Finite Group Databasebeta

← #21461343

Subgroups — #21461343

Order 7808.

242 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 58 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#16840782C211yesmaximal, characteristic, complemented
2#16840779C211yesmaximal, characteristic, complemented
3#16840621C212yesmaximal, complemented
4#16840620C212yesmaximal, complemented
5#16840307C211yesmaximal, characteristic
6#14519844C2212yes—
7#14519844C2212yes—
8C22⋊#92420—21no—
9C22⋊#92420—21no—
10#14519832—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—44no—
33C2×D244C2×C411yescharacteristic
34C2×C4×D61—21no—
35C2×Dic122—21no—
36C2×#92420—22no—
37C2×#92420—22no—
38C4⋊C4×C61C2×C411yescharacteristic
39C22⋊C4×C61—21no—
40C22⋊Dic61—21no—
41#11758198—21no—
42#11758198—21no—
43C4⋊Dic61C2×C411yescharacteristic
44#11758196—21no—
45C4×Dic61C2×C411yescharacteristic
46C4×Dic61D411yescharacteristic
47C4×Dic61D411yescharacteristic
48C4×Dic61C2311yescharacteristic
49C23×C61—21no—
50C23×C61C22⋊C411yescharacteristic
51C22×D61—21no—
52D4×C61—41no—
53D4×C61—42no—
54C2×C4×C61—21no—
55C2×C4×C61—41no—
56C2×C4×C61C22⋊C411yescharacteristic
57C2×C4×C61C22×C411yescharacteristic
58C22⋊D61—42no—
59C22⋊D61—42no—
60C22⋊D61—42no—
61C2×Dic61—22no—
62C2×Dic61—22no—
63C2×Dic61—21no—
64C2×Dic61—42no—
65C2×Dic61C22⋊C411yescharacteristic
66C2×Dic61C22⋊C411yescharacteristic
67C2×Dic61C2×D411yescharacteristic
68C2×Dic61C2×D411yescharacteristic
69D244—41no—
70C4×D61—42no—
71Dic122—42no—
72#92420—42no—
73#92420—42no—
74C22×C61—21no—
75C22×C61—21no—
76C22×C61—21no—
77C22×C61—41no—
78C22×C61—41no—
79C22×C61—41no—
80C22×C61C2×C22⋊C411yescharacteristic
81C2×D61—41no—
82C2×D61—41no—
83C2×D61—41no—
84C4×C61—21no—
85C4×C61—21no—
86C4×C61—41no—
87Dic61—21no—
88Dic61—21no—
89Dic61—41no—
90Dic61#13512yes—
91Dic61AGL(1,ℤ/8)12yes—
92#1553—611nomaximal, Sylow
93C2×C61—41no—
94C2×C61—81no—
95C2×C61#41311yescharacteristic
96C2×C61#41611yescharacteristic
97C2×C61#41811yescharacteristic
98D61—81no—
99#532—611no—
100#432—611no—
101#431—611no—
102#332—612no—
103#331—612no—
104C61#155311yescharacteristic, complemented, Sylow
105C2×#41—1221no—
106C4⋊Q8—611no—
107#127—611no—
108#124—1221no—
109#121—611no—
110#121—1221no—
111#121#692311yescharacteristic
112C4×D4—611no—
113C4×D4—611no—
114C4×D4—1221no—
115C2×C42—611no—
116C4⋊C8—612no—
117C4⋊C8—612no—
118C22⋊C8—1221no—
119C22⋊C8—1221no—
120#97—1221no—
121C4×C8—1221no—
122#41—2444no—
123C2×Q8—1221no—
124C2×D4—21no—
125C2×D4—611no—
126C2×D4—1221no—
127C2×D4—1221no—
128C2×D4—1221no—
129C2×D4C2×#692311yescharacteristic
130C22×C4—611no—
131C22×C4—611no—
132C22×C4—1221no—
133C22×C4—1221no—
134C22×C4C2×#692311yescharacteristic
135C2×C8—1222no—
136C2×C8—1222no—
137C4⋊C4—611no—
138C4⋊C4—1221no—
139C4⋊C4C2×#692311yescharacteristic
140C22⋊C4—21no—
141C22⋊C4—1221no—
142C22⋊C4—1221no—
143C22⋊C4—1221no—
144C42—611no—
145C42—611no—
146C42—611no—
147C42—611no—
148C23—21no—
149C23—1221no—
150C23C22⋊#692311yescharacteristic
151Q8—2442no—
152D4—41no—
153D4—42no—
154D4—2441no—
155D4—2442no—
156D4—2442no—
157D4—2442no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—611no—
161C2×C4—611no—
162C2×C4—611no—
163C2×C4—611no—
164C2×C4—1222no—
165C2×C4—1222no—
166C2×C4—1221no—
167C2×C4—2442no—
168C2×C4—2442no—
169C2×C4C22⋊#692311yescharacteristic
170C2×C4C22×#692311yescharacteristic
171C8—2442no—
172C8—2442no—
173C22—21no—
174C22—21no—
175C22—21no—
176C22—41no—
177C22—41no—
178C22—41no—
179C22—2441no—
180C22—2441no—
181C22—2441no—
182C22C2×C22⋊#692311yescharacteristic
183C4—21no—
184C4—21no—
185C4—41no—
186C4—612no—
187C4—612no—
188C4—1221no—
189C4—1221no—
190C4—2441no—
191C2—41no—
192C2—81no—
193C2—4881no—
194C2#1684074911yescharacteristic
195C2#1684075211yescharacteristic
196C2#1684075411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#121×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#121#6923
hypocenterC61#1553
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. #16840782C2semidirect
2. #16840779C2semidirect
3. #16840621C2semidirect
4. #16840620C2semidirect
104. C61#1553semidirect