Finite Group Databasebeta

← C2×#31774032 #46845541

Subgroups — C2×#31774032 #46845541

Order 34688.

1048 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×D271C211yesmaximal, characteristic, complemented
2C22×D2168C211yesmaximal, characteristic, complemented
3C22×#16864639C211yesmaximal, characteristic, complemented
4C2×#22576135C211yesmaximal, characteristic, complemented
5#31774032C218yesmaximal, direct product factor
6C2×#22576080C211yesmaximal, characteristic, complemented
7C2×(C2×D271)⋊C8C211yesmaximal, characteristic, complemented
8C2×#102×C271C211yesmaximal, characteristic, complemented
9C24×D271—21no—
10C22×D1084—21no—
11C22×D1084C2211yescharacteristic
12C22×D1084C2211yescharacteristic, complemented
13C22×C22⋊D271—21no—
14C2×D4×D271—24no—
15C2×D4×D271—22no—
16C2×D4×D271—24no—
17C2×D4×D271C2214yescomplemented
18C22×C4×D271C2211yescharacteristic
19C2×D2168—24no—
20C2×D2168C2214yescomplemented
21C2×#16864639—24no—
22C2×#16864639C2214yescomplemented
23C22×C271⋊C8C2211yescharacteristic, complemented
24#22576135—22no—
25#22576135C2214yescomplemented
26C2×(C2×D271)⋊C4—21no—
27#22576080C2214yescomplemented
28(C2×D271)⋊C8C2214yescomplemented
29C22×D4×C271C2211yescharacteristic
30C22×C8×C271C2211yescharacteristic, complemented
31C2×C4⋊C4×C271C2211yescharacteristic, complemented
32#102×C271C2214yescomplemented
33C23×D271—28no—
34C23×D271—24no—
35C23×D271—21no—
36C23×D271—21no—
37C23×D271—44no—
38C23×D271—44no—
39C23×D271D411yescharacteristic
40C2×D1084—24no—
41C2×D1084—21no—
42C2×D1084—22no—
43C2×D1084—22no—
44C2×D1084—22no—
45C2×D1084—21no—
46C2×D1084—44no—
47C2×D1084D414yescomplemented
48C2×D1084C2312yes—
49C2×D1084C2312yescomplemented
50C2×C22⋊D271—28no—
51C2×C22⋊D271—24no—
52D4×D271—216no—
53D4×D271—28no—
54D4×D271—28no—
55C22×Dic271D411yescharacteristic
56C2×C4×D271—22no—
57C2×C4×D271—22no—
58C2×C4×D271D412yes—
59C2×C4×D271C2312yes—
60D2168—28no—
61#16864639—28no—
62C2×C271⋊C8—22no—
63C2×C271⋊C8C2312yescomplemented
64(C2×D271)⋊C4—24no—
65C24×C271—21no—
66C2×D4×C271—21no—
67C2×D4×C271—22no—
68C2×D4×C271D414yescomplemented
69C2×D4×C271C2312yes—
70C22×C4×C271—21no—
71C22×C4×C271C2311yescharacteristic
72C2×C8×C271—22no—
73C2×C8×C271C2312yescomplemented
74C4⋊C4×C271—21no—
75C4⋊C4×C271C2312yescomplemented
76C22×D271—22no—
77C22×D271—22no—
78C22×D271—216no—
79C22×D271—24no—
80C22×D271—22no—
81C22×D271—22no—
82C22×D271—48no—
83C22×D271—432no—
84C22×D271—42no—
85C22×D271—42no—
86C22×D271—48no—
87C22×D271—42no—
88C22×D271—42no—
89C22×D271—42no—
90C22×D271D814yescomplemented
91C22×D271C2×D412yes—
92D1084—24no—
93D1084—22no—
94D1084—22no—
95D1084—22no—
96D1084—48no—
97D1084—42no—
98D1084C2×D414yescomplemented
99C22⋊D271—216no—
100C2×Dic271—22no—
101C2×Dic271C2×D412yes—
102C4×D271—24no—
103C4×D271—22no—
104C4×D271—22no—
105C271⋊C8—22no—
106C23×C271—24no—
