Finite Group Databasebeta

← #21451959

Subgroups — #21451959

Order 7808.

534 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 137 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×#14519765C211yesmaximal, characteristic, complemented
2#16839684C212yesmaximal, complemented
3#16839682C211yesmaximal, characteristic, complemented
4#16839679C211yesmaximal, characteristic, complemented
5#16839678C212yesmaximal, complemented
6#16839674C211yesmaximal, characteristic, complemented
7#16839671C211yesmaximal, characteristic
8#16839662C212yesmaximal, complemented
9#16839652C212yesmaximal, complemented
10C4×C4⋊Dic61C211yesmaximal, characteristic, complemented
11C2×#126×C61C211yesmaximal, characteristic, complemented
12C22×Dic122C2211yescharacteristic
13C22×D244C2211yescharacteristic
14C22×C22⋊D61C2212yes—
15#14519765—24no—
16C2×C4⋊Dic61C2212yes—
17C2×#11758196C2212yes—
18C2×C22⋊Dic61C2212yes—
19C2×#11758198C2212yes—
20C2×#11758198C2212yes—
21C2×#11758198C2212yes—
22C2×#11758198C2212yes—
23C2×#11758198C2212yes—
24C2×C4×Dic61C2212yes—
25#14519684C2211yescharacteristic
26#14519684C2212yes—
27#14519684C2212yes—
28#14519684C2211yescharacteristic
29#126×C61—24no—
30C2×C4⋊C4×C61C2211yescharacteristic
31C2×C4⋊C4×C61C2211yescharacteristic
32C2×C4⋊C4×C61C2211yescharacteristic
33C2×C22⋊C4×C61C2211yescharacteristic
34C2×C22⋊C4×C61C2211yescharacteristic
35C2×C22⋊C4×C61C2211yescharacteristic
36C2×C42×C61C2211yescharacteristic
37C24×C61C2311yescharacteristic
38C23×D61C2312yes—
39C22×C4×C61C2311yescharacteristic
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2311yescharacteristic
43C22×C4×C61C2311yescharacteristic
44C22×C4×C61C2311yescharacteristic
45C2×C22⋊D61—24no—
46C2×C22⋊D61—42no—
47C2×C22⋊D61—42no—
48C22×Dic61C2312yes—
49C22×Dic61C2312yes—
50C22×Dic61C2312yes—
51C2×D244—22no—
52C2×D244—42no—
53C2×Dic122—22no—
54C2×Dic122—42no—
55C4⋊C4×C61—22no—
56C4⋊C4×C61—22no—
57C4⋊C4×C61—22no—
58C22⋊C4×C61—22no—
59C22⋊C4×C61—22no—
60C22⋊C4×C61—22no—
61C42×C61D414yescomplemented
62C22⋊Dic61—42no—
63#11758198—24no—
64#11758198—24no—
65#11758198—24no—
66#11758198—42no—
67#11758198—42no—
68C4⋊Dic61—24no—
69#11758196—42no—
70C4×Dic61—42no—
71C23×C61—21no—
72C23×C61—22no—
73C23×C61—22no—
74C23×C61—21no—
75C23×C61—21no—
76C23×C61C2411yescharacteristic
77C22×D61—22no—
78C22×D61—22no—
79C22×D61—22no—
80C22×D61—22no—
81C22×D61—22no—
82C22×D61—22no—
83C22×D61—22no—
84C2×C4×C61—22no—
85C2×C4×C61—21no—
86C2×C4×C61—22no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61C2×D412yes—
96C2×C4×C61C2×D412yes—
97C2×C4×C61C2×D412yes—
98C22⋊D61—48no—
99C2×Dic61—22no—
100C2×Dic61—22no—
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61—22no—
104C2×Dic61—22no—
105C2×Dic61—22no—
106C2×Dic61—22no—
107C2×Dic61#4114yes—
108D244—44no—
109Dic122—44no—
110C22×C61—41no—
111C22×C61—41no—
112C22×C61—41no—
113C22×C61—42no—
114C22×C61—42no—
115C22×C61C22×D411yescharacteristic
116C22×C61C2×#4112yes—
117C22×C61H(5,𝔽2)12yes—
118C22×C61H(5,𝔽2)11yescharacteristic
119C22×C612−1+411yescharacteristic
120C2×D61—42no—
121C2×D61—42no—
122C2×D61—42no—
123C2×D61—42no—
124C2×D61—42no—
125C2×D61—42no—
126C2×D61—42no—
127C4×C61—22no—
128C4×C61—22no—
129C4×C61—22no—
130C4×C61—41no—
131C4×C61—41no—
132C4×C61—41no—
133Dic61—24no—
134Dic61—42no—
135Dic61—42no—
136#2662—611nomaximal, Sylow
137C2×C61—81no—
