Finite Group Databasebeta

← #21451501

Subgroups — #21451501

Order 7808.

576 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 139 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×#14519766C211yesmaximal, characteristic, complemented
2C2×#14519735C211yesmaximal, characteristic, complemented
3#16839679C211yesmaximal, characteristic, complemented
4#16839673C211yesmaximal, characteristic, complemented
5#16839672C211yesmaximal, characteristic
6#16839663C212yesmaximal, complemented
7#16839654C212yesmaximal, complemented
8#16839652C212yesmaximal, complemented
9#16839640C212yesmaximal, complemented
10#16839607C211yesmaximal, characteristic, complemented
11C61×#395C211yesmaximal, characteristic, complemented
12C22×D244C2212yes—
13C22×D244C2211yescharacteristic
14C22×C4×D61C2211yescharacteristic
15#14519766—24no—
16#14519735—24no—
17C2×C4⋊Dic61C2211yescharacteristic
18C2×#11758198C2211yescharacteristic
19C2×#11758198C2211yescharacteristic
20C2×#11758198C2212yes—
21C2×#11758198C2212yes—
22C2×#11758198C2212yes—
23C2×#11758198C2212yes—
24C2×#11758198C2212yes—
25C2×#11758198C2212yes—
26C2×C4×Dic61C2211yescharacteristic
27C2×C4×Dic61C2212yes—
28C2×C4×Dic61C2211yescharacteristic
29#14519684C2212yes—
30#14519684C2211yescharacteristic
31#14519684C2212yes—
32C22×Q8×C61C2211yescharacteristic
33C2×C4⋊C4×C61C2211yescharacteristic
34C2×C4⋊C4×C61C2212yes—
35#95×C61C2211yescharacteristic
36#95×C61C2212yes—
37C23×D61C2312yes—
38C23×D61C2311yescharacteristic
39C2×Q8×C61—22no—
40C2×Q8×C61—42no—
41C22×C4×C61C2312yes—
42C22×C4×C61C2311yescharacteristic
43C22×C4×C61C2311yescharacteristic
44C22×C4×C61C2311yescharacteristic
45C22×C4×C61C2312yes—
46C22×Dic61C2312yes—
47C22×Dic61C2311yescharacteristic
48C22×Dic61C2311yescharacteristic
49C22×Dic61C2311yescharacteristic
50C2×D244—24no—
51C2×D244—22no—
52C2×D244—24no—
53C2×D244—42no—
54C2×D244—42no—
55C2×C4×D61—22no—
56C2×C4×D61—22no—
57C2×C4×D61—22no—
58C4⋊C4×C61—22no—
59C4⋊C4×C61—42no—
60#11758198—22no—
61#11758198—24no—
62#11758198—24no—
63#11758198—22no—
64#11758198—24no—
65#11758198—24no—
66#11758198—42no—
67#11758198—42no—
68C4⋊Dic61—22no—
69C4×Dic61—24no—
70C4×Dic61—22no—
71C4×Dic61D414yescomplemented
72C23×C61C2411yescharacteristic
73C22×D61—21no—
74C22×D61—21no—
75C22×D61—22no—
76C22×D61—22no—
77C22×D61—22no—
78C22×D61—22no—
79C22×D61—22no—
80C22×D61—22no—
81C22×D61—22no—
82C22×D61—22no—
83C22×D61—22no—
84C22×D61#4112yes—
85Q8×C61—44no—
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61—22no—
89C2×C4×C61—22no—
90C2×C4×C61—22no—
91C2×C4×C61—21no—
92C2×C4×C61—22no—
93C2×C4×C61—22no—
94C2×C4×C61—22no—
95C2×C4×C61—22no—
96C2×C4×C61C2×D412yes—
97C2×C4×C61#4114yes—
98C2×C4×C61#4112yes—
99C2×Dic61—22no—
100C2×Dic61—21no—
101C2×Dic61—21no—
102C2×Dic61—21no—
103C2×Dic61—22no—
104C2×Dic61—22no—
105C2×Dic61—22no—
106C2×Dic61—22no—
107C2×Dic61C2×D412yes—
108C2×Dic61C2×D412yes—
109D244—48no—
110D244—44no—
111C4×D61—28no—
112C22×C61C22×D411yescharacteristic
113C22×C61C2×#4111yescharacteristic
114C22×C61C2×#4111yescharacteristic
115C22×C61C2×#4112yes—
116C22×C61H(5,𝔽2)12yes—
117C2×D61—22no—
118C2×D61—24no—
119C2×D61—41no—
120C2×D61—41no—
121C2×D61—42no—
122C2×D61—42no—
123C2×D61—42no—
124C2×D61—42no—
125C2×D61—42no—
126C2×D61—42no—
127C2×D61—42no—
