Finite Group Databasebeta

← #21450706

Subgroups — #21450706

Order 7808.

800 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519758C211yesmaximal, characteristic, complemented
2C2×D4×Dic61C211yesmaximal, characteristic, complemented
3C22×C22⋊Dic61C211yesmaximal, characteristic, complemented
4#16839685C212yesmaximal, complemented
5#16839676C212yesmaximal, complemented
6#16839656C212yesmaximal, complemented
7#16839642C212yesmaximal, complemented
8#16839623C211yesmaximal, characteristic, complemented
9#16839620C211yesmaximal, characteristic, complemented
10#16839618C211yesmaximal, characteristic, complemented
11C2×#120×C61C211yesmaximal, characteristic
12C23×Dic61C2211yescharacteristic
13C23×Dic61C2211yescharacteristic
14C23×Dic61C2211yescharacteristic, complemented
15#14519758—24no—
16D4×Dic61—24no—
17C2×C4⋊Dic61C2211yescharacteristic, complemented
18C2×#11758196C2212yescomplemented
19C2×#11758196C2212yescomplemented
20C2×C22⋊Dic61—24no—
21C2×C22⋊Dic61C2212yes—
22C2×C22⋊Dic61C2212yes—
23C2×C22⋊Dic61C2211yescharacteristic
24C2×C22⋊Dic61C2211yescharacteristic
25C2×C22⋊Dic61C2212yes—
26C2×C22⋊Dic61C2212yes—
27C2×C22⋊Dic61C2211yescharacteristic, complemented
28C2×C22⋊Dic61C2212yescomplemented
29C2×C4×Dic61C2211yescharacteristic, complemented
30#14519684C2212yescomplemented
31#14519684C2212yescomplemented
32#14519684C2212yescomplemented
33C25×C61C2211yescharacteristic
34C22×D4×C61C2212yes—
35C22×D4×C61C2211yescharacteristic
36#120×C61—24no—
37C2×C22⋊C4×C61C2212yes—
38C2×C22⋊C4×C61C2211yescharacteristic
39C24×C61—22no—
40C24×C61—24no—
41C24×C61—22no—
42C24×C61—22no—
43C24×C61—42no—
44C24×C61C2311yescharacteristic
45C24×C61C2312yes—
46C24×C61C2311yescharacteristic
47C2×D4×C61—22no—
48C2×D4×C61—22no—
49C2×D4×C61—24no—
50C2×D4×C61—24no—
51C2×D4×C61—42no—
52C2×D4×C61D414yes—
53C22×C4×C61C2312yes—
54C22×C4×C61C2311yescharacteristic
55C22×Dic61—22no—
56C22×Dic61—22no—
57C22×Dic61—22no—
58C22×Dic61—22no—
59C22×Dic61—42no—
60C22×Dic61—42no—
61C22×Dic61D414yescomplemented
62C22×Dic61C2312yes—
63C22×Dic61C2311yescharacteristic
64C22×Dic61C2311yescharacteristic
65C22×Dic61C2312yes—
66C22×Dic61C2311yescharacteristic
67C22×Dic61C2311yescharacteristic
68C22⋊C4×C61—22no—
69C22⋊C4×C61—24no—
70C22⋊Dic61—22no—
71C22⋊Dic61—22no—
72C22⋊Dic61—24no—
73C22⋊Dic61—24no—
74C22⋊Dic61—24no—
75C22⋊Dic61—24no—
76C22⋊Dic61—22no—
77C22⋊Dic61—42no—
78C4⋊Dic61—22no—
79#11758196—24no—
80#11758196—42no—
81C4×Dic61—22no—
82C23×C61—22no—
83C23×C61—22no—
84C23×C61—28no—
85C23×C61—22no—
86C23×C61—21no—
87C23×C61—22no—
88C23×C61—21no—
89C23×C61—22no—
90C23×C61—22no—
91C23×C61—22no—
92C23×C61—22no—
93C23×C61—22no—
