Finite Group Databasebeta

← #23767669

Subgroups — #23767669

Order 10112.

672 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 672 conjugacy classes of subgroups — too many to draw. Only its 139 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×#14579119C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D79C211yesmaximal, characteristic
3#19098500C211yesmaximal, characteristic, complemented
4#19098499C211yesmaximal, characteristic, complemented
5#19098489C211yesmaximal, characteristic, complemented
6#19098456C212yesmaximal, complemented
7#19098452C212yesmaximal, complemented
8#19098437C212yesmaximal, complemented
9#19098425C211yesmaximal, characteristic, complemented
10#19098418C212yesmaximal
11#397×C79C211yesmaximal, characteristic, complemented
12C24×D79C2211yescharacteristic
13C22×C4×D79C2211yescharacteristic
14C22×C4×D79C2211yescharacteristic
15#14579119—24no—
16C2×C4⋊Dic79C2211yescharacteristic, complemented
17C2×C4⋊Dic79C2212yescomplemented
18C2×Dic79⋊C4C2212yescomplemented
19C2×C22⋊Dic79C2211yescharacteristic
20C2×C22⋊Dic79C2212yes—
21C2×(C2×D79)⋊C4C2212yes—
22C2×(C2×D79)⋊C4C2212yes—
23C2×(C2×D79)⋊C4C2212yes—
24C2×(C2×D79)⋊C4C2211yescharacteristic
25C2×(C2×D79)⋊C4C2211yescharacteristic
26C2×(C2×D79)⋊C4C2212yes—
27C22⋊C4×D79—24no—
28C2×C4×Dic79C2212yescomplemented
29C79⋊#95C2212yescomplemented
30C79⋊#95C2211yescharacteristic, complemented
31C79⋊#95C2212yescomplemented
32C2×C4⋊C4×C79C2211yescharacteristic, complemented
33C2×C22⋊C4×C79C2212yes—
34C2×C22⋊C4×C79C2211yescharacteristic
35#95×C79C2211yescharacteristic, complemented
36#95×C79C2212yescomplemented
37C23×D79—22no—
38C23×D79—22no—
39C23×D79—22no—
40C23×D79—24no—
41C23×D79—42no—
42C23×D79C2311yescharacteristic
43C23×D79C2311yescharacteristic
44C22×Dic79C2312yes—
45C22×Dic79C2311yescharacteristic
46C22×Dic79C2312yes—
47C22×Dic79C2311yescharacteristic
48C2×C4×D79—22no—
49C2×C4×D79—24no—
50C2×C4×D79—42no—
51C2×C4×D79D414yes—
52C4⋊Dic79—22no—
53C4⋊Dic79—42no—
54Dic79⋊C4—42no—
55C22⋊Dic79—22no—
56C22⋊Dic79—42no—
57(C2×D79)⋊C4—22no—
58(C2×D79)⋊C4—24no—
59(C2×D79)⋊C4—24no—
60(C2×D79)⋊C4—24no—
61(C2×D79)⋊C4—22no—
62(C2×D79)⋊C4—42no—
63C4×Dic79—24no—
64C24×C79C2311yescharacteristic
65C22×C4×C79C2312yes—
66C22×C4×C79C2311yescharacteristic
67C22×C4×C79C2312yes—
68C22×C4×C79C2311yescharacteristic
69C4⋊C4×C79—22no—
70C22⋊C4×C79—24no—
71C22⋊C4×C79—22no—
72C23×C79—21no—
73C23×C79—21no—
74C23×C79—22no—
75C23×C79—22no—
76C23×C79#4112yes—
77C23×C79C2411yescharacteristic
78C22×D79—21no—
79C22×D79—21no—
80C22×D79—22no—
81C22×D79—28no—
82C22×D79—21no—
83C22×D79—22no—
84C22×D79—21no—
85C22×D79—22no—
86C22×D79—48no—
87C22×D79—48no—
88C22×D79—44no—
89C22×D79—44no—
90C22×D79C2×D412yes—
91C22×D79#4112yes—
92C22×D79#4114yes—
93C2×C4×C79—22no—
94C2×C4×C79—22no—
95C2×C4×C79—21no—
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×C79C2×D412yes—
103C2×Dic79—22no—
104C2×Dic79—22no—
105C2×Dic79—21no—
106C2×Dic79—22no—
107C2×Dic79—22no—
108C2×Dic79—22no—
109C2×Dic79—22no—
110C2×Dic79—22no—
111C2×Dic79—22no—
112C2×Dic79C2×D412yes—
113C4×D79—28no—
114C4×D79—44no—
115C22×C79—22no—
116C22×C79—24no—
117C22×C79—41no—
118C22×C79—41no—
119C22×C79—42no—
120C22×C79C22×D411yescharacteristic
121C22×C79C2×#4112yes—
122C22×C79C2×#4111yescharacteristic
123C22×C79C2×#4111yescharacteristic
124C22×C79H(5,𝔽2)12yes—
125C2×D79—22no—
126C2×D79—22no—
127C2×D79—24no—
128C2×D79—24no—
129C2×D79—22no—
130C2×D79—24no—
131C2×D79—416no—
132C2×D79—41no—
133C2×D79—41no—
134C2×D79—42no—
135C2×D79#12314yes—
136C4×C79—22no—
137C4×C79—42no—
138C4×C79—41no—
139C4×C79—42no—
140Dic79—22no—
141Dic79—41no—
142Dic79—42no—
143Dic79—42no—
144C2×C79—42no—
145C2×C79C2×#12311yescharacteristic
