Finite Group Databasebeta

← #23770919

Subgroups — #23770919

Order 10112.

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

normal subgroups only

This group has 392 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#19098505C212yesmaximal, complemented
2#19098505C212yesmaximal, complemented
3#19098499C211yesmaximal, characteristic
4#19098458C212yesmaximal, complemented
5#19098456C212yesmaximal
6#19098448C212yesmaximal, complemented
7#19098435C212yesmaximal
8#19098424C211yesmaximal, characteristic
9#397×C79C211yesmaximal, characteristic
10C23×Dic79C2211yescharacteristic
11C2×C4⋊Dic79C2212yes—
12C2×C4⋊Dic79C2211yescharacteristic
13C2×Dic79⋊C4C2212yes—
14C2×Dic79⋊C4C2212yes—
15C2×Dic79⋊C4C2212yes—
16C2×C22⋊Dic79C2212yes—
17C2×C22⋊Dic79C2211yescharacteristic
18C2×C4×Dic79C2212yes—
19C79⋊#95C2212yes—
20C79⋊#95C2212yes—
21C79⋊#95C2212yes—
22C79⋊#95C2212yes—
23C79⋊#95C2211yescharacteristic
24C79⋊#95C2212yes—
25C79⋊#95C2212yes—
26C2×C4⋊C4×C79C2211yescharacteristic
27C2×C22⋊C4×C79C2212yes—
28C2×C22⋊C4×C79C2211yescharacteristic
29#95×C79C2212yes—
30#95×C79C2211yescharacteristic
31C22×Dic79—22no—
32C22×Dic79—41no—
33C22×Dic79—41no—
34C22×Dic79C2312yes—
35C22×Dic79C2312yes—
36C22×Dic79C2312yes—
37C22×Dic79C2312yes—
38C4⋊Dic79—24no—
39C4⋊Dic79—41no—
40Dic79⋊C4—24no—
41Dic79⋊C4—42no—
42Dic79⋊C4—42no—
43C22⋊Dic79—24no—
44C22⋊Dic79—41no—
45C4×Dic79—42no—
46C24×C79C2311yescharacteristic
47C22×C4×C79C2312yes—
48C22×C4×C79C2311yescharacteristic
49C22×C4×C79C2311yescharacteristic
50C22×C4×C79C2312yes—
51C4⋊C4×C79—41no—
52C22⋊C4×C79—24no—
53C22⋊C4×C79—41no—
54C23×C79—22no—
55C23×C79—21no—
56C23×C79—21no—
57C23×C79—22no—
58C23×C79#4112yes—
59C23×C79C2411yescharacteristic
60C2×C4×C79—22no—
61C2×C4×C79—22no—
62C2×C4×C79—22no—
63C2×C4×C79—22no—
64C2×C4×C79—22no—
65C2×C4×C79—22no—
66C2×C4×C79—21no—
67C2×C4×C79—21no—
68C2×C4×C79—22no—
69C2×C4×C79—22no—
70C2×Dic79—22no—
71C2×Dic79—22no—
72C2×Dic79—22no—
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—44no—
82C2×Dic79#4114yes—
83C22×C79—22no—
84C22×C79—24no—
85C22×C79—42no—
86C22×C79—41no—
87C22×C79—41no—
88C22×C79C2×#4112yes—
89C22×C79C2×#4111yescharacteristic
90C22×C79H(5,𝔽2)11yescharacteristic
91C22×C79H(5,𝔽2)11yescharacteristic
92C22×C792−1+412yes—
93C4×C79—42no—
94C4×C79—42no—
95C4×C79—41no—
96C4×C79—41no—
97Dic79—24no—
98Dic79—42no—
99Dic79—42no—
100Dic79—42no—
101C2×C79—42no—
102C2×C79#53811yescharacteristic
103C2×C79#53912yes—
104C2×C79#55212yes—
105C2×C79#55911yescharacteristic
106C2×C79#56311yescharacteristic
107#2771—791nomaximal, Sylow
108C79#277111yescharacteristic, complemented, Sylow
109#400—792no—
110#400—792no—
111#399—791no—
112#397D7911yescharacteristic
113#389—792no—
114#388—792no—
115#387—792no—
116#385—792no—
117#381—791no—
118C23×C4—791no—
119C2×C4⋊C4—792no—
120C2×C4⋊C4—792no—
121C2×C4⋊C4—791no—
122C2×C4⋊C4—792no—
123C2×C4⋊C4—792no—
124C2×C4⋊C4C2×D7911yescharacteristic
125C2×C22⋊C4—791no—
126C2×C22⋊C4—792no—
127C2×C22⋊C4C2×D7912yes—
128C2×C22⋊C4C2×D7911yescharacteristic
129C2×C42—792no—
130#95—792no—
131#95—792no—
132#95—792no—
133#95—792no—
134#95—791no—
135#95—792no—
136#95—792no—
137#95C2×D7912yes—
138#95C2×D7911yescharacteristic
139C24C22×D7911yescharacteristic
140C22×C4—3161no—
141C22×C4—3161no—
142C22×C4—792no—
143C22×C4—792no—
144C22×C4—792no—
145C22×C4—792no—
146C22×C4—1582no—
147C22×C4C22×D7912yes—
148C22×C4C22×D7911yescharacteristic
149C22×C4C22×D7911yescharacteristic
150C22×C4C22×D7912yes—
151C4⋊C4—41no—
152C4⋊C4—3162no—
153C4⋊C4—3162no—
154C4⋊C4—3161no—
155C4⋊C4—1584no—
156C4⋊C4—1584no—
157C22⋊C4—24no—
158C22⋊C4—41no—
159C22⋊C4—3161no—
160C22⋊C4—1584no—
161C42—3162no—
162C23—22no—
163C23—21no—
164C23—21no—
165C23—22no—
166C23#1192962312yes—
167C23C23×D7911yescharacteristic
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—3164no—
179C2×C4—794no—
180C2×C4—1582no—
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—
191C22—22no—
192C22—24no—
193C22—42no—
194C22—41no—
195C22—41no—
196C22#41×D7912yes—
197C22C2×#1192962311yescharacteristic
198C22#1457920611yescharacteristic
199C22#1457920711yescharacteristic
200C22#1457920812yes—
201C4—42no—
202C4—42no—
203C4—41no—
204C4—41no—
205C4—3162no—
206C4—3162no—
207C4—3162no—
208C4—1584no—
209C2—42no—
210C2#1909915011yescharacteristic
211C2#1909915412yes—
212C2#1909925012yes—
213C2#1909929711yescharacteristic
214C2#1909931311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#397×C79C2
prime radicalC24×C79C23
hypercenter#397D79
hypocenterC79#2771
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. #19098505C2semidirect
2. #19098505C2semidirect
4. #19098458C2semidirect
6. #19098448C2semidirect
108. C79#2771semidirect