Finite Group Databasebeta

← #21456624

Subgroups — #21456624

Order 7808.

462 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 115 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
1C22⋊Q8×D61C211yesmaximal, characteristic, complemented
2C2×#14519752C211yesmaximal, characteristic
3#16840097C211yesmaximal, characteristic, complemented
4#16840077C212yesmaximal, complemented
5#16840011C212yesmaximal, complemented
6#16840009C212yesmaximal, complemented
7#16839915C211yesmaximal, characteristic, complemented
8#16839912C211yesmaximal, characteristic, complemented
9#16839902C212yesmaximal, complemented
10#16839724C211yesmaximal, characteristic, complemented
11C61×#484C211yesmaximal, characteristic, complemented
12C2×Q8×D61C2211yescharacteristic, complemented
13C22×D244—21no—
14C22×D244C2211yescharacteristic
15C22×C4×D61C2211yescharacteristic
16C2×#11758190C2212yescomplemented
17C2×#11758201C2212yescomplemented
18C2×#11758189C2212yescomplemented
19#14519757C2211yescharacteristic, complemented
20#14519756C2211yescharacteristic
21#14519755—21no—
22#14519754—21no—
23#14519753C2211yescharacteristic, complemented
24#14519752—21no—
25#14519752—21no—
26#14519752C2212yes—
27#14519752C2212yes—
28C4⋊C4×D61—21no—
29C4⋊C4×D61C2211yescharacteristic, complemented
30C2×#11758198—21no—
31C22⋊C4×D61—21no—
32#14519710C2212yescomplemented
33#14519700C2212yescomplemented
34#14519699C2212yescomplemented
35#14519697C2212yescomplemented
36C22⋊#92418C2211yescharacteristic
37#14519689C2212yescomplemented
38C22⋊Q8×C61C2211yescharacteristic
39C2×C4⋊C4×C61C2211yescharacteristic
40#107×C61C2212yescomplemented
41#103×C61C2212yescomplemented
42C22⋊C8×C61C2211yescharacteristic
43C23×D61—21no—
44C23×D61D411yescharacteristic
45C2×Q8×C61C2311yescharacteristic
46C22×C4×C61—21no—
47C22×C4×C61C2311yescharacteristic
48C22×Dic61D411yescharacteristic
49Q8×D61—42no—
50C2×D244—22no—
51C2×D244—22no—
52C2×D244—21no—
53C2×D244—42no—
54C2×D244—44no—
55C2×D244C2312yes—
56C2×C4×D61—21no—
57C2×C4×D61—21no—
58C2×C4×D61—42no—
59C2×C4×D61D411yescharacteristic
60C2×C4×D61D411yescharacteristic
61C2×C4×D61C2311yescharacteristic
62C2×C4×D61C2311yescharacteristic
63C2×Dic122—21no—
64C2×Dic122C2311yescharacteristic
65C2×C8×C61C2312yes—
66C4⋊C4×C61—21no—
67C4⋊C4×C61—21no—
68C4⋊C4×C61C2312yes—
69C4⋊C4×C61C2311yescharacteristic
70C22⋊C4×C61—21no—
71C22⋊Dic61—21no—
72#11758201—42no—
73#11758198—21no—
74#11758198—21no—
75#11758198—22no—
76#11758198—22no—
77C4⋊Dic61—21no—
78C4⋊Dic61C2311yescharacteristic
79#11758196—21no—
80#11758196—21no—
81#11758196—21no—
82C2×#92418C2312yes—
83#11758190—42no—
84#11758189—42no—
85C23×C61C2×D411yescharacteristic
86C22×D61—22no—
87C22×D61—22no—
88C22×D61—22no—
89C22×D61—41no—
90C22×D61—42no—
91C22×D61—42no—
92C22×D61—42no—
93C22×D61C2×D411yescharacteristic
94C22×D61C2×D411yescharacteristic
95Q8×C61—22no—
96C2×C4×C61—22no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—22no—
100C2×C4×C61—42no—
101C2×C4×C61C2×D411yescharacteristic
102C2×C4×C61C2411yescharacteristic
103C2×Dic61—21no—
104C2×Dic61—21no—
105C2×Dic61—41no—
106C2×Dic61C2×D411yescharacteristic
107C2×Dic61C2×D411yescharacteristic
108D244—22no—
109D244—22no—
110D244—42no—
111D244—44no—
112D244—44no—
113C4×D61—22no—
114C4×D61—22no—
115C4×D61—41no—
116C4×D61—41no—
117C4×D61—42no—
118C4×D61—42no—
119Dic122—22no—
120Dic122—42no—
121C8×C61—22no—
122#92418—22no—
123C22×C61—21no—
124C22×C61—21no—
125C22×C61#13712yes—
126C22×C61C22×D411yescharacteristic
127C2×D61—21no—
128C2×D61—21no—
129C2×D61—21no—
130C2×D61—21no—
131C2×D61—21no—
132C2×D61—44no—
133C2×D61—42no—
134C2×D61—42no—
135C2×D61—42no—
136C2×D61—84no—
137C2×D61AGL(1,ℤ/8)12yes—
138C4×C61—21no—
139C4×C61—41no—
140C4×C61—41no—
141C4×C61—42no—
142C4×C61H(5,𝔽2)12yes—
143Dic61—21no—
144Dic61—21no—
145Dic61—41no—
146Dic61—41no—
147#3193—611nomaximal, Sylow
148C2×C61—22no—
