Finite Group Databasebeta

← #23769962

Subgroups — #23769962

Order 10112.

680 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 680 conjugacy classes of subgroups — too many to draw. Only its 137 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×#14579142C211yesmaximal, characteristic, complemented
2C2×#14579129C211yesmaximal, characteristic
3#19098488C212yesmaximal, complemented
4#19098485C212yesmaximal, complemented
5#19098479C212yesmaximal, complemented
6#19098454C212yesmaximal, complemented
7#19098440C212yesmaximal, complemented
8#19098418C212yesmaximal, complemented
9#390×C79C211yesmaximal, characteristic, complemented
10C24×D79C2211yescharacteristic
11C22×C22⋊D79C2212yes—
12C23×Dic79C2211yescharacteristic, complemented
13#14579142—24no—
14#14579129—24no—
15C2×C4⋊Dic79C2212yescomplemented
16C2×Dic79⋊C4C2212yescomplemented
17C2×C22⋊Dic79C2212yes—
18C2×C22⋊Dic79C2211yescharacteristic
19C2×C22⋊Dic79C2211yescharacteristic, complemented
20C2×(C2×D79)⋊C4C2212yes—
21C2×(C2×D79)⋊C4C2212yes—
22C2×(C2×D79)⋊C4C2212yes—
23C2×(C2×D79)⋊C4C2212yes—
24C2×(C2×D79)⋊C4C2212yes—
25C79⋊#95C2212yescomplemented
26C79⋊#95C2212yescomplemented
27C79⋊#95C2212yescomplemented
28C22×D4×C79C2211yescharacteristic
29C2×C4⋊C4×C79C2211yescharacteristic, complemented
30C2×C22⋊C4×C79C2212yes—
31C2×C22⋊C4×C79C2212yescomplemented
32C2×C42×C79C2211yescharacteristic, complemented
33C23×D79—22no—
34C23×D79—24no—
35C23×D79—41no—
36C23×D79—41no—
37C23×D79—42no—
38C23×D79C2312yes—
39C2×C22⋊D79—24no—
40C2×C22⋊D79—24no—
41C2×C22⋊D79—42no—
42C22×Dic79—22no—
43C22×Dic79—41no—
44C22×Dic79—41no—
45C22×Dic79C2312yes—
46C22×Dic79C2312yes—
47C22×Dic79C2312yes—
48C4⋊Dic79—42no—
49Dic79⋊C4—24no—
50C22⋊Dic79—22no—
51C22⋊Dic79—24no—
52C22⋊Dic79—22no—
53(C2×D79)⋊C4—24no—
54(C2×D79)⋊C4—24no—
55(C2×D79)⋊C4—42no—
56(C2×D79)⋊C4—42no—
57(C2×D79)⋊C4—42no—
58C24×C79C2311yescharacteristic
59C24×C79C2311yescharacteristic
60C2×D4×C79—41no—
61C2×D4×C79—41no—
62C2×D4×C79D414yes—
63C22×C4×C79C2312yes—
64C22×C4×C79C2312yes—
65C22×C4×C79C2311yescharacteristic
66C4⋊C4×C79—41no—
67C22⋊C4×C79—42no—
68C22⋊C4×C79—42no—
69C42×C79—41no—
70C23×C79—22no—
71C23×C79—22no—
72C23×C79—21no—
73C23×C79—21no—
74C23×C79—22no—
75C23×C79—22no—
76C23×C79—21no—
77C23×C79—21no—
78C23×C79C2×D412yes—
79C23×C79C2×D412yes—
80C23×C79C2411yescharacteristic
81C22×D79—22no—
82C22×D79—22no—
83C22×D79—22no—
84C22×D79—22no—
85C22×D79—22no—
86C22×D79—22no—
87C22×D79—44no—
88C22×D79—48no—
89C22×D79—48no—
90C22×D79—44no—
91C22×D79—44no—
92C22×D79#4114yes—
93D4×C79—44no—
94C2×C4×C79—21no—
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—
103C22⋊D79—48no—
104C2×Dic79—22no—
105C2×Dic79—22no—
106C2×Dic79—22no—
107C2×Dic79—22no—
108C2×Dic79—22no—
109C2×Dic79—22no—
110C2×Dic79—22no—
111C2×Dic79—22no—
112C2×Dic79—22no—
113C2×Dic79—44no—
114C22×C79—22no—
115C22×C79—22no—
116C22×C79—24no—
117C22×C79—24no—
118C22×C79—42no—
119C22×C79—42no—
120C22×C79—41no—
121C22×C79—41no—
122C22×C79—41no—
123C22×C79—41no—
124C22×C79C22×D411yescharacteristic
125C22×C79C2×#4112yes—
126C22×C79H(5,𝔽2)11yescharacteristic
127C22×C79H(5,𝔽2)11yescharacteristic
128C22×C79H(5,𝔽2)12yes—
129C2×D79—24no—
130C2×D79—24no—
131C2×D79—24no—
132C2×D79—416no—
133C2×D79—42no—
134C2×D79—42no—
135C2×D79—42no—
136C2×D79—42no—
137C4×C79—22no—
138C4×C79—42no—
139C4×C79—42no—
140Dic79—42no—
141Dic79—42no—
142Dic79—42no—
143C2×C79—42no—
144C2×C79—42no—
145C2×C79#53411yescharacteristic
146C2×C79#53812yes—
147C2×C79#54612yes—
148C2×C79#55111yescharacteristic
149C2×C79#56011yescharacteristic
