Finite Group Databasebeta

← #21444508

Subgroups — #21444508

Order 7808.

216 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 73 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#16839784C211yesmaximal, characteristic
3C4⋊C8×D61C211yesmaximal, characteristic
4#16839510C211yesmaximal, characteristic, complemented
5#16839510C211yesmaximal, characteristic, complemented
6#16839508C211yesmaximal, characteristic, complemented
7C61×#332C211yesmaximal, characteristic, complemented
8C2×#11758189—21no—
9C2×C8×D61—21no—
10#14519777C2211yescharacteristic
11#14519768—21no—
12#14519757C412yes—
13#14519753—21no—
14Q8×Dic61—21no—
15#14519742C412yes—
16#14519735—21no—
17C42×D61C2211yescharacteristic
18C4⋊#92418C2211yescharacteristic
19C4⋊#92418C2211yescharacteristic
20#14519706—21no—
21#14519706—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—
46#11758189—42no—
47C8×D61—42no—
48C22×D61C22⋊C411yescharacteristic
49Q8×C61—41no—
50Q8×C61—41no—
51C2×C4×C61—22no—
52C2×C4×C61C22×C411yescharacteristic
53C2×C4×C61C2×D411yescharacteristic
54C2×C4×C61C2×D411yescharacteristic
55C2×Dic61—22no—
56C2×Dic61C22⋊C411yescharacteristic
57C2×Dic61C22⋊C411yescharacteristic
58C2×Dic61C22⋊C411yescharacteristic
59C4×D61—21no—
60C4×D61—21no—
61C4×D61—41no—
62C4×D61SD1612yes—
63C4×D61Q1612yes—
64Dic122—42no—
65C8×C61—41no—
66C8×C61—41no—
67#92418—41no—
68#92418—41no—
69C22×C61C2×C22⋊C411yescharacteristic
70C2×D61—21no—
71C2×D61—21no—
72C2×D61#10312yes—
73C4×C61—21no—
74C4×C61—42no—
75C4×C61C2×SD1611yescharacteristic
76C4×C61C2×Q1611yescharacteristic
77C4×C61AGL(1,ℤ/8)11yescharacteristic
78C4×C61#13711yescharacteristic
79Dic61—21no—
80Dic61—21no—
81Dic61—42no—
82Dic61#10312yes—
83#1550—611nomaximal, Sylow
84C2×C61#41311yescharacteristic
85C2×C61C2×#10311yescharacteristic
86C2×C61#41711yescharacteristic
87D61—22no—
88#533—611no—
89#423—611no—
90C2×C4⋊C8—611no—
91#333—611no—
92#333—611no—
93#332—611no—
94#332D6111yescharacteristic, complemented
95C61#155011yescharacteristic, complemented, Sylow
96C2×M16—1221no—
97C22×C8—1221no—
98C4⋊Q8—611no—
99C4⋊Q8C2×D6111yescharacteristic
100#125—1221no—
101C22⋊Q8—612no—
102C22⋊Q8—1221no—
103C4×Q8—612no—
104C4×Q8—1221no—
105#117—1221no—
106C2×C42—611no—
107C4⋊C8—611no—
108C4⋊C8—611no—
109C4⋊C8—1221no—
110C4⋊C8—1221no—
111C4⋊C8C2×D6111yescharacteristic
112C4⋊C8C2×D6111yescharacteristic
113C2×Q8—21no—
114C2×Q8—612no—
115C22×C4—611no—
116C22×C4—611no—
117C22×C4—611no—
118M16—2442no—
119C2×C8—21no—
120C2×C8—21no—
121C2×C8—1221no—
122C2×C8—1221no—
123C2×C8—2442no—
124C4⋊C4—21no—
125C4⋊C4—1222no—
126C4⋊C4—1222no—
127C4⋊C4—1221no—
128C4⋊C4—1221no—
129C4⋊C4C4×D6112yes—
130C22⋊C4—1222no—
131C42—611no—
132C42—611no—
133C42—611no—
134C42—1222no—
135C42C22×D6111yescharacteristic
136C23—611no—
137Q8—41no—
138Q8—41no—
139Q8—2442no—
140C2×C4—22no—
141C2×C4—611no—
142C2×C4—612no—
143C2×C4—612no—
144C2×C4—611no—
145C2×C4—611no—
146C2×C4—1221no—
147C2×C4—1221no—
148C2×C4—1222no—
149C2×C4—2441no—
150C2×C4C2×C4×D6111yescharacteristic
151C2×C4D4×D6111yescharacteristic
152C2×C4D4×D6111yescharacteristic
153C8—41no—
154C8—41no—
155C8—2441no—
156C8—2441no—
157C22—612no—
158C22—1221no—
159C22—1221no—
160C22C22⋊C4×D6111yescharacteristic
161C4—21no—
162C4—42no—
163C4—612no—
164C4—1221no—
165C4—1221no—
166C4—2442no—
167C4SD16×D6111yescharacteristic
168C4Q16×D6111yescharacteristic
169C4#1451980111yescharacteristic
170C4#1451980611yescharacteristic
171C2—1222no—
172C2#1683974511yescharacteristic
173C2#103×D6111yescharacteristic
174C2#1683976011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#332C2
socleC22×C61C2×C22⋊C4
hypercenter#332D61
hypocenterC61#1550
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
94. #332D61semidirect
95. C61#1550semidirect