149C2×C61#53411yescharacteristic
150C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
151C2×C61C2×#13711yescharacteristic
152D61—22no—
153D61—41no—
154D61—82no—
155C2×C22⋊Q8—611no—
156C2×#121—611no—
157#484—611no—
158#484D6111yescharacteristic, complemented
159#480—612no—
160#468—612no—
161#468—612no—
162#450—611no—
163#450—611no—
164#448—612no—
165#407—611no—
166C61#319311yescharacteristic, complemented, Sylow
167C22×Q8—611no—
168C22×D4—611no—
169C22×D4—1221no—
170C23×C4—611no—
171C2×SD16—612no—
172C2×SD16—612no—
173C2×M16—612no—
174C22⋊Q8—611no—
175C22⋊Q8—611no—
176C22⋊Q8—611no—
177C22⋊Q8—1221no—
178C22⋊Q8—1221no—
179C22⋊Q8C2×D6111yescharacteristic
180#121—612no—
181#121—612no—
182#121—1221no—
183#121—1221no—
184C2×C4⋊C4—611no—
185C2×C4⋊C4—1221no—
186C2×C4⋊C4C2×D6111yescharacteristic
187C2×C22⋊C4—1221no—
188C2×C22⋊C4—1221no—
189#107—612no—
190#107C2×D6112yescomplemented
191#103—612no—
192#103C2×D6112yescomplemented
193#102—612no—
194#102—612no—
195C22⋊C8—611no—
196C22⋊C8—612no—
197C22⋊C8C2×D6111yescharacteristic
198C24—611no—
199C24—1221no—
200C2×Q8—611no—
201C2×Q8—1221no—
202C2×Q8—2442no—
203C2×Q8C22×D6111yescharacteristic
204C2×D4—612no—
205C2×D4—1222no—
206C2×D4—1222no—
207C2×D4—1221no—
208C2×D4—2442no—
209C2×D4—2444no—
210C22×C4—21no—
211C22×C4—611no—
212C22×C4—611no—
213C22×C4—611no—
214C22×C4—611no—
215C22×C4—611no—
216C22×C4—1221no—
217C22×C4—1221no—
218C22×C4—2442no—
219C22×C4C22×D6111yescharacteristic
220SD16—2442no—
221SD16—2442no—
222M16—2442no—
223C2×C8—612no—
224C2×C8C22×D6112yes—
225C4⋊C4—21no—
226C4⋊C4—21no—
227C4⋊C4—611no—
228C4⋊C4—1221no—
229C4⋊C4—1221no—
230C4⋊C4—1221no—
231C4⋊C4—1221no—
232C4⋊C4C22×D6111yescharacteristic
233C4⋊C4C22×D6112yes—
234C22⋊C4—21no—
235C22⋊C4—1222no—
236C22⋊C4—1222no—
237C22⋊C4—1221no—
238C22⋊C4—1221no—
239C22⋊C4—1221no—
240C23—611no—
241C23—611no—
242C23—1222no—
243C23—1222no—
244C23—1222no—
245C23—2441no—
246C23—2442no—
247C23—2442no—
248C23—2442no—
249C23D4×D6111yescharacteristic
250Q8—22no—
251Q8—1222no—
252Q8—2442no—
253D4—1222no—
254D4—1222no—
255D4—2442no—
256D4—2444no—
257D4—2444no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—42no—
263C2×C4—611no—
264C2×C4—611no—
265C2×C4—1222no—
266C2×C4—1222no—
267C2×C4—1221no—
268C2×C4—1221no—
269C2×C4—2441no—
270C2×C4—2441no—
271C2×C4—2442no—
272C2×C4—2442no—
273C2×C4—2441no—
274C2×C4D4×D6111yescharacteristic
275C2×C4C23×D6111yescharacteristic
276C8—22no—
277C8—1222no—
278C22—21no—
279C22—21no—
280C22—612no—
281C22—1221no—
282C22—1221no—
283C22—1221no—
284C22—1221no—
285C22—1221no—
286C22—4884no—
287C22—2444no—
288C22—2442no—
289C22—2442no—
290C22—2442no—
291C22#1451980912yes—
292C22C2×D4×D6111yescharacteristic
293C4—21no—
294C4—42no—
295C4—41no—
296C4—41no—
297C4—1221no—
298C4—1221no—
299C4—2441no—
300C4—2441no—
301C4#1451982312yes—
302C2—22no—
303C2—1222no—
304C2—4882no—
305C2—2441no—
306C2#1684032311yescharacteristic
307C2AGL(1,ℤ/8)×D6111yescharacteristic
308C2C2×#1451980911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#484C2
socleC22×C61C22×D4
hypercenter#484D61
hypocenterC61#3193
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
1. C22⋊Q8×D61C2semidirect
3. #16840097C2semidirect
4. #16840077C2semidirect
5. #16840011C2semidirect
6. #16840009C2semidirect
7. #16839915C2semidirect
8. #16839912C2semidirect
9. #16839902C2semidirect
10. #16839724C2semidirect
11. C61×#484C2semidirect
12. C2×Q8×D61C22semidirect
16. C2×#11758190C22semidirect
17. C2×#11758201C22semidirect
18. C2×#11758189C22semidirect
19. #14519757C22semidirect
23. #14519753C22semidirect
29. C4⋊C4×D61C22semidirect
32. #14519710C22semidirect
33. #14519700C22semidirect
34. #14519699C22semidirect
35. #14519697C22semidirect
37. #14519689C22semidirect
40. #107×C61C22semidirect
41. #103×C61C22semidirect
158. #484D61semidirect
166. C61#3193semidirect
190. #107C2×D61semidirect
192. #103C2×D61semidirect