138C2×C61#53211yescharacteristic
139C2×C61#53511yescharacteristic
140C2×C61#53711yescharacteristic
141C2×C61#53812yes—
142C2×C61#54212yes—
143D61—82no—
144C2×#126D6111yescharacteristic, complemented
145C2×#124—611no—
146#396—612no—
147#395—611no—
148#394—611no—
149#394—612no—
150#393—611no—
151#392—611no—
152#390—612no—
153#388—612no—
154C4×C4⋊C4—611no—
155C61#266211yescharacteristic, complemented, Sylow
156C22×Q8—611no—
157C22×D4—612no—
158C22×D4—611no—
159#126—24no—
160#124—1224no—
161C2×C4⋊C4—612no—
162C2×C4⋊C4—612no—
163C2×C4⋊C4C2×D6111yescharacteristic
164C2×C4⋊C4C2×D6111yescharacteristic
165C2×C4⋊C4C2×D6111yescharacteristic
166C2×C22⋊C4—612no—
167C2×C22⋊C4—612no—
168C2×C22⋊C4—612no—
169C2×C22⋊C4—612no—
170C2×C22⋊C4—612no—
171C2×C22⋊C4—612no—
172C2×C22⋊C4C2×D6111yescharacteristic
173C2×C22⋊C4C2×D6111yescharacteristic
174C2×C22⋊C4C2×D6111yescharacteristic
175C2×C42—612no—
176C2×C42C2×D6111yescharacteristic
177#95—611no—
178#95—611no—
179#95—612no—
180#95—612no—
181C24—612no—
182C24C22×D6111yescharacteristic
183C2×Q8—1222no—
184C2×Q8—2442no—
185C2×D4—1224no—
186C2×D4—1222no—
187C2×D4—2442no—
188C2×D4—2442no—
189C2×D4—2442no—
190C22×C4—612no—
191C22×C4—612no—
192C22×C4—612no—
193C22×C4C22×D6111yescharacteristic
194C22×C4C22×D6111yescharacteristic
195C22×C4C22×D6111yescharacteristic
196C22×C4C22×D6111yescharacteristic
197C22×C4C22×D6111yescharacteristic
198C22×C4C22×D6111yescharacteristic
199C4⋊C4—22no—
200C4⋊C4—22no—
201C4⋊C4—22no—
202C4⋊C4—1224no—
203C4⋊C4—2442no—
204C22⋊C4—22no—
205C22⋊C4—22no—
206C22⋊C4—22no—
207C22⋊C4—1224no—
208C22⋊C4—1224no—
209C22⋊C4—1224no—
210C22⋊C4—2442no—
211C22⋊C4—2442no—
212C22⋊C4—2442no—
213C42—2442no—
214C42C22⋊D6114yescomplemented
215C23—21no—
216C23—22no—
217C23—22no—
218C23—21no—
219C23—21no—
220C23—1222no—
221C23—1222no—
222C23—1222no—
223C23—1222no—
224C23—1222no—
225C23—1222no—
226C23—1222no—
227C23C23×D6111yescharacteristic
228Q8—2444no—
229D4—2444no—
230D4—2448no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—614no—
243C2×C4—1222no—
244C2×C4—1222no—
245C2×C4—1222no—
246C2×C4—1222no—
247C2×C4—1222no—
248C2×C4—1222no—
249C2×C4—1222no—
250C2×C4—1222no—
251C2×C4C2×C22⋊D6112yes—
252C2×C4C2×C22⋊D6112yes—
253C2×C4C2×C22⋊D6112yes—
254C22—41no—
255C22—41no—
256C22—41no—
257C22—42no—
258C22—42no—
259C22—2442no—
260C22—2442no—
261C22—2442no—
262C22—2442no—
263C22—2442no—
264C22—2442no—
265C22—2442no—
266C22C22×C22⋊D6111yescharacteristic
267C22#41×D6112yes—
268C22#1451982312yes—
269C22#1451982311yescharacteristic
270C22#1451982411yescharacteristic
271C4—22no—
272C4—22no—
273C4—22no—
274C4—41no—
275C4—41no—
276C4—41no—
277C4—1224no—
278C4—2442no—
279C4—2442no—
280C2—81no—
281C2—4882no—
282C2#1684030811yescharacteristic
283C2#1684032611yescharacteristic
284C2#1684034011yescharacteristic
285C2#1684035112yes—
286C2#1684037812yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#126×C61C2
hypercenterC2×#126D61
hypocenterC61#2662
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. C2×#14519765C2semidirect
2. #16839684C2semidirect
3. #16839682C2semidirect
4. #16839679C2semidirect
5. #16839678C2semidirect
6. #16839674C2semidirect
8. #16839662C2semidirect
9. #16839652C2semidirect
10. C4×C4⋊Dic61C2semidirect
11. C2×#126×C61C2semidirect
61. C42×C61D4semidirect
144. C2×#126D61semidirect
155. C61#2662semidirect
214. C42C22⋊D61semidirect