Finite Group Databasebeta

← #21461577

Subgroups — #21461577

Order 7808.

284 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 86 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×#14519864C211yesmaximal, characteristic
2#16840749C211yesmaximal, characteristic
3#16840726C212yesmaximal, complemented
4#16840643C212yesmaximal, complemented
5#16839734C211yesmaximal, characteristic
6#14519864—22no—
7#14519864—22no—
8C2×#11758213C411yescharacteristic, complemented
9C2×#11758217C411yescharacteristic, complemented
10C2×#11758217C2212yes—
11C2×#11758217C2211yescharacteristic
12C2×D61⋊C8C411yescharacteristic, complemented
13C22×#92420C411yescharacteristic, complemented
14C22×#92420C2211yescharacteristic
15#14519838C412yescomplemented
16#14519837C412yescomplemented
17#14519832—22no—
18C4×#92420—22no—
19C2×#11758224C2211yescharacteristic
20#14519733C2212yes—
21#14519692C411yescharacteristic
22#14519691C412yes—
23#99×C61C411yescharacteristic
24C2×D4×C61C2×C411yescharacteristic
25C2×C22⋊D61C2×C411yescharacteristic
26C2×C22⋊D61C2×C411yescharacteristic
27C22×Dic61C2×C411yescharacteristic
28C22×Dic61C2311yescharacteristic
29#11758224—22no—
30#11758224—22no—
31C2×C4×D61C2×C411yescharacteristic
32C2×Dic122C2×C411yescharacteristic
33#11758217—22no—
34#11758217—22no—
35#11758217—22no—
36#11758217C2×C414yes—
37C2×#92420—22no—
38C2×#92420—21no—
39C2×#92420—21no—
40C2×#92420C2×C411yescharacteristic
41C2×#92420C2×C411yescharacteristic
42C2×#92420C2×C411yescharacteristic
43C2×#92420C2×C411yescharacteristic
44C2×#92420D412yes—
45C2×#92420D412yes—
46#11758213—22no—
47D61⋊C8—21no—
48D61⋊C8—21no—
49C22⋊C4×C61C2×C412yes—
50C22⋊Dic61C2×C412yes—
51#11758196—22no—
52C4×Dic61—22no—
53C23×C61C4211yescharacteristic
54C23×C61C22×C411yescharacteristic
55C22×D61C4211yescharacteristic
56D4×C61—22no—
57C2×C4×C61—22no—
58C2×C4×C61C4211yescharacteristic
59C22⋊D61—22no—
60C22⋊D61—22no—
61C2×Dic61—21no—
62C2×Dic61—21no—
63C2×Dic61—22no—
64C2×Dic61C4211yescharacteristic
65C2×Dic61C22×C411yescharacteristic
66C2×Dic61C22×C411yescharacteristic
67C2×Dic61C2×D412yes—
68C2×Dic61#4112yes—
69C4×D61—21no—
70C4×D61—21no—
71Dic122—22no—
72#92420—21no—
73#92420—21no—
74#92420—24no—
75#92420C22⋊C411yescharacteristic
76#92420C22⋊C411yescharacteristic
77#92420C22⋊C412yes—
78C22×C61—21no—
79C22×C61—41no—
80C22×C61—41no—
81C22×C61C2×C4211yescharacteristic
82C22×C61C4×D412yes—
83C2×D61—21no—
84C2×D61—41no—
85C4×C61—21no—
86C4×C61—42no—
87Dic61—21no—
88Dic61—42no—
89Dic61C2×C22⋊C411yescharacteristic
90Dic61#11711yescharacteristic
91Dic61C4×D412yes—
92#1757—611nomaximal, Sylow
93C2×C61—22no—
94C2×C61—21no—
95C2×C61—41no—
96C2×C61C4×C22⋊C411yescharacteristic
97D61—41no—
98C2×#131—611no—
99#413—611no—
100#410—611no—
101#405—612no—
102#344—612no—
103C61#175711yescharacteristic, complemented, Sylow
104C2×#41—611no—
105#131—1222no—
106#131—1222no—
107C2×M16—611no—
108C2×M16—611no—
109C2×M16—611no—
110C2×M16—612no—
111C22×C8—611no—
112C22×C8—611no—
113C22×C8—611no—
114#117—612no—
115#101—612no—
116#100—612no—
117#99—611no—
118#99—612no—
119#99#692311yescharacteristic
120#97—1222no—
121C4×C8—1222no—
122#41—1222no—
123#41—1222no—
124C2×Q8—611no—
125C2×D4—611no—
126C2×D4—611no—
127C2×D4C2×#692311yescharacteristic
128C22×C4—611no—
129C22×C4—611no—
130C22×C4—611no—
131M16—614no—
132M16—1222no—
133M16—1222no—
134M16—1222no—
135M16—1222no—
136C2×C8—612no—
137C2×C8—612no—
138C2×C8—611no—
139C2×C8—611no—
140C2×C8—611no—
141C2×C8—611no—
142C2×C8—1221no—
143C2×C8—1221no—
144C2×C8—1221no—
145C2×C8—1221no—
146C2×C8—1222no—
147C4⋊C4—1222no—
148C22⋊C4—612no—
149C22⋊C4C2×#692312yes—
150C42—1222no—
151C23—611no—
152C23C4×#692311yescharacteristic
153C23C22×#692311yescharacteristic
154Q8—1222no—
155D4—22no—
156D4—1222no—
157D4—1222no—
158C2×C4—22no—
159C2×C4—611no—
160C2×C4—611no—
161C2×C4—612no—
162C2×C4—612no—
163C2×C4—611no—
164C2×C4—1221no—
165C2×C4—1221no—
166C2×C4—1221no—
167C2×C4—1221no—
168C2×C4—1222no—
169C2×C4C4×#692311yescharacteristic
170C8—611no—
171C8—611no—
172C8—612no—
173C8—1221no—
174C8—1221no—
175C8—1224no—
176C22—21no—
177C22—41no—
178C22—41no—
179C22—1221no—
180C22—2441no—
181C22C2×C4×#692311yescharacteristic
182C22D4×#692312yes—
183C4—21no—
184C4—42no—
185C4—611no—
186C4—611no—
187C4—612no—
188C4—1221no—
189C4—2442no—
190C2—22no—
191C2—21no—
192C2—41no—
193C2—2441no—
194C2C22⋊C4×#692311yescharacteristic
subgroupG/H
centerC2C22⋊C4×#6923
commutatorC22×C61C2×C42
FrattiniC23C22×#6923
Fitting#99×C61C4
socleC2×C61C4×C22⋊C4
hypercenter#99#6923
hypocenterC61#1757
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
3. #16840726C2semidirect
4. #16840643C2semidirect
8. C2×#11758213C4semidirect
9. C2×#11758217C4semidirect
12. C2×D61⋊C8C4semidirect
13. C22×#92420C4semidirect
15. #14519838C4semidirect
16. #14519837C4semidirect
103. C61#1757semidirect