Finite Group Databasebeta

← #23770306

Subgroups — #23770306

Order 10112.

448 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14579154C212yesmaximal
2#19098495C212yesmaximal, complemented
3#19098493C212yesmaximal, complemented
4#19098488C211yesmaximal, characteristic
5#19098488C211yesmaximal, characteristic
6#19098462C212yesmaximal, complemented
7#19098448C212yesmaximal, complemented
8#19098423C212yesmaximal
9#385×C79C211yesmaximal, characteristic
10#14579154—28no—
11C2×C4⋊Dic79C2212yes—
12C2×C4⋊Dic79C2212yes—
13C2×C4⋊Dic79C2212yes—
14C2×C4⋊Dic79C2211yescharacteristic
15C2×C4⋊Dic79C2211yescharacteristic
16C2×Dic79⋊C4C2212yes—
17C2×Dic79⋊C4C2212yes—
18C2×C22⋊Dic79C2212yes—
19C2×C22⋊Dic79C2212yes—
20C2×C4×Dic79C2212yes—
21C79⋊#95C2212yes—
22C79⋊#95C2212yes—
23C79⋊#95C2211yescharacteristic
24C79⋊#95C2212yes—
25C79⋊#95C2212yes—
26C79⋊#95C2211yescharacteristic
27C23×C4×C79C2211yescharacteristic
28C2×C4⋊C4×C79C2212yes—
29C2×C22⋊C4×C79C2211yescharacteristic
30C2×C22⋊C4×C79C2211yescharacteristic
31#95×C79C2212yes—
32C22×Dic79C2312yes—
33C22×Dic79C2312yes—
34C22×Dic79C2312yes—
35C22×Dic79C2312yes—
36C4⋊Dic79—24no—
37C4⋊Dic79—24no—
38C4⋊Dic79—42no—
39C4⋊Dic79—41no—
40C4⋊Dic79—41no—
41Dic79⋊C4—24no—
42Dic79⋊C4—24no—
43C22⋊Dic79—24no—
44C22⋊Dic79—24no—
45C4×Dic79—24no—
46C24×C79C2311yescharacteristic
47C22×C4×C79—24no—
48C22×C4×C79—41no—
49C22×C4×C79C2311yescharacteristic
50C22×C4×C79C2311yescharacteristic
51C22×C4×C79C2312yes—
52C22×C4×C79C2312yes—
53C4⋊C4×C79—24no—
54C22⋊C4×C79—41no—
55C22⋊C4×C79D414yes—
56C23×C79—22no—
57C23×C79—21no—
58C23×C79—22no—
59C23×C79—21no—
60C23×C79C2×D412yes—
61C23×C79C2411yescharacteristic
62C2×C4×C79—22no—
63C2×C4×C79—22no—
64C2×C4×C79—22no—
65C2×C4×C79—22no—
66C2×C4×C79—22no—
67C2×C4×C79—21no—
68C2×C4×C79—21no—
69C2×C4×C79—22no—
70C2×C4×C79—44no—
71C2×C4×C79C2×D414yes—
72C2×C4×C79#4114yes—
73C2×Dic79—22no—
74C2×Dic79—22no—
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—
85C22×C79—22no—
86C22×C79—24no—
87C22×C79—42no—
88C22×C79—41no—
89C22×C79—41no—
90C22×C79C22×D411yescharacteristic
91C22×C79C2×#4112yes—
92C22×C79H(5,𝔽2)11yescharacteristic
93C22×C792−1+412yes—
94C22×C792−1+411yescharacteristic
95C4×C79—24no—
96C4×C79—24no—
97C4×C79—41no—
98C4×C79—41no—
99Dic79—42no—
100Dic79—42no—
101Dic79—42no—
102Dic79—42no—
103C2×C79—42no—
104C2×C79#53711yescharacteristic
105C2×C79#54112yes—
106C2×C79#54712yes—
107C2×C79#55111yescharacteristic
108C2×C79#56311yescharacteristic
109#2722—791nomaximal, Sylow
110C79#272211yescharacteristic, complemented, Sylow
111C2×#126—792no—
112#398—792no—
113#398—792no—
114#397—791no—
115#397—791no—
116#389—792no—
117#387—792no—
118#385D7911yescharacteristic
119#380—792no—
120C23×C4C2×D7911yescharacteristic
121#126—1588no—
122C2×C4⋊C4—792no—
123C2×C4⋊C4—791no—
124C2×C4⋊C4—791no—
125C2×C4⋊C4—792no—
126C2×C4⋊C4—792no—
127C2×C4⋊C4—792no—
128C2×C4⋊C4—792no—
129C2×C4⋊C4C2×D7912yes—
130C2×C22⋊C4—792no—
131C2×C22⋊C4—792no—
132C2×C22⋊C4C2×D7911yescharacteristic
133C2×C22⋊C4C2×D7911yescharacteristic
134C2×C42—792no—
135#95—792no—
136#95—792no—
137#95—791no—
138#95—792no—
139#95—792no—
140#95—791no—
141#95C2×D7912yes—
142C24C22×D7911yescharacteristic
143C22×C4—24no—
144C22×C4—41no—
145C22×C4—792no—
146C22×C4—792no—
147C22×C4—792no—
148C22×C4—792no—
149C22×C4C22×D7911yescharacteristic
150C22×C4C22×D7911yescharacteristic
151C22×C4C22×D7912yes—
152C22×C4C22×D7912yes—
153C4⋊C4—24no—
154C4⋊C4—3162no—
155C4⋊C4—3161no—
156C4⋊C4—3161no—
157C4⋊C4—1584no—
158C4⋊C4—1584no—
159C4⋊C4—1584no—
160C4⋊C4—1584no—
161C22⋊C4—41no—
162C22⋊C4—1584no—
163C22⋊C4—1584no—
164C22⋊C4D31614yes—
165C42—1584no—
166C23—22no—
167C23—21no—
168C23—22no—
169C23—21no—
170C23C2×D31612yes—
171C23C23×D7911yescharacteristic
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—44no—
181C2×C4—1582no—
182C2×C4—1582no—
183C2×C4—1582no—
184C2×C4—1582no—
185C2×C4—1582no—
186C2×C4—1582no—
187C2×C4—1582no—
188C2×C4—1582no—
189C2×C4—1582no—
190C2×C4—1582no—
191C2×C4—1582no—
192C2×C4—1582no—
193C2×C4C2×D31614yes—
194C2×C4#1192962314yes—
195C22—22no—
196C22—24no—
197C22—42no—
198C22—41no—
199C22—41no—
200C22C22×D31611yescharacteristic
201C22C2×#1192962312yes—
202C22#1457920611yescharacteristic
203C22#1457920812yes—
204C22#1457920911yescharacteristic
205C4—24no—
206C4—24no—
207C4—41no—
208C4—41no—
209C4—3162no—
210C4—3162no—
211C4—3162no—
212C4—3162no—
213C2—42no—
214C2#1909914411yescharacteristic
215C2#1909917312yes—
216C2#1909921712yes—
217C2#1909924411yescharacteristic
218C2#1909931611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#385×C79C2
prime radicalC24×C79C23
hypercenter#385D79
hypocenterC79#2722
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. #19098495C2semidirect
3. #19098493C2semidirect
6. #19098462C2semidirect
7. #19098448C2semidirect
110. C79#2722semidirect