Finite Group Databasebeta

← #24915296

Subgroups — #24915296

Order 10624.

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#19127640C211yesmaximal, characteristic, complemented
2#19127624C212yesmaximal, complemented
3#19127615C212yesmaximal
4#19127594C212yesmaximal, complemented
5#19127589C212yesmaximal, complemented
6#19127589C212yesmaximal, complemented
7#19127583C212yesmaximal, complemented
8#19127570C211yesmaximal, characteristic, complemented
9#394×C83C211yesmaximal, characteristic
10C2×C4⋊Dic83C2211yescharacteristic
11C2×C4⋊Dic83C2211yescharacteristic
12C2×Dic83⋊C4C2212yes—
13C2×Dic83⋊C4C2212yes—
14C2×Dic83⋊C4C2212yes—
15C2×C22⋊Dic83C2212yes—
16C2×C22⋊Dic83C2212yes—
17C2×C22⋊Dic83C2212yes—
18C2×C22⋊Dic83C2212yes—
19C2×C4×Dic83C2211yescharacteristic
20C2×C4×Dic83C2212yes—
21C83⋊#95C2212yes—
22C83⋊#95C2212yes—
23C83⋊#95C2212yes—
24C83⋊#95C2211yescharacteristic
25C83⋊#95C2212yes—
26C22×D4×C83C2211yescharacteristic
27C2×C4⋊C4×C83C2211yescharacteristic
28C2×C22⋊C4×C83C2212yes—
29C2×C22⋊C4×C83C2212yes—
30#95×C83C2211yescharacteristic
31C22×Dic83C2312yes—
32C22×Dic83C2312yes—
33C22×Dic83C2312yes—
34C22×Dic83C2312yes—
35C4⋊Dic83—41no—
36C4⋊Dic83—41no—
37Dic83⋊C4—24no—
38Dic83⋊C4—42no—
39Dic83⋊C4—42no—
40C22⋊Dic83—24no—
41C22⋊Dic83—24no—
42C22⋊Dic83—42no—
43C22⋊Dic83—42no—
44C4×Dic83—22no—
45C4×Dic83—42no—
46C24×C83C2312yes—
47C2×D4×C83—41no—
48C2×D4×C83—42no—
49C22×C4×C83C2312yes—
50C22×C4×C83C2311yescharacteristic
51C22×C4×C83C2311yescharacteristic
52C22×C4×C83C2311yescharacteristic
53C4⋊C4×C83—41no—
54C22⋊C4×C83—24no—
55C22⋊C4×C83—42no—
56C23×C83—22no—
57C23×C83—22no—
58C23×C83—22no—
59C23×C83—22no—
60C23×C83—22no—
61C23×C83—22no—
62C23×C83—22no—
63C23×C83C2411yescharacteristic
64D4×C83—44no—
65C2×C4×C83—21no—
66C2×C4×C83—21no—
67C2×C4×C83—22no—
68C2×C4×C83—22no—
69C2×C4×C83—22no—
70C2×C4×C83—22no—
71C2×C4×C83—21no—
72C2×C4×C83—21no—
73C2×C4×C83—22no—
74C2×C4×C83#4112yes—
75C2×Dic83—22no—
76C2×Dic83—22no—
77C2×Dic83—22no—
78C2×Dic83—22no—
79C2×Dic83—22no—
80C2×Dic83—22no—
81C2×Dic83—22no—
82C2×Dic83—22no—
83C2×Dic83—22no—
84C2×Dic83—22no—
85C2×Dic83—22no—
86C2×Dic83#4114yes—
87C22×C83—42no—
88C22×C83—42no—
89C22×C83—42no—
90C22×C83—42no—
91C22×C83—42no—
92C22×C83—42no—
93C22×C83—42no—
94C22×C83C2×#4112yes—
95C22×C83C2×#4111yescharacteristic
96C22×C83H(5,𝔽2)11yescharacteristic
97C22×C83H(5,𝔽2)12yes—
98C22×C832−1+411yescharacteristic
99C4×C83—22no—
100C4×C83—42no—
101C4×C83—41no—
102C4×C83—41no—
103Dic83—24no—
104Dic83—42no—
105Dic83—42no—
106Dic83—42no—
107C2×C83—82no—
108C2×C83#53911yescharacteristic
109C2×C83#54212yes—
110C2×C83#55312yes—
111C2×C83#55511yescharacteristic
