Finite Group Databasebeta

← #21450708

Subgroups — #21450708

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×#14519745C211yesmaximal, characteristic
2C2×D4×Dic61C211yesmaximal, characteristic, complemented
3C22×#11758198C211yesmaximal, characteristic, complemented
4#16839684C212yesmaximal, complemented
5#16839677C212yesmaximal, complemented
6#16839652C212yesmaximal, complemented
7#16839639C212yesmaximal, complemented
8#16839625C211yesmaximal, characteristic, complemented
9#16839620C211yesmaximal, characteristic, complemented
10#16839617C211yesmaximal, characteristic, complemented
11C2×#123×C61C211yesmaximal, characteristic, complemented
12C24×D61C2211yescharacteristic
13C22×C22⋊D61C2212yes—
14C23×Dic61C2211yescharacteristic
15C23×Dic61C2211yescharacteristic, complemented
16#14519745—24no—
17D4×Dic61—24no—
18C2×C4⋊Dic61C2211yescharacteristic, complemented
19C2×#11758196C2212yescomplemented
20C2×C22⋊Dic61C2211yescharacteristic
21C2×C22⋊Dic61C2211yescharacteristic
22C2×C22⋊Dic61C2211yescharacteristic, complemented
23C2×#11758198—24no—
24C2×#11758198C2212yes—
25C2×#11758198C2212yes—
26C2×#11758198C2212yes—
27C2×#11758198C2212yes—
28C2×#11758198C2212yes—
29C2×C4×Dic61C2211yescharacteristic, complemented
30#14519684C2212yescomplemented
31#14519684C2212yescomplemented
32#14519684C2212yescomplemented
33C22×D4×C61C2211yescharacteristic
34C23×C4×C61C2211yescharacteristic
35#123×C61—24no—
36C2×C4⋊C4×C61C2212yescomplemented
37C2×C22⋊C4×C61C2211yescharacteristic
38C2×C22⋊C4×C61C2212yescomplemented
39C24×C61C2311yescharacteristic
40C24×C61C2311yescharacteristic
41C23×D61—22no—
42C23×D61—24no—
43C23×D61—22no—
44C23×D61—22no—
45C23×D61—42no—
46C23×D61C2312yes—
47C2×D4×C61—22no—
48C2×D4×C61—22no—
49C2×D4×C61D414yes—
50C22×C4×C61—22no—
51C22×C4×C61—22no—
52C22×C4×C61—22no—
53C22×C4×C61C2312yes—
54C22×C4×C61C2312yes—
55C22×C4×C61C2311yescharacteristic
56C2×C22⋊D61—24no—
57C2×C22⋊D61—24no—
58C2×C22⋊D61—42no—
59C22×Dic61—22no—
60C22×Dic61—42no—
61C22×Dic61—42no—
62C22×Dic61D414yescomplemented
63C22×Dic61C2311yescharacteristic
64C22×Dic61C2312yes—
65C22×Dic61C2311yescharacteristic
66C22×Dic61C2311yescharacteristic
67C22×Dic61C2311yescharacteristic
68C4⋊C4×C61—24no—
69C22⋊C4×C61—22no—
70C22⋊C4×C61—24no—
71C22⋊Dic61—22no—
72C22⋊Dic61—22no—
73C22⋊Dic61—22no—
74#11758198—24no—
75#11758198—24no—
76#11758198—24no—
77#11758198—24no—
78#11758198—42no—
79C4⋊Dic61—22no—
80#11758196—42no—
81C4×Dic61—22no—
82C23×C61—22no—
83C23×C61—22no—
84C23×C61—21no—
85C23×C61—22no—
86C23×C61—21no—
87C23×C61—22no—
88C23×C61C2×D412yes—
89C23×C61C2×D412yes—
90C23×C61C2×D412yes—
91C23×C61#4112yes—
92C23×C61C2411yescharacteristic
93C22×D61—28no—
94C22×D61—22no—
95C22×D61—22no—
96C22×D61—22no—
97C22×D61—22no—
98C22×D61—22no—
99C22×D61—22no—
100C22×D61—48no—
101C22×D61—48no—
102C22×D61—44no—
103C22×D61—44no—
104C22×D61#4114yes—
105D4×C61—28no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—22no—
109C2×C4×C61—22no—
110C2×C4×C61—22no—
111C2×C4×C61—22no—
112C2×C4×C61—22no—
113C2×C4×C61—22no—
114C2×C4×C61—44no—
115C2×C4×C61C2×D412yes—
116C22⋊D61—48no—
117C2×Dic61—22no—
118C2×Dic61—22no—
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×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—41no—
137C22×C61—41no—
138C22×C61—42no—
139C22×C61#12114yes—
140C22×C61C22×D411yescharacteristic
141C22×C61C22×D411yescharacteristic
142C22×C61C2×#4112yes—
143C22×C61C2×#4111yescharacteristic
144C22×C61H(5,𝔽2)12yes—
145C2×D61—24no—
146C2×D61—24no—
147C2×D61—24no—
148C2×D61—416no—
149C2×D61—42no—
150C2×D61—42no—
151C2×D61—42no—
152C2×D61—42no—
153C4×C61—22no—
154C4×C61—42no—
155C4×C61—42no—
156Dic61—22no—
157Dic61—22no—
158Dic61—41no—
159Dic61—41no—
160Dic61—42no—
161#2534—611nomaximal, Sylow
162C2×C61—24no—
163C2×C61—42no—
