Finite Group Databasebeta

← #21456192

Subgroups — #21456192

Order 7808.

484 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 121 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
1#16840318C211yesmaximal, characteristic, complemented
2#127×D61C211yesmaximal, characteristic
3#16840128C211yesmaximal, characteristic, complemented
4#16840127C211yesmaximal, characteristic, complemented
5#16840126C211yesmaximal, characteristic, complemented
6#16840107C214yesmaximal, complemented
7#16839765C214yesmaximal, complemented
8#16839714C211yesmaximal, characteristic, complemented
9C61×#490C211yesmaximal, characteristic, complemented
10C2×D4×D61—22no—
11C2×D4×D61C2212yes—
12C2×#11758189C2212yes—
13#14519776C2212yescomplemented
14#14519774C2211yescharacteristic
15#14519773—22no—
16#14519773C2212yes—
17#14519769C2211yescharacteristic, complemented
18#14519755—22no—
19#14519742—22no—
20#14519735C2212yes—
21C42×D61C2211yescharacteristic
22#14519699C2214yescomplemented
23#14519698C2214yescomplemented
24#14519697C2214yescomplemented
25#14519688C2211yescharacteristic, complemented
26C8×Dic61C2212yescomplemented
27#127×C61C2211yescharacteristic
28#125×C61C2211yescharacteristic, complemented
29#102×C61C2214yescomplemented
30#97×C61C2211yescharacteristic, complemented
31C23×D61—22no—
32C2×D4×C61—22no—
33C2×D4×C61C2312yes—
34C2×C22⋊D61—24no—
35C2×C22⋊D61—22no—
36D4×D61—28no—
37D4×D61—48no—
38C2×D244—22no—
39C2×D244C2312yes—
40C2×C4×D61D412yes—
41C2×C4×D61C2311yescharacteristic
42C2×Dic122—22no—
43C2×C8×C61C2312yes—
44C4⋊C4×C61—22no—
45C4⋊C4×C61C2312yes—
46C42×C61C2311yescharacteristic
47#11758198—22no—
48C4⋊Dic61C2312yes—
49#11758196—22no—
50#11758196—22no—
51C4×Dic61—22no—
52C4×Dic61D412yes—
53C4×Dic61C2311yescharacteristic
54C2×#92418C2312yes—
55#11758189—24no—
56C23×C61—22no—
57C22×D61—22no—
58C22×D61—48no—
59C22×D61—44no—
60C22×D61C2×D411yescharacteristic
61D4×C61—24no—
62D4×C61—44no—
63C2×C4×C61—22no—
64C2×C4×C61C2×D412yes—
65C2×C4×C61C2411yescharacteristic
66C22⋊D61—44no—
67C22⋊D61—48no—
68C2×Dic61—22no—
69C2×Dic61C2×D411yescharacteristic
70C2×Dic61C2×D412yes—
71D244—24no—
72D244—44no—
73C4×D61—24no—
74C4×D61#4114yes—
75Dic122—44no—
76C8×C61—22no—
77#92418—22no—
78C22×C61—42no—
79C22×C61—44no—
80C22×C61C22×D411yescharacteristic
81C2×D61—22no—
82C2×D61—42no—
83C2×D61—44no—
84C2×D61—88no—
85C2×D61#12412yes—
86C4×C61—22no—
87C4×C61—42no—
88C4×C61C2×#4112yes—
89Dic61—42no—
90Dic61#12412yes—
91Dic61AGL(1,ℤ/8)14yes—
92#3138—611nomaximal, Sylow
93C2×C61—82no—
94C2×C61C2×#12411yescharacteristic
95C2×C61C2×AGL(1,ℤ/8)12yes—
96D61—22no—
97D61—82no—
98#533—611no—
99C2×#127—611no—
100#490—611no—
101#490—611no—
102#490—611no—
103#490D6111yescharacteristic, complemented
104#486—614no—
105#418—614no—
106C4×M16—611no—
107C61#313811yescharacteristic, complemented, Sylow
108C22×D4—612no—
109C22×D4—1222no—
110C2×M16—612no—
111C4⋊Q8—612no—
112#127—612no—
113#127—611no—
114#127—1222no—
115#127C2×D6111yescharacteristic
116#125—611no—
117#125C2×D6111yescharacteristic, complemented
118C22⋊Q8—1222no—
119C4×Q8—1222no—
120#117—612no—
121C2×C42—611no—
122#102—614no—
123#102—614no—
124#102—614no—
125#102C2×D6114yescomplemented
126#97—611no—
127#97C2×D6111yescharacteristic, complemented
128C4×C8—612no—
129C24—1222no—
130C2×Q8—1222no—
131C2×D4—22no—
132C2×D4—612no—
133C2×D4—1228no—
134C2×D4—1224no—
135C2×D4—1222no—
136C2×D4—1222no—
137C2×D4—2448no—
138C2×D4C22×D6112yes—
139C22×C4—611no—
140C22×C4—612no—
141M16—1224no—
142C2×C8—612no—
143C2×C8C22×D6112yes—
144C4⋊C4—22no—
145C4⋊C4—612no—
146C4⋊C4—1222no—
147C4⋊C4—1222no—
148C4⋊C4C22×D6112yes—
149C22⋊C4—1222no—
150C42—612no—
151C42—611no—
152C42—1222no—
153C42C22×D6111yescharacteristic
154C23—22no—
155C23—611no—
156C23—1222no—
157C23—2444no—
158C23—2448no—
159Q8—2444no—
160D4—24no—
161D4—44no—
162D4—1224no—
163D4—2444no—
164D4—2444no—
165D4—2448no—
166C2×C4—22no—
167C2×C4—611no—
168C2×C4—612no—
169C2×C4—614no—
170C2×C4—1224no—
171C2×C4—1222no—
172C2×C4D4×D6112yes—
173C2×C4C23×D6111yescharacteristic
174C8—22no—
175C8—1222no—
176C22—42no—
177C22—44no—
178C22—612no—
179C22—1222no—
180C22—4888no—
181C22—2442no—
182C22—2444no—
183C22C2×D4×D6111yescharacteristic
184C4—22no—
185C4—42no—
186C4—612no—
187C4—614no—
188C4—2442no—
189C4#41×D6112yes—
190C2—82no—
191C2—1222no—
192C2—4882no—
193C2#124×D6111yescharacteristic
194C2AGL(1,ℤ/8)×D6112yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#490C2
socleC22×C61C22×D4
hypercenter#490D61
hypocenterC61#3138
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #16840318C2semidirect
3. #16840128C2semidirect
4. #16840127C2semidirect
5. #16840126C2semidirect
6. #16840107C2semidirect
7. #16839765C2semidirect
8. #16839714C2semidirect
9. C61×#490C2semidirect
13. #14519776C22semidirect
17. #14519769C22semidirect
22. #14519699C22semidirect
23. #14519698C22semidirect
24. #14519697C22semidirect
25. #14519688C22semidirect
26. C8×Dic61C22semidirect
28. #125×C61C22semidirect
29. #102×C61C22semidirect
30. #97×C61C22semidirect
103. #490D61semidirect
107. C61#3138semidirect
117. #125C2×D61semidirect
125. #102C2×D61semidirect
127. #97C2×D61semidirect