Finite Group Databasebeta

← #21450711

Subgroups — #21450711

Order 7808.

800 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 800 conjugacy classes of subgroups — too many to draw. Only its 161 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×#14519761C211yesmaximal, characteristic, complemented
2C2×#14519747C211yesmaximal, characteristic
3C2×C4×C22⋊D61C211yesmaximal, characteristic, complemented
4C22×#11758198C211yesmaximal, characteristic, complemented
5#16839684C212yesmaximal, complemented
6#16839679C212yesmaximal, complemented
7#16839654C212yesmaximal, complemented
8#16839640C212yesmaximal, complemented
9#16839623C211yesmaximal, characteristic, complemented
10#16839617C211yesmaximal, characteristic, complemented
11C61×#380C211yesmaximal, characteristic, complemented
12C24×D61C2211yescharacteristic
13C22×D244C2212yes—
14C22×C22⋊D61C2211yescharacteristic
15C23×Dic61C2211yescharacteristic
16C22×C4×D61C2211yescharacteristic, complemented
17#14519761—24no—
18#14519747—24no—
19C4×C22⋊D61—24no—
20C2×C4⋊Dic61C2212yescomplemented
21C2×#11758196C2211yescharacteristic, complemented
22C2×C22⋊Dic61C2211yescharacteristic
23C2×#11758198—24no—
24C2×#11758198C2212yes—
25C2×#11758198C2212yes—
26C2×#11758198C2212yes—
27C2×#11758198C2212yes—
28C2×#11758198C2212yes—
29C2×#11758198C2211yescharacteristic, complemented
30C2×#11758198C2212yescomplemented
31C2×C4×Dic61C2211yescharacteristic, complemented
32#14519684C2212yescomplemented
33#14519684C2212yescomplemented
34C23×C4×C61C2211yescharacteristic
35C2×C4⋊C4×C61C2212yescomplemented
36C2×C22⋊C4×C61C2211yescharacteristic
37C2×C22⋊C4×C61C2211yescharacteristic
38#95×C61C2212yescomplemented
39C24×C61C2311yescharacteristic
40C23×D61—22no—
41C23×D61—24no—
42C23×D61—22no—
43C23×D61—22no—
44C23×D61—42no—
45C23×D61C2311yescharacteristic
46C23×D61C2312yes—
47C22×C4×C61—42no—
48C22×C4×C61D414yescomplemented
49C22×C4×C61C2312yes—
50C22×C4×C61C2312yes—
51C22×C4×C61C2311yescharacteristic
52C22×C4×C61C2311yescharacteristic
53C2×C22⋊D61—22no—
54C2×C22⋊D61—22no—
55C2×C22⋊D61D414yes—
56C22×Dic61—22no—
57C22×Dic61—22no—
58C22×Dic61—22no—
59C22×Dic61C2311yescharacteristic
60C22×Dic61C2312yes—
61C22×Dic61C2311yescharacteristic
62C22×Dic61C2311yescharacteristic
63C2×D244—24no—
64C2×D244—24no—
65C2×D244—42no—
66C2×C4×D61—22no—
67C2×C4×D61—42no—
68C4⋊C4×C61—42no—
69C22⋊C4×C61—22no—
70C22⋊C4×C61—22no—
71C22⋊Dic61—22no—
72#11758198—24no—
73#11758198—24no—
74#11758198—24no—
75#11758198—24no—
76#11758198—22no—
77#11758198—24no—
78#11758198—42no—
79C4⋊Dic61—24no—
80#11758196—22no—
81C4×Dic61—22no—
82C23×C61—22no—
83C23×C61—22no—
84C23×C61C2×D412yes—
85C23×C61C2×D412yes—
86C23×C61#4112yes—
87C23×C61C2411yescharacteristic
88C22×D61—28no—
