Finite Group Databasebeta

← #24912847

Subgroups — #24912847

Order 10624.

468 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C2×#14581782C211yesmaximal, characteristic
2C2×#14581757C211yesmaximal, characteristic
3#19127632C211yesmaximal, characteristic
4#19127622C211yesmaximal, characteristic
5#19127621C211yesmaximal, characteristic
6#19127598C212yesmaximal
7#19127598C212yesmaximal
8#19127597C212yesmaximal
9#19127596C212yesmaximal
10#19127552C211yesmaximal, characteristic
11#398×C83C211yesmaximal, characteristic
12C22×Dic166C2211yescharacteristic
13#14581782—24no—
14#14581757—24no—
15C2×C4⋊Dic83C2212yes—
16C2×C4⋊Dic83C2211yescharacteristic
17C2×Dic83⋊C4C2211yescharacteristic
18C2×Dic83⋊C4C2211yescharacteristic
19C2×Dic83⋊C4C2212yes—
20C2×Dic83⋊C4C2212yes—
21C2×Dic83⋊C4C2211yescharacteristic
22C2×Dic83⋊C4C2211yescharacteristic
23C2×Dic83⋊C4C2212yes—
24C2×Dic83⋊C4C2212yes—
25C2×C4×Dic83C2212yes—
26C2×C4×Dic83C2212yes—
27C2×C4×Dic83C2211yescharacteristic
28C83⋊#95C2211yescharacteristic
29C83⋊#95C2212yes—
30C83⋊#95C2212yes—
31C83⋊#95C2212yes—
32C2×C4⋊C4×C83C2211yescharacteristic
33C2×C4⋊C4×C83C2211yescharacteristic
34C2×C4⋊C4×C83C2212yes—
35#95×C83C2211yescharacteristic
36#95×C83C2212yes—
37C2×Dic166—22no—
38C2×Dic166—24no—
39C22×Dic83C2311yescharacteristic
40C22×Dic83C2311yescharacteristic
41C22×Dic83C2311yescharacteristic
42C22×Dic83C2312yes—
43C22×Dic83C2312yes—
44C22×Dic83C2311yescharacteristic
45C4⋊Dic83—22no—
46C4⋊Dic83—24no—
47Dic83⋊C4—22no—
48Dic83⋊C4—22no—
49Dic83⋊C4—22no—
50Dic83⋊C4—22no—
51Dic83⋊C4—24no—
52Dic83⋊C4—24no—
53Dic83⋊C4—42no—
54Dic83⋊C4Q818yescomplemented
55C4×Dic83—24no—
56C4×Dic83—42no—
57C4×Dic83D414yes—
58C22×C4×C83C2311yescharacteristic
59C22×C4×C83C2312yes—
60C22×C4×C83C2311yescharacteristic
61C22×C4×C83C2311yescharacteristic
62C22×C4×C83C2312yes—
63C4⋊C4×C83—22no—
64C4⋊C4×C83—22no—
65C4⋊C4×C83—42no—
66C23×C83C2411yescharacteristic
67C2×C4×C83—22no—
68C2×C4×C83—22no—
69C2×C4×C83—22no—
70C2×C4×C83—22no—
71C2×C4×C83—21no—
72C2×C4×C83—21no—
73C2×C4×C83—22no—
74C2×C4×C83—21no—
75C2×C4×C83—22no—
76C2×C4×C83—22no—
77C2×C4×C83—21no—
78C2×C4×C83C2×D412yes—
79C2×C4×C83C2×Q814yes—
80C2×Dic83—22no—
81C2×Dic83—22no—
82C2×Dic83—22no—
83C2×Dic83—21no—
84C2×Dic83—22no—
85C2×Dic83—21no—
86C2×Dic83—21no—
87C2×Dic83—21no—
88C2×Dic83—22no—
89C2×Dic83—21no—
90C2×Dic83—21no—
91C2×Dic83C2×D412yes—
92C2×Dic83C2×D412yes—
93C2×Dic83C2×Q814yes—
94C2×Dic83C2×Q814yes—
95C2×Dic83#4114yes—
96Dic166—28no—
97C22×C83C22×D411yescharacteristic
98C22×C83C22×Q812yes—
99C22×C83C2×#4112yes—
100C22×C83H(5,𝔽2)11yescharacteristic
101C22×C832−1+411yescharacteristic
102C4×C83—22no—
103C4×C83—24no—
104C4×C83—41no—
105C4×C83—42no—
106C4×C83—41no—
107Dic83—24no—
108Dic83—22no—
109Dic83—24no—
110Dic83—41no—
111Dic83—41no—
