Finite Group Databasebeta

← #21456736

Subgroups — #21456736

Order 7808.

532 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 123 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
1#16840309C211yesmaximal, characteristic, complemented
2#127×D61C211yesmaximal, characteristic, complemented
3#16840137C212yesmaximal, complemented
4#16840107C212yesmaximal, complemented
5#16839958C211yesmaximal, characteristic, complemented
6#16839957C211yesmaximal, characteristic, complemented
7#16839954C211yesmaximal, characteristic, complemented
8#16839897C212yesmaximal, complemented
9#16839894C212yesmaximal, complemented
10#16839814C211yesmaximal, characteristic, complemented
11C61×#459C211yesmaximal, characteristic, complemented
12C2×#11758222—21no—
13C2×D4×D61—21no—
14C2×D4×D61—21no—
15C2×D4×D61C2212yes—
16C2×D488C2212yescomplemented
17C2×#11758199C2212yescomplemented
18C2×#11758199C2212yescomplemented
19#14519776C2211yescharacteristic, complemented
20#14519774C2211yescharacteristic
21#14519773—21no—
22#14519773—21no—
23#14519773C2212yes—
24#14519773C2211yescharacteristic, complemented
25#14519763—21no—
26#14519752C2211yescharacteristic
27#14519750—21no—
28#14519748C2211yescharacteristic
29C4×D244C2211yescharacteristic, complemented
30C4×C22⋊D61—21no—
31C42×D61C2211yescharacteristic
32C4⋊#92418C2211yescharacteristic, complemented
33#14519699C2212yescomplemented
34#14519698C2212yescomplemented
35#14519697C2212yescomplemented
36#14519689C2212yes—
37C8×Dic61C2212yescomplemented
38C2×D8×C61C2212yescomplemented
39#127×C61C2211yescharacteristic
40C4×D4×C61C2211yescharacteristic, complemented
41C4⋊C8×C61C2211yescharacteristic, complemented
42#102×C61C2212yescomplemented
43C23×D61—22no—
44C2×D4×C61—21no—
45C2×D4×C61—21no—
46C2×D4×C61C2312yes—
47C2×D4×C61C2311yescharacteristic
48C22×C4×C61—21no—
49C2×C22⋊D61—21no—
50C2×C22⋊D61—22no—
51C2×C22⋊D61—22no—
52C2×C22⋊D61—22no—
53C2×C22⋊D61—21no—
54C2×C22⋊D61—21no—
55D4×D61—42no—
56D4×D61—42no—
57D4×D61—44no—
58D4×D61—44no—
59#11758222—44no—
60C2×D244—21no—
61C2×D244—21no—
62C2×D244—21no—
63C2×D244C2312yes—
64C2×D244C2311yescharacteristic
65C2×C4×D61—21no—
66C2×C4×D61D411yescharacteristic
67C2×C4×D61D411yescharacteristic
68C2×C4×D61C2311yescharacteristic
69C2×Dic122—21no—
70D8×C61—42no—
71C2×C8×C61C2312yes—
72C4⋊C4×C61C2311yescharacteristic
73C22⋊C4×C61—21no—
74C42×C61C2311yescharacteristic
75C22⋊Dic61—21no—
76#11758199—42no—
77#11758199—42no—
78#11758198—21no—
79#11758198—21no—
80C4⋊Dic61C2311yescharacteristic
81#11758196—21no—
82C4×Dic61D411yescharacteristic
83C4×Dic61D411yescharacteristic
84C4×Dic61C2311yescharacteristic
85C2×#92418C2312yes—
86D488—42no—
87C23×C61—21no—
88C23×C61—22no—
89C22×D61—21no—
90C22×D61—22no—
91C22×D61—44no—