89C22×D61—22no—
90C22×D61—21no—
91C22×D61—22no—
92C22×D61—22no—
93C22×D61—21no—
94C22×D61—22no—
95C22×D61—22no—
96C22×D61—22no—
97C22×D61—22no—
98C22×D61—22no—
99C22×D61—48no—
100C22×D61—48no—
101C22×D61—44no—
102C22×D61—44no—
103C22×D61C2×D412yes—
104C22×D61#4114yes—
105C2×C4×C61—22no—
106C2×C4×C61—22no—
107C2×C4×C61—22no—
108C2×C4×C61—22no—
109C2×C4×C61—22no—
110C2×C4×C61—22no—
111C2×C4×C61—22no—
112C2×C4×C61—22no—
113C2×C4×C61—44no—
114C2×C4×C61C2×D412yes—
115C2×C4×C61C2×D412yes—
116C22⋊D61—28no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—22no—
122C2×Dic61—22no—
123C2×Dic61—22no—
124C2×Dic61—22no—
125C2×Dic61—22no—
126C2×Dic61—44no—
127C2×Dic61C2×D412yes—
128D244—48no—
129C4×D61—44no—
130C22×C61—22no—
131C22×C61—22no—
132C22×C61—24no—
133C22×C61—24no—
134C22×C61#12114yes—
135C22×C61C22×D411yescharacteristic
136C22×C61C22×D411yescharacteristic
137C22×C61C2×#4112yes—
138C22×C61C2×#4111yescharacteristic
139C22×C61H(5,𝔽2)12yes—
140C2×D61—22no—
141C2×D61—24no—
142C2×D61—24no—
143C2×D61—24no—
144C2×D61—24no—
145C2×D61—416no—
146C2×D61—42no—
147C2×D61—41no—
148C2×D61—41no—
149C2×D61—42no—
150C2×D61—42no—
151C2×D61—42no—
152C2×D61—42no—
153C4×C61—22no—
154C4×C61—22no—
155C4×C61—42no—
156C4×C61—42no—
157Dic61—22no—
158Dic61—42no—
159Dic61—41no—
160Dic61—41no—
161#2534—611nomaximal, Sylow
162C2×C61—24no—
163C2×C61C2×#12111yescharacteristic
164C2×C61#52511yescharacteristic
165C2×C61#53411yescharacteristic
166C2×C61#54612yes—
167C2×C61#55112yes—
168D61—42no—
169D61—44no—
170C2×#123—611no—
171C2×#120—611no—
172C2×C4×D4—611no—
173C22×C22⋊C4—611no—
174#396—612no—
175#394—612no—
176#388—612no—
177#386—612no—
178#381—611no—
179#380D6111yescharacteristic, complemented
180#379—611no—
181C61#253411yescharacteristic, complemented, Sylow
182C25—611no—
183C22×D4—611no—
184C22×D4—612no—
185C23×C4—611no—
186C23×C4—611no—
187C23×C4C2×D6111yescharacteristic
188#123—1224no—
189#120—1224no—
190C4×D4—1224no—
191C2×C4⋊C4—611no—
192C2×C4⋊C4—612no—
193C2×C4⋊C4C2×D6112yescomplemented
194C2×C22⋊C4—611no—
195C2×C22⋊C4—612no—
196C2×C22⋊C4—612no—
197C2×C22⋊C4—611no—
198C2×C22⋊C4—612no—
199C2×C22⋊C4—612no—
200C2×C22⋊C4—612no—
201C2×C22⋊C4—612no—
202C2×C22⋊C4—1224no—
203C2×C22⋊C4C2×D6111yescharacteristic
204C2×C22⋊C4C2×D6111yescharacteristic
205C2×C42—611no—
206#95—612no—
207#95—612no—
208#95C2×D6112yescomplemented
209C24—612no—
210C24—611no—
211C24—1224no—
212C24—1222no—
213C24—1222no—
214C24—1222no—
215C24—2442no—
216C24C22×D6111yescharacteristic
217C2×D4—614no—
218C2×D4—1224no—
219C2×D4—1224no—
220C2×D4—1222no—
221C2×D4—1222no—
222C2×D4—2442no—
223C22×C4—42no—
224C22×C4—611no—
225C22×C4—611no—
226C22×C4—612no—
227C22×C4—611no—
228C22×C4—1222no—
229C22×C4—1222no—
230C22×C4—1222no—
