Finite Group Databasebeta

← #23768552

Subgroups — #23768552

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×#14579141C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D79C211yesmaximal, characteristic
3#19098489C211yesmaximal, characteristic, complemented
4#19098476C211yesmaximal, characteristic, complemented
5#19098475C211yesmaximal, characteristic, complemented
6#19098456C212yesmaximal, complemented
7#19098455C212yesmaximal, complemented
8#19098425C212yesmaximal, complemented
9#19098418C212yesmaximal
10#19098410C211yesmaximal, characteristic, complemented
11#397×C79C211yesmaximal, characteristic, complemented
12C24×D79C2211yescharacteristic
13C22×Dic158C2211yescharacteristic, complemented
14C22×C4×D79C2211yescharacteristic
15C22×C4×D79C2211yescharacteristic
16#14579141—24no—
17C2×C4⋊Dic79C2212yescomplemented
18C2×C22⋊Dic79C2211yescharacteristic
19C2×C22⋊Dic79C2212yes—
20C2×(C2×D79)⋊C4C2212yes—
21C2×(C2×D79)⋊C4C2212yes—
22C2×(C2×D79)⋊C4C2212yes—
23C2×(C2×D79)⋊C4C2211yescharacteristic
24C2×(C2×D79)⋊C4C2211yescharacteristic
25C2×(C2×D79)⋊C4C2212yes—
26C22⋊C4×D79—24no—
27C2×C4×Dic79C2212yescomplemented
28C79⋊#95C2211yescharacteristic, complemented
29C79⋊#95C2212yescomplemented
30C79⋊#95C2212yescomplemented
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
44C2×Dic158—22no—
45C2×Dic158—42no—
46C22×Dic79C2312yes—
47C22×Dic79C2311yescharacteristic
48C22×Dic79C2312yes—
49C22×Dic79C2311yescharacteristic
50C2×C4×D79—22no—
51C2×C4×D79—24no—
52C2×C4×D79—42no—
53C2×C4×D79D414yes—
54C4⋊Dic79—24no—
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—42no—
64C24×C79C2311yescharacteristic
65C22×C4×C79C2311yescharacteristic
66C22×C4×C79C2312yes—
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—21no—
105C2×Dic79—22no—
106C2×Dic79—22no—
107C2×Dic79—22no—
108C2×Dic79—22no—
109C2×Dic79—22no—
110C2×Dic79—22no—
111C2×Dic79—22no—
112C2×Dic79C2×D412yes—
113C4×D79—44no—
114C4×D79—44no—
115Dic158—44no—
116C22×C79—22no—
117C22×C79—24no—
118C22×C79—41no—
119C22×C79—41no—
120C22×C79—42no—
121C22×C79C22×D411yescharacteristic
122C22×C79C2×#4111yescharacteristic
123C22×C79C2×#4112yes—
124C22×C79C2×#4111yescharacteristic
125C22×C79H(5,𝔽2)12yes—
126C2×D79—22no—
127C2×D79—22no—
128C2×D79—24no—
129C2×D79—24no—
130C2×D79—22no—
131C2×D79—24no—
132C2×D79—416no—
133C2×D79—41no—
134C2×D79—41no—
135C2×D79—42no—
136C2×D79#12414yes—
137C4×C79—22no—
138C4×C79—42no—
139C4×C79—41no—
140C4×C79—42no—
141Dic79—22no—
142Dic79—41no—
143Dic79—42no—
144Dic79—42no—
145C2×C79—42no—
146C2×C79#52511yescharacteristic
147C2×C79C2×#12411yescharacteristic
148C2×C79#53411yescharacteristic
149C2×C79#55112yes—
150C2×C79#55112yes—
151D79—24no—
152D79—42no—
153#2561—791nomaximal, Sylow
154C79#256111yescharacteristic, complemented, Sylow
155C2×C22⋊Q8—791no—
156C22×C22⋊C4—791no—
157#397—791no—
158#397D7911yescharacteristic, complemented
159#393—791no—
160#393—791no—
161#388—792no—
162#388—792no—
163#381—792no—
164#379—792no—
165C4×C22⋊C4—791no—
166C25—791no—
