Finite Group Databasebeta

← #21461271

Subgroups — #21461271

Order 7808.

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

normal subgroups only

This group has 234 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
1C4×#11758213C211yesmaximal, characteristic, complemented
2#16840721C211yesmaximal, characteristic, complemented
3#16840619C212yesmaximal, complemented
4#16840618C212yesmaximal, complemented
5#16840299C211yesmaximal, characteristic
6C2×#11758213—21no—
7C2×D61⋊C8—21no—
8#14519832—21no—
9#14519832C2212yes—
10#14519832C2212yes—
11C4×#92420—21no—
12#14519772—21no—
13#14519768C2211yescharacteristic
14#14519766C2211yescharacteristic
15#14519762—21no—
16#14519753C411yescharacteristic
17#14519752C411yescharacteristic
18C4×D244—21no—
19C4×D244C411yescharacteristic
20#14519734—21no—
21C42×D61C2211yescharacteristic
22C4×Q8×C61C411yescharacteristic
23C2×Q8×C61C2×C411yescharacteristic
24C2×D244—21no—
25C2×D244C2×C411yescharacteristic
26C2×C4×D61—21no—
27C2×C4×D61C2×C411yescharacteristic
28C2×C4×D61D411yescharacteristic
29C2×C4×D61D411yescharacteristic
30C2×#92420—22no—
31C2×#92420—22no—
32#11758213—24no—
33D61⋊C8—24no—
34C4⋊C4×C61—21no—
35C4⋊C4×C61C2×C411yescharacteristic
36C42×C61—21no—
37C42×C61C2×C411yescharacteristic
38#11758198—21no—
39#11758198—21no—
40#11758198—21no—
41#11758198—21no—
42#11758198—21no—
43C4⋊Dic61—21no—
44C4⋊Dic61C2×C411yescharacteristic
45#11758196—21no—
46#11758196—21no—
47C4×Dic61D411yescharacteristic
48C4×Dic61D411yescharacteristic
49C4×Dic61C2311yescharacteristic
50C22×D61—21no—
51C22×D61C22⋊C411yescharacteristic
52Q8×C61—41no—
53C2×C4×C61—21no—
54C2×C4×C61—21no—
55C2×C4×C61C22⋊C411yescharacteristic
56C2×C4×C61C22⋊C411yescharacteristic
57C2×C4×C61C22×C411yescharacteristic
58C2×Dic61—21no—
59C2×Dic61C22⋊C411yescharacteristic
60C2×Dic61C2×D411yescharacteristic
61C2×Dic61C2×D411yescharacteristic
62D244—41no—
63D244—42no—
64C4×D61—22no—
65C4×D61—22no—
66C4×D61—41no—
67C4×D61—42no—
68#92420—24no—
69#92420—24no—
70C22×C61C2×C22⋊C411yescharacteristic
71C2×D61—21no—
72C2×D61—21no—
73C2×D61—41no—
74C2×D61—41no—
75C2×D61—41no—
76C2×D61#10412yes—
77C4×C61—21no—
78C4×C61—21no—
79C4×C61—41no—
80C4×C61—41no—
81C4×C61#10412yes—
82Dic61—21no—
83Dic61—21no—
84Dic61—21no—
85Dic61—41no—
86#1524—611nomaximal, Sylow
87C2×C61#41311yescharacteristic
88C2×C61C2×#10411yescharacteristic
89C2×C61C2×#10411yescharacteristic
90D61—22no—
91D61—81no—
92#529—611no—
93C4×M16—611no—
94C2×#97—611no—
95#330—612no—
96#329—612no—
97C61#152411yescharacteristic, complemented, Sylow
98C2×M16—1221no—
99C22×C8—1221no—
100#126—1221no—
101#125—611no—
102#124—611no—
103#123—1221no—
104C22⋊Q8—611no—
105#121—611no—
106C4×Q8#692311yescharacteristic
107C4×D4—611no—
108C4×D4—1221no—
109#117—1221no—
110C2×C42—611no—
111#97—612no—
112#97—612no—
113#97—1221no—
114C4×C8—1221no—
115C2×Q8C2×#692311yescharacteristic
116C2×D4—611no—
117C2×D4—1221no—
118C22×C4—611no—
119C22×C4—611no—
120C22×C4—611no—
121C22×C4—1221no—
122M16—1224no—
123C2×C8—1222no—
124C2×C8—1222no—
125C2×C8—1224no—
126C4⋊C4—21no—
127C4⋊C4—611no—
128C4⋊C4—1221no—
129C4⋊C4—1221no—
130C4⋊C4—1221no—
131C4⋊C4C2×#692311yescharacteristic
132C22⋊C4—1221no—
133C22⋊C4—1221no—
134C22⋊C4—1221no—
135C22⋊C4—1221no—
136C22⋊C4—1221no—
137C42—21no—
138C42—611no—
139C42—611no—
140C42—611no—
141C42C2×#692311yescharacteristic
142C23—611no—
143C23—1221no—
144Q8—41no—
145D4—2441no—
146D4—2442no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—611no—
150C2×C4—611no—
151C2×C4—611no—
152C2×C4—1222no—
153C2×C4—1222no—
154C2×C4—1221no—
155C2×C4—2441no—
156C2×C4—2442no—
157C2×C4C22⋊#692311yescharacteristic
158C2×C4C22⋊#692311yescharacteristic
159C2×C4C22×#692311yescharacteristic
160C8—1224no—
161C8—1224no—
162C22—612no—
163C22—1221no—
164C22—1221no—
165C22—2441no—
166C22—2441no—
167C22—2441no—
168C22C2×C22⋊#692311yescharacteristic
169C4—21no—
170C4—21no—
171C4—41no—
172C4—41no—
173C4—1221no—
174C4—1221no—
175C4—1221no—
176C4—2441no—
177C4#1451984212yes—
178C2—1222no—
179C2—4881no—
180C2#1684074811yescharacteristic
181C2D61⋊#10411yescharacteristic
182C2C2×#1451984211yescharacteristic
subgroupG/H
centerC2×C4C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC4×Q8×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC4×Q8#6923
hypocenterC61#1524
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C4×#11758213C2semidirect
2. #16840721C2semidirect
3. #16840619C2semidirect
4. #16840618C2semidirect
97. C61#1524semidirect