Finite Group Databasebeta

← #21461122

Subgroups — #21461122

Order 7808.

248 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 78 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#16840780C211yesmaximal, characteristic
3#16840612C212yesmaximal, complemented
4Q8⋊#92420C212yesmaximal, complemented
5C4×Q8×D61C211yesmaximal, characteristic
6#14519844—21no—
7C4⋊#92420C2212yes—
8#14519834—21no—
9#14519834—21no—
10C4×#92420—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×D61C814yescomplemented
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—
35C4⋊C4×C61—21no—
36C4⋊C4×C61C2×C411yescharacteristic
37C42×C61—21no—
38C42×C61C2×C411yescharacteristic
39C4⋊Dic61—21no—
40C4⋊Dic61C2×C411yescharacteristic
41#11758196—21no—
42#11758196—21no—
43#11758196—21no—
44C4×Dic61—21no—
45C4×Dic61—21no—
46C4×Dic61—21no—
47C4×Dic61D411yescharacteristic
48C4×Dic61D411yescharacteristic
49C4×Dic61C2311yescharacteristic
50C22×D61C22⋊C411yescharacteristic
51Q8×C61—21no—
52Q8×C61C2×C812yes—
53C2×C4×C61—21no—
54C2×C4×C61—21no—
55C2×C4×C61C22⋊C411yescharacteristic
56C2×C4×C61C22⋊C411yescharacteristic
57C2×C4×C61C22×C411yescharacteristic
58C2×Dic61—21no—
59C2×Dic61—21no—
60C2×Dic61C22⋊C411yescharacteristic
61C2×Dic61C2×D411yescharacteristic
62C2×Dic61C2×D411yescharacteristic
63C4×D61—24no—
64C4×D61—22no—
65C4×D61—41no—
66C4×D61—42no—
67C4×D61C2×C812yes—
68C4×D61M1612yes—
69Dic122—21no—
70Dic122—24no—
71Dic122C2×C812yes—
72#92420—42no—
73#92420—42no—
74C22×C61C2×C22⋊C411yescharacteristic
75C2×D61—21no—
76C2×D61—21no—
77C2×D61C22⋊C812yes—
78C4×C61—22no—
79C4×C61—21no—
80C4×C61—21no—
81C4×C61—41no—
82C4×C61C22×C811yescharacteristic
83C4×C61C2×M1611yescharacteristic
84Dic61—22no—
85Dic61—21no—
86Dic61—41no—
87Dic61C22⋊C812yes—
88Dic61#13712yes—
89#1479—611nomaximal, Sylow
90C2×C61C2×C22⋊C811yescharacteristic
91C2×C61#41911yescharacteristic
92C2×C61#42111yescharacteristic
93D61—22no—
94C2×C4×Q8—611no—
95#431—611no—
96#431—611no—
97Q8⋊C8—612no—
98Q8⋊C8—612no—
99C61#147911yescharacteristic, complemented, Sylow
100C22×Q8—611no—
101C4×Q8—611no—
102C4×Q8—611no—
103C4×Q8—611no—
104C4×Q8—1221no—
105C4×Q8—1221no—
106C4×Q8#692311yescharacteristic
107C2×C4⋊C4—611no—
108C2×C4⋊C4—1221no—
109C2×C42—611no—
110C2×C42—1221no—
111C4⋊C8—612no—
112C4⋊C8—1221no—
113C22⋊C8—1221no—
114C22⋊C8—1221no—
115C4×C8—612no—
116C4×C8—1221no—
117C2×Q8—614no—
118C2×Q8—611no—
119C2×Q8—1221no—
120C2×Q8—1222no—
121C2×Q8C2×#692311yescharacteristic
122C22×C4—611no—
123C22×C4—611no—
124C22×C4—611no—
125C22×C4—1221no—
126C22×C4—1221no—
127C2×C8—1222no—
128C2×C8—1222no—
129C4⋊C4—21no—
130C4⋊C4—611no—
131C4⋊C4—1221no—
132C4⋊C4—1221no—
133C4⋊C4—1221no—
134C4⋊C4—1221no—
135C4⋊C4C2×#692311yescharacteristic
136C42—21no—
137C42—611no—
138C42—611no—
139C42—611no—
140C42—1221no—
141C42—1221no—
142C42—1221no—
143C42C2×#692311yescharacteristic
144C23—611no—
145Q8—21no—
146Q8—612no—
147Q8—1224no—
148Q8—1221no—
149Q8D61⋊C812yes—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—611no—
153C2×C4—611no—
154C2×C4—612no—
155C2×C4—612no—
156C2×C4—611no—
157C2×C4—1222no—
158C2×C4—1224no—
159C2×C4—1221no—
160C2×C4—1221no—
161C2×C4—2441no—
162C2×C4—2442no—
163C2×C4C22⋊#692311yescharacteristic
164C2×C4C22⋊#692311yescharacteristic
165C2×C4C22×#692311yescharacteristic
166C8—2442no—
167C8—2442no—
168C22—612no—
169C22—1221no—
170C22—1221no—
171C22C2×C22⋊#692311yescharacteristic
172C4—22no—
173C4—21no—
174C4—21no—
175C4—41no—
176C4—612no—
177C4—612no—
178C4—1222no—
179C4—1221no—
180C4—2441no—
181C4C2×D61⋊C811yescharacteristic
182C4D61⋊M1611yescharacteristic
183C2—1222no—
184C2D61⋊(C22⋊C8)11yescharacteristic
185C2#1684075511yescharacteristic
186C2#1684075911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC4×C61C22×C8
FrattiniC2×C4C22×#6923
FittingC4×Q8×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC4×Q8#6923
hypocenterC61#1479
LCSG ▷ 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
25. Q8×D61C8semidirect
99. C61#1479semidirect