Finite Group Databasebeta

← #21444546

Subgroups — #21444546

Order 7808.

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

normal subgroups only

This group has 202 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#16839784C211yesmaximal, characteristic
4#16839511C211yesmaximal, characteristic, complemented
5#16839509C211yesmaximal, characteristic, complemented
6#16839507C211yesmaximal, characteristic, complemented
7C61×#333C211yesmaximal, characteristic, complemented
8C2×#11758189—21no—
9#14519777C2211yescharacteristic
10#14519768—21no—
11#14519757—21no—
12#14519753C412yes—
13Q8×Dic61C412yes—
14#14519742—21no—
15#14519735—21no—
16C42×D61C2211yescharacteristic
17C4⋊#92418C2211yescharacteristic
18C4⋊#92418C2211yescharacteristic
19#14519706—21no—
20#14519689—21no—
21#14519687—21no—
22C4⋊Q8×C61C2211yescharacteristic
23C4⋊C8×C61C2211yescharacteristic
24C4⋊C8×C61C2211yescharacteristic
25C2×Q8×C61C2×C412yes—
26C2×C4×D61C2×C411yescharacteristic
27C2×C4×D61D411yescharacteristic
28C2×C4×D61D411yescharacteristic
29C2×Dic122—21no—
30C2×C8×C61—21no—
31C2×C8×C61—21no—
32C4⋊C4×C61—21no—
33C4⋊C4×C61—21no—
34C42×C61C2311yescharacteristic
35#11758198—22no—
36C4⋊Dic61—21no—
37C4⋊Dic61—22no—
38C4⋊Dic61C2×C412yes—
39#11758196—22no—
40C4×Dic61—22no—
41C4×Dic61C2×C411yescharacteristic
42C4×Dic61D411yescharacteristic
43C4×Dic61D411yescharacteristic
44C2×#92418—21no—
45C2×#92418—21no—
46#11758189—42no—
47C22×D61C22⋊C411yescharacteristic
48Q8×C61—42no—
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—41no—
63Dic122—41no—
64C8×C61—41no—
65C8×C61—41no—
66#92418—41no—
67#92418—41no—
68C22×C61C2×C22⋊C411yescharacteristic
69C2×D61—21no—
70C2×D61—21no—
71C2×D61—21no—
72C4×C61—21no—
73C4×C61—42no—
74C4×C61AGL(1,ℤ/8)11yescharacteristic
75C4×C61#13711yescharacteristic
76C4×C61#13711yescharacteristic
77C4×C61#13711yescharacteristic
78Dic61—21no—
79Dic61—21no—
80Dic61—21no—
81Dic61—42no—
82#1559—611nomaximal, Sylow
83C2×C61#41311yescharacteristic
84C2×C61#41711yescharacteristic
85C2×C61#41911yescharacteristic
86D61—41no—
87#533—611no—
88#432—611no—
89#423—611no—
90#333—611no—
91#333D6111yescharacteristic, complemented
92#332—611no—
93#332—611no—
94C61#155911yescharacteristic, complemented, Sylow
95C2×M16—1221no—
96C4⋊Q8—611no—
97C4⋊Q8C2×D6111yescharacteristic
98#125—1221no—
99C22⋊Q8—612no—
100C22⋊Q8—1221no—
101C4×Q8—612no—
102C4×Q8—1221no—
103#117—1221no—
104C2×C42—611no—
105C4⋊C8—611no—
106C4⋊C8—611no—
107C4⋊C8—1221no—
108C4⋊C8C2×D6111yescharacteristic
109C4⋊C8C2×D6111yescharacteristic
110C22⋊C8—1221no—
111#97—1221no—
112C2×Q8—1221no—
113C2×Q8C4×D6112yes—
114C22×C4—611no—
115C22×C4—611no—
116C22×C4—611no—
117M16—2442no—
118C2×C8—21no—
119C2×C8—21no—
120C2×C8—1221no—
121C2×C8—1221no—
122C4⋊C4—21no—
123C4⋊C4—21no—
124C4⋊C4—612no—
125C4⋊C4—1222no—
126C4⋊C4—1222no—
127C4⋊C4—1221no—
128C22⋊C4—1222no—
129C42—611no—
130C42—611no—
131C42—611no—
132C42—1222no—
133C42C22×D6111yescharacteristic
134C23—611no—
135Q8—42no—
136Q8—2441no—
137Q8—2441no—
138C2×C4—22no—
139C2×C4—611no—
140C2×C4—611no—
141C2×C4—611no—
142C2×C4—1221no—
143C2×C4—1221no—
144C2×C4—1221no—
145C2×C4—1221no—
146C2×C4—1222no—
147C2×C4—2441no—
148C2×C4C2×C4×D6111yescharacteristic
149C2×C4D4×D6111yescharacteristic
150C2×C4D4×D6111yescharacteristic
151C8—41no—
152C8—41no—
153C8—2441no—
154C8—2441no—
155C22—1221no—
156C22—1221no—
157C22—1221no—
158C22C22⋊C4×D6111yescharacteristic
159C4—21no—
160C4—42no—
161C4—1221no—
162C4—1221no—
163C4—1221no—
164C4—2442no—
165C4#1451980411yescharacteristic
166C4#1451980611yescharacteristic
167C4#1451980911yescharacteristic
168C4#1451980911yescharacteristic
169C2—2441no—
170C2#1683974311yescharacteristic
171C2#1683976211yescharacteristic
172C2#1683976911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#333C2
socleC22×C61C2×C22⋊C4
hypercenter#333D61
hypocenterC61#1559
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
4. #16839511C2semidirect
5. #16839509C2semidirect
6. #16839507C2semidirect
7. C61×#333C2semidirect
91. #333D61semidirect
94. C61#1559semidirect