Finite Group Databasebeta

← #21451517

Subgroups — #21451517

Order 7808.

476 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C2×#14519769C211yesmaximal, characteristic, complemented
2#16839701C211yesmaximal, characteristic, complemented
3#16839698C211yesmaximal, characteristic
4#16839692C211yesmaximal, characteristic, complemented
5#16839687C211yesmaximal, characteristic
6#16839657C212yesmaximal, complemented
7#16839656C212yesmaximal
8#16839646C212yesmaximal, complemented
9#16839635C212yesmaximal
10#16839608C211yesmaximal, characteristic, complemented
11C2×#117×C61C211yesmaximal, characteristic
12#14519769—24no—
13C2×C4⋊Dic61C2211yescharacteristic
14C2×C4⋊Dic61C2211yescharacteristic
15C2×#11758196C2212yes—
16C2×#11758196C2212yes—
17C2×#11758196C2212yes—
18C2×#11758196C2212yes—
19C2×C22⋊Dic61C2212yes—
20C2×C22⋊Dic61C2212yes—
21C2×C4×Dic61C2212yes—
22#14519684C2211yescharacteristic
23#14519684C2212yes—
24#14519684C2211yescharacteristic
25#14519684C2212yes—
26#14519684C2212yes—
27#14519684C2212yes—
28#14519684C2212yes—
29C23×C4×C61C2211yescharacteristic
30#117×C61—24no—
31C2×C4⋊C4×C61C2211yescharacteristic
32C2×C4⋊C4×C61C2211yescharacteristic
33C2×C22⋊C4×C61C2211yescharacteristic
34C2×C22⋊C4×C61C2211yescharacteristic
35C2×C42×C61C2211yescharacteristic
36C2×C42×C61C2211yescharacteristic
37C24×C61C2311yescharacteristic
38C22×C4×C61—22no—
39C22×C4×C61—22no—
40C22×C4×C61—22no—
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2311yescharacteristic
43C22×C4×C61C2311yescharacteristic
44C22×C4×C61C2311yescharacteristic
45C22×C4×C61C2311yescharacteristic
46C22×C4×C61C2311yescharacteristic
47C22×Dic61C2312yes—
48C22×Dic61C2312yes—
49C22×Dic61C2312yes—
50C22×Dic61C2312yes—
51C4⋊C4×C61—22no—
52C4⋊C4×C61—22no—
53C22⋊C4×C61—22no—
54C22⋊C4×C61—22no—
55C42×C61—22no—
56C42×C61D414yes—
57C22⋊Dic61—24no—
58C22⋊Dic61—24no—
59C4⋊Dic61—22no—
60C4⋊Dic61—22no—
61#11758196—24no—
62#11758196—24no—
63#11758196—24no—
64#11758196—24no—
65C4×Dic61—24no—
66C23×C61—21no—
67C23×C61—22no—
68C23×C61—21no—
69C23×C61—22no—
70C23×C61#4112yes—
71C23×C61C2411yescharacteristic
72C2×C4×C61—28no—
73C2×C4×C61—21no—
74C2×C4×C61—22no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—22no—
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61C2×D412yes—
84C2×C4×C61C2×D412yes—
85C2×C4×C61C2×D412yes—
86C2×C4×C61#4112yes—
87C2×Dic61—22no—
88C2×Dic61—22no—
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61—22no—
97C2×Dic61—22no—
98C2×Dic61#4114yes—
99C22×C61—22no—
100C22×C61—24no—
101C22×C61—41no—
102C22×C61—41no—
103C22×C61—42no—
104C22×C61C22×D411yescharacteristic
105C22×C61C2×#4112yes—
106C22×C61C2×#4111yescharacteristic
107C22×C61C2×#4111yescharacteristic
108C22×C612−1+412yes—
109C4×C61—22no—
110C4×C61—22no—
111C4×C61—22no—
112C4×C61—22no—
113C4×C61—41no—
114C4×C61—41no—
115Dic61—24no—
116Dic61—42no—
117Dic61—42no—
118Dic61—42no—
119#2611—611nomaximal, Sylow
