Finite Group Databasebeta

← #21453233

Subgroups — #21453233

Order 7808.

424 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 137 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#16839704C212yesmaximal, complemented
2#16839682C212yesmaximal, complemented
3#16839674C211yesmaximal, characteristic
4#16839674C211yesmaximal, characteristic
5#16839666C212yesmaximal, complemented
6#16839655C212yesmaximal
7#16839635C212yesmaximal
8#16839627C212yesmaximal, complemented
9C61×#385C211yesmaximal, characteristic
10C22×Dic122C2211yescharacteristic
11C22×Dic122C2211yescharacteristic
12C2×C4⋊Dic61C2212yes—
13C2×#11758196C2212yes—
14C2×#11758196C2212yes—
15C2×C22⋊Dic61C2212yes—
16C2×C22⋊Dic61C2212yes—
17C2×C4×Dic61C2212yes—
18#14519684C2212yes—
19#14519684C2212yes—
20#14519684C2212yes—
21#14519684C2211yescharacteristic
22#14519684C2212yes—
23#14519684C2212yes—
24#14519684C2211yescharacteristic
25#14519684C2212yes—
26C23×C4×C61C2211yescharacteristic
27C2×C4⋊C4×C61C2212yes—
28C2×C22⋊C4×C61C2211yescharacteristic
29C2×C22⋊C4×C61C2211yescharacteristic
30#95×C61C2212yes—
31C24×C61C2311yescharacteristic
32C22×C4×C61—41no—
33C22×C4×C61—42no—
34C22×C4×C61C2311yescharacteristic
35C22×C4×C61C2311yescharacteristic
36C22×C4×C61C2312yes—
37C22×C4×C61C2312yes—
38C22×Dic61C2312yes—
39C22×Dic61C2312yes—
40C22×Dic61C2312yes—
41C22×Dic61C2312yes—
42C2×Dic122—24no—
43C2×Dic122—41no—
44C2×Dic122—41no—
45C2×Dic122—42no—
46C4⋊C4×C61—42no—
47C22⋊C4×C61—41no—
48C22⋊C4×C61Q814yescomplemented
49C22⋊Dic61—24no—
50C22⋊Dic61—42no—
51C4⋊Dic61—42no—
52#11758196—42no—
53#11758196—42no—
54C4×Dic61—24no—
55C23×C61—22no—
56C23×C61—22no—
57C23×C61—21no—
58C23×C61—21no—
59C23×C61C2×Q812yes—
60C23×C61C2411yescharacteristic
61C2×C4×C61—22no—
62C2×C4×C61—22no—
63C2×C4×C61—22no—
64C2×C4×C61—22no—
65C2×C4×C61—22no—
66C2×C4×C61—21no—
67C2×C4×C61—21no—
68C2×C4×C61—22no—
69C2×C4×C61—22no—
70C2×C4×C61—44no—
71C2×C4×C61C2×Q814yes—
72C2×Dic61—22no—
73C2×Dic61—22no—
74C2×Dic61—22no—
75C2×Dic61—22no—
76C2×Dic61—22no—
77C2×Dic61—22no—
78C2×Dic61—22no—
79C2×Dic61—22no—
80C2×Dic61—22no—
81C2×Dic61—22no—
82C2×Dic61—22no—
83C2×Dic61#4114yes—
84Dic122—44no—
85Dic122—44no—
86C22×C61—22no—
87C22×C61—24no—
88C22×C61—42no—
89C22×C61—41no—
90C22×C61—41no—
91C22×C61C22×Q811yescharacteristic
92C22×C61C2×#4112yes—
93C22×C61H(5,𝔽2)12yes—
94C22×C61H(5,𝔽2)11yescharacteristic
95C22×C612−1+411yescharacteristic
96C4×C61—24no—
97C4×C61—41no—
98C4×C61—41no—
99C4×C61—42no—
100Dic61—24no—
101Dic61—42no—
102Dic61—42no—
103Dic61—42no—
104#2763—611nomaximal, Sylow
105C2×C61—42no—
106C2×C61#54212yes—
107C2×C61#54411yescharacteristic
108C2×C61#55111yescharacteristic
109C2×C61#55412yes—
110C2×C61H(3,𝔽4)11yescharacteristic
111#400—612no—
112#395—612no—
113#393—611no—
114#393—611no—
115#391—612no—
116#388—612no—
117#385—612no—
118#385D6111yescharacteristic
119#382—612no—
120C61#276311yescharacteristic, complemented, Sylow
121C22×Q8—611no—
122C22×Q8—611no—
123C23×C4C2×D6111yescharacteristic
124C2×C4⋊C4—612no—
125C2×C4⋊C4—612no—
126C2×C4⋊C4—612no—
127C2×C4⋊C4C2×D6112yes—
128C2×C22⋊C4—612no—
129C2×C22⋊C4—612no—
130C2×C22⋊C4C2×D6111yescharacteristic
131C2×C22⋊C4C2×D6111yescharacteristic
132C2×C42—612no—
133#95—611no—
134#95—612no—
135#95—612no—
136#95—612no—
137#95—612no—
138#95—612no—
139#95—612no—
140#95—611no—
141#95C2×D6112yes—
142C24C22×D6111yescharacteristic
143C2×Q8—1224no—
144C2×Q8—2441no—
145C2×Q8—2441no—
146C2×Q8—2442no—
147C22×C4—42no—
148C22×C4—41no—
149C22×C4—612no—
150C22×C4—612no—
151C22×C4—612no—
152C22×C4—612no—
153C22×C4C22×D6111yescharacteristic
154C22×C4C22×D6111yescharacteristic
155C22×C4C22×D6112yes—
156C22×C4C22×D6112yes—
157C4⋊C4—42no—
158C4⋊C4—2442no—
159C4⋊C4—2442no—
160C4⋊C4—2442no—
161C22⋊C4—41no—
162C22⋊C4—1224no—
163C22⋊C4—2442no—
164C22⋊C4Dic12214yescomplemented
165C42—1224no—
166C23—22no—
167C23—21no—
168C23—22no—
169C23—21no—
170C23C2×Dic12212yes—
171C23C23×D6111yescharacteristic
172Q8—2444no—
173Q8—2444no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—44no—
184C2×C4—614no—
185C2×C4—1222no—
186C2×C4—1222no—
187C2×C4—1222no—
188C2×C4—1222no—
189C2×C4—1222no—
190C2×C4—1222no—
191C2×C4—1222no—
192C2×C4—1222no—
193C2×C4—1222no—
194C2×C4—1222no—
195C2×C4—1222no—
196C2×C4C2×Dic12214yes—
197C22—24no—
198C22—22no—
199C22—41no—
200C22—42no—
201C22—41no—
202C22C22×Dic12211yescharacteristic
203C22#41×D6112yes—
204C22#1451982212yes—
205C22#1451982211yescharacteristic
206C22#1451982511yescharacteristic
207C4—24no—
208C4—42no—
209C4—41no—
210C4—41no—
211C4—1224no—
212C4—2442no—
213C4—2442no—
214C4—2442no—
215C2—42no—
216C2#1684038212yes—
217C2#1684039311yescharacteristic
218C2#1684044011yescharacteristic
219C2#1684047112yes—
220C2#1684050511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#385C2
hypercenter#385D61
hypocenterC61#2763
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. #16839704C2semidirect
2. #16839682C2semidirect
5. #16839666C2semidirect
8. #16839627C2semidirect
48. C22⋊C4×C61Q8semidirect
120. C61#2763semidirect
164. C22⋊C4Dic122semidirect