Finite Group Databasebeta

← #24912832

Subgroups — #24912832

Order 10624.

484 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 161 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×#14581757C212yesmaximal
2#19127634C212yesmaximal
3#19127631C211yesmaximal, characteristic
4#19127605C212yesmaximal
5#19127605C212yesmaximal
6#19127598C212yesmaximal
7#19127596C212yesmaximal
8#19127570C211yesmaximal, characteristic
9#398×C83C211yesmaximal, characteristic
10C22×Dic166C2212yes—
11#14581757—28no—
12C2×C4⋊Dic83C2211yescharacteristic
13C2×C4⋊Dic83C2211yescharacteristic
14C2×Dic83⋊C4C2212yes—
15C2×Dic83⋊C4C2212yes—
16C2×Dic83⋊C4C2212yes—
17C2×Dic83⋊C4C2212yes—
18C2×Dic83⋊C4C2212yes—
19C2×C4×Dic83C2212yes—
20C2×C4×Dic83C2212yes—
21C2×C4×Dic83C2211yescharacteristic
22C83⋊#95C2212yes—
23C83⋊#95C2212yes—
24C83⋊#95C2212yes—
25C83⋊#95C2211yescharacteristic
26C83⋊#95C2212yes—
27C2×C4⋊C4×C83C2212yes—
28C2×C4⋊C4×C83C2211yescharacteristic
29C2×C4⋊C4×C83C2211yescharacteristic
30#95×C83C2212yes—
31#95×C83C2211yescharacteristic
32C2×Dic166—24no—
33C2×Dic166—24no—
34C2×Dic166Q818yescomplemented
35C22×Dic83C2312yes—
36C22×Dic83C2312yes—
37C22×Dic83C2312yes—
38C22×Dic83C2312yes—
39C4⋊Dic83—41no—
40C4⋊Dic83—41no—
41Dic83⋊C4—24no—
42Dic83⋊C4—24no—
43Dic83⋊C4—24no—
44Dic83⋊C4—24no—
45Dic83⋊C4—42no—
46C4×Dic83—24no—
47C4×Dic83—24no—
48C4×Dic83D414yes—
49C22×C4×C83C2311yescharacteristic
50C22×C4×C83C2311yescharacteristic
51C22×C4×C83C2312yes—
52C22×C4×C83C2311yescharacteristic
53C22×C4×C83C2312yes—
54C4⋊C4×C83—24no—
55C4⋊C4×C83—41no—
56C4⋊C4×C83—41no—
57C23×C83C2411yescharacteristic
58C2×C4×C83—22no—
59C2×C4×C83—22no—
60C2×C4×C83—21no—
61C2×C4×C83—21no—
62C2×C4×C83—22no—
63C2×C4×C83—22no—
64C2×C4×C83—22no—
65C2×C4×C83—21no—
66C2×C4×C83—22no—
67C2×C4×C83—21no—
68C2×C4×C83—22no—
69C2×C4×C83C2×D412yes—
70C2×C4×C83C2×Q814yes—
71C2×Dic83—22no—
72C2×Dic83—22no—
73C2×Dic83—22no—
74C2×Dic83—22no—
75C2×Dic83—22no—
76C2×Dic83—22no—
77C2×Dic83—22no—
78C2×Dic83—22no—
79C2×Dic83C2×D414yes—
80C2×Dic83C2×Q814yes—
81C2×Dic83C2×Q814yes—
82C2×Dic83#4114yes—
83Dic166—216no—
84C22×C83C22×D411yescharacteristic
85C22×C83C22×Q812yes—
86C22×C83C2×#4112yes—
87C22×C83H(5,𝔽2)11yescharacteristic
88C22×C832−1+411yescharacteristic
89C4×C83—24no—
90C4×C83—22no—
91C4×C83—42no—
92C4×C83—41no—
93C4×C83—41no—
94Dic83—24no—
95Dic83—42no—
96Dic83—42no—
97Dic83C22⋊Q818yes—
98C2×C83C2×C22⋊Q812yes—
99C2×C83#53711yescharacteristic
100C2×C83#55712yes—
101C2×C83Q8211yescharacteristic
102C2×C83#55911yescharacteristic
103#2582—831nomaximal, Sylow
104C83#258211yescharacteristic, complemented, Sylow
105C2×C4×Q8—832no—
106#398—831no—
107#398—832no—
108#398D8311yescharacteristic
109#391—832no—
110#391—832no—
111#389—832no—
112#389—832no—
113#384—831no—
114C22×Q8—832no—
115C4×Q8—1668no—
116C2×C4⋊C4—831no—
117C2×C4⋊C4—832no—
118C2×C4⋊C4—831no—
119C2×C4⋊C4—832no—
120C2×C4⋊C4—832no—
121C2×C4⋊C4—832no—
122C2×C4⋊C4—832no—
123C2×C4⋊C4C2×D8312yes—
124C2×C4⋊C4C2×D8311yescharacteristic
125C2×C4⋊C4C2×D8311yescharacteristic
126C2×C42—831no—
127C2×C42—832no—
128C2×C42—832no—
129#95—832no—
130#95—832no—
131#95—832no—
132#95—831no—
133#95—832no—
134#95C2×D8312yes—
135#95C2×D8311yescharacteristic
136C2×Q8—838no—
137C2×Q8—1664no—
138C2×Q8—1664no—
139C22×C4—832no—
140C22×C4—832no—
141C22×C4—832no—
142C22×C4—832no—
143C22×C4C22×D8311yescharacteristic
144C22×C4C22×D8311yescharacteristic
145C22×C4C22×D8312yes—
146C22×C4C22×D8311yescharacteristic
147C22×C4C22×D8312yes—
148C4⋊C4—24no—
149C4⋊C4—41no—
150C4⋊C4—41no—
151C4⋊C4—3322no—
152C4⋊C4—3321no—
153C4⋊C4—3321no—
154C4⋊C4—1664no—
155C4⋊C4—1664no—
156C4⋊C4—1664no—
157C4⋊C4—1664no—
158C42—834no—
159C42—1664no—
160C42—1664no—
161C23C23×D8311yescharacteristic
162Q8—16616no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—834no—
175C2×C4—834no—
176C2×C4—834no—
177C2×C4—834no—
178C2×C4—1662no—
179C2×C4—1662no—
180C2×C4—1662no—
181C2×C4—1662no—
182C2×C4—1662no—
183C2×C4—1662no—
184C2×C4—1662no—
185C2×C4—1662no—
186C2×C4D4×D8312yes—
187C2×C4Q8×D8314yes—
188C22C2×D4×D8311yescharacteristic
189C22C2×Q8×D8312yes—
190C22#41×D8312yes—
191C22#1458183711yescharacteristic
192C22#1458183911yescharacteristic
193C4—24no—
194C4—22no—
195C4—41no—
196C4—41no—
197C4—42no—
198C4—3322no—
199C4—3322no—
200C4—838no—
201C4—1664no—
202C2C22⋊Q8×D8312yes—
203C2#1912827811yescharacteristic
204C2#1912842812yes—
205C2#1912843111yescharacteristic
206C2#1912843511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, prime radical, cosocleC23×C83C24
Fitting#398×C83C2
hypercenter#398D83
hypocenterC83#2582
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
34. C2×Dic166Q8semidirect
104. C83#2582semidirect

Maximal subgroups

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

subgroupindex
C2×#145817572
#191276342
#191276312
#191276052
#191275982
#191275962
#191275702
#398×C832
#258283