Finite Group Databasebeta

← #46846928

Subgroups — #46846928

Order 34688.

380 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31774431C211yesmaximal, characteristic, complemented
2#31774296C211yesmaximal, characteristic, complemented
3#31774279C211yesmaximal, characteristic, complemented
4#31774254C211yesmaximal, characteristic, complemented
5#31774251C211yesmaximal, characteristic, complemented
6#31774136C211yesmaximal, characteristic, complemented
7#31774131C211yesmaximal, characteristic
8#31774128C211yesmaximal, characteristic, complemented
9#31774124C211yesmaximal, characteristic, complemented
10C4×#16864644C211yesmaximal, characteristic, complemented
11C4×#16864641C211yesmaximal, characteristic, complemented
12C4×#16864642C211yesmaximal, characteristic, complemented
13C4×#16864639C211yesmaximal, characteristic, complemented
14C2×C4×C271⋊C8C211yesmaximal, characteristic, complemented
15#529×C271C211yesmaximal, characteristic, complemented
16C2×#16864644C2211yescharacteristic
17C2×#16864642C2211yescharacteristic
18C2×#16864641C2211yescharacteristic
19C2×#16864639C2211yescharacteristic
20C22×C271⋊C8C2211yescharacteristic
21C22×C271⋊C8C2211yescharacteristic
22#22576154—21no—
23#22576152C2211yescharacteristic
24#22576148C2211yescharacteristic
25#22576143—21no—
26#22576139C2211yescharacteristic
27#22576134C2211yescharacteristic
28C4×Dic542C2211yescharacteristic
29C4×D1084C2211yescharacteristic
30C4×C22⋊D271—21no—
31#22576117—21no—
32#22576093C2211yescharacteristic
33#22576093C2211yescharacteristic
34#22576091C2211yescharacteristic
35#22576091C2211yescharacteristic
36#22576084C2211yescharacteristic
37#22576084C2211yescharacteristic
38#22576083C2211yescharacteristic
39#22576083C2211yescharacteristic
40#22576081C2211yescharacteristic
41#22576081C2211yescharacteristic
42#22576080C2211yescharacteristic
43#22576080C2211yescharacteristic
44C4×C271⋊C8C2211yescharacteristic
45C4×C271⋊C8C2211yescharacteristic
46C4×C271⋊C8C2211yescharacteristic
47C4×C271⋊C8C2211yescharacteristic
48#126×C271—21no—
49#125×C271C2211yescharacteristic
50#124×C271C2211yescharacteristic
51#123×C271—21no—
52C22⋊Q8×C271C2211yescharacteristic
53#121×C271C2211yescharacteristic
54C4×Q8×C271C2211yescharacteristic
55C4×D4×C271—21no—
56C4×D4×C271C2211yescharacteristic
57#117×C271—21no—
58C2×C42×C271C2211yescharacteristic
59C2×Dic542C2311yescharacteristic
60C2×D1084C2311yescharacteristic
61C2×C22⋊D271—21no—
62C2×C4×D271—21no—
63#16864644—22no—
64#16864642—22no—
65#16864641—22no—
66#16864639—22no—
67C2×C271⋊C8—22no—
68C2×C271⋊C8—22no—
69C2×C271⋊C8C2311yescharacteristic
70C2×C271⋊C8C2311yescharacteristic
71C2×C271⋊C8C2311yescharacteristic
72C2×C271⋊C8C2311yescharacteristic
73C4⋊Dic271C2311yescharacteristic
74C4⋊Dic271C2311yescharacteristic
75Dic271⋊C4—21no—
76Dic271⋊C4—21no—
77Dic271⋊C4—21no—
78Dic271⋊C4—21no—
79C22⋊Dic271—21no—
80(C2×D271)⋊C4—21no—
81(C2×D271)⋊C4—21no—
82(C2×D271)⋊C4—21no—
83(C2×D271)⋊C4—21no—
84C4×Dic271—21no—
85C2×Q8×C271C2311yescharacteristic
86C2×D4×C271—21no—
87C2×D4×C271C2311yescharacteristic
88C22×C4×C271—21no—
