Finite Group Databasebeta

← #21462081

Subgroups — #21462081

Order 7808.

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

normal subgroups only

This group has 234 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#16840748C211yesmaximal, characteristic
2#16840741C211yesmaximal, characteristic
3#16840664C214yesmaximal, complemented
4#16840336C211yesmaximal, characteristic
5D61⋊M16—21no—
6#14519856—21no—
7#14519838—21no—
8#14519837C2212yes—
9#14519836—21no—
10#14519835C2212yes—
11C2×#11758222C2211yescharacteristic
12#14519775—21no—
13#14519766—21no—
14#14519760C412yescomplemented
15#14519760C2212yes—
16#14519753—21no—
17#14519753—21no—
18#14519736C411yescharacteristic, complemented
19C22×Q8×C61C411yescharacteristic, complemented
20C2×Q8×C61—21no—
21C2×Q8×C61—21no—
22C2×Q8×C61—41no—
23C2×Q8×C61—41no—
24C22×C4×C61C2×C411yescharacteristic
25C22×C4×C61C2×C412yes—
26C2×C22⋊D61C2×C411yescharacteristic
27C2×C22⋊D61C2311yescharacteristic
28#11758222—41no—
29#11758222—41no—
30C2×D244D411yescharacteristic
31C2×C4×D61D411yescharacteristic
32C2×C4×D61D411yescharacteristic
33C2×Dic122D411yescharacteristic
34C22⋊#6923—22no—
35#11758217—22no—
36C4⋊#6923—41no—
37C4×#6923—41no—
38#11758213—41no—
39D61⋊C8—41no—
40C22⋊Dic61C2×C412yes—
41#11758198—22no—
42#11758198—22no—
43C4⋊Dic61—21no—
44#11758196—22no—
45#11758196—22no—
46C4×Dic61—21no—
47C23×C61C22×C411yescharacteristic
48C22×D61C22⋊C411yescharacteristic
49C22×D61C2×D411yescharacteristic
50C2×#6923—42no—
51Q8×C61—42no—
52Q8×C61—41no—
53Q8×C61—41no—
54C2×C4×C61—21no—
55C2×C4×C61—21no—
56C2×C4×C61—22no—
57C2×C4×C61—42no—
58C2×C4×C61C22⋊C411yescharacteristic
59C2×C4×C61C22⋊C411yescharacteristic
60C22⋊D61—41no—
61C22⋊D61—41no—
62C2×Dic61—22no—
63C2×Dic61C22⋊C411yescharacteristic
64C2×Dic61C2×D411yescharacteristic
65D244—41no—
66C4×D61—21no—
67C4×D61—21no—
68C4×D61—21no—
69C4×D61—21no—
70Dic122—41no—
71#92420—42no—
72C22×C61—21no—
73C22×C61—41no—
74C22×C61C2×C22⋊C411yescharacteristic
75C2×D61—21no—
76C2×D61—21no—
77C2×D61—41no—
78C2×D61—41no—
79#6923—82no—
80C4×C61—21no—
81C4×C61—42no—
82C4×C61#9911yescharacteristic
83C4×C61#9911yescharacteristic
84Dic61—21no—
85Dic61—21no—
86Dic61—42no—
87#2123—611nomaximal, Sylow
88C2×C61—21no—
89C2×C61—41no—
90C2×C61C2×#9911yescharacteristic
91D61—41no—
92D61—41no—
93#536—611no—
94#413—611no—
95#410—611no—
96#352—614no—
97C61#212311yescharacteristic, complemented, Sylow
98C2×#41—611no—
99C22×Q8#692311yescharacteristic, complemented
100C2×M16—1221no—
101C4⋊Q8—1221no—
102#124—1221no—
103#123—612no—
104#123—612no—
105C22⋊Q8—1221no—
106C22⋊Q8—1221no—
107#117—611no—
108#117—1221no—
109#101—1221no—
110#100—612no—
111#99—612no—
112#99—1221no—
113#41—2441no—
114#41—2441no—
115C2×Q8—21no—
116C2×Q8—21no—
117C2×Q8—41no—
118C2×Q8—41no—
119C2×Q8—611no—
120C2×D4—611no—
121C2×D4—611no—
122C2×D4—611no—
123C22×C4—611no—
124C22×C4—611no—
125C22×C4C2×#692312yes—
126C22×C4C2×#692311yescharacteristic
127M16—1222no—
128M16—2441no—
129C2×C8—2441no—
130C4⋊C4—1222no—
131C4⋊C4—1222no—
132C4⋊C4—1221no—
133C4⋊C4—2441no—
134C22⋊C4—612no—
135C22⋊C4—1222no—
136C22⋊C4—1222no—
137C22⋊C4—1222no—
138C42—1221no—
139C42—2441no—
140C23—611no—
141C23—611no—
142C23C22×#692311yescharacteristic
143Q8—42no—
144Q8—41no—
145Q8—41no—
146Q8—2441no—
147D4—2441no—
148D4—2441no—
149D4—2441no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—22no—
153C2×C4—42no—
154C2×C4—611no—
155C2×C4—611no—
156C2×C4—1221no—
157C2×C4—1221no—
158C2×C4—1221no—
159C2×C4—1221no—
160C2×C4—1222no—
161C2×C4—2442no—
162C2×C4C22⋊#692311yescharacteristic
163C2×C4C22⋊#692311yescharacteristic
164C8—2442no—
165C22—21no—
166C22—41no—
167C22—1221no—
168C22—1221no—
169C22—2441no—
170C22—2441no—
171C22C2×C22⋊#692311yescharacteristic
172C4—21no—
173C4—42no—
174C4—1221no—
175C4—1221no—
176C4—4882no—
177C4—2442no—
178C4#1451983511yescharacteristic
179C4#1451983511yescharacteristic
180C2—21no—
181C2—41no—
182C2—2441no—
183C2—2441no—
184C2C2×#1451983511yescharacteristic
subgroupG/H
centerC2C2×#14519835
commutatorC23×C61C22×C4
FrattiniC23C22×#6923
FittingC22×Q8×C61C4
socleC2×C61C2×#99
hypercenterC22×Q8#6923
hypocenterC61#2123
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
3. #16840664C2semidirect
14. #14519760C4semidirect
18. #14519736C4semidirect
19. C22×Q8×C61C4semidirect
97. C61#2123semidirect
99. C22×Q8#6923semidirect