Finite Group Databasebeta

← #23771571

Subgroups — #23771571

Order 10112.

416 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 117 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#19098488C212yesmaximal, complemented
3#19098483C211yesmaximal, characteristic, complemented
4#19098477C212yesmaximal
5#19098475C212yesmaximal, complemented
6#19098475C212yesmaximal, complemented
7#19098468C211yesmaximal, characteristic, complemented
8#19098456C212yesmaximal, complemented
9#394×C79C211yesmaximal, characteristic
10C22×Dic158C2211yescharacteristic
11C22×Dic158C2211yescharacteristic
12C2×C4⋊Dic79C2212yes—
13C2×Dic79⋊C4C2212yes—
14C2×C22⋊Dic79C2212yes—
15C2×C22⋊Dic79C2212yes—
16C2×C22⋊Dic79C2212yes—
17C2×C22⋊Dic79C2212yes—
18C2×C4×Dic79C2211yescharacteristic
19C79⋊#95C2212yes—
20C79⋊#95C2212yes—
21C79⋊#95C2212yes—
22C79⋊#95C2212yes—
23C79⋊#95C2212yes—
24C79⋊#95C2212yes—
25C79⋊#95C2211yescharacteristic
26C22×D4×C79C2211yescharacteristic
27C2×C4⋊C4×C79C2211yescharacteristic
28C2×C22⋊C4×C79C2212yes—
29C2×C22⋊C4×C79C2212yes—
30#95×C79C2211yescharacteristic
31C2×Dic158—22no—
32C2×Dic158—41no—
33C2×Dic158—41no—
34C2×Dic158—42no—
35C2×Dic158—41no—
36C22×Dic79C2312yes—
37C22×Dic79C2312yes—
38C22×Dic79C2312yes—
39C22×Dic79C2312yes—
40C4⋊Dic79—42no—
41Dic79⋊C4—42no—
42C22⋊Dic79—42no—
43C22⋊Dic79—42no—
44C22⋊Dic79—42no—
45C22⋊Dic79—42no—
46C4×Dic79—41no—
47C24×C79C2312yes—
48C2×D4×C79—42no—
49C2×D4×C79—41no—
50C22×C4×C79C2311yescharacteristic
51C22×C4×C79C2312yes—
52C22×C4×C79C2311yescharacteristic
53C22×C4×C79C2311yescharacteristic
54C4⋊C4×C79—41no—
55C22⋊C4×C79—24no—
56C22⋊C4×C79—42no—
57C23×C79—22no—
58C23×C79—22no—
59C23×C79—22no—
60C23×C79—22no—
61C23×C79—22no—
62C23×C79—22no—
63C23×C79—22no—
64C23×C79C2411yescharacteristic
65D4×C79—44no—
66C2×C4×C79—21no—
67C2×C4×C79—21no—
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#4112yes—
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—22no—
87C2×Dic79—22no—
88Dic158—44no—
89Dic158—44no—
90C22×C79—42no—
91C22×C79—42no—
92C22×C79—42no—
93C22×C79—42no—
94C22×C79—42no—
95C22×C79—42no—
96C22×C79—42no—
97C22×C79C2×#4111yescharacteristic
98C22×C79H(5,𝔽2)11yescharacteristic
99C22×C79H(5,𝔽2)12yes—
100C22×C79H(5,𝔽2)11yescharacteristic
101C22×C792−1+412yes—
102C4×C79—22no—
103C4×C79—42no—
104C4×C79—41no—
105C4×C79—41no—
106Dic79—42no—
107Dic79—42no—
108Dic79—42no—
109Dic79—42no—
110C2×C79—82no—
111C2×C79#53811yescharacteristic
112C2×C79#54212yes—
113C2×C79H(3,𝔽4)11yescharacteristic
114C2×C79#56212yes—
115C2×C79#56311yescharacteristic
116#2832—791nomaximal, Sylow
117C79#283211yescharacteristic, complemented, Sylow
118#400—792no—
119#397—792no—
120#395—791no—
121#394—792no—
122#394D7911yescharacteristic
123#393—792no—
124#393—792no—
125#391—791no—
126#388—792no—
127C22×Q8—791no—
128C22×Q8—791no—
129C22×D4C2×D7911yescharacteristic
130C2×C4⋊C4—792no—
131C2×C4⋊C4—792no—
132C2×C4⋊C4C2×D7911yescharacteristic
133C2×C22⋊C4—792no—
134C2×C22⋊C4—792no—
135C2×C22⋊C4—792no—
136C2×C22⋊C4—792no—
137C2×C22⋊C4C2×D7912yes—
138C2×C22⋊C4C2×D7912yes—
139C2×C42—791no—
140#95—792no—
141#95—792no—
142#95—792no—
143#95—792no—
144#95—792no—
145#95—792no—
146#95—791no—
147#95C2×D7911yescharacteristic
148C24C22×D7912yes—
149C2×Q8—3161no—
150C2×Q8—3161no—
151C2×Q8—3162no—
152C2×Q8—3161no—
153C2×Q8—1582no—
154C2×D4—41no—
155C2×D4—42no—
156C22×C4—792no—
157C22×C4—792no—
158C22×C4—792no—
159C22×C4—792no—
160C22×C4C22×D7912yes—
161C22×C4C22×D7911yescharacteristic
162C22×C4C22×D7911yescharacteristic
163C22×C4C22×D7911yescharacteristic
164C4⋊C4—41no—
165C4⋊C4—3162no—
166C4⋊C4—3162no—
167C22⋊C4—24no—
168C22⋊C4—42no—
169C22⋊C4—3162no—
170C22⋊C4—3162no—
171C22⋊C4—3162no—
172C22⋊C4—3162no—
173C42—3161no—
174C23—22no—
175C23—22no—
176C23—22no—
177C23—22no—
178C23—22no—
179C23—22no—
180C23—22no—
181C23C23×D7911yescharacteristic
182Q8—3164no—
183Q8—3164no—
184D4—44no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—1582no—
195C2×C4—1582no—
196C2×C4—1582no—
197C2×C4—1582no—
198C2×C4—1582no—
199C2×C4—1582no—
200C2×C4—1582no—
201C2×C4—1582no—
202C2×C4—1582no—
203C2×C4—1582no—
204C2×C4—1582no—
205C2×C4—1582no—
206C2×C4#1192962312yes—
207C22—42no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—42no—
212C22—42no—
213C22—42no—
214C22C2×#1192962311yescharacteristic
215C22#1457920611yescharacteristic
216C22#1457920612yes—
217C22#1457920711yescharacteristic
218C22#1457920812yes—
219C4—22no—
220C4—42no—
221C4—41no—
222C4—41no—
223C4—3162no—
224C4—3162no—
225C4—3162no—
226C4—3162no—
227C2—82no—
228C2#1909915011yescharacteristic
229C2#1909918012yes—
230C2#1909930611yescharacteristic
231C2#1909931012yes—
232C2#1909931311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#394×C79C2
prime radicalC22×D4×C79C22
hypercenter#394D79
hypocenterC79#2832
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #19098505C2semidirect
2. #19098488C2semidirect
3. #19098483C2semidirect
5. #19098475C2semidirect
6. #19098475C2semidirect
7. #19098468C2semidirect
8. #19098456C2semidirect
117. C79#2832semidirect