Finite Group Databasebeta

← #21461191

Subgroups — #21461191

Order 7808.

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

normal subgroups only

This group has 238 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#16840780C211yesmaximal, characteristic, complemented
2#16840698C211yesmaximal, characteristic, complemented
3#16840616C212yesmaximal, complemented
4#16840613C212yesmaximal
5#16840291C211yesmaximal, characteristic
6C2×C4×#6923—21no—
7#14519844—21no—
8#14519834C2212yes—
9C4×#92420—21no—
10(C2×#6923)⋊C4—21no—
11(C2×#6923)⋊C4C2212yes—
12#14519770—21no—
13#14519769C411yescharacteristic, complemented
14#14519759—21no—
15#14519753C2211yescharacteristic
16#14519748C2211yescharacteristic
17Q8×Dic61C411yescharacteristic, complemented
18D4×Dic61C411yescharacteristic, complemented
19#14519737—21no—
20#14519733—21no—
21C42×D61C2211yescharacteristic
22#124×C61C411yescharacteristic, complemented
23C22×#6923—22no—
24C2×Q8×C61C2×C411yescharacteristic
25C2×D4×C61C2×C411yescharacteristic
26C2×C22⋊D61—21no—
27C22×Dic61—21no—
28C2×C4×D61D411yescharacteristic
29C2×C4×D61D411yescharacteristic
30C2×C4×D61C2311yescharacteristic
31C2×#92420—22no—
32C4×#6923—24no—
33C22⋊C4×C61—21no—
34C22⋊C4×C61—21no—
35C42×C61C2×C411yescharacteristic
36C22⋊Dic61—21no—
37C22⋊Dic61—21no—
38#11758198—21no—
39C4⋊Dic61—21no—
40C4⋊Dic61C2×C411yescharacteristic
41C4⋊Dic61C2×C411yescharacteristic
42#11758196—21no—
43#11758196—21no—
44#11758196—21no—
45C4×Dic61—21no—
46C4×Dic61C2×C411yescharacteristic
47C4×Dic61D411yescharacteristic
48C4×Dic61D411yescharacteristic
49C23×C61—21no—
50C22×D61C2×D411yescharacteristic
51C2×#6923—24no—
52C2×#6923—42no—
53C2×#6923—42no—
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—
61C2×Dic61—21no—
62C2×Dic61—21no—
63C2×Dic61—42no—
64C2×Dic61C22⋊C411yescharacteristic
65C2×Dic61C22⋊C411yescharacteristic
66C2×Dic61C2×D411yescharacteristic
67C4×D61—22no—
68C4×D61—22no—
69C4×D61—41no—
70#92420—42no—
71C22×C61—41no—
72C22×C61—41no—
73C22×C61—41no—
74C22×C61C2×C22⋊C411yescharacteristic
75C2×D61—21no—
76C2×D61—21no—
77C2×D61#13512yes—
78#6923—44no—
79C4×C61—21no—
80C4×C61—21no—
81C4×C61—21no—
82C4×C61—41no—
83Dic61—21no—
84Dic61—21no—
85Dic61—41no—
86Dic61—41no—
87Dic61#10412yes—
88#1500—611nomaximal, Sylow
89C2×C61—81no—
90C2×C61#41011yescharacteristic
91C2×C61#41611yescharacteristic
92C2×C61C2×#10411yescharacteristic
93D61—22no—
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#692311yescharacteristic, complemented
103#123—1221no—
104C22⋊Q8—611no—
105#121—611no—
106C4×Q8—611no—
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—1221no—
119C2×D4C2×#692311yescharacteristic
120C22×C4—611no—
121C22×C4—611no—
122C22×C4—611no—
123C22×C4—1221no—
124C22×C4—1222no—
125C2×C8—1222no—
126C4⋊C4—611no—
127C4⋊C4—611no—
128C4⋊C4—1221no—
129C4⋊C4—1221no—
130C4⋊C4—1221no—
131C4⋊C4—1221no—
132C22⋊C4—21no—
133C22⋊C4—21no—
134C22⋊C4—1221no—
135C22⋊C4—1221no—
136C22⋊C4—1221no—
137C42—611no—
138C42—611no—
139C42—611no—
140C42—1221no—
141C42—1224no—
142C42C2×#692311yescharacteristic
143C23—21no—
144C23—611no—
145Q8—41no—
146D4—41no—
147D4—2442no—
148C2×C4—21no—
149C2×C4—611no—
150C2×C4—611no—
151C2×C4—611no—
152C2×C4—1222no—
153C2×C4—1222no—
154C2×C4—1224no—
155C2×C4—1221no—
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—41no—
166C22—41no—
167C22—41no—
168C22—612no—
169C22—1221no—
170C22—1221no—
171C22C2×C22⋊#692311yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—41no—
176C4—612no—
177C4—1221no—
178C4—1221no—
179C4—2444no—
180C4—2441no—
181C4—2441no—
182C2—81no—
183C2—1222no—
184C2#1684074211yescharacteristic
185C2#1684075211yescharacteristic
186C2D61⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#124×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#124#6923
hypocenterC61#1500
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. #16840780C2semidirect
2. #16840698C2semidirect
3. #16840616C2semidirect
13. #14519769C4semidirect
17. Q8×Dic61C4semidirect
18. D4×Dic61C4semidirect
22. #124×C61C4semidirect
99. C61#1500semidirect
102. #124#6923semidirect