Finite Group Databasebeta

← #24915263

Subgroups — #24915263

Order 10624.

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

normal subgroups only

This group has 384 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#19127631C212yesmaximal
2#19127622C212yesmaximal
3#19127621C211yesmaximal, characteristic
4#19127600C212yesmaximal
5#19127598C212yesmaximal
6#19127583C212yesmaximal
7#19127582C212yesmaximal
8#19127570C211yesmaximal, characteristic
9#398×C83C211yesmaximal, characteristic
10C22×Dic166C2211yescharacteristic
11C2×C4⋊Dic83C2211yescharacteristic
12C2×C4⋊Dic83C2212yes—
13C2×C4⋊Dic83C2212yes—
14C2×Dic83⋊C4C2212yes—
15C2×Dic83⋊C4C2212yes—
16C2×Dic83⋊C4C2212yes—
17C2×Dic83⋊C4C2212yes—
18C2×C4×Dic83C2211yescharacteristic
19C2×C4×Dic83C2212yes—
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×C83C2212yes—
30#95×C83C2211yescharacteristic
31C2×Dic166—42no—
32C2×Dic166—41no—
33C22×Dic83C2312yes—
34C22×Dic83C2312yes—
35C22×Dic83C2312yes—
36C22×Dic83C2312yes—
37C4⋊Dic83—42no—
38C4⋊Dic83—41no—
39C4⋊Dic83—42no—
40Dic83⋊C4—42no—
41Dic83⋊C4—42no—
42Dic83⋊C4—42no—
43Dic83⋊C4Q818yescomplemented
44C4×Dic83—22no—
45C4×Dic83—42no—
46C22×C4×C83C2311yescharacteristic
47C22×C4×C83C2312yes—
48C22×C4×C83C2311yescharacteristic
49C22×C4×C83C2312yes—
50C22×C4×C83C2311yescharacteristic
51C4⋊C4×C83—24no—
52C4⋊C4×C83—41no—
53C4⋊C4×C83—41no—
54C23×C83C2411yescharacteristic
55C2×C4×C83—22no—
56C2×C4×C83—21no—
57C2×C4×C83—22no—
58C2×C4×C83—21no—
59C2×C4×C83—22no—
60C2×C4×C83—21no—
61C2×C4×C83—22no—
62C2×C4×C83—21no—
63C2×C4×C83—22no—
64C2×C4×C83—22no—
65C2×C4×C83—22no—
66C2×C4×C83C2×Q814yes—
67C2×C4×C83#4112yes—
68C2×Dic83—22no—
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—
80Dic166—44no—
81C22×C83C22×Q812yes—
82C22×C83C2×#4111yescharacteristic
83C22×C83H(5,𝔽2)11yescharacteristic
84C22×C83H(5,𝔽2)12yes—
85C22×C832−1+411yescharacteristic
86C4×C83—22no—
87C4×C83—24no—
88C4×C83—42no—
89C4×C83—41no—
90C4×C83—41no—
91Dic83—24no—
92Dic83—24no—
93Dic83—42no—
94Dic83—42no—
95C2×C83#53911yescharacteristic
96C2×C83#54412yes—
97C2×C83#55412yes—
98C2×C83Q8211yescharacteristic
99C2×C83#56011yescharacteristic
100#2792—831nomaximal, Sylow
101C83#279211yescharacteristic, complemented, Sylow
102#398—832no—
103#398D8311yescharacteristic
104#395—831no—
105#395—832no—
106#389—832no—
107#389—832no—
108#387—832no—
109#387—832no—
110#384—831no—
111C22×Q8—831no—
112C2×C4⋊C4—832no—
113C2×C4⋊C4—831no—
114C2×C4⋊C4—832no—
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—832no—
123C2×C42—831no—
124#95—831no—
125#95—832no—
126#95—832no—
127#95—832no—
128#95—832no—
129#95—832no—
130#95C2×D8312yes—
131#95C2×D8311yescharacteristic
132C2×Q8—3321no—
133C2×Q8—3322no—
134C22×C4—832no—
135C22×C4—832no—
136C22×C4—832no—
137C22×C4—832no—
138C22×C4C22×D8312yes—
139C22×C4C22×D8311yescharacteristic
140C22×C4C22×D8311yescharacteristic
141C22×C4C22×D8312yes—
142C22×C4C22×D8311yescharacteristic
143C4⋊C4—24no—
144C4⋊C4—41no—
145C4⋊C4—41no—
146C4⋊C4—3322no—
147C4⋊C4—3322no—
148C4⋊C4—3322no—
149C4⋊C4—3321no—
150C4⋊C4—3322no—
151C4⋊C4—3322no—
152C4⋊C4—838no—
153C42—3322no—
154C42—1662no—
155C23C23×D8311yescharacteristic
156Q8—3324no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—21no—
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—834no—
169C2×C4—834no—
170C2×C4—1662no—
171C2×C4—1662no—
172C2×C4—1662no—
173C2×C4—1662no—
174C2×C4—1662no—
175C2×C4—1662no—
176C2×C4—1662no—
177C2×C4—1662no—
178C2×C4—1662no—
179C2×C4—1662no—
180C2×C4Q8×D8314yes—
181C2×C4#1305058912yes—
182C22C2×Q8×D8312yes—
183C22C2×#1305058911yescharacteristic
184C22#1458183711yescharacteristic
185C22#1458183812yes—
186C22#1458183911yescharacteristic
187C4—24no—
188C4—22no—
189C4—41no—
190C4—41no—
191C4—42no—
192C4—3322no—
193C4—3322no—
194C4—1664no—
195C4—1664no—
196C2#1912829611yescharacteristic
197C2#1912833112yes—
198C2#1912840912yes—
199C2#1912843111yescharacteristic
200C2#1912844111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, prime radical, cosocleC23×C83C24
Fitting#398×C83C2
hypercenter#398D83
hypocenterC83#2792
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
43. Dic83⋊C4Q8semidirect
101. C83#2792semidirect

Maximal subgroups

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

subgroupindex
#191276312
#191276222
#191276212
#191276002
#191275982
#191275832
#191275822
#191275702
#398×C832
#279283