Finite Group Databasebeta

← #21451001

Subgroups — #21451001

Order 7808.

584 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 161 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×C4×C22⋊D61C211yesmaximal, characteristic
2#16839700C211yesmaximal, characteristic, complemented
3#16839697C211yesmaximal, characteristic, complemented
4#16839681C211yesmaximal, characteristic, complemented
5#16839673C211yesmaximal, characteristic, complemented
6#16839643C212yesmaximal, complemented
7#16839639C212yesmaximal
8#16839633C212yesmaximal, complemented
9#16839620C212yesmaximal, complemented
10C2×#14519684C211yesmaximal, characteristic, complemented
11C2×C22⋊Q8×C61C211yesmaximal, characteristic, complemented
12C22×C22⋊D61C2211yescharacteristic
13C23×Dic61C2212yes—
14C22×C4×D61C2211yescharacteristic
15C4×C22⋊D61—24no—
16C2×#11758196C2211yescharacteristic
17C2×#11758196C2212yes—
18C2×#11758196C2212yes—
19C2×C22⋊Dic61C2211yescharacteristic
20C2×#11758198C2211yescharacteristic
21C2×#11758198C2212yes—
22C2×#11758198C2212yes—
23C2×C4×Dic61C2211yescharacteristic
24#14519684C2211yescharacteristic
25#14519684C2212yes—
26#14519684C2211yescharacteristic
27#14519684C2212yes—
28#14519684C2212yes—
29#14519684C2212yes—
30#14519684C2212yes—
31C22×Q8×C61C2211yescharacteristic
32C23×C4×C61C2211yescharacteristic
33C22⋊Q8×C61—24no—
34C2×C4⋊C4×C61C2211yescharacteristic
35C2×C4⋊C4×C61C2212yes—
36C2×C22⋊C4×C61C2212yes—
37C24×C61C2311yescharacteristic
38C23×D61C2311yescharacteristic
39C2×Q8×C61—22no—
40C2×Q8×C61—42no—
41C22×C4×C61—42no—
42C22×C4×C61D414yes—
43C22×C4×C61C2312yes—
44C22×C4×C61C2312yes—
45C22×C4×C61C2311yescharacteristic
46C22×C4×C61C2311yescharacteristic
47C2×C22⋊D61—22no—
48C2×C22⋊D61—22no—
49C2×C22⋊D61Q814yescomplemented
50C22×Dic61—24no—
51C22×Dic61—24no—
52C22×Dic61—42no—
53C22×Dic61C2311yescharacteristic
54C22×Dic61C2312yes—
55C22×Dic61C2311yescharacteristic
56C22×Dic61C2311yescharacteristic
57C22×Dic61C2312yes—
58C2×C4×D61—22no—
59C2×C4×D61—42no—
60C4⋊C4×C61—22no—
61C4⋊C4×C61—24no—
62C22⋊C4×C61—24no—
63C22⋊Dic61—22no—
64#11758198—22no—
65#11758198—24no—
66#11758198—42no—
67#11758196—22no—
68#11758196—24no—
69#11758196—42no—
70C4×Dic61—22no—
71C23×C61—22no—
72C23×C61—22no—
73C23×C61C2×D412yes—
74C23×C61C2×Q812yes—
75C23×C61#4112yes—
76C23×C61C2411yescharacteristic
77C22×D61—21no—
78C22×D61—22no—
79C22×D61—21no—
80C22×D61—22no—
81C22×D61C2×Q812yes—
82Q8×C61—44no—
83C2×C4×C61—22no—
84C2×C4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61—22no—
87C2×C4×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61—22no—
90C2×C4×C61—22no—
91C2×C4×C61—44no—
92C2×C4×C61C2×D412yes—
93C2×C4×C61C2×D412yes—
94C22⋊D61—28no—
95C2×Dic61—21no—
96C2×Dic61—22no—
97C2×Dic61—21no—
98C2×Dic61—22no—
99C2×Dic61—21no—
100C2×Dic61—21no—
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61—22no—
104C2×Dic61—22no—
105C2×Dic61—22no—
106C2×Dic61—48no—
107C2×Dic61C2×Q812yes—
108C2×Dic61#4114yes—
109C4×D61—44no—
110C22×C61—22no—
111C22×C61—22no—
112C22×C61—24no—
113C22×C61—24no—
114C22×C61C22⋊Q814yes—
115C22×C61C22×D411yescharacteristic
116C22×C61C22×Q811yescharacteristic
117C22×C61C2×#4112yes—
118C22×C61C2×#4111yescharacteristic
119C22×C61H(5,𝔽2)12yes—
120C2×D61—22no—
121C2×D61—24no—
122C2×D61—41no—
123C2×D61—41no—
124C2×D61—42no—
125C4×C61—22no—
126C4×C61—22no—
127C4×C61—42no—
128C4×C61—42no—