167C22×Q8—791no—
168C23×C4—791no—
169C23×C4—791no—
170C22⋊Q8—1584no—
171C2×C4⋊C4—792no—
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—791no—
186#95—792no—
187#95—792no—
188#95—792no—
189#95C2×D7911yescharacteristic, complemented
190#95C2×D7912yescomplemented
191C24—3162no—
192C24—791no—
193C24—791no—
194C24—1584no—
195C24—1582no—
196C24—1582no—
197C24—1582no—
198C24C22×D7911yescharacteristic
199C2×Q8—3162no—
200C2×Q8—1582no—
201C22×C4—3162no—
202C22×C4—794no—
203C22×C4—791no—
204C22×C4—791no—
205C22×C4—792no—
206C22×C4—792no—
207C22×C4—1582no—
208C22×C4—1584no—
209C22×C4C22×D7911yescharacteristic
210C22×C4C22×D7912yes—
211C22×C4C22×D7912yes—
212C22×C4C22×D7911yescharacteristic
213C4⋊C4—22no—
214C4⋊C4—1584no—
215C22⋊C4—24no—
216C22⋊C4—22no—
217C22⋊C4—3162no—
218C22⋊C4—3162no—
219C22⋊C4—1582no—
220C22⋊C4—1584no—
221C22⋊C4—1584no—
222C22⋊C4—1584no—
223C22⋊C4—1582no—
224C22⋊C4—1582no—
225C42—3162no—
226C23—22no—
227C23—21no—
228C23—22no—
229C23—21no—
230C23—3168no—
231C23—3164no—
232C23—3164no—
233C23—3168no—
234C23—794no—
235C23—792no—
236C23—792no—
237C23—1588no—
238C23—1582no—
239C23—1581no—
240C23—1582no—
241C23—1581no—
242C23—1581no—
243C23—1581no—
244C23—1582no—
245C23#1192962312yes—
246C23C23×D7911yescharacteristic
247Q8—3164no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—3164no—
258C2×C4—3164no—
259C2×C4—792no—
260C2×C4—1582no—
261C2×C4—1582no—
262C2×C4—1582no—
263C2×C4—1582no—
264C2×C4—1582no—
265C2×C4—1582no—
266C2×C4—1581no—
267C2×C4—1582no—
268C2×C4—1582no—
269C2×C4D4×D7912yes—
270C22—24no—
271C22—22no—
272C22—42no—
273C22—41no—
274C22—41no—
275C22—31616no—
276C22—3162no—
277C22—3161no—
278C22—3161no—
279C22—794no—
280C22—1584no—
281C22—1582no—
282C22—1584no—
283C22—1584no—
284C22—1582no—
285C22—1582no—
286C22C2×D4×D7911yescharacteristic
287C22#41×D7912yes—
288C22#41×D7911yescharacteristic
289C22C2×#1192962311yescharacteristic
290C22#1457920712yes—
291C4—22no—
292C4—42no—
293C4—42no—
294C4—41no—
295C4—3162no—
296C4—3161no—
297C4—3162no—
298C4—1582no—
299C2—42no—
300C2—3162no—
301C2—1584no—
302C2#1909907311yescharacteristic
303C2#124×D7911yescharacteristic
304C2#1909912411yescharacteristic
305C2#1909923612yes—
306C2#1909923812yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#397×C79C2
prime radicalC24×D79C22
hypercenter#397D79
hypocenterC79#2561
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#14579141C2semidirect
3. #19098489C2semidirect
4. #19098476C2semidirect
5. #19098475C2semidirect
6. #19098456C2semidirect
7. #19098455C2semidirect
8. #19098425C2semidirect
10. #19098410C2semidirect
11. #397×C79C2semidirect
13. C22×Dic158C22semidirect
17. C2×C4⋊Dic79C22semidirect
27. C2×C4×Dic79C22semidirect
28. C79⋊#95C22semidirect
29. C79⋊#95C22semidirect
30. C79⋊#95C22semidirect
31. C79⋊#95C22semidirect
32. C2×C4⋊C4×C79C22semidirect
35. #95×C79C22semidirect
36. #95×C79C22semidirect
154. C79#2561semidirect
158. #397D79semidirect
172. C2×C4⋊C4C2×D79semidirect
189. #95C2×D79semidirect
190. #95C2×D79semidirect