Finite Group Databasebeta

← #23767673

Subgroups — #23767673

Order 10112.

672 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 145 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×#14579117C211yesmaximal, characteristic, complemented
2C22×(C2×D79)⋊C4C211yesmaximal, characteristic
3#19098498C212yesmaximal, complemented
4#19098492C212yesmaximal, complemented
5#19098453C212yesmaximal, complemented
6#19098452C212yesmaximal, complemented
7#19098436C211yesmaximal, characteristic, complemented
8#19098424C211yesmaximal, characteristic, complemented
9#19098418C211yesmaximal, characteristic
10#19098418C211yesmaximal, characteristic
11#385×C79C211yesmaximal, characteristic, complemented
12C24×D79C2211yescharacteristic
13C23×Dic79C2211yescharacteristic
14#14579117—24no—
15C2×Dic79⋊C4C2211yescharacteristic, complemented
16C2×Dic79⋊C4C2211yescharacteristic, complemented
17C2×Dic79⋊C4C2212yescomplemented
18C2×C22⋊Dic79C2211yescharacteristic
19C2×C22⋊Dic79C2211yescharacteristic
20C2×(C2×D79)⋊C4—24no—
21C2×(C2×D79)⋊C4C2212yes—
22C2×(C2×D79)⋊C4C2212yes—
23C2×(C2×D79)⋊C4C2212yes—
24C2×(C2×D79)⋊C4C2212yes—
25C2×(C2×D79)⋊C4C2212yes—
26C2×(C2×D79)⋊C4C2212yes—
27C2×C4×Dic79C2211yescharacteristic, complemented
28C2×C4×Dic79C2211yescharacteristic, complemented
29C79⋊#95C2212yescomplemented
30C79⋊#95C2212yescomplemented
31C79⋊#95C2212yescomplemented
32C23×C4×C79C2211yescharacteristic
33C2×C4⋊C4×C79C2212yescomplemented
34C2×C22⋊C4×C79C2211yescharacteristic
35C2×C22⋊C4×C79C2211yescharacteristic
36#95×C79C2212yescomplemented
37C23×D79—22no—
38C23×D79—24no—
39C23×D79—22no—
40C23×D79—22no—
41C23×D79—42no—
42C23×D79C2312yes—
43C22×Dic79—22no—
44C22×Dic79—22no—
45C22×Dic79D414yes—
46C22×Dic79C2312yes—
47C22×Dic79C2311yescharacteristic
48C22×Dic79C2311yescharacteristic
49C22×Dic79C2311yescharacteristic
50C22×Dic79C2311yescharacteristic
51Dic79⋊C4—22no—
52Dic79⋊C4—22no—
53Dic79⋊C4—42no—
54C22⋊Dic79—22no—
55C22⋊Dic79—22no—
56(C2×D79)⋊C4—24no—
57(C2×D79)⋊C4—24no—
58(C2×D79)⋊C4—24no—
59(C2×D79)⋊C4—24no—
60(C2×D79)⋊C4—42no—
61(C2×D79)⋊C4—42no—
62C4×Dic79—22no—
63C4×Dic79—22no—
64C24×C79C2311yescharacteristic
65C22×C4×C79—22no—
66C22×C4×C79—42no—
67C22×C4×C79C2311yescharacteristic
68C22×C4×C79C2312yes—
69C22×C4×C79C2312yes—
70C22×C4×C79C2311yescharacteristic
71C4⋊C4×C79—42no—
72C22⋊C4×C79—22no—
73C22⋊C4×C79—22no—
74C23×C79—22no—
75C23×C79—22no—
76C23×C79C2×D412yes—
77C23×C79#4112yes—
78C23×C79#4112yes—
79C23×C79C2411yescharacteristic
80C22×D79—28no—
81C22×D79—22no—
82C22×D79—22no—
83C22×D79—22no—
84C22×D79—22no—
85C22×D79—22no—
86C22×D79—22no—
87C22×D79—48no—
88C22×D79—48no—
89C22×D79—44no—
90C22×D79—44no—
91C22×D79#4114yes—
92C2×C4×C79—21no—
93C2×C4×C79—21no—
94C2×C4×C79—22no—
95C2×C4×C79—22no—
96C2×C4×C79—22no—
97C2×C4×C79—22no—
98C2×C4×C79—22no—
99C2×C4×C79—22no—
100C2×C4×C79—22no—
101C2×C4×C79—22no—
102C2×C4×C79—44no—
103C2×Dic79—28no—
104C2×Dic79—21no—
105C2×Dic79—21no—
106C2×Dic79—21no—
107C2×Dic79—21no—
108C2×Dic79—21no—
109C2×Dic79—21no—
110C2×Dic79—22no—
111C2×Dic79—22no—
112C2×Dic79—22no—
113C2×Dic79—22no—
114C2×Dic79—22no—
115C2×Dic79C2×D412yes—
116C2×Dic79C2×D412yes—
117C22×C79—22no—
118C22×C79—22no—
119C22×C79—24no—
120C22×C79—24no—
121C22×C79#12314yes—
122C22×C79C22×D411yescharacteristic
123C22×C79C2×#4112yes—
124C22×C79C2×#4111yescharacteristic
125C22×C79C2×#4111yescharacteristic
126C22×C79H(5,𝔽2)12yes—
127C2×D79—24no—
128C2×D79—24no—
129C2×D79—24no—
130C2×D79—416no—
131C2×D79—42no—
132C2×D79—42no—
133C2×D79—42no—
134C2×D79—42no—
135C4×C79—41no—
136C4×C79—41no—
137C4×C79—42no—
138C4×C79—42no—
139Dic79—22no—
140Dic79—22no—
141Dic79—41no—
142Dic79—41no—
143Dic79—42no—
144C2×C79—24no—
