Finite Group Databasebeta

← #21461192

Subgroups — #21461192

Order 7808.

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

normal subgroups only

This group has 238 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#16840781C211yesmaximal, characteristic, complemented
2#16840698C211yesmaximal, characteristic, complemented
3#16840616C212yesmaximal, complemented
4#16840614C212yesmaximal
5#16840299C211yesmaximal, characteristic
6C2×C4×#6923—21no—
7C4⋊#92420—21no—
8#14519834C2212yes—
9C4×#92420—21no—
10(C2×#6923)⋊C4—21no—
11(C2×#6923)⋊C4C2212yes—
12#14519772—21no—
13#14519768C411yescharacteristic, complemented
14#14519766C411yescharacteristic, complemented
15#14519762—21no—
16#14519753C2211yescharacteristic
17#14519752C2211yescharacteristic
18C4×D244—21no—
19C4×D244C411yescharacteristic, complemented
20#14519734—21no—
21C42×D61C2211yescharacteristic
22C4×Q8×C61C411yescharacteristic, complemented
23C22×#6923—22no—
24C2×Q8×C61C2×C411yescharacteristic
25C2×D244—21no—
26C2×D244C2×C411yescharacteristic
27C2×C4×D61—21no—
28C2×C4×D61D411yescharacteristic
29C2×C4×D61D411yescharacteristic
30C2×C4×D61C2311yescharacteristic
31C2×#92420—22no—
32C4×#6923—24no—
33C4⋊C4×C61—21no—
34C4⋊C4×C61C2×C411yescharacteristic
35C42×C61—21no—
36C42×C61C2×C411yescharacteristic
37#11758198—21no—
38#11758198—21no—
39#11758198—21no—
40#11758198—21no—
41#11758198—21no—
42C4⋊Dic61—21no—
43C4⋊Dic61C2×C411yescharacteristic
44#11758196—21no—
45#11758196—21no—
46C4×Dic61C2×C411yescharacteristic
47C4×Dic61D411yescharacteristic
48C4×Dic61D411yescharacteristic
49C22×D61—21no—
50C22×D61C2×D411yescharacteristic
51C2×#6923—24no—
52C2×#6923—42no—
53C2×#6923—42no—
54Q8×C61—41no—
55C2×C4×C61—21no—
56C2×C4×C61—21no—
57C2×C4×C61C22⋊C411yescharacteristic
58C2×C4×C61C22⋊C411yescharacteristic
59C2×C4×C61C22×C411yescharacteristic
60C2×Dic61—21no—
61C2×Dic61C22⋊C411yescharacteristic
62C2×Dic61C22⋊C411yescharacteristic
63C2×Dic61C2×D411yescharacteristic
64D244—41no—
65D244—42no—
66C4×D61—22no—
67C4×D61—22no—
68C4×D61—41no—
69C4×D61—42no—
70#92420—42no—
71C22×C61C2×C22⋊C411yescharacteristic
72C2×D61—21no—
73C2×D61—21no—
74C2×D61—41no—
75C2×D61—41no—
76C2×D61—41no—
77C2×D61#13512yes—
78#6923—44no—
79C4×C61—21no—
80C4×C61—21no—
81C4×C61—41no—
82C4×C61—41no—
83C4×C61#10412yes—
84Dic61—21no—
85Dic61—21no—
86Dic61—21no—
87Dic61—41no—
88#1500—611nomaximal, Sylow
89C2×C61#41011yescharacteristic
90C2×C61#41611yescharacteristic
91C2×C61C2×#10411yescharacteristic
92D61—22no—
93D61—81no—
94#529—611no—
95#431—611no—
96#376—611no—
97#328—612no—
98#327—612no—
99C61#150011yescharacteristic, complemented, Sylow
100#126—1221no—
101#125—611no—
102#124—611no—
103#123—1221no—
104C22⋊Q8—611no—
105#121—611no—
106C4×Q8#692311yescharacteristic, complemented
107C4×D4—611no—
108C4×D4—1221no—
109#117—1221no—
110C2×C42—611no—
111C2×C42—1221no—
112C4⋊C8—1221no—
113C22⋊C8—612no—
114C4×C8—1221no—
115#95—612no—
116#95—1221no—
117C2×Q8C2×#692311yescharacteristic
118C2×D4—611no—
119C2×D4—1221no—
120C22×C4—611no—
121C22×C4—611no—
122C22×C4—611no—
123C22×C4—1222no—
124C22×C4—1221no—
125C2×C8—1222no—
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—
141C42—1224no—
142C42C2×#692311yescharacteristic
143C23—611no—
144C23—1221no—
145Q8—41no—
146D4—2441no—
147D4—2442no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—611no—
151C2×C4—611no—
152C2×C4—611no—
153C2×C4—1222no—
154C2×C4—1222no—
155C2×C4—1224no—
156C2×C4—1221no—
157C2×C4—2441no—
158C2×C4—2442no—
159C2×C4—2442no—
160C2×C4—2442no—
161C2×C4C22⋊#692311yescharacteristic
162C2×C4C22⋊#692311yescharacteristic
163C2×C4C22×#692311yescharacteristic
164C8—2442no—
165C22—612no—
166C22—1221no—
167C22—1221no—
168C22—2441no—
169C22—2441no—
170C22—2441no—
171C22C2×C22⋊#692311yescharacteristic
172C4—21no—
173C4—21no—
174C4—41no—
175C4—41no—
176C4—1221no—
177C4—1221no—
178C4—1221no—
179C4—2444no—
180C4—2441no—
181C4#1451984212yes—
182C2—1222no—
183C2—4881no—
184C2#1684074111yescharacteristic
185C2#1684075211yescharacteristic
186C2C2×#1451984211yescharacteristic
subgroupG/H
centerC2×C4C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC4×Q8×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC4×Q8#6923
hypocenterC61#1500
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. #16840781C2semidirect
2. #16840698C2semidirect
3. #16840616C2semidirect
13. #14519768C4semidirect
14. #14519766C4semidirect
19. C4×D244C4semidirect
22. C4×Q8×C61C4semidirect
99. C61#1500semidirect
106. C4×Q8#6923semidirect