Finite Group Databasebeta

← #21450725

Subgroups — #21450725

Order 7808.

604 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 147 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×#14519755C212yesmaximal, complemented
2C2×#14519742C211yesmaximal, characteristic, complemented
3C2×#14519739C211yesmaximal, characteristic
4#16839693C211yesmaximal, characteristic, complemented
5#16839680C211yesmaximal, characteristic
6#16839679C211yesmaximal, characteristic
7#16839652C212yesmaximal, complemented
8#16839651C212yesmaximal, complemented
9#16839626C211yesmaximal, characteristic, complemented
10#16839621C212yesmaximal, complemented
11C61×#398C211yesmaximal, characteristic, complemented
12C22×Dic122C2211yescharacteristic
13C22×D244C2211yescharacteristic
14C22×C4×D61C2212yes—
15#14519755—28no—
16#14519742—24no—
17#14519739—24no—
18C2×#11758196C2211yescharacteristic
19C2×#11758196C2212yes—
20C2×#11758196C2211yescharacteristic
21C2×#11758196C2212yes—
22C2×#11758198C2212yes—
23C2×#11758198C2212yes—
24C2×#11758198C2212yes—
25C2×#11758198C2212yes—
26C2×#11758198C2212yes—
27C2×C4×Dic61C2211yescharacteristic
28C2×C4×Dic61C2211yescharacteristic
29C2×C4×Dic61C2211yescharacteristic
30#14519684C2212yes—
31#14519684C2211yescharacteristic
32#14519684C2212yes—
33C2×C4⋊C4×C61C2211yescharacteristic
34C2×C4⋊C4×C61C2211yescharacteristic
35C2×C4⋊C4×C61C2212yes—
36#95×C61C2211yescharacteristic
37#95×C61C2212yes—
38C23×D61C2312yes—
39C22×C4×C61C2312yes—
40C22×C4×C61C2312yes—
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2311yescharacteristic
43C22×C4×C61C2311yescharacteristic
44C22×Dic61C2312yes—
45C22×Dic61C2311yescharacteristic
46C22×Dic61C2311yescharacteristic
47C22×Dic61C2311yescharacteristic
48C22×Dic61C2311yescharacteristic
49C2×D244—24no—
50C2×D244—22no—
51C2×C4×D61—24no—
52C2×C4×D61—24no—
53C2×C4×D61—24no—
54C2×Dic122—22no—
55C2×Dic122—22no—
56C2×Dic122D414yescomplemented
57C4⋊C4×C61—22no—
58C4⋊C4×C61—22no—
59C4⋊C4×C61—24no—
60#11758198—24no—
61#11758198—24no—
62#11758198—24no—
63#11758198—24no—
64#11758198—24no—
65#11758196—22no—
66#11758196—22no—
67#11758196—24no—
68#11758196—24no—
69C4×Dic61—22no—
70C4×Dic61—22no—
71C4×Dic61D414yes—
72C23×C61C2411yescharacteristic
73C22×D61—22no—
74C22×D61—22no—
75C22×D61—22no—
76C22×D61—22no—
77C22×D61—22no—
78C22×D61—22no—
79C22×D61#4114yes—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—22no—
83C2×C4×C61—21no—
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×C61C2×D412yes—
92C2×C4×C61C2×D412yes—
93C2×Dic61—21no—
94C2×Dic61—21no—
95C2×Dic61—22no—
96C2×Dic61—21no—
97C2×Dic61—22no—
98C2×Dic61—22no—
99C2×Dic61—22no—
100C2×Dic61—22no—
101C2×Dic61C2×D412yes—
102C2×Dic61C2×D412yes—
103C2×Dic61C2×D412yes—
104C2×Dic61C2×D412yes—
105C2×Dic61#4112yes—
106D244—28no—
107C4×D61—48no—
108Dic122—28no—
109C22×C61C22×D411yescharacteristic
110C22×C61C22×D411yescharacteristic
111C22×C61C2×#4111yescharacteristic
112C22×C61C2×#4112yes—
113C22×C612−1+412yes—
114C2×D61—24no—
115C2×D61—24no—
116C2×D61—24no—
117C2×D61—42no—
118C2×D61—42no—
119C2×D61—42no—
120C2×D61—42no—
121C4×C61—22no—
122C4×C61—22no—
123C4×C61—42no—
124C4×C61—41no—
125C4×C61—42no—
