Finite Group Databasebeta

← #21461691

Subgroups — #21461691

Order 7808.

312 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 80 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
1#16840766C211yesmaximal, characteristic, complemented
2C2×#14519841C212yesmaximal
3C4×C4⋊#6923C211yesmaximal, characteristic, complemented
4#16840632C212yesmaximal, complemented
5C4×#11758224C211yesmaximal, characteristic
6C2×#11758213C2212yes—
7C2×C4⋊#6923—21no—
8C2×C4×#6923C2212yes—
9C4⋊#92420—21no—
10C4⋊#92420—21no—
11#14519841—24no—
12(C2×#6923)⋊C4—21no—
13C2×#11758224C2211yescharacteristic
14C4×Dic122C411yescharacteristic, complemented
15#14519742C411yescharacteristic, complemented
16D4×Dic61C411yescharacteristic, complemented
17C4×C22⋊D61—21no—
18#14519737—21no—
19#14519735C2211yescharacteristic
20#14519733—21no—
21C2×C4×Dic61—21no—
22C42×D61C2211yescharacteristic
23C4×D4×C61C411yescharacteristic, complemented
24C22×#6923—22no—
25C2×D4×C61C2×C411yescharacteristic
26C22×C4×C61—21no—
27C2×C22⋊D61—21no—
28C22×Dic61—21no—
29C22×Dic61—21no—
30#11758224—21no—
31#11758224—21no—
32#11758224D412yes—
33#11758224Q812yes—
34C2×C4×D61D411yescharacteristic
35C2×C4×D61D411yescharacteristic
36C2×C4×D61C2311yescharacteristic
37C2×Dic122C2×C411yescharacteristic
38C2×#92420—22no—
39C4⋊#6923—24no—
40C4×#6923—22no—
41C4×#6923—22no—
42#11758213—22no—
43#11758213—22no—
44C4⋊C4×C61C2×C411yescharacteristic
45C22⋊C4×C61—21no—
46C42×C61C2×C411yescharacteristic
47C22⋊Dic61—21no—
48#11758198—21no—
49C4⋊Dic61C2×C411yescharacteristic
50#11758196—21no—
51#11758196—21no—
52C4×Dic61—21no—
53C4×Dic61—21no—
54C4×Dic61—21no—
55C4×Dic61C2×C411yescharacteristic
56C4×Dic61D411yescharacteristic
57C4×Dic61D411yescharacteristic
58C23×C61—21no—
59C22×D61C2×D411yescharacteristic
60C2×#6923—24no—
61C2×#6923—42no—
62C2×#6923—42no—
63D4×C61—21no—
64D4×C61C4⋊C412yescomplemented
65C2×C4×C61—21no—
66C2×C4×C61—42no—
67C2×C4×C61C22⋊C411yescharacteristic
68C2×C4×C61C22⋊C411yescharacteristic
69C2×C4×C61C22×C411yescharacteristic
70C22⋊D61—22no—
71C22⋊D61—22no—
72C2×Dic61—21no—
73C2×Dic61—22no—
74C2×Dic61—22no—
75C2×Dic61—21no—
76C2×Dic61—42no—
77C2×Dic61C22⋊C411yescharacteristic
78C2×Dic61C22⋊C411yescharacteristic
79C2×Dic61C2×D411yescharacteristic
80C4×D61—22no—
81C4×D61—41no—
82C4×D61C2×D411yescharacteristic
83C4×D61C2×Q811yescharacteristic
84C4×D61#4111yescharacteristic
85C4×D61#4111yescharacteristic
86Dic122—21no—
87Dic122C4⋊C412yescomplemented
88#92420—42no—
89C22×C61—22no—
90C22×C61—41no—
91C22×C61—41no—
92C22×C61C2×C22⋊C411yescharacteristic
93C2×D61—21no—
94C2×D61—21no—
95C2×D61#12111yescharacteristic
96C2×D61C22⋊Q811yescharacteristic
97#6923—44no—
98C4×C61—21no—
99C4×C61—41no—
100C4×C61#10412yescomplemented
101C4×C61C2×C4⋊C411yescharacteristic
102C4×C61#11711yescharacteristic
103Dic61—22no—
104Dic61—21no—
105Dic61—21no—
106Dic61—41no—
107Dic61#12111yescharacteristic
