Finite Group Databasebeta

← #13120773

Subgroups — #13120773

Order 1664.

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

normal subgroups only

This group has 500 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
1C2×#88190C211yesmaximal, characteristic
2C2×#88142C211yesmaximal, characteristic, complemented
3C13×#390C211yesmaximal, characteristic
4#11718882C211yesmaximal, characteristic
5#11718635C211yesmaximal, characteristic, complemented
6#11718613C214yesmaximal, complemented
7#11718608C214yesmaximal, complemented
8#11718593C211yesmaximal, characteristic, complemented
9#11718590C211yesmaximal, characteristic, complemented
10C22×D4×C13C2211yescharacteristic
11C22×Dic26C2211yescharacteristic
12C22×Dic26C2212yes—
13C2×C13×C4⋊C4C2211yescharacteristic
14C2×C13×C22⋊C4C2214yes—
15C2×C42×C13C2211yescharacteristic
16C2×C22⋊Dic13C2212yes—
17C2×C22⋊Dic13C2212yes—
18C2×C22⋊Dic13C2214yes—
19#88190—24no—
20C2×C4⋊Dic13C2211yescharacteristic
21C2×#6101C2212yes—
22C2×C4×Dic13C2211yescharacteristic
23C2×C4×Dic13C2211yescharacteristic
24#88142—24no—
25#88071C2214yes—
26#88071C2212yes—
27#88071C2212yes—
28#88071C2214yes—
29C24×C13C2312yes—
30C2×D4×C13—22no—
31C2×D4×C13—22no—
32C2×D4×C13—22no—
33C22×C4×C13C2312yes—
34C22×C4×C13C2312yes—
35C22×C4×C13C2311yescharacteristic
36C22×Dic13C2312yes—
37C22×Dic13C2312yes—
38C22×Dic13C2312yes—
39C22×Dic13C2311yescharacteristic
40C22×Dic13C2311yescharacteristic
41C2×Dic26—22no—
42C2×Dic26—22no—
43C2×Dic26—22no—
44C2×Dic26—24no—
45C2×Dic26—44no—
46C13×C4⋊C4—22no—
47C13×C22⋊C4—44no—
48C42×C13—22no—
49C22⋊Dic13—24no—
50C22⋊Dic13—24no—
51C22⋊Dic13—44no—
52C4⋊Dic13—22no—
53#6101—24no—
54C4×Dic13—22no—
55C4×Dic13D414yes—
56#2640—131nomaximal, Sylow
57C23×C13—22no—
58C23×C13—22no—
59C23×C13—22no—
60C23×C13—24no—
61C23×C13—24no—
62C23×C13C2411yescharacteristic
63D4×C13—44no—
64C2×C4×C13—22no—
65C2×C4×C13—22no—
66C2×C4×C13—22no—
67C2×C4×C13—24no—
68C2×C4×C13—22no—
69C2×C4×C13C2×D412yes—
70C2×C4×C13#4112yes—
71C2×C4×C13#4112yes—
72C2×Dic13—22no—
73C2×Dic13—22no—
74C2×Dic13—22no—
75C2×Dic13—22no—
76C2×Dic13—22no—
77C2×Dic13—22no—
78C2×Dic13—22no—
79C2×Dic13—22no—
80C2×Dic13—24no—
81C2×Dic13—22no—
82C2×Dic13C2×D412yes—
83C2×Dic13C2×D412yes—
84Dic26—48no—
85Dic26—44no—
86C2×C4⋊Q8—131no—
87C2×#124—131no—
88#397—134no—
89#393—134no—
90#391—131no—
91#391—131no—
92#390—131no—
93#390D1311yescharacteristic
94#376—131no—
95C22×C13—42no—
96C22×C13—42no—
97C22×C13—42no—
98C22×C13—44no—
99C22×C13—44no—
100C22×C13C22×D411yescharacteristic
101C22×C13C2×#4111yescharacteristic
102C22×C13C2×#4111yescharacteristic
103C22×C13H(5,𝔽2)12yes—
104C22×C132−1+412yes—
105C4×C13—42no—
