Finite Group Databasebeta

← #21462007

Subgroups — #21462007

Order 7808.

244 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 70 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#16840767C211yesmaximal, characteristic
2#16840698C211yesmaximal, characteristic
3#16840632C214yesmaximal
4#16840317C211yesmaximal, characteristic
5C2×#11758213C2212yes—
6C2×C4×#6923C2212yes—
7#14519844—21no—
8#14519844—21no—
9(C2×#6923)⋊C4—21no—
10(C2×#6923)⋊C4—21no—
11#14519777C411yescharacteristic, complemented
12#14519768C412yescomplemented
13#14519757—21no—
14#14519753—21no—
15Q8×Dic61—21no—
16#14519742—21no—
17#14519735C2212yes—
18C42×D61C2211yescharacteristic
19C4⋊Q8×C61C411yescharacteristic, complemented
20C22×#6923—22no—
21C2×Q8×C61—21no—
22C2×C4×D61D411yescharacteristic
23C2×C4×D61D411yescharacteristic
24C2×C4×D61C2311yescharacteristic
25C2×Dic122—21no—
26C2×#92420—22no—
27C4×#6923—22no—
28C4×#6923Q814yescomplemented
29#11758213—24no—
30C4⋊C4×C61—21no—
31C4⋊C4×C61C2×C412yes—
32C42×C61C2×C411yescharacteristic
33#11758198—22no—
34C4⋊Dic61—21no—
35C4⋊Dic61—22no—
36C4⋊Dic61C2×C412yes—
37#11758196—22no—
38C4×Dic61—22no—
39C4×Dic61C2×C411yescharacteristic
40C4×Dic61D411yescharacteristic
41C4×Dic61D411yescharacteristic
42C22×D61C2×D411yescharacteristic
43C2×#6923—24no—
44C2×#6923—42no—
45C2×#6923—42no—
46Q8×C61—42no—
47C2×C4×C61—22no—
48C2×C4×C61C22⋊C411yescharacteristic
49C2×C4×C61C22⋊C411yescharacteristic
50C2×C4×C61C22×C411yescharacteristic
51C2×Dic61—22no—
52C2×Dic61C22⋊C411yescharacteristic
53C2×Dic61C22⋊C411yescharacteristic
54C2×Dic61C2×D411yescharacteristic
55C4×D61—41no—
56C4×D61—41no—
57C4×D61C2×Q812yes—
58C4×D61#4112yes—
59Dic122—42no—
60#92420—42no—
61C22×C61C2×C22⋊C411yescharacteristic
62C2×D61—21no—
63C2×D61—21no—
64C2×D61C22⋊Q812yes—
65#6923—44no—
66C4×C61—21no—
67C4×C61—21no—
68C4×C61—42no—
69C4×C61C4×Q812yes—
70Dic61—21no—
71Dic61—21no—
72Dic61—42no—
73Dic61#12411yescharacteristic
74Dic61C4⋊Q811yescharacteristic
75#1995—611nomaximal, Sylow
76C2×C61#39111yescharacteristic
77C2×C61#42111yescharacteristic
78C2×C61#42111yescharacteristic
79D61—22no—
80#533—611no—
81#423—611no—
82#376—611no—
83#339—614no—
84C61#199511yescharacteristic, complemented, Sylow
85C2×M16—612no—
86C4⋊Q8—611no—
87C4⋊Q8#692311yescharacteristic, complemented
88#125—612no—
89C22⋊Q8—1221no—
90C22⋊Q8—1221no—
91C4×Q8—1221no—
92C4×Q8—1221no—
93#117—612no—
94C2×C42—611no—
95C2×C42—612no—
96C4⋊C8—1221no—
97C4⋊C8—1221no—
98#95—1221no—
99#95—1221no—
100C2×Q8—21no—
101C2×Q8—1221no—
102C22×C4—611no—
103C22×C4—611no—
104C22×C4—611no—
105C22×C4—1222no—
106M16—1224no—
107C2×C8—1222no—
108C4⋊C4—21no—
109C4⋊C4—612no—
110C4⋊C4—1222no—
111C4⋊C4—1222no—
112C4⋊C4—1221no—
113C4⋊C4C2×#692312yes—
114C22⋊C4—1222no—
115C42—611no—
116C42—611no—
117C42—611no—
118C42—614no—
119C42—1222no—
120C42—1222no—
121C42C2×#692311yescharacteristic
122C23—611no—
123Q8—42no—
124Q8—2442no—
125C2×C4—22no—
126C2×C4—611no—
127C2×C4—612no—
128C2×C4—612no—
129C2×C4—611no—
130C2×C4—611no—
131C2×C4—1224no—
132C2×C4—1222no—
133C2×C4—2441no—
134C2×C4—2441no—
135C2×C4—2442no—
136C2×C4—2442no—
137C2×C4C22⋊#692311yescharacteristic
138C2×C4C22⋊#692311yescharacteristic
139C2×C4C22×#692311yescharacteristic
140C8—2442no—
141C22—612no—
142C22—1221no—
143C22—1221no—
144C22C2×C22⋊#692311yescharacteristic
145C4—21no—
146C4—21no—
147C4—42no—
148C4—611no—
149C4—611no—
150C4—1221no—
151C4—1221no—
152C4—2444no—
153C4—2442no—
154C4Q8×#692312yes—
155C2—1222no—
156C2(C2×#6923)⋊Q811yescharacteristic
157C2#1684076011yescharacteristic
158C2#1684076111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC4⋊Q8×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC4⋊Q8#6923
hypocenterC61#1995
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
11. #14519777C4semidirect
12. #14519768C4semidirect
19. C4⋊Q8×C61C4semidirect
28. C4×#6923Q8semidirect
84. C61#1995semidirect
87. C4⋊Q8#6923semidirect