Finite Group Databasebeta

← #29662722

Subgroups — #29662722

Order 15616.

704 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456398C211yesmaximal, characteristic, complemented
2#21455274C212yesmaximal, complemented
3#21445387C212yesmaximal, complemented
4#21445380C212yesmaximal, complemented
5#21445337C211yesmaximal, characteristic, complemented
6#21445332C211yesmaximal, characteristic, complemented
7#21445303C211yesmaximal, characteristic, complemented
8#21445298C211yesmaximal, characteristic, complemented
9C2×#16839513C211yesmaximal, characteristic, complemented
10#21444466C212yesmaximal, complemented
11C61×#2965C211yesmaximal, characteristic, complemented
12C2×#14519797—22no—
13#16840312C2212yes—
14#16840167C2211yescharacteristic
15#16840139C2211yescharacteristic
16#16840109C2212yes—
17#16839998—21no—
18#16839998—21no—
19#16839984—22no—
20#16839977—22no—
21#16839972C2212yes—
22#16839967C2212yes—
23#16839962C2212yes—
24#16839957C2212yes—
25C4×D488—21no—
26C4×D488—21no—
27C2×C4⋊#92418C2212yes—
28#16839756—22no—
29#16839513C2212yes—
30#16839513C2211yescharacteristic
31#16839513C2211yescharacteristic
32#16839507C2212yes—
33#16839507C2212yes—
34#16839505C2212yes—
35#16839505C2212yes—
36C4×#41×C61C2211yescharacteristic
37C61×#446C2211yescharacteristic
38C61×#446C2211yescharacteristic
39C61×#436C2211yescharacteristic
40C61×#436C2211yescharacteristic
41C61×#435—21no—
42C61×#435—21no—
43C61×#431—21no—
44C61×#431C2211yescharacteristic
45C4×M16×C61—21no—
46C2×C4×C8×C61C2211yescharacteristic
47C2×#11758222—22no—
48#14519797—48no—
49C2×#11758202—22no—
50C2×#11758200—22no—
51C2×#11758201—22no—
52C2×D488—21no—
53C2×D488—21no—
54C2×#11758199—22no—
55C22×#92418—22no—
56#14519777C2312yes—
57#14519774C2312yes—
58#14519765—22no—
59#14519751—22no—
60#14519751—22no—
61C4×D244—22no—
62C4×D244—22no—
63#14519711—21no—
64#14519711—21no—
65C4⋊#92418—22no—
66C4⋊#92418C2312yes—
67C4⋊#92418C2312yes—
68#14519700—22no—
69#14519700—22no—
70#14519699—22no—
71#14519699—22no—
72#14519697—22no—
73#14519697—22no—
74C2×#41×C61D411yescharacteristic
75C2×M16×C61—21no—
76C2×M16×C61—21no—
77C22×C8×C61D411yescharacteristic
78C22×C8×C61D411yescharacteristic
79C4×Q8×C61D411yescharacteristic
80C4×Q8×C61C2311yescharacteristic
81C4×D4×C61—21no—
82C4×D4×C61—21no—
83C4×D4×C61D411yescharacteristic
84C4×D4×C61C2311yescharacteristic
85#117×C61—21no—
86#117×C61D411yescharacteristic
87C2×C42×C61—21no—
88C2×C42×C61C2311yescharacteristic
89C4⋊C8×C61—21no—
90C4⋊C8×C61—21no—
91C4⋊C8×C61C2311yescharacteristic
92C4⋊C8×C61C2311yescharacteristic
93C22⋊C8×C61—21no—
94C22⋊C8×C61—21no—
95C22⋊C8×C61—21no—
96#97×C61—21no—
97#97×C61—21no—
98C4×C8×C61—21no—
99C4×C8×C61D411yescharacteristic
100C4×C8×C61D411yescharacteristic