107C23×C271—22no—
108C23×C271—42no—
109C23×C271—42no—
110C23×C271C2×D411yescharacteristic
111D4×C271—24no—
112D4×C271—22no—
113D4×C271C2×D414yescomplemented
114C2×C4×C271—22no—
115C2×C4×C271—42no—
116C2×C4×C271C2×D411yescharacteristic
117C2×C4×C271C2×D412yes—
118C2×C4×C271C2×D412yes—
119C2×C4×C271C2411yescharacteristic
120C8×C271—22no—
121C22×C271—24no—
122C22×C271—42no—
123C22×C271—42no—
124C22×C271—48no—
125C22×C271#12012yes—
126C22×C271C2×D812yes—
127C22×C271AGL(1,ℤ/8)12yes—
128C22×C271C22×D411yescharacteristic
129C2×D271—22no—
130C2×D271—22no—
131C2×D271—28no—
132C2×D271—24no—
133C2×D271—432no—
134C2×D271—42no—
135C2×D271—42no—
136C2×D271—48no—
137C2×D271—42no—
138C2×D271—42no—
139C2×D271—42no—
140C2×D271—84no—
141C2×D271C2×D814yescomplemented
142C4×C271—42no—
143C4×C271#12012yes—
144C4×C271C22×D411yescharacteristic
145C4×C271C22×D411yescharacteristic
146Dic271—22no—
147C2×C271—44no—
148C2×C271#44714yescomplemented
149C2×C271C2×#12011yescharacteristic
150C2×C271C22×D811yescharacteristic
151C2×C271C2×AGL(1,ℤ/8)11yescharacteristic
152D271—24no—
153D271—44no—
154D271—82no—
155C271C2×#44711yescharacteristic, complemented, Sylow
156C2×#447—2711nomaximal, Sylow
157C23×D4—2711no—
158C22×D8—2711no—
159C22×D8—2711no—
160C2×#121—2711no—
161#447—2718no—
162C2×#102—2711no—
163C2×#102D27111yescharacteristic, complemented
164C2×C22⋊C8—2711no—
165C25—5421no—
166C22×D4—2714no—
167C22×D4—2711no—
168C22×D4—2711no—
169C22×D4—5421no—
170C22×D4—5422no—
171C22×D4—5421no—
172C22×D4—5424no—
173C22×D4—5424no—
174C22×D4C2×D27111yescharacteristic
175C23×C4—2711no—
176C2×D8—2714no—
177C2×D8—2714no—
178C2×D8—5424no—
179C2×D8—5424no—
180C22×C8—2711no—
181C22×C8C2×D27111yescharacteristic, complemented
182#121—2714no—
183#121—5422no—
184C2×C4⋊C4C2×D27111yescharacteristic, complemented
185C2×C22⋊C4—5421no—
186#102—2714no—
187#102C2×D27114yescomplemented
188C22⋊C8—2714no—
189C24—21no—
190C24—2711no—
191C24—5424no—
192C24—5428no—
193C24—5421no—
194C24—5421no—
195C24—10844no—
196C24—10844no—
197C2×D4—21no—
198C2×D4—22no—
199C2×D4—2714no—
200C2×D4—2712no—
201C2×D4—2712no—
202C2×D4—5424no—
203C2×D4—5424no—
204C2×D4—5428no—
205C2×D4—54216no—
206C2×D4—5428no—
207C2×D4—5428no—
208C2×D4—5421no—
209C2×D4—5422no—
210C2×D4—5421no—
211C2×D4—5422no—
212C2×D4—5422no—
213C2×D4—10844no—
214C2×D4D108414yescomplemented
215C2×D4C22×D27112yes—
216C22×C4—21no—
217C22×C4—2711no—
218C22×C4—2712no—
219C22×C4—2712no—
220C22×C4—5422no—
221C22×C4—5422no—
222C22×C4C22×D27111yescharacteristic
223D8—5428no—
224D8—5428no—
225C2×C8—22no—
226C2×C8—2712no—
227C2×C8—5422no—
228C2×C8C22×D27112yescomplemented
229C4⋊C4—21no—
230C4⋊C4C22×D27112yescomplemented
231C22⋊C4—5424no—
232C23—24no—
233C23—22no—
234C23—42no—
235C23—42no—
236C23—2714no—
237C23—2712no—
238C23—54216no—
239C23—5422no—
240C23—5422no—
241C23—5424no—
242C23—5422no—
