Finite Group Databasebeta

← #21454693

Subgroups — #21454693

Order 7808.

484 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 181 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
2#16840243C212yesmaximal, complemented
3#16839861C214yesmaximal, complemented
4#16839856C212yesmaximal, complemented
5#16839844C212yesmaximal, complemented
6#16839761C212yesmaximal, complemented
7#16839717C211yesmaximal, characteristic, complemented
8C2×#107×C61C211yesmaximal, characteristic, complemented
9C2×#11758222C2212yes—
10#14519799C418yescomplemented
11C2×Dic244C2211yescharacteristic
12C2×#11758190C2212yes—
13C2×D488C2211yescharacteristic
14C2×#11758194C2211yescharacteristic
15#14519742C2214yes—
16#14519739C2214yes—
17C4×C22⋊D61—24no—
18#14519736C2211yescharacteristic
19#14519735—22no—
20C4⋊C4×D61—22no—
21#14519700C2214yes—
22#14519697C2214yes—
23#14519687C2212yes—
24C8×Dic61C2212yes—
25C22×C8×C61C2211yescharacteristic
26C2×C4⋊C4×C61C2212yes—
27#107×C61C2212yes—
28#107×C61C2212yes—
29C22×C4×C61—22no—
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×C61C2×C414yescomplemented
39C2×C8×C61C2311yescharacteristic
40C2×C8×C61C2311yescharacteristic
41C4⋊C4×C61—22no—
42C4⋊C4×C61C2314yes—
43C22⋊Dic61D412yes—
44#11758198—24no—
45C4⋊Dic61D411yescharacteristic
46C4⋊Dic61D411yescharacteristic
47#11758196—24no—
48C4×Dic61—24no—
49C4×Dic61C2312yes—
50#11758194—22no—
51C2×#92418C2312yes—
52Dic244C2×C414yescomplemented
53D488C2×C414yescomplemented
54#11758190C2×C418yescomplemented
55C23×C61C2×D411yescharacteristic
56C22×D61—22no—
57C2×C4×C61—24no—
58C2×C4×C61—82no—
59C2×C4×C61C22×C412yes—
60C2×C4×C61C2×D411yescharacteristic
61C2×C4×C61#4112yes—
62C2×C4×C61C2411yescharacteristic
63C22⋊D61—28no—
64C2×Dic61—22no—
65C2×Dic61C2×D412yes—
66C2×Dic61C2×D412yes—
67D244—22no—
68D244C22×C414yes—
69C4×D61—28no—
70C4×D61—84no—
71Dic122—22no—
72Dic122C22×C414yes—
73C8×C61C22×C412yes—
74C8×C61C22×C412yes—
75#92418—22no—
76C22×C61—21no—
77C22×C61—21no—
78C22×C61C4×D412yes—
79C22×C61C22×D411yescharacteristic
80C2×D61—24no—
81C2×D61—42no—
82C2×D61—42no—
83C4×C61—44no—
84C4×C61C4×D412yes—
85C4×C61C23×C411yescharacteristic
86C4×C61C2×#4111yescharacteristic
87Dic61—24no—
88Dic61—22no—
89Dic61—22no—
90#2951—611nomaximal, Sylow
91C2×C61—22no—
92C2×C61C2×C4×D411yescharacteristic
93C2×C61#57611yescharacteristic
94C2×C61#57811yescharacteristic
95D61—44no—
96C2×#135—611no—
97#520—612no—
98#440—614no—
99C4×Q16—612no—
100C4×D8—612no—
101C2×#107D6111yescharacteristic, complemented
102#417—612no—
103#405—611no—
104C61#295111yescharacteristic, complemented, Sylow
105C2×#41—612no—
106#135—618no—
107C2×Q16—611no—
108C2×SD16—612no—
109C2×D8—611no—
110C2×M16—611no—
111C22×C8C2×D6111yescharacteristic
112C4×Q8—614no—
113C4×D4—614no—
114C4×D4—1224no—
115#117—611no—
116#117—1222no—
117C2×C4⋊C4—1222no—
118C2×C4⋊C4C2×D6112yes—
119#107C2×D6112yes—
120#107C2×D6112yes—
121#103—614no—
122#102—614no—
123#97—612no—
124C4×C8—612no—
125#41—618no—
126#41—1224no—
127C2×Q8—612no—
128C2×D4—612no—
129C2×D4—1222no—
130C22×C4—22no—
131C22×C4—1224no—
132C22×C4—1222no—
133C22×C4C22×D6111yescharacteristic
134Q16—614no—
135SD16—618no—
136D8—614no—
137M16—1222no—
138C2×C8—612no—
139C2×C8C4×D6114yescomplemented
140C2×C8C22×D6111yescharacteristic
141C2×C8C22×D6111yescharacteristic
142C4⋊C4—22no—
143C4⋊C4—611no—
144C4⋊C4—611no—
145C4⋊C4—1224no—
146C4⋊C4C22×D6114yes—
147C22⋊C4—612no—
148C22⋊C4—1224no—
149C42—612no—
150C42—1224no—
151C23—1222no—
152C23D4×D6111yescharacteristic
153Q8—614no—
154Q8—1222no—
155D4—614no—
156D4—1228no—
157D4—1222no—
158C2×C4—24no—
159C2×C4—82no—
160C2×C4—612no—
161C2×C4—612no—
162C2×C4—1222no—
163C2×C4—1228no—
164C2×C4—4884no—
165C2×C4C2×C4×D6112yes—
166C2×C4D4×D6111yescharacteristic
167C2×C4#1175822612yes—
168C2×C4C23×D6111yescharacteristic
169C8—1222no—
170C8C2×C4×D6112yes—
171C8C2×C4×D6112yes—
172C22—21no—
173C22—21no—
174C22—1224no—
175C22—2442no—
176C22—2442no—
177C22#1451973912yes—
178C22C2×D4×D6111yescharacteristic
179C4—44no—
180C4—1224no—
181C4—1222no—
182C4—1222no—
183C4#1451973912yes—
184C4C22×C4×D6111yescharacteristic
185C4C2×#1175822611yescharacteristic
186C2—22no—
187C2—2444no—
188C2C2×#1451973911yescharacteristic
189C2#1684056311yescharacteristic
190C2#1684057511yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC4×C61C23×C4
FrattiniC2×C4C23×D61
FittingC2×#107×C61C2
socleC22×C61C22×D4
hypercenterC2×#107D61
hypocenterC61#2951
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. #16840243C2semidirect
3. #16839861C2semidirect
4. #16839856C2semidirect
5. #16839844C2semidirect
6. #16839761C2semidirect
7. #16839717C2semidirect
8. C2×#107×C61C2semidirect
10. #14519799C4semidirect
33. #11758222C2×C4semidirect
38. C2×C8×C61C2×C4semidirect
52. Dic244C2×C4semidirect
53. D488C2×C4semidirect
54. #11758190C2×C4semidirect
101. C2×#107D61semidirect
104. C61#2951semidirect
139. C2×C8C4×D61semidirect