C2×C4×C61C22×Q811yescharacteristic
225C2×C4×C61H(5,𝔽2)11yescharacteristic
226C2×C4×C61H(5,𝔽2)11yescharacteristic
227C2×C4×C612−1+411yescharacteristic
228C2×C4×C612−1+411yescharacteristic
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—28no—
236C2×Dic61—44no—
237C2×Dic61—41no—
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×Dic61C2×C4⋊C412yes—
250C2×Dic61C2×C4⋊C412yes—
251C2×Dic61C2×C4⋊C412yes—
252C2×Dic61C2×C4⋊C412yes—
253C2×Dic61#13512yes—
254C2×Dic61#13512yes—
255C8×C61—22no—
256C8×C61—22no—
257#92418—22no—
258#92418—22no—
259#21985—611nomaximal, Sylow
260C22×C61—22no—
261C22×C61—22no—
262C22×C61—22no—
263C22×C61—41no—
264C22×C61—41no—
265C22×C61—41no—
266C22×C61—41no—
267C22×C61C22×C4⋊C411yescharacteristic
268C22×C61#53511yescharacteristic
269C22×C61#53611yescharacteristic
270C22×C61C2×#13511yescharacteristic
271C22×C61C2×#13511yescharacteristic
272C22×C61#57511yescharacteristic
273C22×C61#57511yescharacteristic
274C4×C61—22no—
275C4×C61—81no—
276C4×C61—81no—
277C4×C61—81no—
278C4×C61—81no—
279C4×C61#52011yescharacteristic
280C4×C61#52011yescharacteristic
281C4×C61#54411yescharacteristic
282C4×C61#54411yescharacteristic
283Dic61—22no—
284Dic61—22no—
285Dic61—22no—
286Dic61—81no—
287Dic61—81no—
288Dic61—81no—
289Dic61—81no—
290Dic61#42714yes—
291C2×#431—611no—
292#2285—611no—
293#2283—611no—
294#1948—611no—
295#1948—611no—
296#1947—611no—
297#1947—611no—
298#1854—611no—
299#1854—611no—
300#1854—611no—
301#1854D6111yescharacteristic
302#1846—611no—
303#1846—611no—
304#1835—611no—
305#1835—611no—
306C2×C61—42no—
307C2×C61#231711yescharacteristic
308C2×C61C2×#42711yescharacteristic
309C2×C61#291111yescharacteristic
310C2×C61#321211yescharacteristic
311C2×C61#321211yescharacteristic
312C2×C61#323311yescharacteristic
313C2×C61#323311yescharacteristic
314C2×#117—611no—
315C2×#117C2×D6111yescharacteristic
316C22×C42—611no—
317#431—618no—
318C2×#107—611no—
319C2×#107—611no—
320C2×#107—611no—
321C2×#107C2×D6111yescharacteristic
322C2×#106—611no—
323C2×#106—611no—
324C2×#106—611no—
325C2×#106C2×D6111yescharacteristic
326C2×C4⋊C8—611no—
327C2×C4⋊C8—611no—
328C2×C22⋊C8—611no—
329C2×C22⋊C8C2×D6111yescharacteristic
330C2×C4×C8—611no—
331C2×C4×C8—611no—
332#384—611no—
333#384—611no—
334#383—1221no—
335#382—611no—
336#382—611no—
337#382—611no—
338#382—611no—
339#381—1221no—
340#380—611no—
341#380—1221no—
342#380—1221no—
343#380C2×D6111yescharacteristic
344C4×C4⋊C4—611no—
345C4×C4⋊C4—611no—
346C4×C4⋊C4—1221no—
347C4×C4⋊C4—1221no—
348C4×C22⋊C4—1221no—
349#376—1221no—
350#340—611no—
351#340—611no—
352#340—611no—
353#340—611no—
354#340—611no—
355#340—611no—
356#340C2×D6111yescharacteristic
357#340C2×D6111yescharacteristic
358C61#2198511yescharacteristic, complemented, Sylow
359C23×C4—611no—
360C23×C4—611no—
361C23×C4C22×D6111yescharacteristic
362C22×C8—611no—
363C22×C8—611no—
364C22×C8C22×D6111yescharacteristic
365C22×C8C22×D6111yescharacteristic
366#117—41no—
367#117—41no—
368#117—2441no—
369#117—2441no—
370C2×C4⋊C4—611no—
371C2×C4⋊C4—611no—
372C2×C4⋊C4—611no—
373C2×C4⋊C4—611no—
374C2×C4⋊C4—1221no—
375C2×C4⋊C4—1221no—
376C2×C4⋊C4—1221no—
377C2×C4⋊C4—1221no—
378C2×C4⋊C4C22×D6111yescharacteristic
379C2×C4⋊C4C22×D6111yescharacteristic
380C2×C4⋊C4C22×D6111yescharacteristic
381C2×C4⋊C4C22×D6111yescharacteristic
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—1221no—
385C2×C22⋊C4—1221no—
386C2×C42—21no—
387C2×C42—614no—
388C2×C42—611no—
389C2×C42—611no—
390C2×C42—614no—
391C2×C42—611no—
392C2×C42—611no—
393C2×C42—1221no—
394C2×C42—1221no—
395C2×C42—1221no—
396#107—41no—
397#107—2441no—
398#107—2441no—
399#107—2441no—
400#106—41no—
401#106—2441no—
402#106—2441no—
403#106—2441no—
404C4⋊C8—614no—