146C2×C79#52511yescharacteristic
147C2×C79#53511yescharacteristic
148C2×C79#55112yes—
149C2×C79#55112yes—
150D79—24no—
151D79—42no—
152#2482—791nomaximal, Sylow
153C79#248211yescharacteristic, complemented, Sylow
154C2×#117—791no—
155C22×C22⋊C4—791no—
156#399—791no—
157#399—791no—
158#397—791no—
159#397D7911yescharacteristic, complemented
160#388—792no—
161#388—792no—
162#385—792no—
163#381—791no—
164#379—792no—
165C25—791no—
166C23×C4—791no—
167C23×C4—791no—
168#117—1584no—
169C2×C4⋊C4—792no—
170C2×C4⋊C4—792no—
171C2×C4⋊C4—791no—
172C2×C4⋊C4C2×D7911yescharacteristic, complemented
173C2×C22⋊C4—792no—
174C2×C22⋊C4—792no—
175C2×C22⋊C4—791no—
176C2×C22⋊C4—791no—
177C2×C22⋊C4—791no—
178C2×C22⋊C4—792no—
179C2×C22⋊C4—792no—
180C2×C22⋊C4—792no—
181C2×C22⋊C4—1584no—
182C2×C22⋊C4C2×D7911yescharacteristic
183C2×C22⋊C4C2×D7912yes—
184C2×C42—792no—
185#95—792no—
186#95—791no—
187#95—792no—
188#95C2×D7911yescharacteristic, complemented
189#95C2×D7912yescomplemented
190C24—3162no—
191C24—791no—
192C24—791no—
193C24—1584no—
194C24—1582no—
195C24—1582no—
196C24—1582no—
197C24C22×D7911yescharacteristic
198C22×C4—3162no—
199C22×C4—791no—
200C22×C4—794no—
201C22×C4—792no—
202C22×C4—791no—
203C22×C4—792no—
204C22×C4—1582no—
205C22×C4—1584no—
206C22×C4C22×D7912yes—
207C22×C4C22×D7912yes—
208C22×C4C22×D7911yescharacteristic
209C22×C4C22×D7911yescharacteristic
210C4⋊C4—22no—
211C4⋊C4—3162no—
212C4⋊C4—3162no—
213C4⋊C4—1582no—
214C22⋊C4—24no—
215C22⋊C4—22no—
216C22⋊C4—3162no—
217C22⋊C4—3162no—
218C22⋊C4—1582no—
219C22⋊C4—1584no—
220C22⋊C4—1584no—
221C22⋊C4—1584no—
222C22⋊C4—1582no—
223C22⋊C4—1582no—
224C42—1584no—
225C23—22no—
226C23—21no—
227C23—22no—
228C23—21no—
229C23—3168no—
230C23—3164no—
231C23—3164no—
232C23—3168no—
233C23—794no—
234C23—792no—
235C23—792no—
236C23—1588no—
237C23—1582no—
238C23—1581no—
239C23—1582no—
240C23—1581no—
241C23—1581no—
242C23—1581no—
243C23—1582no—
244C23#1192962312yes—
245C23C23×D7911yescharacteristic
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—3164no—
256C2×C4—792no—
257C2×C4—1588no—
258C2×C4—1582no—
259C2×C4—1582no—
260C2×C4—1582no—
261C2×C4—1582no—
262C2×C4—1582no—
263C2×C4—1582no—
264C2×C4—1582no—
265C2×C4—1581no—
266C2×C4—1582no—
267C2×C4D4×D7912yes—
268C22—24no—
269C22—22no—
270C22—42no—
271C22—41no—
272C22—41no—
273C22—31616no—
274C22—3162no—
275C22—3161no—
276C22—3161no—
277C22—794no—
278C22—1584no—
279C22—1582no—
280C22—1584no—
281C22—1584no—
282C22—1582no—
283C22—1582no—
284C22C2×D4×D7911yescharacteristic
285C22#41×D7912yes—
286C22#41×D7911yescharacteristic
287C22C2×#1192962311yescharacteristic
288C22#1457920712yes—
289C4—22no—
290C4—42no—
291C4—42no—
292C4—41no—
293C4—3162no—
294C4—3161no—
295C4—3162no—
296C4—1582no—
297C2—42no—
298C2—3162no—
299C2—1584no—
300C2#123×D7911yescharacteristic
301C2#1909907311yescharacteristic
302C2#1909913111yescharacteristic
303C2#1909923612yes—
304C2#1909923812yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#397×C79C2
prime radicalC24×D79C22
hypercenter#397D79
hypocenterC79#2482
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#14579119C2semidirect
3. #19098500C2semidirect
4. #19098499C2semidirect
5. #19098489C2semidirect
6. #19098456C2semidirect
7. #19098452C2semidirect
8. #19098437C2semidirect
9. #19098425C2semidirect
11. #397×C79C2semidirect
16. C2×C4⋊Dic79C22semidirect
17. C2×C4⋊Dic79C22semidirect
18. C2×Dic79⋊C4C22semidirect
28. C2×C4×Dic79C22semidirect
29. C79⋊#95C22semidirect
30. C79⋊#95C22semidirect
31. C79⋊#95C22semidirect
32. C2×C4⋊C4×C79C22semidirect
35. #95×C79C22semidirect
36. #95×C79C22semidirect
153. C79#2482semidirect
159. #397D79semidirect
172. C2×C4⋊C4C2×D79semidirect
188. #95C2×D79semidirect
189. #95C2×D79semidirect