Finite Group Databasebeta

← #21454621

Subgroups — #21454621

Order 7808.

492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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×#14519799C211yesmaximal, characteristic
2C4×#11758222C212yesmaximal, complemented
3#16839875C212yesmaximal, complemented
4#16839870C212yesmaximal, complemented
5#16839864C214yesmaximal, complemented
6#16839800C211yesmaximal, characteristic, complemented
7#16839759C212yesmaximal, complemented
8C2×#97×C61C211yesmaximal, characteristic, complemented
9C2×#11758222C2212yes—
10#14519799C418yescomplemented
11C2×Dic244C2211yescharacteristic
12C2×#11758190C2212yes—
13C2×D488C2211yescharacteristic
14C4×Dic122C2214yes—
15C4×D244C2214yes—
16C4×C22⋊D61—24no—
17#14519736C2212yes—
18#14519734—22no—
19C42×D61—22no—
20#14519711C2212yes—
21#14519709C2212yes—
22#14519702C2214yes—
23#14519699C2214yes—
24C22×C8×C61C2211yescharacteristic
25C22×C8×C61C2211yescharacteristic
26C2×C42×C61C2211yescharacteristic
27#97×C61C2212yes—
28#97×C61C2212yes—
29C22×C4×C61D412yes—
30C22×C4×C61C2311yescharacteristic
31C2×C22⋊D61—22no—
32#11758222—24no—
33#11758222C2×C418yescomplemented
34C2×D244C2312yes—
35C2×C4×D61—22no—
36C2×C4×D61—24no—
37C2×Dic122C2312yes—
38C2×C8×C61—22no—
39C2×C8×C61C2×C414yescomplemented
40C2×C8×C61C2312yes—
41C2×C8×C61C2311yescharacteristic
42C2×C8×C61C2311yescharacteristic
43C42×C61D412yes—
44C42×C61C2312yes—
45C22⋊Dic61—22no—
46#11758198—24no—
47C4⋊Dic61C2314yes—
48#11758196—24no—
49C4×Dic61—22no—
50C4×Dic61—24no—
51Dic244C2×C414yescomplemented
52D488C2×C414yescomplemented
53#11758190C2×C418yescomplemented
54C23×C61C2×D411yescharacteristic
55C22×D61—22no—
56C2×C4×C61—42no—
57C2×C4×C61C22×C412yes—
58C2×C4×C61C2×D414yes—
59C2×C4×C61C2×D411yescharacteristic
60C2×C4×C61#4112yes—
61C2×C4×C61C2411yescharacteristic
62C22⋊D61—28no—
63C2×Dic61—22no—
64C2×Dic61—24no—
65D244—22no—
66D244C22×C414yes—
67C4×D61—28no—
68C4×D61—48no—
69Dic122—22no—
70Dic122C22×C414yes—
71C8×C61—22no—
72C8×C61C22×C412yes—
73C8×C61C22×C412yes—
74C22×C61—22no—
75C22×C61C4×D412yes—
76C22×C61C22×D411yescharacteristic
77C2×D61—24no—
78C2×D61—44no—
79C4×C61—24no—
80C4×C61C4×D412yes—
81C4×C61C23×C411yescharacteristic
82C4×C61C2×#4111yescharacteristic
83Dic61—24no—
84Dic61—44no—
85#2943—611nomaximal, Sylow
86C2×C61—22no—
87C2×C61C2×C4×D411yescharacteristic
88C2×C61#57512yes—
89D61—44no—
90C2×#135—611no—
91C4×#41—612no—
92#442—612no—
93#441—612no—
94#440—614no—
95#427—611no—
96#416—612no—
97C2×#97D6111yescharacteristic, complemented
98C61#294311yescharacteristic, complemented, Sylow
99C2×#41—612no—
100#135—618no—
101C2×Q16—611no—
102C2×SD16—612no—
103C2×D8—611no—
104C22×C8C2×D6111yescharacteristic
105C22×C8C2×D6111yescharacteristic
106C4×Q8—614no—
107C4×D4—614no—
108C4×D4—1224no—
109#117—612no—
110#117—1222no—
111C2×C42—1222no—
112C2×C42C2×D6111yescharacteristic
113#107—612no—
114#106—612no—
115#103—614no—
116#102—614no—
117#97C2×D6112yes—
118#97C2×D6112yes—
119#41—618no—
120#41—1224no—
121C2×Q8—612no—
122C2×D4—612no—
123C2×D4—1222no—
124C22×C4—1222no—
125C22×C4—1224no—
126C22×C4D24412yes—
127C22×C4C22×D6111yescharacteristic
128Q16—614no—
129SD16—618no—
130D8—614no—
131C2×C8—22no—
132C2×C8C4×D6114yescomplemented
133C2×C8C22×D6112yes—
134C2×C8C22×D6111yescharacteristic
135C2×C8C22×D6111yescharacteristic
136C4⋊C4—614no—
137C4⋊C4—1224no—
138C22⋊C4—1222no—
139C22⋊C4—1224no—
140C42—1224no—
141C42—1222no—
142C42D24412yes—
143C42C22×D6112yes—
144C23—1222no—
145C23C2×D24411yescharacteristic
146Q8—614no—
147Q8—1222no—
148D4—614no—
149D4—1228no—
150D4—1222no—
151C2×C4—42no—
152C2×C4—1222no—
153C2×C4—1228no—
154C2×C4—1224no—
155C2×C4—2448no—
156C2×C4C2×C4×D6112yes—
157C2×C4C2×D24414yes—
158C2×C4C2×D24411yescharacteristic
159C2×C4#1175822212yes—
160C2×C4C23×D6111yescharacteristic
161C8—22no—
162C8C2×C4×D6112yes—
163C8C2×C4×D6112yes—
164C22—22no—
165C22—1224no—
166C22—2444no—
167C22C4×D24412yes—
168C22C22×D24411yescharacteristic
169C4—24no—
170C4—1224no—
171C4—2444no—
172C4C4×D24412yes—
173C4C22×C4×D6111yescharacteristic
174C4C2×#1175822211yescharacteristic
175C2—22no—
176C2—2444no—
177C2C2×C4×D24411yescharacteristic
178C2#1684056212yes—
subgroupG/H
centerC2×C4C2×D244
commutatorC4×C61C23×C4
FrattiniC2×C4C23×D61
FittingC2×#97×C61C2
socleC22×C61C22×D4
hypercenterC2×#97D61
hypocenterC61#2943
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
2. C4×#11758222C2semidirect
3. #16839875C2semidirect
4. #16839870C2semidirect
5. #16839864C2semidirect
6. #16839800C2semidirect
7. #16839759C2semidirect
8. C2×#97×C61C2semidirect
10. #14519799C4semidirect
33. #11758222C2×C4semidirect
39. C2×C8×C61C2×C4semidirect
51. Dic244C2×C4semidirect
52. D488C2×C4semidirect
53. #11758190C2×C4semidirect
97. C2×#97D61semidirect
98. C61#2943semidirect
132. C2×C8C4×D61semidirect