Finite Group Databasebeta

← #21451386

Subgroups — #21451386

Order 7808.

604 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 135 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×#14519739C211yesmaximal, characteristic, complemented
2C2×#14519733C211yesmaximal, characteristic, complemented
3#16839700C211yesmaximal, characteristic, complemented
4#16839680C211yesmaximal, characteristic, complemented
5#16839671C211yesmaximal, characteristic
6#16839652C212yesmaximal, complemented
7#16839639C212yesmaximal, complemented
8#16839638C212yesmaximal, complemented
9#16839633C212yesmaximal, complemented
10#16839629C211yesmaximal, characteristic, complemented
11C61×#399C211yesmaximal, characteristic, complemented
12C22×D244C2211yescharacteristic
13C22×C22⋊D61C2212yes—
14C23×Dic61C2211yescharacteristic
15C22×C4×D61C2212yes—
16#14519739—24no—
17#14519733—24no—
18C2×#11758196C2211yescharacteristic
19C2×#11758196C2211yescharacteristic
20C2×C22⋊Dic61C2211yescharacteristic
21C2×#11758198C2212yes—
22C2×#11758198C2212yes—
23C2×#11758198C2212yes—
24C2×#11758198C2212yes—
25C2×C4×Dic61C2211yescharacteristic
26C2×C4×Dic61C2211yescharacteristic
27#14519684C2211yescharacteristic
28#14519684C2212yes—
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32C2×C4⋊C4×C61C2211yescharacteristic
33C2×C4⋊C4×C61C2212yes—
34C2×C22⋊C4×C61C2211yescharacteristic
35C2×C22⋊C4×C61C2212yes—
36#95×C61C2211yescharacteristic
37C24×C61C2311yescharacteristic
38C23×D61C2312yes—
39C22×C4×C61C2312yes—
40C22×C4×C61C2312yes—
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2311yescharacteristic
43C2×C22⋊D61—24no—
44C2×C22⋊D61—24no—
45C2×C22⋊D61—42no—
46C22×Dic61—22no—
47C22×Dic61—22no—
48C22×Dic61—22no—
49C22×Dic61C2312yes—
50C22×Dic61C2311yescharacteristic
51C22×Dic61C2311yescharacteristic
52C22×Dic61C2311yescharacteristic
53C22×Dic61C2311yescharacteristic
54C2×D244—24no—
55C2×D244—22no—
56C2×C4×D61—24no—
57C2×C4×D61—42no—
58C2×C4×D61—42no—
59C4⋊C4×C61—22no—
60C4⋊C4×C61—42no—
61C22⋊C4×C61—22no—
62C22⋊C4×C61—42no—
63C22⋊Dic61—22no—
64#11758198—24no—
65#11758198—24no—
66#11758198—24no—
67#11758198—42no—
68#11758196—22no—
69#11758196—22no—
70C4×Dic61—22no—
71C4×Dic61D414yescomplemented
72C23×C61—21no—
73C23×C61—21no—
74C23×C61—22no—
75C23×C61—22no—
76C23×C61#4112yes—
77C23×C61C2411yescharacteristic
78C22×D61—22no—
79C22×D61—22no—
80C22×D61—22no—
81C22×D61—22no—
82C22×D61—22no—
83C22×D61—22no—
84C22×D61#4114yes—
85C2×C4×C61—22no—
86C2×C4×C61—21no—
87C2×C4×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61—22no—
90C2×C4×C61—22no—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61—22no—
94C2×C4×C61C2×D412yes—
95C22⋊D61—48no—
96C2×Dic61—28no—
97C2×Dic61—21no—
98C2×Dic61—21no—
99C2×Dic61—21no—
100C2×Dic61—21no—
101C2×Dic61—22no—
102C2×Dic61—21no—
103C2×Dic61—22no—
104C2×Dic61—22no—
105C2×Dic61—22no—
106C2×Dic61—22no—
107C2×Dic61C2×D412yes—
108C2×Dic61C2×D412yes—
109C2×Dic61#4112yes—
110D244—28no—
111C4×D61—48no—
112C22×C61—22no—
113C22×C61—24no—
114C22×C61—41no—
115C22×C61—41no—
116C22×C61—42no—
117C22×C61C22×D411yescharacteristic
118C22×C61C2×#4112yes—
119C22×C61C2×#4111yescharacteristic
120C22×C61C2×#4111yescharacteristic
121C22×C61H(5,𝔽2)12yes—
122C2×D61—24no—
123C2×D61—24no—
124C2×D61—24no—
125C2×D61—42no—
126C2×D61—42no—
127C2×D61—42no—
128C2×D61—42no—
129C4×C61—22no—
130C4×C61—42no—
131C4×C61—41no—
