Finite Group Databasebeta

← #21451315

Subgroups — #21451315

Order 7808.

440 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 129 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#16839701C211yesmaximal, characteristic, complemented
2#16839692C211yesmaximal, characteristic, complemented
3#16839676C212yesmaximal
4#16839656C212yesmaximal, complemented
5#16839656C212yesmaximal, complemented
6#16839655C212yesmaximal, complemented
7#16839655C212yesmaximal, complemented
8C4×#11758196C212yesmaximal, complemented
9C61×#390C211yesmaximal, characteristic
10C2×C4⋊Dic61C2211yescharacteristic
11C2×C4⋊Dic61C2211yescharacteristic
12C2×#11758196C2212yes—
13C2×#11758196C2212yes—
14C2×C22⋊Dic61C2212yes—
15C2×C22⋊Dic61C2212yes—
16C2×C22⋊Dic61C2212yes—
17C2×C22⋊Dic61C2212yes—
18C2×C4×Dic61C2212yes—
19C2×C4×Dic61C2212yes—
20#14519684C2212yes—
21#14519684C2211yescharacteristic
22#14519684C2212yes—
23#14519684C2212yes—
24#14519684C2211yescharacteristic
25#14519684C2212yes—
26C22×D4×C61C2211yescharacteristic
27C2×C4⋊C4×C61C2211yescharacteristic
28C2×C22⋊C4×C61C2212yes—
29C2×C22⋊C4×C61C2212yes—
30C2×C42×C61C2211yescharacteristic
31C24×C61C2312yes—
32C2×D4×C61—22no—
33C2×D4×C61—41no—
34C2×D4×C61—41no—
35C22×C4×C61C2311yescharacteristic
36C22×C4×C61C2311yescharacteristic
37C22×C4×C61C2312yes—
38C22×C4×C61C2311yescharacteristic
39C22×Dic61C2312yes—
40C22×Dic61C2312yes—
41C22×Dic61C2312yes—
42C22×Dic61C2312yes—
43C4⋊C4×C61—41no—
44C22⋊C4×C61—24no—
45C22⋊C4×C61—24no—
46C42×C61—41no—
47C22⋊Dic61—24no—
48C22⋊Dic61—24no—
49C22⋊Dic61—42no—
50C22⋊Dic61—42no—
51C4⋊Dic61—41no—
52C4⋊Dic61—41no—
53#11758196—24no—
54#11758196—24no—
55C4×Dic61—24no—
56C4×Dic61—42no—
57C23×C61—22no—
58C23×C61—22no—
59C23×C61—22no—
60C23×C61—22no—
61C23×C61—22no—
62C23×C61—22no—
63C23×C61—22no—
64C23×C61C2411yescharacteristic
65D4×C61—44no—
66C2×C4×C61—22no—
67C2×C4×C61—22no—
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61#4112yes—
75C2×C4×C61#4114yes—
76C2×Dic61—22no—
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—22no—
86C2×Dic61—22no—
87C2×Dic61#4114yes—
88C22×C61—42no—
89C22×C61—42no—
90C22×C61—42no—
91C22×C61—42no—
92C22×C61—42no—
93C22×C61—42no—
94C22×C61—42no—
95C22×C61C2×#4112yes—
96C22×C61C2×#4112yes—
97C22×C61C2×#4111yescharacteristic
98C22×C61H(5,𝔽2)11yescharacteristic
99C22×C61H(5,𝔽2)11yescharacteristic
100C4×C61—22no—
101C4×C61—24no—
102C4×C61—41no—
103C4×C61—41no—
104Dic61—24no—
105Dic61—42no—
106Dic61—42no—
107Dic61—42no—
108#2593—611nomaximal, Sylow
109C2×C61—82no—
110C2×C61#52912yes—
111C2×C61#53811yescharacteristic
112C2×C61#55312yes—
113C2×C61#55511yescharacteristic
114C2×C61#55911yescharacteristic
115#400—611no—
116#398—611no—
117#394—612no—
118#390D6111yescharacteristic
119#388—612no—
120#388—612no—
121#388—612no—
122#388—612no—
123C4×C4⋊C4—612no—
124C61#259311yescharacteristic, complemented, Sylow
125C22×D4C2×D6111yescharacteristic
126C2×C4⋊C4—612no—
127C2×C4⋊C4—612no—
128C2×C4⋊C4—611no—
129C2×C4⋊C4—611no—
130C2×C4⋊C4C2×D6111yescharacteristic
131C2×C22⋊C4—612no—
132C2×C22⋊C4—612no—
133C2×C22⋊C4—612no—
134C2×C22⋊C4—612no—
135C2×C22⋊C4C2×D6112yes—
136C2×C22⋊C4C2×D6112yes—
137C2×C42—612no—
138C2×C42—612no—
139C2×C42C2×D6111yescharacteristic
140#95—612no—
141#95—612no—
142#95—611no—
143#95—612no—
144#95—612no—
145#95—611no—
146C24C22×D6112yes—
147C2×D4—22no—
148C2×D4—41no—
149C2×D4—41no—
150C22×C4—612no—
151C22×C4—612no—
152C22×C4—612no—
153C22×C4—612no—
154C22×C4C22×D6111yescharacteristic
155C22×C4C22×D6111yescharacteristic
156C22×C4C22×D6111yescharacteristic
157C22×C4C22×D6112yes—
158C4⋊C4—41no—
159C4⋊C4—1224no—
160C4⋊C4—1224no—
161C4⋊C4—2441no—
162C4⋊C4—2441no—
163C22⋊C4—24no—
164C22⋊C4—24no—
165C22⋊C4—1224no—
166C22⋊C4—1224no—
167C22⋊C4—2442no—
168C22⋊C4—2442no—
169C42—41no—
170C42—1224no—
171C42—2442no—
172C23—22no—
173C23—22no—
174C23—22no—
175C23—22no—
176C23—22no—
177C23—22no—
178C23—22no—
179C23C23×D6111yescharacteristic
180D4—44no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—614no—
190C2×C4—1222no—
191C2×C4—1222no—
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—1222no—
201C2×C4#1175822212yes—
202C2×C4#1175822414yes—
203C22—42no—
204C22—42no—
205C22—42no—
206C22—42no—
207C22—42no—
208C22—42no—
209C22—42no—
210C22#41×D6112yes—
211C22C2×#1175822412yes—
212C22C2×#1175822211yescharacteristic
213C22#1451982211yescharacteristic
214C22#1451982211yescharacteristic
215C4—24no—
216C4—22no—
217C4—41no—
218C4—41no—
219C4—1224no—
220C4—2442no—
221C4—2442no—
222C4—2442no—
223C2—82no—
224C2#1684029412yes—
225C2#1684035011yescharacteristic
226C2#1684045512yes—
227C2#1684047411yescharacteristic
228C2#1684049811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#390C2
hypercenter#390D61
hypocenterC61#2593
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #16839701C2semidirect
2. #16839692C2semidirect
4. #16839656C2semidirect
5. #16839656C2semidirect
6. #16839655C2semidirect
7. #16839655C2semidirect
8. C4×#11758196C2semidirect
124. C61#2593semidirect