129Dic61—22no—
130Dic61—24no—
131Dic61—41no—
132Dic61—41no—
133Dic61—42no—
134#2564—611nomaximal, Sylow
135C2×C61—24no—
136C2×C61C2×C22⋊Q811yescharacteristic
137C2×C61#53211yescharacteristic
138C2×C61#53411yescharacteristic
139C2×C61#55112yes—
140C2×C61#55412yes—
141D61—42no—
142C2×C22⋊Q8D6111yescharacteristic, complemented
143C2×C4×D4—611no—
144#400—611no—
145#399—611no—
146#395—611no—
147#393—611no—
148#387—612no—
149#386—612no—
150#385—612no—
151#380—612no—
152C2×#95—611no—
153C61#256411yescharacteristic, complemented, Sylow
154C22×Q8C2×D6111yescharacteristic
155C22×D4—611no—
156C23×C4—612no—
157C23×C4—611no—
158C23×C4C2×D6111yescharacteristic
159C22⋊Q8—24no—
160C4×D4—1224no—
161C2×C4⋊C4—611no—
162C2×C4⋊C4—612no—
163C2×C4⋊C4—612no—
164C2×C4⋊C4C2×D6112yes—
165C2×C4⋊C4C2×D6111yescharacteristic
166C2×C22⋊C4—611no—
167C2×C22⋊C4—611no—
168C2×C22⋊C4—612no—
169C2×C22⋊C4—612no—
170C2×C22⋊C4C2×D6112yes—
171C2×C42—611no—
172#95—612no—
173#95—611no—
174#95—611no—
175#95—612no—
176#95—612no—
177#95—612no—
178#95—612no—
179C24—611no—
180C24C22×D6111yescharacteristic
181C2×Q8—22no—
182C2×Q8—42no—
183C2×D4—614no—
184C2×D4—1222no—
185C2×D4—1222no—
186C22×C4—42no—
187C22×C4—611no—
188C22×C4—612no—
189C22×C4—612no—
190C22×C4—611no—
191C22×C4—611no—
192C22×C4—1224no—
193C22×C4—1224no—
194C22×C4—1222no—
195C22×C4—2442no—
196C22×C4—2442no—
197C22×C4C22⋊D6114yes—
198C22×C4C22×D6112yes—
199C22×C4C22×D6112yes—
200C22×C4C22×D6111yescharacteristic
201C22×C4C22×D6111yescharacteristic
202C4⋊C4—22no—
203C4⋊C4—24no—
204C4⋊C4—1224no—
205C4⋊C4—1222no—
206C4⋊C4—2442no—
207C22⋊C4—24no—
208C22⋊C4—1224no—
209C22⋊C4—1222no—
210C22⋊C4—1222no—
211C22⋊C4—2442no—
212C42—1222no—
213C23—22no—
214C23—22no—
215C23—612no—
216C23—1221no—
217C23—1222no—
218C23—1221no—
219C23—1222no—
220C23Q8×D6112yes—
221C23#1175822612yes—
222C23C2×C22⋊D6112yes—
223C23C23×D6111yescharacteristic
224Q8—44no—
225D4—1228no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—44no—
235C2×C4—612no—
236C2×C4—614no—
237C2×C4—1221no—
238C2×C4—1222no—
239C2×C4—1221no—
240C2×C4—1222no—
241C2×C4—1221no—
242C2×C4—1221no—
243C2×C4—1222no—
244C2×C4—1222no—
245C2×C4—1222no—
246C2×C4—1222no—
247C2×C4—1222no—
248C2×C4—2444no—
249C2×C4—2448no—
250C2×C4C2×C22⋊D6112yes—
251C2×C4C2×C22⋊D6112yes—
252C22—24no—
253C22—22no—
254C22—22no—
255C22—24no—
256C22—1224no—
257C22—1222no—
258C22—2441no—
259C22—2441no—
260C22—2442no—
261C22#1451975314yes—
262C22C22×C22⋊D6111yescharacteristic
263C22C2×Q8×D6111yescharacteristic
264C22#41×D6112yes—
265C22C2×#1175822611yescharacteristic
266C22#1451982212yes—
267C4—22no—
268C4—22no—
269C4—42no—
270C4—42no—
271C4—1222no—
272C4—1224no—
273C4—2441no—
274C4—2441no—
275C4—2442no—
276C2—24no—
277C2—2442no—
278C2C2×#1451975311yescharacteristic
279C2#1684030811yescharacteristic
280C2#1684032111yescharacteristic
281C2#1684043912yes—
282C2#1684046612yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×C22⋊Q8×C61C2
hypercenterC2×C22⋊Q8D61
hypocenterC61#2564
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #16839700C2semidirect
3. #16839697C2semidirect
4. #16839681C2semidirect
5. #16839673C2semidirect
6. #16839643C2semidirect
8. #16839633C2semidirect
9. #16839620C2semidirect
10. C2×#14519684C2semidirect
11. C2×C22⋊Q8×C61C2semidirect
49. C2×C22⋊D61Q8semidirect
142. C2×C22⋊Q8D61semidirect
153. C61#2564semidirect