Finite Group Databasebeta

← #21453903

Subgroups — #21453903

Order 7808.

472 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 117 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#16839689C212yesmaximal, complemented
3#16839680C212yesmaximal, complemented
4#16839678C212yesmaximal, complemented
5#16839673C212yesmaximal, complemented
6#16839671C211yesmaximal, characteristic
7#16839639C212yesmaximal, complemented
8#16839634C211yesmaximal, characteristic, complemented
9C61×#393C211yesmaximal, characteristic, complemented
10C22×D244C2211yescharacteristic
11C22×C22⋊D61C2212yes—
12C23×Dic61C2211yescharacteristic
13C2×C4⋊Dic61C2212yes—
14C2×#11758196C2212yes—
15C2×C22⋊Dic61C2211yescharacteristic
16C2×#11758198C2212yes—
17C2×#11758198C2212yes—
18C2×#11758198C2212yes—
19C2×#11758198C2212yes—
20C2×#11758198C2212yes—
21#14519684C2212yes—
22#14519684C2212yes—
23#14519684C2211yescharacteristic
24#14519684C2212yes—
25#14519684C2212yes—
26C22×Q8×C61C2211yescharacteristic
27C2×C22⋊C4×C61C2211yescharacteristic
28C2×C22⋊C4×C61C2212yes—
29#95×C61C2212yes—
30#95×C61C2211yescharacteristic
31C24×C61C2311yescharacteristic
32C23×D61C2312yes—
33C2×Q8×C61—42no—
34C2×Q8×C61—41no—
35C22×C4×C61C2311yescharacteristic
36C22×C4×C61C2312yes—
37C22×C4×C61C2312yes—
38C22×C4×C61C2311yescharacteristic
39C2×C22⋊D61—24no—
40C2×C22⋊D61—42no—
41C2×C22⋊D61—42no—
42C22×Dic61—42no—
43C22×Dic61—41no—
44C22×Dic61C2312yes—
45C22×Dic61C2312yes—
46C22×Dic61C2312yes—
47C2×D244—42no—
48C2×D244—41no—
49C22⋊C4×C61—42no—
50C22⋊C4×C61—41no—
51C22⋊Dic61—22no—
52#11758198—42no—
53#11758198—42no—
54#11758198—42no—
55#11758198—42no—
56#11758198—42no—
57C4⋊Dic61—42no—
58#11758196—42no—
59C23×C61—21no—
60C23×C61—22no—
61C23×C61—22no—
62C23×C61—21no—
63C23×C61#4112yes—
64C23×C61C2411yescharacteristic
65C22×D61—22no—
66C22×D61—22no—
67C22×D61—22no—
68C22×D61—22no—
69C22×D61—22no—
70C22×D61—22no—
71C22×D61—22no—
72Q8×C61—44no—
73C2×C4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—21no—
80C2×C4×C61—22no—
81C2×C4×C61—21no—
82C2×C4×C61—22no—
83C22⋊D61—48no—
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61—22no—
87C2×Dic61—22no—
88C2×Dic61—22no—
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—44no—
94D244—44no—
95C22×C61—24no—
96C22×C61—22no—
97C22×C61—41no—
98C22×C61—41no—
99C22×C61—42no—
100C22×C61C2×#4111yescharacteristic
101C22×C61H(5,𝔽2)12yes—
102C22×C61H(5,𝔽2)11yescharacteristic
103C22×C61H(5,𝔽2)12yes—
104C22×C612−1+411yescharacteristic
105C2×D61—42no—
106C2×D61—42no—
107C2×D61—42no—
108C2×D61—42no—
109C2×D61—42no—
110C2×D61—42no—
111C2×D61—42no—
112C4×C61—41no—
113C4×C61—42no—
114C4×C61—41no—
115C4×C61—42no—
116Dic61—42no—
117Dic61—42no—
118Dic61—42no—
119#2824—611nomaximal, Sylow
120C2×C61—42no—
121C2×C61#53812yes—
122C2×C61#53911yescharacteristic
123C2×C61#56011yescharacteristic
124C2×C61H(3,𝔽4)11yescharacteristic
125C2×C61#56212yes—
126D61—82no—
127#400—612no—
128#397—612no—
129#394—612no—
130#394—612no—
131#393—612no—
132#393D6111yescharacteristic, complemented
133#392—611no—
134#386—612no—
135#385—611no—
136C61#282411yescharacteristic, complemented, Sylow
137C22×Q8C2×D6111yescharacteristic
138C22×D4—612no—
139C22×D4—611no—
140C23×C4—611no—
141C2×C4⋊C4—612no—
142C2×C4⋊C4—612no—
143C2×C22⋊C4—611no—
144C2×C22⋊C4—612no—
145C2×C22⋊C4—612no—
146C2×C22⋊C4—612no—
147C2×C22⋊C4—612no—
148C2×C22⋊C4—612no—
149C2×C22⋊C4C2×D6111yescharacteristic
150C2×C22⋊C4C2×D6112yes—
151#95—612no—
152#95—612no—
153#95—612no—
154#95—611no—
155#95—612no—
156#95C2×D6112yes—
157#95C2×D6111yescharacteristic
158C24—612no—
159C24C22×D6111yescharacteristic
160C2×Q8—41no—
161C2×Q8—42no—
162C2×D4—1224no—
163C2×D4—2441no—
164C2×D4—2442no—
165C2×D4—2442no—
166C2×D4—2442no—
167C22×C4—612no—
168C22×C4—612no—
169C22×C4—612no—
170C22×C4—2441no—
171C22×C4—2442no—
172C22×C4C22×D6111yescharacteristic
173C22×C4C22×D6112yes—
174C22×C4C22×D6112yes—
175C22×C4C22×D6111yescharacteristic
176C4⋊C4—2442no—
177C4⋊C4—2442no—
178C22⋊C4—42no—
179C22⋊C4—41no—
180C22⋊C4—1222no—
181C22⋊C4—2442no—
182C22⋊C4—2442no—
183C22⋊C4—2442no—
184C22⋊C4—2442no—
185C22⋊C4—2442no—
186C23—21no—
187C23—22no—
188C23—22no—
189C23—21no—
190C23—1222no—
191C23—1222no—
192C23—1222no—
193C23—1222no—
194C23—1222no—
195C23—1222no—
196C23—1222no—
197C23#1175822612yes—
198C23C23×D6111yescharacteristic
199Q8—44no—
200D4—2444no—
201D4—2448no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
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—2444no—
222C22—24no—
223C22—22no—
224C22—41no—
225C22—41no—
226C22—42no—
227C22—2442no—
228C22—2442no—
229C22—2442no—
230C22—2442no—
231C22—2442no—
232C22—2442no—
233C22—2442no—
234C22C2×#1175822611yescharacteristic
235C22#1451982211yescharacteristic
236C22#1451982212yes—
237C22#1451982312yes—
238C22#1451982411yescharacteristic
239C4—41no—
240C4—42no—
241C4—41no—
242C4—42no—
243C4—2442no—
244C4—2442no—
245C4—2442no—
246C2—42no—
247C2—4882no—
248C2#1684035212yes—
249C2#1684036111yescharacteristic
250C2#1684050111yescharacteristic
251C2#1684050411yescharacteristic
252C2#1684050612yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#393C2
hypercenter#393D61
hypocenterC61#2824
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. #16839704C2semidirect
2. #16839689C2semidirect
3. #16839680C2semidirect
4. #16839678C2semidirect
5. #16839673C2semidirect
7. #16839639C2semidirect
8. #16839634C2semidirect
9. C61×#393C2semidirect
132. #393D61semidirect
136. C61#2824semidirect