Finite Group Databasebeta

← #21451508

Subgroups — #21451508

Order 7808.

576 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14519734C211yesmaximal, characteristic, complemented
2#16839681C211yesmaximal, characteristic, complemented
3#16839676C211yesmaximal, characteristic, complemented
4#16839673C211yesmaximal, characteristic, complemented
5#16839670C211yesmaximal, characteristic
6#16839662C212yesmaximal, complemented
7#16839656C212yesmaximal, complemented
8#16839650C212yesmaximal, complemented
9#16839638C212yesmaximal, complemented
10#16839608C211yesmaximal, characteristic, complemented
11C2×#124×C61C211yesmaximal, characteristic, complemented
12C22×C22⋊D61C2212yes—
13C22×C4×D61C2211yescharacteristic
14#14519734—24no—
15C2×#11758196C2211yescharacteristic
16C2×#11758196C2211yescharacteristic
17C2×#11758196C2212yes—
18C2×C22⋊Dic61C2212yes—
19C2×C22⋊Dic61C2212yes—
20C2×C22⋊Dic61C2212yes—
21C2×#11758198C2211yescharacteristic
22C2×#11758198C2211yescharacteristic
23C2×#11758198C2212yes—
24C2×C4×Dic61C2211yescharacteristic
25C2×C4×Dic61C2212yes—
26#14519684C2211yescharacteristic
27#14519684C2212yes—
28#14519684C2212yes—
29#14519684C2211yescharacteristic
30#14519684C2212yes—
31C22×Q8×C61C2211yescharacteristic
32C22×D4×C61C2211yescharacteristic
33#124×C61—24no—
34C2×C22⋊C4×C61C2212yes—
35C2×C22⋊C4×C61C2212yes—
36C2×C42×C61C2211yescharacteristic
37C24×C61C2312yes—
38C23×D61C2311yescharacteristic
39C2×Q8×C61—22no—
40C2×Q8×C61—42no—
41C2×D4×C61—22no—
42C2×D4×C61—42no—
43C22×C4×C61C2312yes—
44C22×C4×C61C2311yescharacteristic
45C22×C4×C61C2311yescharacteristic
46C22×C4×C61C2311yescharacteristic
47C2×C22⋊D61—24no—
48C2×C22⋊D61—24no—
49C2×C22⋊D61—42no—
50C22×Dic61C2312yes—
51C22×Dic61C2311yescharacteristic
52C22×Dic61C2311yescharacteristic
53C22×Dic61C2311yescharacteristic
54C22×Dic61C2312yes—
55C2×C4×D61—22no—
56C2×C4×D61—22no—
57C2×C4×D61—22no—
58C22⋊C4×C61—24no—
59C22⋊C4×C61—24no—
60C42×C61D414yescomplemented
61C22⋊Dic61—24no—
62C22⋊Dic61—24no—
63C22⋊Dic61—42no—
64#11758198—22no—
65#11758198—22no—
66#11758198—42no—
67#11758196—22no—
68#11758196—22no—
69#11758196—42no—
70C4×Dic61—22no—
71C4×Dic61—24no—
72C23×C61—22no—
73C23×C61—22no—
74C23×C61—22no—
75C23×C61—22no—
76C23×C61—22no—
77C23×C61—22no—
78C23×C61—22no—
79C23×C61C2411yescharacteristic
80C22×D61—21no—
81C22×D61—21no—
82C22×D61—22no—
83C22×D61—22no—
84C22×D61#4112yes—
85Q8×C61—44no—
86D4×C61—44no—
87C2×C4×C61—22no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—22no—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61—22no—
94C2×C4×C61C2×D412yes—
95C2×C4×C61C2×D412yes—
96C2×C4×C61C2×D412yes—
97C22⋊D61—48no—
98C2×Dic61—21no—
99C2×Dic61—21no—
100C2×Dic61—22no—
101C2×Dic61—22no—
102C2×Dic61—21no—
103C2×Dic61—21no—
104C2×Dic61—22no—
105C2×Dic61—22no—
106C2×Dic61—22no—
107C2×Dic61—22no—
108C2×Dic61—22no—
109C2×Dic61#4114yes—
110C2×Dic61#4112yes—
111C4×D61—28no—
112C22×C61—42no—
113C22×C61—42no—
114C22×C61—42no—
115C22×C61—42no—
116C22×C61—42no—
117C22×C61—42no—
118C22×C61—42no—
119C22×C61C22×D411yescharacteristic
120C22×C61C2×#4111yescharacteristic
121C22×C61C2×#4111yescharacteristic
122C22×C61C2×#4112yes—
123C22×C61H(5,𝔽2)12yes—
124C2×D61—22no—
125C2×D61—24no—
126C2×D61—41no—
127C2×D61—41no—
128C2×D61—42no—
129C4×C61—22no—
130C4×C61—22no—
131C4×C61—22no—
132C4×C61—42no—
133Dic61—22no—
134Dic61—24no—
135Dic61—41no—
136Dic61—41no—
