Finite Group Databasebeta

← #21457503

Subgroups — #21457503

Order 7808.

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

normal subgroups only

This group has 526 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
1C2×#14519800C211yesmaximal, characteristic, complemented
2C2×D8×D61C211yesmaximal, characteristic, complemented
3#16840405C212yesmaximal, complemented
4#16840000C211yesmaximal, characteristic, complemented
5#16839995C211yesmaximal, characteristic, complemented
6#16839974C212yesmaximal, complemented
7#16839911C212yesmaximal, complemented
8#16839906C212yesmaximal, complemented
9C4×D488C211yesmaximal, characteristic, complemented
10C8×D244C211yesmaximal, characteristic, complemented
11C61×#495C211yesmaximal, characteristic, complemented
12C2×#11758226C2212yescomplemented
13C2×D4×D61C2212yes—
14#14519800—24no—
15C2×#11758201C2212yescomplemented
16C2×D488C2211yescharacteristic
17C2×#11758199C2212yes—
18D8×D61—24no—
19C2×C8×D61C2211yescharacteristic
20C2×C8×D61C2211yescharacteristic, complemented
21#14519759—22no—
22#14519753C2212yes—
23#14519750—22no—
24#14519748C2212yescomplemented
25#14519747—22no—
26C4×D244C2211yescharacteristic
27C4×D244C2212yescomplemented
28C22⋊C4×D61—22no—
29#14519711C2211yescharacteristic, complemented
30C4⋊#92418C2211yescharacteristic, complemented
31#14519701C2212yescomplemented
32#14519699C2212yescomplemented
33#14519698C2212yescomplemented
34#14519689C2211yescharacteristic
35#14519689C2211yescharacteristic, complemented
36C2×Q16×C61C2211yescharacteristic, complemented
37C2×SD16×C61C2212yescomplemented
38C2×D8×C61C2211yescharacteristic
39#124×C61C2212yescomplemented
40C4×C8×C61C2211yescharacteristic, complemented
41C23×D61—22no—
42C2×Q8×C61C2312yes—
43C2×D4×C61C2312yes—
44C2×C22⋊D61—22no—
45C2×C22⋊D61—22no—
46#11758226—24no—
47#11758226—42no—
48D4×D61—24no—
49D4×D61—42no—
50C2×D244—22no—
51C2×D244D411yescharacteristic
52C2×D244C2312yes—
53C2×C4×D61—22no—
54C2×C4×D61—22no—
55C2×C4×D61C2311yescharacteristic
56C2×C4×D61C2311yescharacteristic
57Q16×C61—22no—
58SD16×C61—42no—
59D8×C61—22no—
60C2×C8×C61C2311yescharacteristic
61C2×C8×C61C2311yescharacteristic
62C22⋊C4×C61—22no—
63C22⋊C4×C61—22no—
64C42×C61C2311yescharacteristic
65C22⋊Dic61—22no—
66#11758201—24no—
67#11758199—24no—
68#11758198—22no—
69#11758198—22no—
70#11758198D411yescharacteristic
71#11758198D411yescharacteristic
72C4⋊Dic61D411yescharacteristic
73C4⋊Dic61C2312yes—
74#11758196—22no—
75C2×#92418C2311yescharacteristic
76C2×#92418C2311yescharacteristic
77D488D414yescomplemented
78C8×D61—22no—
79C8×D61—22no—
80C23×C61—22no—
81C22×D61—22no—
82C22×D61—44no—
83C22×D61—44no—
84C22×D61—82no—
85C22×D61C2×D411yescharacteristic
86C22×D61C2×D411yescharacteristic
87Q8×C61—22no—
88Q8×C61—22no—
89D4×C61—22no—
90D4×C61—22no—
91C2×C4×C61—22no—
92C2×C4×C61C2×D411yescharacteristic
93C2×C4×C61C2×D411yescharacteristic
94C2×C4×C61C2411yescharacteristic
95C22⋊D61—44no—
96C22⋊D61—82no—
97C2×Dic61—22no—
98C2×Dic61C2×D411yescharacteristic
99C2×Dic61C2×D411yescharacteristic
100D244—22no—
101D244—22no—
102D244—44no—
103D244C2×D414yes—
104C4×D61—21no—
105C4×D61—21no—
106C4×D61—21no—
107C4×D61—21no—
108C4×D61—44no—
109C4×D61—82no—
110C8×C61—21no—
111C8×C61C2×D412yes—
112#92418—21no—
113#92418—21no—
114C22×C61—42no—
115C22×C61—42no—
116C22×C61—42no—
117C22×C61C22×D411yescharacteristic
118C2×D61—21no—
119C2×D61—21no—
120C2×D61—21no—
121C2×D61—24no—
122C2×D61—21no—
123C2×D61—21no—
124C2×D61—42no—
125C2×D61—42no—
126C2×D61—88no—
127C2×D61#13512yescomplemented
128C4×C61—21no—
129C4×C61—21no—
130C4×C61—42no—
131C4×C61C22×D411yescharacteristic
132C4×C61H(5,𝔽2)11yescharacteristic
133Dic61—21no—
134Dic61—21no—
135Dic61—42no—
136#3280—611nomaximal, Sylow
137C2×C61—82no—
138C2×C61D4211yescharacteristic
139C2×C61C2×#13511yescharacteristic
