Finite Group Databasebeta

← #21453653

Subgroups — #21453653

Order 7808.

420 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 121 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#16839684C212yesmaximal, complemented
2#16839680C212yesmaximal
3#16839679C211yesmaximal, characteristic
4#16839654C212yesmaximal, complemented
5#16839654C212yesmaximal, complemented
6#16839651C212yesmaximal, complemented
7#16839645C212yesmaximal, complemented
8#16839631C211yesmaximal, characteristic, complemented
9C61×#400C211yesmaximal, characteristic, complemented
10C22×D244C2211yescharacteristic
11C2×C4⋊Dic61C2212yes—
12C2×C4⋊Dic61C2211yescharacteristic
13C2×#11758196C2212yes—
14C2×#11758196C2212yes—
15C2×#11758198C2212yes—
16C2×#11758198C2212yes—
17C2×#11758198C2212yes—
18C2×#11758198C2212yes—
19C2×#11758198C2212yes—
20C2×#11758198C2212yes—
21C2×C4×Dic61C2211yescharacteristic
22C2×C4×Dic61C2212yes—
23#14519684C2212yes—
24#14519684C2211yescharacteristic
25#14519684C2212yes—
26C2×C4⋊C4×C61C2211yescharacteristic
27C2×C4⋊C4×C61C2211yescharacteristic
28#95×C61C2212yes—
29#95×C61C2211yescharacteristic
30#95×C61C2212yes—
31C23×D61C2312yes—
32C22×C4×C61C2311yescharacteristic
33C22×C4×C61C2312yes—
34C22×C4×C61C2312yes—
35C22×C4×C61C2311yescharacteristic
36C22×C4×C61C2311yescharacteristic
37C22×Dic61C2312yes—
38C22×Dic61C2312yes—
39C22×Dic61C2312yes—
40C2×D244—42no—
41C2×D244—41no—
42C4⋊C4×C61—41no—
43C4⋊C4×C61—41no—
44#11758198—24no—
45#11758198—24no—
46#11758198—24no—
47#11758198—42no—
48#11758198—42no—
49#11758198—42no—
50C4⋊Dic61—24no—
51C4⋊Dic61—41no—
52#11758196—42no—
53#11758196—42no—
54C4×Dic61—22no—
55C4×Dic61—42no—
56C23×C61C2411yescharacteristic
57C22×D61—22no—
58C22×D61—22no—
59C22×D61—22no—
60C22×D61—22no—
61C22×D61—22no—
62C22×D61—22no—
63C22×D61—22no—
64C2×C4×C61—21no—
65C2×C4×C61—21no—
66C2×C4×C61—22no—
67C2×C4×C61—22no—
68C2×C4×C61—22no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61—22no—
76C2×C4×C61#4112yes—
77C2×Dic61—22no—
78C2×Dic61—22no—
79C2×Dic61—22no—
80C2×Dic61—22no—
81C2×Dic61—22no—
82C2×Dic61—22no—
83C2×Dic61—22no—
84C2×Dic61—22no—
85C2×Dic61#4114yes—
86D244—44no—
87C22×C61C2×#4112yes—
88C22×C61C2×#4111yescharacteristic
89C22×C61H(5,𝔽2)11yescharacteristic
90C22×C61H(5,𝔽2)12yes—
91C22×C612−1+411yescharacteristic
92C2×D61—42no—
93C2×D61—42no—
94C2×D61—42no—
95C2×D61—42no—
96C2×D61—42no—
97C2×D61—42no—
98C2×D61—42no—
99C4×C61—22no—
100C4×C61—42no—
101C4×C61—42no—
102C4×C61—41no—
103C4×C61—41no—
104Dic61—24no—
105Dic61—42no—
106Dic61—42no—
107#2795—611nomaximal, Sylow
108C2×C61#53911yescharacteristic
109C2×C61#54212yes—
110C2×C61#55312yes—
111C2×C61#55511yescharacteristic
112C2×C61#56011yescharacteristic
113D61—82no—
114#400D6111yescharacteristic, complemented
115#396—612no—
116#394—611no—
117#394—612no—
118#388—612no—
119#388—612no—
120#388—612no—
121#387—612no—
122#384—611no—
123C61#279511yescharacteristic, complemented, Sylow
124C22×D4—611no—
125C2×C4⋊C4—612no—
126C2×C4⋊C4—612no—
127C2×C4⋊C4—611no—
128C2×C4⋊C4—612no—
129C2×C4⋊C4C2×D6111yescharacteristic
130C2×C4⋊C4C2×D6111yescharacteristic
131C2×C22⋊C4—612no—
132C2×C22⋊C4—612no—
133C2×C22⋊C4—612no—
134C2×C22⋊C4—612no—
135C2×C22⋊C4—612no—
136C2×C22⋊C4—612no—
137C2×C42—611no—
138C2×C42—612no—
139#95—611no—
140#95—612no—
141#95—612no—
142#95C2×D6112yes—
143#95C2×D6111yescharacteristic
144#95C2×D6112yes—
145C24—612no—
146C2×D4—2441no—
147C2×D4—2442no—
148C22×C4—612no—
149C22×C4—612no—
150C22×C4—612no—
151C22×C4C22×D6112yes—
152C22×C4C22×D6112yes—
153C22×C4C22×D6111yescharacteristic
154C22×C4C22×D6111yescharacteristic
155C22×C4C22×D6111yescharacteristic
156C4⋊C4—41no—
157C4⋊C4—41no—
158C4⋊C4—1224no—
159C4⋊C4—2442no—
160C4⋊C4—2442no—
161C4⋊C4—2441no—
162C22⋊C4—1224no—
163C22⋊C4—1224no—
164C22⋊C4—1224no—
165C22⋊C4—2442no—
166C22⋊C4—2442no—
167C22⋊C4—2442no—
168C42—1222no—
169C42—2442no—
170C23—1222no—
171C23—1222no—
172C23—1222no—
173C23—1222no—
174C23—1222no—
175C23—1222no—
176C23—1222no—
177C23C23×D6111yescharacteristic
178D4—2444no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—614no—
192C2×C4—1222no—
193C2×C4—1222no—
194C2×C4—1222no—
195C2×C4—1222no—
196C2×C4—1222no—
197C2×C4—1222no—
198C2×C4—1222no—
199C2×C4—1222no—
200C2×C4#1175822612yes—
201C22—2442no—
202C22—2442no—
203C22—2442no—
204C22—2442no—
205C22—2442no—
206C22—2442no—
207C22—2442no—
208C22#41×D6112yes—
209C22C2×#1175822611yescharacteristic
210C22#1451982211yescharacteristic
211C22#1451982312yes—
212C22#1451982411yescharacteristic
213C4—22no—
214C4—42no—
215C4—41no—
216C4—41no—
217C4—42no—
218C4—1224no—
219C4—2442no—
220C4—2442no—
221C2—4882no—
222C2#1684036111yescharacteristic
223C2#1684037812yes—
224C2#1684046512yes—
225C2#1684047411yescharacteristic
226C2#1684050211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#400C2
hypercenter#400D61
hypocenterC61#2795
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. #16839684C2semidirect
4. #16839654C2semidirect
5. #16839654C2semidirect
6. #16839651C2semidirect
7. #16839645C2semidirect
8. #16839631C2semidirect
9. C61×#400C2semidirect
114. #400D61semidirect
123. C61#2795semidirect