Finite Group Databasebeta

← #21453852

Subgroups — #21453852

Order 7808.

528 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 125 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×#14519755C211yesmaximal, characteristic, complemented
2C2×#14519752C211yesmaximal, characteristic
3#16839697C212yesmaximal, complemented
4#16839693C211yesmaximal, characteristic, complemented
5#16839680C211yesmaximal, characteristic, complemented
6#16839680C212yesmaximal, complemented
7#16839679C211yesmaximal, characteristic, complemented
8#16839679C212yesmaximal, complemented
9#16839675C212yesmaximal, complemented
10#16839624C211yesmaximal, characteristic, complemented
11C61×#398C211yesmaximal, characteristic, complemented
12C22×Dic122C2211yescharacteristic
13C22×D244C2212yes—
14C22×D244C2211yescharacteristic
15C22×C4×D61C2211yescharacteristic
16#14519755—24no—
17#14519752—24no—
18C2×#11758196C2211yescharacteristic
19C2×#11758196C2211yescharacteristic
20C2×#11758196C2212yes—
21C2×#11758198C2211yescharacteristic
22C2×#11758198C2212yes—
23C2×#11758198C2211yescharacteristic
24C2×#11758198C2212yes—
25C2×#11758198C2212yes—
26C2×#11758198C2212yes—
27C2×#11758198C2212yes—
28C2×#11758198C2212yes—
29#14519684C2211yescharacteristic
30#14519684C2212yes—
31#14519684C2212yes—
32C2×C4⋊C4×C61C2211yescharacteristic
33C2×C4⋊C4×C61C2211yescharacteristic
34C2×C4⋊C4×C61C2212yes—
35#95×C61C2211yescharacteristic
36#95×C61C2212yes—
37C23×D61C2312yes—
38C23×D61C2311yescharacteristic
39C22×C4×C61C2312yes—
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2312yes—
42C22×C4×C61C2311yescharacteristic
43C22×C4×C61C2311yescharacteristic
44C22×Dic61C2311yescharacteristic
45C22×Dic61C2312yes—
46C22×Dic61C2311yescharacteristic
47C22×Dic61C2311yescharacteristic
48C2×D244—24no—
49C2×D244—22no—
50C2×D244—42no—
51C2×D244—42no—
52C2×D244—42no—
53C2×C4×D61—42no—
54C2×C4×D61D414yes—
55C2×Dic122—22no—
56C2×Dic122—42no—
57C4⋊C4×C61—22no—
58C4⋊C4×C61—22no—
59C4⋊C4×C61—42no—
60#11758198—22no—
61#11758198—22no—
62#11758198—24no—
63#11758198—42no—
64#11758198—42no—
65#11758198—42no—
66#11758198—42no—
67#11758198—42no—
68#11758196—22no—
69#11758196—22no—
70#11758196—42no—
71C23×C61C2411yescharacteristic
72C22×D61—22no—
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×D61C2×D412yes—
84C2×C4×C61—22no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61—21no—
90C2×C4×C61—22no—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61—21no—
94C2×C4×C61—22no—
95C2×C4×C61—22no—
96C2×C4×C61C2×D412yes—
97C2×Dic61—22no—
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×Dic61C2×D412yes—
107D244—44no—
108D244—48no—
109C4×D61—44no—
110Dic122—44no—
111C22×C61C22×D411yescharacteristic
112C22×C61H(5,𝔽2)11yescharacteristic
113C22×C61H(5,𝔽2)12yes—
114C22×C61H(5,𝔽2)11yescharacteristic
115C22×C612−1+412yes—
116C2×D61—22no—
117C2×D61—22no—
118C2×D61—22no—
119C2×D61—42no—
120C2×D61—42no—
121C2×D61—42no—
122C2×D61—42no—
123C2×D61—42no—
124C2×D61—42no—
125C2×D61—42no—
126C2×D61—42no—
127C2×D61—42no—
128C4×C61—22no—
129C4×C61—41no—
130C4×C61—42no—
131C4×C61—41no—
132C4×C61—42no—
133Dic61—22no—
134Dic61—41no—
135Dic61—41no—
136Dic61—42no—
137#2816—611nomaximal, Sylow