89C22×C4×C271D411yescharacteristic
90C22×C4×C271D411yescharacteristic
91C22×C4×C271C2311yescharacteristic
92C4⋊C4×C271—21no—
93C4⋊C4×C271—21no—
94C4⋊C4×C271—21no—
95C4⋊C4×C271—21no—
96C4⋊C4×C271C2311yescharacteristic
97C4⋊C4×C271C2311yescharacteristic
98C22⋊C4×C271—21no—
99C22⋊C4×C271—21no—
100C22⋊C4×C271—21no—
101C22⋊C4×C271—21no—
102C22⋊C4×C271—21no—
103C42×C271—21no—
104C42×C271D411yescharacteristic
105C42×C271D411yescharacteristic
106C42×C271C2311yescharacteristic
107C42×C271C2311yescharacteristic
108C22×D271—21no—
109Dic542—21no—
110Dic542—21no—
111D1084—21no—
112D1084—21no—
113C22⋊D271—42no—
114C2×Dic271—21no—
115C2×Dic271—21no—
116C2×Dic271—21no—
117C4×D271—42no—
118C271⋊C8—21no—
119C271⋊C8—21no—
120C271⋊C8#4112yes—
121C271⋊C8#4112yes—
122C23×C271—21no—
123C23×C271C2×D411yescharacteristic
124Q8×C271—21no—
125Q8×C271—21no—
126D4×C271—21no—
127D4×C271—21no—
128D4×C271—42no—
129C2×C4×C271—22no—
130C2×C4×C271—22no—
131C2×C4×C271—21no—
132C2×C4×C271—21no—
133C2×C4×C271—21no—
134C2×C4×C271—21no—
135C2×C4×C271—21no—
136C2×C4×C271—42no—
137C2×C4×C271C2×D411yescharacteristic
138C2×C4×C271C2×D411yescharacteristic
139C2×C4×C271C2×D411yescharacteristic
140C2×C4×C271C2×D411yescharacteristic
141C2×C4×C271C2×D411yescharacteristic
142C2×C4×C271C2411yescharacteristic
143C22×C271—21no—
144C22×C271—21no—
145C22×C271—41no—
146C22×C271—41no—
147C22×C271—41no—
148C22×C271#13512yes—
149C22×C271C22×D411yescharacteristic
150C2×D271—41no—
151C2×D271—41no—
152C2×D271—41no—
153C4×C271—21no—
154C4×C271—21no—
155C4×C271—21no—
156C4×C271—21no—
157C4×C271—41no—
158C4×C271—41no—
159C4×C271—41no—
160C4×C271#13512yes—
161C4×C271C2×#4111yescharacteristic
162C4×C271C2×#4111yescharacteristic
163Dic271—41no—
164Dic271—41no—
165Dic271—41no—
166C2×C271—22no—
167C2×C271—81no—
168C2×C271#53211yescharacteristic
169C2×C271C2×#13511yescharacteristic
170C2×C271C2×#13511yescharacteristic
171D271—81no—
172C271#316811yescharacteristic, complemented, Sylow
173#3168—2711nomaximal, Sylow
174#529—2711no—
175#529D27111yescharacteristic, complemented
176#499—2711no—
177#495—2711no—
178#488—2711no—
179#488—2711no—
180#467—2711no—
181#466—2711no—
182#465—2711no—
183#465—2711no—
184C4×Q16—2711no—
185C4×SD16—2711no—
186C4×SD16—2711no—
187C4×D8—2711no—
188C2×C4×C8—2711no—
189C2×Q16—2711no—
190C2×SD16—2711no—
191C2×SD16—2711no—
192C2×D8—2711no—
193C22×C8—2711no—
194C22×C8—2711no—
195#126—21no—
196#126—5421no—
197#125—2711no—
198#125C2×D27111yescharacteristic
199#124—2711no—
200#124C2×D27111yescharacteristic
201#123—21no—
202#123—5421no—
203C22⋊Q8—2711no—
204C22⋊Q8C2×D27111yescharacteristic
205#121—2711no—
206#121C2×D27111yescharacteristic
207C4×Q8—2711no—
208C4×Q8C2×D27111yescharacteristic
209C4×D4—21no—
210C4×D4—2711no—
211C4×D4—5421no—
212C4×D4C2×D27111yescharacteristic
213#117—21no—
214#117—5421no—
215C2×C42C2×D27111yescharacteristic
216#107—2711no—
217#107—2711no—
218#106—2711no—
219#106—2711no—
220#103—2711no—
221#103—2711no—
222#103—2711no—
223#103—2711no—
224#102—2711no—
225#102—2711no—
226#102—2711no—
227#102—2711no—