405C4⋊C8—614no—
406C22⋊C8—614no—
407C22⋊C8C4×D6114yes—
408C4×C8—614no—
409C4×C8—614no—
410#95—21no—
411#95—1221no—
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—
421#95—1221no—
422C24D4×D6111yescharacteristic
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—611no—
432C22×C4—611no—
433C22×C4—611no—
434C22×C4—611no—
435C22×C4—614no—
436C22×C4—614no—
437C22×C4—1222no—
438C22×C4—1222no—
439C22×C4—1221no—
440C22×C4—1221no—
441C22×C4—1221no—
442C22×C4—1221no—
443C22×C4—2441no—
444C22×C4—2441no—
445C22×C4C2×C4×D6112yes—
446C22×C4D4×D6111yescharacteristic
447C22×C4Q8×D6112yes—
448C22×C4C23×D6111yescharacteristic
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—612no—
454C2×C8—612no—
455C2×C8—1221no—
456C2×C8—1221no—
457C2×C8—1221no—
458C2×C8—1221no—
459C2×C8C2×C4×D6112yes—
460C2×C8C2×C4×D6112yes—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4—1221no—
473C4⋊C4—1221no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C4⋊C4—1221no—
477C4⋊C4—2442no—
478C4⋊C4—2442no—
479C4⋊C4—2442no—
480C4⋊C4—2442no—
481C22⋊C4—42no—
482C22⋊C4—42no—
483C22⋊C4—2442no—
484C22⋊C4—2442no—
485C42—42no—
486C42—612no—
487C42—612no—
488C42—612no—
489C42—612no—
490C42—614no—
491C42—614no—
492C42—2442no—
493C42—2442no—
494C42—2442no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23C4⋊C4×D6112yes—
502C23C2×D4×D6111yescharacteristic
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
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—41no—
521C2×C4—612no—
522C2×C4—612no—
523C2×C4—612no—
524C2×C4—612no—
525C2×C4—612no—
526C2×C4—612no—
527C2×C4—1228no—
528C2×C4—1221no—
529C2×C4—1221no—
530C2×C4—1221no—
531C2×C4—1221no—
532C2×C4—1221no—
533C2×C4—1221no—
534C2×C4—2444no—
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×C4—2441no—
546C2×C4—2441no—
547C2×C4C4⋊C4×D6112yes—
548C2×C4C22×C4×D6111yescharacteristic
549C2×C4C2×Q8×D6111yescharacteristic
550C2×C4#1451982211yescharacteristic
551C2×C4#1451982211yescharacteristic
552C2×C4#1451982411yescharacteristic
553C2×C4#1451982411yescharacteristic
554C8—22no—
555C8—22no—
556C8—1222no—
557C8—1222no—
558C22—22no—
559C22—22no—
560C22—22no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22C2×C4⋊C4×D6111yescharacteristic
566C22#1684032711yescharacteristic
567C22#1684033411yescharacteristic
568C22#135×D6111yescharacteristic
569C22#135×D6111yescharacteristic
570C22#1684055811yescharacteristic
571C22#1684056111yescharacteristic
572C4—22no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4—614no—
578C4—1222no—
579C4—1222no—
580C4—1222no—
581C4—4881no—
582C4—4881no—
583C4—4881no—
584C4—4881no—
585C4#1684024111yescharacteristic
586C4#1684024111yescharacteristic
587C4#1684039111yescharacteristic
588C4#1684039111yescharacteristic
589C2—42no—
590C2#2144843811yescharacteristic
591C2#427×D6111yescharacteristic
592C2#2145440611yescharacteristic
593C2#2145679211yescharacteristic
594C2#2145679811yescharacteristic
595C2#2145699511yescharacteristic
596C2#2145700111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1854C2
socleC23×C61C22×D4
prime radicalC24×C61C2×D4
cosocleC22×C4×C61C24
hypercenter#1854D61
hypocenterC61#21985
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
4. #21446581C2semidirect
5. #21446579C2semidirect
6. #21446576C2semidirect
7. #21446574C2semidirect
11. #21445982C2semidirect
12. #21445980C2semidirect
13. #21445948C2semidirect
14. #21445948C2semidirect
18. #16839812C4semidirect
358. C61#21985semidirect

Maximal subgroups

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

subgroupindex
C2×#168398122
#214482222
#214482142
#214465812
#214465792
#214465762
#214465742
#214460202
#214460182
#214460162
#214459822
#214459802
#214459482
C61×#18542
#2198561