106C4×C13—42no—
107C4×C13#12414yes—
108Dic13—22no—
109Dic13—22no—
110Dic13—42no—
111Dic13—42no—
112Dic13—42no—
113C22×Q8—131no—
114C22×Q8—132no—
115C22×D4C2×D1311yescharacteristic
116C4⋊Q8—264no—
117#124—264no—
118C2×C4⋊C4—132no—
119C2×C4⋊C4—131no—
120C2×C4⋊C4C2×D1311yescharacteristic
121C2×C22⋊C4—132no—
122C2×C22⋊C4—132no—
123C2×C22⋊C4—134no—
124C2×C22⋊C4C2×D1314yes—
125C2×C42—131no—
126C2×C42—131no—
127C2×C42C2×D1311yescharacteristic
128#95—132no—
129#95—132no—
130#95—134no—
131#95—134no—
132C2×C13—82no—
133C2×C13C2×#12411yescharacteristic
134C2×C13#53511yescharacteristic
135C2×C13#53611yescharacteristic
136C2×C13#54212yes—
137C2×C13#54212yes—
138C24C22×D1312yes—
139C2×Q8—264no—
140C2×Q8—262no—
141C2×Q8—262no—
142C2×Q8—262no—
143C2×Q8—524no—
144C2×D4—22no—
145C2×D4—22no—
146C2×D4—22no—
147C22×C4—131no—
148C22×C4—131no—
149C22×C4—132no—
150C22×C4—132no—
151C22×C4—132no—
152C22×C4C22×D1312yes—
153C22×C4C22×D1312yes—
154C22×C4C22×D1311yescharacteristic
155C4⋊C4—22no—
156C4⋊C4—264no—
157C4⋊C4—262no—
158C22⋊C4—44no—
159C22⋊C4—264no—
160C22⋊C4—264no—
161C22⋊C4—524no—
162C42—22no—
163C42—134no—
164C42—262no—
165C13#264011yescharacteristic, complemented, Sylow
166C23—22no—
167C23—22no—
168C23—22no—
169C23—24no—
170C23—24no—
171C23C23×D1311yescharacteristic
172Q8—528no—
173Q8—524no—
174D4—44no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—24no—
179C2×C4—22no—
180C2×C4—132no—
181C2×C4—132no—
182C2×C4—262no—
183C2×C4—262no—
184C2×C4—262no—
185C2×C4—262no—
186C2×C4—262no—
187C2×C4—262no—
188C2×C4—262no—
189C2×C4—262no—
190C2×C4—264no—
191C2×C4—262no—
192C2×C4#612712yes—
193C2×C4D4×D1312yes—
194C2×C4#612912yes—
195C22—42no—
196C22—44no—
197C22—44no—
198C22—42no—
199C22—42no—
200C22C2×#612711yescharacteristic
201C22C2×D4×D1311yescharacteristic
202C22C2×#612911yescharacteristic
203C22#8825112yes—
204C22#8825712yes—
205C4—42no—
206C4—42no—
207C4—262no—
208C4—262no—
209C4—522no—
210C4—522no—
211C4—522no—
212C4#8813914yes—
213C2—82no—
214C2C2×#8813911yescharacteristic
215C2#1171926612yes—
216C2#1171930812yes—
217C2#1171938011yescharacteristic
218C2#1171942011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#390C2
prime radicalC22×D4×C13C22
hypercenter#390D13
hypocenterC13#2640
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×#88142C2semidirect
5. #11718635C2semidirect
6. #11718613C2semidirect
7. #11718608C2semidirect
8. #11718593C2semidirect
9. #11718590C2semidirect
165. C13#2640semidirect

Maximal subgroups

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

subgroupindex
C2×#881902
C2×#881422
C13×#3902
#117188822
#117186352
#117186132
#117186082
#117185932
#117185902
#264013