Finite Group Databasebeta

← #21461171

Subgroups — #21461171

Order 7808.

230 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 62 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#16840784C211yesmaximal, characteristic, complemented
2C4×D61⋊C8C211yesmaximal, characteristic, complemented
3Q8⋊#92420C212yesmaximal, complemented
4D4⋊#92420C212yesmaximal, complemented
5#16840291C211yesmaximal, characteristic
6C2×D61⋊C8—21no—
7C4⋊#92420C2212yes—
8#14519834—21no—
9#14519832—21no—
10C4×#92420—21no—
11C4×#92420C2212yes—
12#14519770—21no—
13#14519769C411yescharacteristic
14#14519759—21no—
15#14519753C411yescharacteristic
16#14519748C411yescharacteristic
17Q8×Dic61C2211yescharacteristic
18D4×Dic61C2211yescharacteristic
19#14519737—21no—
20#14519733—21no—
21C42×D61C2211yescharacteristic
22#124×C61C411yescharacteristic
23C2×Q8×C61C2×C411yescharacteristic
24C2×D4×C61C2×C411yescharacteristic
25C2×C22⋊D61—21no—
26C22×Dic61—21no—
27C2×C4×D61C2×C411yescharacteristic
28C2×C4×D61D411yescharacteristic
29C2×C4×D61D411yescharacteristic
30C2×#92420—22no—
31C2×#92420—22no—
32D61⋊C8—24no—
33C22⋊C4×C61—21no—
34C22⋊C4×C61—21no—
35C42×C61C2×C411yescharacteristic
36C22⋊Dic61—21no—
37C22⋊Dic61—21no—
38#11758198—21no—
39C4⋊Dic61—21no—
40C4⋊Dic61C2×C411yescharacteristic
41C4⋊Dic61C2×C411yescharacteristic
42#11758196—21no—
43#11758196—21no—
44#11758196—21no—
45C4×Dic61—21no—
46C4×Dic61D411yescharacteristic
47C4×Dic61D411yescharacteristic
48C4×Dic61C2311yescharacteristic
49C23×C61—21no—
50C22×D61C22⋊C411yescharacteristic
51Q8×C61—22no—
52D4×C61—22no—
53C2×C4×C61—21no—
54C2×C4×C61C22⋊C411yescharacteristic
55C2×C4×C61C22⋊C411yescharacteristic
56C2×C4×C61C22×C411yescharacteristic
57C22⋊D61—42no—
58C2×Dic61—21no—
59C2×Dic61—21no—
60C2×Dic61—42no—
61C2×Dic61C22⋊C411yescharacteristic
62C2×Dic61C2×D411yescharacteristic
63C2×Dic61C2×D411yescharacteristic
64C4×D61—22no—
65C4×D61—22no—
66C4×D61—22no—
67#92420—24no—
68#92420—42no—
69C22×C61—41no—
70C22×C61—41no—
71C22×C61—41no—
72C22×C61C2×C22⋊C411yescharacteristic
73C2×D61—21no—
74C2×D61—21no—
75C2×D61#10412yes—
76C4×C61—21no—
77C4×C61—21no—
78C4×C61—41no—
79C4×C61#13112yes—
80Dic61—21no—
81Dic61—21no—
82Dic61—41no—
83Dic61—41no—
84Dic61#13512yes—
85#1494—611nomaximal, Sylow
86C2×C61—81no—
87C2×C61#40811yescharacteristic
88C2×C61#41611yescharacteristic
89C2×C61C2×#10411yescharacteristic
90D61—22no—
91#529—611no—
92#432—611no—
93C2×C4×C8—611no—
94Q8⋊C8—612no—
95D4⋊C8—612no—
96C61#149411yescharacteristic, complemented, Sylow
97C22×C8—1221no—
98#126—1221no—
99#125—611no—
100#124#692311yescharacteristic
101#123—1221no—
102C22⋊Q8—611no—
103#121—611no—
104C4×Q8—611no—
105C4×D4—611no—
106C4×D4—1221no—
107#117—1221no—
108C2×C42—611no—
109C4⋊C8—612no—
110C22⋊C8—1221no—
111#97—1221no—
112C4×C8—612no—
113C4×C8—1221no—
114C2×Q8C2×#692311yescharacteristic
115C2×D4—1221no—
116C2×D4C2×#692311yescharacteristic
117C22×C4—611no—
118C22×C4—611no—
119C22×C4—611no—
120C22×C4—1221no—
121C2×C8—1222no—
122C2×C8—1224no—
123C2×C8—1222no—
124C4⋊C4—611no—
125C4⋊C4—611no—
126C4⋊C4—1221no—
127C4⋊C4—1221no—
128C4⋊C4—1221no—
129C4⋊C4—1221no—
130C22⋊C4—21no—
131C22⋊C4—21no—
132C22⋊C4—1221no—
133C22⋊C4—1221no—
134C22⋊C4—1221no—
135C42—611no—
136C42—611no—
137C42—611no—
138C42—1221no—
139C42C2×#692311yescharacteristic
140C23—21no—
141C23—611no—
142Q8—22no—
143D4—22no—
144D4—2442no—
145C2×C4—21no—
146C2×C4—611no—
147C2×C4—611no—
148C2×C4—611no—
149C2×C4—1222no—
150C2×C4—1222no—
151C2×C4—1222no—
152C2×C4—1221no—
153C2×C4—1221no—
154C2×C4—2442no—
155C2×C4C22⋊#692311yescharacteristic
156C2×C4C22⋊#692311yescharacteristic
157C2×C4C22×#692311yescharacteristic
158C8—1224no—
159C8—2442no—
160C22—41no—
161C22—41no—
162C22—41no—
163C22—612no—
164C22—1221no—
165C22—1221no—
166C22C2×C22⋊#692311yescharacteristic
167C4—21no—
168C4—21no—
169C4—41no—
170C4—612no—
171C4—1221no—
172C4—1221no—
173C4—2441no—
174C4—2441no—
175C4#1451986412yes—
176C2—81no—
177C2—1222no—
178C2#1684073611yescharacteristic
179C2#1684075211yescharacteristic
180C2D61⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#124×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#124#6923
hypocenterC61#1494
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #16840784C2semidirect
2. C4×D61⋊C8C2semidirect
3. Q8⋊#92420C2semidirect
4. D4⋊#92420C2semidirect
96. C61#1494semidirect