145C2×C79C2×#12311yescharacteristic
146C2×C79#52511yescharacteristic
147C2×C79#53511yescharacteristic
148C2×C79#55112yes—
149C2×C79#55112yes—
150D79—44no—
151#2482—791nomaximal, Sylow
152C79#248211yescharacteristic, complemented, Sylow
153C2×#117—791no—
154C22×C22⋊C4—791no—
155#399—792no—
156#397—792no—
157#388—792no—
158#388—792no—
159#385—791no—
160#385D7911yescharacteristic, complemented
161#381—791no—
162#379—791no—
163#379—791no—
164C25—791no—
165C23×C4—791no—
166C23×C4C2×D7911yescharacteristic
167#117—1584no—
168C2×C4⋊C4—792no—
169C2×C4⋊C4—791no—
170C2×C4⋊C4—791no—
171C2×C4⋊C4C2×D7912yescomplemented
172C2×C22⋊C4—792no—
173C2×C22⋊C4—792no—
174C2×C22⋊C4—791no—
175C2×C22⋊C4—791no—
176C2×C22⋊C4—792no—
177C2×C22⋊C4—792no—
178C2×C22⋊C4—792no—
179C2×C22⋊C4—792no—
180C2×C22⋊C4—1584no—
181C2×C22⋊C4C2×D7911yescharacteristic
182C2×C22⋊C4C2×D7911yescharacteristic
183C2×C42—791no—
184C2×C42—791no—
185#95—792no—
186#95—792no—
187#95—792no—
188#95C2×D7912yescomplemented
189C24—3162no—
190C24—792no—
191C24—1584no—
192C24—1582no—
193C24—1582no—
194C24—1582no—
195C24C22×D7911yescharacteristic
196C22×C4—22no—
197C22×C4—42no—
198C22×C4—794no—
199C22×C4—791no—
200C22×C4—791no—
201C22×C4—792no—
202C22×C4—791no—
203C22×C4—791no—
204C22×C4—1582no—
205C22×C4—1582no—
206C22×C4C22×D7912yes—
207C22×C4C22×D7912yes—
208C22×C4C22×D7911yescharacteristic
209C22×C4C22×D7911yescharacteristic
210C4⋊C4—42no—
211C4⋊C4—3162no—
212C4⋊C4—1582no—
213C4⋊C4—1582no—
214C22⋊C4—22no—
215C22⋊C4—22no—
216C22⋊C4—3162no—
217C22⋊C4—3162no—
218C22⋊C4—1584no—
219C22⋊C4—1584no—
220C22⋊C4—1584no—
221C22⋊C4—1584no—
222C22⋊C4—1582no—
223C22⋊C4—1582no—
224C42—1582no—
225C42—1582no—
226C23—22no—
227C23—22no—
228C23—3164no—
229C23—3168no—
230C23—3168no—
231C23—3164no—
232C23—794no—
233C23—1588no—
234C23—1582no—
235C23—1582no—
236C23—1582no—
237C23—1582no—
238C23—1582no—
239C23—1582no—
240C23D4×D7912yes—
241C23#1192962412yes—
242C23#1192962512yes—
243C23C23×D7911yescharacteristic
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—22no—
254C2×C4—44no—
255C2×C4—792no—
256C2×C4—792no—
257C2×C4—1582no—
258C2×C4—1582no—
259C2×C4—1582no—
260C2×C4—1582no—
261C2×C4—1582no—
262C2×C4—1581no—
263C2×C4—1581no—
264C2×C4—1581no—
265C2×C4—1581no—
266C2×C4—1581no—
267C2×C4—1581no—
268C2×C4—1588no—
269C22—24no—
270C22—24no—
271C22—22no—
272C22—22no—
273C22—31616no—
274C22—3162no—
275C22—3162no—
276C22—3162no—
277C22—3162no—
278C22—1584no—
279C22—1584no—
280C22—1584no—
281C22#1457914614yes—
282C22C2×D4×D7911yescharacteristic
283C22#41×D7912yes—
284C22C2×#1192962411yescharacteristic
285C22C2×#1192962511yescharacteristic
286C22#1457920612yes—
287C4—42no—
288C4—41no—
289C4—42no—
290C4—41no—
291C4—3162no—
292C4—3161no—
293C4—3161no—
294C4—1582no—
295C4—1582no—
296C2—24no—
297C2—3164no—
298C2C2×#1457914611yescharacteristic
299C2#1909907111yescharacteristic
300C2#1909912811yescharacteristic
301C2#1909924012yes—
302C2#1909924212yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#385×C79C2
prime radicalC24×D79C22
hypercenter#385D79
hypocenterC79#2482
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×#14579117C2semidirect
3. #19098498C2semidirect
4. #19098492C2semidirect
5. #19098453C2semidirect
6. #19098452C2semidirect
7. #19098436C2semidirect
8. #19098424C2semidirect
11. #385×C79C2semidirect
15. C2×Dic79⋊C4C22semidirect
16. C2×Dic79⋊C4C22semidirect
17. C2×Dic79⋊C4C22semidirect
27. C2×C4×Dic79C22semidirect
28. C2×C4×Dic79C22semidirect
29. C79⋊#95C22semidirect
30. C79⋊#95C22semidirect
31. C79⋊#95C22semidirect
33. C2×C4⋊C4×C79C22semidirect
36. #95×C79C22semidirect
152. C79#2482semidirect
160. #385D79semidirect
171. C2×C4⋊C4C2×D79semidirect
188. #95C2×D79semidirect