Finite Group Databasebeta

← #21456764

Subgroups — #21456764

Order 7808.

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

normal subgroups only

This group has 384 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#16840141C212yesmaximal, complemented
3#16840114C212yesmaximal, complemented
4#16839972C214yesmaximal, complemented
5#16839917C214yesmaximal
6#16839815C211yesmaximal, characteristic
7C61×#533C211yesmaximal, characteristic
8C22×Dic122C2212yes—
9C2×#11758202C2218yes—
10#14519777—21no—
11#14519777—21no—
12#14519777C2212yes—
13#14519777C2212yes—
14C2×C4⋊Dic61—21no—
15C2×C4⋊Dic61—21no—
16C4⋊#92418C2212yes—
17#14519700C2218yes—
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—44no—
37C2×Dic122C2314yes—
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
50#11758202—48no—
51C4⋊Dic61—22no—
52C4⋊Dic61—22no—
53C4⋊Dic61—22no—
54C4⋊Dic61—22no—
55C2×#92418C2314yes—
56C23×C61C2×D411yescharacteristic
57Q8×C61—24no—
58Q8×C61—42no—
59C2×C4×C61—22no—
60C2×C4×C61—22no—
61C2×C4×C61—22no—
62C2×C4×C61—22no—
63C2×C4×C61Q1614yescomplemented
64C2×C4×C61C2×D411yescharacteristic
65C2×C4×C61C2×D411yescharacteristic
66C2×C4×C61C2×D411yescharacteristic
67C2×C4×C61C2×D411yescharacteristic
68C2×C4×C61C2×D411yescharacteristic
69C2×C4×C61C2411yescharacteristic
70C2×Dic61—24no—
71C2×Dic61—44no—
72Dic122—28no—
73Dic122—44no—
74#92418—24no—
75C22×C61—21no—
76C22×C61—21no—
77C22×C61C2×Q1612yes—
78C22×C61C22×D411yescharacteristic
79C4×C61—21no—
80C4×C61—21no—
81C4×C61—42no—
82C4×C61—42no—
83C4×C61C2×Q1612yes—
84C4×C61C2×Q1612yes—
85C4×C61#13712yes—
86C4×C61H(5,𝔽2)12yes—
87Dic61—44no—
88#3209—611nomaximal, Sylow
89C2×C61—22no—
90C2×C61#53511yescharacteristic
91C2×C61C22×Q1611yescharacteristic
92C2×C61C2×#13711yescharacteristic
93#533D6111yescharacteristic
94C2×C4⋊Q8—611no—
95#494—612no—
96#487—612no—
97#462—614no—
98#451—614no—
99#431—611no—
100C61#320911yescharacteristic, complemented, Sylow
101C22×Q8—612no—
102C2×Q16—618no—
103C4⋊Q8—612no—
104C4⋊Q8—612no—
105C4⋊Q8—1221no—
106C4⋊Q8—1221no—
107C4⋊Q8C2×D6111yescharacteristic
108C4⋊Q8C2×D6111yescharacteristic
109#125—21no—
110C22⋊Q8—21no—
111C22⋊Q8C2×D6112yes—
112C4×Q8—21no—
113C4×Q8C2×D6112yes—
114#117—21no—
115C2×C4⋊C4—1221no—
116C2×C4⋊C4—1221no—
117C2×C42C2×D6111yescharacteristic
118C4⋊C8—612no—
119#103—618no—
120C22⋊C8—612no—
121C4×C8—612no—
122C2×Q8—21no—
123C2×Q8—614no—
124C2×Q8—1222no—
125C2×Q8—2444no—
126C2×Q8C22×D6112yes—
127C22×C4—1222no—
128C22×C4C22⋊D6111yescharacteristic
129C22×C4C22⋊D6111yescharacteristic
130C22×C4C22×D6111yescharacteristic
131Q16—2448no—
132C2×C8—614no—
133C4⋊C4—21no—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—22no—
137C4⋊C4—22no—
138C4⋊C4—1222no—
139C4⋊C4—1222no—
140C4⋊C4—1222no—
141C4⋊C4—1222no—
142C4⋊C4C22×D6112yes—
143C22⋊C4—22no—
144C42—22no—
145C42C22⋊D6111yescharacteristic
146C42C22⋊D6111yescharacteristic
147C42C22×D6111yescharacteristic
148C42C22×D6111yescharacteristic
149C23C2×C22⋊D6111yescharacteristic
150Q8—24no—
151Q8—42no—
152Q8—1228no—
153Q8—2444no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—1224no—
159C2×C4—2444no—
160C2×C4#1175820214yescomplemented
161C2×C4C2×C22⋊D6111yescharacteristic
162C2×C4C2×C22⋊D6111yescharacteristic
163C2×C4C2×C22⋊D6111yescharacteristic
164C2×C4C2×C22⋊D6111yescharacteristic
165C2×C4C2×C22⋊D6111yescharacteristic
166C2×C4C23×D6111yescharacteristic
167C8—1224no—
168C22—21no—
169C22—21no—
170C22C2×#1175820212yes—
171C22C22×C22⋊D6111yescharacteristic
172C4—21no—
173C4—21no—
174C4—42no—
175C4—42no—
176C4—2444no—
177C4C2×#1175820212yes—
178C4C2×#1175820212yes—
179C4#1451980712yes—
180C4#1451982312yes—
181C2—22no—
182C2#1684032611yescharacteristic
183C2C22×#1175820211yescharacteristic
184C2C2×#1451980711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#533C2
socleC22×C61C22×D4
hypercenter#533D61
hypocenterC61#3209
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. #16840141C2semidirect
3. #16840114C2semidirect
4. #16839972C2semidirect
63. C2×C4×C61Q16semidirect
100. C61#3209semidirect
160. C2×C4#11758202semidirect