Finite Group Databasebeta

← #24915643

Subgroups — #24915643

Order 10624.

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

normal subgroups only

This group has 332 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
1C83⋊#401C212yesmaximal
2#19127643C212yesmaximal
3#19127641C212yesmaximal
4#19127640C211yesmaximal, characteristic
5#19127634C212yesmaximal
6#19127621C212yesmaximal
7#19127606C211yesmaximal, characteristic
8#19127587C212yesmaximal
9#398×C83C211yesmaximal, characteristic
10C22×Dic166C2211yescharacteristic
11C2×C4⋊Dic83C2212yes—
12C2×C4⋊Dic83C2211yescharacteristic
13C2×Dic83⋊C4C2212yes—
14C2×Dic83⋊C4C2212yes—
15C2×C4×Dic83C2211yescharacteristic
16C83⋊#95C2212yes—
17C83⋊#95C2212yes—
18C83⋊#95C2212yes—
19C83⋊#95C2212yes—
20C83⋊#95C2212yes—
21C83⋊#95C2212yes—
22C83⋊#95C2212yes—
23C83⋊#95C2212yes—
24C83⋊#95C2212yes—
25C83⋊#95C2211yescharacteristic
26C2×C4⋊C4×C83C2212yes—
27C2×C4⋊C4×C83C2211yescharacteristic
28C2×C4⋊C4×C83C2211yescharacteristic
29#95×C83C2212yes—
30#95×C83C2211yescharacteristic
31C2×Dic166—22no—
32C2×Dic166—41no—
33C2×Dic166—41no—
34C22×Dic83C2312yes—
35C22×Dic83C2312yes—
36C22×Dic83C2312yes—
37C22×Dic83C2312yes—
38C4⋊Dic83—42no—
39C4⋊Dic83—41no—
40Dic83⋊C4—42no—
41Dic83⋊C4—42no—
42C4×Dic83—41no—
43C22×C4×C83C2312yes—
44C22×C4×C83C2311yescharacteristic
45C22×C4×C83C2311yescharacteristic
46C22×C4×C83C2312yes—
47C22×C4×C83C2311yescharacteristic
48C4⋊C4×C83—24no—
49C4⋊C4×C83—41no—
50C4⋊C4×C83—41no—
51C23×C83C2411yescharacteristic
52C2×C4×C83—21no—
53C2×C4×C83—21no—
54C2×C4×C83—22no—
55C2×C4×C83—22no—
56C2×C4×C83—21no—
57C2×C4×C83—22no—
58C2×C4×C83—21no—
59C2×C4×C83—22no—
60C2×C4×C83—22no—
61C2×C4×C83—22no—
62C2×C4×C83—22no—
63C2×C4×C83—22no—
64C2×C4×C83#4112yes—
65C2×Dic83—22no—
66C2×Dic83—22no—
67C2×Dic83—22no—
68C2×Dic83—22no—
69C2×Dic83—22no—
70C2×Dic83—22no—
71C2×Dic83—22no—
72C2×Dic83—22no—
73C2×Dic83—22no—
74C2×Dic83—24no—
75C2×Dic83—22no—
76Dic166—44no—
77C22×C83C2×#4111yescharacteristic
78C22×C83H(5,𝔽2)11yescharacteristic
79C22×C83H(5,𝔽2)11yescharacteristic
80C22×C832−1+412yes—
81C22×C832−1+412yes—
82C4×C83—22no—
83C4×C83—42no—
84C4×C83—42no—
85C4×C83—41no—
86C4×C83—41no—
87Dic83—42no—
88Dic83—42no—
89Dic83—42no—
90Dic83—42no—
91C2×C83#53811yescharacteristic
92C2×C83#54112yes—
93C2×C83#56311yescharacteristic
94C2×C83#56311yescharacteristic
95C2×C83#56312yes—
96#2833—831nomaximal, Sylow
97C83#283311yescharacteristic, complemented, Sylow
98#401—832no—
99#400—831no—
100#400—832no—
101#400—832no—
102#398—832no—
103#398D8311yescharacteristic
104#395—832no—
105#391—831no—
106#387—832no—
107C22×Q8—831no—
108C2×C4⋊C4—832no—
109C2×C4⋊C4—832no—
110C2×C4⋊C4—832no—
111C2×C4⋊C4—831no—
112C2×C4⋊C4C2×D8312yes—
113C2×C4⋊C4C2×D8311yescharacteristic
114C2×C4⋊C4C2×D8311yescharacteristic
115C2×C42—831no—
116#95—832no—
117#95—832no—
118#95—832no—
119#95—832no—
120#95—832no—
121#95—832no—
122#95—832no—
123#95—832no—
124#95—832no—
125#95—831no—
126#95C2×D8312yes—
127#95C2×D8311yescharacteristic
128C2×Q8—3321no—
129C2×Q8—3321no—
130C2×Q8—1662no—
131C22×C4—832no—
132C22×C4—832no—
133C22×C4—832no—
134C22×C4—832no—
135C22×C4C22×D8312yes—
136C22×C4C22×D8311yescharacteristic
137C22×C4C22×D8311yescharacteristic
138C22×C4C22×D8312yes—
139C22×C4C22×D8311yescharacteristic
140C4⋊C4—24no—
141C4⋊C4—41no—
142C4⋊C4—41no—
143C4⋊C4—3322no—
144C4⋊C4—3322no—
145C4⋊C4—3321no—
146C4⋊C4—3322no—
147C42—3321no—
148C23C23×D8311yescharacteristic
149Q8—3324no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—1662no—
163C2×C4—1662no—
164C2×C4—1662no—
165C2×C4—1662no—
166C2×C4—1662no—
167C2×C4—1662no—
168C2×C4—1662no—
169C2×C4—1662no—
170C2×C4—1664no—
171C2×C4—1662no—
172C2×C4—1662no—
173C2×C4#1305058912yes—
174C22C2×#1305058911yescharacteristic
175C22#1458183711yescharacteristic
176C22#1458183811yescharacteristic
177C22#1458183912yes—
178C22#1458184012yes—
179C4—22no—
180C4—41no—
181C4—41no—
182C4—42no—
183C4—42no—
184C4—3322no—
185C4—3322no—
186C4—3322no—
187C4—3322no—
188C2#1912828811yescharacteristic
189C2#1912831112yes—
190C2#1912845011yescharacteristic
191C2#1912845411yescharacteristic
192C2#1912845512yes—
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, prime radical, cosocleC23×C83C24
Fitting#398×C83C2
hypercenter#398D83
hypocenterC83#2833
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
97. C83#2833semidirect

Maximal subgroups

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

subgroupindex
C83⋊#4012
#191276432
#191276412
#191276402
#191276342
#191276212
#191276062
#191275872
#398×C832
#283383