137Dic61—42no—
138#2610—611nomaximal, Sylow
139C2×C61—82no—
140C2×C61#52511yescharacteristic
141C2×C61#53211yescharacteristic
142C2×C61#53511yescharacteristic
143C2×C61#55112yes—
144C2×C61#55512yes—
145D61—42no—
146C2×#124D6111yescharacteristic, complemented
147C2×#117—611no—
148#395—611no—
149#394—611no—
150#393—611no—
151#392—611no—
152#390—612no—
153#388—612no—
154#388—612no—
155#386—612no—
156#376—611no—
157C61#261011yescharacteristic, complemented, Sylow
158C22×Q8C2×D6111yescharacteristic
159C22×D4—612no—
160C22×D4C2×D6111yescharacteristic
161C23×C4—611no—
162#124—24no—
163#117—1224no—
164C2×C4⋊C4—611no—
165C2×C4⋊C4—611no—
166C2×C4⋊C4—612no—
167C2×C22⋊C4—612no—
168C2×C22⋊C4—612no—
169C2×C22⋊C4—611no—
170C2×C22⋊C4—611no—
171C2×C22⋊C4—612no—
172C2×C22⋊C4—612no—
173C2×C22⋊C4C2×D6112yes—
174C2×C22⋊C4C2×D6112yes—
175C2×C42—611no—
176C2×C42—612no—
177C2×C42C2×D6111yescharacteristic
178#95—612no—
179#95—611no—
180#95—611no—
181#95—612no—
182#95—612no—
183C24—611no—
184C24C22×D6112yes—
185C2×Q8—22no—
186C2×Q8—42no—
187C2×D4—22no—
188C2×D4—42no—
189C2×D4—1224no—
190C2×D4—1224no—
191C2×D4—2442no—
192C22×C4—612no—
193C22×C4—611no—
194C22×C4—612no—
195C22×C4—611no—
196C22×C4—611no—
197C22×C4—1222no—
198C22×C4—1222no—
199C22×C4—1222no—
200C22×C4C22×D6112yes—
201C22×C4C22×D6111yescharacteristic
202C22×C4C22×D6111yescharacteristic
203C22×C4C22×D6111yescharacteristic
204C4⋊C4—1222no—
205C4⋊C4—1222no—
206C4⋊C4—2442no—
207C22⋊C4—24no—
208C22⋊C4—24no—
209C22⋊C4—1224no—
210C22⋊C4—1224no—
211C22⋊C4—1222no—
212C22⋊C4—1222no—
213C22⋊C4—2442no—
214C22⋊C4—2442no—
215C42—1224no—
216C42—1222no—
217C42C22⋊D6114yescomplemented
218C23—22no—
219C23—22no—
220C23—22no—
221C23—22no—
222C23—22no—
223C23—22no—
224C23—22no—
225C23—612no—
226C23—1221no—
227C23—1221no—
228C23—1222no—
229C23—1222no—
230C23C23×D6111yescharacteristic
231Q8—44no—
232D4—44no—
233D4—2448no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—614no—
242C2×C4—612no—
243C2×C4—1228no—
244C2×C4—1221no—
245C2×C4—1221no—
246C2×C4—1222no—
247C2×C4—1222no—
248C2×C4—1221no—
249C2×C4—1221no—
250C2×C4—1222no—
251C2×C4—1222no—
252C2×C4—1222no—
253C2×C4—1222no—
254C2×C4—1222no—
255C2×C4C2×C22⋊D6112yes—
256C2×C4C2×C22⋊D6112yes—
257C2×C4C2×C22⋊D6112yes—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—42no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—1222no—
266C22—1224no—
267C22—2442no—
268C22—2441no—
269C22—2441no—
270C22C22×C22⋊D6111yescharacteristic
271C22#41×D6111yescharacteristic
272C22#41×D6112yes—
273C22#41×D6111yescharacteristic
274C22#1451982212yes—
275C4—22no—
276C4—22no—
277C4—22no—
278C4—42no—
279C4—1222no—
280C4—1224no—
281C4—2442no—
282C4—2441no—
283C4—2441no—
284C2—82no—
285C2—2442no—
286C2#1684026911yescharacteristic
287C2#1684030811yescharacteristic
288C2#1684032911yescharacteristic
289C2#1684044212yes—
290C2#1684047412yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#124×C61C2
hypercenterC2×#124D61
hypocenterC61#2610
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#14519734C2semidirect
2. #16839681C2semidirect
3. #16839676C2semidirect
4. #16839673C2semidirect
6. #16839662C2semidirect
7. #16839656C2semidirect
8. #16839650C2semidirect
9. #16839638C2semidirect
10. #16839608C2semidirect
11. C2×#124×C61C2semidirect
60. C42×C61D4semidirect
146. C2×#124D61semidirect
157. C61#2610semidirect
217. C42C22⋊D61semidirect