Finite Group Databasebeta

← #23769165

Subgroups — #23769165

Order 10112.

528 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 143 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×#14579160C211yesmaximal, characteristic, complemented
2C2×#14579138C212yesmaximal
3C2×#14579117C211yesmaximal, characteristic
4#19098497C212yesmaximal, complemented
5#19098495C211yesmaximal, characteristic, complemented
6#19098494C211yesmaximal, characteristic, complemented
7#19098491C212yesmaximal
8#19098488C211yesmaximal, characteristic
9#19098467C212yesmaximal, complemented
10#19098427C211yesmaximal, characteristic, complemented
11#397×C79C211yesmaximal, characteristic
12C22×Dic158C2212yes—
13C23×Dic79C2211yescharacteristic
14#14579160—24no—
15#14579138—28no—
16#14579117—24no—
17C2×C4⋊Dic79C2211yescharacteristic
18C2×C4⋊Dic79C2212yes—
19C2×Dic79⋊C4C2212yes—
20C2×Dic79⋊C4C2212yes—
21C2×Dic79⋊C4C2211yescharacteristic
22C2×Dic79⋊C4C2212yes—
23C2×Dic79⋊C4C2211yescharacteristic
24C2×C22⋊Dic79C2212yes—
25C2×C22⋊Dic79C2211yescharacteristic
26C2×C4×Dic79C2211yescharacteristic
27C2×C4×Dic79C2211yescharacteristic
28C79⋊#95C2211yescharacteristic
29C79⋊#95C2212yes—
30C79⋊#95C2212yes—
31C79⋊#95C2212yes—
32C79⋊#95C2212yes—
33C2×C4⋊C4×C79C2211yescharacteristic
34C2×C22⋊C4×C79C2211yescharacteristic
35C2×C22⋊C4×C79C2212yes—
36#95×C79C2211yescharacteristic
37#95×C79C2212yes—
38C2×Dic158—24no—
39C2×Dic158—24no—
40C2×Dic158—24no—
41C22×Dic79—22no—
42C22×Dic79—22no—
43C22×Dic79D414yes—
44C22×Dic79C2312yes—
45C22×Dic79C2311yescharacteristic
46C22×Dic79C2312yes—
47C22×Dic79C2311yescharacteristic
48C22×Dic79C2311yescharacteristic
49C22×Dic79C2311yescharacteristic
50C4⋊Dic79—24no—
51C4⋊Dic79—22no—
52Dic79⋊C4—22no—
53Dic79⋊C4—24no—
54Dic79⋊C4—24no—
55Dic79⋊C4—24no—
56Dic79⋊C4—22no—
57C22⋊Dic79—22no—
58C22⋊Dic79—24no—
59C4×Dic79—22no—
60C4×Dic79D414yes—
61C24×C79C2311yescharacteristic
62C22×C4×C79C2312yes—
63C22×C4×C79C2311yescharacteristic
64C22×C4×C79C2312yes—
65C22×C4×C79C2311yescharacteristic
66C4⋊C4×C79—22no—
67C22⋊C4×C79—24no—
68C22⋊C4×C79—22no—
69C23×C79—21no—
70C23×C79—21no—
71C23×C79—22no—
72C23×C79—22no—
73C23×C79C2×D412yes—
74C23×C79C2411yescharacteristic
75C2×C4×C79—22no—
76C2×C4×C79—21no—
77C2×C4×C79—22no—
78C2×C4×C79—22no—
79C2×C4×C79—22no—
80C2×C4×C79—22no—
81C2×C4×C79—22no—
82C2×C4×C79—22no—
83C2×C4×C79—22no—
84C2×C4×C79C2×D412yes—
85C2×Dic79—21no—
86C2×Dic79—21no—
87C2×Dic79—22no—
88C2×Dic79—28no—
89C2×Dic79—21no—
90C2×Dic79—22no—
91C2×Dic79—22no—
92C2×Dic79—22no—
93C2×Dic79—22no—
94C2×Dic79—22no—
95C2×Dic79—22no—
96C2×Dic79—22no—
97C2×Dic79C2×D412yes—
98C2×Dic79C2×D412yes—
99C2×Dic79C2×D412yes—
100C2×Dic79C2×D412yes—
101C2×Dic79#4112yes—
102Dic158—48no—
103C22×C79—22no—
104C22×C79—24no—
105C22×C79—41no—
106C22×C79—41no—
107C22×C79—42no—
108C22×C79C22×D411yescharacteristic
109C22×C79C22×D411yescharacteristic
110C22×C79C2×#4111yescharacteristic
111C22×C792−1+412yes—
112C22×C792−1+412yes—
113C4×C79—22no—
114C4×C79—42no—
