Finite Group Databasebeta

← #24912868

Subgroups — #24912868

Order 10624.

412 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 145 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#19127621C211yesmaximal, characteristic
2#19127621C212yesmaximal
3#19127606C211yesmaximal, characteristic
4#19127605C212yesmaximal
5#19127596C212yesmaximal
6#19127586C212yesmaximal
7#19127584C212yesmaximal
8C4⋊C4×Dic83C212yesmaximal
9#398×C83C211yesmaximal, characteristic
10C22×Dic166C2211yescharacteristic
11C22×Dic166C2211yescharacteristic
12C2×C4⋊Dic83C2212yes—
13C2×Dic83⋊C4C2212yes—
14C2×Dic83⋊C4C2212yes—
15C2×Dic83⋊C4C2212yes—
16C2×C4×Dic83C2212yes—
17C2×C4×Dic83C2211yescharacteristic
18C2×C4×Dic83C2212yes—
19C83⋊#95C2212yes—
20C83⋊#95C2212yes—
21C83⋊#95C2212yes—
22C83⋊#95C2212yes—
23C83⋊#95C2212yes—
24C83⋊#95C2211yescharacteristic
25C83⋊#95C2212yes—
26C2×C4⋊C4×C83C2212yes—
27C2×C4⋊C4×C83C2211yescharacteristic
28C2×C4⋊C4×C83C2211yescharacteristic
29#95×C83C2211yescharacteristic
30#95×C83C2212yes—
31C2×Dic166—22no—
32C2×Dic166—24no—
33C2×Dic166—41no—
34C2×Dic166—41no—
35C2×Dic166—41no—
36C22×Dic83C2312yes—
37C22×Dic83C2312yes—
38C22×Dic83C2312yes—
39C22×Dic83C2312yes—
40C4⋊Dic83Q818yescomplemented
41Dic83⋊C4—24no—
42Dic83⋊C4—42no—
43Dic83⋊C4—42no—
44C4×Dic83—24no—
45C4×Dic83—41no—
46C4×Dic83—42no—
47C22×C4×C83C2311yescharacteristic
48C22×C4×C83C2311yescharacteristic
49C22×C4×C83C2312yes—
50C22×C4×C83C2312yes—
51C22×C4×C83C2311yescharacteristic
52C4⋊C4×C83—24no—
53C4⋊C4×C83—41no—
54C4⋊C4×C83—41no—
55C23×C83C2411yescharacteristic
56C2×C4×C83—22no—
57C2×C4×C83—22no—
58C2×C4×C83—21no—
59C2×C4×C83—21no—
60C2×C4×C83—22no—
61C2×C4×C83—22no—
62C2×C4×C83—22no—
63C2×C4×C83—21no—
64C2×C4×C83—22no—
65C2×C4×C83—21no—
66C2×C4×C83—22no—
67C2×C4×C83C2×Q814yes—
68C2×C4×C83#4112yes—
69C2×Dic83—22no—
70C2×Dic83—22no—
71C2×Dic83—22no—
72C2×Dic83—22no—
73C2×Dic83—22no—
74C2×Dic83—22no—
75C2×Dic83—22no—
76C2×Dic83—22no—
77C2×Dic83—22no—
78C2×Dic83C2×Q814yes—
79C2×Dic83C2×Q814yes—
80C2×Dic83#4114yes—
81Dic166—44no—
82Dic166—44no—
83C22×C83C22×Q812yes—
84C22×C83C2×#4112yes—
85C22×C83C2×#4111yescharacteristic
86C22×C83H(5,𝔽2)11yescharacteristic
87C22×C83H(5,𝔽2)11yescharacteristic
88C4×C83—24no—
89C4×C83—22no—
90C4×C83—42no—
91C4×C83—41no—
92C4×C83—41no—
93Dic83—24no—
94Dic83—24no—
95Dic83—24no—
96Dic83—42no—
97C2×C83#53312yes—
98C2×C83#53811yescharacteristic
99C2×C83#55111yescharacteristic
100C2×C83#55412yes—
101C2×C83Q8211yescharacteristic
102#2586—831nomaximal, Sylow
103C83#258611yescharacteristic, complemented, Sylow
104#398D8311yescharacteristic
105#395—831no—
106#395—832no—
107#391—831no—
108#391—832no—
109#389—832no—
110#387—832no—
111#387—832no—
112C4×C4⋊C4—832no—
113C22×Q8—831no—
114C22×Q8—831no—
115C2×C4⋊C4—832no—
116C2×C4⋊C4—832no—
117C2×C4⋊C4—832no—
118C2×C4⋊C4—832no—
119C2×C4⋊C4C2×D8312yes—
120C2×C4⋊C4C2×D8311yescharacteristic
121C2×C4⋊C4C2×D8311yescharacteristic
122C2×C42—831no—
123C2×C42—832no—
124C2×C42—832no—
125#95—832no—
126#95—832no—
127#95—831no—
128#95—832no—
129#95—832no—
130#95—832no—
131#95—832no—
132#95C2×D8311yescharacteristic
133#95C2×D8312yes—
134C2×Q8—3321no—
135C2×Q8—3321no—
136C2×Q8—3321no—
137C2×Q8—1664no—
138C2×Q8—1662no—
139C22×C4—832no—
140C22×C4—832no—
141C22×C4—832no—
142C22×C4—832no—
143C22×C4C22×D8311yescharacteristic
144C22×C4C22×D8311yescharacteristic
145C22×C4C22×D8312yes—
146C22×C4C22×D8312yes—
147C22×C4C22×D8311yescharacteristic
148C4⋊C4—24no—
149C4⋊C4—41no—
150C4⋊C4—41no—
151C4⋊C4—3322no—
152C4⋊C4—3322no—
153C4⋊C4—838no—
154C4⋊C4—1664no—
155C42—3321no—
156C42—3322no—
157C42—1664no—
158C23C23×D8311yescharacteristic
159Q8—3324no—
160Q8—3324no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—834no—
173C2×C4—834no—
174C2×C4—834no—
175C2×C4—1662no—
176C2×C4—1662no—
177C2×C4—1662no—
178C2×C4—1662no—
179C2×C4—1662no—
180C2×C4—1662no—
181C2×C4—1662no—
182C2×C4—1662no—
183C2×C4—1662no—
184C2×C4Q8×D8314yes—
185C2×C4#1305058912yes—
186C22C2×Q8×D8312yes—
187C22#41×D8312yes—
188C22C2×#1305058911yescharacteristic
189C22#1458183711yescharacteristic
190C22#1458183811yescharacteristic
191C4—24no—
192C4—22no—
193C4—41no—
194C4—41no—
195C4—42no—
196C4—3322no—
197C4—1664no—
198C4—1664no—
199C4—1664no—
200C2#1912825312yes—
201C2#1912828811yescharacteristic
202C2#1912837911yescharacteristic
203C2#1912840712yes—
204C2#1912843111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, prime radical, cosocleC23×C83C24
Fitting#398×C83C2
hypercenter#398D83
hypocenterC83#2586
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
40. C4⋊Dic83Q8semidirect
103. C83#2586semidirect

Maximal subgroups

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

subgroupindex
#191276212
#191276062
#191276052
#191275962
#191275862
#191275842
C4⋊C4×Dic832
#398×C832
#258683