94C23×C61—22no—
95C23×C61—48no—
96C23×C61—48no—
97C23×C61—44no—
98C23×C61—44no—
99C23×C61C2×D412yes—
100C23×C61C2×D412yes—
101C23×C61C2×D412yes—
102C23×C61#4114yes—
103C23×C61#4112yes—
104C23×C61C2411yescharacteristic
105D4×C61—28no—
106D4×C61—48no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—22no—
110C2×C4×C61—22no—
111C2×C4×C61—22no—
112C2×C4×C61C2×D412yes—
113C2×Dic61—22no—
114C2×Dic61—22no—
115C2×Dic61—21no—
116C2×Dic61—22no—
117C2×Dic61—22no—
118C2×Dic61—21no—
119C2×Dic61—22no—
120C2×Dic61—22no—
121C2×Dic61—22no—
122C2×Dic61—22no—
123C2×Dic61—22no—
124C2×Dic61—22no—
125C2×Dic61—44no—
126C2×Dic61—44no—
127C2×Dic61—44no—
128C2×Dic61C2×D412yes—
129C2×Dic61C2×D412yes—
130C22×C61—22no—
131C22×C61—22no—
132C22×C61—24no—
133C22×C61—24no—
134C22×C61—22no—
135C22×C61—24no—
136C22×C61—24no—
137C22×C61—24no—
138C22×C61—24no—
139C22×C61—416no—
140C22×C61—42no—
141C22×C61—41no—
142C22×C61—41no—
143C22×C61—42no—
144C22×C61—42no—
145C22×C61—42no—
146C22×C61—42no—
147C22×C61#12114yes—
148C22×C61C22×D411yescharacteristic
149C22×C61C22×D411yescharacteristic
150C22×C61C2×#4111yescharacteristic
151C22×C61C2×#4112yes—
152C22×C61H(5,𝔽2)12yes—
153C4×C61—22no—
154C4×C61—42no—
155Dic61—22no—
156Dic61—22no—
157Dic61—42no—
158Dic61—41no—
159Dic61—41no—
160Dic61—42no—
161#2534—611nomaximal, Sylow
162C2×C61—24no—
163C2×C61—42no—
164C2×C61—44no—
165C2×C61C2×#12111yescharacteristic
166C2×C61#52511yescharacteristic
167C2×C61#53411yescharacteristic
168C2×C61#54612yes—
169C2×C61#55112yes—
170C2×#123—611no—
171C2×#120D6111yescharacteristic
172C2×C4×D4—611no—
173C22×C22⋊C4—611no—
174#396—612no—
175#394—612no—
176#388—612no—
177#386—612no—
178#381—611no—
179#380—611no—
180#379—611no—
181C61#253411yescharacteristic, complemented, Sylow
182C25C2×D6111yescharacteristic
183C22×D4C2×D6112yes—
184C22×D4C2×D6111yescharacteristic
185C23×C4—611no—
186C23×C4—611no—
187C23×C4—611no—
188#123—1224no—
189#120—24no—
190C4×D4—1224no—
191C2×C4⋊C4—611no—
192C2×C4⋊C4—612no—
193C2×C4⋊C4—612no—
194C2×C22⋊C4—612no—
195C2×C22⋊C4—612no—
196C2×C22⋊C4—611no—
197C2×C22⋊C4—611no—
198C2×C22⋊C4—611no—
199C2×C22⋊C4—612no—
200C2×C22⋊C4—612no—
201C2×C22⋊C4—612no—
202C2×C22⋊C4—1224no—
203C2×C22⋊C4C2×D6111yescharacteristic
204C2×C22⋊C4C2×D6112yes—
205C2×C42—611no—
206#95—612no—
207#95—612no—
208#95—612no—
209C24—22no—
210C24—24no—
211C24—22no—
212C24—22no—
213C24—42no—
214C24C22×D6112yes—
215C24C22×D6111yescharacteristic
216C24C22×D6111yescharacteristic
217C2×D4—22no—
218C2×D4—22no—
219C2×D4—24no—
220C2×D4—24no—
221C2×D4—42no—
222C2×D4C22⋊D6114yes—
223C22×C4—611no—
224C22×C4—611no—
225C22×C4—614no—
226C22×C4—611no—
227C22×C4—612no—
