Finite Group Databasebeta

← #21461306

Subgroups — #21461306

Order 7808.

200 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 54 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#16840782C211yesmaximal, characteristic, complemented
3#16840619C212yesmaximal, complemented
4#16840618C212yesmaximal, complemented
5#16840298C211yesmaximal, characteristic
6#14519844—21no—
7C4⋊#92420—21no—
8C22⋊#92420—21no—
9C22⋊#92420—21no—
10#14519832C2212yes—
11#14519832C2212yes—
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—
30C2×#92420—22no—
31C2×#92420—22no—
32C4⋊C4×C61—21no—
33C4⋊C4×C61C2×C411yescharacteristic
34C22⋊C4×C61—21no—
35#11758198—21no—
36#11758198—21no—
37#11758198—21no—
38#11758198—21no—
39C4⋊Dic61—21no—
40C4⋊Dic61—21no—
41C4⋊Dic61C2×C411yescharacteristic
42#11758196—21no—
43C4×Dic61—21no—
44C4×Dic61C2×C411yescharacteristic
45C4×Dic61D411yescharacteristic
46C4×Dic61D411yescharacteristic
47C4×Dic61C2311yescharacteristic
48C23×C61C22⋊C411yescharacteristic
49C22×D61—21no—
50Q8×C61—41no—
51C2×C4×C61—21no—
52C2×C4×C61—21no—
53C2×C4×C61—41no—
54C2×C4×C61C22⋊C411yescharacteristic
55C2×C4×C61C22×C411yescharacteristic
56C22⋊D61—42no—
57C2×Dic61—21no—
58C2×Dic61—41no—
59C2×Dic61—41no—
60C2×Dic61C22⋊C411yescharacteristic
61C2×Dic61C22⋊C411yescharacteristic
62C2×Dic61C2×D411yescharacteristic
63C2×Dic61C2×D411yescharacteristic
64D244—41no—
65C4×D61—42no—
66#92420—42no—
67#92420—42no—
68C22×C61—21no—
69C22×C61—21no—
70C22×C61—21no—
71C22×C61C2×C22⋊C411yescharacteristic
72C2×D61—41no—
73C2×D61—41no—
74C2×D61—41no—
75C4×C61—21no—
76C4×C61—21no—
77C4×C61—41no—
78C4×C61—41no—
79Dic61—21no—
80Dic61—21no—
81Dic61—21no—
82Dic61—21no—
83Dic61—41no—
84#1535—611nomaximal, Sylow
85C2×C61—41no—
86C2×C61#41311yescharacteristic
87C2×C61#42111yescharacteristic
88C2×C61#42111yescharacteristic
89D61—81no—
90#529—611no—
91#432—611no—
92#432—611no—
93#330—612no—
94#329—612no—
95C61#153511yescharacteristic, complemented, Sylow
96#126—1221no—
97#125—611no—
98#124—611no—
99#123—1221no—
100C22⋊Q8#692311yescharacteristic
101#121—611no—
102C4×Q8—611no—
103C4×D4—611no—
104C4×D4—1221no—
105#117—1221no—
106C2×C42—611no—
107C4⋊C8—1221no—
108C4⋊C8—1221no—
109C22⋊C8—1221no—
110C22⋊C8—1221no—
111#97—612no—
112#97—612no—
113C2×Q8C2×#692311yescharacteristic
114C2×D4—611no—
115C2×D4—1221no—
116C22×C4—611no—
117C22×C4—611no—
118C22×C4—1221no—
119C22×C4C2×#692311yescharacteristic
120C2×C8—1222no—
121C2×C8—1222no—
122C4⋊C4—21no—
123C4⋊C4—611no—
124C4⋊C4—1221no—
125C4⋊C4—1221no—
126C4⋊C4—1221no—
127C4⋊C4C2×#692311yescharacteristic
128C22⋊C4—21no—
129C22⋊C4—1221no—
130C22⋊C4—1221no—
131C22⋊C4—1221no—
132C22⋊C4—1221no—
133C42—611no—
134C42—611no—
135C42—611no—
136C42—611no—
137C42—1221no—
138C23—1221no—
139C23C22⋊#692311yescharacteristic
140Q8—41no—
141D4—2441no—
142D4—2442no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—41no—
146C2×C4—611no—
147C2×C4—611no—
148C2×C4—611no—
149C2×C4—611no—
150C2×C4—1221no—
151C2×C4—2442no—
152C2×C4—2441no—
153C2×C4—2441no—
154C2×C4C22⋊#692311yescharacteristic
155C2×C4C22×#692311yescharacteristic
156C8—2442no—
157C8—2442no—
158C22—21no—
159C22—21no—
160C22—21no—
161C22—2441no—
162C22—2441no—
163C22—2441no—
164C22C2×C22⋊#692311yescharacteristic
165C4—21no—
166C4—21no—
167C4—41no—
168C4—41no—
169C4—1221no—
170C4—1221no—
171C4—1221no—
172C4—1221no—
173C4—2441no—
174C2—41no—
175C2—4881no—
176C2#1684074911yescharacteristic
177C2#1684075911yescharacteristic
178C2#1684076111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC22⋊Q8×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC22⋊Q8#6923
hypocenterC61#1535
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. #16840783C2semidirect
2. #16840782C2semidirect
3. #16840619C2semidirect
4. #16840618C2semidirect
95. C61#1535semidirect