164C2×C61C2×#12111yescharacteristic
165C2×C61#52511yescharacteristic
166C2×C61#53411yescharacteristic
167C2×C61#54612yes—
168C2×C61#55112yes—
169D61—44no—
170C2×#123D6111yescharacteristic, complemented
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#380—611no—
180#379—611no—
181C61#253411yescharacteristic, complemented, Sylow
182C25—611no—
183C22×D4—612no—
184C22×D4C2×D6111yescharacteristic
185C23×C4—611no—
186C23×C4—611no—
187C23×C4C2×D6111yescharacteristic
188#123—24no—
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—611no—
196C2×C22⋊C4—611no—
197C2×C22⋊C4—612no—
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×D6112yescomplemented
205C2×C42—611no—
206#95—612no—
207#95—612no—
208#95—612no—
209C24—612no—
210C24—1224no—
211C24—1222no—
212C24—1222no—
213C24—1222no—
214C24—2442no—
215C24C22×D6111yescharacteristic
216C24C22×D6111yescharacteristic
217C2×D4—22no—
218C2×D4—22no—
219C2×D4—1224no—
220C2×D4—1224no—
221C2×D4—2442no—
222C2×D4C22⋊D6114yes—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—611no—
227C22×C4—611no—
228C22×C4—614no—
229C22×C4—612no—
230C22×C4—611no—
231C22×C4—611no—
232C22×C4—1222no—
233C22×C4—2442no—
234C22×C4—2442no—
235C22×C4C22×D6112yes—
236C22×C4C22×D6112yes—
237C22×C4C22×D6111yescharacteristic
238C4⋊C4—24no—
239C4⋊C4—1222no—
240C4⋊C4—2442no—
241C22⋊C4—22no—
242C22⋊C4—24no—
243C22⋊C4—1224no—
244C22⋊C4—1224no—
245C22⋊C4—1224no—
246C22⋊C4—1222no—
247C22⋊C4—1222no—
248C22⋊C4—1222no—
249C22⋊C4—1224no—
250C22⋊C4—2442no—
251C42—1222no—
252C23—22no—
253C23—22no—
254C23—21no—
255C23—22no—
256C23—21no—
257C23—22no—
258C23—614no—
259C23—1228no—
260C23—1222no—
261C23—1222no—
262C23—1222no—
263C23—1222no—
264C23—1222no—
265C23—1222no—
266C23—2448no—
267C23—2448no—
268C23—2444no—
269C23—2444no—
270C23D4×D6112yes—
271C23#1175822412yes—
272C23C2×C22⋊D6112yes—
273C23C2×C22⋊D6112yes—
274C23C23×D6111yescharacteristic
275D4—28no—
276D4—2448no—
277C2×C4—21no—
278C2×C4—21no—
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—612no—
288C2×C4—1222no—
289C2×C4—1222no—
290C2×C4—1221no—
291C2×C4—1221no—
292C2×C4—1222no—
293C2×C4—1222no—
294C2×C4—1222no—
295C2×C4—1222no—
296C2×C4—1222no—
297C2×C4—2444no—
298C2×C4—2444no—
299C2×C4C2×C22⋊D6112yes—
300C22—22no—
301C22—22no—
302C22—24no—
303C22—24no—
304C22—22no—
305C22—24no—
306C22—41no—
307C22—41no—
308C22—42no—
309C22—1224no—
310C22—1224no—
311C22—1224no—
312C22—24416no—
313C22—2442no—
314C22—2442no—
315C22—2442no—
316C22—2442no—
317C22#1451974914yes—
318C22C2×D4×D6111yescharacteristic
319C22C22×C22⋊D6111yescharacteristic
320C22#41×D6112yes—
321C22C2×#1175822411yescharacteristic
322C22#1451982312yes—
323C4—22no—
324C4—42no—
325C4—42no—
326C4—1222no—
327C4—1222no—
328C4—2441no—
329C4—2441no—
330C4—2442no—
331C2—24no—
332C2—42no—
333C2—2444no—
334C2C2×#1451974911yescharacteristic
335C2#1684027011yescharacteristic
336C2#1684032311yescharacteristic
337C2#1684040012yes—
338C2#1684043512yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#123×C61C2
hypercenterC2×#123D61
hypocenterC61#2534
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
2. C2×D4×Dic61C2semidirect
3. C22×#11758198C2semidirect
4. #16839684C2semidirect
5. #16839677C2semidirect
6. #16839652C2semidirect
7. #16839639C2semidirect
8. #16839625C2semidirect
9. #16839620C2semidirect
10. #16839617C2semidirect
11. C2×#123×C61C2semidirect
15. C23×Dic61C22semidirect
18. C2×C4⋊Dic61C22semidirect
19. C2×#11758196C22semidirect
22. C2×C22⋊Dic61C22semidirect
29. C2×C4×Dic61C22semidirect
30. #14519684C22semidirect
31. #14519684C22semidirect
32. #14519684C22semidirect
36. C2×C4⋊C4×C61C22semidirect
38. C2×C22⋊C4×C61C22semidirect
62. C22×Dic61D4semidirect
170. C2×#123D61semidirect
181. C61#2534semidirect
193. C2×C4⋊C4C2×D61semidirect
204. C2×C22⋊C4C2×D61semidirect