Finite Group Databasebeta

← #15775513

Subgroups — #15775513

Order 3328.

372 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 59 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#13123108C211yesmaximal, characteristic, complemented
2#13113805C212yesmaximal
3#13112865C212yesmaximal, complemented
4#13112780C211yesmaximal, characteristic, complemented
5C13×#2040C211yesmaximal, characteristic
6C13×#537C2211yescharacteristic
7C2×C13×#104—21no—
8C13×#417—21no—
9C13×#382C2211yescharacteristic
10#11718701—22no—
11#11718647—21no—
12#11718640C2212yes—
13#11718597—21no—
14#11718321—22no—
15#11718317—22no—
16C13×#343C2211yescharacteristic
17#11718129—22no—
18#11718120C2212yes—
19C2×C13×#41—21no—
20C22×Dic26D412yes—
21C2×C13×M16—21no—
22C13×C22⋊Q8—41no—
23C13×#121—22no—
24C13×#121—41no—
25C2×C13×C4⋊C4D411yescharacteristic
26C2×C13×C4⋊C4C2311yescharacteristic
27C2×C42×C13D411yescharacteristic
28C2×#6105—42no—
29C2×C4⋊Dic13—21no—
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13—21no—
32C2×#6101—22no—
33C13×#104—42no—
34C13×#103—41no—
35C13×#102—41no—
36C13×#95—22no—
37#88071—22no—
38#88071—22no—
39#88071—21no—
40#88071—22no—
41#88071D412yes—
42C22⋊#1055—22no—
43#88050—42no—
44#12184—131nomaximal, Sylow
45C13×#41—41no—
46C13×#41—41no—
47C13×#41—41no—
48C13×#41—41no—
49C2×Q8×C13—21no—
50C2×D4×C13—21no—
51C2×D4×C13—22no—
52C2×D4×C13—41no—
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—41no—
56C22×C4×C13C2×D412yes—
57C22×C4×C13C2×D411yescharacteristic
58C22×Dic13—22no—
59C22×Dic13—22no—
60C2×Dic26—42no—
61C2×Dic26—82no—
62C13×M16—41no—
63C13×M16—41no—
64C2×C8×C13—41no—
65C13×C4⋊C4—22no—
66C13×C4⋊C4—41no—
67C13×C4⋊C4—41no—
68C13×C22⋊C4—42no—
69C42×C13—21no—
70C42×C13SD1612yescomplemented
71#6105—84no—
72C4⋊Dic13—81no—
73C4⋊Dic13—81no—
74C4⋊Dic13—81no—
75#6101—82no—
76C2×#1055—42no—
77#2844—131no—
78#2040D1311yescharacteristic
79#1604—132no—
80#1354—132no—
81#1324—131no—
82C23×C13—41no—
83C23×C13#12011yescharacteristic
84Q8×C13—41no—
85Q8×C13—41no—
86D4×C13—41no—
87D4×C13—41no—
88D4×C13—82no—
89D4×C13—81no—
90D4×C13—81no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13—41no—
96C2×C4×C13—41no—
97C2×C4×C13—42no—
98C2×C4×C13—42no—
99C2×C4×C13—41no—
100C2×C4×C13—41no—
101C2×C4×C13—81no—
102C2×C4×C13—81no—
103C2×C4×C13C2×SD1611yescharacteristic
104C2×C4×C13#13711yescharacteristic
105C2×Dic13—42no—
106C2×Dic13—42no—
107C2×Dic13—42no—
108C2×Dic13—42no—
109C2×Dic13—42no—
110C2×Dic13—42no—
111Dic26—44no—
112Dic26—82no—
113C8×C13—81no—
114#1055—82no—
115#537C2×D1311yescharacteristic
116#448—262no—
117C2×#104—21no—
118#417—21no—
119#400—262no—
120#400—261no—
121#395—132no—
122#395—262no—
123#382—261no—
124#382C2×D1311yescharacteristic
125#343C2×D1311yescharacteristic
126#327—262no—
127#324—132no—
128C22×C13—21no—
129C22×C13—21no—
130C22×C13—81no—
131C22×C13—81no—
132C22×C13—81no—
133C22×C13#44811yescharacteristic
134C22×C13#45411yescharacteristic
