Finite Group Databasebeta

← #13124366

Subgroups — #13124366

Order 1664.

458 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 149 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×#519C211yesmaximal, characteristic, complemented
2C22×#6107C211yesmaximal, characteristic, complemented
3C2×#88196C211yesmaximal, characteristic
4#11719231C211yesmaximal, characteristic
5#11718692C214yesmaximal, complemented
6#11718689C214yesmaximal, complemented
7#11718665C211yesmaximal, characteristic, complemented
8#11718663C211yesmaximal, characteristic
9#11718660C211yesmaximal, characteristic, complemented
10C22×Q8×C13C2211yescharacteristic
11C2×#6127C2211yescharacteristic
12C22×Dic26C2211yescharacteristic
13C4×Q8×C13—22no—
14C4×Q8×C13C2214yes—
15C13×#117—22no—
16C13×#117C2211yescharacteristic
17C13×#117C2211yescharacteristic
18C2×#6107—24no—
19C2×#6107C2214yes—
20C2×#6107C2212yes—
21#88196—24no—
22C2×#6106C2212yes—
23C2×#6099C2211yescharacteristic
24C22×#1055C2211yescharacteristic
25#88151—22no—
26#88140—22no—
27#88129C2212yes—
28#88123C2212yes—
29#88050C2212yes—
30#88050C2214yes—
31#88049C2212yes—
32C4⋊#1055C2214yes—
33C2×Q8×C13—21no—
34C2×Q8×C13—22no—
35C2×Q8×C13D414yes—
36C2×Q8×C13C2312yes—
37C22×C4×C13—21no—
38C22×C4×C13C2311yescharacteristic
39C2×C22⋊D13—21no—
40C22×Dic13—21no—
41#6127—22no—
42#6127—22no—
43C2×D52C2311yescharacteristic
44C2×C4×D13—21no—
45C2×Dic26—22no—
46C2×Dic26—22no—
47C2×Dic26—21no—
48C2×Dic26C2311yescharacteristic
49C2×Dic26C2312yes—
50C13×C4⋊C4—24no—
51C13×C4⋊C4D412yes—
52C13×C4⋊C4C2312yes—
53C13×C22⋊C4—21no—
54C13×C22⋊C4D412yes—
55C42×C13—24no—
56C42×C13—21no—
57C42×C13C2312yes—
58#6107—24no—
59#6107—28no—
60#6106—24no—
61#6103—24no—
62C4⋊Dic13—24no—
63#6099—22no—
64C2×#1055—22no—
65C2×#1055C2312yes—
66C2×#1055C2312yes—
67#3044—131nomaximal, Sylow
68C23×C13C2×D411yescharacteristic
69C22×D13—21no—
70Q8×C13—24no—
71Q8×C13—22no—
72Q8×C13C2×D414yes—
73C2×C4×C13—24no—
74C2×C4×C13—22no—
75C2×C4×C13—22no—
76C2×C4×C13C2×D414yes—
77C2×C4×C13C2×D411yescharacteristic
78C2×C4×C13C2×D412yes—
79C2×C4×C13#4112yes—
80C2×C4×C13C2411yescharacteristic
81C22⋊D13—42no—
82C2×Dic13—21no—
83C2×Dic13—22no—
84C2×Dic13—42no—
85D52—21no—
86D52—21no—
87C4×D13—42no—
88Dic26—22no—
89Dic26—21no—
90Dic26—22no—
91Dic26—21no—
92Dic26—42no—
93#1055—22no—
94#1055—22no—
95C2×#137—131no—
96C22×Q16—131no—
97#536—131no—
98#519D1311yescharacteristic, complemented
99#464—134no—
100#462—134no—
101#424—131no—
102#419—131no—
103#416—131no—
104C22×C13—22no—
105C22×C13#12112yes—
106C22×C13C22×D411yescharacteristic
107C2×D13—41no—
108C2×D13—42no—
109C4×C13—24no—
110C4×C13—24no—
111C4×C13—42no—
112C4×C13#12112yes—
113C4×C13C22×D411yescharacteristic
