Finite Group Databasebeta

← #21461351

Subgroups — #21461351

Order 7808.

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

normal subgroups only

This group has 246 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#16840765C211yesmaximal, characteristic, complemented
3#16840621C212yesmaximal, complemented
4#16840620C212yesmaximal, complemented
5#16840307C211yesmaximal, characteristic
6C2×#11758217—21no—
7#14519844C2212yes—
8#14519844C2212yes—
9C4⋊#92420—21no—
10C22⋊#92420—21no—
11#14519832—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—
36#11758217—42no—
37C2×#92420—22no—
38C2×#92420—22no—
39C4⋊C4×C61C2×C411yescharacteristic
40C22⋊C4×C61—21no—
41C22⋊Dic61—21no—
42#11758198—21no—
43#11758198—21no—
44C4⋊Dic61C2×C411yescharacteristic
45#11758196—21no—
46C4×Dic61C2×C411yescharacteristic
47C4×Dic61D411yescharacteristic
48C4×Dic61D411yescharacteristic
49C4×Dic61C2311yescharacteristic
50C23×C61—21no—
51C23×C61C22⋊C411yescharacteristic
52C22×D61—21no—
53D4×C61—41no—
54D4×C61—42no—
55C2×C4×C61—21no—
56C2×C4×C61—41no—
57C2×C4×C61C22⋊C411yescharacteristic
58C2×C4×C61C22×C411yescharacteristic
59C22⋊D61—42no—
60C22⋊D61—42no—
61C22⋊D61—41no—
62C22⋊D61—41no—
63C2×Dic61—21no—
64C2×Dic61—22no—
65C2×Dic61—21no—
66C2×Dic61—21no—
67C2×Dic61—42no—
68C2×Dic61C22⋊C411yescharacteristic
69C2×Dic61C22⋊C411yescharacteristic
70C2×Dic61C2×D411yescharacteristic
71C2×Dic61C2×D411yescharacteristic
72D244—41no—
73C4×D61—42no—
74Dic122—42no—
75#92420—42no—
76#92420—42no—
77C22×C61—21no—
78C22×C61—21no—
79C22×C61—21no—
80C22×C61—41no—
81C22×C61—41no—
82C22×C61—41no—
83C22×C61C2×C22⋊C411yescharacteristic
84C2×D61—41no—
85C2×D61—41no—
86C2×D61—41no—
87C4×C61—21no—
88C4×C61—21no—
89C4×C61—41no—
90Dic61—21no—
91Dic61—21no—
92Dic61—41no—
93Dic61AGL(1,ℤ/8)11yescharacteristic
94Dic61AGL(1,ℤ/8)12yes—
95Dic61#13711yescharacteristic
96#1557—611nomaximal, Sylow
97C2×C61—41no—
98C2×C61—81no—
99C2×C61#41311yescharacteristic
100C2×C61#41711yescharacteristic
101C2×C61#41811yescharacteristic
102D61—81no—
103#532—611no—
104#432—611no—
105#423—611no—
106#332—612no—
107#331—612no—
108C61#155711yescharacteristic, complemented, Sylow
109C2×#41—1221no—
110C2×M16—1221no—
111C4⋊Q8—611no—
112#127—611no—
113#124—1221no—
114#121—611no—
115#121—1221no—
116#121#692311yescharacteristic
117C4×D4—611no—
118C4×D4—611no—
119C4×D4—1221no—
120C2×C42—611no—
121C4⋊C8—612no—
122C4⋊C8—612no—
123C4⋊C8—1221no—
124C22⋊C8—1221no—
125#97—1221no—
126#41—2444no—
127C2×Q8—1221no—
128C2×D4—21no—
129C2×D4—611no—
130C2×D4—1221no—
131C2×D4—1221no—
132C2×D4—1221no—
133C2×D4C2×#692311yescharacteristic
134C22×C4—611no—
135C22×C4—611no—
136C22×C4—1221no—
137C22×C4—1221no—
138C22×C4C2×#692311yescharacteristic
139M16—2442no—
140C2×C8—1222no—
141C2×C8—1222no—
142C4⋊C4—611no—
143C4⋊C4—1221no—
144C4⋊C4C2×#692311yescharacteristic
145C22⋊C4—21no—
146C22⋊C4—1221no—
147C22⋊C4—1221no—
148C22⋊C4—1221no—
149C42—611no—
150C42—611no—
151C42—611no—
152C42—611no—
153C23—21no—
154C23—1221no—
155C23C22⋊#692311yescharacteristic
156Q8—2442no—
157D4—41no—
158D4—42no—
159D4—2441no—
160D4—2441no—
161D4—2441no—
162D4—2442no—
163D4—2442no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—611no—
167C2×C4—611no—
168C2×C4—611no—
169C2×C4—611no—
170C2×C4—1221no—
171C2×C4—1221no—
172C2×C4—1222no—
173C2×C4—1221no—
174C2×C4—2442no—
175C2×C4—2442no—
176C2×C4C22⋊#692311yescharacteristic
177C2×C4C22×#692311yescharacteristic
178C8—2442no—
179C8—2442no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—41no—
184C22—41no—
185C22—41no—
186C22—2441no—
187C22—2441no—
188C22—2441no—
189C22C2×C22⋊#692311yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—611no—
194C4—611no—
195C4—612no—
196C4—1221no—
197C4—1221no—
198C4—2441no—
199C2—41no—
200C2—81no—
201C2—4881no—
202C2#1684074911yescharacteristic
203C2#1684075311yescharacteristic
204C2#1684075411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#121×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#121#6923
hypocenterC61#1557
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. #16840765C2semidirect
3. #16840621C2semidirect
4. #16840620C2semidirect
108. C61#1557semidirect