Finite Group Databasebeta

← #23769709

Subgroups — #23769709

Order 10112.

544 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14579159C212yesmaximal, complemented
2C2×#14579138C212yesmaximal
3#19098499C211yesmaximal, characteristic
4#19098497C212yesmaximal, complemented
5#19098484C212yesmaximal, complemented
6#19098457C212yesmaximal
7#19098445C212yesmaximal, complemented
8#19098435C211yesmaximal, characteristic
9#393×C79C211yesmaximal, characteristic
10C22×Dic158C2212yes—
11C23×Dic79C2211yescharacteristic
12#14579159—28no—
13#14579138—28no—
14C2×C4⋊Dic79C2212yes—
15C2×C4⋊Dic79C2211yescharacteristic
16C2×Dic79⋊C4C2212yes—
17C2×Dic79⋊C4C2212yes—
18C2×Dic79⋊C4C2212yes—
19C2×Dic79⋊C4C2212yes—
20C2×Dic79⋊C4C2212yes—
21C2×C22⋊Dic79C2212yes—
22C2×C22⋊Dic79C2211yescharacteristic
23C2×C4×Dic79C2212yes—
24C79⋊#95C2212yes—
25C79⋊#95C2211yescharacteristic
26C79⋊#95C2212yes—
27C79⋊#95C2212yes—
28C22×Q8×C79C2211yescharacteristic
29C2×C22⋊C4×C79C2212yes—
30C2×C22⋊C4×C79C2211yescharacteristic
31#95×C79C2212yes—
32#95×C79C2211yescharacteristic
33C2×Dic158—24no—
34C2×Dic158—24no—
35C2×Dic158—42no—
36C22×Dic79—24no—
37C22×Dic79—41no—
38C22×Dic79C2312yes—
39C22×Dic79C2312yes—
40C22×Dic79C2312yes—
41C22×Dic79C2312yes—
42C4⋊Dic79—24no—
43C4⋊Dic79—41no—
44Dic79⋊C4—24no—
45Dic79⋊C4—24no—
46Dic79⋊C4—24no—
47Dic79⋊C4—24no—
48Dic79⋊C4D418yes—
49C22⋊Dic79—24no—
50C22⋊Dic79Q814yescomplemented
51C4×Dic79—24no—
52C24×C79C2311yescharacteristic
53C2×Q8×C79—24no—
54C2×Q8×C79—41no—
55C22×C4×C79C2311yescharacteristic
56C22×C4×C79C2312yes—
57C22×C4×C79C2311yescharacteristic
58C22×C4×C79C2312yes—
59C22⋊C4×C79—24no—
60C22⋊C4×C79—41no—
61C23×C79—22no—
62C23×C79—21no—
63C23×C79—21no—
64C23×C79—22no—
65C23×C79C2×Q812yes—
66C23×C79C2411yescharacteristic
67Q8×C79—44no—
68C2×C4×C79—22no—
69C2×C4×C79—22no—
70C2×C4×C79—22no—
71C2×C4×C79—22no—
72C2×C4×C79—21no—
73C2×C4×C79—21no—
74C2×C4×C79—22no—
75C2×C4×C79—22no—
76C2×C4×C79—22no—
77C2×C4×C79C2×D414yes—
78C2×Dic79—22no—
79C2×Dic79—22no—
80C2×Dic79—22no—
81C2×Dic79—22no—
82C2×Dic79—22no—
83C2×Dic79—22no—
84C2×Dic79—22no—
85C2×Dic79—22no—
86C2×Dic79—22no—
87C2×Dic79—44no—
88C2×Dic79C2×D414yes—
89C2×Dic79C2×D414yes—
90C2×Dic79C2×Q814yes—
91Dic158—48no—
92C22×C79—22no—
93C22×C79—24no—
94C22×C79—42no—
95C22×C79—41no—
96C22×C79—41no—
97C22×C79C22×D412yes—
98C22×C79C22×Q811yescharacteristic
99C22×C79H(5,𝔽2)11yescharacteristic
100C22×C792−1+411yescharacteristic
101C22×C792−1+412yes—
102C4×C79—24no—
103C4×C79—42no—
104C4×C79—41no—
105C4×C79—41no—
106Dic79—24no—
107Dic79—24no—
108Dic79—24no—
109Dic79—42no—
110C2×C79—42no—
