Finite Group Databasebeta

← #23769270

Subgroups — #23769270

Order 10112.

512 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 129 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×#14579151C211yesmaximal, characteristic, complemented
2C2×#14579123C211yesmaximal, characteristic
3#19098498C212yesmaximal, complemented
4#19098494C211yesmaximal, characteristic, complemented
5#19098492C212yesmaximal, complemented
6#19098481C211yesmaximal, characteristic
7#19098480C211yesmaximal, characteristic
8#19098437C212yesmaximal, complemented
9#19098434C212yesmaximal, complemented
10#19098430C211yesmaximal, characteristic, complemented
11#398×C79C211yesmaximal, characteristic, complemented
12C22×D316C2211yescharacteristic
13C22×C4×D79C2212yes—
14#14579151—24no—
15#14579123—24no—
16C2×C4⋊Dic79C2211yescharacteristic
17C2×Dic79⋊C4C2211yescharacteristic
18C2×Dic79⋊C4C2211yescharacteristic
19C2×Dic79⋊C4C2211yescharacteristic
20C2×Dic79⋊C4C2211yescharacteristic
21C2×Dic79⋊C4C2212yes—
22C2×(C2×D79)⋊C4C2212yes—
23C2×(C2×D79)⋊C4C2212yes—
24C2×(C2×D79)⋊C4C2212yes—
25C2×(C2×D79)⋊C4C2212yes—
26C2×(C2×D79)⋊C4C2212yes—
27C2×C4×Dic79C2211yescharacteristic
28C79⋊#95C2212yes—
29C79⋊#95C2211yescharacteristic
30C79⋊#95C2212yes—
31C79⋊#95C2212yes—
32C2×C4⋊C4×C79C2211yescharacteristic
33C2×C4⋊C4×C79C2211yescharacteristic
34C2×C4⋊C4×C79C2212yes—
35#95×C79C2211yescharacteristic
36#95×C79C2212yes—
37C23×D79C2312yes—
38C2×D316—24no—
39C2×D316—22no—
40C22×Dic79C2312yes—
41C22×Dic79C2311yescharacteristic
42C22×Dic79C2311yescharacteristic
43C22×Dic79C2311yescharacteristic
44C22×Dic79C2311yescharacteristic
45C2×C4×D79—24no—
46C2×C4×D79—42no—
47C2×C4×D79—42no—
48C4⋊Dic79—22no—
49Dic79⋊C4—22no—
50Dic79⋊C4—22no—
51Dic79⋊C4—22no—
52Dic79⋊C4—22no—
53Dic79⋊C4—42no—
54(C2×D79)⋊C4—24no—
55(C2×D79)⋊C4—24no—
56(C2×D79)⋊C4—24no—
57(C2×D79)⋊C4—42no—
58(C2×D79)⋊C4—42no—
59C4×Dic79D414yes—
60C22×C4×C79C2312yes—
61C22×C4×C79C2311yescharacteristic
62C22×C4×C79C2312yes—
63C22×C4×C79C2311yescharacteristic
64C22×C4×C79C2311yescharacteristic
65C4⋊C4×C79—22no—
66C4⋊C4×C79—22no—
67C4⋊C4×C79—42no—
68C23×C79C2411yescharacteristic
69C22×D79—22no—
70C22×D79—22no—
71C22×D79—22no—
72C22×D79—22no—
73C22×D79—22no—
74C22×D79—22no—
75C22×D79#4114yes—
76C2×C4×C79—22no—
77C2×C4×C79—22no—
78C2×C4×C79—21no—
79C2×C4×C79—21no—
80C2×C4×C79—22no—
81C2×C4×C79—22no—
82C2×C4×C79—21no—
83C2×C4×C79—22no—
84C2×C4×C79—22no—
85C2×C4×C79—22no—
86C2×C4×C79—21no—
87C2×C4×C79—22no—
88C2×C4×C79C2×D412yes—
89C2×Dic79—21no—
90C2×Dic79—21no—
91C2×Dic79—22no—
92C2×Dic79—21no—
93C2×Dic79—21no—
94C2×Dic79—22no—
95C2×Dic79—22no—
96C2×Dic79—21no—
97C2×Dic79—22no—
98C2×Dic79—21no—
99C2×Dic79—22no—
100C2×Dic79C2×D412yes—
101C2×Dic79C2×D412yes—
102D316—28no—
103C4×D79—48no—
104C22×C79C22×D411yescharacteristic
105C22×C79C2×#4112yes—
106C22×C79H(5,𝔽2)11yescharacteristic
107C22×C79H(5,𝔽2)11yescharacteristic
108C22×C792−1+412yes—
109C2×D79—24no—
110C2×D79—24no—
111C2×D79—24no—
112C2×D79—42no—
113C2×D79—42no—
114C2×D79—42no—
115C2×D79—42no—
116C4×C79—22no—
117C4×C79—41no—
118C4×C79—41no—
