Finite Group Databasebeta

← #24912676

Subgroups — #24912676

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×#14581791C211yesmaximal, characteristic
2C2×#14581757C211yesmaximal, characteristic
3#19127642C214yesmaximal
4#19127607C211yesmaximal, characteristic
5#19127606C211yesmaximal, characteristic
6#19127605C214yesmaximal
7#19127566C211yesmaximal, characteristic
8C4×Dic83⋊C4C211yesmaximal, characteristic
9#382×C83C211yesmaximal, characteristic
10C22×Dic166C2212yes—
11C22×Dic166C2211yescharacteristic
12#14581791—24no—
13#14581757—24no—
14C2×C4⋊Dic83C2211yescharacteristic
15C2×Dic83⋊C4C2212yes—
16C2×Dic83⋊C4C2212yes—
17C2×Dic83⋊C4C2212yes—
18C2×C4×Dic83C2211yescharacteristic
19C2×C4×Dic83C2212yes—
20C2×C4×Dic83C2211yescharacteristic
21C83⋊#95C2212yes—
22C83⋊#95C2214yes—
23C83⋊#95C2214yes—
24C83⋊#95C2214yes—
25C2×C4⋊C4×C83C2211yescharacteristic
26C2×C4⋊C4×C83C2211yescharacteristic
27C2×C42×C83C2211yescharacteristic
28#95×C83C2214yes—
29C2×Dic166—22no—
30C2×Dic166—22no—
31C2×Dic166—24no—
32C2×Dic166—28no—
33C2×Dic166Q814yescomplemented
34C22×Dic83C2312yes—
35C22×Dic83C2312yes—
36C22×Dic83C2311yescharacteristic
37C22×Dic83C2312yes—
38C22×Dic83C2311yescharacteristic
39C4⋊Dic83—22no—
40Dic83⋊C4—24no—
41Dic83⋊C4—24no—
42Dic83⋊C4—24no—
43C4×Dic83—22no—
44C4×Dic83—24no—
45C4×Dic83D414yes—
46C22×C4×C83C2312yes—
47C22×C4×C83C2312yes—
48C22×C4×C83C2312yes—
49C22×C4×C83C2311yescharacteristic
50C4⋊C4×C83—22no—
51C4⋊C4×C83—22no—
52C42×C83—22no—
53C23×C83C2411yescharacteristic
54C2×C4×C83—22no—
55C2×C4×C83—22no—
56C2×C4×C83—22no—
57C2×C4×C83—22no—
58C2×C4×C83—24no—
59C2×C4×C83—24no—
60C2×C4×C83—22no—
61C2×C4×C83C2×D412yes—
62C2×C4×C83C2×Q812yes—
63C2×C4×C83#4112yes—
64C2×Dic83—22no—
65C2×Dic83—22no—
66C2×Dic83—22no—
67C2×Dic83—22no—
68C2×Dic83—22no—
69C2×Dic83—22no—
70C2×Dic83—24no—
71C2×Dic83—22no—
72C2×Dic83C2×D412yes—
73C2×Dic83C2×D412yes—
74C2×Dic83C2×Q814yes—
75C2×Dic83#4114yes—
76Dic166—28no—
77Dic166—48no—
78C22×C83C22×D411yescharacteristic
79C22×C83C22×Q811yescharacteristic
80C22×C83C2×#4112yes—
81C22×C83C2×#4111yescharacteristic
82C22×C832−1+412yes—
83C4×C83—42no—
84C4×C83—42no—
85C4×C83—42no—
86C4×C83C22⋊Q814yes—
87Dic83—24no—
88Dic83—22no—
89Dic83—42no—
90Dic83—42no—
91Dic83#12414yes—
92C2×C83C2×C22⋊Q811yescharacteristic
93C2×C83C2×#12411yescharacteristic
94C2×C83#53611yescharacteristic
95C2×C83#55612yes—
96C2×C83#55712yes—
97#2568—831nomaximal, Sylow
98C83#256811yescharacteristic, complemented, Sylow
99C2×C4⋊Q8—831no—
100C2×C4×Q8—831no—
101#400—834no—
102#391—831no—
103#391—831no—
104#391—834no—
105#382—831no—
106#382D8311yescharacteristic
107C4×C4⋊C4—831no—
108C22×Q8—831no—
109C22×Q8—832no—
110C4⋊Q8—1664no—
111C4×Q8—1664no—
112C2×C4⋊C4—832no—
113C2×C4⋊C4—831no—
114C2×C4⋊C4—832no—
115C2×C4⋊C4—832no—
116C2×C4⋊C4C2×D8311yescharacteristic
117C2×C4⋊C4C2×D8311yescharacteristic
118C2×C42—831no—
119C2×C42—832no—
120C2×C42—831no—
121C2×C42C2×D8311yescharacteristic
122#95—832no—
123#95—834no—
124#95—834no—
125#95—834no—
126#95C2×D8314yes—
127C2×Q8—834no—
128C2×Q8—1664no—
129C2×Q8—1668no—
130C2×Q8—1662no—
131C2×Q8—1662no—
132C22×C4—831no—
133C22×C4—832no—
134C22×C4—831no—
135C22×C4—832no—
136C22×C4—832no—
137C22×C4C22×D8312yes—
138C22×C4C22×D8312yes—
139C22×C4C22×D8312yes—
140C22×C4C22×D8311yescharacteristic
141C4⋊C4—22no—
142C4⋊C4—22no—
143C4⋊C4—1664no—
144C4⋊C4—1664no—
145C4⋊C4—1664no—
146C4⋊C4—1662no—
147C42—22no—
148C42—834no—
149C42—1664no—
150C42—1662no—
151C23C23×D8311yescharacteristic
152Q8—3328no—
153Q8—1668no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—24no—
161C2×C4—832no—
162C2×C4—834no—
163C2×C4—832no—
164C2×C4—834no—
165C2×C4—1662no—
166C2×C4—1662no—
167C2×C4—1664no—
168C2×C4—1662no—
169C2×C4—1662no—
170C2×C4—1662no—
171C2×C4—1662no—
172C2×C4—1662no—
173C2×C4D4×D8312yes—
174C2×C4Q8×D8312yes—
175C2×C4#1305059012yes—
176C22C2×D4×D8311yescharacteristic
177C22C2×Q8×D8311yescharacteristic
178C22#41×D8312yes—
179C22C2×#1305059011yescharacteristic
180C22#1458183912yes—
181C4—42no—
182C4—42no—
183C4—42no—
184C4—3322no—
185C4—3322no—
186C4—834no—
187C4—1664no—
188C4—1662no—
189C4#1458177014yes—
190C2C2×#1458177011yescharacteristic
191C2#124×D8311yescharacteristic
192C2#1912827111yescharacteristic
193C2#1912841912yes—
194C2#1912842812yes—
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, prime radical, cosocleC23×C83C24
Fitting#382×C83C2
hypercenter#382D83
hypocenterC83#2568
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
33. C2×Dic166Q8semidirect
98. C83#2568semidirect

Maximal subgroups

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

subgroupindex
C2×#145817912
C2×#145817572
#191276422
#191276072
#191276062
#191276052
#191275662
C4×Dic83⋊C42
#382×C832
#256883