Finite Group Databasebeta

← #21452948

Subgroups — #21452948

Order 7808.

416 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 141 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#16839701C212yesmaximal, complemented
2#16839698C211yesmaximal, characteristic
3#16839683C212yesmaximal, complemented
4#16839674C211yesmaximal, characteristic
5#16839661C212yesmaximal, complemented
6#16839655C212yesmaximal
7#16839645C212yesmaximal, complemented
8#16839622C212yesmaximal
9C61×#385C211yesmaximal, characteristic
10C22×Dic122C2211yescharacteristic
11C2×C4⋊Dic61C2212yes—
12C2×C4⋊Dic61C2212yes—
13C2×C4⋊Dic61C2212yes—
14C2×C4⋊Dic61C2211yescharacteristic
15C2×#11758196C2212yes—
16C2×C22⋊Dic61C2212yes—
17C2×C22⋊Dic61C2212yes—
18C2×C4×Dic61C2212yes—
19#14519684C2212yes—
20#14519684C2212yes—
21#14519684C2211yescharacteristic
22#14519684C2212yes—
23#14519684C2212yes—
24#14519684C2212yes—
25#14519684C2211yescharacteristic
26C23×C4×C61C2211yescharacteristic
27C2×C4⋊C4×C61C2212yes—
28C2×C22⋊C4×C61C2211yescharacteristic
29C2×C22⋊C4×C61C2211yescharacteristic
30#95×C61C2212yes—
31C24×C61C2311yescharacteristic
32C22×C4×C61—24no—
33C22×C4×C61—41no—
34C22×C4×C61C2311yescharacteristic
35C22×C4×C61C2311yescharacteristic
36C22×C4×C61C2312yes—
37C22×C4×C61C2312yes—
38C22×Dic61C2312yes—
39C22×Dic61C2312yes—
40C22×Dic61C2312yes—
41C22×Dic61C2312yes—
42C2×Dic122—41no—
43C2×Dic122—42no—
44C4⋊C4×C61—24no—
45C22⋊C4×C61—41no—
46C22⋊C4×C61Q814yescomplemented
47C22⋊Dic61—42no—
48C22⋊Dic61—42no—
49C4⋊Dic61—24no—
50C4⋊Dic61—41no—
51C4⋊Dic61—42no—
52C4⋊Dic61—42no—
53#11758196—42no—
54C4×Dic61—42no—
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—22no—
67C2×C4×C61—21no—
68C2×C4×C61—21no—
69C2×C4×C61—44no—
70C2×C4×C61C2×Q814yes—
71C2×C4×C61#4114yes—
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—22no—
84Dic122—44no—
85C22×C61—22no—
86C22×C61—24no—
87C22×C61—42no—
88C22×C61—41no—
89C22×C61—41no—
90C22×C61C22×Q811yescharacteristic
91C22×C61C2×#4112yes—
92C22×C61H(5,𝔽2)11yescharacteristic
93C22×C61H(5,𝔽2)12yes—
94C22×C612−1+411yescharacteristic
95C4×C61—24no—
96C4×C61—24no—
97C4×C61—41no—
98C4×C61—41no—
99Dic61—42no—
100Dic61—42no—
101Dic61—42no—
102Dic61—42no—
103#2742—611nomaximal, Sylow
104C2×C61—42no—
105C2×C61#54212yes—
106C2×C61#54411yescharacteristic
107C2×C61#55111yescharacteristic
108C2×C61#55412yes—
109C2×C61#56011yescharacteristic
110#400—612no—
111#399—611no—
112#395—612no—
113#393—611no—
114#389—612no—
115#388—612no—
116#387—612no—
117#385D6111yescharacteristic
118#380—612no—
119C61#274211yescharacteristic, complemented, Sylow
120C22×Q8—611no—
121C23×C4C2×D6111yescharacteristic
122C2×C4⋊C4—612no—
123C2×C4⋊C4—612no—
124C2×C4⋊C4—612no—
125C2×C4⋊C4—612no—
126C2×C4⋊C4—611no—
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—612no—
134#95—612no—
135#95—611no—
136#95—612no—
137#95—612no—
138#95—612no—
139#95—611no—
140#95C2×D6112yes—
141C24C22×D6111yescharacteristic
142C2×Q8—2441no—
143C2×Q8—2442no—
144C22×C4—24no—
145C22×C4—41no—
146C22×C4—612no—
147C22×C4—612no—
148C22×C4—612no—
149C22×C4—612no—
150C22×C4C22×D6111yescharacteristic
151C22×C4C22×D6111yescharacteristic
152C22×C4C22×D6112yes—
153C22×C4C22×D6112yes—
154C4⋊C4—24no—
155C4⋊C4—1224no—
156C4⋊C4—2442no—
157C4⋊C4—2442no—
158C4⋊C4—2442no—
159C4⋊C4—2441no—
160C22⋊C4—41no—
161C22⋊C4—2442no—
162C22⋊C4—2442no—
163C22⋊C4Dic12214yescomplemented
164C42—2442no—
165C23—22no—
166C23—21no—
167C23—22no—
168C23—21no—
169C23C2×Dic12212yes—
170C23C23×D6111yescharacteristic
171Q8—2444no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—44no—
181C2×C4—1222no—
182C2×C4—1222no—
183C2×C4—1222no—
184C2×C4—1222no—
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×C4C2×Dic12214yes—
194C2×C4#1175822414yes—
195C22—24no—
196C22—22no—
197C22—41no—
198C22—42no—
199C22—41no—
200C22C22×Dic12211yescharacteristic
201C22C2×#1175822412yes—
202C22#1451982211yescharacteristic
203C22#1451982312yes—
204C22#1451982511yescharacteristic
205C4—24no—
206C4—24no—
207C4—41no—
208C4—41no—
209C4—2442no—
210C4—2442no—
211C4—2442no—
212C4—2442no—
213C2—42no—
214C2#1684038512yes—
215C2#1684039311yescharacteristic
216C2#1684044311yescharacteristic
217C2#1684046912yes—
218C2#1684050211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#385C2
hypercenter#385D61
hypocenterC61#2742
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. #16839701C2semidirect
3. #16839683C2semidirect
5. #16839661C2semidirect
7. #16839645C2semidirect
46. C22⋊C4×C61Q8semidirect
119. C61#2742semidirect
163. C22⋊C4Dic122semidirect