Finite Group Databasebeta

← #21444450

Subgroups — #21444450

Order 7808.

200 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 73 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#16839819C211yesmaximal, characteristic, complemented
2#16839819C211yesmaximal, characteristic, complemented
3#16839504C212yesmaximal, complemented
4#16839502C212yesmaximal, complemented
5C61×#529C211yesmaximal, characteristic
6C4⋊#92418—21no—
7C4⋊#92418—21no—
8C22⋊#92418—21no—
9C22⋊#92418—21no—
10#14519688C2212yes—
11#14519688C2212yes—
12#126×C61—21no—
13#125×C61C2211yescharacteristic
14#124×C61C2211yescharacteristic
15#123×C61—21no—
16C22⋊Q8×C61C411yescharacteristic
17#121×C61C411yescharacteristic
18C4×Q8×C61C411yescharacteristic
19C4×D4×C61—21no—
20C4×D4×C61C411yescharacteristic
21#117×C61—21no—
22C2×C42×C61C2211yescharacteristic
23C2×Q8×C61C2×C411yescharacteristic
24C2×D4×C61—21no—
25C2×D4×C61C2×C411yescharacteristic
26C22×C4×C61—21no—
27C22×C4×C61C2×C411yescharacteristic
28C22×C4×C61D411yescharacteristic
29C22×C4×C61D411yescharacteristic
30C4⋊C4×C61—21no—
31C4⋊C4×C61—21no—
32C4⋊C4×C61—21no—
33C4⋊C4×C61—21no—
34C4⋊C4×C61C2×C411yescharacteristic
35C4⋊C4×C61C2×C411yescharacteristic
36C22⋊C4×C61—21no—
37C22⋊C4×C61—21no—
38C22⋊C4×C61—21no—
39C22⋊C4×C61—21no—
40C22⋊C4×C61—21no—
41C42×C61—21no—
42C42×C61C2×C411yescharacteristic
43C42×C61D411yescharacteristic
44C42×C61D411yescharacteristic
45C42×C61C2311yescharacteristic
46C2×#92418—22no—
47C2×#92418—22no—
48C23×C61—21no—
49C23×C61C22⋊C411yescharacteristic
50Q8×C61—41no—
51D4×C61—41no—
52D4×C61—42no—
53C2×C4×C61—21no—
54C2×C4×C61—21no—
55C2×C4×C61—21no—
56C2×C4×C61—41no—
57C2×C4×C61—41no—
58C2×C4×C61—41no—
59C2×C4×C61—42no—
60C2×C4×C61C22⋊C411yescharacteristic
61C2×C4×C61C22⋊C411yescharacteristic
62C2×C4×C61C22⋊C411yescharacteristic
63C2×C4×C61C22×C411yescharacteristic
64C2×C4×C61C2×D411yescharacteristic
65C2×C4×C61C2×D411yescharacteristic
66#92418—42no—
67#92418—42no—
68C22×C61—21no—
69C22×C61—21no—
70C22×C61—21no—
71C22×C61—41no—
72C22×C61—41no—
73C22×C61—41no—
74C22×C61C2×C22⋊C411yescharacteristic
75C4×C61—21no—
76C4×C61—21no—
77C4×C61—21no—
78C4×C61—21no—
79C4×C61—21no—
80C4×C61—21no—
81C4×C61—41no—
82C4×C61—41no—
83C4×C61—41no—
84#1535—611nomaximal, Sylow
85C2×C61—41no—
86C2×C61—81no—
87C2×C61#41311yescharacteristic
88C2×C61#42111yescharacteristic
89C2×C61#42111yescharacteristic
90#529D6111yescharacteristic
91#432—611no—
92#432—611no—
93#330—612no—
94#329—612no—
95C61#153511yescharacteristic, complemented, Sylow
96#126—21no—
97#125C2×D6111yescharacteristic
98#124C2×D6111yescharacteristic
99#123—21no—
100C22⋊Q8Dic6111yescharacteristic
101#121Dic6111yescharacteristic
102C4×Q8Dic6111yescharacteristic
103C4×D4—21no—
104C4×D4Dic6111yescharacteristic
105#117—21no—
106C2×C42C2×D6111yescharacteristic
107C4⋊C8—1221no—
108C4⋊C8—1221no—
109C22⋊C8—1221no—
110C22⋊C8—1221no—
111#97—612no—
112#97—612no—
113C2×Q8C2×Dic6111yescharacteristic
114C2×D4—21no—
115C2×D4C2×Dic6111yescharacteristic
116C22×C4—21no—
117C22×C4C2×Dic6111yescharacteristic
118C22×C4C22⋊D6111yescharacteristic
119C22×C4C22⋊D6111yescharacteristic
120C2×C8—1222no—
121C2×C8—1222no—
122C4⋊C4—21no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4C2×Dic6111yescharacteristic
127C4⋊C4C2×Dic6111yescharacteristic
128C22⋊C4—21no—
129C22⋊C4—21no—
130C22⋊C4—21no—
131C22⋊C4—21no—
132C22⋊C4—21no—
133C42—21no—
134C42C2×Dic6111yescharacteristic
135C42C22⋊D6111yescharacteristic
136C42C22⋊D6111yescharacteristic
137C42C22×D6111yescharacteristic
138C23—21no—
139C23C22⋊Dic6111yescharacteristic
140Q8—41no—
141D4—41no—
142D4—42no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—42no—
150C2×C4C22⋊Dic6111yescharacteristic
151C2×C4C22⋊Dic6111yescharacteristic
152C2×C4C22⋊Dic6111yescharacteristic
153C2×C4C22×Dic6111yescharacteristic
154C2×C4C2×C22⋊D6111yescharacteristic
155C2×C4C2×C22⋊D6111yescharacteristic
156C8—2442no—
157C8—2442no—
158C22—21no—
159C22—21no—
160C22—21no—
161C22—41no—
162C22—41no—
163C22—41no—
164C22C2×C22⋊Dic6111yescharacteristic
165C4—21no—
166C4—21no—
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—41no—
172C4—41no—
173C4—41no—
174C2—41no—
175C2—81no—
176C2#1683974611yescharacteristic
177C2#1683977911yescharacteristic
178C2#1683977911yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#529C2
socleC22×C61C2×C22⋊C4
hypercenter#529D61
hypocenterC61#1535
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #16839819C2semidirect
2. #16839819C2semidirect
3. #16839504C2semidirect
4. #16839502C2semidirect
95. C61#1535semidirect