Finite Group Databasebeta

← #24908405

Subgroups — #24908405

Order 10624.

260 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 85 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#19128254C211yesmaximal, characteristic
2M16×Dic83C211yesmaximal, characteristic
3C4×Dic83⋊C4C211yesmaximal, characteristic
4#19127462C211yesmaximal, characteristic
5#19127461C211yesmaximal, characteristic
6#19127460C211yesmaximal, characteristic
7#339×C83C211yesmaximal, characteristic
8C2×#13050574C2211yescharacteristic
9#14581791C411yescharacteristic, complemented
10#14581791C411yescharacteristic, complemented
11#14581783C411yescharacteristic, complemented
12#14581783C411yescharacteristic, complemented
13#14581769—21no—
14#14581769—21no—
15C4×Dic166—21no—
16C4×Dic166—21no—
17#14581751C2211yescharacteristic
18C2×Dic83⋊C4—21no—
19C2×C4×Dic83C2211yescharacteristic
20C2×C4×Dic83C2211yescharacteristic
21#14581702—21no—
22C8×Dic83—21no—
23C83⋊#95—21no—
24C2×M16×C83C2211yescharacteristic
25#117×C83C2211yescharacteristic
26C2×C42×C83C2211yescharacteristic
27C2×Dic166—21no—
28C2×Dic166—21no—
29C22×Dic83—21no—
30C22×Dic83D411yescharacteristic
31C22×Dic83D411yescharacteristic
32#13050574—21no—
33#13050574Q812yescomplemented
34C2×C83⋊C8—21no—
35C4⋊Dic83—21no—
36C4⋊Dic83—21no—
37C4⋊Dic83C2×C411yescharacteristic
38C4⋊Dic83C2×C411yescharacteristic
39Dic83⋊C4—24no—
40Dic83⋊C4—21no—
41Dic83⋊C4—21no—
42Dic83⋊C4—21no—
43Dic83⋊C4—21no—
44C22⋊Dic83—21no—
45C4×Dic83—21no—
46C4×Dic83—21no—
47C4×Dic83—21no—
48C4×Dic83C2×C411yescharacteristic
49C4×Dic83C2×C411yescharacteristic
50C4×Dic83D411yescharacteristic
51C4×Dic83D411yescharacteristic
52C22×C4×C83—21no—
53C22×C4×C83C2311yescharacteristic
54M16×C83—21no—
55M16×C83Q812yescomplemented
56C2×C8×C83—21no—
57C4⋊C4×C83C2×C411yescharacteristic
58C4⋊C4×C83C2×C411yescharacteristic
59C22⋊C4×C83—21no—
60C42×C83—21no—
61C42×C83—21no—
62C42×C83—21no—
63C23×C83C2×D411yescharacteristic
64C2×C4×C83—22no—
65C2×C4×C83—21no—
66C2×C4×C83—21no—
67C2×C4×C83—41no—
68C2×C4×C83—41no—
69C2×C4×C83C22×C411yescharacteristic
70C2×C4×C83C2×D411yescharacteristic
71C2×C4×C83C2×Q811yescharacteristic
72C2×C4×C83C2×Q811yescharacteristic
73C2×C4×C83#4111yescharacteristic
74C2×C4×C83#4111yescharacteristic
75C2×Dic83—22no—
76C2×Dic83—22no—
77C2×Dic83—21no—
78C2×Dic83—21no—
79C2×Dic83—41no—
80C2×Dic83—41no—
81C2×Dic83—41no—
82C2×Dic83C22⋊C411yescharacteristic
83C2×Dic83C22⋊C411yescharacteristic
84C2×Dic83C22⋊C411yescharacteristic
85C2×Dic83C22⋊C411yescharacteristic
86Dic166—42no—
87Dic166—42no—
88C8×C83—22no—
89C83⋊C8—22no—
90C22×C83—21no—
91C22×C83—21no—
92C22×C83C2×C22⋊C411yescharacteristic
93C22×C83#12411yescharacteristic
94C22×C83C4⋊Q811yescharacteristic
95C4×C83—42no—
96C4×C83—41no—
97C4×C83—41no—
98C4×C83C4×Q811yescharacteristic
99C4×C83C4×Q811yescharacteristic
100C4×C83C22⋊Q811yescharacteristic
101C4×C83C22⋊Q811yescharacteristic
102Dic83—21no—
103Dic83—21no—
104Dic83—21no—
105Dic83—42no—
106Dic83—41no—
107Dic83—41no—
108Dic83#10412yes—
109C2×C83—21no—
110C2×C83—21no—
