Finite Group Databasebeta

← #24912449

Subgroups — #24912449

Order 10624.

540 conjugacy classes of subgroups; only the 185 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 185 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×#14581790C211yesmaximal, characteristic
2C2×#14581790C211yesmaximal, characteristic
3C2×Q8×Dic83C211yesmaximal, characteristic
4#19127634C214yesmaximal
5#19127608C211yesmaximal, characteristic
6#19127607C211yesmaximal, characteristic
7#19127596C214yesmaximal
8C4×Dic83⋊C4C211yesmaximal, characteristic
9C2×C4⋊Q8×C83C211yesmaximal, characteristic
10C22×Dic166C2211yescharacteristic
11#14581790—24no—
12#14581790—24no—
13Q8×Dic83—24no—
14C2×C4⋊Dic83C2211yescharacteristic
15C2×C4⋊Dic83C2212yes—
16C2×Dic83⋊C4C2212yes—
17C2×Dic83⋊C4C2214yes—
18C2×Dic83⋊C4C2212yes—
19C2×Dic83⋊C4C2212yes—
20C2×C4×Dic83C2211yescharacteristic
21C2×C4×Dic83C2212yes—
22C2×C4×Dic83C2211yescharacteristic
23C83⋊#95C2212yes—
24C83⋊#95C2214yes—
25C83⋊#95C2214yes—
26C22×Q8×C83C2211yescharacteristic
27C22×Q8×C83C2211yescharacteristic
28C4⋊Q8×C83—24no—
29C2×C4⋊C4×C83C2214yes—
30C2×C42×C83C2211yescharacteristic
31C2×Dic166—22no—
32C2×Dic166—22no—
33C2×Dic166—22no—
34C22×Dic83C2312yes—
35C22×Dic83C2312yes—
36C22×Dic83C2311yescharacteristic
37C22×Dic83C2312yes—
38C22×Dic83C2311yescharacteristic
39C4⋊Dic83—22no—
40C4⋊Dic83—24no—
41Dic83⋊C4—28no—
42Dic83⋊C4—24no—
43Dic83⋊C4—24no—
44Dic83⋊C4Q818yescomplemented
45C4×Dic83—22no—
46C4×Dic83—24no—
47C4×Dic83D414yes—
48C2×Q8×C83—22no—
49C2×Q8×C83—22no—
50C2×Q8×C83—22no—
51C2×Q8×C83—22no—
52C2×Q8×C83—22no—
53C2×Q8×C83D414yes—
54C22×C4×C83C2312yes—
55C22×C4×C83C2312yes—
56C22×C4×C83C2312yes—
57C22×C4×C83C2311yescharacteristic
58C4⋊C4×C83—28no—
59C42×C83—22no—
60C23×C83C2411yescharacteristic
61Q8×C83—28no—
62Q8×C83—44no—
63C2×C4×C83—22no—
64C2×C4×C83—22no—
65C2×C4×C83—22no—
66C2×C4×C83—22no—
67C2×C4×C83—22no—
68C2×C4×C83—22no—
69C2×C4×C83—22no—
70C2×C4×C83C2×D412yes—
71C2×C4×C83C2×D414yes—
72C2×C4×C83C2×D412yes—
73C2×C4×C83C2×Q814yes—
74C2×C4×C83#4112yes—
75C2×Dic83—22no—
76C2×Dic83—22no—
77C2×Dic83—22no—
78C2×Dic83—22no—
79C2×Dic83—22no—
80C2×Dic83—22no—
81C2×Dic83—22no—
82C2×Dic83—24no—
83C2×Dic83C2×D412yes—
84C2×Dic83C2×D412yes—
85C2×Dic83C2×Q814yes—
86C2×Dic83C2×Q814yes—
87Dic166—44no—
88C22×C83C22×D411yescharacteristic
89C22×C83C22×D411yescharacteristic
90C22×C83C22×Q812yes—
91C22×C83C2×#4111yescharacteristic
92C22×C832−1+412yes—
93C4×C83—24no—
94C4×C83—24no—
95C4×C83—42no—
96C4×C83#12114yes—
97Dic83—22no—
98Dic83—24no—
99Dic83—42no—
100Dic83—42no—
101Dic83C4⋊Q814yescomplemented
102C2×C83C2×#12111yescharacteristic
