Finite Group Databasebeta

← #23769217

Subgroups — #23769217

Order 10112.

508 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 157 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×#14579138C211yesmaximal, characteristic
2C22×C4⋊Dic79C211yesmaximal, characteristic
3#19098505C212yesmaximal, complemented
4#19098497C212yesmaximal, complemented
5#19098495C212yesmaximal, complemented
6#19098484C212yesmaximal, complemented
7#19098438C211yesmaximal, characteristic
8#19098435C211yesmaximal, characteristic
9#19098426C211yesmaximal, characteristic
10#19098421C211yesmaximal, characteristic
11#381×C79C211yesmaximal, characteristic
12C22×Dic158C2211yescharacteristic
13C23×Dic79C2211yescharacteristic
14C23×Dic79C2211yescharacteristic
15#14579138—24no—
16C2×C4⋊Dic79—24no—
17C2×C4⋊Dic79C2212yes—
18C2×C4⋊Dic79C2211yescharacteristic
19C2×C4⋊Dic79C2212yes—
20C2×C4⋊Dic79C2212yes—
21C2×Dic79⋊C4C2211yescharacteristic
22C2×Dic79⋊C4C2211yescharacteristic
23C2×Dic79⋊C4C2212yes—
24C2×Dic79⋊C4C2212yes—
25C2×C22⋊Dic79C2211yescharacteristic
26C2×C22⋊Dic79C2211yescharacteristic
27C79⋊#95C2212yes—
28C79⋊#95C2212yes—
29C79⋊#95C2212yes—
30C79⋊#95C2212yes—
31C79⋊#95C2212yes—
32C23×C4×C79C2211yescharacteristic
33C2×C22⋊C4×C79C2211yescharacteristic
34C2×C22⋊C4×C79C2211yescharacteristic
35#95×C79C2212yes—
36#95×C79C2212yes—
37C2×Dic158—22no—
38C2×Dic158—42no—
39C22×Dic79—22no—
40C22×Dic79—42no—
41C22×Dic79—42no—
42C22×Dic79D414yes—
43C22×Dic79C2311yescharacteristic
44C22×Dic79C2311yescharacteristic
45C22×Dic79C2312yes—
46C22×Dic79C2312yes—
47C22×Dic79C2311yescharacteristic
48C22×Dic79C2311yescharacteristic
49C4⋊Dic79—24no—
50C4⋊Dic79—24no—
51C4⋊Dic79—22no—
52C4⋊Dic79—42no—
53Dic79⋊C4—22no—
54Dic79⋊C4—22no—
55Dic79⋊C4—42no—
56Dic79⋊C4—42no—
57C22⋊Dic79—22no—
58C22⋊Dic79—22no—
59C24×C79C2311yescharacteristic
60C22×C4×C79—22no—
61C22×C4×C79—22no—
62C22×C4×C79Q814yescomplemented
63C22×C4×C79C2311yescharacteristic
64C22×C4×C79C2311yescharacteristic
65C22×C4×C79C2312yes—
66C22×C4×C79C2312yes—
67C22⋊C4×C79—22no—
68C22⋊C4×C79—22no—
69C23×C79—22no—
70C23×C79—22no—
71C23×C79C2×D412yes—
72C23×C79C2×Q812yes—
73C23×C79#4112yes—
74C23×C79C2411yescharacteristic
75C2×C4×C79—28no—
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—22no—
83C2×C4×C79—22no—
84C2×C4×C79—22no—
85C2×C4×C79C2×Q814yes—
86C2×Dic79—22no—
87C2×Dic79—22no—
88C2×Dic79—21no—
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×Dic79—22no—
98C2×Dic79—44no—
99C2×Dic79—44no—
100C2×Dic79C2×D412yes—
101C2×Dic79C2×D412yes—
102Dic158—44no—
103C22×C79—22no—
104C22×C79—22no—
105C22×C79—24no—
106C22×C79—24no—
107C22×C79C22⋊Q814yes—
108C22×C79C22×D411yescharacteristic
109C22×C79C22×Q811yescharacteristic
110C22×C79C2×#4111yescharacteristic
111C22×C79H(5,𝔽2)12yes—
112C22×C792−1+412yes—
113C4×C79—24no—
114C4×C79—41no—
115C4×C79—41no—
116C4×C79—42no—
117Dic79—22no—
118Dic79—22no—
119Dic79—41no—
120Dic79—42no—
121Dic79—41no—
122Dic79—42no—
123C2×C79—24no—