120C2×C61—42no—
121C2×C61#52511yescharacteristic
122C2×C61#53211yescharacteristic
123C2×C61#53611yescharacteristic
124C2×C61#55212yes—
125C2×C61#55212yes—
126C2×#125—611no—
127C2×#117D6111yescharacteristic
128#400—611no—
129#399—611no—
130#398—611no—
131#397—611no—
132#389—612no—
133#388—612no—
134#387—612no—
135#385—612no—
136#376—611no—
137C61#261111yescharacteristic, complemented, Sylow
138C23×C4C2×D6111yescharacteristic
139#125—1224no—
140#117—24no—
141C2×C4⋊C4—612no—
142C2×C4⋊C4—612no—
143C2×C4⋊C4—611no—
144C2×C4⋊C4—611no—
145C2×C4⋊C4—612no—
146C2×C4⋊C4—612no—
147C2×C4⋊C4C2×D6111yescharacteristic
148C2×C4⋊C4C2×D6111yescharacteristic
149C2×C22⋊C4—612no—
150C2×C22⋊C4—612no—
151C2×C22⋊C4C2×D6111yescharacteristic
152C2×C22⋊C4C2×D6111yescharacteristic
153C2×C42—612no—
154C2×C42C2×D6111yescharacteristic
155C2×C42C2×D6111yescharacteristic
156#95—612no—
157#95—611no—
158#95—611no—
159#95—612no—
160#95—612no—
161#95—612no—
162#95—612no—
163C24C22×D6111yescharacteristic
164C22×C4—22no—
165C22×C4—22no—
166C22×C4—22no—
167C22×C4—612no—
168C22×C4—612no—
169C22×C4—612no—
170C22×C4—612no—
171C22×C4C22×D6111yescharacteristic
172C22×C4C22×D6111yescharacteristic
173C22×C4C22×D6111yescharacteristic
174C22×C4C22×D6111yescharacteristic
175C22×C4C22×D6111yescharacteristic
176C22×C4C22×D6111yescharacteristic
177C4⋊C4—22no—
178C4⋊C4—22no—
179C4⋊C4—1224no—
180C4⋊C4—1224no—
181C4⋊C4—1224no—
182C4⋊C4—1224no—
183C4⋊C4—1222no—
184C4⋊C4—1222no—
185C22⋊C4—22no—
186C22⋊C4—22no—
187C22⋊C4—1224no—
188C22⋊C4—1224no—
189C42—22no—
190C42—1224no—
191C42C22⋊D6114yes—
192C23—21no—
193C23—22no—
194C23—21no—
195C23—22no—
196C23#1175822212yes—
197C23C23×D6111yescharacteristic
198C2×C4—28no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—614no—
210C2×C4—1222no—
211C2×C4—1222no—
212C2×C4—1222no—
213C2×C4—1222no—
214C2×C4—1222no—
215C2×C4—1222no—
216C2×C4—1222no—
217C2×C4—1222no—
218C2×C4—1222no—
219C2×C4—1222no—
220C2×C4—1222no—
221C2×C4#1175822212yes—
222C2×C4C2×C22⋊D6112yes—
223C2×C4C2×C22⋊D6112yes—
224C2×C4C2×C22⋊D6112yes—
225C22—22no—
226C22—24no—
227C22—42no—
228C22—41no—
229C22—41no—
230C22C22×C22⋊D6111yescharacteristic
231C22#41×D6112yes—
232C22C2×#1175822211yescharacteristic
233C22C2×#1175822211yescharacteristic
234C22#1451982412yes—
235C4—22no—
236C4—22no—
237C4—22no—
238C4—22no—
239C4—41no—
240C4—41no—
241C4—1224no—
242C4—2442no—
243C4—2442no—
244C4—2442no—
245C2—42no—
246C2#1684027311yescharacteristic
247C2#1684030811yescharacteristic
248C2#1684033311yescharacteristic
249C2#1684044512yes—
250C2#1684045112yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#117×C61C2
hypercenterC2×#117D61
hypocenterC61#2611
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. C2×#14519769C2semidirect
2. #16839701C2semidirect
4. #16839692C2semidirect
6. #16839657C2semidirect
8. #16839646C2semidirect
10. #16839608C2semidirect
137. C61#2611semidirect