Finite Group Databasebeta

← #24912701

Subgroups — #24912701

Order 10624.

380 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 141 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#19127643C212yesmaximal
2#19127640C211yesmaximal, characteristic
3#19127598C212yesmaximal
4#19127596C212yesmaximal
5#19127570C211yesmaximal, characteristic
6#19127565C212yesmaximal
7#19127565C212yesmaximal
8#19127552C212yesmaximal
9#400×C83C211yesmaximal, characteristic
10C2×C4⋊Dic83C2211yescharacteristic
11C2×C4⋊Dic83C2211yescharacteristic
12C2×Dic83⋊C4C2212yes—
13C2×Dic83⋊C4C2212yes—
14C2×Dic83⋊C4C2212yes—
15C2×Dic83⋊C4C2212yes—
16C2×Dic83⋊C4C2212yes—
17C2×C4×Dic83C2212yes—
18C2×C4×Dic83C2212yes—
19C2×C4×Dic83C2211yescharacteristic
20C83⋊#95C2212yes—
21C83⋊#95C2211yescharacteristic
22C83⋊#95C2212yes—
23C83⋊#95C2212yes—
24C83⋊#95C2212yes—
25C83⋊#95C2212yes—
26C2×C4⋊C4×C83C2211yescharacteristic
27C2×C4⋊C4×C83C2211yescharacteristic
28#95×C83C2212yes—
29#95×C83C2211yescharacteristic
30#95×C83C2212yes—
31C22×Dic83C2312yes—
32C22×Dic83C2312yes—
33C22×Dic83C2312yes—
34C22×Dic83C2312yes—
35C4⋊Dic83—41no—
36C4⋊Dic83—41no—
37Dic83⋊C4—24no—
38Dic83⋊C4—24no—
39Dic83⋊C4—24no—
40Dic83⋊C4—24no—
41Dic83⋊C4—42no—
42C4×Dic83—24no—
43C4×Dic83—24no—
44C4×Dic83Q814yes—
45C22×C4×C83C2312yes—
46C22×C4×C83C2312yes—
47C22×C4×C83C2311yescharacteristic
48C22×C4×C83C2311yescharacteristic
49C22×C4×C83C2311yescharacteristic
50C4⋊C4×C83—41no—
51C4⋊C4×C83—41no—
52C23×C83C2411yescharacteristic
53C2×C4×C83—21no—
54C2×C4×C83—21no—
55C2×C4×C83—22no—
56C2×C4×C83—22no—
57C2×C4×C83—22no—
58C2×C4×C83—22no—
59C2×C4×C83—22no—
60C2×C4×C83—22no—
61C2×C4×C83—21no—
62C2×C4×C83—22no—
63C2×C4×C83—21no—
64C2×C4×C83—22no—
65C2×C4×C83C2×Q812yes—
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—22no—
75C2×Dic83C2×Q814yes—
76C2×Dic83#4114yes—
77C2×Dic83#4114yes—
78C22×C83C22×Q811yescharacteristic
79C22×C83C2×#4112yes—
80C22×C83C2×#4112yes—
81C22×C83H(5,𝔽2)11yescharacteristic
82C22×C832−1+411yescharacteristic
83C4×C83—22no—
84C4×C83—42no—
85C4×C83—42no—
86C4×C83—41no—
87C4×C83—41no—
88Dic83—42no—
89Dic83—42no—
90Dic83—42no—
91Dic83#12518yes—
92C2×C83C2×#12512yes—
93C2×C83#54411yescharacteristic
94C2×C83#55511yescharacteristic
95C2×C83#55612yes—
96C2×C83#55911yescharacteristic
97#2571—831nomaximal, Sylow
98C83#257111yescharacteristic, complemented, Sylow
99#400—831no—
100#400—832no—
101#400D8311yescharacteristic
102#389—832no—
103#389—832no—
104#384—831no—
105#382—832no—
106#382—832no—
107C4×C4⋊C4—832no—
108C2×C4⋊C4—831no—
109C2×C4⋊C4—832no—
110C2×C4⋊C4—831no—
111C2×C4⋊C4—832no—
112C2×C4⋊C4—832no—
113C2×C4⋊C4—832no—
114C2×C4⋊C4—832no—
115C2×C4⋊C4C2×D8311yescharacteristic
116C2×C4⋊C4C2×D8311yescharacteristic
117C2×C42—831no—
118C2×C42—832no—
119C2×C42—832no—
120#95—832no—
121#95—831no—
122#95—832no—
123#95—832no—
124#95—832no—
125#95—832no—
126#95C2×D8312yes—
127#95C2×D8311yescharacteristic
128#95C2×D8312yes—
129C22×C4—832no—
130C22×C4—832no—
131C22×C4—832no—
132C22×C4—832no—
133C22×C4C22×D8312yes—
134C22×C4C22×D8311yescharacteristic
135C22×C4C22×D8312yes—
136C22×C4C22×D8311yescharacteristic
137C22×C4C22×D8311yescharacteristic
138C4⋊C4—41no—
139C4⋊C4—41no—
140C4⋊C4—3322no—
141C4⋊C4—3321no—
142C4⋊C4—3321no—
143C4⋊C4—1664no—
144C4⋊C4—1664no—
145C4⋊C4—1664no—
146C4⋊C4—1664no—
147C42—834no—
148C42—1664no—
149C42—1664no—
150C23C23×D8311yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—21no—
162C2×C4—22no—
163C2×C4—834no—
164C2×C4—834no—
165C2×C4—834no—
166C2×C4—1662no—
167C2×C4—1662no—
168C2×C4—1662no—
169C2×C4—1662no—
170C2×C4—1662no—
171C2×C4—1662no—
172C2×C4—1662no—
173C2×C4—1662no—
174C2×C4—1662no—
175C2×C4Q8×D8312yes—
176C22C2×Q8×D8311yescharacteristic
177C22#41×D8312yes—
178C22#41×D8312yes—
179C22#1458183711yescharacteristic
180C22#1458183911yescharacteristic
181C4—22no—
182C4—42no—
183C4—42no—
184C4—41no—
185C4—41no—
186C4—3322no—
187C4—3322no—
188C4—3322no—
189C4—838no—
190C2#125×D8312yes—
191C2#1912833011yescharacteristic
192C2#1912841311yescharacteristic
193C2#1912841812yes—
194C2#1912843511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, prime radical, cosocleC23×C83C24
Fitting#400×C83C2
hypercenter#400D83
hypocenterC83#2571
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
98. C83#2571semidirect

Maximal subgroups

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

subgroupindex
#191276432
#191276402
#191275982
#191275962
#191275702
#191275652
#191275522
#400×C832
#257183