Finite Group Databasebeta

← #21461138

Subgroups — #21461138

Order 7808.

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

normal subgroups only

This group has 262 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#16840778C211yesmaximal, characteristic, complemented
2C4×#11758217C211yesmaximal, characteristic, complemented
3#16840610C212yesmaximal, complemented
4D4⋊#92420C212yesmaximal, complemented
5#16840307C211yesmaximal, characteristic
6C2×#11758217—21no—
7C4⋊#92420C2212yes—
8C22⋊#92420—21no—
9#14519832—21no—
10C4×#92420—21no—
11C4×#92420C2212yes—
12C2×#11758224—21no—
13#14519776C411yescharacteristic
14#14519773C411yescharacteristic
15#14519763—21no—
16#14519751C411yescharacteristic
17#14519749—21no—
18D4×Dic61C2211yescharacteristic
19#14519739C2211yescharacteristic
20#14519737—21no—
21C2×C4×Dic61C2211yescharacteristic
22#121×C61C411yescharacteristic
23C2×D4×C61—21no—
24C2×D4×C61C2×C411yescharacteristic
25C22×C4×C61C2×C411yescharacteristic
26C2×C22⋊D61—21no—
27C2×C22⋊D61—21no—
28C2×C22⋊D61—21no—
29C22×Dic61—21no—
30C22×Dic61D411yescharacteristic
31C22×Dic61D411yescharacteristic
32#11758224—44no—
33C2×D244C2×C411yescharacteristic
34C2×C4×D61—21no—
35C2×Dic122—21no—
36#11758217—24no—
37C2×#92420—22no—
38C2×#92420—22no—
39C4⋊C4×C61C2×C411yescharacteristic
40C22⋊C4×C61—21no—
41C22⋊Dic61—21no—
42#11758198—21no—
43#11758198—21no—
44C4⋊Dic61C2×C411yescharacteristic
45#11758196—21no—
46C4×Dic61C2×C411yescharacteristic
47C4×Dic61D411yescharacteristic
48C4×Dic61D411yescharacteristic
49C4×Dic61C2311yescharacteristic
50C23×C61—21no—
51C23×C61C22⋊C411yescharacteristic
52C22×D61—21no—
53D4×C61—22no—
54D4×C61—42no—
55C2×C4×C61—22no—
56C2×C4×C61—21no—
57C2×C4×C61C22⋊C411yescharacteristic
58C2×C4×C61C22×C411yescharacteristic
59C22⋊D61—42no—
60C22⋊D61—42no—
61C22⋊D61—42no—
62C2×Dic61—22no—
63C2×Dic61—22no—
64C2×Dic61—21no—
65C2×Dic61—42no—
66C2×Dic61C22⋊C411yescharacteristic
67C2×Dic61C22⋊C411yescharacteristic
68C2×Dic61C2×D411yescharacteristic
69C2×Dic61C2×D411yescharacteristic
70D244—22no—
71C4×D61—42no—
72Dic122—42no—
73#92420—24no—
74#92420—42no—
75C22×C61—21no—
76C22×C61—21no—
77C22×C61—21no—
78C22×C61—41no—
79C22×C61—41no—
80C22×C61—41no—
81C22×C61C2×C22⋊C411yescharacteristic
82C2×D61—41no—
83C2×D61—41no—
84C2×D61—41no—
85C4×C61—21no—
86C4×C61—41no—
87C4×C61#13112yes—
88Dic61—21no—
89Dic61—21no—
90Dic61—41no—
91Dic61#10412yes—
92Dic61AGL(1,ℤ/8)12yes—
93#1484—611nomaximal, Sylow
94C2×C61—41no—
95C2×C61—81no—
96C2×C61#40811yescharacteristic
97C2×C61#41811yescharacteristic
98C2×C61C2×#10411yescharacteristic
99D61—81no—
100#532—611no—
101#431—611no—
102C4×M16—611no—
103D4⋊C8—612no—
104D4⋊C8—612no—
105C61#148411yescharacteristic, complemented, Sylow
106C2×#41—1221no—
107C2×M16—1221no—
108C4⋊Q8—611no—
109#127—611no—
110#124—1221no—
111#121—611no—
112#121—1221no—
113#121#692311yescharacteristic
114C4×D4—611no—
115C4×D4—611no—
116C4×D4—1221no—
117C2×C42—611no—
118C4⋊C8—612no—
119C22⋊C8—1221no—
120#97—1221no—
121C4×C8—612no—
122C4×C8—1221no—
123#41—2444no—
124C2×Q8—1221no—
125C2×D4—21no—
126C2×D4—611no—
127C2×D4—1221no—
128C2×D4—1221no—
129C2×D4—1221no—
130C2×D4C2×#692311yescharacteristic
131C22×C4—611no—
132C22×C4—611no—
133C22×C4—1221no—
134C22×C4—1221no—
135C22×C4C2×#692311yescharacteristic
136M16—1224no—
137C2×C8—1222no—
138C2×C8—1222no—
139C4⋊C4—611no—
140C4⋊C4—1221no—
141C4⋊C4C2×#692311yescharacteristic
142C22⋊C4—21no—
143C22⋊C4—1221no—
144C22⋊C4—1221no—
145C22⋊C4—1221no—
146C42—611no—
147C42—611no—
148C42—611no—
149C42—611no—
150C23—21no—
151C23—1221no—
152C23C22⋊#692311yescharacteristic
153Q8—2442no—
154D4—22no—
155D4—42no—
156D4—1222no—
157D4—2442no—
158D4—2442no—
159D4—2442no—
160C2×C4—22no—
161C2×C4—21no—
162C2×C4—611no—
163C2×C4—611no—
164C2×C4—611no—
165C2×C4—611no—
166C2×C4—1222no—
167C2×C4—1222no—
168C2×C4—1221no—
169C2×C4—2442no—
170C2×C4—2442no—
171C2×C4C22⋊#692311yescharacteristic
172C2×C4C22×#692311yescharacteristic
173C8—1224no—
174C8—2442no—
175C22—21no—
176C22—21no—
177C22—21no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—2441no—
182C22—2441no—
183C22—2441no—
184C22C2×C22⋊#692311yescharacteristic
185C4—21no—
186C4—41no—
187C4—612no—
188C4—612no—
189C4—1221no—
190C4—1221no—
191C4—2441no—
192C4#1451986412yes—
193C2—41no—
194C2—81no—
195C2—4881no—
196C2#1684073511yescharacteristic
197C2#1684075411yescharacteristic
198C2D61⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#121×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#121#6923
hypocenterC61#1484
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #16840778C2semidirect
2. C4×#11758217C2semidirect
3. #16840610C2semidirect
4. D4⋊#92420C2semidirect
105. C61#1484semidirect