132C4×C61—42no—
133Dic61—22no—
134Dic61—22no—
135Dic61—22no—
136Dic61—41no—
137Dic61—42no—
138#2598—611nomaximal, Sylow
139C2×C61—42no—
140C2×C61#52511yescharacteristic
141C2×C61#52511yescharacteristic
142C2×C61#53511yescharacteristic
143C2×C61#55112yes—
144C2×C61#55312yes—
145D61—44no—
146C2×C4×D4—611no—
147C2×#117—611no—
148#400—611no—
149#399D6111yescharacteristic, complemented
150#394—611no—
151#392—611no—
152#388—612no—
153#386—612no—
154#386—612no—
155#385—612no—
156#383—611no—
157C61#259811yescharacteristic, complemented, Sylow
158C22×D4—612no—
159C22×D4—611no—
160C23×C4—611no—
161C23×C4—612no—
162C4×D4—1224no—
163#117—1224no—
164C2×C4⋊C4—611no—
165C2×C4⋊C4—611no—
166C2×C4⋊C4C2×D6111yescharacteristic
167C2×C4⋊C4C2×D6112yes—
168C2×C22⋊C4—611no—
169C2×C22⋊C4—612no—
170C2×C22⋊C4—612no—
171C2×C22⋊C4—612no—
172C2×C22⋊C4—612no—
173C2×C22⋊C4C2×D6111yescharacteristic
174C2×C22⋊C4C2×D6112yes—
175C2×C42—611no—
176C2×C42—611no—
177#95—612no—
178#95—612no—
179#95—611no—
180#95—612no—
181#95—612no—
182#95C2×D6111yescharacteristic
183C24—612no—
184C24C22×D6111yescharacteristic
185C2×D4—1224no—
186C2×D4—1224no—
187C2×D4—1224no—
188C2×D4—1222no—
189C2×D4—2442no—
190C22×C4—611no—
191C22×C4—611no—
192C22×C4—611no—
193C22×C4—612no—
194C22×C4—611no—
195C22×C4—1224no—
196C22×C4—1222no—
197C22×C4—1222no—
198C22×C4—1222no—
199C22×C4—2442no—
200C22×C4—2442no—
201C22×C4C22×D6112yes—
202C22×C4C22×D6112yes—
203C22×C4C22×D6111yescharacteristic
204C22×C4C22×D6111yescharacteristic
205C4⋊C4—22no—
206C4⋊C4—42no—
207C4⋊C4—1222no—
208C4⋊C4—1222no—
209C22⋊C4—22no—
210C22⋊C4—42no—
211C22⋊C4—1224no—
212C22⋊C4—1224no—
213C22⋊C4—1224no—
214C22⋊C4—1222no—
215C22⋊C4—2442no—
216C42—614no—
217C42—1222no—
218C23—21no—
219C23—21no—
220C23—22no—
221C23—22no—
222C23—614no—
223C23—1222no—
224C23—1222no—
225C23—1222no—
226C23—1222no—
227C23—1222no—
228C23—1222no—
229C23#1175822612yes—
230C23C23×D6111yescharacteristic
231D4—1228no—
232D4—2448no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—612no—
243C2×C4—612no—
244C2×C4—612no—
245C2×C4—1228no—
246C2×C4—1221no—
247C2×C4—1221no—
248C2×C4—1221no—
249C2×C4—1221no—
250C2×C4—1222no—
251C2×C4—1221no—
252C2×C4—1222no—
253C2×C4—1222no—
254C2×C4—1222no—
255C2×C4—1222no—
256C2×C4—2448no—
257C2×C4D4×D6112yes—
258C22—22no—
259C22—24no—
260C22—42no—
261C22—41no—
262C22—41no—
263C22—1224no—
264C22—1224no—
265C22—1224no—
266C22—2442no—
267C22—2442no—
268C22—2442no—
269C22—2442no—
270C22C2×D4×D6111yescharacteristic
271C22#41×D6111yescharacteristic
272C22#41×D6112yes—
273C22C2×#1175822611yescharacteristic
274C22#1451982212yes—
275C4—22no—
276C4—42no—
277C4—41no—
278C4—42no—
279C4—1222no—
280C4—1222no—
281C4—1222no—
282C4—2441no—
283C4—2442no—
284C2—42no—
285C2—2444no—
286C2#1684027011yescharacteristic
287C2#1684027511yescharacteristic
288C2#1684032511yescharacteristic
289C2#1684043912yes—
290C2#1684045712yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#399C2
hypercenter#399D61
hypocenterC61#2598
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#14519739C2semidirect
2. C2×#14519733C2semidirect
3. #16839700C2semidirect
4. #16839680C2semidirect
6. #16839652C2semidirect
7. #16839639C2semidirect
8. #16839638C2semidirect
9. #16839633C2semidirect
10. #16839629C2semidirect
11. C61×#399C2semidirect
71. C4×Dic61D4semidirect
149. #399D61semidirect
157. C61#2598semidirect