101C4×C8×C61C2311yescharacteristic
102C4×C8×C61C2311yescharacteristic
103#41×C61—24no—
104C2×Q8×C61C2×D411yescharacteristic
105C2×D4×C61—21no—
106C2×D4×C61C2×D411yescharacteristic
107C22×C4×C61—21no—
108C22×C4×C61—21no—
109C22×C4×C61—21no—
110C22×C4×C61C2×D411yescharacteristic
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61#4111yescharacteristic
113C2×C22⋊D61—42no—
114#11758222—44no—
115#11758222—44no—
116C2×D244—22no—
117C2×D244—22no—
118C2×D244—22no—
119C2×C4×D61—42no—
120C2×Dic122—22no—
121M16×C61—42no—
122M16×C61—42no—
123C2×C8×C61—22no—
124C2×C8×C61—21no—
125C2×C8×C61—21no—
126C2×C8×C61—41no—
127C2×C8×C61C2×D411yescharacteristic
128C2×C8×C61C2×D411yescharacteristic
129C2×C8×C61C2×D411yescharacteristic
130C2×C8×C61C2×D411yescharacteristic
131C4⋊C4×C61—21no—
132C4⋊C4×C61—21no—
133C4⋊C4×C61C2×D411yescharacteristic
134C4⋊C4×C61C2×D411yescharacteristic
135C22⋊C4×C61—21no—
136C22⋊C4×C61—21no—
137C22⋊C4×C61—21no—
138C42×C61—21no—
139C42×C61—21no—
140C42×C61—21no—
141C42×C61C2×D411yescharacteristic
142C42×C61C2×D411yescharacteristic
143C42×C61#4111yescharacteristic
144C42×C61C2411yescharacteristic
145#11758202—44no—
146#11758201—44no—
147#11758200—44no—
148#11758199—44no—
149#11758198—42no—
150#11758198—42no—
151C4⋊Dic61—22no—
152C4⋊Dic61—22no—
153C2×#92418—22no—
154C2×#92418—22no—
155C2×#92418—44no—
156D488—42no—
157D488—42no—
158C23×C61—21no—
159C23×C61#12111yescharacteristic
160C22×D61—42no—
161Q8×C61—22no—
162D4×C61—22no—
163D4×C61—42no—
164C2×C4×C61—21no—
165C2×C4×C61—21no—
166C2×C4×C61—21no—
167C2×C4×C61—21no—
168C2×C4×C61—21no—
169C2×C4×C61—41no—
170C2×C4×C61—42no—
171C2×C4×C61—41no—
172C2×C4×C61—41no—
173C2×C4×C61—42no—
174C2×C4×C61#12111yescharacteristic
175C2×C4×C61#12111yescharacteristic
176C2×C4×C61#12111yescharacteristic
177C2×C4×C61AGL(1,ℤ/8)14yes—
178C2×C4×C61C22×D411yescharacteristic
179C2×C4×C61C22×D411yescharacteristic
180C2×C4×C61C2×#4111yescharacteristic
181C22⋊D61—84no—
182C2×Dic61—42no—
183D244—42no—
184D244—42no—
185D244—42no—
186D244—42no—
187D244—82no—
188C4×D61—84no—
189Dic122—42no—
190Dic122—42no—
191C8×C61—21no—
192C8×C61—21no—
193C8×C61—21no—
194C8×C61—41no—
195C8×C61—41no—
196C8×C61#13512yescomplemented
197#92418—42no—
198#92418—42no—
199#19157—611nomaximal, Sylow
200C22×C61—21no—
201C22×C61—21no—
202C22×C61—41no—
203C22×C61—41no—
204C22×C61—41no—
205C22×C61#46912yes—
206C22×C61C2×#12111yescharacteristic
207C2×D61—82no—
208C2×D61—82no—
209C2×D61—82no—
210C4×C61—21no—
211C4×C61—21no—
212C4×C61—21no—
213C4×C61—41no—
214C4×C61—41no—
215C4×C61—41no—
216C4×C61#46912yes—
217C4×C61C2×#13511yescharacteristic
218C4×C61C2×AGL(1,ℤ/8)12yes—
219C4×C61#57511yescharacteristic
220Dic61—82no—
221#3169—611no—
222#3035—612no—
223#2965D6111yescharacteristic, complemented
