Finite Group Databasebeta

← #21461687

Subgroups — #21461687

Order 7808.

372 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 94 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
1D61⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
2C2×#14519839C212yesmaximal
3#16840708C211yesmaximal, characteristic, complemented
4#16840635C212yesmaximal, complemented
5C4×D4×D61C211yesmaximal, characteristic
6C2×D61⋊C8C2212yes—
7C2×C4⋊#6923—21no—
8C2×C4⋊#6923—21no—
9C2×C4⋊#6923C2212yes—
10#14519844—21no—
11C4⋊#92420—21no—
12#14519839—24no—
13C2×D4×D61C2211yescharacteristic
14C22×C4×D61—21no—
15C4×D244C411yescharacteristic, complemented
16D4×Dic61C411yescharacteristic, complemented
17#14519739C411yescharacteristic, complemented
18C4×C22⋊D61—21no—
19#14519737—21no—
20C4⋊C4×D61C2211yescharacteristic
21C22⋊C4×D61—21no—
22C42×D61C2211yescharacteristic
23C4×D4×C61C411yescharacteristic, complemented
24C23×D61—21no—
25C22×#6923—22no—
26C2×D4×C61C2×C411yescharacteristic
27C22×C4×C61—21no—
28C2×C22⋊D61—21no—
29C22×Dic61—21no—
30D4×D61—21no—
31D4×D61—21no—
32D4×D61D412yes—
33D4×D61Q812yes—
34C2×D244C2×C411yescharacteristic
35C2×C4×D61—21no—
36C2×C4×D61—21no—
37C2×C4×D61—21no—
38C2×C4×D61—42no—
39C2×C4×D61—42no—
40C2×C4×D61D411yescharacteristic
41C2×C4×D61D411yescharacteristic
42C2×C4×D61C2311yescharacteristic
43C2×#92420—22no—
44C4⋊#6923—22no—
45C4⋊#6923—22no—
46C4⋊#6923—42no—
47C4⋊#6923—42no—
48D61⋊C8—22no—
49D61⋊C8—22no—
50C4⋊C4×C61C2×C411yescharacteristic
51C22⋊C4×C61—21no—
52C42×C61C2×C411yescharacteristic
53C22⋊Dic61—21no—
54#11758198—21no—
55#11758198—21no—
56C4⋊Dic61C2×C411yescharacteristic
57#11758196—21no—
58C4×Dic61C2×C411yescharacteristic
59C4×Dic61D411yescharacteristic
60C4×Dic61D411yescharacteristic
61C23×C61—21no—
62C22×D61—21no—
63C22×D61—22no—
64C22×D61—22no—
65C22×D61—41no—
66C22×D61—41no—
67C22×D61—41no—
68C22×D61—41no—
69C22×D61C2×D411yescharacteristic
70C2×#6923—42no—
71C2×#6923—42no—
72C2×#6923—42no—
73D4×C61—21no—
74D4×C61C4⋊C412yescomplemented
75C2×C4×C61—21no—
76C2×C4×C61—42no—
77C2×C4×C61C22⋊C411yescharacteristic
78C2×C4×C61C22⋊C411yescharacteristic
79C2×C4×C61C22×C411yescharacteristic
80C22⋊D61—22no—
81C22⋊D61—22no—
82C2×Dic61—21no—
83C2×Dic61—42no—
84C2×Dic61C22⋊C411yescharacteristic
85C2×Dic61C22⋊C411yescharacteristic
86C2×Dic61C2×D411yescharacteristic
87D244—21no—
88D244C4⋊C412yescomplemented
89C4×D61—21no—
90C4×D61—21no—
91C4×D61—41no—
92C4×D61—41no—
93C4×D61—42no—
94C4×D61—42no—
95C4×D61D812yes—
96C4×D61SD1612yes—
97C4×D61C2×D411yescharacteristic
98C4×D61C2×Q811yescharacteristic
99C4×D61#4111yescharacteristic
100C4×D61#4111yescharacteristic
101#92420—42no—
102C22×C61—22no—
103C22×C61—41no—
104C22×C61—41no—
105C22×C61C2×C22⋊C411yescharacteristic
106C2×D61—22no—
107C2×D61—41no—
108C2×D61—41no—
109C2×D61—42no—
110C2×D61—42no—
111C2×D61—42no—
112C2×D61—42no—
113C2×D61#12111yescharacteristic
114C2×D61C22⋊Q811yescharacteristic
115C2×D61C2×D811yescharacteristic
116C2×D61C2×SD1611yescharacteristic
117C2×D61AGL(1,ℤ/8)11yescharacteristic
118C2×D61#13711yescharacteristic
119#6923—82no—
120C4×C61—21no—
121C4×C61—41no—
122C4×C61#10212yescomplemented
123C4×C61C2×C4⋊C411yescharacteristic
124C4×C61#11711yescharacteristic
125Dic61—21no—
126Dic61—41no—
127Dic61#10212yescomplemented
128Dic61#12111yescharacteristic
129Dic61C22⋊Q811yescharacteristic
130#1802—611nomaximal, Sylow
