Finite Group Databasebeta

← #23771234

Subgroups — #23771234

Order 10112.

420 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 121 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#19098485C212yesmaximal, complemented
2#19098481C212yesmaximal
3#19098480C211yesmaximal, characteristic
4#19098455C212yesmaximal, complemented
5#19098455C212yesmaximal, complemented
6#19098452C212yesmaximal, complemented
7#19098446C212yesmaximal, complemented
8#19098432C211yesmaximal, characteristic, complemented
9#400×C79C211yesmaximal, characteristic, complemented
10C22×D316C2211yescharacteristic
11C2×C4⋊Dic79C2212yes—
12C2×C4⋊Dic79C2211yescharacteristic
13C2×Dic79⋊C4C2212yes—
14C2×Dic79⋊C4C2212yes—
15C2×(C2×D79)⋊C4C2212yes—
16C2×(C2×D79)⋊C4C2212yes—
17C2×(C2×D79)⋊C4C2212yes—
18C2×(C2×D79)⋊C4C2212yes—
19C2×(C2×D79)⋊C4C2212yes—
20C2×(C2×D79)⋊C4C2212yes—
21C2×C4×Dic79C2211yescharacteristic
22C2×C4×Dic79C2212yes—
23C79⋊#95C2211yescharacteristic
24C79⋊#95C2212yes—
25C79⋊#95C2212yes—
26C2×C4⋊C4×C79C2211yescharacteristic
27C2×C4⋊C4×C79C2211yescharacteristic
28#95×C79C2212yes—
29#95×C79C2211yescharacteristic
30#95×C79C2212yes—
31C23×D79C2312yes—
32C2×D316—42no—
33C2×D316—41no—
34C22×Dic79C2312yes—
35C22×Dic79C2312yes—
36C22×Dic79C2312yes—
37C4⋊Dic79—24no—
38C4⋊Dic79—41no—
39Dic79⋊C4—42no—
40Dic79⋊C4—42no—
41(C2×D79)⋊C4—24no—
42(C2×D79)⋊C4—24no—
43(C2×D79)⋊C4—24no—
44(C2×D79)⋊C4—42no—
45(C2×D79)⋊C4—42no—
46(C2×D79)⋊C4—42no—
47C4×Dic79—22no—
48C4×Dic79—42no—
49C22×C4×C79C2312yes—
50C22×C4×C79C2312yes—
51C22×C4×C79C2311yescharacteristic
52C22×C4×C79C2311yescharacteristic
53C22×C4×C79C2311yescharacteristic
54C4⋊C4×C79—41no—
55C4⋊C4×C79—41no—
56C23×C79C2411yescharacteristic
57C22×D79—22no—
58C22×D79—22no—
59C22×D79—22no—
60C22×D79—22no—
61C22×D79—22no—
62C22×D79—22no—
63C22×D79—22no—
64C2×C4×C79—21no—
65C2×C4×C79—21no—
66C2×C4×C79—22no—
67C2×C4×C79—22no—
68C2×C4×C79—22no—
69C2×C4×C79—22no—
70C2×C4×C79—22no—
71C2×C4×C79—22no—
72C2×C4×C79—22no—
73C2×C4×C79—21no—
74C2×C4×C79—21no—
75C2×C4×C79—22no—
76C2×C4×C79#4112yes—
77C2×Dic79—22no—
78C2×Dic79—22no—
79C2×Dic79—22no—
80C2×Dic79—22no—
81C2×Dic79—22no—
82C2×Dic79—22no—
83C2×Dic79—22no—
84C2×Dic79—22no—
85C2×Dic79#4114yes—
86D316—44no—
87C22×C79C2×#4112yes—
88C22×C79C2×#4111yescharacteristic
89C22×C79H(5,𝔽2)11yescharacteristic
90C22×C79H(5,𝔽2)12yes—
91C22×C792−1+411yescharacteristic
92C2×D79—42no—
93C2×D79—42no—
94C2×D79—42no—
95C2×D79—42no—
96C2×D79—42no—
97C2×D79—42no—
98C2×D79—42no—
99C4×C79—22no—
100C4×C79—42no—
101C4×C79—42no—
102C4×C79—41no—
103C4×C79—41no—
104Dic79—24no—
105Dic79—42no—
106Dic79—42no—
