Finite Group Databasebeta

← #21461152

Subgroups — #21461152

Order 7808.

246 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 64 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#16840783C211yesmaximal, characteristic, complemented
2#16840779C211yesmaximal, characteristic, complemented
3#16840612C212yesmaximal, complemented
4#16840610C212yesmaximal, complemented
5#16840230C211yesmaximal, characteristic
6#14519844—21no—
7C4⋊#92420C2212yes—
8C22⋊#92420—21no—
9C22⋊#92420—21no—
10#14519832—21no—
11C4×#92420C2212yes—
12C2×#11758222C411yescharacteristic
13#14519742C411yescharacteristic
14#14519742C2211yescharacteristic
15#14519739C411yescharacteristic
16#14519739C2211yescharacteristic
17#14519737—21no—
18#14519737—21no—
19#14519734—21no—
20C2×C4×Dic61C2211yescharacteristic
21C42×D61—21no—
22#117×C61C411yescharacteristic
23C22×C4×C61C2×C411yescharacteristic
24C2×C22⋊D61—21no—
25C22×Dic61D411yescharacteristic
26C22×Dic61D411yescharacteristic
27#11758222—22no—
28#11758222—22no—
29C2×D244C2×C411yescharacteristic
30C2×C4×D61—21no—
31C2×C4×D61—21no—
32C2×C4×D61—21no—
33C2×Dic122C2×C411yescharacteristic
34C2×#92420—22no—
35C2×#92420—22no—
36C4⋊C4×C61C2×C411yescharacteristic
37C4⋊C4×C61C2×C411yescharacteristic
38C22⋊C4×C61—21no—
39C42×C61—21no—
40#11758198—21no—
41#11758198—21no—
42#11758196—21no—
43#11758196—21no—
44C4×Dic61—21no—
45C4×Dic61—21no—
46C4×Dic61C2×C411yescharacteristic
47C4×Dic61D411yescharacteristic
48C4×Dic61D411yescharacteristic
49C4×Dic61C2311yescharacteristic
50C23×C61C22⋊C411yescharacteristic
51C22×D61—21no—
52C2×C4×C61—21no—
53C2×C4×C61—21no—
54C2×C4×C61—21no—
55C2×C4×C61—21no—
56C2×C4×C61C22⋊C411yescharacteristic
57C2×C4×C61C22×C411yescharacteristic
58C22⋊D61—24no—
59C2×Dic61—21no—
60C2×Dic61—22no—
61C2×Dic61—41no—
62C2×Dic61C22⋊C411yescharacteristic
63C2×Dic61C22⋊C411yescharacteristic
64C2×Dic61C2×D411yescharacteristic
65C2×Dic61C2×D411yescharacteristic
66D244—21no—
67D244M1612yes—
68C4×D61—24no—
69C4×D61—42no—
70C4×D61—42no—
71Dic122—21no—
72Dic122M1612yes—
73#92420—42no—
74#92420—42no—
75C22×C61—21no—
76C22×C61—21no—
77C22×C61—21no—
78C22×C61C2×C22⋊C411yescharacteristic
79C2×D61—22no—
80C2×D61—41no—
81C2×D61—41no—
82C4×C61—21no—
83C4×C61—41no—
84C4×C61—41no—
85C4×C61C2×M1611yescharacteristic
86C4×C61C2×M1611yescharacteristic
87Dic61—22no—
88Dic61—21no—
89Dic61—21no—
90Dic61—21no—
91Dic61#13512yes—
92#1488—611nomaximal, Sylow
93C2×C61—41no—
94C2×C61#40711yescharacteristic
95C2×C61#41611yescharacteristic
96C2×C61#42111yescharacteristic
97D61—42no—
98C4×#41—611no—
99#432—611no—
100#431—611no—
101Q8⋊C8—612no—
102D4⋊C8—612no—
103C61#148811yescharacteristic, complemented, Sylow
104C2×#41—611no—
105C4×Q8—611no—
106C4×Q8—611no—
107C4×D4—611no—
108C4×D4—611no—
109C4×D4—1221no—
110C4×D4—1221no—
111#117—1221no—
112#117#692311yescharacteristic
113C2×C42—611no—
114C2×C42—1221no—
115C4⋊C8—612no—
116C4⋊C8—1221no—
117C22⋊C8—1221no—
118C22⋊C8—1221no—
119#97—1221no—
120C4×C8—612no—
121#41—1222no—
122#41—1222no—
123C2×Q8—611no—
124C2×D4—611no—
125C2×D4—1221no—
126C22×C4—611no—
127C22×C4—611no—
128C22×C4—1221no—
129C22×C4—1221no—
130C22×C4—1221no—
131C22×C4C2×#692311yescharacteristic
132C2×C8—1222no—
133C2×C8—1222no—
134C4⋊C4—1221no—
135C4⋊C4—1221no—
136C4⋊C4C2×#692311yescharacteristic
137C4⋊C4C2×#692311yescharacteristic
138C22⋊C4—21no—
139C22⋊C4—1221no—
140C22⋊C4—1221no—
141C42—21no—
142C42—611no—
143C42—611no—
144C42—611no—
145C42—611no—
146C42—1221no—
147C42—1221no—
148C23—1221no—
149C23C22⋊#692311yescharacteristic
150Q8—612no—
151Q8—1221no—
152D4—612no—
153D4—1224no—
154D4—1221no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—611no—
160C2×C4—611no—
161C2×C4—611no—
162C2×C4—611no—
163C2×C4—1224no—
164C2×C4—1222no—
165C2×C4—1221no—
166C2×C4—2442no—
167C2×C4—2442no—
168C2×C4—2441no—
169C2×C4C22⋊#692311yescharacteristic
170C2×C4C22×#692311yescharacteristic
171C8—2442no—
172C8—2442no—
173C22—21no—
174C22—21no—
175C22—21no—
176C22—1222no—
177C22—2441no—
178C22—2441no—
179C22C2×C22⋊#692311yescharacteristic
180C4—21no—
181C4—41no—
182C4—41no—
183C4—612no—
184C4—1222no—
185C4—1221no—
186C4—1221no—
187C4—1221no—
188C4D61⋊M1611yescharacteristic
189C4D61⋊M1611yescharacteristic
190C2—41no—
191C2—2442no—
192C2#1684073411yescharacteristic
193C2#1684075211yescharacteristic
194C2#1684075911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#117×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#117#6923
hypocenterC61#1488
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #16840783C2semidirect
2. #16840779C2semidirect
3. #16840612C2semidirect
4. #16840610C2semidirect
103. C61#1488semidirect