228C4×C8—2711no—
229C4×C8—2711no—
230C4×C8—2711no—
231C4×C8—2711no—
232C2×Q8—2711no—
233C2×Q8C22×D27111yescharacteristic
234C2×D4—21no—
235C2×D4—2711no—
236C2×D4—5421no—
237C2×D4C22×D27111yescharacteristic
238C22×C4—21no—
239C22×C4—5421no—
240C22×C4C22⋊D27111yescharacteristic
241C22×C4C22⋊D27111yescharacteristic
242C22×C4C22×D27111yescharacteristic
243Q16—5422no—
244SD16—5422no—
245SD16—5422no—
246D8—5422no—
247C2×C8—2711no—
248C2×C8—2711no—
249C2×C8—2711no—
250C2×C8—2711no—
251C2×C8—5422no—
252C2×C8—5422no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—2711no—
258C4⋊C4—2711no—
259C4⋊C4—5421no—
260C4⋊C4—5421no—
261C4⋊C4—5421no—
262C4⋊C4—5421no—
263C4⋊C4C22×D27111yescharacteristic
264C4⋊C4C22×D27111yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—5421no—
271C22⋊C4—5421no—
272C22⋊C4—5421no—
273C22⋊C4—5421no—
274C22⋊C4—5421no—
275C42—21no—
276C42—5421no—
277C42C22⋊D27111yescharacteristic
278C42C22⋊D27111yescharacteristic
279C42C22×D27111yescharacteristic
280C42C22×D27111yescharacteristic
281C23—21no—
282C23—5421no—
283C23C2×C22⋊D27111yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—5421no—
287Q8—5421no—
288D4—21no—
289D4—21no—
290D4—42no—
291D4—5421no—
292D4—5421no—
293D4—10842no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—42no—
302C2×C4—5421no—
303C2×C4—5421no—
304C2×C4—5421no—
305C2×C4—10842no—
306C2×C4C2×C22⋊D27111yescharacteristic
307C2×C4C2×C22⋊D27111yescharacteristic
308C2×C4C2×C22⋊D27111yescharacteristic
309C2×C4C2×C22⋊D27111yescharacteristic
310C2×C4C2×C22⋊D27111yescharacteristic
311C2×C4C23×D27111yescharacteristic
312C8—2712no—
313C8—2712no—
314C8—5421no—
315C8—5421no—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—10841no—
322C22—10841no—
323C22—10841no—
324C22#2257618012yes—
325C22C22×C22⋊D27111yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—10841no—
334C4—10841no—
335C4—10841no—
336C4#2257618012yes—
337C4#41×D27111yescharacteristic
338C4#41×D27111yescharacteristic
339C2—22no—
340C2—81no—
341C2—21681no—
342C2#3177444311yescharacteristic
343C2C2×#2257618011yescharacteristic
344C2C2×#2257618011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D271
commutator, cosocleC2×C4×C271C24
FrattiniC2×C4C23×D271
Fitting#529×C271C2
socleC22×C271C22×D4
prime radical#31774131C2
hypercenter#529D271
hypocenterC271#3168
LCSG ▷ C2×C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #31774431C2semidirect
2. #31774296C2semidirect
3. #31774279C2semidirect
4. #31774254C2semidirect
5. #31774251C2semidirect
6. #31774136C2semidirect
8. #31774128C2semidirect
9. #31774124C2semidirect
10. C4×#16864644C2semidirect
11. C4×#16864641C2semidirect
12. C4×#16864642C2semidirect
13. C4×#16864639C2semidirect
14. C2×C4×C271⋊C8C2semidirect
15. #529×C271C2semidirect
172. C271#3168semidirect
175. #529D271semidirect

Maximal subgroups

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

subgroupindex
#317744312
#317742962
#317742792
#317742542
#317742512
#317741362
#317741312
#317741282
#317741242
C4×#168646442
C4×#168646412
C4×#168646422
C4×#168646392
C2×C4×C271⋊C82
#529×C2712
#3168271