92C22×D61—44no—
93C22×D61—44no—
94C22×D61C2×D411yescharacteristic
95D4×C61—21no—
96D4×C61—22no—
97D4×C61—21no—
98D4×C61—22no—
99D4×C61—42no—
100D4×C61—42no—
101C2×C4×C61—21no—
102C2×C4×C61—42no—
103C2×C4×C61C2×D411yescharacteristic
104C2×C4×C61C2×D411yescharacteristic
105C2×C4×C61C2411yescharacteristic
106C22⋊D61—44no—
107C22⋊D61—42no—
108C22⋊D61—42no—
109C22⋊D61—44no—
110C22⋊D61—44no—
111C22⋊D61—42no—
112C2×Dic61—21no—
113C2×Dic61C2×D411yescharacteristic
114C2×Dic61C2×D411yescharacteristic
115C2×Dic61C2×D411yescharacteristic
116D244—21no—
117D244—22no—
118D244—21no—
119D244—22no—
120D244—42no—
121D244—42no—
122D244—42no—
123C4×D61—21no—
124C4×D61—21no—
125C4×D61—22no—
126C4×D61—42no—
127C4×D61D814yescomplemented
128Dic122—42no—
129C8×C61—22no—
130#92418—22no—
131C22×C61—42no—
132C22×C61—41no—
133C22×C61—41no—
134C22×C61—42no—
135C22×C61—42no—
136C22×C61—41no—
137C22×C61C22×D411yescharacteristic
138C2×D61—21no—
139C2×D61—21no—
140C2×D61—42no—
141C2×D61—41no—
142C2×D61—41no—
143C2×D61—42no—
144C2×D61—42no—
145C2×D61—41no—
146C2×D61—88no—
147C2×D61C2×D812yes—
148C4×C61—21no—
149C4×C61—41no—
150C4×C61C2×D812yes—
151C4×C61H(5,𝔽2)11yescharacteristic
152C4×C61H(5,𝔽2)11yescharacteristic
153Dic61—21no—
154Dic61—41no—
155Dic61C2×D812yes—
156Dic61AGL(1,ℤ/8)12yes—
157#3205—611nomaximal, Sylow
158C2×C61—82no—
159C2×C61—81no—
160C2×C61#53511yescharacteristic
161C2×C61C22×D811yescharacteristic
162C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
163D61—22no—
164D61—81no—
165D61—82no—
166#532—611no—
167C2×#127—611no—
168#493—612no—
169#486—612no—
170#459—611no—
171#459—611no—
172#459—611no—
173#459D6111yescharacteristic, complemented
174#447—612no—
175#447—612no—
176#431—611no—
177C61#320511yescharacteristic, complemented, Sylow
178C2×#41—1221no—
179C22×D4—612no—
180C22×D4—1221no—
181C22×D4—1221no—
182C2×D8—612no—
183C2×D8—612no—
184C2×D8—612no—
185C2×D8C2×D6112yescomplemented
186C4⋊Q8—611no—
187#127—612no—
188#127—611no—
189#127—611no—
190#127—1221no—
191#127—1221no—
192#127C2×D6111yescharacteristic
193#124—1221no—
194#121—611no—
195#121—611no—
196#121—1221no—
197C4×D4—611no—
198C4×D4—1221no—
199C4×D4C2×D6111yescharacteristic, complemented
200C2×C42—611no—
201C4⋊C8—611no—
202C4⋊C8C2×D6111yescharacteristic, complemented
203#102—612no—
204#102—612no—
205#102—612no—
206#102C2×D6112yescomplemented
207C22⋊C8—612no—
208C4×C8—612no—
209C24—1222no—
210#41—2444no—
211C2×Q8—1221no—
212C2×D4—21no—
213C2×D4—21no—
214C2×D4—612no—
215C2×D4—611no—
216C2×D4—1221no—
217C2×D4—1221no—
218C2×D4—1221no—
219C2×D4—1222no—
220C2×D4—1222no—
221C2×D4—1222no—
222C2×D4—1221no—
223C2×D4—1221no—
224C2×D4—1221no—
225C2×D4—2444no—
226C2×D4—2442no—
227C2×D4—2442no—
228C2×D4—2444no—
229C2×D4C22×D6112yes—