243C23—5422no—
244C23—10848no—
245C23—108432no—
246C23—10848no—
247C23—10842no—
248C23—10842no—
249C23—10842no—
250C23—10842no—
251C23—10842no—
252C23D4×D27111yescharacteristic
253D4—24no—
254D4—22no—
255D4—2714no—
256D4—54216no—
257D4—5424no—
258D4—5422no—
259D4—5422no—
260D4—5422no—
261D4—10848no—
262D4—10842no—
263D4C2×D108414yescomplemented
264C2×C4—22no—
265C2×C4—42no—
266C2×C4—2712no—
267C2×C4—5422no—
268C2×C4—5424no—
269C2×C4—5422no—
270C2×C4—5422no—
271C2×C4D4×D27111yescharacteristic
272C2×C4D4×D27112yes—
273C2×C4C2×D108412yes—
274C2×C4C23×D27111yescharacteristic
275C8—22no—
276C8—5422no—
277C22—24no—
278C22—48no—
279C22—42no—
280C22—42no—
281C22—2714no—
282C22—5428no—
283C22—5422no—
284C22—5422no—
285C22—5424no—
286C22—108432no—
287C22—10848no—
288C22—10842no—
289C22—10842no—
290C22—10842no—
291C22—10842no—
292C22—10842no—
293C22—21684no—
294C22#2257613012yes—
295C22D8×D27112yes—
296C22#2257618712yes—
297C22C2×D4×D27111yescharacteristic
298C4—42no—
299C4—5422no—
300C4#2257613012yes—
301C4C2×D4×D27111yescharacteristic
302C4C22×D108411yescharacteristic
303C2—44no—
304C2—5424no—
305C2—10844no—
306C2—21682no—
307C2#3177403214yesdirect product factor
308C2C2×#2257613011yescharacteristic
309C2C2×D8×D27111yescharacteristic
310C2C2×#2257618711yescharacteristic
subgroupG/H
centerC23D4×D271
commutator, cosocleC2×C4×C271C24
FrattiniC2×C4C23×D271
FittingC2×#102×C271C2
socleC23×C271C2×D4
hypercenterC2×#102D271
hypocenterC271C2×#447
LCSG ▷ C2×C4×C271 ▷ C2×C271 ▷ C271
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C22×D4×D271C2semidirect
2. C22×D2168C2semidirect
3. C22×#16864639C2semidirect
4. C2×#22576135C2semidirect
5. #31774032C2direct (N × H)
6. C2×#22576080C2semidirect
7. C2×(C2×D271)⋊C8C2semidirect
8. C2×#102×C271C2semidirect
12. C22×D1084C22semidirect
17. C2×D4×D271C22semidirect
20. C2×D2168C22semidirect
22. C2×#16864639C22semidirect
23. C22×C271⋊C8C22semidirect
25. #22576135C22semidirect
27. #22576080C22semidirect
28. (C2×D271)⋊C8C22semidirect
30. C22×C8×C271C22semidirect
31. C2×C4⋊C4×C271C22semidirect
32. #102×C271C22semidirect
47. C2×D1084D4semidirect
49. C2×D1084C23semidirect
63. C2×C271⋊C8C23semidirect
68. C2×D4×C271D4semidirect
73. C2×C8×C271C23semidirect
75. C4⋊C4×C271C23semidirect
90. C22×D271D8semidirect
98. D1084C2×D4semidirect
113. D4×C271C2×D4semidirect
141. C2×D271C2×D8semidirect
148. C2×C271#447semidirect
155. C271C2×#447semidirect
163. C2×#102D271semidirect
181. C22×C8C2×D271semidirect
184. C2×C4⋊C4C2×D271semidirect
187. #102C2×D271semidirect
214. C2×D4D1084semidirect
228. C2×C8C22×D271semidirect
230. C4⋊C4C22×D271semidirect
263. D4C2×D1084semidirect
307. C2#31774032direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×D2712
C22×D21682
C22×#168646392
C2×#225761352
#317740322
C2×#225760802
C2×(C2×D271)⋊C82
C2×#102×C2712
C2×#447271