Finite Group Databasebeta

← #21461175

Subgroups — #21461175

Order 7808.

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

normal subgroups only

This group has 216 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#16840780C211yesmaximal, characteristic, complemented
2#16840766C211yesmaximal, characteristic, complemented
3Q8⋊#92420C212yesmaximal, complemented
4D4⋊#92420C212yesmaximal, complemented
5#16840291C211yesmaximal, characteristic
6C2×#11758213—21no—
7#14519844—21no—
8C4⋊#92420—21no—
9C4⋊#92420C2212yes—
10#14519834—21no—
11C4×#92420C2212yes—
12#14519770—21no—
13#14519769C411yescharacteristic
14#14519759—21no—
15#14519753C411yescharacteristic
16#14519748C411yescharacteristic
17Q8×Dic61C2211yescharacteristic
18D4×Dic61C2211yescharacteristic
19#14519737—21no—
20#14519733—21no—
21C42×D61C2211yescharacteristic
22#124×C61C411yescharacteristic
23C2×Q8×C61C2×C411yescharacteristic
24C2×D4×C61C2×C411yescharacteristic
25C2×C22⋊D61—21no—
26C22×Dic61—21no—
27C2×C4×D61C2×C411yescharacteristic
28C2×C4×D61D411yescharacteristic
29C2×C4×D61D411yescharacteristic
30C2×#92420—22no—
31C2×#92420—22no—
32#11758213—42no—
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×Dic61D411yescharacteristic
47C4×Dic61D411yescharacteristic
48C4×Dic61C2311yescharacteristic
49C23×C61—21no—
50C22×D61C22⋊C411yescharacteristic
51Q8×C61—22no—
52D4×C61—22no—
53C2×C4×C61—21no—
54C2×C4×C61C22⋊C411yescharacteristic
55C2×C4×C61C22⋊C411yescharacteristic
56C2×C4×C61C22×C411yescharacteristic
57C22⋊D61—42no—
58C2×Dic61—21no—
59C2×Dic61—21no—
60C2×Dic61—41no—
61C2×Dic61—41no—
62C2×Dic61C22⋊C411yescharacteristic
63C2×Dic61C2×D411yescharacteristic
64C2×Dic61C2×D411yescharacteristic
65C4×D61—22no—
66C4×D61—21no—
67C4×D61—21no—
68C4×D61—41no—
69#92420—42no—
70#92420—42no—
71C22×C61—41no—
72C22×C61—41no—
73C22×C61—41no—
74C22×C61C2×C22⋊C411yescharacteristic
75C2×D61—21no—
76C2×D61—21no—
77C2×D61—21no—
78C4×C61—21no—
79C4×C61—21no—
80C4×C61—41no—
81C4×C61#13112yes—
82Dic61—21no—
83Dic61—21no—
84Dic61—41no—
85Dic61—41no—
86Dic61AGL(1,ℤ/8)11yescharacteristic
87Dic61#13711yescharacteristic
88#1495—611nomaximal, Sylow
89C2×C61—81no—
90C2×C61#40811yescharacteristic
91C2×C61#41711yescharacteristic
92C2×C61#42111yescharacteristic
93D61—41no—
94#529—611no—
95#431—611no—
96#423—611no—
97Q8⋊C8—612no—
98D4⋊C8—612no—
99C61#149511yescharacteristic, complemented, Sylow
100C2×M16—1221no—
101#126—1221no—
102#125—611no—
103#124#692311yescharacteristic
104#123—1221no—
105C22⋊Q8—611no—
106#121—611no—
107C4×Q8—611no—
108C4×D4—611no—
109C4×D4—1221no—
110#117—1221no—
111C2×C42—611no—
112C4⋊C8—612no—
113C4⋊C8—1221no—
114C4⋊C8—1221no—
115C22⋊C8—1221no—
116C4×C8—612no—
117C2×Q8C2×#692311yescharacteristic
118C2×D4—1221no—
119C2×D4C2×#692311yescharacteristic
120C22×C4—611no—
121C22×C4—611no—
122C22×C4—611no—
123C22×C4—1221no—
124M16—2442no—
125C2×C8—1222no—
126C2×C8—1222no—
127C4⋊C4—611no—
128C4⋊C4—611no—
129C4⋊C4—1221no—
130C4⋊C4—1221no—
131C4⋊C4—1221no—
132C4⋊C4—1221no—
133C22⋊C4—21no—
134C22⋊C4—21no—
135C22⋊C4—1221no—
136C22⋊C4—1221no—
137C22⋊C4—1221no—
138C42—611no—
139C42—611no—
140C42—611no—
141C42—1221no—
142C42C2×#692311yescharacteristic
143C23—21no—
144C23—611no—
145Q8—22no—
146D4—22no—
147D4—2442no—
148C2×C4—21no—
149C2×C4—611no—
150C2×C4—611no—
151C2×C4—611no—
152C2×C4—1221no—
153C2×C4—1221no—
154C2×C4—1222no—
155C2×C4—1221no—
156C2×C4—1221no—
157C2×C4—2441no—
158C2×C4—2441no—
159C2×C4—2441no—
160C2×C4C22⋊#692311yescharacteristic
161C2×C4C22⋊#692311yescharacteristic
162C2×C4C22×#692311yescharacteristic
163C8—2442no—
164C8—2442no—
165C22—41no—
166C22—41no—
167C22—41no—
168C22—1221no—
169C22—1221no—
170C22—1221no—
171C22C2×C22⋊#692311yescharacteristic
172C4—21no—
173C4—21no—
174C4—41no—
175C4—611no—
176C4—611no—
177C4—1221no—
178C4—1221no—
179C4—2441no—
180C4—2441no—
181C4#1451986412yes—
182C2—81no—
183C2—2441no—
184C2#1684073611yescharacteristic
185C2#1684075311yescharacteristic
186C2#1684075911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#124×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#124#6923
hypocenterC61#1495
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #16840780C2semidirect
2. #16840766C2semidirect
3. Q8⋊#92420C2semidirect
4. D4⋊#92420C2semidirect
99. C61#1495semidirect