Finite Group Databasebeta

← #23771233

Subgroups — #23771233

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#19098502C211yesmaximal, characteristic, complemented
2#19098486C212yesmaximal, complemented
3#19098477C212yesmaximal
4#19098456C212yesmaximal, complemented
5#19098451C212yesmaximal, complemented
6#19098451C212yesmaximal, complemented
7#19098445C212yesmaximal, complemented
8#19098432C211yesmaximal, characteristic, complemented
9#394×C79C211yesmaximal, characteristic
10C2×C4⋊Dic79C2211yescharacteristic
11C2×C4⋊Dic79C2211yescharacteristic
12C2×Dic79⋊C4C2212yes—
13C2×Dic79⋊C4C2212yes—
14C2×Dic79⋊C4C2212yes—
15C2×C22⋊Dic79C2212yes—
16C2×C22⋊Dic79C2212yes—
17C2×C22⋊Dic79C2212yes—
18C2×C22⋊Dic79C2212yes—
19C2×C4×Dic79C2211yescharacteristic
20C2×C4×Dic79C2212yes—
21C79⋊#95C2212yes—
22C79⋊#95C2212yes—
23C79⋊#95C2212yes—
24C79⋊#95C2211yescharacteristic
25C79⋊#95C2212yes—
26C22×D4×C79C2211yescharacteristic
27C2×C4⋊C4×C79C2211yescharacteristic
28C2×C22⋊C4×C79C2212yes—
29C2×C22⋊C4×C79C2212yes—
30#95×C79C2211yescharacteristic
31C22×Dic79C2312yes—
32C22×Dic79C2312yes—
33C22×Dic79C2312yes—
34C22×Dic79C2312yes—
35C4⋊Dic79—41no—
36C4⋊Dic79—41no—
37Dic79⋊C4—24no—
38Dic79⋊C4—42no—
39Dic79⋊C4—42no—
40C22⋊Dic79—24no—
41C22⋊Dic79—24no—
42C22⋊Dic79—42no—
43C22⋊Dic79—42no—
44C4×Dic79—22no—
45C4×Dic79—42no—
46C24×C79C2312yes—
47C2×D4×C79—42no—
48C2×D4×C79—41no—
49C22×C4×C79C2312yes—
50C22×C4×C79C2311yescharacteristic
51C22×C4×C79C2311yescharacteristic
52C22×C4×C79C2311yescharacteristic
53C4⋊C4×C79—41no—
54C22⋊C4×C79—24no—
55C22⋊C4×C79—42no—
56C23×C79—22no—
57C23×C79—22no—
58C23×C79—22no—
59C23×C79—22no—
60C23×C79—22no—
61C23×C79—22no—
62C23×C79—22no—
63C23×C79C2411yescharacteristic
64D4×C79—44no—
65C2×C4×C79—21no—
66C2×C4×C79—21no—
67C2×C4×C79—22no—
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#4112yes—
75C2×Dic79—22no—
76C2×Dic79—22no—
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—22no—
86C2×Dic79#4114yes—
87C22×C79—42no—
88C22×C79—42no—
89C22×C79—42no—
90C22×C79—42no—
91C22×C79—42no—
92C22×C79—42no—
93C22×C79—42no—
94C22×C79C2×#4112yes—
95C22×C79C2×#4111yescharacteristic
96C22×C79H(5,𝔽2)11yescharacteristic
97C22×C79H(5,𝔽2)12yes—
98C22×C792−1+411yescharacteristic
99C4×C79—22no—
100C4×C79—42no—
101C4×C79—41no—
102C4×C79—41no—
103Dic79—24no—
104Dic79—42no—
105Dic79—42no—
106Dic79—42no—
107C2×C79—82no—
108C2×C79#53911yescharacteristic
109C2×C79#54212yes—
110C2×C79#55312yes—
111C2×C79#55511yescharacteristic
112C2×C79#56011yescharacteristic
113#2795—791nomaximal, Sylow
114C79#279511yescharacteristic, complemented, Sylow
115#400—791no—
116#396—792no—
117#394—792no—
118#394D7911yescharacteristic
119#388—792no—
120#388—792no—
121#388—792no—
122#387—792no—
123#384—791no—
124C22×D4C2×D7911yescharacteristic
125C2×C4⋊C4—792no—
126C2×C4⋊C4—791no—
127C2×C4⋊C4—792no—
128C2×C4⋊C4—791no—
129C2×C4⋊C4—792no—
130C2×C4⋊C4C2×D7911yescharacteristic
131C2×C22⋊C4—792no—
132C2×C22⋊C4—792no—
133C2×C22⋊C4—792no—
134C2×C22⋊C4—792no—
135C2×C22⋊C4C2×D7912yes—
136C2×C22⋊C4C2×D7912yes—
137C2×C42—792no—
138C2×C42—791no—
139#95—792no—
140#95—792no—
141#95—792no—
142#95—791no—
143#95—792no—
144#95C2×D7911yescharacteristic
145C24C22×D7912yes—
146C2×D4—41no—
147C2×D4—42no—
148C22×C4—792no—
149C22×C4—792no—
150C22×C4—792no—
151C22×C4—792no—
152C22×C4C22×D7912yes—
153C22×C4C22×D7911yescharacteristic
154C22×C4C22×D7911yescharacteristic
155C22×C4C22×D7911yescharacteristic
156C4⋊C4—41no—
157C4⋊C4—3162no—
158C4⋊C4—3162no—
159C4⋊C4—3161no—
160C4⋊C4—3161no—
161C4⋊C4—1584no—
162C22⋊C4—24no—
163C22⋊C4—42no—
164C22⋊C4—3162no—
165C22⋊C4—3162no—
166C22⋊C4—1584no—
167C22⋊C4—1584no—
168C42—3162no—
169C42—1582no—
170C23—22no—
171C23—22no—
172C23—22no—
173C23—22no—
174C23—22no—
175C23—22no—
176C23—22no—
177C23C23×D7911yescharacteristic
178D4—44no—
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—794no—
189C2×C4—1582no—
190C2×C4—1582no—
191C2×C4—1582no—
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#1192962312yes—
201C22—42no—
202C22—42no—
203C22—42no—
204C22—42no—
205C22—42no—
206C22—42no—
207C22—42no—
208C22#41×D7912yes—
209C22C2×#1192962311yescharacteristic
210C22#1457920611yescharacteristic
211C22#1457920612yes—
212C22#1457920811yescharacteristic
213C4—22no—
214C4—42no—
215C4—41no—
216C4—41no—
217C4—3162no—
218C4—3162no—
219C4—3162no—
220C4—1584no—
221C2—82no—
222C2#1909915811yescharacteristic
223C2#1909918112yes—
224C2#1909926012yes—
225C2#1909927511yescharacteristic
226C2#1909930211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#394×C79C2
prime radicalC22×D4×C79C22
hypercenter#394D79
hypocenterC79#2795
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #19098502C2semidirect
2. #19098486C2semidirect
4. #19098456C2semidirect
5. #19098451C2semidirect
6. #19098451C2semidirect
7. #19098445C2semidirect
8. #19098432C2semidirect
114. C79#2795semidirect