138C2×C61#53411yescharacteristic
139C2×C61#53511yescharacteristic
140C2×C61#53611yescharacteristic
141C2×C61#56212yes—
142C2×C61#56212yes—
143D61—42no—
144D61—82no—
145C2×C22⋊Q8—611no—
146C2×#121—611no—
147#399—612no—
148#398—611no—
149#398D6111yescharacteristic, complemented
150#394—611no—
151#394—612no—
152#394—611no—
153#394—612no—
154#393—612no—
155#381—611no—
156C61#281611yescharacteristic, complemented, Sylow
157C22×Q8—611no—
158C22×D4—612no—
159C22×D4—611no—
160C23×C4—611no—
161C22⋊Q8—1224no—
162#121—1224no—
163C2×C4⋊C4—611no—
164C2×C4⋊C4—611no—
165C2×C4⋊C4—612no—
166C2×C4⋊C4C2×D6111yescharacteristic
167C2×C4⋊C4C2×D6111yescharacteristic
168C2×C4⋊C4C2×D6112yes—
169C2×C22⋊C4—612no—
170C2×C22⋊C4—611no—
171C2×C22⋊C4—611no—
172C2×C22⋊C4—612no—
173C2×C22⋊C4—612no—
174C2×C22⋊C4—612no—
175C2×C22⋊C4—612no—
176C2×C22⋊C4—612no—
177#95—612no—
178#95—611no—
179#95—612no—
180#95C2×D6111yescharacteristic
181#95C2×D6112yes—
182C24—611no—
183C24—612no—
184C2×Q8—1222no—
185C2×Q8—2442no—
186C2×D4—1224no—
187C2×D4—1222no—
188C2×D4—2442no—
189C2×D4—2442no—
190C2×D4—2442no—
191C22×C4—611no—
192C22×C4—614no—
193C22×C4—612no—
194C22×C4—611no—
195C22×C4—611no—
196C22×C4—2442no—
197C22×C4C22×D6112yes—
198C22×C4C22×D6112yes—
199C22×C4C22×D6111yescharacteristic
200C22×C4C22×D6111yescharacteristic
201C22×C4C22×D6111yescharacteristic
202C4⋊C4—22no—
203C4⋊C4—22no—
204C4⋊C4—42no—
205C4⋊C4—1222no—
206C4⋊C4—1222no—
207C4⋊C4—2442no—
208C22⋊C4—1224no—
209C22⋊C4—1222no—
210C22⋊C4—1222no—
211C22⋊C4—2442no—
212C22⋊C4—2442no—
213C22⋊C4—2442no—
214C22⋊C4—2442no—
215C22⋊C4—2442no—
216C23—612no—
217C23—1221no—
218C23—1222no—
219C23—1221no—
220C23—1222no—
221C23—1222no—
222C23—1222no—
223C23—1222no—
224C23—1222no—
225C23—1222no—
226C23—1222no—
227C23—1222no—
228C23C23×D6111yescharacteristic
229Q8—2444no—
230D4—2444no—
231D4—2448no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—612no—
245C2×C4—1222no—
246C2×C4—1221no—
247C2×C4—1221no—
248C2×C4—1221no—
249C2×C4—1222no—
250C2×C4—1222no—
251C2×C4—1222no—
252C2×C4—1221no—
253C2×C4—1222no—
254C2×C4—2444no—
255C2×C4D4×D6112yes—
256C22—1222no—
257C22—1222no—
258C22—1222no—
259C22—2442no—
260C22—2442no—
261C22—2442no—
262C22—2442no—
263C22—2442no—
264C22—2442no—
265C22—2442no—
266C22—2442no—
267C22—2442no—
268C22C2×D4×D6111yescharacteristic
269C22#1451982211yescharacteristic
270C22#1451982312yes—
271C22#1451982311yescharacteristic
272C22#1451982512yes—
273C4—22no—
274C4—42no—
275C4—41no—
276C4—41no—
277C4—42no—
278C4—1222no—
279C4—2442no—
280C4—2441no—
281C4—2441no—
282C2—4882no—
283C2—2442no—
284C2#1684032311yescharacteristic
285C2#1684032811yescharacteristic
286C2#1684033711yescharacteristic
287C2#1684050812yes—
288C2#1684051012yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#398C2
hypercenter#398D61
hypocenterC61#2816
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#14519755C2semidirect
3. #16839697C2semidirect
4. #16839693C2semidirect
5. #16839680C2semidirect
6. #16839680C2semidirect
7. #16839679C2semidirect
8. #16839679C2semidirect
9. #16839675C2semidirect
10. #16839624C2semidirect
11. C61×#398C2semidirect
149. #398D61semidirect
156. C61#2816semidirect