111C2×C79#53612yes—
112C2×C79#54411yescharacteristic
113C2×C79D4211yescharacteristic
114C2×C79D4×Q812yes—
115C2×C79#56311yescharacteristic
116#2677—791nomaximal, Sylow
117C79#267711yescharacteristic, complemented, Sylow
118C2×C4⋊Q8—792no—
119C2×C22⋊Q8—792no—
120#399—791no—
121#398—792no—
122#395—792no—
123#393D7911yescharacteristic
124#388—792no—
125#387—792no—
126#385—791no—
127C22×Q8—792no—
128C22×Q8C2×D7911yescharacteristic
129C23×C4—791no—
130C4⋊Q8—1588no—
131C22⋊Q8—1588no—
132C2×C4⋊C4—791no—
133C2×C4⋊C4—792no—
134C2×C4⋊C4—792no—
135C2×C4⋊C4—792no—
136C2×C4⋊C4—792no—
137C2×C4⋊C4—792no—
138C2×C4⋊C4—792no—
139C2×C22⋊C4—791no—
140C2×C22⋊C4—792no—
141C2×C22⋊C4C2×D7912yes—
142C2×C22⋊C4C2×D7911yescharacteristic
143C2×C42—792no—
144#95—792no—
145#95—791no—
146#95—792no—
147#95—792no—
148#95C2×D7912yes—
149#95C2×D7911yescharacteristic
150C24C22×D7911yescharacteristic
151C2×Q8—24no—
152C2×Q8—41no—
153C2×Q8—3162no—
154C2×Q8—1584no—
155C2×Q8—1584no—
156C22×C4—3161no—
157C22×C4—792no—
158C22×C4—792no—
159C22×C4—792no—
160C22×C4—792no—
161C22×C4—1584no—
162C22×C4C22×D7911yescharacteristic
163C22×C4C22×D7912yes—
164C22×C4C22×D7911yescharacteristic
165C22×C4C22×D7912yes—
166C4⋊C4—3161no—
167C4⋊C4—798no—
168C4⋊C4—1584no—
169C4⋊C4—1584no—
170C4⋊C4—1584no—
171C4⋊C4—1584no—
172C4⋊C4—1584no—
173C22⋊C4—24no—
174C22⋊C4—41no—
175C22⋊C4—794no—
176C22⋊C4—1584no—
177C42—1584no—
178C23—21no—
179C23—21no—
180C23—22no—
181C23—22no—
182C23Q8×D7912yes—
183C23C23×D7911yescharacteristic
184Q8—44no—
185Q8—3168no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—3164no—
196C2×C4—794no—
197C2×C4—794no—
198C2×C4—794no—
199C2×C4—1582no—
200C2×C4—1582no—
201C2×C4—1582no—
202C2×C4—1582no—
203C2×C4—1582no—
204C2×C4—1582no—
205C2×C4—1582no—
206C2×C4—1582no—
207C2×C4—1582no—
208C2×C4D4×D7914yes—
209C22—22no—
210C22—24no—
211C22—41no—
212C22—41no—
213C22—42no—
214C22C2×D4×D7912yes—
215C22C2×Q8×D7911yescharacteristic
216C22#1457920611yescharacteristic
217C22#1457920811yescharacteristic
218C22#1457920812yes—
219C4—24no—
220C4—41no—
221C4—41no—
222C4—42no—
223C4—3162no—
224C4—1584no—
225C4—1584no—
226C4—1584no—
227C2—42no—
228C2#1909913312yes—
229C2#1909919211yescharacteristic
230C2#1909919511yescharacteristic
231C2#1909922612yes—
232C2#1909931311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#393×C79C2
prime radicalC24×C79C23
hypercenter#393D79
hypocenterC79#2677
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#14579159C2semidirect
4. #19098497C2semidirect
5. #19098484C2semidirect
7. #19098445C2semidirect
50. C22⋊Dic79Q8semidirect
117. C79#2677semidirect