126Dic61—22no—
127Dic61—22no—
128Dic61—41no—
129Dic61—42no—
130Dic61#12114yes—
131#2536—611nomaximal, Sylow
132C2×C61C2×#12111yescharacteristic
133C2×C61#52511yescharacteristic
134C2×C61#53611yescharacteristic
135C2×C61#54812yes—
136C2×C61#55212yes—
137D61—44no—
138C2×C22⋊Q8—612no—
139C2×C4×Q8—611no—
140C2×C4×D4—611no—
141#398—611no—
142#398D6111yescharacteristic, complemented
143#394—611no—
144#394—611no—
145#388—612no—
146#388—612no—
147#382—611no—
148#380—612no—
149C61#253611yescharacteristic, complemented, Sylow
150C22×Q8—611no—
151C22×D4—611no—
152C23×C4—612no—
153C22⋊Q8—1228no—
154C4×Q8—1224no—
155C4×D4—1224no—
156C2×C4⋊C4—611no—
157C2×C4⋊C4—611no—
158C2×C4⋊C4—612no—
159C2×C4⋊C4—612no—
160C2×C4⋊C4C2×D6111yescharacteristic
161C2×C4⋊C4C2×D6111yescharacteristic
162C2×C4⋊C4C2×D6112yes—
163C2×C22⋊C4—612no—
164C2×C22⋊C4—612no—
165C2×C22⋊C4—612no—
166C2×C22⋊C4—612no—
167C2×C22⋊C4—612no—
168C2×C42—611no—
169C2×C42—611no—
170C2×C42—611no—
171#95—612no—
172#95—612no—
173#95—611no—
174#95C2×D6112yes—
175#95C2×D6111yescharacteristic
176C24—612no—
177C2×Q8—614no—
178C2×Q8—1222no—
179C2×Q8—1222no—
180C2×D4—1224no—
181C2×D4—1222no—
182C22×C4—611no—
183C22×C4—611no—
184C22×C4—611no—
185C22×C4—612no—
186C22×C4—611no—
187C22×C4—1224no—
188C22×C4—1224no—
189C22×C4—1224no—
190C22×C4C22×D6112yes—
191C22×C4C22×D6112yes—
192C22×C4C22×D6111yescharacteristic
193C22×C4C22×D6111yescharacteristic
194C22×C4C22×D6111yescharacteristic
195C4⋊C4—22no—
196C4⋊C4—22no—
197C4⋊C4—24no—
198C4⋊C4—1222no—
199C4⋊C4—1224no—
200C4⋊C4—1224no—
201C4⋊C4—1222no—
202C22⋊C4—1224no—
203C22⋊C4—1224no—
204C22⋊C4—1224no—
205C22⋊C4—1224no—
206C22⋊C4—1224no—
207C42—614no—
208C42—1222no—
209C42—1222no—
210C23—614no—
211C23—1222no—
212C23—1222no—
213C23—1222no—
214C23—1222no—
215C23—1222no—
216C23—1222no—
217C23C23×D6111yescharacteristic
218Q8—1228no—
219D4—1228no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—612no—
232C2×C4—612no—
233C2×C4—612no—
234C2×C4—612no—
235C2×C4—612no—
236C2×C4—1221no—
237C2×C4—1221no—
238C2×C4—1222no—
239C2×C4—1221no—
240C2×C4—1222no—
241C2×C4—1222no—
242C2×C4—1222no—
243C2×C4—1222no—
244C2×C4—2448no—
245C2×C4D4×D6112yes—
246C2×C4D4×D6112yes—
247C22—1224no—
248C22—1224no—
249C22—1224no—
250C22—2442no—
251C22—2442no—
252C22—2442no—
253C22—2442no—
254C22C2×D4×D6111yescharacteristic
255C22C2×D4×D6111yescharacteristic
256C22#41×D6111yescharacteristic
257C22#41×D6112yes—
258C22#1451982512yes—
259C4—22no—
260C4—22no—
261C4—42no—
262C4—41no—
263C4—42no—
264C4—614no—
265C4—1222no—
266C4—1222no—
267C4—2441no—
268C4—2442no—
269C2—2444no—
270C2#121×D6111yescharacteristic
271C2#1684027011yescharacteristic
272C2#1684033711yescharacteristic
273C2#1684042212yes—
274C2#1684044412yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#398C2
hypercenter#398D61
hypocenterC61#2536
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#14519755C2semidirect
2. C2×#14519742C2semidirect
4. #16839693C2semidirect
7. #16839652C2semidirect
8. #16839651C2semidirect
9. #16839626C2semidirect
10. #16839621C2semidirect
11. C61×#398C2semidirect
56. C2×Dic122D4semidirect
142. #398D61semidirect
149. C61#2536semidirect