Finite Group Databasebeta

← #21453814

Subgroups — #21453814

Order 7808.

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

normal subgroups only

This group has 712 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×#14519746C211yesmaximal, characteristic, complemented
2#16839690C213yesmaximal, complemented
3#16839677C213yesmaximal, complemented
4#16839676C213yesmaximal, complemented
5#16839670C213yesmaximal, complemented
6#16839618C211yesmaximal, characteristic, complemented
7C2×#120×C61C211yesmaximal, characteristic, complemented
8C22×C22⋊D61C2213yes—
9C22×C22⋊D61C2211yescharacteristic, complemented
10#14519746—24no—
11C2×#11758196C2213yescomplemented
12C2×C22⋊Dic61C2213yes—
13C2×C22⋊Dic61C2213yes—
14C2×C22⋊Dic61C2213yes—
15C2×C22⋊Dic61C2213yescomplemented
16C2×#11758198C2213yescomplemented
17#14519684C2213yescomplemented
18#14519684C2213yescomplemented
19C25×C61C2211yescharacteristic
20C22×D4×C61C2213yes—
21#120×C61—24no—
22C2×C22⋊C4×C61C2213yes—
23C24×C61—43no—
24C24×C61—43no—
25C24×C61D414yescomplemented
26C24×C61C2311yescharacteristic
27C24×C61C2313yes—
28C23×D61C2311yescharacteristic
29C2×D4×C61—26no—
30C2×D4×C61—43no—
31C2×D4×C61—43no—
32C22×C4×C61C2313yes—
33C2×C22⋊D61—26no—
34C2×C22⋊D61—43no—
35C2×C22⋊D61—43no—
36C2×C22⋊D61—43no—
37C22×Dic61C2313yes—
38C22×Dic61C2311yescharacteristic
39C22×Dic61C2313yes—
40C22⋊C4×C61—26no—
41C22⋊Dic61—26no—
42C22⋊Dic61—43no—
43C22⋊Dic61—43no—
44C22⋊Dic61—43no—
45#11758198—43no—
46#11758196—43no—
47C23×C61—23no—
48C23×C61—23no—
49C23×C61—23no—
50C23×C61—23no—
51C23×C61—23no—
52C23×C61—23no—
53C23×C61—21no—
54C23×C61—23no—
55C23×C61—23no—
56C23×C61—412no—
57C23×C61—412no—
58C23×C61—44no—
59C23×C61C2×D416yes—
60C23×C61C2411yescharacteristic
61C22×D61—21no—
62C22×D61—23no—
63C22×D61—23no—
64D4×C61—412no—
65C2×C4×C61—23no—
66C2×C4×C61—23no—
67C2×C4×C61—23no—
68C22⋊D61—412no—
69C22⋊D61—44no—
70C2×Dic61—23no—
71C2×Dic61—23no—
72C2×Dic61—23no—
73C2×Dic61—23no—
74C2×Dic61—23no—
75C2×Dic61—23no—
76C2×Dic61—23no—
77C22×C61—26no—
78C22×C61—26no—
79C22×C61—26no—
80C22×C61—416no—
81C22×C61—43no—
82C22×C61—43no—
83C22×C61—43no—
84C22×C61—43no—
85C22×C61—43no—
86C22×C61—43no—
87C22×C61—41no—
88C22×C61C22×D411yescharacteristic
89C22×C61H(5,𝔽2)13yes—
90C22×C61H(5,𝔽2)13yes—
91C2×D61—43no—
92C2×D61—43no—
93C2×D61—41no—
94C4×C61—43no—
95Dic61—43no—
96Dic61—43no—
97Dic61—41no—
98#2812—611nomaximal, Sylow
99C2×C61—46no—
100C2×C61—81no—
101C2×C61#53413yes—
102C2×C61#56013yes—
103C2×C61H(3,𝔽4)11yescharacteristic
104D61—81no—
105C2×#120—611no—
106C2×#120D6111yescharacteristic, complemented
107#397—613no—
108#394—613no—
109#394—613no—
110#392—613no—
111#379—611no—
112C61#281211yescharacteristic, complemented, Sylow
113C25C2×D6111yescharacteristic
114C22×D4—613no—
115C22×D4—611no—
116C22×D4C2×D6113yes—
117#120—24no—
118#120—1224no—
119C2×C4⋊C4—613no—
120C2×C22⋊C4—613no—
121C2×C22⋊C4—613no—
122C2×C22⋊C4—613no—
123C2×C22⋊C4—613no—
124C2×C22⋊C4—613no—
125C2×C22⋊C4C2×D6113yes—
126#95—613no—
127#95—613no—
128C24—43no—
129C24—43no—
130C24—611no—
131C24C22⋊D6114yescomplemented
132C24C22×D6111yescharacteristic
133C24C22×D6113yes—
134C2×D4—26no—
135C2×D4—43no—
136C2×D4—43no—
137C2×D4—1226no—
138C2×D4—2443no—
139C2×D4—2443no—
140C2×D4—2443no—
141C22×C4—611no—
142C22×C4—613no—
143C22×C4—613no—
144C22×C4C22×D6113yes—
145C4⋊C4—2443no—
146C22⋊C4—26no—
147C22⋊C4—1226no—
148C22⋊C4—2443no—
149C22⋊C4—2443no—
150C22⋊C4—2443no—
151C22⋊C4—2443no—
152C23—23no—
153C23—23no—
154C23—23no—
155C23—23no—
156C23—23no—
157C23—23no—
158C23—21no—
159C23—23no—
160C23—23no—
161C23—412no—
162C23—412no—
163C23—44no—
164C23—1221no—
165C23—1223no—
166C23—1223no—
167C23C2×C22⋊D6116yes—
168C23C23×D6111yescharacteristic
169D4—412no—
170D4—24412no—
171D4—2444no—
172C2×C4—23no—
173C2×C4—23no—
174C2×C4—23no—
175C2×C4—1223no—
176C2×C4—1223no—
177C2×C4—1223no—
178C2×C4—1223no—
179C2×C4—1223no—
180C2×C4—1223no—
181C2×C4—1223no—
182C22—26no—
183C22—26no—
184C22—26no—
185C22—416no—
186C22—43no—
187C22—43no—
188C22—43no—
189C22—43no—
190C22—43no—
191C22—41no—
192C22—43no—
193C22—2443no—
194C22—2441no—
195C22—2443no—
196C22C22×C22⋊D6111yescharacteristic
197C22#1451982213yes—
198C22#1451982213yes—
199C4—43no—
200C4—2443no—
201C4—2441no—
202C4—2443no—
203C2—46no—
204C2—81no—
205C2—4881no—
206C2#1684032113yes—
207C2#1684050113yes—
208C2#1684050511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#120×C61C2
hypercenterC2×#120D61
hypocenterC61#2812
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×#14519746C2semidirect
2. #16839690C2semidirect
3. #16839677C2semidirect
4. #16839676C2semidirect
5. #16839670C2semidirect
6. #16839618C2semidirect
7. C2×#120×C61C2semidirect
9. C22×C22⋊D61C22semidirect
11. C2×#11758196C22semidirect
15. C2×C22⋊Dic61C22semidirect
16. C2×#11758198C22semidirect
17. #14519684C22semidirect
18. #14519684C22semidirect
25. C24×C61D4semidirect
106. C2×#120D61semidirect
112. C61#2812semidirect
131. C24C22⋊D61semidirect