103C2×C83C2×C4⋊Q811yescharacteristic
104C2×C83#53611yescharacteristic
105C2×C83D4×Q812yes—
106C2×C83#55712yes—
107#2546—831nomaximal, Sylow
108C83#254611yescharacteristic, complemented, Sylow
109C2×C4⋊Q8—831no—
110C2×C4⋊Q8—831no—
111C2×C4⋊Q8D8311yescharacteristic
112C2×C4×Q8—831no—
113#398—834no—
114#391—831no—
115#391—831no—
116#389—834no—
117C4×C4⋊C4—831no—
118C22×Q8—831no—
119C22×Q8C2×D8311yescharacteristic
120C22×Q8C2×D8311yescharacteristic
121C4⋊Q8—24no—
122C4⋊Q8—1664no—
123C4⋊Q8—1664no—
124C4×Q8—1664no—
125C2×C4⋊C4—832no—
126C2×C4⋊C4—831no—
127C2×C4⋊C4—832no—
128C2×C4⋊C4—832no—
129C2×C4⋊C4—834no—
130C2×C4⋊C4—832no—
131C2×C4⋊C4C2×D8314yes—
132C2×C42—831no—
133C2×C42—832no—
134C2×C42—831no—
135C2×C42C2×D8311yescharacteristic
136#95—832no—
137#95—834no—
138#95—834no—
139C2×Q8—22no—
140C2×Q8—22no—
141C2×Q8—22no—
142C2×Q8—22no—
143C2×Q8—22no—
144C2×Q8—1662no—
145C2×Q8—1662no—
146C2×Q8—1662no—
147C2×Q8C22⋊D8314yes—
148C22×C4—831no—
149C22×C4—832no—
150C22×C4—831no—
151C22×C4—832no—
152C22×C4—832no—
153C22×C4C22×D8312yes—
154C22×C4C22×D8312yes—
155C22×C4C22×D8312yes—
156C22×C4C22×D8311yescharacteristic
157C4⋊C4—28no—
158C4⋊C4—838no—
159C4⋊C4—1664no—
160C4⋊C4—1664no—
161C4⋊C4—1664no—
162C4⋊C4—1662no—
163C4⋊C4—1668no—
164C42—22no—
165C42—834no—
166C42—1664no—
167C42—1662no—
168C23C23×D8311yescharacteristic
169Q8—28no—
170Q8—44no—
171Q8—3324no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—832no—
180C2×C4—834no—
181C2×C4—832no—
182C2×C4—834no—
183C2×C4—1662no—
184C2×C4—1662no—
185C2×C4—1662no—
186C2×C4—1662no—
187C2×C4—1664no—
188C2×C4—1662no—
189C2×C4—1662no—
190C2×C4—1662no—
191C2×C4D4×D8312yes—
192C2×C4C2×C22⋊D8314yes—
193C2×C4C2×C22⋊D8312yes—
194C2×C4Q8×D8314yes—
195C2×C4#1305058912yes—
196C22C2×D4×D8311yescharacteristic
197C22C22×C22⋊D8311yescharacteristic
198C22C2×Q8×D8312yes—
199C22C2×#1305058911yescharacteristic
200C22#1458184012yes—
201C4—24no—
202C4—24no—
203C4—42no—
204C4—3322no—
205C4—3322no—
206C4—834no—
207C4—1664no—
208C4—1662no—
209C4#1458176414yes—
210C2C2×#1458176411yescharacteristic
211C2C4⋊Q8×D8311yescharacteristic
212C2#1912827611yescharacteristic
213C2Q8×C22⋊D8312yes—
214C2#1912842612yes—
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, prime radical, cosocleC23×C83C24
FittingC2×C4⋊Q8×C83C2
hypercenterC2×C4⋊Q8D83
hypocenterC83#2546
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
44. Dic83⋊C4Q8semidirect
101. Dic83C4⋊Q8semidirect
108. C83#2546semidirect

Maximal subgroups

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

subgroupindex
C2×#145817902
C2×Q8×Dic832
#191276342
#191276082
#191276072
#191275962
C4×Dic83⋊C42
C2×C4⋊Q8×C832
#254683