Finite Group Databasebeta

← #21461692

Subgroups — #21461692

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×#14519842C212yesmaximal
3C4×C4⋊#6923C211yesmaximal, characteristic, complemented
4#16840632C212yesmaximal, complemented
5C4×#11758226C211yesmaximal, characteristic
6C2×#11758213C2212yes—
7C2×C4⋊#6923—21no—
8C2×C4×#6923C2212yes—
9C4⋊#92420—21no—
10C4⋊#92420—21no—
11#14519842—24no—
12(C2×#6923)⋊C4—21no—
13C2×#11758226C2211yescharacteristic
14Q8×Dic61C411yescharacteristic, complemented
15C4×D244—21no—
16C4×D244C411yescharacteristic, complemented
17#14519739—21no—
18#14519739C411yescharacteristic, complemented
19#14519735—21no—
20#14519735C2211yescharacteristic
21C42×D61—21no—
22C42×D61C2211yescharacteristic
23C4×Q8×C61C411yescharacteristic, complemented
24C22×#6923—22no—
25C2×Q8×C61C2×C411yescharacteristic
26#11758226—21no—
27#11758226—21no—
28#11758226D412yes—
29#11758226Q812yes—
30C2×D244—21no—
31C2×D244C2×C411yescharacteristic
32C2×C4×D61—21no—
33C2×C4×D61—21no—
34C2×C4×D61—21no—
35C2×C4×D61D411yescharacteristic
36C2×C4×D61D411yescharacteristic
37C2×C4×D61C2311yescharacteristic
38C2×#92420—22no—
39C4⋊#6923—24no—
40C4×#6923—22no—
41C4×#6923—22no—
42#11758213—22no—
43#11758213—22no—
44C4⋊C4×C61—21no—
45C4⋊C4×C61C2×C411yescharacteristic
46C42×C61—21no—
47C42×C61C2×C411yescharacteristic
48#11758198—21no—
49#11758198—21no—
50#11758198—21no—
51C4⋊Dic61—21no—
52C4⋊Dic61C2×C411yescharacteristic
53C4×Dic61—21no—
54C4×Dic61—21no—
55C4×Dic61C2×C411yescharacteristic
56C4×Dic61D411yescharacteristic
57C4×Dic61D411yescharacteristic
58C22×D61—21no—
59C22×D61C2×D411yescharacteristic
60C2×#6923—24no—
61C2×#6923—42no—
62C2×#6923—42no—
63Q8×C61—21no—
64Q8×C61C4⋊C412yescomplemented
65C2×C4×C61—21no—
66C2×C4×C61—21no—
67C2×C4×C61C22⋊C411yescharacteristic
68C2×C4×C61C22⋊C411yescharacteristic
69C2×C4×C61C22×C411yescharacteristic
70C2×Dic61—21no—
71C2×Dic61C22⋊C411yescharacteristic
72C2×Dic61C22⋊C411yescharacteristic
73C2×Dic61C2×D411yescharacteristic
74D244—22no—
75D244—22no—
76D244—21no—
77D244C4⋊C412yescomplemented
78C4×D61—22no—
79C4×D61—22no—
80C4×D61—22no—
81C4×D61—41no—
82C4×D61—42no—
83C4×D61—42no—
84C4×D61C2×D411yescharacteristic
85C4×D61C2×Q811yescharacteristic
86C4×D61#4111yescharacteristic
87C4×D61#4111yescharacteristic
88#92420—42no—
89C22×C61C2×C22⋊C411yescharacteristic
90C2×D61—21no—
91C2×D61—21no—
92C2×D61—22no—
93C2×D61—41no—
94C2×D61—41no—
95C2×D61#12111yescharacteristic
96C2×D61C22⋊Q811yescharacteristic
97#6923—44no—
98C4×C61—22no—
99C4×C61—21no—
100C4×C61—41no—
101C4×C61#10412yescomplemented
102C4×C61C2×C4⋊C411yescharacteristic
103C4×C61#11711yescharacteristic
104Dic61—21no—
105Dic61—21no—
106Dic61—41no—
107Dic61#12111yescharacteristic
108Dic61C22⋊Q811yescharacteristic
109#1806—611nomaximal, Sylow
110C2×C61#38011yescharacteristic
111C2×C61C2×#10411yescharacteristic
112C2×C61#42111yescharacteristic
113D61—21no—
114D61—21no—
115D61—42no—
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#692311yescharacteristic, complemented
126C4×D4—611no—
127C4×D4—611no—
128C4×D4—1221no—
129C4×D4—1221no—
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×Q8C2×#692311yescharacteristic
145C2×D4—611no—
146C2×D4—1221no—
147C22×C4—611no—
148C22×C4—611no—
149C22×C4—611no—
150C22×C4—1221no—
151C22×C4—1221no—
152C22×C4—1222no—
153C22×C4—1221no—
154M16—1222no—
155M16—1222no—
156C2×C8—1222no—
157C4⋊C4—21no—
158C4⋊C4—611no—
159C4⋊C4—1221no—
160C4⋊C4—1224no—
161C4⋊C4C2×#692311yescharacteristic
162C22⋊C4—1221no—
163C22⋊C4—1221no—
164C22⋊C4—1221no—
165C42—21no—
166C42—611no—
167C42—611no—
168C42—611no—
169C42—1221no—
170C42—1221no—
171C42—1222no—
172C42—1222no—
173C42C2×#692311yescharacteristic
174C23—611no—
175C23—1221no—
176Q8—21no—
177Q8C4⋊#692312yescomplemented
178D4—612no—
179D4—1222no—
180D4—1222no—
181D4—1221no—
182C2×C4—21no—
183C2×C4—21no—
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—1222no—
194C2×C4—1224no—
195C2×C4—1221no—
196C2×C4—2441no—
197C2×C4—2442no—
198C2×C4—2442no—
199C2×C4—2442no—
200C2×C4—2442no—
201C2×C4C22⋊#692311yescharacteristic
202C2×C4C22⋊#692311yescharacteristic
203C2×C4C22×#692311yescharacteristic
204C8—2442no—
205C22—611no—
206C22—611no—
207C22—1221no—
208C22—1221no—
209C22—1222no—
210C22—2441no—
211C22—2441no—
212C22C2×C22⋊#692311yescharacteristic
213C4—22no—
214C4—21no—
215C4—41no—
216C4—611no—
217C4—611no—
218C4—1221no—
219C4—1221no—
220C4—2444no—
221C4—2441no—
222C4#1451984212yescomplemented
223C4C2×C4⋊#692311yescharacteristic
224C4#1451985611yescharacteristic
225C2—1221no—
226C2—1221no—
227C2—2442no—
228C2#1684070411yescharacteristic
229C2C2×#1451984211yescharacteristic
230C2#1684075911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC4×Q8×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC4×Q8#6923
hypocenterC61#1806
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #16840766C2semidirect
3. C4×C4⋊#6923C2semidirect
4. #16840632C2semidirect
14. Q8×Dic61C4semidirect
16. C4×D244C4semidirect
18. #14519739C4semidirect
23. C4×Q8×C61C4semidirect
64. Q8×C61C4⋊C4semidirect
77. D244C4⋊C4semidirect
101. C4×C61#104semidirect
121. C61#1806semidirect
125. C4×Q8#6923semidirect
177. Q8C4⋊#6923semidirect
222. C4#14519842semidirect