Finite Group Databasebeta

← #21461148

Subgroups — #21461148

Order 7808.

248 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 76 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#16840781C211yesmaximal, characteristic
2#16840766C211yesmaximal, characteristic
3#16840612C212yesmaximal, complemented
4Q8⋊#92420C212yesmaximal, complemented
5C4×Q8×D61C211yesmaximal, characteristic
6C2×#11758213—21no—
7C4⋊#92420—21no—
8C4⋊#92420—21no—
9C4⋊#92420C2212yes—
10#14519834—21no—
11C4×#92420C2212yes—
12C2×Q8×D61C411yescharacteristic
13Q8×Dic61C2211yescharacteristic
14C4×Dic122—21no—
15C4×Dic122C411yescharacteristic
16#14519742—21no—
17#14519742C2211yescharacteristic
18C4⋊C4×D61—21no—
19C4⋊C4×D61C411yescharacteristic
20C42×D61—21no—
21C42×D61C2211yescharacteristic
22C4×Q8×C61C411yescharacteristic
23C2×Q8×C61C2×C411yescharacteristic
24Q8×D61—22no—
25Q8×D61—22no—
26C2×C4×D61—21no—
27C2×C4×D61—21no—
28C2×C4×D61C2×C411yescharacteristic
29C2×C4×D61D411yescharacteristic
30C2×C4×D61D411yescharacteristic
31C2×Dic122—21no—
32C2×Dic122C2×C411yescharacteristic
33C2×#92420—22no—
34C2×#92420—22no—
35#11758213—42no—
36C4⋊C4×C61—21no—
37C4⋊C4×C61C2×C411yescharacteristic
38C42×C61—21no—
39C42×C61C2×C411yescharacteristic
40C4⋊Dic61—21no—
41C4⋊Dic61C2×C411yescharacteristic
42#11758196—21no—
43#11758196—21no—
44#11758196—21no—
45C4×Dic61—21no—
46C4×Dic61—21no—
47C4×Dic61—21no—
48C4×Dic61D411yescharacteristic
49C4×Dic61D411yescharacteristic
50C4×Dic61C2311yescharacteristic
51C22×D61C22⋊C411yescharacteristic
52Q8×C61—21no—
53Q8×C61M1612yescomplemented
54C2×C4×C61—21no—
55C2×C4×C61—21no—
56C2×C4×C61C22⋊C411yescharacteristic
57C2×C4×C61C22⋊C411yescharacteristic
58C2×C4×C61C22×C411yescharacteristic
59C2×Dic61—21no—
60C2×Dic61—21no—
61C2×Dic61C22⋊C411yescharacteristic
62C2×Dic61C2×D411yescharacteristic
63C2×Dic61C2×D411yescharacteristic
64C4×D61—24no—
65C4×D61—21no—
66C4×D61—21no—
67C4×D61—41no—
68C4×D61—42no—
69C4×D61SD1612yes—
70C4×D61Q1612yes—
71Dic122—24no—
72Dic122—21no—
73Dic122M1612yescomplemented
74#92420—42no—
75#92420—42no—
76C22×C61C2×C22⋊C411yescharacteristic
77C2×D61—21no—
78C2×D61—21no—
79C2×D61#10312yes—
80C4×C61—22no—
81C4×C61—21no—
82C4×C61—41no—
83C4×C61#10312yes—
84C4×C61C2×M1611yescharacteristic
85C4×C61C2×M1611yescharacteristic
86Dic61—21no—
87Dic61—22no—
88Dic61—21no—
89Dic61—41no—
90Dic61C2×SD1611yescharacteristic
91Dic61C2×Q1611yescharacteristic
92#1487—611nomaximal, Sylow
93C2×C61#40711yescharacteristic
94C2×C61C2×#10311yescharacteristic
95C2×C61#42111yescharacteristic
96D61—22no—
97C2×C4×Q8—611no—
98#431—611no—
99#423—611no—
100Q8⋊C8—612no—
101Q8⋊C8—612no—
102C61#148711yescharacteristic, complemented, Sylow
103C22×Q8—611no—
104C2×M16—1221no—
105C4×Q8—611no—
106C4×Q8—611no—
107C4×Q8—611no—
108C4×Q8—1221no—
109C4×Q8—1221no—
110C4×Q8#692311yescharacteristic
111C2×C4⋊C4—611no—
112C2×C4⋊C4—1221no—
113C2×C42—611no—
114C2×C42—1221no—
115C4⋊C8—612no—
116C4⋊C8—1221no—
117C4⋊C8—1221no—
118C22⋊C8—1221no—
119C4×C8—612no—
120C2×Q8—611no—
121C2×Q8—1221no—
122C2×Q8—1222no—
123C2×Q8—1222no—
124C2×Q8C2×#692311yescharacteristic
125C22×C4—611no—
126C22×C4—611no—
127C22×C4—611no—
128C22×C4—1221no—
129C22×C4—1221no—
130M16—2442no—
131C2×C8—1222no—
132C2×C8—1222no—
133C4⋊C4—21no—
134C4⋊C4—611no—
135C4⋊C4—1221no—
136C4⋊C4—1221no—
137C4⋊C4—1221no—
138C4⋊C4—1221no—
139C4⋊C4C2×#692311yescharacteristic
140C42—21no—
141C42—611no—
142C42—611no—
143C42—611no—
144C42—1221no—
145C42—1221no—
146C42—1221no—
147C42C2×#692311yescharacteristic
148C23—611no—
149Q8—21no—
150Q8—612no—
151Q8—1224no—
152Q8—1221no—
153Q8#1175821312yescomplemented
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—611no—
157C2×C4—612no—
158C2×C4—612no—
159C2×C4—611no—
160C2×C4—611no—
161C2×C4—1224no—
162C2×C4—1221no—
163C2×C4—1221no—
164C2×C4—1221no—
165C2×C4—1221no—
166C2×C4—2441no—
167C2×C4—2442no—
168C2×C4C22⋊#692311yescharacteristic
169C2×C4C22⋊#692311yescharacteristic
170C2×C4C22×#692311yescharacteristic
171C8—2442no—
172C8—2442no—
173C22—612no—
174C22—1221no—
175C22—1221no—
176C22C2×C22⋊#692311yescharacteristic
177C4—22no—
178C4—21no—
179C4—41no—
180C4—611no—
181C4—611no—
182C4—1221no—
183C4—1222no—
184C4—1221no—
185C4—2441no—
186C4#1451984012yes—
187C4D61⋊M1611yescharacteristic
188C4C2×#1175821311yescharacteristic
189C2—1222no—
190C2#1684073311yescharacteristic
191C2C2×#1451984011yescharacteristic
192C2#1684075911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC4×Q8×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC4×Q8#6923
hypocenterC61#1487
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
3. #16840612C2semidirect
4. Q8⋊#92420C2semidirect
53. Q8×C61M16semidirect
73. Dic122M16semidirect
102. C61#1487semidirect
153. Q8#11758213semidirect