230C2×D4C22×D6111yescharacteristic
231C22×C4—21no—
232C22×C4—611no—
233C22×C4—611no—
234C22×C4—611no—
235C22×C4—1221no—
236D8—42no—
237D8—2442no—
238D8—2442no—
239D8—2442no—
240C2×C8—612no—
241C2×C8C22×D6112yes—
242C4⋊C4—611no—
243C4⋊C4—1221no—
244C4⋊C4C22×D6111yescharacteristic
245C22⋊C4—21no—
246C22⋊C4—1221no—
247C22⋊C4—1221no—
248C22⋊C4—1221no—
249C42—611no—
250C42—611no—
251C42—611no—
252C42C22×D6111yescharacteristic
253C23—21no—
254C23—22no—
255C23—611no—
256C23—1221no—
257C23—1222no—
258C23—2444no—
259C23—2444no—
260C23—2444no—
261Q8—2442no—
262D4—21no—
263D4—22no—
264D4—21no—
265D4—22no—
266D4—42no—
267D4—42no—
268D4—1221no—
269D4—1222no—
270D4—1221no—
271D4—1222no—
272D4—2442no—
273D4—2442no—
274D4—2442no—
275D4—2444no—
276D4—2444no—
277D4—2442no—
278D4—2444no—
279D4—2442no—
280D4—2442no—
281C2×C4—21no—
282C2×C4—42no—
283C2×C4—611no—
284C2×C4—611no—
285C2×C4—614no—
286C2×C4—611no—
287C2×C4—1222no—
288C2×C4—1221no—
289C2×C4—1221no—
290C2×C4—1221no—
291C2×C4—2442no—
292C2×C4D4×D6111yescharacteristic
293C2×C4D4×D6111yescharacteristic
294C2×C4C23×D6111yescharacteristic
295C8—22no—
296C8—1222no—
297C22—41no—
298C22—42no—
299C22—42no—
300C22—41no—
301C22—42no—
302C22—41no—
303C22—612no—
304C22—1221no—
305C22—1221no—
306C22—4888no—
307C22—2441no—
308C22—2442no—
309C22—2442no—
310C22—2441no—
311C22—2442no—
312C22—2441no—
313C22C2×D4×D6111yescharacteristic
314C4—21no—
315C4—41no—
316C4—612no—
317C4—612no—
318C4—1221no—
319C4—2441no—
320C4D8×D6112yes—
321C4#1451982211yescharacteristic
322C4#1451982311yescharacteristic
323C2—82no—
324C2—81no—
325C2—1222no—
326C2—4882no—
327C2—4881no—
328C2#1684032811yescharacteristic
329C2C2×D8×D6111yescharacteristic
330C2AGL(1,ℤ/8)×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#459C2
socleC22×C61C22×D4
hypercenter#459D61
hypocenterC61#3205
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #16840309C2semidirect
2. #127×D61C2semidirect
3. #16840137C2semidirect
4. #16840107C2semidirect
5. #16839958C2semidirect
6. #16839957C2semidirect
7. #16839954C2semidirect
8. #16839897C2semidirect
9. #16839894C2semidirect
10. #16839814C2semidirect
11. C61×#459C2semidirect
16. C2×D488C22semidirect
17. C2×#11758199C22semidirect
18. C2×#11758199C22semidirect
19. #14519776C22semidirect
24. #14519773C22semidirect
29. C4×D244C22semidirect
32. C4⋊#92418C22semidirect
33. #14519699C22semidirect
34. #14519698C22semidirect
35. #14519697C22semidirect
37. C8×Dic61C22semidirect
38. C2×D8×C61C22semidirect
40. C4×D4×C61C22semidirect
41. C4⋊C8×C61C22semidirect
42. #102×C61C22semidirect
127. C4×D61D8semidirect
173. #459D61semidirect
177. C61#3205semidirect
185. C2×D8C2×D61semidirect
199. C4×D4C2×D61semidirect
202. C4⋊C8C2×D61semidirect
206. #102C2×D61semidirect