Finite Group Databasebeta

← #21444316

Subgroups — #21444316

Order 7808.

240 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 71 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#16840314C211yesmaximal, characteristic
2#16839812C211yesmaximal, characteristic
3#16839613C211yesmaximal, characteristic
4#16839500C211yesmaximal, characteristic
5#16839499C211yesmaximal, characteristic
6#16839498C211yesmaximal, characteristic
7C61×#328C211yesmaximal, characteristic
8#14519776C411yescharacteristic, complemented
9#14519775C411yescharacteristic, complemented
10#14519767—21no—
11#14519756C2211yescharacteristic
12#14519754—21no—
13Q8×Dic61C411yescharacteristic, complemented
14#14519742—21no—
15#14519742C411yescharacteristic, complemented
16#14519733—21no—
17C2×#11758196—21no—
18C2×C4×Dic61—21no—
19C2×C4×Dic61C2211yescharacteristic
20#14519706—21no—
21C22⋊#92418C2211yescharacteristic
22C8×Dic61—21no—
23#14519684C2211yescharacteristic
24C22⋊Q8×C61C2211yescharacteristic
25C22⋊C8×C61C2211yescharacteristic
26#95×C61C2211yescharacteristic
27C2×Q8×C61C2×C411yescharacteristic
28C22×C4×C61—21no—
29C22×C4×C61C2311yescharacteristic
30C22×Dic61—21no—
31C22×Dic61D411yescharacteristic
32C22×Dic61D411yescharacteristic
33C2×Dic122—21no—
34C2×Dic122C2×C411yescharacteristic
35C2×C8×C61—21no—
36C4⋊C4×C61—21no—
37C4⋊C4×C61C2×C411yescharacteristic
38C22⋊C4×C61—21no—
39C22⋊Dic61—21no—
40C4⋊Dic61—21no—
41C4⋊Dic61C2×C411yescharacteristic
42#11758196—24no—
43#11758196—21no—
44#11758196—21no—
45#11758196—21no—
46#11758196—21no—
47#11758196—21no—
48C4×Dic61—21no—
49C4×Dic61—21no—
50C4×Dic61—42no—
51C4×Dic61C2×C411yescharacteristic
52C4×Dic61C2×C411yescharacteristic
53C4×Dic61D411yescharacteristic
54C4×Dic61D411yescharacteristic
55C2×#92418—21no—
56C23×C61C2×D411yescharacteristic
57Q8×C61—41no—
58C2×C4×C61—22no—
59C2×C4×C61—21no—
60C2×C4×C61—21no—
61C2×C4×C61—41no—
62C2×C4×C61—41no—
63C2×C4×C61—41no—
64C2×C4×C61C22×C411yescharacteristic
65C2×C4×C61C2×D411yescharacteristic
66C2×Dic61—22no—
67C2×Dic61—22no—
68C2×Dic61—21no—
69C2×Dic61—21no—
70C2×Dic61—41no—
71C2×Dic61—41no—
72C2×Dic61C22⋊C411yescharacteristic
73C2×Dic61C22⋊C411yescharacteristic
74C2×Dic61C22⋊C411yescharacteristic
75C2×Dic61C22⋊C411yescharacteristic
76C2×Dic61SD1612yes—
77C2×Dic61Q1612yes—
78Dic122—42no—
79Dic122—41no—
80C8×C61—41no—
81#92418—41no—
82C22×C61—21no—
83C22×C61—21no—
84C22×C61C2×C22⋊C411yescharacteristic
85C22×C61C2×SD1611yescharacteristic
86C22×C61C2×Q1611yescharacteristic
87C4×C61—21no—
88C4×C61—21no—
89C4×C61—42no—
90C4×C61—41no—
91C4×C61—41no—
92Dic61—21no—
93Dic61—42no—
94Dic61—41no—
95Dic61—41no—
96Dic61#10312yes—
97Dic61#10312yes—
98Dic61#10412yes—
99#1503—611nomaximal, Sylow
100C2×C61—21no—
101C2×C61—21no—
102C2×C61#41011yescharacteristic
103C2×C61C2×#10311yescharacteristic
104C2×C61C2×#10411yescharacteristic
105#533—611no—
106#431—611no—
107C4×C4⋊C4—611no—
108#328—611no—
109#328—611no—
110#328—611no—
111#328D6111yescharacteristic
112C61#150311yescharacteristic, complemented, Sylow
113C4⋊Q8—611no—
114C4⋊Q8—611no—
115#125—1221no—
116C22⋊Q8—611no—
117C22⋊Q8—1221no—
118C22⋊Q8C2×D6111yescharacteristic
119C4×Q8—611no—
120C4×Q8—611no—
121C4×Q8—1221no—
122#117—1221no—
123C2×C4⋊C4—1221no—
124C2×C42—611no—
125C2×C42—1221no—
126C4⋊C8—1221no—
127C22⋊C8—611no—
128C22⋊C8C2×D6111yescharacteristic
129C4×C8—1221no—
130#95—611no—
131#95C2×D6111yescharacteristic
132C2×Q8—611no—
133C2×Q8—1221no—
134C2×Q8C4×D6111yescharacteristic
135C22×C4—21no—
136C22×C4—611no—
137C22×C4—611no—
138C22×C4—1221no—
139C22×C4C22×D6111yescharacteristic
140C2×C8—21no—
141C2×C8—1221no—
142C4⋊C4—21no—
143C4⋊C4—611no—
144C4⋊C4—1221no—
145C4⋊C4—1221no—
146C4⋊C4—1221no—
147C4⋊C4—1221no—
148C4⋊C4—1221no—
149C4⋊C4—1224no—
150C4⋊C4—1221no—
151C4⋊C4C4×D6111yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—1221no—
154C42—611no—
155C42—611no—
156C42—611no—
157C42—611no—
158C42—1221no—
159C42—1221no—
160C42—2442no—
161C23D4×D6111yescharacteristic
162Q8—41no—
163Q8—2441no—
164Q8—2442no—
165C2×C4—22no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—611no—
172C2×C4—611no—
173C2×C4—611no—
174C2×C4—612no—
175C2×C4—612no—
176C2×C4—611no—
177C2×C4—1222no—
178C2×C4—1222no—
179C2×C4—1221no—
180C2×C4—1221no—
181C2×C4—2441no—
182C2×C4—2441no—
183C2×C4C2×C4×D6111yescharacteristic
184C2×C4D4×D6111yescharacteristic
185C8—41no—
186C8—2441no—
187C22—21no—
188C22—21no—
189C22C22⋊C4×D6111yescharacteristic
190C22SD16×D6111yescharacteristic
191C22Q16×D6111yescharacteristic
192C4—21no—
193C4—21no—
194C4—42no—
195C4—41no—
196C4—41no—
197C4—612no—
198C4—612no—
199C4—612no—
200C4—1221no—
201C4—2442no—
202C4—2441no—
203C4—2441no—
204C2—21no—
205C2—21no—
206C2#1683973411yescharacteristic
207C2#103×D6111yescharacteristic
208C2#104×D6111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#328C2
socleC22×C61C2×C22⋊C4
hypercenter#328D61
hypocenterC61#1503
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
8. #14519776C4semidirect
9. #14519775C4semidirect
13. Q8×Dic61C4semidirect
15. #14519742C4semidirect
112. C61#1503semidirect