119C4×C79—42no—
120C4×C79—42no—
121Dic79—22no—
122Dic79—22no—
123Dic79—41no—
124Dic79—41no—
125Dic79—42no—
126C2×C79#52511yescharacteristic
127C2×C79#53511yescharacteristic
128C2×C79#53611yescharacteristic
129C2×C79#53912yes—
130C2×C79#53912yes—
131D79—44no—
132#2633—791nomaximal, Sylow
133C79#263311yescharacteristic, complemented, Sylow
134C2×#125—791no—
135C2×C4×D4—791no—
136#399—792no—
137#398—791no—
138#398D7911yescharacteristic, complemented
139#397—792no—
140#394—791no—
141#394—791no—
142#385—792no—
143#385—792no—
144#383—791no—
145C22×D4—791no—
146C23×C4—792no—
147#125—1584no—
148C4×D4—1584no—
149C2×C4⋊C4—792no—
150C2×C4⋊C4—791no—
151C2×C4⋊C4—791no—
152C2×C4⋊C4—791no—
153C2×C4⋊C4—791no—
154C2×C4⋊C4—791no—
155C2×C4⋊C4C2×D7911yescharacteristic
156C2×C4⋊C4C2×D7911yescharacteristic
157C2×C4⋊C4C2×D7912yes—
158C2×C22⋊C4—792no—
159C2×C22⋊C4—792no—
160C2×C22⋊C4—792no—
161C2×C22⋊C4—792no—
162C2×C22⋊C4—792no—
163C2×C42—791no—
164#95—792no—
165#95—791no—
166#95—792no—
167#95—792no—
168#95C2×D7911yescharacteristic
169#95C2×D7912yes—
170C24—792no—
171C2×D4—1584no—
172C2×D4—1582no—
173C22×C4—3162no—
174C22×C4—3162no—
175C22×C4—791no—
176C22×C4—791no—
177C22×C4—792no—
178C22×C4—791no—
179C22×C4—791no—
180C22×C4—1584no—
181C22×C4C22×D7912yes—
182C22×C4C22×D7912yes—
183C22×C4C22×D7911yescharacteristic
184C22×C4C22×D7911yescharacteristic
185C22×C4C22×D7911yescharacteristic
186C4⋊C4—22no—
187C4⋊C4—22no—
188C4⋊C4—42no—
189C4⋊C4—3162no—
190C4⋊C4—1582no—
191C4⋊C4—1582no—
192C4⋊C4—1582no—
193C4⋊C4—1582no—
194C4⋊C4—1582no—
195C22⋊C4—3162no—
196C22⋊C4—3162no—
197C22⋊C4—1584no—
198C22⋊C4—1584no—
199C22⋊C4—1584no—
200C42—794no—
201C23—794no—
202C23—1582no—
203C23—1582no—
204C23—1582no—
205C23—1582no—
206C23—1582no—
207C23—1582no—
208C23C23×D7911yescharacteristic
209D4—1588no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—3168no—
223C2×C4—792no—
224C2×C4—792no—
225C2×C4—1582no—
226C2×C4—1582no—
227C2×C4—1581no—
228C2×C4—1582no—
229C2×C4—1581no—
230C2×C4—1582no—
231C2×C4—1581no—
232C2×C4—1581no—
233C2×C4—1581no—
234C2×C4—1581no—
235C2×C4—1582no—
236C2×C4D4×D7912yes—
237C22—3162no—
238C22—3162no—
239C22—3162no—
240C22—3162no—
241C22—1584no—
242C22—1584no—
243C22—1584no—
244C22C2×D4×D7911yescharacteristic
245C22#41×D7912yes—
246C22#1457920611yescharacteristic
247C22#1457920711yescharacteristic
248C22#1457920912yes—
249C4—22no—
250C4—42no—
251C4—41no—
252C4—42no—
253C4—41no—
254C4—3162no—
255C4—3161no—
256C4—3161no—
257C4—1582no—
258C4—1582no—
259C2—3164no—
260C2#1909907111yescharacteristic
261C2#1909912911yescharacteristic
262C2#1909913811yescharacteristic
263C2#1909915912yes—
264C2#1909916112yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#398×C79C2
prime radicalC22×D316C22
hypercenter#398D79
hypocenterC79#2633
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#14579151C2semidirect
3. #19098498C2semidirect
4. #19098494C2semidirect
5. #19098492C2semidirect
8. #19098437C2semidirect
9. #19098434C2semidirect
10. #19098430C2semidirect
11. #398×C79C2semidirect
133. C79#2633semidirect
138. #398D79semidirect