Finite Group Databasebeta

← #21461995

Subgroups — #21461995

Order 7808.

260 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C4×#11758213C211yesmaximal, characteristic
2C4×C4⋊#6923C211yesmaximal, characteristic
3#16840632C214yesmaximal
4#16840317C211yesmaximal, characteristic
5C2×#11758213C2212yes—
6C2×C4⋊#6923—21no—
7C2×C4×#6923C2212yes—
8#14519832—21no—
9C4×#92420—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—24no—
28C4×#6923—24no—
29#11758213—22no—
30#11758213Q814yescomplemented
31C4⋊C4×C61—21no—
32C4⋊C4×C61C2×C412yes—
33C42×C61C2×C411yescharacteristic
34#11758198—22no—
35C4⋊Dic61—21no—
36C4⋊Dic61—22no—
37C4⋊Dic61C2×C412yes—
38#11758196—22no—
39C4×Dic61—22no—
40C4×Dic61C2×C411yescharacteristic
41C4×Dic61D411yescharacteristic
42C4×Dic61D411yescharacteristic
43C22×D61C2×D411yescharacteristic
44C2×#6923—24no—
45C2×#6923—42no—
46C2×#6923—42no—
47Q8×C61—42no—
48C2×C4×C61—22no—
49C2×C4×C61C22⋊C411yescharacteristic
50C2×C4×C61C22⋊C411yescharacteristic
51C2×C4×C61C22×C411yescharacteristic
52C2×Dic61—22no—
53C2×Dic61C22⋊C411yescharacteristic
54C2×Dic61C22⋊C411yescharacteristic
55C2×Dic61C2×D411yescharacteristic
56C4×D61—22no—
57C4×D61—41no—
58C4×D61C2×Q812yes—
59C4×D61#4112yes—
60Dic122—42no—
61#92420—24no—
62C22×C61C2×C22⋊C411yescharacteristic
63C2×D61—21no—
64C2×D61—21no—
65C2×D61#12411yescharacteristic
66C2×D61C4⋊Q811yescharacteristic
67#6923—44no—
68C4×C61—21no—
69C4×C61—42no—
70C4×C61#10412yes—
71C4×C61C4×Q812yes—
72Dic61—21no—
73Dic61—21no—
74Dic61—42no—
75Dic61C22⋊Q812yes—
76#1986—611nomaximal, Sylow
77C2×C61#39111yescharacteristic
78C2×C61C2×#10411yescharacteristic
79C2×C61#42111yescharacteristic
80D61—21no—
81D61—21no—
82#533—611no—
83C4×M16—611no—
84C4×C4⋊C4—611no—
85#339—614no—
86C61#198611yescharacteristic, complemented, Sylow
87C2×M16—612no—
88C4⋊Q8—611no—
89C4⋊Q8#692311yescharacteristic, complemented
90#125—612no—
91C22⋊Q8—1221no—
92C22⋊Q8—1221no—
93C4×Q8—1221no—
94C4×Q8—1221no—
95#117—612no—
96C2×C4⋊C4—1221no—
97C2×C42—611no—
98C2×C42—612no—
99#97—1221no—
100C4×C8—1221no—
101#95—1221no—
102C2×Q8—21no—
103C2×Q8—1221no—
104C22×C4—611no—
105C22×C4—611no—
106C22×C4—611no—
107C22×C4—1222no—
108M16—614no—
109M16—1222no—
110C2×C8—1222no—
111C4⋊C4—21no—
112C4⋊C4—612no—
113C4⋊C4—1222no—
114C4⋊C4—1222no—
115C4⋊C4—1224no—
116C4⋊C4—1221no—
117C4⋊C4C2×#692312yes—
118C22⋊C4—1222no—
119C42—611no—
120C42—611no—
121C42—611no—
122C42—1222no—
123C42—1224no—
124C42C2×#692311yescharacteristic
125C23—611no—
126Q8—42no—
127Q8—2442no—
128C2×C4—22no—
129C2×C4—611no—
130C2×C4—612no—
131C2×C4—612no—
132C2×C4—611no—
133C2×C4—611no—
134C2×C4—1222no—
135C2×C4—1224no—
136C2×C4—1222no—
137C2×C4—2441no—
138C2×C4—2442no—
139C2×C4—2442no—
140C2×C4C22⋊#692311yescharacteristic
141C2×C4C22⋊#692311yescharacteristic
142C2×C4C22×#692311yescharacteristic
143C8—1224no—
144C22—611no—
145C22—611no—
146C22—1221no—
147C22—1221no—
148C22C2×C22⋊#692311yescharacteristic
149C4—21no—
150C4—42no—
151C4—612no—
152C4—1221no—
153C4—1221no—
154C4—2444no—
155C4—2442no—
156C4#1451984112yes—
157C4Q8×#692312yes—
158C2—1221no—
159C2—1221no—
160C2(C2×#6923)⋊Q811yescharacteristic
161C2C2×#1451984111yescharacteristic
162C2#1684076111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC4⋊Q8×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC4⋊Q8#6923
hypocenterC61#1986
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
30. #11758213Q8semidirect
86. C61#1986semidirect
89. C4⋊Q8#6923semidirect