Finite Group Databasebeta

← #21461199

Subgroups — #21461199

Order 7808.

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

normal subgroups only

This group has 284 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#16840781C211yesmaximal, characteristic, complemented
2C4×C4⋊#6923C211yesmaximal, characteristic, complemented
3#16840613C214yesmaximal, complemented
4#16840310C211yesmaximal, characteristic
5C2×C4⋊#6923—21no—
6C2×C4×#6923—21no—
7C4⋊#92420—21no—
8#14519834C2212yes—
9C4×#92420—21no—
10(C2×#6923)⋊C4C2212yes—
11C2×#11758224—21no—
12#14519777C411yescharacteristic, complemented
13#14519764—21no—
14#14519748—21no—
15#14519748C2212yes—
16D4×Dic61—21no—
17D4×Dic61C412yescomplemented
18C42×D61C2211yescharacteristic
19#127×C61C411yescharacteristic, complemented
20C22×#6923—22no—
21C2×D4×C61—21no—
22C2×D4×C61—21no—
23C2×D4×C61C2×C412yes—
24C2×C22⋊D61—22no—
25C22×Dic61—22no—
26#11758224—42no—
27#11758224—42no—
28C2×C4×D61D411yescharacteristic
29C2×C4×D61D411yescharacteristic
30C2×C4×D61C2311yescharacteristic
31C2×Dic122—21no—
32C2×#92420—22no—
33C4⋊#6923—24no—
34C4×#6923—42no—
35C42×C61C2×C411yescharacteristic
36C22⋊Dic61—22no—
37C22⋊Dic61—22no—
38C4⋊Dic61—21no—
39C4⋊Dic61C2×C412yes—
40C4×Dic61C2×C411yescharacteristic
41C4×Dic61D411yescharacteristic
42C4×Dic61D411yescharacteristic
43C23×C61—22no—
44C22×D61C2×D411yescharacteristic
45C2×#6923—24no—
46C2×#6923—42no—
47C2×#6923—42no—
48D4×C61—42no—
49D4×C61—42no—
50D4×C61—42no—
51C2×C4×C61C22⋊C411yescharacteristic
52C2×C4×C61C22⋊C411yescharacteristic
53C2×C4×C61C22×C411yescharacteristic
54C22⋊D61—42no—
55C22⋊D61—42no—
56C2×Dic61—22no—
57C2×Dic61—44no—
58C2×Dic61C22⋊C411yescharacteristic
59C2×Dic61C22⋊C411yescharacteristic
60C2×Dic61C2×D411yescharacteristic
61C4×D61—22no—
62C4×D61—41no—
63C4×D61D812yes—
64C4×D61SD1612yes—
65Dic122—42no—
66#92420—42no—
67C22×C61—42no—
68C22×C61—42no—
69C22×C61—42no—
70C22×C61C2×C22⋊C411yescharacteristic
71C2×D61—21no—
72C2×D61—21no—
73C2×D61C2×D811yescharacteristic
74C2×D61C2×SD1611yescharacteristic
75#6923—44no—
76C4×C61—21no—
77C4×C61#10212yes—
78C4×C61#10412yes—
79Dic61—21no—
80Dic61—21no—
81Dic61—42no—
82Dic61#10212yes—
83#1502—611nomaximal, Sylow
84C2×C61—82no—
85C2×C61#41011yescharacteristic
86C2×C61C2×#10211yescharacteristic
87C2×C61C2×#10411yescharacteristic
88D61—21no—
89D61—21no—
90#532—611no—
91#431—611no—
92C4×C4⋊C4—611no—
93#327—614no—
94C61#150211yescharacteristic, complemented, Sylow
95C2×#41—1221no—
96C4⋊Q8—611no—
97#127#692311yescharacteristic, complemented
98#124—1221no—
99#121—612no—
100#121—1221no—
101C4×D4—612no—
102C4×D4—1221no—
103C2×C4⋊C4—1221no—
104C2×C42—611no—
105C2×C42—1221no—
106C4⋊C8—1221no—
107C22⋊C8—612no—
108C4×C8—1221no—
109#95—612no—
110#41—2442no—
111#41—2442no—
112C2×Q8—1221no—
113C2×D4—21no—
114C2×D4—21no—
115C2×D4—1222no—
116C2×D4C2×#692312yes—
117C22×C4—611no—
118C22×C4—611no—
119C22×C4—611no—
120C22×C4—1222no—
121C22×C4—1222no—
122C2×C8—1222no—
123C4⋊C4—612no—
124C4⋊C4—1224no—
125C4⋊C4—1221no—
126C22⋊C4—1222no—
127C22⋊C4—1222no—
128C42—611no—
129C42—611no—
130C42—611no—
131C42—2442no—
132C42C2×#692311yescharacteristic
133C23—22no—
134C23—611no—
135Q8—2442no—
136D4—42no—
137D4—42no—
138D4—42no—
139D4—2442no—
140D4—2442no—
141C2×C4—611no—
142C2×C4—612no—
143C2×C4—612no—
144C2×C4—611no—
145C2×C4—611no—
146C2×C4—1222no—
147C2×C4—1224no—
148C2×C4—1222no—
149C2×C4—2441no—
150C2×C4—2444no—
151C2×C4—2442no—
152C2×C4—2442no—
153C2×C4C22⋊#692311yescharacteristic
154C2×C4C22⋊#692311yescharacteristic
155C2×C4C22×#692311yescharacteristic
156C8—2442no—
157C22—42no—
158C22—42no—
159C22—42no—
160C22—611no—
161C22—611no—
162C22—1221no—
163C22—1221no—
164C22C2×C22⋊#692311yescharacteristic
165C4—21no—
166C4—612no—
167C4—1221no—
168C4—1221no—
169C4—2444no—
170C4—2442no—
171C4#1451983912yes—
172C4#1451984112yes—
173C2—82no—
174C2—1221no—
175C2—1221no—
176C2#1684074211yescharacteristic
177C2C2×#1451983911yescharacteristic
178C2C2×#1451984111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#127×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#127#6923
hypocenterC61#1502
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #16840781C2semidirect
2. C4×C4⋊#6923C2semidirect
3. #16840613C2semidirect
12. #14519777C4semidirect
17. D4×Dic61C4semidirect
19. #127×C61C4semidirect
94. C61#1502semidirect
97. #127#6923semidirect