Finite Group Databasebeta

← #21461112

Subgroups — #21461112

Order 7808.

276 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 86 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
2C2×C4×#92420C211yesmaximal, characteristic, complemented
3#16840612C212yesmaximal, complemented
4#16840610C212yesmaximal, complemented
5#16840230C211yesmaximal, characteristic
6C22×#92420—21no—
7C4⋊#92420C2212yes—
8C22⋊#92420—21no—
9C4×#92420—21no—
10C4×#92420—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#11758222C814yescomplemented
29C2×D244C2×C411yescharacteristic
30C2×C4×D61—21no—
31C2×C4×D61—21no—
32C2×C4×D61—21no—
33C2×Dic122C2×C411yescharacteristic
34C2×#92420—24no—
35C2×#92420—22no—
36C2×#92420—22no—
37C4⋊C4×C61C2×C411yescharacteristic
38C4⋊C4×C61C2×C411yescharacteristic
39C22⋊C4×C61—21no—
40C42×C61—21no—
41#11758198—21no—
42#11758198—21no—
43#11758196—21no—
44#11758196—21no—
45C4×Dic61—21no—
46C4×Dic61—21no—
47C4×Dic61C2×C411yescharacteristic
48C4×Dic61D411yescharacteristic
49C4×Dic61D411yescharacteristic
50C4×Dic61C2311yescharacteristic
51C23×C61C22⋊C411yescharacteristic
52C22×D61—21no—
53C2×C4×C61—21no—
54C2×C4×C61—21no—
55C2×C4×C61C22⋊C411yescharacteristic
56C2×C4×C61C2×C812yes—
57C2×C4×C61M1612yes—
58C2×C4×C61C22×C411yescharacteristic
59C22⋊D61—24no—
60C2×Dic61—21no—
61C2×Dic61—22no—
62C2×Dic61—22no—
63C2×Dic61C22⋊C411yescharacteristic
64C2×Dic61C22⋊C411yescharacteristic
65C2×Dic61C2×D411yescharacteristic
66C2×Dic61C2×D411yescharacteristic
67D244—21no—
68D244C2×C812yescomplemented
69C4×D61—24no—
70C4×D61—42no—
71C4×D61—42no—
72Dic122—21no—
73Dic122C2×C812yescomplemented
74#92420—24no—
75#92420—42no—
76C22×C61—21no—
77C22×C61—21no—
78C22×C61C22⋊C812yes—
79C22×C61C2×C22⋊C411yescharacteristic
80C2×D61—22no—
81C2×D61—41no—
82C2×D61—41no—
83C4×C61—41no—
84C4×C61—41no—
85C4×C61C22⋊C812yes—
86C4×C61C22×C811yescharacteristic
87C4×C61C2×M1611yescharacteristic
88Dic61—22no—
89Dic61—21no—
90Dic61—21no—
91Dic61#10412yes—
92Dic61#13512yes—
93#1476—611nomaximal, Sylow
94C2×C61—22no—
95C2×C61C2×C22⋊C811yescharacteristic
96C2×C61#41611yescharacteristic
97C2×C61C2×#10411yescharacteristic
98D61—42no—
99C4×#41—611no—
100#431—611no—
101C2×C4×C8—611no—
102Q8⋊C8—612no—
103D4⋊C8—612no—
104C61#147611yescharacteristic, complemented, Sylow
105C2×#41—611no—
106C22×C8—1221no—
107C4×Q8—611no—
108C4×Q8—611no—
109C4×D4—611no—
110C4×D4—611no—
111C4×D4—1221no—
112C4×D4—1221no—
113#117—1221no—
114#117#692311yescharacteristic
115C2×C42—611no—
116C2×C42—1221no—
117C4⋊C8—612no—
118C22⋊C8—1221no—
119C4×C8—612no—
120C4×C8—1221no—
121C4×C8—1221no—
122#41—614no—
123#41—1222no—
124C2×Q8—611no—
125C2×D4—611no—
126C2×D4—1221no—
127C22×C4—611no—
128C22×C4—611no—
129C22×C4—1221no—
130C22×C4—1221no—
131C22×C4—1221no—
132C22×C4C2×#692311yescharacteristic
133C2×C8—1222no—
134C2×C8—1224no—
135C2×C8—1222no—
136C4⋊C4—1221no—
137C4⋊C4—1221no—
138C4⋊C4C2×#692311yescharacteristic
139C4⋊C4C2×#692311yescharacteristic
140C22⋊C4—21no—
141C22⋊C4—1221no—
142C22⋊C4—1221no—
143C42—21no—
144C42—611no—
145C42—611no—
146C42—611no—
147C42—611no—
148C42—1221no—
149C42—1221no—
150C23—1221no—
151C23C22⋊#692311yescharacteristic
152Q8—612no—
153Q8—1221no—
154D4—612no—
155D4—1224no—
156D4—1221no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—611no—
160C2×C4—611no—
161C2×C4—611no—
162C2×C4—611no—
163C2×C4—1222no—
164C2×C4—1222no—
165C2×C4—1221no—
166C2×C4—1224no—
167C2×C4—2442no—
168C2×C4—2442no—
169C2×C4D61⋊C812yes—
170C2×C4#1175821312yes—
171C2×C4C22⋊#692311yescharacteristic
172C2×C4C22×#692311yescharacteristic
173C8—1224no—
174C8—2442no—
175C22—21no—
176C22—21no—
177C22—1222no—
178C22—2441no—
179C22—2441no—
180C22#1451983412yes—
181C22C2×C22⋊#692311yescharacteristic
182C4—41no—
183C4—41no—
184C4—612no—
185C4—612no—
186C4—1222no—
187C4—1221no—
188C4—1221no—
189C4#1451983412yes—
190C4C2×D61⋊C811yescharacteristic
191C4C2×#1175821311yescharacteristic
192C2—22no—
193C2—2442no—
194C2C2×#1451983411yescharacteristic
195C2#1684075211yescharacteristic
196C2D61⋊#10411yescharacteristic
subgroupG/H
centerC2×C4C22⋊#6923
commutatorC4×C61C22×C8
FrattiniC2×C4C22×#6923
Fitting#117×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#117#6923
hypocenterC61#1476
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #16840778C2semidirect
2. C2×C4×#92420C2semidirect
3. #16840612C2semidirect
4. #16840610C2semidirect
28. #11758222C8semidirect
68. D244C2×C8semidirect
73. Dic122C2×C8semidirect
104. C61#1476semidirect