Finite Group Databasebeta

← #46848290

Subgroups — #46848290

Order 34688.

398 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31774610C211yesmaximal, characteristic, complemented
2#31774549C211yesmaximal, characteristic, complemented
3#31774246C211yesmaximal, characteristic, complemented
4#31774240C211yesmaximal, characteristic, complemented
5#31774186C211yesmaximal, characteristic, complemented
6#31774128C211yesmaximal, characteristic, complemented
7#31774127C211yesmaximal, characteristic, complemented
8#31774101C211yesmaximal, characteristic, complemented
9#31774045C211yesmaximal, characteristic, complemented
10#31774044C211yesmaximal, characteristic, complemented
11#31773979C211yesmaximal, characteristic, complemented
12(C22⋊D271)⋊C8C211yesmaximal, characteristic, complemented
13#31773892C211yesmaximal, characteristic, complemented
14#31773891C211yesmaximal, characteristic, complemented
15#485×C271C211yesmaximal, characteristic, complemented
16C2×#16864655C2211yescharacteristic
17C2×#16864654C2211yescharacteristic
18C2×#16864643C2211yescharacteristic
19C2×#16864641C2211yescharacteristic
20C2×D2168C2211yescharacteristic
21C22×C271⋊C8C2211yescharacteristic
22C2×C8×D271C2211yescharacteristic
23#22576159C2211yescharacteristic
24#22576158C2211yescharacteristic
25#22576148—21no—
26#22576146—21no—
27#22576145—21no—
28#22576142—21no—
29#22576140C2211yescharacteristic
30#22576135C2211yescharacteristic
31#22576134C2211yescharacteristic
32#22576133—21no—
33#22576133—21no—
34#22576122C2211yescharacteristic
35#22576122C2211yescharacteristic
36C4×C22⋊D271C2211yescharacteristic
37#22576118C2211yescharacteristic
38#22576117—21no—
39C4⋊C4×D271—21no—
40#22576091C2211yescharacteristic
41Dic271⋊C8C2211yescharacteristic
42#22576085C2211yescharacteristic
43#22576084C2211yescharacteristic
44#22576083C2211yescharacteristic
45#22576083C2211yescharacteristic
46#22576082C2211yescharacteristic
47#22576080C2211yescharacteristic
48#22576080C2211yescharacteristic
49#22576080C2211yescharacteristic
50(C2×D271)⋊C8C2211yescharacteristic
51C8×Dic271C2211yescharacteristic
52C22⋊Q8×C271C2211yescharacteristic
53#117×C271C2211yescharacteristic
54#107×C271C2211yescharacteristic
55#106×C271C2211yescharacteristic
56#103×C271C2211yescharacteristic
57#103×C271C2211yescharacteristic
58C22⋊C8×C271C2211yescharacteristic
59#16864655—22no—
60#16864655—41no—
61#16864654—22no—
62#16864654—41no—
63C2×Dic542—21no—
64C2×Dic542C2311yescharacteristic
65C2×D1084—21no—
66C2×D1084—21no—
67C2×D1084C2311yescharacteristic
68C2×D1084C2311yescharacteristic
69C2×C22⋊D271—21no—
70C2×C22⋊D271—21no—
71C2×C22⋊D271D411yescharacteristic
72C2×C4×D271—21no—
73C2×C4×D271—21no—
74C2×C4×D271—21no—
75C2×C4×D271—21no—
76C2×C4×D271C2311yescharacteristic
77#16864643—41no—
78#16864641—41no—
79D2168—22no—
80C2×C271⋊C8—41no—
81C2×C271⋊C8C2311yescharacteristic
82C2×C271⋊C8C2311yescharacteristic
83C8×D271—41no—
84C4⋊Dic271—21no—
85C4⋊Dic271C2311yescharacteristic
86Dic271⋊C4—21no—
87Dic271⋊C4—21no—
88Dic271⋊C4—21no—
89Dic271⋊C4D411yescharacteristic
90C22⋊Dic271D411yescharacteristic
91(C2×D271)⋊C4—21no—
92(C2×D271)⋊C4—21no—
93(C2×D271)⋊C4—21no—
94(C2×D271)⋊C4—21no—