114C4×C13C2×#4111yescharacteristic
115Dic13—42no—
116Dic13—41no—
117C2×#41—131no—
118C22×Q8—131no—
119C22×Q8C2×D1311yescharacteristic
120#137—264no—
121C2×Q16—134no—
122C2×Q16—132no—
123C2×Q16—264no—
124C2×SD16—132no—
125C2×M16—131no—
126C22×C8—131no—
127C4⋊Q8—132no—
128#124—132no—
129#123—262no—
130C22⋊Q8—262no—
131C4×Q8—22no—
132C4×Q8C2×D1314yes—
133#117—22no—
134#117C2×D1311yescharacteristic
135#117C2×D1311yescharacteristic
136C4⋊C8—134no—
137#103—132no—
138#103—134no—
139#102—132no—
140C2×C13—22no—
141C2×C13C2×#12111yescharacteristic
142C2×C13#57812yes—
143D13—81no—
144#41—262no—
145#41—262no—
146C2×Q8—22no—
147C2×Q8—21no—
148C2×Q8—132no—
149C2×Q8—131no—
150C2×Q8—261no—
151C2×Q8—262no—
152C2×Q8—262no—
153C2×Q8D5214yes—
154C2×Q8C22×D1312yes—
155C2×D4—131no—
156C2×D4—261no—
157C22×C4—21no—
158C22×C4—261no—
159C22×C4—261no—
160C22×C4C22×D1311yescharacteristic
161Q16—268no—
162Q16—264no—
163SD16—264no—
164M16—262no—
165C2×C8—132no—
166C2×C8—132no—
167C2×C8—262no—
168C4⋊C4—24no—
169C4⋊C4—264no—
170C4⋊C4C22⋊D1312yes—
171C4⋊C4C22×D1312yes—
172C22⋊C4—21no—
173C22⋊C4—264no—
174C22⋊C4C22⋊D1312yes—
175C42—24no—
176C42—21no—
177C42C22×D1312yes—
178C13#304411yescharacteristic, complemented, Sylow
179C23—261no—
180C23C2×C22⋊D1311yescharacteristic
181Q8—24no—
182Q8—22no—
183Q8—262no—
184Q8—261no—
185Q8—262no—
186Q8—261no—
187Q8—522no—
188Q8C2×D5214yes—
189D4—261no—
190D4—261no—
191D4—522no—
192C2×C4—24no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—262no—
196C2×C4—261no—
197C2×C4—522no—
198C2×C4—522no—
199C2×C4C2×D5212yes—
200C2×C4#612712yes—
201C2×C4C2×C22⋊D1314yes—
202C2×C4C2×C22⋊D1311yescharacteristic
203C2×C4C23×D1311yescharacteristic
204C8—262no—
205C8—262no—
206C22—22no—
207C22—521no—
208C22—522no—
209C22#8818412yes—
210C22C22×C22⋊D1311yescharacteristic
211C4—24no—
212C4—24no—
213C4—42no—
214C4—521no—
215C4—522no—
216C4#8818412yes—
217C4C22×D5211yescharacteristic
218C4C2×#612711yescharacteristic
219C2—22no—
220C2—1041no—
221C2C2×#8818411yescharacteristic
222C2#1171954312yes—
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#519C2
socleC22×C13C22×D4
prime radicalC2×#6127C22
hypercenter#519D13
hypocenterC13#3044
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #519

Complements

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

NH ≅ G/Ntype
1. C13×#519C2semidirect
2. C22×#6107C2semidirect
5. #11718692C2semidirect
6. #11718689C2semidirect
7. #11718665C2semidirect
9. #11718660C2semidirect
98. #519D13semidirect
178. C13#3044semidirect

Maximal subgroups

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

subgroupindex
C13×#5192
C22×#61072
C2×#881962
#117192312
#117186922
#117186892
#117186652
#117186632
#117186602
#304413