Finite Group Databasebeta

← #24915288

Subgroups — #24915288

Order 10624.

344 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 344 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#19127643C212yesmaximal
2#19127643C212yesmaximal
3#19127631C211yesmaximal, characteristic
4#19127588C212yesmaximal
5#19127588C212yesmaximal
6#19127586C212yesmaximal
7#19127582C212yesmaximal
8#19127570C211yesmaximal, characteristic
9#400×C83C211yesmaximal, characteristic
10C2×C4⋊Dic83C2212yes—
11C2×C4⋊Dic83C2211yescharacteristic
12C2×C4⋊Dic83C2211yescharacteristic
13C2×Dic83⋊C4C2212yes—
14C2×Dic83⋊C4C2212yes—
15C2×Dic83⋊C4C2212yes—
16C2×C4×Dic83C2211yescharacteristic
17C2×C4×Dic83C2212yes—
18C83⋊#95C2212yes—
19C83⋊#95C2212yes—
20C83⋊#95C2212yes—
21C83⋊#95C2212yes—
22C83⋊#95C2212yes—
23C83⋊#95C2212yes—
24C83⋊#95C2212yes—
25C83⋊#95C2211yescharacteristic
26C2×C4⋊C4×C83C2211yescharacteristic
27C2×C4⋊C4×C83C2211yescharacteristic
28#95×C83C2212yes—
29#95×C83C2212yes—
30#95×C83C2211yescharacteristic
31C22×Dic83C2312yes—
32C22×Dic83C2312yes—
33C22×Dic83C2312yes—
34C22×Dic83C2312yes—
35C4⋊Dic83—24no—
36C4⋊Dic83—41no—
37C4⋊Dic83—41no—
38Dic83⋊C4—24no—
39Dic83⋊C4—24no—
40Dic83⋊C4—24no—
41C4×Dic83—22no—
42C4×Dic83—42no—
43C22×C4×C83C2312yes—
44C22×C4×C83C2312yes—
45C22×C4×C83C2311yescharacteristic
46C22×C4×C83C2311yescharacteristic
47C22×C4×C83C2311yescharacteristic
48C4⋊C4×C83—41no—
49C4⋊C4×C83—41no—
50C23×C83C2411yescharacteristic
51C2×C4×C83—21no—
52C2×C4×C83—21no—
53C2×C4×C83—22no—
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—24no—
62C2×C4×C83#4112yes—
63C2×Dic83—22no—
64C2×Dic83—22no—
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#4114yes—
75C22×C83C2×#4112yes—
76C22×C83C2×#4111yescharacteristic
77C22×C83H(5,𝔽2)11yescharacteristic
78C22×C832−1+411yescharacteristic
79C22×C832−1+412yes—
80C4×C83—22no—
81C4×C83—42no—
82C4×C83—41no—
83C4×C83—41no—
84C4×C83—42no—
85Dic83—24no—
86Dic83—42no—
87Dic83—42no—
88Dic83—42no—
89C2×C83#53911yescharacteristic
90C2×C83#54112yes—
91C2×C83#55212yes—
92C2×C83#55911yescharacteristic
93C2×C83#56311yescharacteristic
94#2794—831nomaximal, Sylow
95C83#279411yescharacteristic, complemented, Sylow
96#400—832no—
97#400—832no—
98#400D8311yescharacteristic
99#398—831no—
100#387—832no—
101#387—832no—
102#387—832no—
103#387—832no—
104#384—831no—
105C2×C4⋊C4—831no—
106C2×C4⋊C4—831no—
107C2×C4⋊C4—832no—
108C2×C4⋊C4—832no—
109C2×C4⋊C4—832no—
110C2×C4⋊C4—832no—
111C2×C4⋊C4C2×D8311yescharacteristic
112C2×C4⋊C4C2×D8311yescharacteristic
113C2×C42—832no—
114C2×C42—831no—
115#95—832no—
116#95—832no—
117#95—832no—
118#95—832no—
119#95—832no—
120#95—832no—
121#95—832no—
122#95—831no—
123#95C2×D8312yes—
124#95C2×D8312yes—
125#95C2×D8311yescharacteristic
126C22×C4—832no—
127C22×C4—832no—
128C22×C4—832no—
129C22×C4—832no—
130C22×C4C22×D8312yes—
131C22×C4C22×D8312yes—
132C22×C4C22×D8311yescharacteristic
133C22×C4C22×D8311yescharacteristic
134C22×C4C22×D8311yescharacteristic
135C4⋊C4—41no—
136C4⋊C4—41no—
137C4⋊C4—3321no—
138C4⋊C4—3321no—
139C4⋊C4—1664no—
140C4⋊C4—1664no—
141C4⋊C4—1664no—
142C4⋊C4—1664no—
143C42—3322no—
144C42—1662no—
145C23C23×D8311yescharacteristic
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—24no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—834no—
158C2×C4—1662no—
159C2×C4—1662no—
160C2×C4—1662no—
161C2×C4—1662no—
162C2×C4—1662no—
163C2×C4—1662no—
164C2×C4—1662no—
165C2×C4—1662no—
166C2×C4—1662no—
167C2×C4—1662no—
168C2×C4—1662no—
169C2×C4#1305059112yes—
170C22#41×D8312yes—
171C22C2×#1305059111yescharacteristic
172C22#1458183711yescharacteristic
173C22#1458183912yes—
174C22#1458183911yescharacteristic
175C4—22no—
176C4—41no—
177C4—41no—
178C4—42no—
179C4—42no—
180C4—3322no—
181C4—3322no—
182C4—3322no—
183C4—1664no—
184C2#1912830011yescharacteristic
185C2#1912830812yes—
186C2#1912838912yes—
187C2#1912843511yescharacteristic
188C2#1912845111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, prime radical, cosocleC23×C83C24
Fitting#400×C83C2
hypercenter#400D83
hypocenterC83#2794
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
95. C83#2794semidirect

Maximal subgroups

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

subgroupindex
#191276432
#191276312
#191275882
#191275862
#191275822
#191275702
#400×C832
#279483