Finite Group Databasebeta

← #21461339

Subgroups — #21461339

Order 7808.

252 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 60 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
2D61⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
3#16840622C212yesmaximal, complemented
4#16840620C212yesmaximal, complemented
5#16840311C211yesmaximal, characteristic
6C2×D61⋊C8—21no—
7#14519844C2212yes—
8#14519844C2212yes—
9C4⋊#92420—21no—
10#14519834—21no—
11#14519832—21no—
12C2×#11758226C411yescharacteristic
13C2×#11758224C411yescharacteristic
14#14519775C2211yescharacteristic
15#14519773C2211yescharacteristic
16#14519765C411yescharacteristic
17#14519750—21no—
18#14519750—21no—
19#14519737—21no—
20#14519737—21no—
21C42×D61C2211yescharacteristic
22#124×C61C411yescharacteristic
23C2×Q8×C61C2×C411yescharacteristic
24C2×D4×C61C2×C411yescharacteristic
25C2×C22⋊D61—21no—
26C2×C22⋊D61—21no—
27C2×C22⋊D61—21no—
28C22×Dic61—21no—
29#11758226—42no—
30#11758224—42no—
31C2×D244—21no—
32C2×D244C2×C411yescharacteristic
33C2×C4×D61—21no—
34C2×C4×D61C2×C411yescharacteristic
35C2×C4×D61D411yescharacteristic
36C2×C4×D61D411yescharacteristic
37C2×Dic122C2×C411yescharacteristic
38C2×#92420—22no—
39C2×#92420—22no—
40D61⋊C8—42no—
41C22⋊C4×C61—21no—
42C22⋊C4×C61—21no—
43C42×C61C2×C411yescharacteristic
44#11758198—21no—
45#11758198—21no—
46#11758196—21no—
47#11758196—21no—
48C4×Dic61D411yescharacteristic
49C4×Dic61D411yescharacteristic
50C4×Dic61C2311yescharacteristic
51C23×C61—21no—
52C22×D61—21no—
53C22×D61C22⋊C411yescharacteristic
54Q8×C61—41no—
55D4×C61—41no—
56C2×C4×C61—21no—
57C2×C4×C61C22⋊C411yescharacteristic
58C2×C4×C61C22⋊C411yescharacteristic
59C2×C4×C61C22×C411yescharacteristic
60C22⋊D61—42no—
61C22⋊D61—42no—
62C22⋊D61—41no—
63C22⋊D61—41no—
64C2×Dic61—21no—
65C2×Dic61—42no—
66C2×Dic61C22⋊C411yescharacteristic
67C2×Dic61C2×D411yescharacteristic
68C2×Dic61C2×D411yescharacteristic
69D244—41no—
70D244—42no—
71C4×D61—22no—
72C4×D61—22no—
73C4×D61—21no—
74C4×D61—21no—
75C4×D61—42no—
76Dic122—41no—
77#92420—42no—
78#92420—42no—
79C22×C61—41no—
80C22×C61—41no—
81C22×C61—41no—
82C22×C61C2×C22⋊C411yescharacteristic
83C2×D61—21no—
84C2×D61—21no—
85C2×D61—41no—
86C2×D61—41no—
87C2×D61—41no—
88C2×D61#10012yes—
89C4×C61—21no—
90C4×C61—21no—
91C4×C61—21no—
92C4×C61—41no—
93Dic61—21no—
94Dic61—41no—
95Dic61#13512yes—
96Dic61AGL(1,ℤ/8)11yescharacteristic
97Dic61#13711yescharacteristic
98#1551—611nomaximal, Sylow
99C2×C61—81no—
100C2×C61C2×#10011yescharacteristic
101C2×C61#41611yescharacteristic
102C2×C61#41711yescharacteristic
103D61—22no—
104D61—81no—
105#532—611no—
106#432—611no—
107C2×C4⋊C8—611no—
108#333—612no—
109#331—612no—
110C61#155111yescharacteristic, complemented, Sylow
111C2×#41—611no—
112C2×#41—611no—
113C22×C8—1221no—
114C4⋊Q8—611no—
115#127—611no—
116#124—611no—
117#124#692311yescharacteristic
118#121—1221no—
119#121—1221no—
120C4×D4—1221no—
121C4×D4—1221no—
122C2×C42—611no—
123C4⋊C8—612no—
124C4⋊C8—612no—
125C4⋊C8—1221no—
126C22⋊C8—1221no—
127#97—1221no—
128#41—2442no—
129#41—2442no—
130C2×Q8—611no—
131C2×Q8C2×#692311yescharacteristic
132C2×D4—611no—
133C2×D4—1221no—
134C2×D4—1221no—
135C2×D4—1221no—
136C2×D4—1221no—
137C2×D4C2×#692311yescharacteristic
138C22×C4—611no—
139C22×C4—611no—
140C22×C4—611no—
141C22×C4—1221no—
142C22×C4—1221no—
143C2×C8—1222no—
144C2×C8—1222no—
145C2×C8—2442no—
146C4⋊C4—1221no—
147C4⋊C4—1221no—
148C22⋊C4—21no—
149C22⋊C4—21no—
150C22⋊C4—1221no—
151C22⋊C4—1221no—
152C42—611no—
153C42—611no—
154C42—611no—
155C42C2×#692311yescharacteristic
156C23—21no—
157C23—611no—
158C23—1221no—
159Q8—41no—
160Q8—2441no—
161D4—41no—
162D4—2441no—
163D4—2442no—
164D4—2442no—
165D4—2441no—
166D4—2441no—
167D4—2442no—
168C2×C4—21no—
169C2×C4—611no—
170C2×C4—611no—
171C2×C4—611no—
172C2×C4—1221no—
173C2×C4—1222no—
174C2×C4—1221no—
175C2×C4—1222no—
176C2×C4—1221no—
177C2×C4—2442no—
178C2×C4—2442no—
179C2×C4C22⋊#692311yescharacteristic
180C2×C4C22⋊#692311yescharacteristic
181C2×C4C22×#692311yescharacteristic
182C8—2442no—
183C8—2442no—
184C22—41no—
185C22—41no—
186C22—41no—
187C22—612no—
188C22—1221no—
189C22—1221no—
190C22—2441no—
191C22—2441no—
192C22—2441no—
193C22C2×C22⋊#692311yescharacteristic
194C4—21no—
195C4—21no—
196C4—21no—
197C4—41no—
198C4—612no—
199C4—611no—
200C4—611no—
201C4—1221no—
202C4—2441no—
203C2—81no—
204C2—1222no—
205C2—4881no—
206C2D61⋊#10011yescharacteristic
207C2#1684075211yescharacteristic
208C2#1684075311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#124×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#124#6923
hypocenterC61#1551
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #16840785C2semidirect
2. D61⋊(C4⋊C8)C2semidirect
3. #16840622C2semidirect
4. #16840620C2semidirect
110. C61#1551semidirect