Finite Group Databasebeta

← #21453869

Subgroups — #21453869

Order 7808.

464 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14519765C211yesmaximal, characteristic
2#16839697C212yesmaximal, complemented
3#16839688C212yesmaximal, complemented
4#16839684C214yesmaximal, complemented
5#16839682C212yesmaximal, complemented
6#16839679C212yesmaximal
7#16839628C211yesmaximal, characteristic, complemented
8C2×#125×C61C211yesmaximal, characteristic, complemented
9C22×Dic122C2211yescharacteristic
10C22×D244C2211yescharacteristic
11#14519765—24no—
12C2×C4⋊Dic61C2212yes—
13C2×#11758196C2214yes—
14C2×#11758198C2212yes—
15C2×#11758198C2212yes—
16C2×#11758198C2214yes—
17C2×#11758198C2214yes—
18#14519684C2214yes—
19#14519684C2212yes—
20#14519684C2212yes—
21#125×C61—24no—
22C2×C4⋊C4×C61C2212yes—
23C2×C4⋊C4×C61C2212yes—
24C2×C4⋊C4×C61C2211yescharacteristic
25C2×C4⋊C4×C61C2211yescharacteristic
26C2×C42×C61C2211yescharacteristic
27C23×D61C2312yes—
28C22×C4×C61C2312yes—
29C22×C4×C61C2312yes—
30C22×C4×C61C2311yescharacteristic
31C22×C4×C61C2311yescharacteristic
32C22×C4×C61C2311yescharacteristic
33C22×Dic61C2312yes—
34C22×Dic61C2314yes—
35C2×D244—22no—
36C2×D244—42no—
37C2×Dic122—22no—
38C2×Dic122—42no—
39C4⋊C4×C61—24no—
40C4⋊C4×C61—22no—
41C4⋊C4×C61—22no—
42C4⋊C4×C61—24no—
43C42×C61D414yes—
44#11758198—24no—
45#11758198—24no—
46#11758198—44no—
47#11758198—44no—
48C4⋊Dic61—42no—
49#11758196—44no—
50C23×C61C2411yescharacteristic
51C22×D61—22no—
52C22×D61—22no—
53C22×D61—24no—
54C22×D61—24no—
55C22×D61—22no—
56C2×C4×C61—21no—
57C2×C4×C61—22no—
58C2×C4×C61—22no—
59C2×C4×C61—21no—
60C2×C4×C61—22no—
61C2×C4×C61—22no—
62C2×C4×C61—24no—
63C2×C4×C61—22no—
64C2×C4×C61—22no—
65C2×C4×C61C2×D412yes—
66C2×C4×C61C2×D412yes—
67C2×C4×C61C2×D412yes—
68C2×Dic61—22no—
69C2×Dic61—24no—
70C2×Dic61—24no—
71C2×Dic61—24no—
72C2×Dic61—24no—
73D244—44no—
74Dic122—44no—
75C22×C61C22×D411yescharacteristic
76C22×C61H(5,𝔽2)12yes—
77C22×C61H(5,𝔽2)11yescharacteristic
78C22×C612−1+411yescharacteristic
79C22×C612−1+412yes—
80C2×D61—42no—
81C2×D61—42no—
82C2×D61—42no—
83C2×D61—44no—
84C2×D61—44no—
85C4×C61—22no—
86C4×C61—22no—
87C4×C61—22no—
88C4×C61—42no—
89C4×C61—42no—
90Dic61—42no—
91Dic61—44no—
92#2820—611nomaximal, Sylow
93C2×C61#53511yescharacteristic
94C2×C61#53611yescharacteristic
95C2×C61#53711yescharacteristic
96C2×C61#56212yes—
97C2×C61#56312yes—
98D61—82no—
99C2×#125D6111yescharacteristic, complemented
100C2×#124—611no—
101#399—612no—
102#397—612no—
103#396—614no—
104#395—612no—
105#394—612no—
106#382—611no—
107C61#282011yescharacteristic, complemented, Sylow
108C22×Q8—611no—
109C22×D4—611no—
110#125—24no—
111#124—1224no—
112C2×C4⋊C4—612no—
113C2×C4⋊C4—614no—
114C2×C4⋊C4C2×D6112yes—
115C2×C4⋊C4C2×D6112yes—
116C2×C4⋊C4C2×D6111yescharacteristic
117C2×C4⋊C4C2×D6111yescharacteristic
118C2×C22⋊C4—612no—
119C2×C22⋊C4—612no—
120C2×C22⋊C4—614no—
121C2×C22⋊C4—614no—
122C2×C42C2×D6111yescharacteristic
123#95—612no—
124#95—612no—
125#95—614no—
126C24—612no—
127C2×Q8—1222no—
128C2×Q8—2442no—
129C2×D4—1222no—
130C2×D4—2442no—
131C22×C4—614no—
132C22×C4—612no—
133C22×C4C22×D6112yes—
134C22×C4C22×D6112yes—
135C22×C4C22×D6111yescharacteristic
136C22×C4C22×D6111yescharacteristic
137C22×C4C22×D6111yescharacteristic
138C4⋊C4—24no—
139C4⋊C4—22no—
140C4⋊C4—22no—
141C4⋊C4—24no—
142C4⋊C4—2444no—
143C4⋊C4—2442no—
144C22⋊C4—1224no—
145C22⋊C4—1224no—
146C22⋊C4—2444no—
147C22⋊C4—2444no—
148C42C22⋊D6114yes—
149C23—1222no—
150C23—1222no—
151C23—1224no—
152C23—1222no—
153C23—1224no—
154C23C23×D6111yescharacteristic
155Q8—2444no—
156D4—2444no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—24no—
165C2×C4—22no—
166C2×C4—1222no—
167C2×C4—1224no—
168C2×C4—1224no—
169C2×C4—1224no—
170C2×C4—1224no—
171C2×C4C2×C22⋊D6112yes—
172C2×C4C2×C22⋊D6112yes—
173C2×C4C2×C22⋊D6112yes—
174C22—2444no—
175C22—2444no—
176C22—2442no—
177C22—2442no—
178C22—2442no—
179C22C22×C22⋊D6111yescharacteristic
180C22#1451982311yescharacteristic
181C22#1451982312yes—
182C22#1451982411yescharacteristic
183C22#1451982512yes—
184C4—22no—
185C4—22no—
186C4—22no—
187C4—42no—
188C4—42no—
189C4—2444no—
190C4—2442no—
191C2—4882no—
192C2#1684032611yescharacteristic
193C2#1684033611yescharacteristic
194C2#1684034011yescharacteristic
195C2#1684051012yes—
196C2#1684051612yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#125×C61C2
hypercenterC2×#125D61
hypocenterC61#2820
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. #16839697C2semidirect
3. #16839688C2semidirect
4. #16839684C2semidirect
5. #16839682C2semidirect
7. #16839628C2semidirect
8. C2×#125×C61C2semidirect
99. C2×#125D61semidirect
107. C61#2820semidirect