Finite Group Databasebeta

← #21456960

Subgroups — #21456960

Order 7808.

360 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C2×#14519777C211yesmaximal, characteristic
2#16840158C212yesmaximal, complemented
3#16840112C212yesmaximal, complemented
4#16840090C214yesmaximal
5#16840047C214yesmaximal, complemented
6#16839815C211yesmaximal, characteristic
7C61×#533C211yesmaximal, characteristic
8C22×Dic122—21no—
9#14519777—21no—
10#14519777—21no—
11#14519777C2212yes—
12#14519777C2212yes—
13C2×C4⋊Dic61—21no—
14C2×C4⋊Dic61C2212yes—
15#14519708C2218yes—
16C4⋊#92418C2212yes—
17#14519701C2218yes—
18C22⋊#92418C2212yes—
19C4×#92418C2212yes—
20C4⋊Q8×C61C2211yescharacteristic
21C4⋊Q8×C61C2211yescharacteristic
22#125×C61—21no—
23C22⋊Q8×C61—21no—
24C22⋊Q8×C61C2212yes—
25C4×Q8×C61—21no—
26C4×Q8×C61C2212yes—
27#117×C61—21no—
28C2×C42×C61C2211yescharacteristic
29C2×Q8×C61—21no—
30C2×Q8×C61C2312yes—
31C22×C4×C61D411yescharacteristic
32C22×C4×C61D411yescharacteristic
33C22×C4×C61C2311yescharacteristic
34C22×Dic61—22no—
35C2×Dic122—22no—
36C2×Dic122—22no—
37C2×Dic122—44no—
38C4⋊C4×C61—21no—
39C4⋊C4×C61—21no—
40C4⋊C4×C61—21no—
41C4⋊C4×C61—22no—
42C4⋊C4×C61—22no—
43C4⋊C4×C61C2312yes—
44C22⋊C4×C61—22no—
45C42×C61—22no—
46C42×C61D411yescharacteristic
47C42×C61D411yescharacteristic
48C42×C61C2311yescharacteristic
49C42×C61C2311yescharacteristic
50C4⋊Dic61—22no—
51C4⋊Dic61—22no—
52C4⋊Dic61—22no—
53C4⋊Dic61C2314yes—
54C2×#92418C2314yes—
55C23×C61C2×D411yescharacteristic
56Q8×C61—24no—
57Q8×C61—42no—
58C2×C4×C61—22no—
59C2×C4×C61—22no—
60C2×C4×C61—22no—
61C2×C4×C61—22no—
62C2×C4×C61SD1614yes—
63C2×C4×C61C2×D411yescharacteristic
64C2×C4×C61C2×D411yescharacteristic
65C2×C4×C61C2×D411yescharacteristic
66C2×C4×C61C2×D411yescharacteristic
67C2×C4×C61C2×D411yescharacteristic
68C2×C4×C61C2411yescharacteristic
69C2×Dic61—24no—
70C2×Dic61—44no—
71Dic122—44no—
72Dic122—44no—
73#92418—24no—
74C22×C61—21no—
75C22×C61—21no—
76C22×C61C2×SD1612yes—
77C22×C61C22×D411yescharacteristic
78C4×C61—21no—
79C4×C61—21no—
80C4×C61—42no—
81C4×C61—42no—
82C4×C61C2×SD1612yes—
83C4×C61C2×SD1612yes—
84C4×C61#13712yes—
85C4×C612−1+412yes—
86Dic61—44no—
87#3229—611nomaximal, Sylow
88C2×C61—22no—
89C2×C61#53611yescharacteristic
90C2×C61C22×SD1611yescharacteristic
91C2×C61C2×#13711yescharacteristic
92#533D6111yescharacteristic
93C2×C4⋊Q8—611no—
94#498—612no—
95#487—612no—
96#483—614no—
97#475—614no—
98#431—611no—
99C61#322911yescharacteristic, complemented, Sylow
100C22×Q8—1221no—
101C4⋊Q8—612no—
102C4⋊Q8—612no—
103C4⋊Q8—1221no—
104C4⋊Q8—1221no—
105C4⋊Q8C2×D6111yescharacteristic
106C4⋊Q8C2×D6111yescharacteristic
107#125—21no—
108C22⋊Q8—21no—
109C22⋊Q8C2×D6112yes—
110C4×Q8—21no—
111C4×Q8C2×D6112yes—
112#117—21no—
113C2×C4⋊C4—612no—
114C2×C4⋊C4—1221no—
115C2×C42C2×D6111yescharacteristic
116#106—618no—
117C4⋊C8—612no—
118#103—618no—
119C22⋊C8—612no—
120C4×C8—612no—
121C2×Q8—21no—
122C2×Q8—1222no—
123C2×Q8—1222no—
124C2×Q8—2444no—
125C2×Q8C22×D6112yes—
126C22×C4—1222no—
127C22×C4C22⋊D6111yescharacteristic
128C22×C4C22⋊D6111yescharacteristic
129C22×C4C22×D6111yescharacteristic
130C2×C8—614no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—22no—
135C4⋊C4—22no—
136C4⋊C4—614no—
137C4⋊C4—1222no—
138C4⋊C4—1222no—
139C4⋊C4—1222no—
140C4⋊C4C22×D6112yes—
141C22⋊C4—22no—
142C42—22no—
143C42C22⋊D6111yescharacteristic
144C42C22⋊D6111yescharacteristic
145C42C22×D6111yescharacteristic
146C42C22×D6111yescharacteristic
147C23C2×C22⋊D6111yescharacteristic
148Q8—24no—
149Q8—42no—
150Q8—2444no—
151Q8—2444no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—1224no—
157C2×C4—2444no—
158C2×C4#1175820114yes—
159C2×C4C2×C22⋊D6111yescharacteristic
160C2×C4C2×C22⋊D6111yescharacteristic
161C2×C4C2×C22⋊D6111yescharacteristic
162C2×C4C2×C22⋊D6111yescharacteristic
163C2×C4C2×C22⋊D6111yescharacteristic
164C2×C4C23×D6111yescharacteristic
165C8—1224no—
166C22—21no—
167C22—21no—
168C22C2×#1175820112yes—
169C22C22×C22⋊D6111yescharacteristic
170C4—21no—
171C4—21no—
172C4—42no—
173C4—42no—
174C4—2444no—
175C4C2×#1175820112yes—
176C4C2×#1175820112yes—
177C4#1451980712yes—
178C4#1451982412yes—
179C2—22no—
180C2#1684033311yescharacteristic
181C2C22×#1175820111yescharacteristic
182C2C2×#1451980711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#533C2
socleC22×C61C22×D4
hypercenter#533D61
hypocenterC61#3229
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #16840158C2semidirect
3. #16840112C2semidirect
5. #16840047C2semidirect
99. C61#3229semidirect