131C2×C61—42no—
132C2×C61#38011yescharacteristic
133C2×C61C2×#10211yescharacteristic
134C2×C61#41711yescharacteristic
135D61—42no—
136D61#45911yescharacteristic
137D61#46111yescharacteristic
138D61#47411yescharacteristic
139D61#47611yescharacteristic
140C2×C4×D4—611no—
141C2×C4⋊C8—611no—
142C2×#102—612no—
143#384—611no—
144#340—612no—
145C61#180211yescharacteristic, complemented, Sylow
146C22×D4—611no—
147C23×C4—1221no—
148C22×C8—612no—
149C4×D4—611no—
150C4×D4—611no—
151C4×D4—611no—
152C4×D4—1221no—
153C4×D4—1221no—
154C4×D4#692311yescharacteristic, complemented
155C2×C4⋊C4—611no—
156C2×C4⋊C4—612no—
157C2×C4⋊C4—1221no—
158C2×C4⋊C4—1221no—
159C2×C22⋊C4—1221no—
160C2×C42—611no—
161C4⋊C8—1221no—
162C4⋊C8—1221no—
163#102—1224no—
164C24—1221no—
165C2×D4—612no—
166C2×D4—612no—
167C2×D4—611no—
168C2×D4—1221no—
169C2×D4—1221no—
170C2×D4—1221no—
171C2×D4C2×#692311yescharacteristic
172C22×C4—21no—
173C22×C4—611no—
174C22×C4—611no—
175C22×C4—611no—
176C22×C4—1221no—
177C22×C4—1221no—
178C22×C4—1221no—
179C22×C4—1221no—
180C22×C4—1222no—
181C22×C4—2442no—
182C22×C4—2442no—
183C2×C8—1222no—
184C2×C8—1222no—
185C2×C8—1222no—
186C4⋊C4—611no—
187C4⋊C4—1221no—
188C4⋊C4—1222no—
189C4⋊C4—1222no—
190C4⋊C4—2442no—
191C4⋊C4—2442no—
192C4⋊C4C2×#692311yescharacteristic
193C22⋊C4—21no—
194C22⋊C4—1221no—
195C22⋊C4—1221no—
196C22⋊C4—1221no—
197C42—611no—
198C42—611no—
199C42—611no—
200C42C2×#692311yescharacteristic
201C23—21no—
202C23—611no—
203C23—1222no—
204C23—1222no—
205C23—1221no—
206C23—2441no—
207C23—2441no—
208C23—2441no—
209C23—2441no—
210D4—21no—
211D4—612no—
212D4—1222no—
213D4—1222no—
214D4—1221no—
215D4C4⋊#692312yescomplemented
216C2×C4—21no—
217C2×C4—42no—
218C2×C4—611no—
219C2×C4—611no—
220C2×C4—612no—
221C2×C4—612no—
222C2×C4—611no—
223C2×C4—611no—
224C2×C4—611no—
225C2×C4—611no—
226C2×C4—611no—
227C2×C4—1221no—
228C2×C4—1221no—
229C2×C4—1221no—
230C2×C4—2442no—
231C2×C4—2441no—
232C2×C4—2441no—
233C2×C4—2442no—
234C2×C4—2442no—
235C2×C4—2442no—
236C2×C4—2442no—
237C2×C4—2442no—
238C2×C4C22⋊#692311yescharacteristic
239C2×C4C22⋊#692311yescharacteristic
240C2×C4C22×#692311yescharacteristic
241C8—2442no—
242C22—22no—
243C22—41no—
244C22—41no—
245C22—611no—
246C22—611no—
247C22—611no—
248C22—611no—
249C22—611no—
250C22—611no—
251C22—1222no—
252C22—2442no—
253C22—2442no—
254C22—2442no—
255C22—2442no—
256C22—2441no—
257C22—2441no—
258C22C2×C22⋊#692311yescharacteristic
259C4—21no—
260C4—41no—
261C4—611no—
262C4—611no—
263C4—612no—
264C4—1221no—
265C4—4882no—
266C4—2441no—
267C4#1451983912yescomplemented
268C4C2×C4⋊#692311yescharacteristic
269C4#1451985611yescharacteristic
270C2—42no—
271C2—611no—
272C2—611no—
273C2—611no—
274C2—611no—
275C2—2442no—
276C2#1684070411yescharacteristic
277C2C2×#1451983911yescharacteristic
278C2#1684075311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC4×D4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC4×D4#6923
hypocenterC61#1802
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. D61⋊(C4⋊C8)C2semidirect
3. #16840708C2semidirect
4. #16840635C2semidirect
15. C4×D244C4semidirect
16. D4×Dic61C4semidirect
17. #14519739C4semidirect
23. C4×D4×C61C4semidirect
74. D4×C61C4⋊C4semidirect
88. D244C4⋊C4semidirect
122. C4×C61#102semidirect
127. Dic61#102semidirect
145. C61#1802semidirect
154. C4×D4#6923semidirect
215. D4C4⋊#6923semidirect
267. C4#14519839semidirect