Finite Group Databasebeta

← #21453835

Subgroups — #21453835

Order 7808.

478 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 125 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×#14519762C211yesmaximal, characteristic
2C2×#14519757C211yesmaximal, characteristic, complemented
3#16839696C212yesmaximal, complemented
4#16839688C211yesmaximal, characteristic, complemented
5#16839688C212yesmaximal, complemented
6#16839684C212yesmaximal, complemented
7#16839682C211yesmaximal, characteristic, complemented
8#16839680C212yesmaximal
9#16839675C211yesmaximal, characteristic, complemented
10#16839621C211yesmaximal, characteristic, complemented
11C61×#398C211yesmaximal, characteristic, complemented
12C22×Dic122C2211yescharacteristic
13C22×D244C2211yescharacteristic
14C22×C4×D61C2211yescharacteristic
15#14519762—24no—
16#14519757—24no—
17C2×C4⋊Dic61C2212yes—
18C2×#11758196C2211yescharacteristic
19C2×#11758196C2212yes—
20C2×#11758196C2212yes—
21C2×#11758198C2212yes—
22C2×#11758198C2211yescharacteristic
23C2×#11758198C2211yescharacteristic
24C2×#11758198C2211yescharacteristic
25C2×#11758198C2212yes—
26C2×#11758198C2212yes—
27C2×#11758198C2212yes—
28#14519684C2212yes—
29#14519684C2211yescharacteristic
30#14519684C2212yes—
31#14519684C2212yes—
32C2×C4⋊C4×C61C2211yescharacteristic
33C2×C4⋊C4×C61C2211yescharacteristic
34C2×C4⋊C4×C61C2212yes—
35#95×C61C2212yes—
36#95×C61C2211yescharacteristic
37C23×D61C2311yescharacteristic
38C23×D61C2311yescharacteristic
39C22×C4×C61C2311yescharacteristic
40C22×C4×C61C2312yes—
41C22×C4×C61C2312yes—
42C22×C4×C61C2311yescharacteristic
43C22×C4×C61C2311yescharacteristic
44C22×Dic61C2312yes—
45C22×Dic61C2311yescharacteristic
46C22×Dic61C2312yes—
47C22×Dic61C2311yescharacteristic
48C2×D244—22no—
49C2×D244—42no—
50C2×C4×D61—42no—
51C2×C4×D61D414yes—
52C2×Dic122—22no—
53C2×Dic122—42no—
54C4⋊C4×C61—22no—
55C4⋊C4×C61—22no—
56C4⋊C4×C61—42no—
57#11758198—24no—
58#11758198—22no—
59#11758198—22no—
60#11758198—22no—
61#11758198—42no—
62#11758198—42no—
63#11758198—42no—
64C4⋊Dic61—24no—
65#11758196—22no—
66#11758196—42no—
67#11758196—42no—
68C23×C61C2411yescharacteristic
69C22×D61—21no—
70C22×D61—22no—
71C22×D61—22no—
72C22×D61—21no—
73C22×D61—21no—
74C22×D61—21no—
75C22×D61—22no—
76C22×D61—22no—
77C22×D61—21no—
78C22×D61C2×D412yes—
79C2×C4×C61—22no—
80C2×C4×C61—21no—
81C2×C4×C61—22no—
82C2×C4×C61—21no—
83C2×C4×C61—22no—
84C2×C4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61—22no—
87C2×C4×C61—21no—
88C2×C4×C61—22no—
89C2×C4×C61—21no—
90C2×C4×C61—22no—
91C2×C4×C61C2×D412yes—
92C2×Dic61—22no—
93C2×Dic61—21no—
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61—22no—
97C2×Dic61—22no—
98C2×Dic61—22no—
99C2×Dic61—22no—
100C2×Dic61—22no—
101C2×Dic61C2×D412yes—
102D244—44no—
103C4×D61—44no—
104Dic122—44no—
105C22×C61C22×D411yescharacteristic
106C22×C61H(5,𝔽2)11yescharacteristic
107C22×C61H(5,𝔽2)12yes—
108C22×C612−1+411yescharacteristic
109C22×C612−1+412yes—
110C2×D61—22no—
111C2×D61—22no—
112C2×D61—22no—
113C2×D61—42no—
114C2×D61—42no—
115C2×D61—41no—
116C2×D61—41no—
117C2×D61—41no—
118C2×D61—42no—
119C2×D61—42no—
120C4×C61—22no—
121C4×C61—41no—