107C2×C79#53911yescharacteristic
108C2×C79#54212yes—
109C2×C79#55312yes—
110C2×C79#55511yescharacteristic
111C2×C79#56011yescharacteristic
112D79—82no—
113#2795—791nomaximal, Sylow
114C79#279511yescharacteristic, complemented, Sylow
115#400D7911yescharacteristic, complemented
116#396—792no—
117#394—791no—
118#394—792no—
119#388—792no—
120#388—792no—
121#388—792no—
122#387—792no—
123#384—791no—
124C22×D4—791no—
125C2×C4⋊C4—792no—
126C2×C4⋊C4—791no—
127C2×C4⋊C4—792no—
128C2×C4⋊C4—792no—
129C2×C4⋊C4C2×D7911yescharacteristic
130C2×C4⋊C4C2×D7911yescharacteristic
131C2×C22⋊C4—792no—
132C2×C22⋊C4—792no—
133C2×C22⋊C4—792no—
134C2×C22⋊C4—792no—
135C2×C22⋊C4—792no—
136C2×C22⋊C4—792no—
137C2×C42—792no—
138C2×C42—791no—
139#95—791no—
140#95—792no—
141#95—792no—
142#95C2×D7912yes—
143#95C2×D7911yescharacteristic
144#95C2×D7912yes—
145C24—792no—
146C2×D4—3161no—
147C2×D4—3162no—
148C22×C4—792no—
149C22×C4—792no—
150C22×C4—792no—
151C22×C4C22×D7912yes—
152C22×C4C22×D7912yes—
153C22×C4C22×D7911yescharacteristic
154C22×C4C22×D7911yescharacteristic
155C22×C4C22×D7911yescharacteristic
156C4⋊C4—41no—
157C4⋊C4—41no—
158C4⋊C4—3162no—
159C4⋊C4—3162no—
160C4⋊C4—3161no—
161C4⋊C4—1584no—
162C22⋊C4—3162no—
163C22⋊C4—3162no—
164C22⋊C4—3162no—
165C22⋊C4—1584no—
166C22⋊C4—1584no—
167C22⋊C4—1584no—
168C42—3162no—
169C42—1582no—
170C23—1582no—
171C23—1582no—
172C23—1582no—
173C23—1582no—
174C23—1582no—
175C23—1582no—
176C23—1582no—
177C23C23×D7911yescharacteristic
178D4—3164no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—794no—
192C2×C4—1582no—
193C2×C4—1582no—
194C2×C4—1582no—
195C2×C4—1582no—
196C2×C4—1582no—
197C2×C4—1582no—
198C2×C4—1582no—
199C2×C4—1582no—
200C2×C4#1192962512yes—
201C22—3162no—
202C22—3162no—
203C22—3162no—
204C22—3162no—
205C22—3162no—
206C22—3162no—
207C22—3162no—
208C22#41×D7912yes—
209C22C2×#1192962511yescharacteristic
210C22#1457920611yescharacteristic
211C22#1457920712yes—
212C22#1457920811yescharacteristic
213C4—22no—
214C4—42no—
215C4—42no—
216C4—41no—
217C4—41no—
218C4—3162no—
219C4—3162no—
220C4—1584no—
221C2—6322no—
222C2#1909916211yescharacteristic
223C2#1909917912yes—
224C2#1909926612yes—
225C2#1909927511yescharacteristic
226C2#1909930311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#400×C79C2
prime radicalC22×D316C22
hypercenter#400D79
hypocenterC79#2795
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. #19098485C2semidirect
4. #19098455C2semidirect
5. #19098455C2semidirect
6. #19098452C2semidirect
7. #19098446C2semidirect
8. #19098432C2semidirect
9. #400×C79C2semidirect
114. C79#2795semidirect
115. #400D79semidirect