228C22×C4—611no—
229C22×C4—612no—
230C22×C4—1222no—
231C22×C4—1222no—
232C22×C4—1222no—
233C22×C4—1222no—
234C22×C4—2442no—
235C22×C4—2442no—
236C22×C4C22×D6112yes—
237C22×C4C22×D6111yescharacteristic
238C4⋊C4—1222no—
239C4⋊C4—1224no—
240C4⋊C4—2442no—
241C22⋊C4—22no—
242C22⋊C4—24no—
243C22⋊C4—1224no—
244C22⋊C4—1224no—
245C22⋊C4—1222no—
246C22⋊C4—1222no—
247C22⋊C4—1224no—
248C22⋊C4—1222no—
249C22⋊C4—1224no—
250C22⋊C4—2442no—
251C42—1222no—
252C23—22no—
253C23—22no—
254C23—28no—
255C23—22no—
256C23—21no—
257C23—22no—
258C23—21no—
259C23—22no—
260C23—22no—
261C23—22no—
262C23—22no—
263C23—22no—
264C23—22no—
265C23—48no—
266C23—48no—
267C23—44no—
268C23—44no—
269C23D4×D6112yes—
270C23#1175822414yes—
271C23#1175822412yes—
272C23C2×C22⋊D6112yes—
273C23C2×C22⋊D6112yes—
274C23C23×D6111yescharacteristic
275D4—28no—
276D4—48no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—612no—
283C2×C4—612no—
284C2×C4—1222no—
285C2×C4—1222no—
286C2×C4—1221no—
287C2×C4—1222no—
288C2×C4—1221no—
289C2×C4—1222no—
290C2×C4—1222no—
291C2×C4—1222no—
292C2×C4—1222no—
293C2×C4—1222no—
294C2×C4—1222no—
295C2×C4—1222no—
296C2×C4—2444no—
297C2×C4—2444no—
298C2×C4—2444no—
299C2×C4C2×C22⋊D6112yes—
300C22—22no—
301C22—22no—
302C22—24no—
303C22—24no—
304C22—22no—
305C22—24no—
306C22—24no—
307C22—24no—
308C22—24no—
309C22—416no—
310C22—42no—
311C22—41no—
312C22—41no—
313C22—42no—
314C22—42no—
315C22—42no—
316C22—42no—
317C22#1451974914yes—
318C22C2×D4×D6111yescharacteristic
319C22C22×C22⋊D6111yescharacteristic
320C22C2×#1175822411yescharacteristic
321C22C2×#1175822412yes—
322C22#1451982212yes—
323C4—22no—
324C4—42no—
325C4—1222no—
326C4—1222no—
327C4—2442no—
328C4—2441no—
329C4—2441no—
330C4—2442no—
331C2—24no—
332C2—44no—
333C2—42no—
334C2C2×#1451974911yescharacteristic
335C2#1684026811yescharacteristic
336C2#1684032211yescharacteristic
337C2#1684040612yes—
338C2#1684044312yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#120×C61C2
hypercenterC2×#120D61
hypocenterC61#2534
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×#14519758C2semidirect
2. C2×D4×Dic61C2semidirect
3. C22×C22⋊Dic61C2semidirect
4. #16839685C2semidirect
5. #16839676C2semidirect
6. #16839656C2semidirect
7. #16839642C2semidirect
8. #16839623C2semidirect
9. #16839620C2semidirect
10. #16839618C2semidirect
14. C23×Dic61C22semidirect
17. C2×C4⋊Dic61C22semidirect
18. C2×#11758196C22semidirect
19. C2×#11758196C22semidirect
27. C2×C22⋊Dic61C22semidirect
28. C2×C22⋊Dic61C22semidirect
29. C2×C4×Dic61C22semidirect
30. #14519684C22semidirect
31. #14519684C22semidirect
32. #14519684C22semidirect
61. C22×Dic61D4semidirect
181. C61#2534semidirect