Finite Group Databasebeta

← #23770613

Subgroups — #23770613

Order 10112.

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

normal subgroups only

This group has 464 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
1#19098499C212yesmaximal, complemented
2#19098496C212yesmaximal, complemented
3#19098486C212yesmaximal, complemented
4#19098447C212yesmaximal, complemented
5#19098443C211yesmaximal, characteristic
6#19098443C211yesmaximal, characteristic
7#19098435C212yesmaximal, complemented
8#19098421C212yesmaximal, complemented
9#390×C79C211yesmaximal, characteristic
10C23×Dic79C2211yescharacteristic
11C23×Dic79C2211yescharacteristic
12C2×C4⋊Dic79C2212yes—
13C2×Dic79⋊C4C2212yes—
14C2×Dic79⋊C4C2212yes—
15C2×Dic79⋊C4C2212yes—
16C2×Dic79⋊C4C2212yes—
17C2×C22⋊Dic79C2212yes—
18C2×C22⋊Dic79C2212yes—
19C2×C22⋊Dic79C2211yescharacteristic
20C2×C22⋊Dic79C2211yescharacteristic
21C79⋊#95C2212yes—
22C79⋊#95C2212yes—
23C79⋊#95C2212yes—
24C79⋊#95C2212yes—
25C79⋊#95C2212yes—
26C22×D4×C79C2211yescharacteristic
27C2×C4⋊C4×C79C2211yescharacteristic
28C2×C22⋊C4×C79C2212yes—
29C2×C22⋊C4×C79C2212yes—
30C2×C42×C79C2211yescharacteristic
31C22×Dic79—24no—
32C22×Dic79—42no—
33C22×Dic79—41no—
34C22×Dic79—41no—
35C22×Dic79C2312yes—
36C22×Dic79C2312yes—
37C22×Dic79C2312yes—
38C22×Dic79C2312yes—
39C4⋊Dic79—42no—
40Dic79⋊C4—24no—
41Dic79⋊C4—42no—
42Dic79⋊C4—42no—
43Dic79⋊C4—42no—
44C22⋊Dic79—24no—
45C22⋊Dic79—42no—
46C22⋊Dic79—41no—
47C22⋊Dic79—41no—
48C24×C79C2311yescharacteristic
49C24×C79C2311yescharacteristic
50C2×D4×C79—41no—
51C2×D4×C79—41no—
52C2×D4×C79Q814yes—
53C22×C4×C79C2312yes—
54C22×C4×C79C2312yes—
55C22×C4×C79C2311yescharacteristic
56C4⋊C4×C79—41no—
57C22⋊C4×C79—42no—
58C22⋊C4×C79—42no—
59C42×C79—41no—
60C23×C79—22no—
61C23×C79—22no—
62C23×C79—22no—
63C23×C79—21no—
64C23×C79—21no—
65C23×C79—22no—
66C23×C79—21no—
67C23×C79—21no—
68C23×C79C2×Q812yes—
69C23×C79C2×Q812yes—
70C23×C79C2411yescharacteristic
71D4×C79—44no—
72C2×C4×C79—21no—
73C2×C4×C79—21no—
74C2×C4×C79—22no—
75C2×C4×C79—22no—
76C2×C4×C79—22no—
77C2×C4×C79—22no—
78C2×C4×C79—22no—
79C2×C4×C79—22no—
80C2×C4×C79C2×Q812yes—
81C2×Dic79—22no—
82C2×Dic79—22no—
83C2×Dic79—22no—
84C2×Dic79—22no—
85C2×Dic79—22no—
86C2×Dic79—22no—
87C2×Dic79—22no—
88C2×Dic79—22no—
89C2×Dic79—22no—
90C2×Dic79—22no—
91C2×Dic79—22no—
92C2×Dic79—44no—
93C2×Dic79—44no—
94C2×Dic79#4114yes—
95C22×C79—22no—
96C22×C79—22no—
97C22×C79—24no—
98C22×C79—24no—
99C22×C79—42no—
100C22×C79—42no—
101C22×C79—41no—
102C22×C79—41no—
103C22×C79—41no—
104C22×C79—41no—
105C22×C79C22×Q811yescharacteristic
106C22×C79C2×#4112yes—
107C22×C79H(5,𝔽2)11yescharacteristic
108C22×C79H(5,𝔽2)12yes—
109C22×C79H(5,𝔽2)11yescharacteristic
110C4×C79—22no—
111C4×C79—42no—
112C4×C79—42no—
113Dic79—24no—
114Dic79—42no—
115Dic79—42no—
116Dic79—42no—
