Finite Group Databasebeta

← #21461173

Subgroups — #21461173

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
3#16840612C212yesmaximal, complemented
4#16840610C212yesmaximal, complemented
5#16840297C211yesmaximal, characteristic
6C2×D61⋊C8—21no—
7C4⋊#92420C2212yes—
8#14519834—21no—
9#14519832—21no—
10C4×#92420—21no—
11C4×#92420C2212yes—
12#14519772—21no—
13#14519765C411yescharacteristic
14#14519762—21no—
15#14519757C411yescharacteristic
16#14519752C411yescharacteristic
17#14519742C2211yescharacteristic
18#14519739—21no—
19#14519739C2211yescharacteristic
20#14519735—21no—
21C42×D61C2211yescharacteristic
22#125×C61C411yescharacteristic
23C2×D244—21no—
24C2×D244C2×C411yescharacteristic
25C2×C4×D61—21no—
26C2×C4×D61C2×C411yescharacteristic
27C2×C4×D61D411yescharacteristic
28C2×C4×D61D411yescharacteristic
29C2×Dic122C2×C411yescharacteristic
30C2×#92420—22no—
31C2×#92420—22no—
32D61⋊C8—24no—
33C4⋊C4×C61—21no—
34C4⋊C4×C61—21no—
35C4⋊C4×C61C2×C411yescharacteristic
36C4⋊C4×C61C2×C411yescharacteristic
37C42×C61C2×C411yescharacteristic
38#11758198—21no—
39#11758198—21no—
40#11758198—21no—
41#11758198—21no—
42#11758198—21no—
43C4⋊Dic61—21no—
44#11758196—21no—
45C4×Dic61—21no—
46C4×Dic61D411yescharacteristic
47C4×Dic61D411yescharacteristic
48C4×Dic61C2311yescharacteristic
49C22×D61—21no—
50C22×D61C22⋊C411yescharacteristic
51C2×C4×C61—21no—
52C2×C4×C61—21no—
53C2×C4×C61C22⋊C411yescharacteristic
54C2×C4×C61C22⋊C411yescharacteristic
55C2×C4×C61C22×C411yescharacteristic
56C2×Dic61—21no—
57C2×Dic61C22⋊C411yescharacteristic
58C2×Dic61C2×D411yescharacteristic
59C2×Dic61C2×D411yescharacteristic
60D244—22no—
61D244—42no—
62C4×D61—22no—
63C4×D61—22no—
64C4×D61—22no—
65C4×D61—42no—
66Dic122—22no—
67#92420—24no—
68#92420—42no—
69C22×C61C2×C22⋊C411yescharacteristic
70C2×D61—21no—
71C2×D61—21no—
72C2×D61—41no—
73C2×D61—41no—
74C2×D61—41no—
75C2×D61#10412yes—
76C4×C61—21no—
77C4×C61—21no—
78C4×C61—41no—
79C4×C61—41no—
80C4×C61#13112yes—
81Dic61—21no—
82Dic61—21no—
83Dic61—41no—
84Dic61#13512yes—
85#1494—611nomaximal, Sylow
86C2×C61#40811yescharacteristic
87C2×C61#41611yescharacteristic
88C2×C61C2×#10411yescharacteristic
89D61—22no—
90D61—81no—
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#692311yescharacteristic
100#124—611no—
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×Q8—611no—
115C2×D4—611no—
116C2×D4—1221no—
117C22×C4—611no—
118C22×C4—611no—
119C22×C4—611no—
120C22×C4—1221no—
121C2×C8—1222no—
122C2×C8—1224no—
123C2×C8—1222no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—1221no—
127C4⋊C4—1221no—
128C4⋊C4C2×#692311yescharacteristic
129C4⋊C4C2×#692311yescharacteristic
130C22⋊C4—1221no—
131C22⋊C4—1221no—
132C22⋊C4—1221no—
133C22⋊C4—1221no—
134C22⋊C4—1221no—
135C42—611no—
136C42—611no—
137C42—611no—
138C42—1221no—
139C42C2×#692311yescharacteristic
140C23—611no—
141C23—1221no—
142Q8—1222no—
143D4—1222no—
144D4—2442no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—611no—
148C2×C4—611no—
149C2×C4—611no—
150C2×C4—1222no—
151C2×C4—1222no—
152C2×C4—1222no—
153C2×C4—1221no—
154C2×C4—2442no—
155C2×C4C22⋊#692311yescharacteristic
156C2×C4C22⋊#692311yescharacteristic
157C2×C4C22×#692311yescharacteristic
158C8—1224no—
159C8—2442no—
160C22—612no—
161C22—1221no—
162C22—1221no—
163C22—2441no—
164C22—2441no—
165C22—2441no—
166C22C2×C22⋊#692311yescharacteristic
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—612no—
172C4—1221no—
173C4—1221no—
174C4—2441no—
175C4#1451986512yes—
176C2—1222no—
177C2—4881no—
178C2#1684073711yescharacteristic
179C2#1684075211yescharacteristic
180C2D61⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#125×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#125#6923
hypocenterC61#1494
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
1. #16840784C2semidirect
2. C4×D61⋊C8C2semidirect
3. #16840612C2semidirect
4. #16840610C2semidirect
96. C61#1494semidirect