231C22×C4—1222no—
232C22×C4—2442no—
233C22×C4D24414yescomplemented
234C22×C4C22×D6112yes—
235C22×C4C22×D6112yes—
236C22×C4C22×D6111yescharacteristic
237C22×C4C22×D6111yescharacteristic
238C4⋊C4—42no—
239C4⋊C4—1224no—
240C4⋊C4—1222no—
241C22⋊C4—22no—
242C22⋊C4—22no—
243C22⋊C4—1224no—
244C22⋊C4—1224no—
245C22⋊C4—1224no—
246C22⋊C4—1222no—
247C22⋊C4—1224no—
248C22⋊C4—1224no—
249C22⋊C4—1222no—
250C22⋊C4—2442no—
251C42—1222no—
252C23—22no—
253C23—22no—
254C23—612no—
255C23—614no—
256C23—1228no—
257C23—1222no—
258C23—1222no—
259C23—1221no—
260C23—1222no—
261C23—1222no—
262C23—1221no—
263C23—1222no—
264C23—1222no—
265C23—1222no—
266C23—1222no—
267C23—2448no—
268C23—2448no—
269C23—2444no—
270C23—2444no—
271C23C2×D24412yes—
272C23D4×D6112yes—
273C23#1175822612yes—
274C23C23×D6111yescharacteristic
275D4—1228no—
276D4—2448no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—44no—
286C2×C4—612no—
287C2×C4—1221no—
288C2×C4—1221no—
289C2×C4—1222no—
290C2×C4—1221no—
291C2×C4—1222no—
292C2×C4—1221no—
293C2×C4—1222no—
294C2×C4—1222no—
295C2×C4—1222no—
296C2×C4—2444no—
297C2×C4—2444no—
298C2×C4C2×D24412yes—
299C2×C4C2×D24412yes—
300C22—22no—
301C22—22no—
302C22—24no—
303C22—24no—
304C22—1222no—
305C22—1224no—
306C22—1224no—
307C22—1224no—
308C22—1224no—
309C22—24416no—
310C22—2442no—
311C22—2441no—
312C22—2441no—
313C22—2442no—
314C22—2442no—
315C22—2442no—
316C22—2442no—
317C22#1451975214yes—
318C22C2×D4×D6111yescharacteristic
319C22C22×D24411yescharacteristic
320C22#41×D6112yes—
321C22C2×#1175822611yescharacteristic
322C22#1451982212yes—
323C4—22no—
324C4—22no—
325C4—42no—
326C4—42no—
327C4—1222no—
328C4—2442no—
329C4—2441no—
330C4—2441no—
331C2—24no—
332C2—2444no—
333C2—2442no—
334C2C2×#1451975211yescharacteristic
335C2#1684027411yescharacteristic
336C2#1684032411yescharacteristic
337C2#1684040112yes—
338C2#1684043912yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#380C2
hypercenter#380D61
hypocenterC61#2534
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
1. C2×#14519761C2semidirect
3. C2×C4×C22⋊D61C2semidirect
4. C22×#11758198C2semidirect
5. #16839684C2semidirect
6. #16839679C2semidirect
7. #16839654C2semidirect
8. #16839640C2semidirect
9. #16839623C2semidirect
10. #16839617C2semidirect
11. C61×#380C2semidirect
16. C22×C4×D61C22semidirect
20. C2×C4⋊Dic61C22semidirect
21. C2×#11758196C22semidirect
29. C2×#11758198C22semidirect
30. C2×#11758198C22semidirect
31. C2×C4×Dic61C22semidirect
32. #14519684C22semidirect
33. #14519684C22semidirect
35. C2×C4⋊C4×C61C22semidirect
38. #95×C61C22semidirect
48. C22×C4×C61D4semidirect
179. #380D61semidirect
181. C61#2534semidirect
193. C2×C4⋊C4C2×D61semidirect
208. #95C2×D61semidirect
233. C22×C4D244semidirect