Finite Group Databasebeta

← #21456623

Subgroups — #21456623

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
1C2×#14519753C211yesmaximal, characteristic, complemented
2#121×D61C211yesmaximal, characteristic
3#16840096C212yesmaximal, complemented
4#16840076C211yesmaximal, characteristic, complemented
5#16840073C211yesmaximal, characteristic, complemented
6#16840011C212yesmaximal, complemented
7#16840005C212yesmaximal, complemented
8#16839911C212yesmaximal, complemented
9#16839901C211yesmaximal, characteristic, complemented
10#16839724C211yesmaximal, characteristic, complemented
11C61×#448C211yesmaximal, characteristic, complemented
12C2×D4×D61—21no—
13C2×D4×D61C2211yescharacteristic
14C22×C4×D61C2211yescharacteristic
15C2×#11758201C2212yescomplemented
16C2×#11758189C2212yescomplemented
17#14519753—21no—
18#14519753—21no—
19#14519753C2212yes—
20#14519753C2212yescomplemented
21#14519752C2211yescharacteristic
22#14519751C2211yescharacteristic
23#14519750—21no—
24#14519749—21no—
25#14519748C2211yescharacteristic
26C2×C4⋊Dic61C2211yescharacteristic, complemented
27C2×#11758196—21no—
28C4⋊C4×D61C2211yescharacteristic
29C2×#11758198—21no—
30C22⋊C4×D61—21no—
31#14519711C2212yescomplemented
32#14519710C2212yescomplemented
33#14519701C2212yescomplemented
34#14519699C2212yescomplemented
35#14519698C2212yescomplemented
36C22⋊#92418C2211yescharacteristic, complemented
37#14519689C2212yes—
38C22×Q8×C61C2211yescharacteristic, complemented
39C2×SD16×C61C2212yescomplemented
40#121×C61C2211yescharacteristic
41#103×C61C2212yescomplemented
42C22⋊C8×C61C2211yescharacteristic, complemented
43C23×D61—21no—
44C23×D61D411yescharacteristic
45C2×Q8×C61—21no—
46C2×Q8×C61—42no—
47C2×Q8×C61C2312yes—
48C2×D4×C61—21no—
49C2×D4×C61C2311yescharacteristic
50C22×C4×C61—21no—
51C22×C4×C61C2311yescharacteristic
52C2×C22⋊D61—21no—
53C2×C22⋊D61—21no—
54C2×C22⋊D61—21no—
55C22×Dic61—21no—
56C22×Dic61D411yescharacteristic
57D4×D61—42no—
58D4×D61—44no—
59C2×D244—21no—
60C2×D244C2311yescharacteristic
61C2×C4×D61—21no—
62C2×C4×D61—42no—
63C2×C4×D61D411yescharacteristic
64C2×C4×D61D411yescharacteristic
65C2×C4×D61C2311yescharacteristic
66C2×C4×D61C2311yescharacteristic
67SD16×C61—42no—
68C2×C8×C61C2312yes—
69C4⋊C4×C61C2311yescharacteristic
70C22⋊C4×C61—21no—
71C22⋊Dic61—21no—
72#11758201—42no—
73#11758198—22no—
74#11758198—22no—
75#11758198—21no—
76#11758198—21no—
77C4⋊Dic61—21no—
78C4⋊Dic61C2312yes—
79C4⋊Dic61C2311yescharacteristic
80#11758196—21no—
81#11758196—22no—
82#11758196—22no—
83C2×#92418C2312yes—
84#11758189—42no—
85C23×C61—21no—
86C23×C61C2×D411yescharacteristic
87C22×D61—22no—
88C22×D61—22no—
89C22×D61—21no—
90C22×D61—41no—
91C22×D61—42no—
92C22×D61—42no—
93C22×D61—42no—
94C22×D61C2×D411yescharacteristic
95C22×D61C2×D411yescharacteristic
96Q8×C61—22no—
97Q8×C61—22no—
98Q8×C61—42no—
99D4×C61—22no—
100D4×C61—42no—
101C2×C4×C61—22no—
102C2×C4×C61—22no—
103C2×C4×C61—21no—
104C2×C4×C61—42no—
105C2×C4×C61C2×D411yescharacteristic
106C2×C4×C61C2411yescharacteristic
107C22⋊D61—42no—
108C22⋊D61—42no—
109C22⋊D61—42no—
110C2×Dic61—22no—
111C2×Dic61—21no—
112C2×Dic61—41no—
113C2×Dic61—42no—
114C2×Dic61C2×D411yescharacteristic
115C2×Dic61C2×D411yescharacteristic
116D244—22no—
117D244—42no—
118C4×D61—22no—
119C4×D61—22no—
120C4×D61—41no—
121C4×D61—41no—
122C4×D61—42no—
123C8×C61—22no—
124#92418—22no—
125C22×C61—21no—
126C22×C61—21no—
127C22×C61—41no—
128C22×C61—41no—
129C22×C61—41no—
130C22×C61AGL(1,ℤ/8)12yes—
131C22×C61C22×D411yescharacteristic
132C2×D61—21no—
133C2×D61—21no—
134C2×D61—21no—
135C2×D61—21no—
136C2×D61—21no—
137C2×D61—44no—
138C2×D61—41no—
139C2×D61—41no—
140C2×D61—41no—
141C2×D61—84no—
142C2×D61#13712yes—
143C4×C61—21no—
144C4×C61—42no—
145C4×C61—41no—
146C4×C61H(5,𝔽2)12yes—
147Dic61—21no—
148Dic61—21no—
149Dic61—41no—
150Dic61—42no—
151#3193—611nomaximal, Sylow
152C2×C61—22no—
153C2×C61—81no—
154C2×C61#53411yescharacteristic
155C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
