Finite Group Databasebeta

← #21444526

Subgroups — #21444526

Order 7808.

198 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 65 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#16840317C211yesmaximal, characteristic
2#16839818C211yesmaximal, characteristic
3#16839814C211yesmaximal, characteristic
4#16839510C211yesmaximal, characteristic, complemented
5#16839510C211yesmaximal, characteristic, complemented
6#16839508C211yesmaximal, characteristic, complemented
7C61×#332C211yesmaximal, characteristic, complemented
8#14519777C2211yescharacteristic
9#14519768—21no—
10#14519757C412yes—
11#14519753—21no—
12Q8×Dic61—21no—
13#14519742C412yes—
14#14519735—21no—
15C42×D61C2211yescharacteristic
16C4⋊#92418C2211yescharacteristic
17C4⋊#92418C2211yescharacteristic
18#14519689—21no—
19#14519689—21no—
20#14519687—21no—
21C8×Dic61—21no—
22C4⋊Q8×C61C2211yescharacteristic
23C4⋊C8×C61C2211yescharacteristic
24C4⋊C8×C61C2211yescharacteristic
25C2×Q8×C61—21no—
26C2×C4×D61C2×C411yescharacteristic
27C2×C4×D61D411yescharacteristic
28C2×C4×D61D411yescharacteristic
29C2×Dic122C2×C412yes—
30C2×C8×C61—21no—
31C2×C8×C61—21no—
32C4⋊C4×C61—21no—
33C4⋊C4×C61C2×C412yes—
34C42×C61C2311yescharacteristic
35#11758198—22no—
36C4⋊Dic61—21no—
37C4⋊Dic61—21no—
38C4⋊Dic61—22no—
39#11758196—22no—
40C4×Dic61—22no—
41C4×Dic61C2×C411yescharacteristic
42C4×Dic61D411yescharacteristic
43C4×Dic61D411yescharacteristic
44C2×#92418—21no—
45C2×#92418—21no—
46C22×D61C22⋊C411yescharacteristic
47Q8×C61—41no—
48Q8×C61—41no—
49C2×C4×C61—22no—
50C2×C4×C61C22×C411yescharacteristic
51C2×C4×C61C2×D411yescharacteristic
52C2×C4×C61C2×D411yescharacteristic
53C2×Dic61—22no—
54C2×Dic61C22⋊C411yescharacteristic
55C2×Dic61C22⋊C411yescharacteristic
56C2×Dic61C22⋊C411yescharacteristic
57C4×D61—21no—
58C4×D61—21no—
59C4×D61—21no—
60C4×D61—21no—
61C4×D61—41no—
62Dic122—42no—
63C8×C61—41no—
64C8×C61—41no—
65#92418—41no—
66#92418—41no—
67C22×C61C2×C22⋊C411yescharacteristic
68C2×D61—21no—
69C2×D61—21no—
70C2×D61—21no—
71C4×C61—21no—
72C4×C61—42no—
73C4×C61#13511yescharacteristic
74C4×C61#13511yescharacteristic
75C4×C61#13711yescharacteristic
76C4×C61#13711yescharacteristic
77Dic61—21no—
78Dic61—21no—
79Dic61—21no—
80Dic61—42no—
81#1554—611nomaximal, Sylow
82C2×C61#41311yescharacteristic
83C2×C61#41611yescharacteristic
84C2×C61#41911yescharacteristic
85D61—41no—
86#533—611no—
87#432—611no—
88#431—611no—
89#333—611no—
90#333—611no—
91#332—611no—
92#332D6111yescharacteristic, complemented
93C61#155411yescharacteristic, complemented, Sylow
94C4⋊Q8—611no—
95C4⋊Q8C2×D6111yescharacteristic
96#125—1221no—
97C22⋊Q8—612no—
98C22⋊Q8—1221no—
99C4×Q8—612no—
100C4×Q8—1221no—
101#117—1221no—
102C2×C42—611no—
103C4⋊C8—611no—
104C4⋊C8—611no—
105C4⋊C8C2×D6111yescharacteristic
106C4⋊C8C2×D6111yescharacteristic
107C22⋊C8—1221no—
108C22⋊C8—1221no—
109#97—1221no—
110C4×C8—1221no—
111C2×Q8—21no—
112C2×Q8—612no—
113C22×C4—611no—
114C22×C4—611no—
115C22×C4—611no—
116C2×C8—21no—
117C2×C8—21no—
118C2×C8—1221no—
119C2×C8—1221no—
120C4⋊C4—21no—
121C4⋊C4—1222no—
122C4⋊C4—1222no—
123C4⋊C4—1221no—
124C4⋊C4—1221no—
125C4⋊C4C4×D6112yes—
126C22⋊C4—1222no—
127C42—611no—
128C42—611no—
129C42—611no—
130C42—1222no—
131C42C22×D6111yescharacteristic
132C23—611no—
133Q8—41no—
134Q8—41no—
135Q8—2442no—
136C2×C4—22no—
137C2×C4—611no—
138C2×C4—611no—
139C2×C4—611no—
140C2×C4—1221no—
141C2×C4—1221no—
142C2×C4—1221no—
143C2×C4—1221no—
144C2×C4—1222no—
145C2×C4—2441no—
146C2×C4C2×C4×D6111yescharacteristic
147C2×C4D4×D6111yescharacteristic
148C2×C4D4×D6111yescharacteristic
149C8—41no—
150C8—41no—
151C8—2441no—
152C8—2441no—
153C22—1221no—
154C22—1221no—
155C22—1221no—
156C22C22⋊C4×D6111yescharacteristic
157C4—21no—
158C4—42no—
159C4—1221no—
160C4—1221no—
161C4—1221no—
162C4—2442no—
163C4#1451979611yescharacteristic
164C4#1451979811yescharacteristic
165C4#1451980611yescharacteristic
166C4#1451980911yescharacteristic
167C2—2441no—
168C2#1683974511yescharacteristic
169C2#1683975511yescharacteristic
170C2#1683976911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#332C2
socleC22×C61C2×C22⋊C4
hypercenter#332D61
hypocenterC61#1554
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
4. #16839510C2semidirect
5. #16839510C2semidirect
6. #16839508C2semidirect
7. C61×#332C2semidirect
92. #332D61semidirect
93. C61#1554semidirect