Finite Group Databasebeta

← #21461327

Subgroups — #21461327

Order 7808.

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

normal subgroups only

This group has 344 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#16840780C211yesmaximal, characteristic, complemented
2#16840767C211yesmaximal, characteristic, complemented
3#16840620C214yesmaximal, complemented
4#127×D61C211yesmaximal, characteristic
5C2×#11758213—21no—
6#14519844—21no—
7#14519844C2212yescomplemented
8#14519844C2212yescomplemented
9#14519834—21no—
10C4×#92420—21no—
11C2×D4×D61—21no—
12C2×D4×D61—21no—
13C2×D4×D61C412yes—
14#14519774C411yescharacteristic
15#14519773—21no—
16#14519773—21no—
17#14519773C2212yes—
18C42×D61C2211yescharacteristic
19#127×C61C411yescharacteristic
20C23×D61—22no—
21C2×D4×C61—21no—
22C2×D4×C61—21no—
23C2×D4×C61C2×C412yes—
24C2×C22⋊D61—22no—
25C2×C22⋊D61—22no—
26C2×C22⋊D61—22no—
27D4×D61—44no—
28D4×D61—44no—
29D4×D61—42no—
30D4×D61—42no—
31C2×D244—21no—
32C2×D244—21no—
33C2×D244C2×C412yes—
34C2×C4×D61C2×C411yescharacteristic
35C2×C4×D61D411yescharacteristic
36C2×C4×D61D411yescharacteristic
37C2×#92420—22no—
38C2×#92420—22no—
39#11758213—42no—
40C42×C61C2×C411yescharacteristic
41C4×Dic61D411yescharacteristic
42C4×Dic61D411yescharacteristic
43C4×Dic61C2311yescharacteristic
44C23×C61—22no—
45C22×D61—22no—
46C22×D61—44no—
47C22×D61—44no—
48C22×D61—44no—
49C22×D61C22⋊C411yescharacteristic
50D4×C61—42no—
51D4×C61—42no—
52D4×C61—42no—
53C2×C4×C61C22⋊C411yescharacteristic
54C2×C4×C61C22⋊C411yescharacteristic
55C2×C4×C61C22×C411yescharacteristic
56C22⋊D61—44no—
57C22⋊D61—42no—
58C22⋊D61—42no—
59C22⋊D61—44no—
60C2×Dic61C22⋊C411yescharacteristic
61C2×Dic61C2×D411yescharacteristic
62C2×Dic61C2×D411yescharacteristic
63D244—42no—
64D244—42no—
65D244—42no—
66C4×D61—22no—
67C4×D61—22no—
68C4×D61D812yes—
69C4×D61SD1612yes—
70#92420—42no—
71#92420—42no—
72C22×C61—42no—
73C22×C61—42no—
74C22×C61—42no—
75C22×C61C2×C22⋊C411yescharacteristic
76C2×D61—21no—
77C2×D61—21no—
78C2×D61—42no—
79C2×D61—42no—
80C2×D61—42no—
81C2×D61—88no—
82C2×D61#10212yes—
83C4×C61—21no—
84C4×C61—21no—
85C4×C61#10212yes—
86Dic61#10012yes—
87Dic61C2×D811yescharacteristic
88Dic61C2×SD1611yescharacteristic
89Dic61AGL(1,ℤ/8)12yes—
90#1545—611nomaximal, Sylow
91C2×C61—82no—
92C2×C61C2×#10011yescharacteristic
93C2×C61C2×#10211yescharacteristic
94C2×C61#41811yescharacteristic
95D61—22no—
96D61—82no—
97C2×#127—611no—
98#431—611no—
99#423—611no—
100#331—614no—
101C61#154511yescharacteristic, complemented, Sylow
102C22×D4—612no—
103C22×D4—1221no—
104C22×D4—1221no—
105C2×M16—1221no—
106#127—612no—
107#127—611no—
108#127—1221no—
109#127—1221no—
110#127#692311yescharacteristic
111C2×C42—611no—
112C4⋊C8—612no—
113C4⋊C8—612no—
114C4⋊C8—1221no—
115C22⋊C8—1221no—
116C4×C8—1221no—
117C24—1222no—
118C2×D4—21no—
119C2×D4—21no—
120C2×D4—612no—
121C2×D4—1222no—
122C2×D4—1222no—
123C2×D4—1222no—
124C2×D4—1221no—
125C2×D4—1221no—
126C2×D4—2442no—
127C2×D4—2442no—
128C2×D4—2444no—
129C2×D4—2444no—
130C2×D4C2×#692312yes—
131C22×C4—611no—
132C22×C4—611no—
133C22×C4—611no—
134M16—2442no—
135C2×C8—1222no—
136C2×C8—1222no—
137C42—611no—
138C42—611no—
139C42—611no—
140C42C2×#692311yescharacteristic
141C23—22no—
142C23—611no—
143C23—1222no—
144C23—2444no—
145C23—2444no—
146C23—2444no—
147D4—42no—
148D4—42no—
149D4—42no—
150D4—2442no—
151D4—2442no—
152D4—2444no—
153D4—2442no—
154D4—2442no—
155D4—2444no—
156D4—2442no—
157C2×C4—611no—
158C2×C4—611no—
159C2×C4—611no—
160C2×C4—612no—
161C2×C4—612no—
162C2×C4—1222no—
163C2×C4—1222no—
164C2×C4C22⋊#692311yescharacteristic
165C2×C4C22⋊#692311yescharacteristic
166C2×C4C22×#692311yescharacteristic
167C8—2442no—
168C8—2442no—
169C22—42no—
170C22—42no—
171C22—42no—
172C22—612no—
173C22—1221no—
174C22—1221no—
175C22—4888no—
176C22—2442no—
177C22—2442no—
178C22—2442no—
179C22C2×C22⋊#692311yescharacteristic
180C4—21no—
181C4—21no—
182C4—612no—
183C4—611no—
184C4—611no—
185C4—612no—
186C4#1451983912yes—
187C2—82no—
188C2—1222no—
189C2—4882no—
190C2D61⋊#10011yescharacteristic
191C2C2×#1451983911yescharacteristic
192C2#1684075411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#127×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#127#6923
hypocenterC61#1545
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. #16840780C2semidirect
2. #16840767C2semidirect
3. #16840620C2semidirect
7. #14519844C22semidirect
8. #14519844C22semidirect
101. C61#1545semidirect