Finite Group Databasebeta

← #21461116

Subgroups — #21461116

Order 7808.

264 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 84 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#16840778C211yesmaximal, characteristic, complemented
2C2×C4⋊#92420C211yesmaximal, characteristic, complemented
3#16840612C212yesmaximal, complemented
4#16840610C212yesmaximal, complemented
5#16840230C211yesmaximal, characteristic
6C22×#92420—21no—
7C4⋊#92420—21no—
8C4⋊#92420—21no—
9C4⋊#92420C2212yes—
10C22⋊#92420—21no—
11C4×#92420C2212yes—
12C2×#11758222C411yescharacteristic
13#14519742C411yescharacteristic
14#14519742C2211yescharacteristic
15#14519739C411yescharacteristic
16#14519739C2211yescharacteristic
17#14519737—21no—
18#14519737—21no—
19#14519734—21no—
20C2×C4×Dic61C2211yescharacteristic
21C42×D61—21no—
22#117×C61C411yescharacteristic
23C22×C4×C61C2×C411yescharacteristic
24C2×C22⋊D61—21no—
25C22×Dic61D411yescharacteristic
26C22×Dic61D411yescharacteristic
27#11758222—22no—
28#11758222C814yescomplemented
29C2×D244C2×C411yescharacteristic
30C2×C4×D61—21no—
31C2×C4×D61—21no—
32C2×C4×D61—21no—
33C2×Dic122C2×C411yescharacteristic
34C2×#92420—22no—
35C2×#92420—22no—
36C2×#92420—42no—
37C4⋊C4×C61C2×C411yescharacteristic
38C4⋊C4×C61C2×C411yescharacteristic
39C22⋊C4×C61—21no—
40C42×C61—21no—
41#11758198—21no—
42#11758198—21no—
43#11758196—21no—
44#11758196—21no—
45C4×Dic61—21no—
46C4×Dic61—21no—
47C4×Dic61C2×C411yescharacteristic
48C4×Dic61D411yescharacteristic
49C4×Dic61D411yescharacteristic
50C4×Dic61C2311yescharacteristic
51C23×C61C22⋊C411yescharacteristic
52C22×D61—21no—
53C2×C4×C61—21no—
54C2×C4×C61—21no—
55C2×C4×C61C22⋊C411yescharacteristic
56C2×C4×C61C2×C812yes—
57C2×C4×C61M1612yes—
58C2×C4×C61C22×C411yescharacteristic
59C22⋊D61—24no—
60C2×Dic61—21no—
61C2×Dic61—21no—
62C2×Dic61—21no—
63C2×Dic61—41no—
64C2×Dic61C22⋊C411yescharacteristic
65C2×Dic61C22⋊C411yescharacteristic
66C2×Dic61C2×D411yescharacteristic
67C2×Dic61C2×D411yescharacteristic
68D244—21no—
69D244C2×C812yescomplemented
70C4×D61—24no—
71C4×D61—42no—
72C4×D61—41no—
73C4×D61—41no—
74Dic122—21no—
75Dic122C2×C812yescomplemented
76#92420—42no—
77#92420—42no—
78C22×C61—21no—
79C22×C61—21no—
80C22×C61C22⋊C812yes—
81C22×C61C2×C22⋊C411yescharacteristic
82C2×D61—22no—
83C2×D61—41no—
84C2×D61—41no—
85C4×C61—41no—
86C4×C61—41no—
87C4×C61C22⋊C812yes—
88C4×C61C22×C811yescharacteristic
89C4×C61C2×M1611yescharacteristic
90Dic61—22no—
91Dic61—21no—
92Dic61—21no—
93Dic61—21no—
94Dic61AGL(1,ℤ/8)11yescharacteristic
95Dic61#13711yescharacteristic
96#1477—611nomaximal, Sylow
97C2×C61—22no—
98C2×C61C2×C22⋊C811yescharacteristic
99C2×C61#41711yescharacteristic
100C2×C61#42111yescharacteristic
101D61—42no—
102C4×#41—611no—
103#431—611no—
104C2×C4⋊C8—611no—
105Q8⋊C8—612no—
106D4⋊C8—612no—
107C61#147711yescharacteristic, complemented, Sylow
108C2×#41—611no—
109C22×C8—1221no—
110C4×Q8—611no—
111C4×Q8—611no—
112C4×D4—611no—
113C4×D4—611no—
114C4×D4—1221no—
115C4×D4—1221no—
116#117—1221no—
117#117#692311yescharacteristic
118C2×C42—611no—
119C2×C42—1221no—
120C4⋊C8—612no—
121C4⋊C8—1221no—
122C4⋊C8—1221no—
123C22⋊C8—1221no—
124C4×C8—612no—
125#41—614no—
126#41—1222no—
127C2×Q8—611no—
128C2×D4—611no—
129C2×D4—1221no—
130C22×C4—611no—
131C22×C4—611no—
132C22×C4—1221no—
133C22×C4—1221no—
134C22×C4—1221no—
135C22×C4C2×#692311yescharacteristic
136C2×C8—1222no—
137C2×C8—1222no—
138C2×C8—2442no—
139C4⋊C4—1221no—
140C4⋊C4—1221no—
141C4⋊C4C2×#692311yescharacteristic
142C4⋊C4C2×#692311yescharacteristic
143C22⋊C4—21no—
144C22⋊C4—1221no—
145C22⋊C4—1221no—
146C42—21no—
147C42—611no—
148C42—611no—
149C42—611no—
150C42—611no—
151C42—1221no—
152C42—1221no—
153C23—1221no—
154C23C22⋊#692311yescharacteristic
155Q8—612no—
156Q8—1221no—
157D4—612no—
158D4—1224no—
159D4—1221no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—611no—
163C2×C4—611no—
164C2×C4—611no—
165C2×C4—611no—
166C2×C4—1221no—
167C2×C4—1221no—
168C2×C4—1221no—
169C2×C4—1224no—
170C2×C4—2441no—
171C2×C4—2441no—
172C2×C4—2442no—
173C2×C4—2441no—
174C2×C4D61⋊C812yes—
175C2×C4#1175821312yes—
176C2×C4C22⋊#692311yescharacteristic
177C2×C4C22×#692311yescharacteristic
178C8—2442no—
179C8—2442no—
180C22—21no—
181C22—21no—
182C22—1222no—
183C22—2441no—
184C22—2441no—
185C22#1451983412yes—
186C22C2×C22⋊#692311yescharacteristic
187C4—41no—
188C4—41no—
189C4—611no—
190C4—611no—
191C4—1222no—
192C4—1221no—
193C4—1221no—
194C4—1221no—
195C4#1451983412yes—
196C4C2×D61⋊C811yescharacteristic
197C4C2×#1175821311yescharacteristic
198C2—22no—
199C2—2442no—
200C2C2×#1451983411yescharacteristic
201C2#1684075311yescharacteristic
202C2#1684075911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC4×C61C22×C8
FrattiniC2×C4C22×#6923
Fitting#117×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#117#6923
hypocenterC61#1477
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #16840778C2semidirect
2. C2×C4⋊#92420C2semidirect
3. #16840612C2semidirect
4. #16840610C2semidirect
28. #11758222C8semidirect
69. D244C2×C8semidirect
75. Dic122C2×C8semidirect
107. C61#1477semidirect