224#1702—612no—
225#1701—612no—
226#1694—611no—
227#1693—611no—
228#1688—611no—
229#1687—611no—
230C2×#334—611no—
231#1540—612no—
232C2×C61—22no—
233C2×C61—81no—
234C2×C61#303511yescharacteristic
235C2×C61C2×#46911yescharacteristic
236C2×C61#306711yescharacteristic
237D61—162no—
238C2×#135—1222no—
239#532—612no—
240C4×#41C2×D6111yescharacteristic
241#500—611no—
242#493—611no—
243#486—612no—
244#466—1221no—
245#466—1221no—
246#464—1222no—
247#463—1222no—
248#462—612no—
249#461—612no—
250#460—612no—
251#459—612no—
252#446C2×D6111yescharacteristic
253#446C2×D6111yescharacteristic
254C4×D8—1221no—
255C4×D8—1221no—
256#436C2×D6111yescharacteristic
257#436C2×D6111yescharacteristic
258#435—21no—
259#435—21no—
260#431—21no—
261#431C2×D6111yescharacteristic
262C2×C4⋊C8—612no—
263#416—1222no—
264C4×M16—21no—
265C2×C4×C8C2×D6111yescharacteristic
266#334—611no—
267#334—611no—
268#334—612no—
269#332—612no—
270#332—612no—
271#331—612no—
272#331—612no—
273C61#1915711yescharacteristic, complemented, Sylow
274C2×#41—1222no—
275C2×#41D24411yescharacteristic
276#135—2448no—
277C2×Q16—1222no—
278C2×SD16—1222no—
279C2×SD16—1222no—
280C2×D8—1222no—
281C2×D8—1221no—
282C2×D8—1221no—
283C2×M16—21no—
284C2×M16—21no—
285C22×C8—1222no—
286C22×C8C22⋊D6111yescharacteristic
287C22×C8C22⋊D6111yescharacteristic
288C4⋊Q8—612no—
289#127—612no—
290#124—1222no—
291#121—1222no—
292#121—1222no—
293C4×Q8D24411yescharacteristic
294C4×Q8C22×D6111yescharacteristic
295C4×D4—21no—
296C4×D4—21no—
297C4×D4—1222no—
298C4×D4—1222no—
299C4×D4D24411yescharacteristic
300C4×D4C22×D6111yescharacteristic
301#117—21no—
302#117D24411yescharacteristic
303C2×C42—21no—
304C2×C42C22×D6111yescharacteristic
305#107—1221no—
306#107—1221no—
307C4⋊C8—21no—
308C4⋊C8—21no—
309C4⋊C8—612no—
310C4⋊C8—612no—
311C4⋊C8—1222no—
312C4⋊C8C22×D6111yescharacteristic
313C4⋊C8C22×D6111yescharacteristic
314#103—1222no—
315#103—1222no—
316#102—1222no—
317#102—1222no—
318#102—1222no—
319#102—1222no—
320C22⋊C8—21no—
321C22⋊C8—21no—
322C22⋊C8—21no—
323#97—21no—
324#97—21no—
325C4×C8—21no—
326C4×C8C22⋊D6111yescharacteristic
327C4×C8C22⋊D6111yescharacteristic
328C4×C8C22×D6111yescharacteristic
329C4×C8C22×D6111yescharacteristic
330#41—24no—
331#41—2444no—
332#41—2444no—
333C2×Q8—1222no—
334C2×Q8C2×D24411yescharacteristic
335C2×D4—21no—
336C2×D4—1222no—
337C2×D4—1222no—
338C2×D4—1222no—
339C2×D4—2442no—
340C2×D4C2×D24411yescharacteristic
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—2442no—
345C22×C4C2×D24411yescharacteristic
346C22×C4#1175822211yescharacteristic
347C22×C4C2×C22⋊D6111yescharacteristic
348Q16—2444no—
349SD16—2444no—
350SD16—2444no—
351D8—2442no—
352D8—2444no—
353D8—2442no—
354M16—42no—
355M16—42no—
356C2×C8—22no—
357C2×C8—21no—
