Finite Group Databasebeta

← #23771547

Subgroups — #23771547

Order 10112.

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

normal subgroups only

This group has 408 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#19098492C212yesmaximal, complemented
2#19098490C212yesmaximal, complemented
3#19098485C212yesmaximal, complemented
4#19098483C211yesmaximal, characteristic, complemented
5#19098480C212yesmaximal
6#19098476C212yesmaximal, complemented
7#19098464C211yesmaximal, characteristic
8#19098449C212yesmaximal, complemented
9#398×C79C211yesmaximal, characteristic, complemented
10C22×Dic158C2211yescharacteristic
11C22×D316C2211yescharacteristic
12C2×C4⋊Dic79C2212yes—
13C2×Dic79⋊C4C2212yes—
14C2×(C2×D79)⋊C4C2212yes—
15C2×(C2×D79)⋊C4C2212yes—
16C2×(C2×D79)⋊C4C2212yes—
17C2×(C2×D79)⋊C4C2212yes—
18C2×(C2×D79)⋊C4C2212yes—
19C2×(C2×D79)⋊C4C2212yes—
20C2×C4×Dic79C2211yescharacteristic
21C79⋊#95C2212yes—
22C79⋊#95C2212yes—
23C79⋊#95C2212yes—
24C79⋊#95C2212yes—
25C79⋊#95C2211yescharacteristic
26C2×C4⋊C4×C79C2212yes—
27C2×C4⋊C4×C79C2211yescharacteristic
28C2×C4⋊C4×C79C2211yescharacteristic
29#95×C79C2212yes—
30#95×C79C2211yescharacteristic
31C23×D79C2312yes—
32C2×Dic158—42no—
33C2×Dic158—41no—
34C2×D316—22no—
35C2×D316—41no—
36C2×D316—41no—
37C22×Dic79C2312yes—
38C22×Dic79C2312yes—
39C22×Dic79C2312yes—
40C4⋊Dic79—42no—
41Dic79⋊C4—42no—
42(C2×D79)⋊C4—42no—
43(C2×D79)⋊C4—42no—
44(C2×D79)⋊C4—42no—
45(C2×D79)⋊C4—42no—
46(C2×D79)⋊C4—42no—
47(C2×D79)⋊C4—42no—
48C4×Dic79—41no—
49C22×C4×C79C2311yescharacteristic
50C22×C4×C79C2312yes—
51C22×C4×C79C2312yes—
52C22×C4×C79C2311yescharacteristic
53C22×C4×C79C2311yescharacteristic
54C4⋊C4×C79—24no—
55C4⋊C4×C79—41no—
56C4⋊C4×C79—41no—
57C23×C79C2411yescharacteristic
58C22×D79—22no—
59C22×D79—22no—
60C22×D79—22no—
61C22×D79—22no—
62C22×D79—22no—
63C22×D79—22no—
64C22×D79—22no—
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—22no—
73C2×C4×C79—22no—
74C2×C4×C79—21no—
75C2×C4×C79—21no—
76C2×C4×C79—22no—
77C2×C4×C79#4112yes—
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—
87D316—44no—
88Dic158—44no—
89C22×C79C2×#4111yescharacteristic
90C22×C79H(5,𝔽2)11yescharacteristic
91C22×C79H(5,𝔽2)11yescharacteristic
92C22×C79H(5,𝔽2)12yes—
93C22×C792−1+412yes—
94C2×D79—42no—
95C2×D79—42no—
96C2×D79—42no—
97C2×D79—42no—
98C2×D79—42no—
99C2×D79—42no—
100C2×D79—42no—
101C4×C79—22no—
102C4×C79—42no—
103C4×C79—42no—
104C4×C79—41no—
105C4×C79—41no—
106Dic79—42no—
107Dic79—42no—
108Dic79—42no—
109C2×C79#53811yescharacteristic
110C2×C79#54212yes—
111C2×C79#56011yescharacteristic
112C2×C79#56212yes—
113C2×C79#56311yescharacteristic
114D79—82no—
115#2830—791nomaximal, Sylow
116C79#283011yescharacteristic, complemented, Sylow
117#398D7911yescharacteristic, complemented
118#397—792no—
119#397—792no—
120#396—792no—
121#395—791no—
122#394—792no—
123#393—792no—
124#390—791no—
125#387—792no—
126C22×Q8—791no—
127C22×D4—791no—
128C2×C4⋊C4—792no—
129C2×C4⋊C4—792no—
130C2×C4⋊C4C2×D7912yes—
131C2×C4⋊C4C2×D7911yescharacteristic
132C2×C4⋊C4C2×D7911yescharacteristic
133C2×C22⋊C4—792no—
134C2×C22⋊C4—792no—
135C2×C22⋊C4—792no—
136C2×C22⋊C4—792no—
137C2×C22⋊C4—792no—
138C2×C22⋊C4—792no—
139C2×C42—791no—
140#95—792no—
141#95—792no—
142#95—792no—
143#95—792no—
144#95—791no—
145#95C2×D7912yes—
146#95C2×D7911yescharacteristic
147C24—792no—
148C2×Q8—3161no—
149C2×Q8—3162no—
150C2×D4—3161no—
151C2×D4—3161no—
152C2×D4—1582no—
153C22×C4—792no—
154C22×C4—792no—
155C22×C4—792no—
156C22×C4C22×D7912yes—
157C22×C4C22×D7911yescharacteristic
158C22×C4C22×D7912yes—
159C22×C4C22×D7911yescharacteristic
160C22×C4C22×D7911yescharacteristic
161C4⋊C4—24no—
162C4⋊C4—41no—
163C4⋊C4—41no—
164C4⋊C4—3162no—
165C4⋊C4—3162no—
166C22⋊C4—3162no—
167C22⋊C4—3162no—
168C22⋊C4—3162no—
169C22⋊C4—3162no—
170C22⋊C4—3162no—
171C22⋊C4—3162no—
172C42—3161no—
173C23—1582no—
174C23—1582no—
175C23—1582no—
176C23—1582no—
177C23—1582no—
178C23—1582no—
179C23—1582no—
180C23C23×D7911yescharacteristic
181Q8—3164no—
182D4—3164no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
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#1192962312yes—
205C22—3162no—
206C22—3162no—
207C22—3162no—
208C22—3162no—
209C22—3162no—
210C22—3162no—
211C22—3162no—
212C22C2×#1192962311yescharacteristic
213C22#1457920611yescharacteristic
214C22#1457920711yescharacteristic
215C22#1457920712yes—
216C22#1457920912yes—
217C4—22no—
218C4—42no—
219C4—42no—
220C4—41no—
221C4—41no—
222C4—3162no—
223C4—3162no—
224C4—3162no—
225C2—6322no—
226C2#1909915011yescharacteristic
227C2#1909918612yes—
228C2#1909930311yescharacteristic
229C2#1909931112yes—
230C2#1909931211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#398×C79C2
prime radicalC22×D316C22
hypercenter#398D79
hypocenterC79#2830
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. #19098492C2semidirect
2. #19098490C2semidirect
3. #19098485C2semidirect
4. #19098483C2semidirect
6. #19098476C2semidirect
8. #19098449C2semidirect
9. #398×C79C2semidirect
116. C79#2830semidirect
117. #398D79semidirect