108Dic61C22⋊Q811yescharacteristic
109#1806—611nomaximal, Sylow
110C2×C61—42no—
111C2×C61#38011yescharacteristic
112C2×C61C2×#10411yescharacteristic
113C2×C61#42111yescharacteristic
114D61—21no—
115D61—21no—
116C4×#41—611no—
117#423—611no—
118C2×#104—612no—
119C4×C4⋊C4—611no—
120#339—612no—
121C61#180611yescharacteristic, complemented, Sylow
122C2×#41—611no—
123C2×M16—612no—
124C4×Q8—611no—
125C4×Q8—611no—
126C4×D4—611no—
127C4×D4—1221no—
128C4×D4—1221no—
129C4×D4#692311yescharacteristic, complemented
130#117—611no—
131#117—1221no—
132C2×C4⋊C4—1221no—
133C2×C42—611no—
134C2×C42—612no—
135C2×C42—1221no—
136C4⋊C8—1221no—
137C4⋊C8—1221no—
138#104—1224no—
139#95—1221no—
140#41—612no—
141#41—612no—
142#41—1221no—
143#41—1221no—
144C2×Q8—611no—
145C2×D4—1221no—
146C2×D4C2×#692311yescharacteristic
147C22×C4—21no—
148C22×C4—611no—
149C22×C4—611no—
150C22×C4—611no—
151C22×C4—1221no—
152C22×C4—1221no—
153C22×C4—1222no—
154M16—1222no—
155M16—1222no—
156C2×C8—1222no—
157C4⋊C4—611no—
158C4⋊C4—1221no—
159C4⋊C4—1224no—
160C4⋊C4—1221no—
161C4⋊C4C2×#692311yescharacteristic
162C22⋊C4—21no—
163C22⋊C4—1221no—
164C22⋊C4—1221no—
165C42—611no—
166C42—611no—
167C42—611no—
168C42—1221no—
169C42—1221no—
170C42—1222no—
171C42—1222no—
172C42—1221no—
173C42C2×#692311yescharacteristic
174C23—21no—
175C23—611no—
176Q8—612no—
177Q8—1221no—
178D4—21no—
179D4—1222no—
180D4—1222no—
181D4C4⋊#692312yescomplemented
182C2×C4—21no—
183C2×C4—42no—
184C2×C4—611no—
185C2×C4—611no—
186C2×C4—611no—
187C2×C4—611no—
188C2×C4—611no—
189C2×C4—611no—
190C2×C4—611no—
191C2×C4—1222no—
192C2×C4—1222no—
193C2×C4—1221no—
194C2×C4—1222no—
195C2×C4—1224no—
196C2×C4—1221no—
197C2×C4—2441no—
198C2×C4—2442no—
199C2×C4—2442no—
200C2×C4—2442no—
201C2×C4C22⋊#692311yescharacteristic
202C2×C4C22⋊#692311yescharacteristic
203C2×C4C22×#692311yescharacteristic
204C8—2442no—
205C22—22no—
206C22—41no—
207C22—41no—
208C22—611no—
209C22—611no—
210C22—1221no—
211C22—1221no—
212C22C2×C22⋊#692311yescharacteristic
213C4—21no—
214C4—41no—
215C4—611no—
216C4—611no—
217C4—1222no—
218C4—1221no—
219C4—1221no—
220C4—2444no—
221C4—2441no—
222C4#1451984112yescomplemented
223C4C2×C4⋊#692311yescharacteristic
224C4#1451985611yescharacteristic
225C2—42no—
226C2—1221no—
227C2—1221no—
228C2#1684070411yescharacteristic
229C2C2×#1451984111yescharacteristic
230C2#1684075911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC4×D4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC4×D4#6923
hypocenterC61#1806
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. #16840766C2semidirect
3. C4×C4⋊#6923C2semidirect
4. #16840632C2semidirect
14. C4×Dic122C4semidirect
15. #14519742C4semidirect
16. D4×Dic61C4semidirect
23. C4×D4×C61C4semidirect
64. D4×C61C4⋊C4semidirect
87. Dic122C4⋊C4semidirect
100. C4×C61#104semidirect
121. C61#1806semidirect
129. C4×D4#6923semidirect
181. D4C4⋊#6923semidirect
222. C4#14519841semidirect