Finite Group Databasebeta

← #21461726

Subgroups — #21461726

Order 7808.

306 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 70 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#16840733C211yesmaximal, characteristic
2C4×C22⋊#6923C211yesmaximal, characteristic
3#16840632C214yesmaximal, complemented
4C2×#14519735C211yesmaximal, characteristic
5C2×#11758213C2212yes—
6C2×C22⋊#6923—21no—
7C2×C4×#6923C2212yes—
8#14519834—21no—
9C22⋊#92420—21no—
10(C2×#6923)⋊C4—21no—
11C22×C4×D61C2211yescharacteristic
12#14519735—21no—
13#14519735—21no—
14#14519735C412yescomplemented
15#14519735C2212yes—
16C2×C4⋊Dic61C411yescharacteristic, complemented
17C2×#11758198—21no—
18C2×C4×Dic61—21no—
19C2×C4⋊C4×C61C411yescharacteristic, complemented
20C23×D61D411yescharacteristic
21C22×#6923—22no—
22C22×C4×C61—21no—
23C22×C4×C61C2×C411yescharacteristic
24C22×Dic61—21no—
25C22×Dic61D411yescharacteristic
26C2×C4×D61—24no—
27C2×C4×D61C2×C411yescharacteristic
28C2×C4×D61D411yescharacteristic
29C2×C4×D61D411yescharacteristic
30C2×C4×D61C2311yescharacteristic
31C22⋊#6923—24no—
32C2×#92420—22no—
33C4×#6923—24no—
34#11758213—24no—
35C4⋊C4×C61—21no—
36C4⋊C4×C61C2×C412yes—
37#11758198—22no—
38#11758198—22no—
39C4⋊Dic61—21no—
40C4⋊Dic61C2×C412yes—
41C4×Dic61—22no—
42C4×Dic61—22no—
43C23×C61C22⋊C411yescharacteristic
44C22×D61—22no—
45C22×D61—22no—
46C22×D61—41no—
47C22×D61C22⋊C411yescharacteristic
48C22×D61C2×D411yescharacteristic
49C2×#6923—24no—
50C2×#6923—42no—
51C2×#6923—42no—
52C2×C4×C61—22no—
53C2×C4×C61—22no—
54C2×C4×C61—42no—
55C2×C4×C61C22⋊C411yescharacteristic
56C2×C4×C61C22×C411yescharacteristic
57C2×Dic61—22no—
58C2×Dic61—22no—
59C2×Dic61—42no—
60C2×Dic61C22⋊C411yescharacteristic
61C2×Dic61C2×D411yescharacteristic
62C4×D61—22no—
63C4×D61—22no—
64C4×D61—22no—
65C4×D61#4114yes—
66#92420—42no—
67C22×C61—21no—
68C22×C61—21no—
69C22×C61#10412yes—
70C22×C61C2×C22⋊C411yescharacteristic
71C2×D61—21no—
72C2×D61—21no—
73C2×D61—21no—
74C2×D61—21no—
75C2×D61—21no—
76C2×D61—44no—
77C2×D61#12312yes—
78#6923—44no—
79C4×C61—21no—
80C4×C61—42no—
81C4×C61#11712yes—
82Dic61—21no—
83Dic61—42no—
84Dic61#12312yes—
85#1826—611nomaximal, Sylow
86C2×C61—22no—
87C2×C61#38111yescharacteristic
88C2×C61C2×#10411yescharacteristic
89C2×C61#42111yescharacteristic
90D61—22no—
91D61—41no—
92C2×#117—611no—
93#407—611no—
94C4×C22⋊C4—611no—
95#339—614no—
96C61#182611yescharacteristic, complemented, Sylow
97C23×C4—611no—
98C2×M16—612no—
99#117—612no—
100#117—612no—
101#117—1221no—
102#117—1221no—
103C2×C4⋊C4—611no—
104C2×C4⋊C4#692311yescharacteristic, complemented
105C2×C22⋊C4—1221no—
106C2×C22⋊C4—1221no—
107C2×C42—612no—
108C2×C42—1221no—
109C22⋊C8—1221no—
110C22⋊C8—1221no—
111#95—1221no—
112C24—611no—
113C22×C4—21no—
114C22×C4—611no—
115C22×C4—611no—
116C22×C4—611no—
117C22×C4—611no—
118C22×C4—611no—
119C22×C4—1224no—
120C22×C4—1222no—
121C22×C4—1221no—
122C22×C4C2×#692311yescharacteristic
123M16—1224no—
124C2×C8—1222no—
125C4⋊C4—21no—
126C4⋊C4—612no—
127C4⋊C4—1221no—
128C4⋊C4C2×#692312yes—
129C22⋊C4—1222no—
130C22⋊C4—1222no—
131C22⋊C4—1224no—
132C42—1222no—
133C42—1222no—
134C42—1224no—
135C23—611no—
136C23—611no—
137C23—1222no—
138C23—1222no—
139C23—2441no—
140C23C22⋊#692311yescharacteristic
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—42no—
144C2×C4—611no—
145C2×C4—614no—
146C2×C4—611no—
147C2×C4—1222no—
148C2×C4—1222no—
149C2×C4—1222no—
150C2×C4—1222no—
151C2×C4—1224no—
152C2×C4—1222no—
153C2×C4—2442no—
154C2×C4—2442no—
155C2×C4—2442no—
156C2×C4C22⋊#692311yescharacteristic
157C2×C4C22×#692311yescharacteristic
158C8—2442no—
159C22—21no—
160C22—21no—
161C22—612no—
162C22—1221no—
163C22—1221no—
164C22—1221no—
165C22—1221no—
166C22—1221no—
167C22—2444no—
168C22#1451984212yes—
169C22C2×C22⋊#692311yescharacteristic
170C4—21no—
171C4—42no—
172C4—612no—
173C4—1221no—
174C4—2444no—
175C4—2442no—
176C4#1451985612yes—
177C2—22no—
178C2—1222no—
179C2—2441no—
180C2#1684070511yescharacteristic
181C2C2×#1451984211yescharacteristic
182C2#1684076011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC2×C4⋊C4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC2×C4⋊C4#6923
hypocenterC61#1826
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #16840632C2semidirect
14. #14519735C4semidirect
16. C2×C4⋊Dic61C4semidirect
19. C2×C4⋊C4×C61C4semidirect
96. C61#1826semidirect
104. C2×C4⋊C4#6923semidirect