Finite Group Databasebeta

← #21461317

Subgroups — #21461317

Order 7808.

256 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 68 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#16840779C211yesmaximal, characteristic, complemented
2C2×#14519844C211yesmaximal, characteristic, complemented
3#16840621C212yesmaximal, complemented
4#16840620C212yesmaximal, complemented
5#16840307C211yesmaximal, characteristic
6C22×#92420—21no—
7#14519844—21no—
8#14519844C2212yes—
9#14519844C2212yes—
10C22⋊#92420—21no—
11C4×#92420—21no—
12C2×#11758224—21no—
13#14519776C2211yescharacteristic
14#14519773C2211yescharacteristic
15#14519763—21no—
16#14519751C411yescharacteristic
17#14519749—21no—
18D4×Dic61C411yescharacteristic
19#14519739C411yescharacteristic
20#14519737—21no—
21C2×C4×Dic61C2211yescharacteristic
22#121×C61C411yescharacteristic
23C2×D4×C61—21no—
24C2×D4×C61C2×C411yescharacteristic
25C22×C4×C61C2×C411yescharacteristic
26C2×C22⋊D61—21no—
27C2×C22⋊D61—21no—
28C2×C22⋊D61—21no—
29C22×Dic61—21no—
30C22×Dic61D411yescharacteristic
31C22×Dic61D411yescharacteristic
32#11758224—42no—
33#11758224—42no—
34C2×D244C2×C411yescharacteristic
35C2×C4×D61—21no—
36C2×Dic122—21no—
37C2×#92420—22no—
38C2×#92420—22no—
39C2×#92420—42no—
40C4⋊C4×C61C2×C411yescharacteristic
41C22⋊C4×C61—21no—
42C22⋊Dic61—21no—
43#11758198—21no—
44#11758198—21no—
45C4⋊Dic61C2×C411yescharacteristic
46#11758196—21no—
47C4×Dic61C2×C411yescharacteristic
48C4×Dic61D411yescharacteristic
49C4×Dic61D411yescharacteristic
50C4×Dic61C2311yescharacteristic
51C23×C61—21no—
52C23×C61C22⋊C411yescharacteristic
53C22×D61—21no—
54D4×C61—41no—
55D4×C61—42no—
56C2×C4×C61—21no—
57C2×C4×C61—41no—
58C2×C4×C61C22⋊C411yescharacteristic
59C2×C4×C61C22×C411yescharacteristic
60C22⋊D61—42no—
61C22⋊D61—41no—
62C22⋊D61—41no—
63C22⋊D61—42no—
64C2×Dic61—22no—
65C2×Dic61—21no—
66C2×Dic61—42no—
67C2×Dic61C22⋊C411yescharacteristic
68C2×Dic61C22⋊C411yescharacteristic
69C2×Dic61D812yes—
70C2×Dic61SD1612yes—
71C2×Dic61C2×D411yescharacteristic
72C2×Dic61C2×D411yescharacteristic
73D244—41no—
74C4×D61—42no—
75Dic122—41no—
76Dic122—41no—
77#92420—42no—
78#92420—42no—
79C22×C61—21no—
80C22×C61—21no—
81C22×C61—41no—
82C22×C61—41no—
83C22×C61—41no—
84C22×C61#10212yes—
85C22×C61C2×C22⋊C411yescharacteristic
86C2×D61—41no—
87C2×D61—41no—
88C2×D61—41no—
89C4×C61—21no—
90C4×C61—21no—
91C4×C61—41no—
92Dic61—21no—
93Dic61—41no—
94Dic61#10212yes—
95Dic61C2×D811yescharacteristic
96Dic61C2×SD1611yescharacteristic
97Dic61#13512yes—
98#1540—611nomaximal, Sylow
99C2×C61—22no—
100C2×C61—81no—
101C2×C61#41311yescharacteristic
102C2×C61C2×#10211yescharacteristic
103C2×C61#41611yescharacteristic
104D61—81no—
105#532—611no—
106#431—611no—
107C2×C4⋊C8—611no—
108#332—612no—
109#331—612no—
110C61#154011yescharacteristic, complemented, Sylow
111C2×#41—1221no—
112C22×C8—1221no—
113C4⋊Q8—611no—
114#127—611no—
115#124—1221no—
116#121—611no—
117#121—1221no—
118#121#692311yescharacteristic
119C4×D4—611no—
120C4×D4—611no—
121C4×D4—1221no—
122C2×C42—611no—
123C4⋊C8—612no—
124C4⋊C8—612no—
125C4⋊C8—1221no—
126C22⋊C8—1221no—
127C4×C8—1221no—
128#41—2442no—
129#41—2442no—
130C2×Q8—1221no—
131C2×D4—21no—
132C2×D4—611no—
133C2×D4—1221no—
134C2×D4—1221no—
135C2×D4—1221no—
136C2×D4C2×#692311yescharacteristic
137C22×C4—611no—
138C22×C4—611no—
139C22×C4—1221no—
140C22×C4—1221no—
141C22×C4C2×#692311yescharacteristic
142C2×C8—1222no—
143C2×C8—1222no—
144C2×C8—2442no—
145C4⋊C4—611no—
146C4⋊C4—1221no—
147C4⋊C4C2×#692311yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—1221no—
150C22⋊C4—1221no—
151C22⋊C4—1221no—
152C42—611no—
153C42—611no—
154C42—611no—
155C42—611no—
156C23—21no—
157C23—1221no—
158C23C22⋊#692311yescharacteristic
159Q8—2441no—
160Q8—2441no—
161D4—41no—
162D4—42no—
163D4—2441no—
164D4—2442no—
165D4—2441no—
166D4—2441no—
167D4—2442no—
168C2×C4—21no—
169C2×C4—41no—
170C2×C4—612no—
171C2×C4—612no—
172C2×C4—611no—
173C2×C4—611no—
174C2×C4—611no—
175C2×C4—611no—
176C2×C4—1222no—
177C2×C4—1221no—
178C2×C4—2442no—
179C2×C4—2442no—
180C2×C4C22⋊#692311yescharacteristic
181C2×C4C22×#692311yescharacteristic
182C8—2442no—
183C8—2442no—
184C22—21no—
185C22—21no—
186C22—41no—
187C22—41no—
188C22—41no—
189C22—2441no—
190C22—2441no—
191C22—2441no—
192C22#1451983912yes—
193C22C2×C22⋊#692311yescharacteristic
194C4—21no—
195C4—21no—
196C4—41no—
197C4—612no—
198C4—611no—
199C4—611no—
200C4—612no—
201C4—1221no—
202C4—2441no—
203C2—22no—
204C2—81no—
205C2—4881no—
206C2#1684074911yescharacteristic
207C2C2×#1451983911yescharacteristic
208C2#1684075211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#121×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#121#6923
hypocenterC61#1540
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #16840779C2semidirect
2. C2×#14519844C2semidirect
3. #16840621C2semidirect
4. #16840620C2semidirect
110. C61#1540semidirect