122C4×C61—42no—
123C4×C61—41no—
124C4×C61—42no—
125Dic61—22no—
126Dic61—42no—
127Dic61—41no—
128Dic61—42no—
129#2814—611nomaximal, Sylow
130C2×C61#53411yescharacteristic
131C2×C61#53611yescharacteristic
132C2×C61#53711yescharacteristic
133C2×C61#56212yes—
134C2×C61#56312yes—
135D61—42no—
136D61—81no—
137C2×#123—611no—
138C2×C22⋊Q8—611no—
139#398—612no—
140#398D6111yescharacteristic, complemented
141#397—611no—
142#397—612no—
143#396—612no—
144#395—611no—
145#394—612no—
146#393—611no—
147#380—611no—
148C61#281411yescharacteristic, complemented, Sylow
149C22×Q8—611no—
150C22×D4—611no—
151C23×C4—611no—
152#123—1224no—
153C22⋊Q8—1224no—
154C2×C4⋊C4—612no—
155C2×C4⋊C4—611no—
156C2×C4⋊C4—612no—
157C2×C4⋊C4—612no—
158C2×C4⋊C4C2×D6111yescharacteristic
159C2×C4⋊C4C2×D6111yescharacteristic
160C2×C4⋊C4C2×D6112yes—
161C2×C22⋊C4—612no—
162C2×C22⋊C4—611no—
163C2×C22⋊C4—611no—
164C2×C22⋊C4—611no—
165C2×C22⋊C4—612no—
166C2×C22⋊C4—612no—
167C2×C22⋊C4—612no—
168#95—611no—
169#95—612no—
170#95—612no—
171#95—612no—
172#95C2×D6111yescharacteristic
173#95C2×D6112yes—
174C24—611no—
175C24—611no—
176C2×Q8—1222no—
177C2×Q8—2442no—
178C2×D4—1222no—
179C2×D4—2442no—
180C22×C4—611no—
181C22×C4—614no—
182C22×C4—611no—
183C22×C4—612no—
184C22×C4—612no—
185C22×C4—2442no—
186C22×C4C22×D6111yescharacteristic
187C22×C4C22×D6112yes—
188C22×C4C22×D6112yes—
189C22×C4C22×D6111yescharacteristic
190C22×C4C22×D6111yescharacteristic
191C4⋊C4—22no—
192C4⋊C4—22no—
193C4⋊C4—42no—
194C4⋊C4—1222no—
195C4⋊C4—1224no—
196C4⋊C4—2442no—
197C4⋊C4—2442no—
198C22⋊C4—1222no—
199C22⋊C4—1224no—
200C22⋊C4—1222no—
201C22⋊C4—1222no—
202C22⋊C4—2442no—
203C22⋊C4—2442no—
204C22⋊C4—2442no—
205C23—612no—
206C23—1221no—
207C23—1222no—
208C23—1221no—
209C23—1222no—
210C23—1221no—
211C23—1221no—
212C23—1222no—
213C23—1221no—
214C23—1222no—
215C23C23×D6111yescharacteristic
216Q8—2444no—
217D4—2444no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—612no—
231C2×C4—1222no—
232C2×C4—1221no—
233C2×C4—1222no—
234C2×C4—1222no—
235C2×C4—1222no—
236C2×C4—1222no—
237C2×C4—1222no—
238C2×C4—1222no—
239C2×C4—1222no—
240C2×C4—2444no—
241C2×C4D4×D6112yes—
242C22—1222no—
243C22—1222no—
244C22—1222no—
245C22—2442no—
246C22—2442no—
247C22—2441no—
248C22—2441no—
249C22—2441no—
250C22—2442no—
251C22—2442no—
252C22C2×D4×D6111yescharacteristic
253C22#1451982211yescharacteristic
254C22#1451982312yes—
255C22#1451982411yescharacteristic
256C22#1451982512yes—
257C4—22no—
258C4—42no—
259C4—41no—
260C4—41no—
261C4—42no—
262C4—1222no—
263C4—2442no—
264C4—2442no—
265C4—2441no—
266C2—4881no—
267C2—2442no—
268C2#1684032311yescharacteristic
269C2#1684033711yescharacteristic
270C2#1684034111yescharacteristic
271C2#1684050812yes—
272C2#1684051612yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#398C2
hypercenter#398D61
hypocenterC61#2814
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
2. C2×#14519757C2semidirect
3. #16839696C2semidirect
4. #16839688C2semidirect
5. #16839688C2semidirect
6. #16839684C2semidirect
7. #16839682C2semidirect
9. #16839675C2semidirect
10. #16839621C2semidirect
11. C61×#398C2semidirect
140. #398D61semidirect
148. C61#2814semidirect