Finite Group Databasebeta

← #13124367

Subgroups — #13124367

Order 1664.

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

normal subgroups only

This group has 458 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×#88163C211yesmaximal, characteristic
2C22×Dic52C211yesmaximal, characteristic, complemented
3#11719231C211yesmaximal, characteristic
4#11719221C211yesmaximal, characteristic, complemented
5C13×#424C211yesmaximal, characteristic, complemented
6#11718781C211yesmaximal, characteristic, complemented
7#11718774C211yesmaximal, characteristic
8#11718510C214yesmaximal, complemented
9#11718506C214yesmaximal, complemented
10C2×#6127C2211yescharacteristic
11C22×Dic26C2211yescharacteristic
12C22×Dic26C2211yescharacteristic
13C2×C13×M16C2211yescharacteristic
14C22×C8×C13C2211yescharacteristic
15C13×#117C2211yescharacteristic
16#88180C2211yescharacteristic
17#88163—24no—
18C2×Dic52—24no—
19C2×Dic52C2214yes—
20C2×Dic52C2212yes—
21C2×#6095C2212yes—
22#88151—22no—
23#88141—22no—
24#88140—22no—
25#88131—22no—
26#88129C2212yes—
27#88123C2212yes—
28C4×Dic26C2214yes—
29C13×C4⋊C8C2214yes—
30#88061C2212yes—
31#88056C2214yes—
32#88056C2212yes—
33C22×C4×C13C2311yescharacteristic
34C2×C22⋊D13—21no—
35C22×Dic13—21no—
36C22×Dic13—21no—
37#6127—22no—
38#6127—22no—
39C2×D52C2311yescharacteristic
40C2×C4×D13—21no—
41C2×Dic26—21no—
42C2×Dic26—22no—
43C2×Dic26—22no—
44C2×Dic26—22no—
45C2×Dic26—21no—
46C2×Dic26D414yes—
47C2×Dic26C2311yescharacteristic
48C2×Dic26C2312yes—
49C2×Dic26C2312yes—
50C13×M16—22no—
51C2×C8×C13—22no—
52C2×C8×C13C2312yes—
53C2×C8×C13C2312yes—
54C13×C4⋊C4D412yes—
55C13×C22⋊C4D412yes—
56C42×C13C2312yes—
57C22⋊Dic13—21no—
58#6103—24no—
59C4⋊Dic13—24no—
60C4⋊Dic13C2312yes—
61#6101—24no—
62C4×Dic13—24no—
63C4×Dic13—21no—
64Dic52—28no—
65Dic52—24no—
66#6095—24no—
67#3044—131nomaximal, Sylow
68C23×C13C2×D411yescharacteristic
69C22×D13—21no—
70C2×C4×C13C2×D414yes—
71C2×C4×C13C2×D411yescharacteristic
72C2×C4×C13C2×D412yes—
73C2×C4×C13#4112yes—
74C2×C4×C13C2411yescharacteristic
75C22⋊D13—42no—
76C2×Dic13—24no—
77C2×Dic13—22no—
78C2×Dic13—22no—
79C2×Dic13—21no—
80C2×Dic13—22no—
81C2×Dic13—42no—
82D52—21no—
83D52—21no—
84C4×D13—42no—
85Dic26—24no—
86Dic26—22no—
87Dic26—22no—
88Dic26—21no—
89Dic26—22no—
90Dic26—21no—
91Dic26—42no—
92Dic26C2×D414yes—
93C8×C13—22no—
94C8×C13—22no—
95C2×#137—131no—
96C22×Q16—131no—
97#536—131no—
98#519—131no—
99#464—134no—
100#462—134no—
101#424D1311yescharacteristic, complemented
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#12112yes—
111C4×C13C22×D411yescharacteristic
112C4×C13C2×#4111yescharacteristic
113Dic13—24no—
114Dic13—42no—
115Dic13—41no—
116Dic13—42no—
117C2×#41—131no—
118C22×Q8—131no—
119C22×Q8—131no—
120#137—264no—
121C2×Q16—134no—
122C2×Q16—132no—
123C2×Q16—264no—
124C2×SD16—132no—
125C2×M16C2×D1311yescharacteristic
126C22×C8C2×D1311yescharacteristic
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⋊C8C2×D1314yes—
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—134no—
147C2×Q8—132no—
148C2×Q8—132no—
149C2×Q8—131no—
150C2×Q8—261no—
151C2×Q8—261no—
152C2×Q8—262no—
153C2×Q8—262no—
154C2×Q8—262no—
155C2×D4—131no—
156C2×D4—261no—
157C22×C4—261no—
158C22×C4—261no—
159C22×C4—261no—
160C22×C4C22×D1311yescharacteristic
161Q16—268no—
162Q16—264no—
163SD16—264no—
164M16—22no—
165C2×C8—22no—
166C2×C8C22×D1312yes—
167C2×C8C22×D1312yes—
168C4⋊C4—132no—
169C4⋊C4—264no—
170C4⋊C4—264no—
171C4⋊C4D5212yes—
172C22⋊C4—261no—
173C22⋊C4—264no—
174C22⋊C4D5212yes—
175C42—261no—
176C42—264no—
177C42C22×D1312yes—
178C13#304411yescharacteristic, complemented, Sylow
179C23—261no—
180C23C2×D5211yescharacteristic
181Q8—134no—
182Q8—264no—
183Q8—262no—
184Q8—262no—
185Q8—261no—
186Q8—262no—
187Q8—261no—
188Q8—522no—
189D4—261no—
190D4—261no—
191D4—522no—
192C2×C4—264no—
193C2×C4—262no—
194C2×C4—262no—
195C2×C4—262no—
196C2×C4—261no—
197C2×C4—522no—
198C2×C4—522no—
199C2×C4C2×D5214yes—
200C2×C4C2×D5211yescharacteristic
201C2×C4D4×D1312yes—
202C2×C4#613112yes—
203C2×C4C23×D1311yescharacteristic
204C8—22no—
205C8—22no—
206C22—22no—
207C22—522no—
208C22—521no—
209C22#8814912yes—
210C22C22×D5211yescharacteristic
211C4—24no—
212C4—264no—
213C4—522no—
214C4—521no—
215C4—522no—
216C4#8814912yes—
217C4C2×D4×D1311yescharacteristic
218C4C2×#613111yescharacteristic
219C2—22no—
220C2—1041no—
221C2C2×#8814911yescharacteristic
222C2#1171945812yes—
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#424C2
socleC22×C13C22×D4
prime radicalC2×#6127C22
hypercenter#424D13
hypocenterC13#3044
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
2. C22×Dic52C2semidirect
4. #11719221C2semidirect
5. C13×#424C2semidirect
6. #11718781C2semidirect
8. #11718510C2semidirect
9. #11718506C2semidirect
101. #424D13semidirect
178. C13#3044semidirect

Maximal subgroups

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

subgroupindex
C2×#881632
C22×Dic522
#117192312
#117192212
C13×#4242
#117187812
#117187742
#117185102
#117185062
#304413