Finite Group Databasebeta

← #13120496

Subgroups — #13120496

Order 1664.

444 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 137 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
1C13×#393C211yesmaximal, characteristic
2#11718891C212yesmaximal, complemented
3#11718610C212yesmaximal
4#11718608C211yesmaximal, characteristic
5#11718604C211yesmaximal, characteristic
6C22⋊C4×Dic13C212yesmaximal
7#11718314C212yesmaximal, complemented
8#11718313C212yesmaximal, complemented
9#11718307C212yesmaximal, complemented
10C22×Q8×C13C2211yescharacteristic
11C23×Dic13C2211yescharacteristic
12C22×Dic26C2211yescharacteristic
13C2×C13×C22⋊C4C2212yes—
14C2×C13×C22⋊C4C2211yescharacteristic
15C2×C22⋊Dic13C2212yes—
16C2×C22⋊Dic13C2211yescharacteristic
17C2×C4⋊Dic13C2212yes—
18C2×#6101C2212yes—
19C2×#6101C2212yes—
20C2×C4×Dic13C2212yes—
21C2×C4×Dic13C2212yes—
22C13×#95C2212yes—
23C13×#95C2211yescharacteristic
24#88071C2212yes—
25#88071C2212yes—
26#88071C2212yes—
27#88071C2212yes—
28#88071C2212yes—
29#88071C2211yescharacteristic
30#88071C2212yes—
31C24×C13C2311yescharacteristic
32C2×Q8×C13—24no—
33C2×Q8×C13—41no—
34C22×C4×C13C2311yescharacteristic
35C22×C4×C13C2311yescharacteristic
36C22×C4×C13C2312yes—
37C22×C4×C13C2312yes—
38C22×Dic13—41no—
39C22×Dic13—41no—
40C22×Dic13Q814yescomplemented
41C22×Dic13C2312yes—
42C22×Dic13C2312yes—
43C22×Dic13C2312yes—
44C22×Dic13C2312yes—
45C2×Dic26—24no—
46C2×Dic26—41no—
47C13×C22⋊C4—24no—
48C13×C22⋊C4—41no—
49C22⋊Dic13—24no—
50C22⋊Dic13—41no—
51C4⋊Dic13—24no—
52#6101—24no—
53#6101—42no—
54C4×Dic13—42no—
55C4×Dic13—42no—
56#2607—131nomaximal, Sylow
57C23×C13—22no—
58C23×C13—22no—
59C23×C13—21no—
60C23×C13—21no—
61C23×C13C2×Q812yes—
62C23×C13C2411yescharacteristic
63Q8×C13—44no—
64C2×C4×C13—22no—
65C2×C4×C13—22no—
66C2×C4×C13—22no—
67C2×C4×C13—22no—
68C2×C4×C13—22no—
69C2×C4×C13—22no—
70C2×C4×C13—22no—
71C2×C4×C13—21no—
72C2×C4×C13—21no—
73C2×C4×C13#4114yes—
74C2×Dic13—22no—
75C2×Dic13—22no—
76C2×Dic13—22no—
77C2×Dic13—22no—
78C2×Dic13—22no—
79C2×Dic13—22no—
80C2×Dic13—22no—
81C2×Dic13—22no—
82C2×Dic13—22no—
83C2×Dic13—22no—
84C2×Dic13—44no—
85C2×Dic13C2×Q814yes—
86C2×Dic13#4114yes—
87Dic26—44no—
88#399—132no—
89#393—131no—
90#393D1311yescharacteristic
91#391—132no—
92#391—132no—
93#387—132no—
94#387—132no—
95#381—131no—
96C4×C22⋊C4—132no—
97C22×C13—24no—
98C22×C13—22no—
99C22×C13—41no—
100C22×C13—41no—
101C22×C13—42no—
102C22×C13C22×Q811yescharacteristic
103C22×C13C2×#4112yes—
104C22×C13C2×#4112yes—
105C22×C13H(5,𝔽2)11yescharacteristic
106C22×C13H(5,𝔽2)11yescharacteristic
107C4×C13—24no—
108C4×C13—41no—