128C2×D61—42no—
129C4×C61—22no—
130C4×C61—22no—
131C4×C61—24no—
132C4×C61—41no—
133C4×C61—42no—
134Dic61—22no—
135Dic61—22no—
136Dic61—41no—
137Dic61—42no—
138#2610—611nomaximal, Sylow
139C2×C61#52511yescharacteristic
140C2×C61#53211yescharacteristic
141C2×C61#53511yescharacteristic
142C2×C61#55112yes—
143C2×C61#55512yes—
144D61—42no—
145D61—82no—
146C2×#124—611no—
147C2×#117—611no—
148#395D6111yescharacteristic, complemented
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×D4—611no—
161C23×C4—611no—
162#124—1224no—
163#117—1224no—
164C2×C4⋊C4—611no—
165C2×C4⋊C4C2×D6111yescharacteristic
166C2×C4⋊C4C2×D6112yes—
167C2×C22⋊C4—611no—
168C2×C22⋊C4—611no—
169C2×C22⋊C4—612no—
170C2×C22⋊C4—612no—
171C2×C22⋊C4—612no—
172C2×C22⋊C4—612no—
173C2×C22⋊C4—612no—
174C2×C22⋊C4—612no—
175C2×C42—611no—
176C2×C42—611no—
177C2×C42—612no—
178#95—612no—
179#95—611no—
180#95—612no—
181#95C2×D6111yescharacteristic
182#95C2×D6112yes—
183C24—611no—
184C24—612no—
185C2×Q8—22no—
186C2×Q8—42no—
187C2×D4—1224no—
188C2×D4—1222no—
189C2×D4—1224no—
190C2×D4—2442no—
191C2×D4—2442no—
192C22×C4—611no—
193C22×C4—611no—
194C22×C4—612no—
195C22×C4—611no—
196C22×C4—1222no—
197C22×C4—1222no—
198C22×C4—1222no—
199C22×C4C22×D6112yes—
200C22×C4C22×D6111yescharacteristic
201C22×C4C22×D6111yescharacteristic
202C22×C4C22×D6112yes—
203C22×C4C22×D6111yescharacteristic
204C4⋊C4—22no—
205C4⋊C4—42no—
206C4⋊C4—1222no—
207C22⋊C4—1222no—
208C22⋊C4—1224no—
209C22⋊C4—1224no—
210C22⋊C4—1222no—
211C22⋊C4—1224no—
212C22⋊C4—1224no—
213C22⋊C4—2442no—
214C22⋊C4—2442no—
215C42—614no—
216C42—1222no—
217C42—1224no—
218C23—612no—
219C23—1221no—
220C23—1221no—
221C23—1222no—
222C23—1222no—
223C23—1222no—
224C23—1222no—
225C23—1222no—
226C23—1222no—
227C23—1222no—
228C23—1222no—
229C23—1222no—
230C23C23×D6111yescharacteristic
231Q8—44no—
232D4—2448no—
233D4—2444no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—612no—
245C2×C4—612no—
246C2×C4—1228no—
247C2×C4—1221no—
248C2×C4—1222no—
249C2×C4—1221no—
250C2×C4—1221no—
251C2×C4—1222no—
252C2×C4—1222no—
253C2×C4—1222no—
254C2×C4—1222no—
255C2×C4D4×D6112yes—
256C2×C4#1175822614yes—
257C2×C4#1175822612yes—
258C22—1222no—
259C22—1224no—
260C22—2442no—
261C22—2442no—
262C22—2442no—
263C22—2442no—
264C22—2442no—
265C22—2442no—
266C22—2442no—
267C22—2442no—
268C22—2441no—
269C22—2441no—
270C22C2×D4×D6111yescharacteristic
271C22#41×D6111yescharacteristic
272C22C2×#1175822611yescharacteristic
273C22C2×#1175822612yes—
274C22#1451982212yes—
275C4—22no—
276C4—22no—
277C4—24no—
278C4—41no—
279C4—42no—
280C4—1222no—
281C4—1222no—
282C4—2442no—
283C4—2441no—
284C2—4882no—
285C2—2442no—
286C2#1684027511yescharacteristic
287C2#1684031311yescharacteristic
288C2#1684032711yescharacteristic
289C2#1684043912yes—
290C2#1684047812yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#395C2
hypercenter#395D61
hypocenterC61#2610
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. C2×#14519766C2semidirect
2. C2×#14519735C2semidirect
3. #16839679C2semidirect
4. #16839673C2semidirect
6. #16839663C2semidirect
7. #16839654C2semidirect
8. #16839652C2semidirect
9. #16839640C2semidirect
10. #16839607C2semidirect
11. C61×#395C2semidirect
71. C4×Dic61D4semidirect
148. #395D61semidirect
157. C61#2610semidirect