Finite Group Databasebeta

← #21461996

Subgroups — #21461996

Order 7808.

260 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 72 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#16840632C212yesmaximal
4#16840632C212yesmaximal
5#16840318C211yesmaximal, characteristic
6C2×#11758213C2212yes—
7C2×C4⋊#6923—21no—
8C2×C4×#6923C2212yes—
9#14519832—21no—
10C4×#92420—21no—
11(C2×#6923)⋊C4—21no—
12#14519776C411yescharacteristic, complemented
13#14519776C411yescharacteristic, complemented
14#14519769C411yescharacteristic, complemented
15#14519755—21no—
16#14519755—21no—
17#14519742—21no—
18#14519742—21no—
19#14519735C2211yescharacteristic
20#14519735C2211yescharacteristic
21C42×D61C2211yescharacteristic
22#125×C61C411yescharacteristic, complemented
23C22×#6923—22no—
24C2×C4×D61D411yescharacteristic
25C2×C4×D61D411yescharacteristic
26C2×C4×D61C2311yescharacteristic
27C2×Dic122—21no—
28C2×Dic122—21no—
29C2×#92420—22no—
30C4⋊#6923—24no—
31C4×#6923—24no—
32#11758213—22no—
33#11758213Q814yescomplemented
34C4⋊C4×C61—21no—
35C4⋊C4×C61—21no—
36C4⋊C4×C61C2×C411yescharacteristic
37C4⋊C4×C61C2×C411yescharacteristic
38C42×C61C2×C411yescharacteristic
39#11758198—21no—
40#11758198—21no—
41C4⋊Dic61C2×C411yescharacteristic
42C4⋊Dic61C2×C411yescharacteristic
43#11758196—21no—
44#11758196—21no—
45#11758196—21no—
46#11758196—21no—
47C4×Dic61—21no—
48C4×Dic61—21no—
49C4×Dic61C2×C411yescharacteristic
50C4×Dic61D411yescharacteristic
51C4×Dic61D411yescharacteristic
52C22×D61C2×D411yescharacteristic
53C2×#6923—24no—
54C2×#6923—42no—
55C2×#6923—42no—
56C2×C4×C61—21no—
57C2×C4×C61—21no—
58C2×C4×C61C22⋊C411yescharacteristic
59C2×C4×C61C22⋊C411yescharacteristic
60C2×C4×C61C22×C411yescharacteristic
61C2×Dic61—21no—
62C2×Dic61—21no—
63C2×Dic61C22⋊C411yescharacteristic
64C2×Dic61C22⋊C411yescharacteristic
65C2×Dic61C2×D411yescharacteristic
66C4×D61—22no—
67C4×D61—41no—
68C4×D61C2×Q812yes—
69C4×D61#4112yes—
70Dic122—42no—
71Dic122—42no—
72#92420—24no—
73C22×C61C2×C22⋊C411yescharacteristic
74C2×D61—21no—
75C2×D61—21no—
76C2×D61#12411yescharacteristic
77C2×D61C4⋊Q811yescharacteristic
78#6923—44no—
79C4×C61—21no—
80C4×C61—21no—
81C4×C61—41no—
82C4×C61—41no—
83C4×C61C4×Q812yes—
84Dic61—21no—
85Dic61—41no—
86Dic61—41no—
87Dic61#10412yes—
88Dic61C22⋊Q812yes—
89#1986—611nomaximal, Sylow
90C2×C61#39111yescharacteristic
91C2×C61C2×#10411yescharacteristic
92C2×C61#42111yescharacteristic
93D61—21no—
94D61—21no—
95#533—611no—
96C4×M16—611no—
97C4×C4⋊C4—611no—
98#339—612no—
99#339—612no—
100C61#198611yescharacteristic, complemented, Sylow
101C2×M16—612no—
102C4⋊Q8—611no—
103C4⋊Q8—611no—
104#125—611no—
105#125#692311yescharacteristic, complemented
106C22⋊Q8—1221no—
107C22⋊Q8—1221no—
108C4×Q8—1221no—
109C4×Q8—1221no—
110#117—611no—
111#117—611no—
112C2×C4⋊C4—1221no—
113C2×C42—611no—
114C2×C42—612no—
115#97—1221no—
116C4×C8—1221no—
117#95—1221no—
118C2×Q8—1221no—
119C2×Q8—1221no—
120C22×C4—611no—
121C22×C4—611no—
122C22×C4—611no—
123C22×C4—1222no—
124M16—614no—
125M16—1222no—
126C2×C8—1222no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—611no—
130C4⋊C4—611no—
131C4⋊C4—1221no—
132C4⋊C4—1221no—
133C4⋊C4—1224no—
134C4⋊C4—1221no—
135C4⋊C4—1221no—
136C4⋊C4C2×#692311yescharacteristic
137C4⋊C4C2×#692311yescharacteristic
138C22⋊C4—1221no—
139C22⋊C4—1221no—
140C42—611no—
141C42—611no—
142C42—611no—
143C42—1221no—
144C42—1221no—
145C42—1224no—
146C42C2×#692311yescharacteristic
147C23—611no—
148Q8—2442no—
149Q8—2442no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—611no—
153C2×C4—611no—
154C2×C4—612no—
155C2×C4—612no—
156C2×C4—611no—
157C2×C4—1222no—
158C2×C4—1224no—
159C2×C4—1221no—
160C2×C4—1221no—
161C2×C4—2441no—
162C2×C4—2442no—
163C2×C4—2442no—
164C2×C4C22⋊#692311yescharacteristic
165C2×C4C22⋊#692311yescharacteristic
166C2×C4C22×#692311yescharacteristic
167C8—1224no—
168C22—611no—
169C22—611no—
170C22—1221no—
171C22—1221no—
172C22C2×C22⋊#692311yescharacteristic
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—612no—
178C4—612no—
179C4—1221no—
180C4—2444no—
181C4—2441no—
182C4—2441no—
183C4Q8×#692312yes—
184C2—1221no—
185C2—1221no—
186C2(C2×#6923)⋊Q811yescharacteristic
187C2D61⋊#10411yescharacteristic
188C2#1684075911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#125×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#125#6923
hypocenterC61#1986
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
12. #14519776C4semidirect
13. #14519776C4semidirect
14. #14519769C4semidirect
22. #125×C61C4semidirect
33. #11758213Q8semidirect
100. C61#1986semidirect
105. #125#6923semidirect