109C4×C13—41no—
110C4×C13—42no—
111Dic13—24no—
112Dic13—24no—
113Dic13—42no—
114Dic13—42no—
115C22×Q8—131no—
116C22×Q8C2×D1311yescharacteristic
117C23×C4—131no—
118C2×C4⋊C4—132no—
119C2×C4⋊C4—132no—
120C2×C4⋊C4—132no—
121C2×C22⋊C4—132no—
122C2×C22⋊C4—131no—
123C2×C22⋊C4C2×D1312yes—
124C2×C22⋊C4C2×D1311yescharacteristic
125C2×C42—132no—
126C2×C42—132no—
127#95—132no—
128#95—132no—
129#95—132no—
130#95—132no—
131#95—131no—
132#95—132no—
133#95—132no—
134#95C2×D1311yescharacteristic
135#95C2×D1312yes—
136C2×C13—42no—
137C2×C13#53312yes—
138C2×C13#54311yescharacteristic
139C2×C13#55111yescharacteristic
140C2×C13#55111yescharacteristic
141C2×C13#55912yes—
142C24C22×D1311yescharacteristic
143C2×Q8—24no—
144C2×Q8—41no—
145C2×Q8—264no—
146C2×Q8—521no—
147C22×C4—132no—
148C22×C4—132no—
149C22×C4—134no—
150C22×C4—132no—
151C22×C4—132no—
152C22×C4—521no—
153C22×C4—521no—
154C22×C4C22×D1311yescharacteristic
155C22×C4C22×D1311yescharacteristic
156C22×C4C22×D1312yes—
157C22×C4C22×D1312yes—
158C4⋊C4—264no—
159C4⋊C4—264no—
160C4⋊C4—522no—
161C22⋊C4—24no—
162C22⋊C4—41no—
163C22⋊C4—264no—
164C22⋊C4—521no—
165C42—522no—
166C42—522no—
167C13#260711yescharacteristic, complemented, Sylow
168C23—22no—
169C23—21no—
170C23—22no—
171C23—21no—
172C23Q8×D1312yes—
173C23C23×D1311yescharacteristic
174Q8—44no—
175Q8—524no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—134no—
186C2×C4—134no—
187C2×C4—262no—
188C2×C4—262no—
189C2×C4—262no—
190C2×C4—262no—
191C2×C4—262no—
192C2×C4—262no—
193C2×C4—262no—
194C2×C4—262no—
195C2×C4—262no—
196C2×C4—262no—
197C2×C4—524no—
198C2×C4#612914yes—
199C22—24no—
200C22—22no—
201C22—41no—
202C22—41no—
203C22—42no—
204C22C2×#612912yes—
205C22#8825111yescharacteristic
206C22C2×Q8×D1311yescharacteristic
207C22#41×D1312yes—
208C22#8825611yescharacteristic
209C4—24no—
210C4—41no—
211C4—41no—
212C4—42no—
213C4—264no—
214C4—264no—
215C4—522no—
216C4—522no—
217C2—42no—
218C2#1171929211yescharacteristic
219C2#1171932712yes—
220C2#1171933911yescharacteristic
221C2#1171938411yescharacteristic
222C2#1171938612yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#393C2
prime radicalC24×C13C23
hypercenter#393D13
hypocenterC13#2607
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
2. #11718891C2semidirect
7. #11718314C2semidirect
8. #11718313C2semidirect
9. #11718307C2semidirect
40. C22×Dic13Q8semidirect
167. C13#2607semidirect

Maximal subgroups

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

subgroupindex
C13×#3932
#117188912
#117186102
#117186082
#117186042
C22⋊C4×Dic132
#117183142
#117183132
#117183072
#260713