Finite Group Databasebeta

← #13124365

Subgroups — #13124365

Order 1664.

458 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 133 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
1#11719521C211yesmaximal, characteristic
2C22×#6107C211yesmaximal, characteristic, complemented
3C2×#88163C211yesmaximal, characteristic
4#11719221C211yesmaximal, characteristic, complemented
5C13×#419C211yesmaximal, characteristic, complemented
6#11718780C211yesmaximal, characteristic, complemented
7#11718663C211yesmaximal, characteristic
8#11718459C214yesmaximal, complemented
9#11718454C214yesmaximal, complemented
10C22×Q8×C13C2211yescharacteristic
11C2×#6127C2211yescharacteristic
12C22×Dic26C2211yescharacteristic
13C2×C13×M16C2211yescharacteristic
14C13×#117C2211yescharacteristic
15#88201C2212yes—
16#88200—22no—
17#88198C2212yes—
18C2×#6107—24no—
19C2×#6107C2214yes—
20#88183—22no—
21#88180C2211yescharacteristic
22C22×#1055C2211yescharacteristic
23#88163—24no—
24C2×Dic52C2212yes—
25C2×#6095C2212yes—
26#88141C2214yes—
27#88131—22no—
28C4×Dic26—22no—
29C13×#103C2214yes—
30#88054C2214yes—
31#88050C2212yes—
32#88049C2212yes—
33C2×Q8×C13—21no—
34C2×Q8×C13—22no—
35C2×Q8×C13—22no—
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—21no—
46C2×Dic26—22no—
47C2×Dic26D414yes—
48C2×Dic26C2311yescharacteristic
49C2×Dic26C2312yes—
50C13×M16—22no—
51C2×C8×C13C2312yes—
52C13×C4⋊C4C2312yes—
53C13×C22⋊C4—21no—
54C42×C13—21no—
55C22⋊Dic13D412yes—
56#6107—28no—
57#6103—24no—
58C4⋊Dic13D412yes—
59#6101—24no—
60#6101—24no—
61C4×Dic13—24no—
62C4×Dic13C2312yes—
63C2×#1055—22no—
64C2×#1055C2312yes—
65Dic52—24no—
66#6095—24no—
67#3044—131nomaximal, Sylow
68C23×C13C2×D411yescharacteristic
69C22×D13—21no—
70Q8×C13—22no—
71Q8×C13—22no—
72Q8×C13—42no—
73C2×C4×C13—22no—
74C2×C4×C13—22no—
75C2×C4×C13—42no—
76C2×C4×C13C2×D411yescharacteristic
77C2×C4×C13C2×D412yes—
78C2×C4×C13#4112yes—
79C2×C4×C13C2411yescharacteristic
80C22⋊D13—42no—
81C2×Dic13—24no—
82C2×Dic13—22no—
83C2×Dic13—21no—
84C2×Dic13C2×D414yes—
85D52—21no—
86D52—21no—
87C4×D13—42no—
88Dic26—24no—
89Dic26—22no—
90Dic26—21no—
91Dic26—21no—
92Dic26C2×D414yes—
93C8×C13—22no—
94#1055—22no—
95C2×#137—131no—
96C22×Q16—131no—
97#536—131no—
98#519—131no—
99#464—134no—
100#462—134no—
101#424—131no—
102#419D1311yescharacteristic, complemented
103#416—131no—
104C22×C13—22no—
105C22×C13#12112yes—
106C22×C13C22×D411yescharacteristic
107C2×D13—41no—
108C2×D13—42no—
109C4×C13—42no—
110C4×C13—42no—
111C4×C13#12112yes—
112C4×C13C22×D411yescharacteristic
113C4×C13C2×#4111yescharacteristic
114Dic13—24no—
115Dic13—24no—
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×M16C2×D1311yescharacteristic
126C22×C8—131no—
127C4⋊Q8—132no—
128#124—132no—
129#123—262no—
130C22⋊Q8—262no—
131C4×Q8—134no—
132C4×Q8—262no—
133#117—131no—
134#117—262no—
135#117C2×D1311yescharacteristic
136C4⋊C8—134no—
137#103—132no—
138#103C2×D1314yes—
139#102—132no—
140C2×C13—22no—
141C2×C13C2×#12111yescharacteristic
142C2×C13#57812yes—
143D13—81no—
144#41—262no—
145#41—262no—
146C2×Q8—21no—
147C2×Q8—22no—
148C2×Q8—22no—
149C2×Q8—134no—
150C2×Q8—132no—
151C2×Q8—131no—
152C2×Q8—262no—
153C2×Q8—261no—
154C2×Q8C22×D1312yes—
155C2×D4—131no—
156C2×D4—261no—
157C22×C4—21no—
158C22×C4—261no—
159C22×C4—261no—
160C22×C4C22×D1311yescharacteristic
161Q16—264no—
162Q16—268no—
163SD16—264no—
164M16—22no—
165C2×C8—132no—
166C2×C8—262no—
167C2×C8C22×D1312yes—
168C4⋊C4—132no—
169C4⋊C4—264no—
170C4⋊C4—264no—
171C4⋊C4C22×D1312yes—
172C22⋊C4—21no—
173C22⋊C4—132no—
174C22⋊C4—264no—
175C42—21no—
176C42—132no—
177C42—264no—
178C13#304411yescharacteristic, complemented, Sylow
179C23—261no—
180C23D4×D1311yescharacteristic
181Q8—22no—
182Q8—22no—
183Q8—42no—
184Q8—134no—
185Q8—264no—
186Q8—262no—
187Q8—261no—
188Q8—261no—
189D4—261no—
190D4—261no—
191D4—522no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—42no—
195C2×C4—134no—
196C2×C4—264no—
197C2×C4—262no—
198C2×C4—261no—
199C2×C4—522no—
200C2×C4#612712yes—
201C2×C4D4×D1311yescharacteristic
202C2×C4D4×D1312yes—
203C2×C4C23×D1311yescharacteristic
204C8—22no—
205C8—262no—
206C22—22no—
207C22—521no—
208C22—522no—
209C22#8813812yes—
210C22C2×D4×D1311yescharacteristic
211C4—42no—
212C4—42no—
213C4—264no—
214C4—264no—
215C4—521no—
216C4#8813812yes—
217C4C2×#612711yescharacteristic
218C4C2×D4×D1311yescharacteristic
219C2—22no—
220C2—1041no—
221C2C2×#8813811yescharacteristic
222C2#1171948412yes—
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#419C2
socleC22×C13C22×D4
prime radicalC2×#6127C22
hypercenter#419D13
hypocenterC13#3044
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
2. C22×#6107C2semidirect
4. #11719221C2semidirect
5. C13×#419C2semidirect
6. #11718780C2semidirect
8. #11718459C2semidirect
9. #11718454C2semidirect
102. #419D13semidirect
178. C13#3044semidirect

Maximal subgroups

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

subgroupindex
#117195212
C22×#61072
C2×#881632
#117192212
C13×#4192
#117187802
#117186632
#117184592
#117184542
#304413