Finite Group Databasebeta

← #21461287

Subgroups — #21461287

Order 7808.

216 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 56 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#16840782C211yesmaximal, characteristic, complemented
2C4×#11758217C211yesmaximal, characteristic, complemented
3#16840619C212yesmaximal, complemented
4#16840618C212yesmaximal, complemented
5#16840298C211yesmaximal, characteristic
6C2×#11758217—21no—
7#14519844—21no—
8C22⋊#92420—21no—
9#14519832C2212yes—
10#14519832C2212yes—
11C4×#92420—21no—
12#14519772—21no—
13#14519768C2211yescharacteristic
14#14519766C2211yescharacteristic
15#14519761—21no—
16#14519751C411yescharacteristic
17Q8×Dic61C411yescharacteristic
18#14519739C411yescharacteristic
19#14519737—21no—
20#14519735—21no—
21C2×C4×Dic61C2211yescharacteristic
22C22⋊Q8×C61C411yescharacteristic
23C2×Q8×C61C2×C411yescharacteristic
24C22×C4×C61C2×C411yescharacteristic
25C2×C22⋊D61—21no—
26C22×Dic61D411yescharacteristic
27C22×Dic61D411yescharacteristic
28C2×D244C2×C411yescharacteristic
29C2×C4×D61—21no—
30#11758217—24no—
31C2×#92420—22no—
32C2×#92420—22no—
33C4⋊C4×C61—21no—
34C4⋊C4×C61C2×C411yescharacteristic
35C22⋊C4×C61—21no—
36#11758198—21no—
37#11758198—21no—
38#11758198—21no—
39#11758198—21no—
40C4⋊Dic61—21no—
41C4⋊Dic61—21no—
42C4⋊Dic61C2×C411yescharacteristic
43#11758196—21no—
44C4×Dic61—21no—
45C4×Dic61C2×C411yescharacteristic
46C4×Dic61D411yescharacteristic
47C4×Dic61D411yescharacteristic
48C4×Dic61C2311yescharacteristic
49C23×C61C22⋊C411yescharacteristic
50C22×D61—21no—
51Q8×C61—41no—
52C2×C4×C61—21no—
53C2×C4×C61—21no—
54C2×C4×C61—41no—
55C2×C4×C61C22⋊C411yescharacteristic
56C2×C4×C61C22×C411yescharacteristic
57C22⋊D61—42no—
58C2×Dic61—22no—
59C2×Dic61—21no—
60C2×Dic61—41no—
61C2×Dic61C22⋊C411yescharacteristic
62C2×Dic61C22⋊C411yescharacteristic
63C2×Dic61C2×D411yescharacteristic
64C2×Dic61C2×D411yescharacteristic
65D244—41no—
66C4×D61—42no—
67#92420—24no—
68#92420—42no—
69C22×C61—21no—
70C22×C61—21no—
71C22×C61—21no—
72C22×C61C2×C22⋊C411yescharacteristic
73C2×D61—41no—
74C2×D61—41no—
75C2×D61—41no—
76C4×C61—21no—
77C4×C61—21no—
78C4×C61—41no—
79C4×C61—41no—
80Dic61—21no—
81Dic61—21no—
82Dic61—21no—
83Dic61—41no—
84Dic61#10412yes—
85#1529—611nomaximal, Sylow
86C2×C61—41no—
87C2×C61#41311yescharacteristic
88C2×C61C2×#10411yescharacteristic
89C2×C61#42111yescharacteristic
90D61—81no—
91#529—611no—
92#432—611no—
93C4×M16—611no—
94#330—612no—
95#329—612no—
96C61#152911yescharacteristic, complemented, Sylow
97C2×M16—1221no—
98#126—1221no—
99#125—611no—
100#124—611no—
101#123—1221no—
102C22⋊Q8#692311yescharacteristic
103#121—611no—
104C4×Q8—611no—
105C4×D4—611no—
106C4×D4—1221no—
107#117—1221no—
108C2×C42—611no—
109C4⋊C8—1221no—
110C22⋊C8—1221no—
111#97—612no—
112#97—612no—
113C4×C8—1221no—
114C2×Q8C2×#692311yescharacteristic
115C2×D4—611no—
116C2×D4—1221no—
117C22×C4—611no—
118C22×C4—611no—
119C22×C4—1221no—
120C22×C4C2×#692311yescharacteristic
121M16—1224no—
122C2×C8—1222no—
123C2×C8—1222no—
124C4⋊C4—21no—
125C4⋊C4—611no—
126C4⋊C4—1221no—
127C4⋊C4—1221no—
128C4⋊C4—1221no—
129C4⋊C4C2×#692311yescharacteristic
130C22⋊C4—21no—
131C22⋊C4—1221no—
132C22⋊C4—1221no—
133C22⋊C4—1221no—
134C22⋊C4—1221no—
135C42—611no—
136C42—611no—
137C42—611no—
138C42—611no—
139C42—1221no—
140C23—1221no—
141C23C22⋊#692311yescharacteristic
142Q8—41no—
143D4—2441no—
144D4—2442no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—611no—
149C2×C4—611no—
150C2×C4—611no—
151C2×C4—611no—
152C2×C4—1222no—
153C2×C4—1221no—
154C2×C4—2442no—
155C2×C4—2441no—
156C2×C4C22⋊#692311yescharacteristic
157C2×C4C22×#692311yescharacteristic
158C8—1224no—
159C8—2442no—
160C22—21no—
161C22—21no—
162C22—21no—
163C22—2441no—
164C22—2441no—
165C22—2441no—
166C22C2×C22⋊#692311yescharacteristic
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—612no—
172C4—1221no—
173C4—1221no—
174C4—1221no—
175C4—2441no—
176C2—41no—
177C2—4881no—
178C2#1684074911yescharacteristic
179C2D61⋊#10411yescharacteristic
180C2#1684076111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC22⋊Q8×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC22⋊Q8#6923
hypocenterC61#1529
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #16840782C2semidirect
2. C4×#11758217C2semidirect
3. #16840619C2semidirect
4. #16840618C2semidirect
96. C61#1529semidirect