117C2×C79—42no—
118C2×C79—42no—
119C2×C79#54012yes—
120C2×C79#54311yescharacteristic
121C2×C79#55111yescharacteristic
122C2×C79#55412yes—
123C2×C79#56011yescharacteristic
124#2748—791nomaximal, Sylow
125C79#274811yescharacteristic, complemented, Sylow
126#399—792no—
127#398—792no—
128#396—792no—
129#390D7911yescharacteristic
130#387—792no—
131#386—791no—
132#386—791no—
133#385—792no—
134#380—792no—
135C22×D4C2×D7911yescharacteristic
136C23×C4—791no—
137C23×C4—791no—
138C2×C4⋊C4—792no—
139C2×C4⋊C4—792no—
140C2×C4⋊C4—792no—
141C2×C4⋊C4—792no—
142C2×C4⋊C4—792no—
143C2×C4⋊C4C2×D7911yescharacteristic
144C2×C22⋊C4—792no—
145C2×C22⋊C4—791no—
146C2×C22⋊C4—791no—
147C2×C22⋊C4—792no—
148C2×C22⋊C4C2×D7912yes—
149C2×C22⋊C4C2×D7912yes—
150C2×C42C2×D7911yescharacteristic
151#95—792no—
152#95—792no—
153#95—792no—
154#95—792no—
155#95—792no—
156C24C22×D7911yescharacteristic
157C24C22×D7911yescharacteristic
158C2×D4—41no—
159C2×D4—41no—
160C2×D4Dic15814yes—
161C22×C4—3162no—
162C22×C4—3161no—
163C22×C4—3161no—
164C22×C4—792no—
165C22×C4—792no—
166C22×C4—792no—
167C22×C4—792no—
168C22×C4—1584no—
169C22×C4C22×D7912yes—
170C22×C4C22×D7912yes—
171C22×C4C22×D7911yescharacteristic
172C4⋊C4—41no—
173C4⋊C4—3162no—
174C4⋊C4—3162no—
175C4⋊C4—3162no—
176C4⋊C4—3162no—
177C4⋊C4—1584no—
178C22⋊C4—42no—
179C22⋊C4—42no—
180C22⋊C4—3161no—
181C22⋊C4—3161no—
182C22⋊C4—3162no—
183C22⋊C4—1584no—
184C42—41no—
185C23—22no—
186C23—22no—
187C23—22no—
188C23—22no—
189C23—21no—
190C23—21no—
191C23—21no—
192C23—21no—
193C23C2×Dic15812yes—
194C23C2×Dic15812yes—
195C23C23×D7911yescharacteristic
196D4—44no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—3164no—
206C2×C4—3164no—
207C2×C4—794no—
208C2×C4—1582no—
209C2×C4—1582no—
210C2×C4—1582no—
211C2×C4—1582no—
212C2×C4—1582no—
213C2×C4—1582no—
214C2×C4—1582no—
215C2×C4—1582no—
216C2×C4—1582no—
217C2×C4—1582no—
218C2×C4—1582no—
219C2×C4C2×Dic15812yes—
220C22—22no—
221C22—22no—
222C22—24no—
223C22—24no—
224C22—42no—
225C22—42no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—41no—
230C22C22×Dic15811yescharacteristic
231C22#41×D7912yes—
232C22#1457920611yescharacteristic
233C22#1457920612yes—
234C22#1457920611yescharacteristic
235C4—22no—
236C4—42no—
237C4—42no—
238C4—3162no—
239C4—3162no—
240C4—3162no—
241C4—1584no—
242C2—42no—
243C2—42no—
244C2#1909916312yes—
245C2#1909918911yescharacteristic
246C2#1909924311yescharacteristic
247C2#1909927212yes—
248C2#1909930011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#390×C79C2
prime radicalC22×D4×C79C22
hypercenter#390D79
hypocenterC79#2748
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #19098499C2semidirect
2. #19098496C2semidirect
3. #19098486C2semidirect
4. #19098447C2semidirect
7. #19098435C2semidirect
8. #19098421C2semidirect
125. C79#2748semidirect