135C22×C13B(4,𝔽2)11yescharacteristic
136C4×C13—21no—
137C4×C13—21no—
138C4×C13—42no—
139C4×C13—42no—
140C4×C13—81no—
141C4×C13—81no—
142Dic13—82no—
143Dic13—82no—
144C2×#41—21no—
145C22×Q8—132no—
146C2×SD16—522no—
147C2×M16—21no—
148C22⋊Q8—41no—
149#121—22no—
150#121—41no—
151C2×C4⋊C4—261no—
152C2×C4⋊C4—261no—
153C2×C4⋊C4—261no—
154C2×C4⋊C4—262no—
155C2×C4⋊C4C22⋊D1311yescharacteristic
156C2×C4⋊C4C22×D1311yescharacteristic
157C2×C42C22⋊D1311yescharacteristic
158#104—42no—
159#103—41no—
160#103—522no—
161#102—41no—
162C22⋊C8—262no—
163#95—22no—
164#95—132no—
165#95—262no—
166#95—262no—
167#95—261no—
168#95—262no—
169C2×C13—21no—
170C2×C13—21no—
171C2×C13—161no—
172C2×C13#159911yescharacteristic
173C2×C13#219911yescharacteristic
174C2×C13#220311yescharacteristic
175#41—41no—
176#41—41no—
177#41—41no—
178#41—41no—
179C2×Q8—21no—
180C2×Q8—522no—
181C2×Q8—1042no—
182C2×D4—21no—
183C2×D4—22no—
184C2×D4—41no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—41no—
188C22×C4—262no—
189C22×C4—262no—
190C22×C4D4×D1312yes—
191C22×C4C2×C22⋊D1311yescharacteristic
192SD16—1044no—
193M16—41no—
194M16—41no—
195C2×C8—41no—
196C2×C8—522no—
197C4⋊C4—22no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—1042no—
201C4⋊C4—1041no—
202C4⋊C4—1041no—
203C4⋊C4—1041no—
204C22⋊C4—42no—
205C42—21no—
206C42#610512yescomplemented
207C13#1218411yescharacteristic, complemented, Sylow
208C23—41no—
209C23#8819111yescharacteristic
210Q8—41no—
211Q8—41no—
212Q8—524no—
213Q8—1042no—
214D4—41no—
215D4—41no—
216D4—82no—
217D4—81no—
218D4—81no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—81no—
230C2×C4—81no—
231C2×C4—522no—
232C2×C4—522no—
233C2×C4—522no—
234C2×C4—522no—
235C2×C4—522no—
236C2×C4—522no—
237C2×C4C2×#610511yescharacteristic
238C2×C4#8820511yescharacteristic
239C8—81no—
240C8—1042no—
241C22—21no—
242C22—21no—
243C22—81no—
244C22—81no—
245C22—81no—
246C22#1171869311yescharacteristic
247C22#1171870111yescharacteristic
248C22#1171872311yescharacteristic
249C4—21no—
250C4—21no—
251C4—42no—
252C4—42no—
253C4—81no—
254C4—81no—
255C4—1042no—
256C4—1042no—
257C2—21no—
258C2—21no—
259C2—161no—
260C2#1311377511yescharacteristic
261C2#1311683611yescharacteristic
262C2#1311685611yescharacteristic
subgroupG/H
centerC22#11718693
commutator, cosocleC2×C13×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2040C2
socleC22×C13B(4,𝔽2)
prime radicalC13×#537C22
hypercenter#2040D13
hypocenterC13#12184
LCSG ▷ C2×C13×C4⋊C4 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2040

Complements

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

NH ≅ G/Ntype
1. #13123108C2semidirect
3. #13112865C2semidirect
4. #13112780C2semidirect
70. C42×C13SD16semidirect
206. C42#6105semidirect
207. C13#12184semidirect

Maximal subgroups

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

subgroupindex
#131231082
#131138052
#131128652
#131127802
C13×#20402
#1218413