Finite Group Databasebeta

← #21451693

Subgroups — #21451693

Order 7808.

512 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 131 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×#14519768C211yesmaximal, characteristic, complemented
2C2×#14519737C211yesmaximal, characteristic
3#16839697C211yesmaximal, characteristic, complemented
4#16839695C212yesmaximal, complemented
5#16839689C211yesmaximal, characteristic, complemented
6#16839687C211yesmaximal, characteristic, complemented
7#16839678C212yesmaximal
8#16839634C212yesmaximal, complemented
9#16839633C212yesmaximal, complemented
10#16839629C211yesmaximal, characteristic, complemented
11C61×#399C211yesmaximal, characteristic, complemented
12C22×C22⋊D61C2211yescharacteristic
13C23×Dic61C2211yescharacteristic
14C22×C4×D61C2211yescharacteristic
15#14519768—24no—
16#14519737—24no—
17C2×C4⋊Dic61C2211yescharacteristic
18C2×C4⋊Dic61C2212yes—
19C2×#11758196C2211yescharacteristic
20C2×#11758196C2212yes—
21C2×#11758196C2212yes—
22C2×C22⋊Dic61C2212yes—
23C2×#11758198C2211yescharacteristic
24C2×#11758198C2212yes—
25C2×#11758198C2212yes—
26C2×C4×Dic61C2211yescharacteristic
27#14519684C2212yes—
28#14519684C2211yescharacteristic
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×D61C2311yescharacteristic
39C22×C4×C61C2311yescharacteristic
40C22×C4×C61C2312yes—
41C22×C4×C61C2312yes—
42C22×C4×C61C2311yescharacteristic
43C2×C22⋊D61—22no—
44C2×C22⋊D61—22no—
45C2×C22⋊D61—22no—
46C22×Dic61—22no—
47C22×Dic61—42no—
48C22×Dic61C2311yescharacteristic
49C22×Dic61C2312yes—
50C22×Dic61C2312yes—
51C22×Dic61C2311yescharacteristic
52C22×Dic61C2311yescharacteristic
53C2×C4×D61—22no—
54C2×C4×D61—42no—
55C4⋊C4×C61—22no—
56C4⋊C4×C61—42no—
57C22⋊C4×C61—22no—
58C22⋊C4×C61—42no—
59C22⋊Dic61—24no—
60#11758198—24no—
61#11758198—22no—
62#11758198—42no—
63C4⋊Dic61—22no—
64C4⋊Dic61—24no—
65#11758196—22no—
66#11758196—24no—
67#11758196—42no—
68C4×Dic61D414yes—
69C23×C61—21no—
70C23×C61—21no—
71C23×C61—22no—
72C23×C61—22no—
73C23×C61#4112yes—
74C23×C61C2411yescharacteristic
75C22×D61—21no—
76C22×D61—21no—
77C22×D61—22no—
78C22×D61—22no—
79C22×D61#4112yes—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—21no—
83C2×C4×C61—22no—
84C2×C4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61—22no—
87C2×C4×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61C2×D412yes—
90C22⋊D61—28no—
91C2×Dic61—21no—
92C2×Dic61—21no—
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—21no—
96C2×Dic61—22no—
97C2×Dic61—22no—
98C2×Dic61—22no—
99C2×Dic61—22no—
100C2×Dic61—22no—
101C2×Dic61—22no—
102C2×Dic61—44no—
103C2×Dic61C2×D412yes—
104C2×Dic61C2×D412yes—
105C4×D61—44no—
106C22×C61—22no—
107C22×C61—24no—
108C22×C61—41no—
109C22×C61—41no—
110C22×C61—42no—
111C22×C61C22×D411yescharacteristic
112C22×C61C2×#4111yescharacteristic
113C22×C61C2×#4111yescharacteristic
114C22×C61H(5,𝔽2)12yes—
115C22×C612−1+412yes—
116C2×D61—22no—
117C2×D61—24no—
118C2×D61—41no—
119C2×D61—41no—
120C2×D61—42no—
121C4×C61—22no—
122C4×C61—41no—
123C4×C61—42no—
124C4×C61—42no—
125Dic61—22no—
126Dic61—22no—
127Dic61—42no—
128Dic61—41no—