156C2×C61C2×#13711yescharacteristic
157D61—22no—
158D61—41no—
159D61—81no—
160C2×C22⋊Q8—611no—
161C2×#121—611no—
162#484—612no—
163#480—611no—
164#480—611no—
165#468—612no—
166#468—612no—
167#450—612no—
168#448—611no—
169#448D6111yescharacteristic, complemented
170#407—611no—
171C61#319311yescharacteristic, complemented, Sylow
172C22×Q8C2×D6111yescharacteristic, complemented
173C22×D4—611no—
174C22×D4—1221no—
175C23×C4—611no—
176C2×SD16—612no—
177C2×SD16C2×D6112yescomplemented
178C2×M16—612no—
179C22⋊Q8—612no—
180C22⋊Q8—612no—
181C22⋊Q8—1221no—
182C22⋊Q8—1221no—
183#121—611no—
184#121—611no—
185#121—611no—
186#121—1221no—
187#121—1221no—
188#121C2×D6111yescharacteristic
189C2×C4⋊C4—611no—
190C2×C4⋊C4—611no—
191C2×C4⋊C4—1221no—
192C2×C22⋊C4—1221no—
193C2×C22⋊C4—1221no—
194#107—612no—
195#107—612no—
196#103—612no—
197#103C2×D6112yescomplemented
198#102—612no—
199#102—612no—
200C22⋊C8—611no—
201C22⋊C8—612no—
202C22⋊C8C2×D6111yescharacteristic, complemented
203C24—611no—
204C24—1221no—
205C2×Q8—21no—
206C2×Q8—42no—
207C2×Q8C22×D6112yes—
208C2×D4—21no—
209C2×D4—611no—
210C2×D4—1221no—
211C2×D4—1221no—
212C2×D4—1221no—
213C2×D4—1221no—
214C2×D4—2442no—
215C2×D4—2444no—
216C2×D4C22×D6111yescharacteristic
217C22×C4—21no—
218C22×C4—611no—
219C22×C4—611no—
220C22×C4—611no—
221C22×C4—611no—
222C22×C4—611no—
223C22×C4—1221no—
224C22×C4—1221no—
225C22×C4—2442no—
226C22×C4C22×D6111yescharacteristic
227SD16—42no—
228SD16—2442no—
229M16—2442no—
230C2×C8—612no—
231C2×C8C22×D6112yes—
232C4⋊C4—612no—
233C4⋊C4—611no—
234C4⋊C4—1221no—
235C4⋊C4—1222no—
236C4⋊C4—1222no—
237C4⋊C4—1221no—
238C4⋊C4C22×D6111yescharacteristic
239C22⋊C4—21no—
240C22⋊C4—1221no—
241C22⋊C4—1222no—
242C22⋊C4—1222no—
243C22⋊C4—1221no—
244C22⋊C4—1221no—
245C23—21no—
246C23—611no—
247C23—611no—
248C23—1222no—
249C23—1222no—
250C23—1221no—
251C23—2441no—
252C23—2442no—
253C23—2442no—
254C23—2442no—
255C23D4×D6111yescharacteristic
256Q8—22no—
257Q8—22no—
258Q8—42no—
259D4—22no—
260D4—42no—
261D4—1222no—
262D4—2442no—
263D4—2442no—
264D4—2442no—
265D4—2442no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—22no—
269C2×C4—42no—
270C2×C4—611no—
271C2×C4—611no—
272C2×C4—1222no—
273C2×C4—1222no—
274C2×C4—1222no—
275C2×C4—1221no—
276C2×C4—2441no—
277C2×C4—2441no—
278C2×C4—2442no—
279C2×C4—2441no—
280C2×C4—2442no—
281C2×C4D4×D6111yescharacteristic
282C2×C4C23×D6111yescharacteristic
283C8—22no—
284C8—1222no—
285C22—21no—
286C22—21no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—612no—
291C22—1221no—
292C22—1221no—
293C22—1221no—
294C22—1221no—
295C22—1221no—
296C22—4884no—
297C22—2444no—
298C22—2441no—
299C22—2441no—
300C22—2441no—
301C22#1451980412yes—
302C22C2×D4×D6111yescharacteristic
303C4—21no—
304C4—41no—
305C4—42no—
306C4—1221no—
307C4—1221no—
308C4—2442no—
309C4—2441no—
310C4#1451982212yes—
311C2—22no—
312C2—81no—
313C2—1222no—
314C2—4881no—
315C2—2441no—
316C2#1684032211yescharacteristic
317C2C2×#1451980411yescharacteristic
318C2#137×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#448C2
socleC22×C61C22×D4
hypercenter#448D61
hypocenterC61#3193
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. C2×#14519753C2semidirect
3. #16840096C2semidirect
4. #16840076C2semidirect
5. #16840073C2semidirect
6. #16840011C2semidirect
7. #16840005C2semidirect
8. #16839911C2semidirect
9. #16839901C2semidirect
10. #16839724C2semidirect
11. C61×#448C2semidirect
15. C2×#11758201C22semidirect
16. C2×#11758189C22semidirect
20. #14519753C22semidirect
26. C2×C4⋊Dic61C22semidirect
31. #14519711C22semidirect
32. #14519710C22semidirect
33. #14519701C22semidirect
34. #14519699C22semidirect
35. #14519698C22semidirect
36. C22⋊#92418C22semidirect
38. C22×Q8×C61C22semidirect
39. C2×SD16×C61C22semidirect
41. #103×C61C22semidirect
42. C22⋊C8×C61C22semidirect
169. #448D61semidirect
171. C61#3193semidirect
172. C22×Q8C2×D61semidirect
177. C2×SD16C2×D61semidirect
197. #103C2×D61semidirect
202. C22⋊C8C2×D61semidirect