95(C2×D271)⋊C4—21no—
96(C2×D271)⋊C4—21no—
97(C2×D271)⋊C4D411yescharacteristic
98C4×Dic271—21no—
99C4×Dic271C2311yescharacteristic
100C2×Q8×C271C2311yescharacteristic
101C22×C4×C271C2311yescharacteristic
102C2×C8×C271C2311yescharacteristic
103C2×C8×C271C2311yescharacteristic
104C4⋊C4×C271—21no—
105C4⋊C4×C271C2311yescharacteristic
106C4⋊C4×C271C2311yescharacteristic
107C4⋊C4×C271C2311yescharacteristic
108C22⋊C4×C271—21no—
109C22⋊C4×C271—21no—
110C42×C271—21no—
111C22×D271—21no—
112C22×D271—21no—
113C22×D271C2×D411yescharacteristic
114Dic542—21no—
115Dic542—21no—
116Dic542—81no—
117D1084—21no—
118D1084—21no—
119D1084—21no—
120D1084—42no—
121D1084—81no—
122D1084#4112yes—
123C22⋊D271—22no—
124C22⋊D271—42no—
125C22⋊D271—81no—
126C2×Dic271—21no—
127C2×Dic271—21no—
128C2×Dic271C2×D411yescharacteristic
129C2×Dic271C2×D411yescharacteristic
130C2×Dic271C2×D411yescharacteristic
131C4×D271—21no—
132C4×D271—21no—
133C4×D271—42no—
134C4×D271—42no—
135C4×D271—42no—
136C4×D271—42no—
137C271⋊C8—21no—
138C271⋊C8—21no—
139C23×C271C2×D411yescharacteristic
140Q8×C271—21no—
141Q8×C271—21no—
142C2×C4×C271—21no—
143C2×C4×C271—21no—
144C2×C4×C271—21no—
145C2×C4×C271—21no—
146C2×C4×C271—21no—
147C2×C4×C271—21no—
148C2×C4×C271C2×D411yescharacteristic
149C2×C4×C271C2411yescharacteristic
150C8×C271—21no—
151C8×C271—21no—
152C22×C271—21no—
153C22×C271—21no—
154C22×C271—21no—
155C22×C271C22×D411yescharacteristic
156C2×D271—21no—
157C2×D271—22no—
158C2×D271—21no—
159C2×D271—21no—
160C2×D271—41no—
161C2×D271—41no—
162C2×D271—41no—
163C2×D271—41no—
164C2×D271—41no—
165C4×C271—21no—
166C4×C271—41no—
167C4×C271—41no—
168C4×C271—41no—
169C4×C271—41no—
170C4×C271C2×#4111yescharacteristic
171C4×C271H(5,𝔽2)11yescharacteristic
172Dic271—21no—
173Dic271—21no—
174Dic271—41no—
175Dic271—41no—
176Dic271#13512yes—
177C2×C271—41no—
178C2×C271#54611yescharacteristic
179C2×C271C2×#13511yescharacteristic
180C2×C271#57711yescharacteristic
181D271—41no—
182D271—42no—
183D271—81no—
184C271#330311yescharacteristic, complemented, Sylow
185#3303—2711nomaximal, Sylow
186#555—2711no—
187#547—2711no—
188#487—2711no—
189#485—2711no—
190#485D27111yescharacteristic, complemented
191#476—2711no—
192#465—2711no—
193#465—2711no—
194#461—2711no—
195#449—2711no—
196#449—2711no—
197C4×D8—2711no—
198C8×D4—2711no—
199#416—2711no—
200#416—2711no—
201C2×#41—2711no—
202C2×#41—2711no—
203C2×SD16—2711no—
204C2×SD16—2711no—
205C2×D8—2711no—
206C22×C8—2711no—
207C22×C8—2711no—
208C4⋊Q8—2711no—
209C4⋊Q8—2711no—
210#124—5421no—
211#124—5421no—
212#123—5421no—
213#123—5421no—
214C22⋊Q8—2711no—
215C22⋊Q8C2×D27111yescharacteristic
216#121—2711no—
217#121—2711no—
218#121—5421no—
219#121—5421no—
220C4×D4—2711no—
221C4×D4—2711no—
222C4×D4—2711no—
223#117—2711no—
224#117—5421no—
225#117C2×D27111yescharacteristic
226C2×C4⋊C4—5421no—
227#107C2×D27111yescharacteristic
228#106—2711no—
229#106C2×D27111yescharacteristic
230C4⋊C8—2711no—
231#103—2711no—
232#103—2711no—
233#103—2711no—
234#103—2711no—
235#103C2×D27111yescharacteristic
236#103C2×D27111yescharacteristic
237#102—2711no—
238#102—2711no—
239#102—2711no—
240#102—2711no—
241C22⋊C8—2711no—
242C22⋊C8C2×D27111yescharacteristic