140C2×C61#57611yescharacteristic
141D61—22no—
142D61—41no—
143D61—44no—
144C2×#135—611no—
145C22×D8—611no—
146#546—612no—
147#495D6111yescharacteristic, complemented
148#467—611no—
149#466—611no—
150#463—612no—
151#450—612no—
152#449—612no—
153C4×D8—611no—
154C8×D4—611no—
155C61#328011yescharacteristic, complemented, Sylow
156C2×#41—612no—
157C22×D4—612no—
158#135—1224no—
159C2×Q16C2×D6111yescharacteristic, complemented
160C2×SD16—612no—
161C2×SD16C2×D6112yescomplemented
162C2×D8—612no—
163C2×D8—611no—
164C2×D8—1224no—
165C2×D8C2×D6111yescharacteristic
166C22×C8—611no—
167C22×C8—611no—
168#124C2×D6112yescomplemented
169#123—1222no—
170C22⋊Q8—612no—
171#121—612no—
172#121—1222no—
173#120—1222no—
174C4×D4—611no—
175C4×D4—612no—
176C2×C22⋊C4—1222no—
177#107—611no—
178C4⋊C8—611no—
179#103—612no—
180#102—612no—
181#102—612no—
182C22⋊C8—611no—
183C22⋊C8—611no—
184C4×C8C2×D6111yescharacteristic, complemented
185C24—1222no—
186#41—1224no—
187#41—2442no—
188C2×Q8C22×D6112yes—
189C2×D4—611no—
190C2×D4—612no—
191C2×D4—1222no—
192C2×D4—1222no—
193C2×D4—1224no—
194C2×D4—1222no—
195C2×D4—2442no—
196C2×D4C22×D6112yes—
197C22×C4—611no—
198C22×C4—611no—
199C22×C4—1222no—
200C22×C4—1222no—
201Q16—22no—
202SD16—42no—
203SD16—1224no—
204D8—22no—
205D8—614no—
206D8—1224no—
207C2×C8—611no—
208C2×C8—611no—
209C2×C8—1222no—
210C2×C8—1222no—
211C2×C8C22×D6111yescharacteristic
212C2×C8C22×D6111yescharacteristic
213C4⋊C4—611no—
214C4⋊C4—612no—
215C4⋊C4—1222no—
216C22⋊C4—22no—
217C22⋊C4—22no—
218C22⋊C4—611no—
219C22⋊C4—611no—
220C22⋊C4—1222no—
221C22⋊C4—1222no—
222C22⋊C4—1222no—
223C42C22×D6111yescharacteristic
224C23—22no—
225C23—611no—
226C23—611no—
227C23—1222no—
228C23—4882no—
229C23—2444no—
230C23—2444no—
231Q8—22no—
232Q8—22no—
233D4—22no—
234D4—22no—
235D4—614no—
236D4—1222no—
237D4—1222no—
238D4—4882no—
239D4—2444no—
240D4—2444no—
241C2×C4—22no—
242C2×C4—611no—
243C2×C4—611no—
244C2×C4—1221no—
245C2×C4—1221no—
246C2×C4—1221no—
247C2×C4—1221no—
248C2×C4—1222no—
249C2×C4—4882no—
250C2×C4—2444no—
251C2×C4D4×D6111yescharacteristic
252C2×C4D4×D6111yescharacteristic
253C2×C4C23×D6111yescharacteristic
254C8—21no—
255C8—1221no—
256C8—1221no—
257C8D4×D6112yes—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—612no—
262C22—1221no—
263C22—1221no—
264C22—1221no—
265C22—1221no—
266C22—1221no—
267C22—1224no—
268C22—4888no—
269C22—2442no—
270C22—2442no—
271C22C2×D4×D6111yescharacteristic
272C4—21no—
273C4—21no—
274C4—42no—
275C4—1221no—
276C4—1221no—
277C4—2442no—
278C4C2×D4×D6111yescharacteristic
279C4#1451982211yescharacteristic
280C2—82no—
281C2—1222no—
282C2—2441no—
283C2—2444no—
284C2#1684039711yescharacteristic
285C2#135×D6111yescharacteristic
286C2#1684056411yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#495C2
socleC22×C61C22×D4
hypercenter#495D61
hypocenterC61#3280
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C2×#14519800C2semidirect
2. C2×D8×D61C2semidirect
3. #16840405C2semidirect
4. #16840000C2semidirect
5. #16839995C2semidirect
6. #16839974C2semidirect
7. #16839911C2semidirect
8. #16839906C2semidirect
9. C4×D488C2semidirect
10. C8×D244C2semidirect
11. C61×#495C2semidirect
12. C2×#11758226C22semidirect
15. C2×#11758201C22semidirect
20. C2×C8×D61C22semidirect
24. #14519748C22semidirect
27. C4×D244C22semidirect
29. #14519711C22semidirect
30. C4⋊#92418C22semidirect
31. #14519701C22semidirect
32. #14519699C22semidirect
33. #14519698C22semidirect
35. #14519689C22semidirect
36. C2×Q16×C61C22semidirect
37. C2×SD16×C61C22semidirect
39. #124×C61C22semidirect
40. C4×C8×C61C22semidirect
77. D488D4semidirect
127. C2×D61#135semidirect
147. #495D61semidirect
155. C61#3280semidirect
159. C2×Q16C2×D61semidirect
161. C2×SD16C2×D61semidirect
168. #124C2×D61semidirect
184. C4×C8C2×D61semidirect