Finite Group Databasebeta

← #21451688

Subgroups — #21451688

Order 7808.

512 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 137 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×C4×D244C211yesmaximal, characteristic
2#16839697C212yesmaximal, complemented
3#16839692C212yesmaximal, complemented
4#16839688C212yesmaximal, complemented
5#16839679C212yesmaximal
6#16839633C214yesmaximal, complemented
7#16839630C211yesmaximal, characteristic, complemented
8C2×#125×C61C211yesmaximal, characteristic, complemented
9C22×D244C2211yescharacteristic
10C22×C4×D61C2212yes—
11C4×D244—24no—
12C2×C4⋊Dic61C2211yescharacteristic
13C2×#11758196C2214yes—
14C2×#11758198C2212yes—
15C2×#11758198C2214yes—
16C2×#11758198C2214yes—
17#14519684C2214yes—
18#14519684C2212yes—
19#14519684C2212yes—
20#14519684C2212yes—
21#125×C61—24no—
22C2×C4⋊C4×C61C2211yescharacteristic
23C2×C4⋊C4×C61C2212yes—
24C2×C4⋊C4×C61C2211yescharacteristic
25C2×C4⋊C4×C61C2212yes—
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—24no—
36C2×D244—22no—
37C2×C4×D61—24no—
38C2×C4×D61—44no—
39C4⋊C4×C61—24no—
40C4⋊C4×C61—22no—
41C4⋊C4×C61—22no—
42C4⋊C4×C61—24no—
43C42×C61D414yes—
44#11758198—28no—
45#11758198—24no—
46#11758198—44no—
47C4⋊Dic61—22no—
48#11758196—44no—
49C23×C61C2411yescharacteristic
50C22×D61—22no—
51C22×D61—22no—
52C22×D61—24no—
53C22×D61—24no—
54C22×D61#4114yes—
55C2×C4×C61—22no—
56C2×C4×C61—22no—
57C2×C4×C61—22no—
58C2×C4×C61—22no—
59C2×C4×C61—22no—
60C2×C4×C61—24no—
61C2×C4×C61—22no—
62C2×C4×C61—22no—
63C2×C4×C61C2×D412yes—
64C2×C4×C61C2×D412yes—
65C2×C4×C61C2×D412yes—
66C2×Dic61—22no—
67C2×Dic61—24no—
68C2×Dic61—24no—
69C2×Dic61—24no—
70C2×Dic61—24no—
71D244—28no—
72C4×D61—48no—
73C22×C61C22×D411yescharacteristic
74C22×C61C2×#4112yes—
75C22×C61H(5,𝔽2)12yes—
76C22×C612−1+412yes—
77C2×D61—24no—
78C2×D61—28no—
79C2×D61—42no—
80C2×D61—42no—
81C2×D61—44no—
82C4×C61—22no—
83C4×C61—22no—
84C4×C61—22no—
85C4×C61—42no—
86C4×C61—42no—
87Dic61—42no—
88Dic61—44no—
89#2633—611nomaximal, Sylow
90C2×C61#52511yescharacteristic
91C2×C61#53511yescharacteristic
92C2×C61#53611yescharacteristic
93C2×C61#53914yes—
94D61—44no—
95C2×#125D6111yescharacteristic, complemented
96C2×C4×D4—611no—
97#399—612no—
98#398—612no—
99#397—612no—
100#394—612no—
101#385—614no—
102#383—611no—
103C61#263311yescharacteristic, complemented, Sylow
104C22×D4—611no—
105C23×C4—612no—
106#125—24no—
107C4×D4—1224no—
108C2×C4⋊C4—611no—
109C2×C4⋊C4—614no—
110C2×C4⋊C4C2×D6112yes—
111C2×C4⋊C4C2×D6112yes—
112C2×C4⋊C4C2×D6111yescharacteristic
113C2×C4⋊C4C2×D6111yescharacteristic
114C2×C22⋊C4—612no—
115C2×C22⋊C4—614no—
116C2×C22⋊C4—614no—
117C2×C42C2×D6111yescharacteristic
118#95—612no—
119#95—612no—
120#95—612no—
121#95—614no—
122C24—612no—
123C2×D4—1224no—
124C2×D4—1222no—
125C22×C4—614no—
126C22×C4—612no—
127C22×C4—1224no—
128C22×C4—2444no—
129C22×C4C22×D6112yes—
130C22×C4C22×D6112yes—
131C22×C4C22×D6111yescharacteristic
132C22×C4C22×D6111yescharacteristic
133C22×C4C22×D6111yescharacteristic
134C4⋊C4—22no—
135C4⋊C4—22no—
136C4⋊C4—24no—
137C4⋊C4—24no—
138C4⋊C4—1222no—
139C4⋊C4—2444no—
140C22⋊C4—1228no—
141C22⋊C4—1224no—
142C22⋊C4—2444no—
143C42C22⋊D6114yes—
144C23—614no—
145C23—1222no—
146C23—1222no—
147C23—1224no—
148C23—1224no—
149C23C23×D6111yescharacteristic
150D4—1228no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—24no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—1222no—
160C2×C4—1224no—
161C2×C4—1224no—
162C2×C4—1224no—
163C2×C4—1224no—
164C2×C4—2448no—
165C2×C4C2×C22⋊D6112yes—
166C2×C4C2×C22⋊D6112yes—
167C2×C4C2×C22⋊D6112yes—
168C22—1224no—
169C22—1228no—
170C22—2442no—
171C22—2442no—
172C22—2444no—
173C22C22×C22⋊D6111yescharacteristic
174C22#41×D6112yes—
175C22#1451982312yes—
176C22#1451982512yes—
177C4—22no—
178C4—22no—
179C4—22no—
180C4—42no—
181C4—42no—
182C4—2442no—
183C4—2444no—
184C2—2444no—
185C2#1684026911yescharacteristic
186C2#1684032611yescharacteristic
187C2#1684033611yescharacteristic
188C2#1684036014yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#125×C61C2
hypercenterC2×#125D61
hypocenterC61#2633
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. #16839692C2semidirect
4. #16839688C2semidirect
6. #16839633C2semidirect
7. #16839630C2semidirect
8. C2×#125×C61C2semidirect
95. C2×#125D61semidirect
103. C61#2633semidirect