112C2×C83#56011yescharacteristic
113#2795—831nomaximal, Sylow
114C83#279511yescharacteristic, complemented, Sylow
115#400—831no—
116#396—832no—
117#394—832no—
118#394D8311yescharacteristic
119#388—832no—
120#388—832no—
121#388—832no—
122#387—832no—
123#384—831no—
124C22×D4C2×D8311yescharacteristic
125C2×C4⋊C4—832no—
126C2×C4⋊C4—831no—
127C2×C4⋊C4—832no—
128C2×C4⋊C4—831no—
129C2×C4⋊C4—832no—
130C2×C4⋊C4C2×D8311yescharacteristic
131C2×C22⋊C4—832no—
132C2×C22⋊C4—832no—
133C2×C22⋊C4—832no—
134C2×C22⋊C4—832no—
135C2×C22⋊C4C2×D8312yes—
136C2×C22⋊C4C2×D8312yes—
137C2×C42—832no—
138C2×C42—831no—
139#95—832no—
140#95—832no—
141#95—832no—
142#95—831no—
143#95—832no—
144#95C2×D8311yescharacteristic
145C24C22×D8312yes—
146C2×D4—41no—
147C2×D4—42no—
148C22×C4—832no—
149C22×C4—832no—
150C22×C4—832no—
151C22×C4—832no—
152C22×C4C22×D8312yes—
153C22×C4C22×D8311yescharacteristic
154C22×C4C22×D8311yescharacteristic
155C22×C4C22×D8311yescharacteristic
156C4⋊C4—41no—
157C4⋊C4—3322no—
158C4⋊C4—3322no—
159C4⋊C4—3321no—
160C4⋊C4—3321no—
161C4⋊C4—1664no—
162C22⋊C4—24no—
163C22⋊C4—42no—
164C22⋊C4—3322no—
165C22⋊C4—3322no—
166C22⋊C4—1664no—
167C22⋊C4—1664no—
168C42—3322no—
169C42—1662no—
170C23—22no—
171C23—22no—
172C23—22no—
173C23—22no—
174C23—22no—
175C23—22no—
176C23—22no—
177C23C23×D8311yescharacteristic
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—834no—
189C2×C4—1662no—
190C2×C4—1662no—
191C2×C4—1662no—
192C2×C4—1662no—
193C2×C4—1662no—
194C2×C4—1662no—
195C2×C4—1662no—
196C2×C4—1662no—
197C2×C4—1662no—
198C2×C4—1662no—
199C2×C4—1662no—
200C2×C4#1305058912yes—
201C22—42no—
202C22—42no—
203C22—42no—
204C22—42no—
205C22—42no—
206C22—42no—
207C22—42no—
208C22#41×D8312yes—
209C22C2×#1305058911yescharacteristic
210C22#1458183712yes—
211C22#1458183711yescharacteristic
212C22#1458183911yescharacteristic
213C4—22no—
214C4—42no—
215C4—41no—
216C4—41no—
217C4—3322no—
218C4—3322no—
219C4—3322no—
220C4—1664no—
221C2—82no—
222C2#1912829611yescharacteristic
223C2#1912831912yes—
224C2#1912839812yes—
225C2#1912841311yescharacteristic
226C2#1912844011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, cosocleC23×C83C24
Fitting#394×C83C2
prime radicalC22×D4×C83C22
hypercenter#394D83
hypocenterC83#2795
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #19127640C2semidirect
2. #19127624C2semidirect
4. #19127594C2semidirect
5. #19127589C2semidirect
6. #19127589C2semidirect
7. #19127583C2semidirect
8. #19127570C2semidirect
114. C83#2795semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191276402
#191276242
#191276152
#191275942
#191275892
#191275832
#191275702
#394×C832
#279583