129Dic61—42no—
130#2633—611nomaximal, Sylow
131C2×C61—42no—
132C2×C61#52511yescharacteristic
133C2×C61#53511yescharacteristic
134C2×C61#53611yescharacteristic
135C2×C61#53912yes—
136C2×C61#53912yes—
137D61—42no—
138C2×#125—611no—
139C2×C4×D4—611no—
140#399—611no—
141#399D6111yescharacteristic, complemented
142#398—612no—
143#397—611no—
144#397—611no—
145#394—612no—
146#385—612no—
147#385—612no—
148#383—611no—
149C61#263311yescharacteristic, complemented, Sylow
150C22×D4—611no—
151C23×C4—611no—
152C23×C4—611no—
153#125—1224no—
154C4×D4—1224no—
155C2×C4⋊C4—611no—
156C2×C4⋊C4—612no—
157C2×C4⋊C4—612no—
158C2×C4⋊C4—611no—
159C2×C4⋊C4—612no—
160C2×C4⋊C4C2×D6111yescharacteristic
161C2×C4⋊C4C2×D6112yes—
162C2×C22⋊C4—612no—
163C2×C22⋊C4—611no—
164C2×C22⋊C4—612no—
165C2×C22⋊C4—612no—
166C2×C22⋊C4C2×D6111yescharacteristic
167C2×C22⋊C4C2×D6112yes—
168C2×C42—611no—
169#95—612no—
170#95—612no—
171#95—611no—
172#95—612no—
173#95—612no—
174#95C2×D6111yescharacteristic
175C24—611no—
176C24C22×D6111yescharacteristic
177C2×D4—1222no—
178C2×D4—1222no—
179C2×D4—1222no—
180C22×C4—611no—
181C22×C4—611no—
182C22×C4—612no—
183C22×C4—612no—
184C22×C4—611no—
185C22×C4—1222no—
186C22×C4—1222no—
187C22×C4—2442no—
188C22×C4—2442no—
189C22×C4C22×D6112yes—
190C22×C4C22×D6111yescharacteristic
191C22×C4C22×D6112yes—
192C22×C4C22×D6111yescharacteristic
193C4⋊C4—22no—
194C4⋊C4—42no—
195C4⋊C4—1222no—
196C4⋊C4—1224no—
197C4⋊C4—1224no—
198C4⋊C4—1222no—
199C4⋊C4—2442no—
200C22⋊C4—22no—
201C22⋊C4—42no—
202C22⋊C4—1224no—
203C22⋊C4—1224no—
204C22⋊C4—1222no—
205C22⋊C4—2442no—
206C42—614no—
207C23—21no—
208C23—21no—
209C23—22no—
210C23—22no—
211C23—612no—
212C23—1221no—
213C23—1221no—
214C23—1222no—
215C23—1222no—
216C23#1175822612yes—
217C23C23×D6111yescharacteristic
218D4—1228no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—612no—
229C2×C4—612no—
230C2×C4—1221no—
231C2×C4—1221no—
232C2×C4—1222no—
233C2×C4—1221no—
234C2×C4—1222no—
235C2×C4—1222no—
236C2×C4—1222no—
237C2×C4—1222no—
238C2×C4—1222no—
239C2×C4—1222no—
240C2×C4—1222no—
241C2×C4—2444no—
242C2×C4—2444no—
243C2×C4D4×D6112yes—
244C22—22no—
245C22—24no—
246C22—41no—
247C22—41no—
248C22—42no—
249C22—1222no—
250C22—1224no—
251C22—2441no—
252C22—2441no—
253C22—2442no—
254C22C2×D4×D6111yescharacteristic
255C22#41×D6111yescharacteristic
256C22C2×#1175822611yescharacteristic
257C22#1451982212yes—
258C22#1451982412yes—
259C4—22no—
260C4—42no—
261C4—41no—
262C4—42no—
263C4—1222no—
264C4—1222no—
265C4—2442no—
266C4—2441no—
267C4—2442no—
268C2—42no—
269C2—2442no—
270C2#1684027511yescharacteristic
271C2#1684032511yescharacteristic
272C2#1684033411yescharacteristic
273C2#1684035512yes—
274C2#1684036112yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#399C2
hypercenter#399D61
hypocenterC61#2633
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#14519768C2semidirect
3. #16839697C2semidirect
4. #16839695C2semidirect
5. #16839689C2semidirect
6. #16839687C2semidirect
8. #16839634C2semidirect
9. #16839633C2semidirect
10. #16839629C2semidirect
11. C61×#399C2semidirect
141. #399D61semidirect
149. C61#2633semidirect