Finite Group Databasebeta

← #21461141

Subgroups — #21461141

Order 7808.

218 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 62 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#16840778C211yesmaximal, characteristic
2C4×#11758217C211yesmaximal, characteristic
3#16840612C212yesmaximal, complemented
4Q8⋊#92420C212yesmaximal, complemented
5#16840314C211yesmaximal, characteristic
6C2×#11758217—21no—
7C4⋊#92420C2212yes—
8C22⋊#92420—21no—
9#14519832—21no—
10C4×#92420—21no—
11C4×#92420C2212yes—
12#14519776C411yescharacteristic
13#14519775C411yescharacteristic
14#14519767—21no—
15#14519756C411yescharacteristic
16#14519754—21no—
17Q8×Dic61C2211yescharacteristic
18#14519742—21no—
19#14519742C2211yescharacteristic
20#14519733—21no—
21C2×C4×Dic61C2211yescharacteristic
22C22⋊Q8×C61C411yescharacteristic
23C2×Q8×C61C2×C411yescharacteristic
24C22×C4×C61C2×C411yescharacteristic
25C22×Dic61D411yescharacteristic
26C22×Dic61D411yescharacteristic
27C2×Dic122—21no—
28C2×Dic122C2×C411yescharacteristic
29#11758217—24no—
30C2×#92420—22no—
31C2×#92420—22no—
32C4⋊C4×C61—21no—
33C4⋊C4×C61C2×C411yescharacteristic
34C22⋊C4×C61—21no—
35C22⋊Dic61—21no—
36C4⋊Dic61—21no—
37C4⋊Dic61C2×C411yescharacteristic
38#11758196—21no—
39#11758196—21no—
40#11758196—21no—
41#11758196—21no—
42#11758196—21no—
43C4×Dic61—21no—
44C4×Dic61—21no—
45C4×Dic61C2×C411yescharacteristic
46C4×Dic61D411yescharacteristic
47C4×Dic61D411yescharacteristic
48C4×Dic61C2311yescharacteristic
49C23×C61C22⋊C411yescharacteristic
50Q8×C61—22no—
51C2×C4×C61—22no—
52C2×C4×C61—21no—
53C2×C4×C61—21no—
54C2×C4×C61C22⋊C411yescharacteristic
55C2×C4×C61C22×C411yescharacteristic
56C2×Dic61—22no—
57C2×Dic61—22no—
58C2×Dic61—21no—
59C2×Dic61—21no—
60C2×Dic61C22⋊C411yescharacteristic
61C2×Dic61C22⋊C411yescharacteristic
62C2×Dic61C2×D411yescharacteristic
63C2×Dic61C2×D411yescharacteristic
64Dic122—22no—
65Dic122—42no—
66#92420—24no—
67#92420—42no—
68C22×C61—21no—
69C22×C61—21no—
70C22×C61—21no—
71C22×C61C2×C22⋊C411yescharacteristic
72C4×C61—21no—
73C4×C61—41no—
74C4×C61—41no—
75C4×C61#13112yes—
76Dic61—21no—
77Dic61—21no—
78Dic61—41no—
79Dic61—41no—
80Dic61#10412yes—
81Dic61#13712yes—
82#1485—611nomaximal, Sylow
83C2×C61—41no—
84C2×C61#40811yescharacteristic
85C2×C61#41911yescharacteristic
86C2×C61C2×#10411yescharacteristic
87#533—611no—
88#431—611no—
89C4×M16—611no—
90Q8⋊C8—612no—
91Q8⋊C8—612no—
92C61#148511yescharacteristic, complemented, Sylow
93C2×M16—1221no—
94C4⋊Q8—611no—
95C4⋊Q8—611no—
96#125—1221no—
97C22⋊Q8—611no—
98C22⋊Q8—1221no—
99C22⋊Q8#692311yescharacteristic
100C4×Q8—611no—
101C4×Q8—611no—
102C4×Q8—1221no—
103#117—1221no—
104C2×C42—611no—
105C4⋊C8—612no—
106C22⋊C8—1221no—
107#97—1221no—
108C4×C8—612no—
109C4×C8—1221no—
110C2×Q8—611no—
111C2×Q8—1221no—
112C2×Q8C2×#692311yescharacteristic
113C22×C4—611no—
114C22×C4—611no—
115C22×C4C2×#692311yescharacteristic
116M16—1224no—
117C2×C8—1222no—
118C2×C8—1222no—
119C4⋊C4—21no—
120C4⋊C4—611no—
121C4⋊C4—1221no—
122C4⋊C4—1221no—
123C4⋊C4—1221no—
124C4⋊C4—1221no—
125C4⋊C4—1221no—
126C4⋊C4—1221no—
127C4⋊C4C2×#692311yescharacteristic
128C22⋊C4—21no—
129C22⋊C4—1221no—
130C42—611no—
131C42—611no—
132C42—611no—
133C42—611no—
134C42—1221no—
135C42—1221no—
136C23C22⋊#692311yescharacteristic
137Q8—22no—
138Q8—1222no—
139Q8—2442no—
140C2×C4—22no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—611no—
144C2×C4—611no—
145C2×C4—611no—
146C2×C4—611no—
147C2×C4—1222no—
148C2×C4—1222no—
149C2×C4—1221no—
150C2×C4—1221no—
151C2×C4C22⋊#692311yescharacteristic
152C2×C4C22×#692311yescharacteristic
153C8—1224no—
154C8—2442no—
155C22—21no—
156C22—21no—
157C22—21no—
158C22C2×C22⋊#692311yescharacteristic
159C4—21no—
160C4—41no—
161C4—41no—
162C4—612no—
163C4—612no—
164C4—1221no—
165C4—1221no—
166C4—2441no—
167C4—2441no—
168C4#1451986412yes—
169C2—41no—
170C2#1684073511yescharacteristic
171C2#1684075511yescharacteristic
172C2D61⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC22⋊Q8×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC22⋊Q8#6923
hypocenterC61#1485
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #16840612C2semidirect
4. Q8⋊#92420C2semidirect
92. C61#1485semidirect