112Dic83C4⋊Q814yes—
113C2×C83#52511yescharacteristic
114C2×C83C2×C4⋊Q811yescharacteristic
115C2×C83#53711yescharacteristic
116C2×C83#55412yes—
117C2×C83#55712yes—
118#2584—831nomaximal, Sylow
119C83#258411yescharacteristic, complemented, Sylow
120C2×#125—831no—
121C2×C4×Q8—831no—
122#398—831no—
123#398D8311yescharacteristic
124#395—831no—
125#395—831no—
126#389—832no—
127#389—832no—
128#389—832no—
129#389—832no—
130C4×C4⋊C4—831no—
131C22×Q8—831no—
132#125—1664no—
133C4×Q8—1664no—
134C2×C4⋊C4—832no—
135C2×C4⋊C4—832no—
136C2×C4⋊C4—832no—
137C2×C4⋊C4—831no—
138C2×C4⋊C4—831no—
139C2×C4⋊C4—831no—
140C2×C4⋊C4—831no—
141C2×C4⋊C4—831no—
142C2×C4⋊C4—832no—
143C2×C4⋊C4—832no—
144C2×C4⋊C4C2×D8311yescharacteristic
145C2×C4⋊C4C2×D8311yescharacteristic
146C2×C4⋊C4C2×D8312yes—
147C2×C42—832no—
148C2×C42—831no—
149C2×C42—832no—
150#95—831no—
151#95—832no—
152#95—832no—
153#95—832no—
154#95C2×D8311yescharacteristic
155#95C2×D8312yes—
156C2×Q8—1664no—
157C2×Q8—1662no—
158C22×C4—831no—
159C22×C4—832no—
160C22×C4—832no—
161C22×C4—831no—
162C22×C4—831no—
163C22×C4—831no—
164C22×C4C22×D8311yescharacteristic
165C22×C4C22×D8312yes—
166C22×C4C22×D8311yescharacteristic
167C22×C4C22×D8311yescharacteristic
168C22×C4C22×D8312yes—
169C4⋊C4—22no—
170C4⋊C4—22no—
171C4⋊C4—42no—
172C4⋊C4—3322no—
173C4⋊C4—838no—
174C4⋊C4—1664no—
175C4⋊C4—1662no—
176C4⋊C4—1662no—
177C4⋊C4—1662no—
178C4⋊C4—1662no—
179C4⋊C4—1664no—
180C4⋊C4—1664no—
181C4⋊C4—1662no—
182C42—3322no—
183C42—834no—
184C42—1664no—
185C23C23×D8311yescharacteristic
186Q8—1668no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—832no—
199C2×C4—834no—
200C2×C4—832no—
201C2×C4—834no—
202C2×C4—834no—
203C2×C4—1661no—
204C2×C4—1661no—
205C2×C4—1662no—
206C2×C4—1661no—
207C2×C4—1661no—
208C2×C4—1662no—
209C2×C4—1662no—
210C2×C4—1662no—
211C2×C4—1661no—
212C2×C4—1662no—
213C2×C4—1661no—
214C2×C4D4×D8312yes—
215C2×C4Q8×D8314yes—
216C22C2×D4×D8311yescharacteristic
217C22C2×Q8×D8312yes—
218C22#41×D8312yes—
219C22#1458183711yescharacteristic
220C22#1458183911yescharacteristic
221C4—24no—
222C4—22no—
223C4—41no—
224C4—42no—
225C4—41no—
226C4—3321no—
227C4—3321no—
228C4—834no—
229C4—1664no—
230C4—1664no—
231C4—1662no—
232C2#1912820911yescharacteristic
233C2C4⋊Q8×D8311yescharacteristic
234C2#1912828011yescharacteristic
235C2#1912840512yes—
236C2#1912842812yes—
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, prime radical, cosocleC23×C83C24
Fitting#398×C83C2
hypercenter#398D83
hypocenterC83#2584
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
54. Dic83⋊C4Q8semidirect
119. C83#2584semidirect

Maximal subgroups

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

subgroupindex
C2×#145817822
C2×#145817572
#191276322
#191276222
#191276212
#191275982
#191275972
#191275962
#191275522
#398×C832
#258483