150D79—44no—
151#2697—791nomaximal, Sylow
152C79#269711yescharacteristic, complemented, Sylow
153C2×#123—791no—
154C2×#120—791no—
155#397—792no—
156#396—792no—
157#394—792no—
158#390D7911yescharacteristic, complemented
159#388—792no—
160#386—792no—
161#379—792no—
162C25—791no—
163C22×D4—792no—
164C22×D4C2×D7911yescharacteristic
165C23×C4—791no—
166#123—1584no—
167#120—1584no—
168C2×C4⋊C4—792no—
169C2×C4⋊C4—792no—
170C2×C4⋊C4C2×D7911yescharacteristic, complemented
171C2×C22⋊C4—792no—
172C2×C22⋊C4—792no—
173C2×C22⋊C4—792no—
174C2×C22⋊C4—791no—
175C2×C22⋊C4—792no—
176C2×C22⋊C4—791no—
177C2×C22⋊C4—792no—
178C2×C22⋊C4—792no—
179C2×C22⋊C4C2×D7912yes—
180C2×C22⋊C4C2×D7912yescomplemented
181C2×C42C2×D7911yescharacteristic, complemented
182#95—792no—
183#95—792no—
184#95—792no—
185C24—3162no—
186C24—3161no—
187C24—3161no—
188C24—792no—
189C24—1584no—
190C24—1582no—
191C24C22×D7911yescharacteristic
192C24C22×D7911yescharacteristic
193C2×D4—41no—
194C2×D4—41no—
195C2×D4—3162no—
196C2×D4—1584no—
197C2×D4—1584no—
198C2×D4D31614yes—
199C22×C4—3161no—
200C22×C4—3161no—
201C22×C4—792no—
202C22×C4—792no—
203C22×C4—792no—
204C22×C4—1582no—
205C22×C4C22×D7912yes—
206C22×C4C22×D7912yes—
207C22×C4C22×D7911yescharacteristic
208C4⋊C4—41no—
209C4⋊C4—3162no—
210C4⋊C4—1584no—
211C22⋊C4—42no—
212C22⋊C4—42no—
213C22⋊C4—3162no—
214C22⋊C4—3162no—
215C22⋊C4—3162no—
216C22⋊C4—1584no—
217C22⋊C4—1582no—
218C22⋊C4—1582no—
219C22⋊C4—1584no—
220C22⋊C4—1584no—
221C42—41no—
222C23—22no—
223C23—22no—
224C23—22no—
225C23—22no—
226C23—21no—
227C23—21no—
228C23—21no—
229C23—21no—
230C23—3164no—
231C23—3168no—
232C23—3164no—
233C23—3168no—
234C23—3164no—
235C23—794no—
236C23—1582no—
237C23—1582no—
238C23—1582no—
239C23—1582no—
240C23—1582no—
241C23—1582no—
242C23C2×D31612yes—
243C23C2×D31612yes—
244C23C23×D7911yescharacteristic
245D4—44no—
246D4—3168no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—3164no—
256C2×C4—1582no—
257C2×C4—1582no—
258C2×C4—1582no—
259C2×C4—1582no—
260C2×C4—1582no—
261C2×C4—1582no—
262C2×C4—1582no—
263C2×C4—1582no—
264C2×C4—1582no—
265C2×C4C2×D31612yes—
266C22—24no—
267C22—24no—
268C22—22no—
269C22—22no—
270C22—42no—
271C22—42no—
272C22—41no—
273C22—41no—
274C22—41no—
275C22—41no—
276C22—31616no—
277C22—3162no—
278C22—3162no—
279C22—3162no—
280C22—3162no—
281C22—1584no—
282C22—1584no—
283C22—1584no—
284C22C22×D31611yescharacteristic
285C22#41×D7912yes—
286C22#1457920611yescharacteristic
287C22#1457920612yes—
288C22#1457920611yescharacteristic
289C4—22no—
290C4—42no—
291C4—42no—
292C4—3162no—
293C4—3162no—
294C4—3162no—
295C2—42no—
296C2—42no—
297C2—3164no—
298C2#1909912511yescharacteristic
299C2#1909914512yes—
300C2#1909920812yes—
301C2#1909924311yescharacteristic
302C2#1909930011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#390×C79C2
prime radicalC2×#14579129C2
hypercenter#390D79
hypocenterC79#2697
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#14579142C2semidirect
3. #19098488C2semidirect
4. #19098485C2semidirect
5. #19098479C2semidirect
6. #19098454C2semidirect
7. #19098440C2semidirect
8. #19098418C2semidirect
9. #390×C79C2semidirect
12. C23×Dic79C22semidirect
15. C2×C4⋊Dic79C22semidirect
16. C2×Dic79⋊C4C22semidirect
19. C2×C22⋊Dic79C22semidirect
25. C79⋊#95C22semidirect
26. C79⋊#95C22semidirect
27. C79⋊#95C22semidirect
29. C2×C4⋊C4×C79C22semidirect
31. C2×C22⋊C4×C79C22semidirect
32. C2×C42×C79C22semidirect
152. C79#2697semidirect
158. #390D79semidirect
170. C2×C4⋊C4C2×D79semidirect
180. C2×C22⋊C4C2×D79semidirect
181. C2×C42C2×D79semidirect