358C2×C8—21no—
359C2×C8—41no—
360C2×C8—1222no—
361C2×C8—1222no—
362C2×C8—2444no—
363C2×C8C2×C22⋊D6111yescharacteristic
364C2×C8C2×C22⋊D6111yescharacteristic
365C2×C8C2×C22⋊D6111yescharacteristic
366C2×C8C2×C22⋊D6111yescharacteristic
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—1222no—
370C4⋊C4—1222no—
371C4⋊C4C2×D24411yescharacteristic
372C4⋊C4C2×D24411yescharacteristic
373C22⋊C4—21no—
374C22⋊C4—21no—
375C22⋊C4—21no—
376C22⋊C4—2442no—
377C22⋊C4—2442no—
378C42—21no—
379C42—21no—
380C42—21no—
381C42C2×D24411yescharacteristic
382C42#1175822211yescharacteristic
383C42C2×C22⋊D6111yescharacteristic
384C42C23×D6111yescharacteristic
385C23—21no—
386C23—2442no—
387C23#1451975111yescharacteristic
388Q8—22no—
389Q8—2442no—
390Q8—2442no—
391D4—22no—
392D4—42no—
393D4—4882no—
394D4—4884no—
395D4—2442no—
396D4—2442no—
397D4—2442no—
398D4—2442no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—4884no—
410C2×C4—2442no—
411C2×C4#1451975111yescharacteristic
412C2×C4#1451975111yescharacteristic
413C2×C4#1451975111yescharacteristic
414C2×C4#1451980514yes—
415C2×C4C22×C22⋊D6111yescharacteristic
416C2×C4C22×D24411yescharacteristic
417C2×C4C2×#1175822211yescharacteristic
418C8—21no—
419C8—21no—
420C8—21no—
421C8—41no—
422C8—41no—
423C8—2442no—
424C8—2442no—
425C8#1451979712yescomplemented
426C22—21no—
427C22—21no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—4882no—
432C22—4882no—
433C22—4882no—
434C22#1684001512yes—
435C22C2×#1451975111yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—41no—
440C4—41no—
441C4—41no—
442C4—4882no—
443C4#1684001512yes—
444C4C2×#1451979711yescharacteristic
445C4C2×#1451980512yes—
446C4#1684056011yescharacteristic
447C2—22no—
448C2—81no—
449C2—9762no—
450C2#2145527411yescharacteristic
451C2C2×#1684001511yescharacteristic
452C2#2145553911yescharacteristic
subgroupG/H
centerC2×C4#14519751
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#2965C2
socleC22×C61C2×#121
hypercenter#2965D61
hypocenterC61#19157
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2965

Complements

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

NH ≅ G/Ntype
1. #21456398C2semidirect
2. #21455274C2semidirect
3. #21445387C2semidirect
4. #21445380C2semidirect
5. #21445337C2semidirect
6. #21445332C2semidirect
7. #21445303C2semidirect
8. #21445298C2semidirect
9. C2×#16839513C2semidirect
10. #21444466C2semidirect
11. C61×#2965C2semidirect
196. C8×C61#135semidirect
223. #2965D61semidirect
273. C61#19157semidirect
425. C8#14519797semidirect

Maximal subgroups

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

subgroupindex
#214563982
#214552742
#214453872
#214453802
#214453372
#214453322
#214453032
#214452982
C2×#168395132
#214444662
C61×#29652
#1915761