111C2×C83#39111yescharacteristic
112C2×C83C2×#10411yescharacteristic
113C2×C83#42111yescharacteristic
114#1986—831nomaximal, Sylow
115C83#198611yescharacteristic, complemented, Sylow
116#533—831no—
117C4×M16—831no—
118C4×C4⋊C4—831no—
119#339—831no—
120#339—831no—
121#339—831no—
122#339D8311yescharacteristic
123C2×M16—831no—
124C2×M16C2×D8311yescharacteristic
125C4⋊Q8—831no—
126C4⋊Q8—831no—
127#125—831no—
128#125—831no—
129C22⋊Q8—1661no—
130C22⋊Q8—1661no—
131C4×Q8—1661no—
132C4×Q8—1661no—
133#117—831no—
134#117C2×D8311yescharacteristic
135C2×C4⋊C4—1661no—
136C2×C42—831no—
137C2×C42—831no—
138C2×C42C2×D8311yescharacteristic
139#97—1661no—
140C4×C8—1661no—
141#95—1661no—
142C2×Q8—1661no—
143C2×Q8—1661no—
144C22×C4—21no—
145C22×C4—831no—
146C22×C4—831no—
147C22×C4—1661no—
148C22×C4C22×D8311yescharacteristic
149M16—21no—
150M16—832no—
151M16—1661no—
152M16Dic16612yescomplemented
153C2×C8—21no—
154C2×C8—1661no—
155C4⋊C4—831no—
156C4⋊C4—831no—
157C4⋊C4—1661no—
158C4⋊C4—1661no—
159C4⋊C4—1661no—
160C4⋊C4—1661no—
161C4⋊C4—1661no—
162C4⋊C4—1661no—
163C4⋊C4—1664no—
164C4⋊C4C4×D8311yescharacteristic
165C4⋊C4C4×D8311yescharacteristic
166C22⋊C4—21no—
167C22⋊C4—1661no—
168C42—21no—
169C42—21no—
170C42—21no—
171C42—831no—
172C42—831no—
173C42—831no—
174C42—831no—
175C42—1661no—
176C42—1661no—
177C42—1661no—
178C23D4×D8311yescharacteristic
179Q8—3322no—
180Q8—3322no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—3321no—
187C2×C4—3321no—
188C2×C4—3321no—
189C2×C4—831no—
190C2×C4—831no—
191C2×C4—831no—
192C2×C4—831no—
193C2×C4—1662no—
194C2×C4—1661no—
195C2×C4—1661no—
196C2×C4—1662no—
197C2×C4C2×C4×D8311yescharacteristic
198C2×C4D4×D8311yescharacteristic
199C2×C4Q8×D8311yescharacteristic
200C2×C4C2×Dic16611yescharacteristic
201C2×C4#1305058911yescharacteristic
202C2×C4#1305059011yescharacteristic
203C8—22no—
204C8—1662no—
205C22—21no—
206C22—21no—
207C22C22⋊C4×D8311yescharacteristic
208C22#1458177811yescharacteristic
209C22#1458179111yescharacteristic
210C4—42no—
211C4—41no—
212C4—41no—
213C4—3322no—
214C4—3321no—
215C4—3321no—
216C4—832no—
217C4—1661no—
218C4—1661no—
219C4—1661no—
220C4#1458175711yescharacteristic
221C4C4×Dic16611yescharacteristic
222C4#1458176911yescharacteristic
223C4#1458177011yescharacteristic
224C2—21no—
225C2—21no—
226C2#1912760511yescharacteristic
227C2#104×D8311yescharacteristic
228C2#1912771611yescharacteristic
subgroupG/H
centerC2×C4D4×D83
commutatorC2×C4×C83C22×C4
FrattiniC22×C4C22×D83
Fitting#339×C83C2
socleC22×C83C2×C22⋊C4
prime radicalC23×C83C2×D4
cosocleC22×C4×C83C23
hypercenter#339D83
hypocenterC83#1986
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
9. #14581791C4semidirect
10. #14581791C4semidirect
11. #14581783C4semidirect
12. #14581783C4semidirect
33. #13050574Q8semidirect
55. M16×C83Q8semidirect
115. C83#1986semidirect
152. M16Dic166semidirect

Maximal subgroups

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

subgroupindex
#191282542
M16×Dic832
C4×Dic83⋊C42
#191274622
#191274612
#191274602
#339×C832
#198683