Finite Group Databasebeta

← #21461350

Subgroups — #21461350

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#16840785C211yesmaximal, characteristic, complemented
2#16840767C211yesmaximal, characteristic, complemented
3#16840621C212yesmaximal, complemented
4#16840620C212yesmaximal, complemented
5#16840309C211yesmaximal, characteristic
6C2×#11758213—21no—
7#14519844—21no—
8#14519844C2212yes—
9#14519844C2212yes—
10#14519834—21no—
11#14519832—21no—
12C2×#11758222—21no—
13#14519776C2211yescharacteristic
14#14519773C2211yescharacteristic
15#14519763—21no—
16#14519752C411yescharacteristic
17#14519750—21no—
18#14519748C411yescharacteristic
19C4×D244C411yescharacteristic
20C4×C22⋊D61—21no—
21C42×D61C2211yescharacteristic
22C4×D4×C61C411yescharacteristic
23C2×D4×C61C2×C411yescharacteristic
24C22×C4×C61—21no—
25C2×C22⋊D61—21no—
26C2×C22⋊D61—21no—
27C2×C22⋊D61—21no—
28#11758222—44no—
29C2×D244—21no—
30C2×D244C2×C411yescharacteristic
31C2×C4×D61—21no—
32C2×C4×D61C2×C411yescharacteristic
33C2×C4×D61D411yescharacteristic
34C2×C4×D61D411yescharacteristic
35C2×Dic122—21no—
36C2×#92420—22no—
37C2×#92420—22no—
38#11758213—42no—
39C4⋊C4×C61C2×C411yescharacteristic
40C22⋊C4×C61—21no—
41C42×C61C2×C411yescharacteristic
42C22⋊Dic61—21no—
43#11758198—21no—
44#11758198—21no—
45C4⋊Dic61C2×C411yescharacteristic
46#11758196—21no—
47C4×Dic61D411yescharacteristic
48C4×Dic61D411yescharacteristic
49C4×Dic61C2311yescharacteristic
50C23×C61—21no—
51C22×D61—21no—
52C22×D61C22⋊C411yescharacteristic
53D4×C61—41no—
54C2×C4×C61—21no—
55C2×C4×C61—42no—
56C2×C4×C61C22⋊C411yescharacteristic
57C2×C4×C61C22⋊C411yescharacteristic
58C2×C4×C61C22×C411yescharacteristic
59C22⋊D61—42no—
60C22⋊D61—42no—
61C22⋊D61—41no—
62C22⋊D61—41no—
63C2×Dic61—21no—
64C2×Dic61C22⋊C411yescharacteristic
65C2×Dic61C2×D411yescharacteristic
66C2×Dic61C2×D411yescharacteristic
67D244—41no—
68D244—42no—
69C4×D61—21no—
70C4×D61—22no—
71C4×D61—21no—
72C4×D61—41no—
73C4×D61—42no—
74Dic122—42no—
75#92420—42no—
76#92420—42no—
77C22×C61—41no—
78C22×C61—41no—
79C22×C61—41no—
80C22×C61C2×C22⋊C411yescharacteristic
81C2×D61—21no—
82C2×D61—21no—
83C2×D61—21no—
84C2×D61—41no—
85C2×D61—41no—
86C2×D61—41no—
87C4×C61—21no—
88C4×C61—21no—
89C4×C61—21no—
90C4×C61—41no—
91Dic61—21no—
92Dic61—41no—
93Dic61AGL(1,ℤ/8)11yescharacteristic
94Dic61AGL(1,ℤ/8)12yes—
95Dic61#13711yescharacteristic
96#1557—611nomaximal, Sylow
97C2×C61—81no—
98C2×C61#41311yescharacteristic
99C2×C61#41711yescharacteristic
100C2×C61#41811yescharacteristic
101D61—41no—
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—611no—
116#121—1221no—
117C4×D4—611no—
118C4×D4—1221no—
119C4×D4#692311yescharacteristic
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—611no—
129C2×D4—1221no—
130C2×D4—1221no—
131C2×D4—1221no—
132C2×D4—1221no—
133C2×D4C2×#692311yescharacteristic
134C22×C4—21no—
135C22×C4—611no—
136C22×C4—611no—
137C22×C4—611no—
138C22×C4—1221no—
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—
152C42C2×#692311yescharacteristic
153C23—21no—
154C23—611no—
155C23—1221no—
156Q8—2442no—
157D4—41no—
158D4—2441no—
159D4—2442no—
160D4—2441no—
161D4—2441no—
162D4—2442no—
163D4—2442no—
164C2×C4—21no—
165C2×C4—42no—
166C2×C4—611no—
167C2×C4—611no—
168C2×C4—611no—
169C2×C4—1221no—
170C2×C4—1221no—
171C2×C4—1222no—
172C2×C4—1221no—
173C2×C4—2441no—
174C2×C4—2442no—
175C2×C4C22⋊#692311yescharacteristic
176C2×C4C22⋊#692311yescharacteristic
177C2×C4C22×#692311yescharacteristic
178C8—2442no—
179C8—2442no—
180C22—41no—
181C22—41no—
182C22—41no—
183C22—1221no—
184C22—1221no—
185C22—1221no—
186C22—2441no—
187C22—2441no—
188C22—2441no—
189C22C2×C22⋊#692311yescharacteristic
190C4—21no—
191C4—21no—
192C4—21no—
193C4—41no—
194C4—611no—
195C4—611no—
196C4—612no—
197C4—1221no—
198C4—2441no—
199C2—81no—
200C2—4881no—
201C2—2441no—
202C2#1684074811yescharacteristic
203C2#1684075311yescharacteristic
204C2#1684075411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC4×D4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC4×D4#6923
hypocenterC61#1557
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #16840785C2semidirect
2. #16840767C2semidirect
3. #16840621C2semidirect
4. #16840620C2semidirect
108. C61#1557semidirect