Finite Group Databasebeta

← #21461867

Subgroups — #21461867

Order 7808.

314 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 66 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#16840830C211yesmaximal, characteristic, complemented
2#16840760C212yesmaximal
3D61⋊#101C211yesmaximal, characteristic, complemented
4#16840629C212yesmaximal, complemented
5#16840332C211yesmaximal, characteristic
6D61⋊M16C2212yes—
7Q8×#6923—24no—
8#14519856—22no—
9#14519856C2212yes—
10#14519841—24no—
11#14519838—22no—
12C2×#11758224C2211yescharacteristic
13C2×Q8×D61C2211yescharacteristic
14#14519777C411yescharacteristic, complemented
15#14519775C411yescharacteristic, complemented
16#14519764C411yescharacteristic, complemented
17#14519759—22no—
18#14519754—22no—
19#14519734C2211yescharacteristic
20#124×C61C411yescharacteristic, complemented
21C2×Q8×C61C2×C411yescharacteristic
22C2×D4×C61C2×C411yescharacteristic
23C2×C22⋊D61—21no—
24C22×Dic61—21no—
25Q8×D61—22no—
26Q8×D61—22no—
27#11758224—22no—
28#11758224—22no—
29C2×C4×D61D412yes—
30C2×C4×D61C2311yescharacteristic
31C2×Dic122C2×C411yescharacteristic
32C2×Dic122C2×C411yescharacteristic
33C2×Dic122D412yes—
34C22⋊#6923—22no—
35#11758217—22no—
36C4⋊#6923—24no—
37C4⋊#6923—22no—
38C4×#6923—24no—
39C4×#6923D414yes—
40#11758213—22no—
41D61⋊C8—22no—
42C22⋊C4×C61—22no—
43C42×C61C2×C411yescharacteristic
44C22⋊Dic61—22no—
45#11758198—21no—
46C4⋊Dic61—22no—
47#11758196—22no—
48#11758196—21no—
49C4×Dic61C2×C411yescharacteristic
50C23×C61—21no—
51C22×D61C2×D411yescharacteristic
52C2×#6923—24no—
53Q8×C61—22no—
54D4×C61—22no—
55C2×C4×C61—21no—
56C2×C4×C61C22⋊C412yes—
57C2×C4×C61C22×C411yescharacteristic
58C22⋊D61—41no—
59C22⋊D61—41no—
60C2×Dic61—21no—
61C2×Dic61—21no—
62C2×Dic61—42no—
63C2×Dic61C22⋊C412yes—
64C2×Dic61C2×D411yescharacteristic
65C4×D61—22no—
66C4×D61—22no—
67C4×D61C2×D412yes—
68C4×D61#4112yes—
69Dic122—22no—
70Dic122—24no—
71Dic122—22no—
72#92420—42no—
73C22×C61—42no—
74C22×C61—41no—
75C22×C61C2×C22⋊C411yescharacteristic
76C2×D61—41no—
77C2×D61#12011yescharacteristic
78C2×D61#12311yescharacteristic
79#6923—44no—
80C4×C61—22no—
81C4×C61—41no—
82C4×C61C4×D412yes—
83Dic61—22no—
84Dic61—41no—
85Dic61—41no—
86Dic61#12112yes—
87#1912—611nomaximal, Sylow
88C2×C61—21no—
89C2×C61—81no—
90C2×C61#38611yescharacteristic
91D61—21no—
92D61—21no—
93#536—611no—
94#519—611no—
95#421—612no—
96C2×#101—611no—
97H(3,ℤ/4)—612no—
98C61#191211yescharacteristic, complemented, Sylow
99C2×#41—611no—
100C22×Q8—611no—
101C2×M16—612no—
102C4⋊Q8—611no—
103C4⋊Q8—611no—
104#124—611no—
105#124#692311yescharacteristic, complemented
106#123—1222no—
107C22⋊Q8—1222no—
108C4×Q8—1224no—
109#117—612no—
110#117—611no—
111#117—1222no—
112#104—1224no—
113#101—1222no—
114#41—1222no—
115#41—1222no—
116C2×Q8—612no—
117C2×Q8—611no—
118C2×Q8—611no—
119C2×Q8—1222no—
120C2×Q8—1222no—
121C2×Q8C2×#692311yescharacteristic
122C2×D4—1221no—
123C2×D4C2×#692311yescharacteristic
124C22×C4—611no—
125C22×C4—612no—
126C22×C4—1221no—
127M16—1222no—
128M16—1222no—
129C2×C8—1222no—
130C4⋊C4—1221no—
131C4⋊C4—1222no—
132C4⋊C4—1222no—
133C4⋊C4—1224no—
134C4⋊C4—1222no—
135C22⋊C4—22no—
136C22⋊C4—1221no—
137C22⋊C4—1222no—
138C22⋊C4—1222no—
139C42—614no—
140C42—611no—
141C42—1224no—
142C42C2×#692311yescharacteristic
143C23—21no—
144C23—611no—
145Q8—22no—
146Q8—1224no—
147Q8—1222no—
148Q8—1222no—
149D4—22no—
150D4—2441no—
151D4—2441no—
152C2×C4—21no—
153C2×C4—611no—
154C2×C4—612no—
155C2×C4—612no—
156C2×C4—612no—
157C2×C4—1222no—
158C2×C4—1222no—
159C2×C4—1224no—
160C2×C4—1221no—
161C2×C4—1221no—
162C2×C4—2442no—
163C2×C4C22⋊#692312yes—
164C2×C4C22×#692311yescharacteristic
165C8—2442no—
166C22—42no—
167C22—41no—
168C22—611no—
169C22—611no—
170C22—2441no—
171C22C2×C22⋊#692311yescharacteristic
172C4—22no—
173C4—41no—
174C4—612no—
175C4—1222no—
176C4—2441no—
177C4—2444no—
178C4—2441no—
179C4D4×#692312yes—
180C2—21no—
181C2—81no—
182C2—1221no—
183C2—1221no—
184C2#1684071011yescharacteristic
subgroupG/H
centerC2#16840710
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#124×C61C4
socleC2×C61#386
hypercenter#124#6923
hypocenterC61#1912
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #16840830C2semidirect
3. D61⋊#101C2semidirect
4. #16840629C2semidirect
14. #14519777C4semidirect
15. #14519775C4semidirect
16. #14519764C4semidirect
20. #124×C61C4semidirect
98. C61#1912semidirect
105. #124#6923semidirect