115C4×C79—41no—
116C4×C79—42no—
117Dic79—22no—
118Dic79—22no—
119Dic79—42no—
120Dic79—41no—
121Dic79—42no—
122Dic79#12114yes—
123C2×C79—42no—
124C2×C79C2×#12111yescharacteristic
125C2×C79#53611yescharacteristic
126C2×C79#53611yescharacteristic
127C2×C79#53612yes—
128C2×C79#54112yes—
129#2621—791nomaximal, Sylow
130C79#262111yescharacteristic, complemented, Sylow
131C2×C4⋊Q8—791no—
132C2×C22⋊Q8—792no—
133C2×#117—791no—
134#398—791no—
135#398—791no—
136#398—792no—
137#397—791no—
138#397—792no—
139#397D7911yescharacteristic
140#391—792no—
141#382—791no—
142C22×Q8—792no—
143C23×C4—791no—
144C4⋊Q8—1584no—
145C22⋊Q8—1588no—
146#117—1584no—
147C2×C4⋊C4—791no—
148C2×C4⋊C4—791no—
149C2×C4⋊C4—792no—
150C2×C4⋊C4—792no—
151C2×C4⋊C4—792no—
152C2×C4⋊C4—792no—
153C2×C4⋊C4—791no—
154C2×C4⋊C4C2×D7911yescharacteristic
155C2×C22⋊C4—791no—
156C2×C22⋊C4—792no—
157C2×C22⋊C4C2×D7911yescharacteristic
158C2×C22⋊C4C2×D7912yes—
159C2×C42—791no—
160C2×C42—791no—
161#95—792no—
162#95—791no—
163#95—792no—
164#95—792no—
165#95—792no—
166#95C2×D7911yescharacteristic
167#95C2×D7912yes—
168C24C22×D7911yescharacteristic
169C2×Q8—1584no—
170C2×Q8—1584no—
171C2×Q8—1584no—
172C22×C4—791no—
173C22×C4—794no—
174C22×C4—791no—
175C22×C4—791no—
176C22×C4—791no—
177C22×C4—792no—
178C22×C4—792no—
179C22×C4—1582no—
180C22×C4—1582no—
181C22×C4C22×D7911yescharacteristic
182C22×C4C22×D7912yes—
183C22×C4C22×D7912yes—
184C22×C4C22×D7911yescharacteristic
185C4⋊C4—22no—
186C4⋊C4—1582no—
187C4⋊C4—1584no—
188C4⋊C4—1584no—
189C4⋊C4—1584no—
190C4⋊C4—1584no—
191C4⋊C4—1582no—
192C4⋊C4—1582no—
193C22⋊C4—24no—
194C22⋊C4—22no—
195C22⋊C4—1582no—
196C22⋊C4—1584no—
197C42—794no—
198C42—1582no—
199C23—21no—
200C23—22no—
201C23—22no—
202C23—21no—
203C23D4×D7912yes—
204C23C23×D7911yescharacteristic
205Q8—3168no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—792no—
216C2×C4—792no—
217C2×C4—792no—
218C2×C4—792no—
219C2×C4—792no—
220C2×C4—1582no—
221C2×C4—1582no—
222C2×C4—1582no—
223C2×C4—1582no—
224C2×C4—1581no—
225C2×C4—1582no—
226C2×C4—1582no—
227C2×C4—1582no—
228C2×C4—1588no—
229C2×C4—1581no—
230C2×C4—1582no—
231C2×C4—1581no—
232C2×C4D4×D7912yes—
233C22—22no—
234C22—24no—
235C22—42no—
236C22—41no—
237C22—41no—
238C22C2×D4×D7911yescharacteristic
239C22C2×D4×D7911yescharacteristic
240C22#41×D7911yescharacteristic
241C22#1457920812yes—
242C22#1457920812yes—
243C4—22no—
244C4—42no—
245C4—41no—
246C4—42no—
247C4—3162no—
248C4—3161no—
249C4—3162no—
250C4—794no—
251C4—1582no—
252C4—1582no—
253C2—42no—
254C2#121×D7911yescharacteristic
255C2#1909913311yescharacteristic
256C2#1909913511yescharacteristic
257C2#1909913512yes—
258C2#1909917012yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#397×C79C2
prime radicalC24×C79C23
hypercenter#397D79
hypocenterC79#2621
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#14579160C2semidirect
4. #19098497C2semidirect
5. #19098495C2semidirect
6. #19098494C2semidirect
9. #19098467C2semidirect
10. #19098427C2semidirect
130. C79#2621semidirect