243C4×C8—2711no—
244#41—5422no—
245#41—5422no—
246#41—10841no—
247#41—10841no—
248C2×Q8—2711no—
249C2×Q8—5421no—
250C2×Q8C22×D27111yescharacteristic
251C2×D4—2711no—
252C2×D4—2711no—
253C2×D4—2711no—
254C2×D4—5421no—
255C2×D4—5421no—
256C2×D4—5421no—
257C2×D4—5421no—
258C22×C4—2711no—
259C22×C4—5421no—
260C22×C4—5421no—
261C22×C4—5421no—
262C22×C4—5421no—
263C22×C4C22×D27111yescharacteristic
264SD16—10841no—
265SD16—10841no—
266D8—5422no—
267C2×C8—2711no—
268C2×C8—2711no—
269C2×C8—10841no—
270C2×C8—10841no—
271C2×C8C22×D27111yescharacteristic
272C2×C8C22×D27111yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—2711no—
275C4⋊C4—2711no—
276C4⋊C4—5421no—
277C4⋊C4—5421no—
278C4⋊C4—5421no—
279C4⋊C4—5421no—
280C4⋊C4C22×D27111yescharacteristic
281C4⋊C4C22×D27111yescharacteristic
282C4⋊C4C22×D27111yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—2711no—
286C22⋊C4—2711no—
287C22⋊C4—5421no—
288C22⋊C4—5421no—
289C22⋊C4—5421no—
290C22⋊C4—5421no—
291C22⋊C4—5421no—
292C22⋊C4—5421no—
293C42—21no—
294C42—2711no—
295C42—5421no—
296C23—2711no—
297C23—5421no—
298C23—5421no—
299C23D4×D27111yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—5421no—
303Q8—5421no—
304Q8—21681no—
305D4—2712no—
306D4—5422no—
307D4—5421no—
308D4—5421no—
309D4—5421no—
310D4—10842no—
311D4—10842no—
312D4—21681no—
313D4—21681no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—2711no—
321C2×C4—2711no—
322C2×C4—2711no—
323C2×C4—5421no—
324C2×C4—5421no—
325C2×C4—5421no—
326C2×C4—5421no—
327C2×C4—10842no—
328C2×C4—10842no—
329C2×C4—10842no—
330C2×C4—10842no—
331C2×C4D4×D27111yescharacteristic
332C2×C4C23×D27111yescharacteristic
333C8—21no—
334C8—21no—
335C8—5421no—
336C8—5421no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—5421no—
341C22—5422no—
342C22—5421no—
343C22—5421no—
344C22—10841no—
345C22—10841no—
346C22—10841no—
347C22—10841no—
348C22—10841no—
349C22C2×D4×D27111yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—2712no—
356C4—5421no—
357C4—5421no—
358C4—10841no—
359C4—10841no—
360C4#41×D27111yescharacteristic
361C4#2257620611yescharacteristic
362C2—41no—
363C2—10841no—
364C2—10842no—
365C2—21681no—
366C2#3177453911yescharacteristic
367C2#135×D27111yescharacteristic
368C2#3177470611yescharacteristic
subgroupG/H
centerC22C2×D4×D271
commutator, cosocleC2×C4×C271C24
FrattiniC2×C4C23×D271
Fitting#485×C271C2
socleC22×C271C22×D4
hypercenter#485D271
hypocenterC271#3303
LCSG ▷ C2×C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #31774610C2semidirect
2. #31774549C2semidirect
3. #31774246C2semidirect
4. #31774240C2semidirect
5. #31774186C2semidirect
6. #31774128C2semidirect
7. #31774127C2semidirect
8. #31774101C2semidirect
9. #31774045C2semidirect
10. #31774044C2semidirect
11. #31773979C2semidirect
12. (C22⋊D271)⋊C8C2semidirect
13. #31773892C2semidirect
14. #31773891C2semidirect
15. #485×C271C2semidirect
184. C271#3303semidirect
190. #485D271semidirect

Maximal subgroups

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

subgroupindex
#317746102
#317745492
#317742462
#317742402
#317741862
#317741282
#317741272
#317741012
#317740452
#317740442
#317739792
(C22⋊D271)⋊C82
#317738922
#317738912
#485×C2712
#3303271