124C2×C79C2×C22⋊Q811yescharacteristic
125C2×C79#53411yescharacteristic
126C2×C79#53611yescharacteristic
127C2×C79#53912yes—
128C2×C79#54412yes—
129#2627—791nomaximal, Sylow
130C79#262711yescharacteristic, complemented, Sylow
131C2×C22⋊Q8—791no—
132C22×C4⋊C4—791no—
133#400—792no—
134#398—792no—
135#398—792no—
136#395—792no—
137#385—791no—
138#385—791no—
139#381—791no—
140#381D7911yescharacteristic
141#380—791no—
142C22×Q8—791no—
143C23×C4—791no—
144C23×C4—791no—
145C23×C4C2×D7911yescharacteristic
146C22⋊Q8—1584no—
147C2×C4⋊C4—792no—
148C2×C4⋊C4—792no—
149C2×C4⋊C4—792no—
150C2×C4⋊C4—792no—
151C2×C4⋊C4—792no—
152C2×C4⋊C4—791no—
153C2×C4⋊C4—791no—
154C2×C4⋊C4—791no—
155C2×C4⋊C4—1584no—
156C2×C22⋊C4—791no—
157C2×C22⋊C4—791no—
158C2×C22⋊C4C2×D7911yescharacteristic
159C2×C22⋊C4C2×D7911yescharacteristic
160#95—792no—
161#95—792no—
162#95—792no—
163#95—792no—
164#95—792no—
165#95C2×D7912yes—
166#95C2×D7912yes—
167C24C22×D7911yescharacteristic
168C2×Q8—3162no—
169C2×Q8—1582no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—3162no—
173C22×C4—3162no—
174C22×C4—794no—
175C22×C4—791no—
176C22×C4—791no—
177C22×C4—792no—
178C22×C4—791no—
179C22×C4—791no—
180C22×C4—792no—
181C22×C4—1582no—
182C22×C4Dic15814yescomplemented
183C22×C4C22×D7912yes—
184C22×C4C22×D7911yescharacteristic
185C22×C4C22×D7911yescharacteristic
186C22×C4C22×D7912yes—
187C4⋊C4—3162no—
188C4⋊C4—3162no—
189C4⋊C4—3162no—
190C4⋊C4—1582no—
191C4⋊C4—1582no—
192C4⋊C4—1584no—
193C4⋊C4—1584no—
194C4⋊C4—1582no—
195C22⋊C4—22no—
196C22⋊C4—22no—
197C22⋊C4—1582no—
198C22⋊C4—1582no—
199C23—22no—
200C23—22no—
201C23D4×D7912yes—
202C23C2×Dic15812yes—
203C23#1192962312yes—
204C23C23×D7911yescharacteristic
205Q8—3164no—
206C2×C4—22no—
207C2×C4—28no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—3164no—
217C2×C4—3164no—
218C2×C4—792no—
219C2×C4—792no—
220C2×C4—1582no—
221C2×C4—1582no—
222C2×C4—1582no—
223C2×C4—1582no—
224C2×C4—1582no—
225C2×C4—1582no—
226C2×C4—1582no—
227C2×C4—1581no—
228C2×C4—1581no—
229C2×C4—1582no—
230C2×C4—1582no—
231C2×C4—1582no—
232C2×C4C2×Dic15814yes—
233C22—24no—
234C22—24no—
235C22—22no—
236C22—22no—
237C22#1457913814yes—
238C22C2×D4×D7911yescharacteristic
239C22C22×Dic15811yescharacteristic
240C22C2×#1192962311yescharacteristic
241C22#1457920712yes—
242C22#1457920812yes—
243C4—24no—
244C4—42no—
245C4—41no—
246C4—41no—
247C4—3162no—
248C4—3162no—
249C4—3161no—
250C4—3161no—
251C4—1582no—
252C4—1582no—
253C2—24no—
254C2C2×#1457913811yescharacteristic
255C2#1909912411yescharacteristic
256C2#1909913511yescharacteristic
257C2#1909915712yes—
258C2#1909919112yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#381×C79C2
prime radicalC24×C79C23
hypercenter#381D79
hypocenterC79#2627
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
3. #19098505C2semidirect
4. #19098497C2semidirect
5. #19098495C2semidirect
6. #19098484C2semidirect
62. C22×C4×C79Q8semidirect
130. C79#2627semidirect
182. C22×C4Dic158semidirect