Finite Group Databasebeta

← #15764255

Subgroups — #15764255

Order 3328.

500 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 97 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×#11718726C212yesmaximal
2#13115655C211yesmaximal, characteristic
3C2×#11718135C212yesmaximal
4#13112717C211yesmaximal, characteristic
5C13×#2822C211yesmaximal, characteristic
6C2×C13×#125C2212yes—
7C2×#88123C2211yescharacteristic
8C13×#400—22no—
9C13×#398—22no—
10C13×#398—22no—
11C13×#382C2211yescharacteristic
12#11718726—24no—
13#11718726—24no—
14C2×#88050—22no—
15C2×#88048—22no—
16C2×#88047—22no—
17C2×#88043C2211yescharacteristic
18C2×#88043C2212yes—
19#11718135—24no—
20C22×Dic26—21no—
21C13×#125—22no—
22C13×#125—22no—
23C13×#125—22no—
24C13×#125—22no—
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4D412yes—
29C2×C13×C4⋊C4D412yes—
30C2×C13×C4⋊C4D412yes—
31C2×C42×C13C2311yescharacteristic
32C2×C4⋊Dic13—22no—
33C22×#1055—22no—
34C22×#1055—21no—
35#88123—22no—
36#88123—21no—
37#88123D412yes—
38C13×#95—24no—
39C13×#95—22no—
40C13×#95—22no—
41#88050—44no—
42#88048—28no—
43#88047—28no—
44#88043—22no—
45#88043—22no—
46#88043D414yes—
47#10087—131nomaximal, Sylow
48C22×C4×C13—22no—
49C22×C4×C13—22no—
50C22×C4×C13—22no—
51C22×C4×C13C2×D412yes—
52C22×C4×C13C2×D411yescharacteristic
53C22×Dic13—41no—
54C2×Dic26—22no—
55C2×Dic26—42no—
56C2×Dic26—42no—
57C2×Dic26—41no—
58C13×C4⋊C4—22no—
59C13×C4⋊C4—22no—
60C13×C4⋊C4—22no—
61C13×C4⋊C4—22no—
62C13×C4⋊C4—42no—
63C13×C4⋊C4—42no—
64C13×C4⋊C4—42no—
65C13×C4⋊C4—42no—
66C13×C4⋊C4—42no—
67C13×C4⋊C4—82no—
68C42×C13C2×D411yescharacteristic
69C42×C13C2×D412yes—
70C42×C13#4111yescharacteristic
71C4⋊Dic13—24no—
72C4⋊Dic13—42no—
73C2×#1055—28no—
74C2×#1055—24no—
75C2×#1055—22no—
76C2×#1055—41no—
77C2×#1055—41no—
78C2×#501—132no—
79#2822D1311yescharacteristic
80#1960—131no—
81C2×#330—132no—
82#1295—131no—
83C23×C13#12011yescharacteristic
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13—24no—
87C2×C4×C13—42no—
88C2×C4×C13—42no—
89C2×C4×C13—42no—
90C2×C4×C13—42no—
91C2×C4×C13—42no—
92C2×C4×C13—44no—
93C2×C4×C13—44no—
94C2×C4×C13#12012yes—
95C2×C4×C13#12111yescharacteristic
96C2×C4×C13#12112yes—
97C2×C4×C13#12711yescharacteristic
98C2×Dic13—42no—
99C2×Dic13—81no—
100C2×Dic13—81no—
101Dic26—44no—
102Dic26—82no—
103#1055—28no—
104#1055—42no—
105C2×C4⋊Q8—131no—
106C2×#125C2×D1312yes—
107#501—264no—
108#501—264no—
109C2×#107—262no—
110C2×#106—262no—
111C2×#103—262no—
112C2×#97—132no—
113C2×#97—131no—
114#400—22no—
115#398—22no—
116#398—22no—
117#382C2×D1311yescharacteristic
118#330—264no—
119C22×C13#39211yescharacteristic
120C22×C13#45311yescharacteristic
121C22×C13#45411yescharacteristic
122C22×C13#45614yes—
123C4×C13—22no—
124C4×C13—22no—
125C4×C13—21no—
126C4×C13—21no—
127C4×C13—82no—
128C4×C13—82no—
129C4×C13—82no—
130Dic13—82no—
131C22×Q8—261no—
132C22×C8—262no—
133C22×C8—261no—
134C4⋊Q8—132no—
135C4⋊Q8—262no—
136C4⋊Q8—261no—
137#125—22no—
138#125—22no—
139#125—22no—
140#125—22no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—262no—
145C2×C4⋊C4C22⋊D1312yes—
146C2×C4⋊C4C22⋊D1312yes—
147C2×C4⋊C4C22⋊D1312yes—
148C2×C42C22×D1311yescharacteristic
149#107—268no—
150#106—268no—
151#103—524no—
152#97—134no—
153#97—262no—
154#97—262no—
155#95—24no—
156#95—22no—
157#95—22no—
158C2×C13#166012yes—
159C2×C13#166312yes—
160C2×C13#200512yes—
161C2×C13#200611yescharacteristic
162C2×Q8—262no—
163C2×Q8—522no—
164C2×Q8—522no—
165C2×Q8—521no—
166C22×C4—22no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—521no—
170C22×C4C2×C22⋊D1312yes—
171C22×C4C2×C22⋊D1311yescharacteristic
172C2×C8—268no—
173C2×C8—264no—
174C2×C8—262no—
175C2×C8—521no—
176C2×C8—521no—
177C4⋊C4—22no—
178C4⋊C4—22no—
179C4⋊C4—22no—
180C4⋊C4—22no—
181C4⋊C4—42no—
182C4⋊C4—42no—
183C4⋊C4—42no—
184C4⋊C4—42no—
185C4⋊C4—42no—
186C4⋊C4—82no—
187C4⋊C4—264no—
188C4⋊C4—522no—
189C42D4×D1311yescharacteristic
190C42D4×D1312yes—
191C42#612911yescharacteristic
192C13#1008711yescharacteristic, complemented, Sylow
193C23#8820711yescharacteristic
194Q8—524no—
195Q8—1042no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—24no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—44no—
205C2×C4—44no—
206C2×C4—522no—
207C2×C4—1041no—
208C2×C4—1041no—
209C2×C4#8819112yes—
210C2×C4#8819211yescharacteristic
211C2×C4#8819312yes—
212C2×C4#8819411yescharacteristic
213C8—268no—
214C8—522no—
215C22#1171888411yescharacteristic
216C22#1171890211yescharacteristic
217C22#1171890611yescharacteristic
218C22#1171890714yes—
219C4—22no—
220C4—22no—
221C4—21no—
222C4—21no—
223C4—82no—
224C4—82no—
225C4—82no—
226C4—1042no—
227C2#1311414712yes—
228C2#1311416412yes—
229C2#1311587012yes—
230C2#1311587811yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2822C2
socle, prime radicalC23×C13#120
hypercenter#2822D13
hypocenterC13#10087
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2822

Complements

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

NH ≅ G/Ntype
192. C13#10087semidirect

Maximal subgroups

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

subgroupindex
C2×#117187262
#131156552
C2×#117181352
#131127172
C13×#28222
#1008713