Finite Group Databasebeta

← #15775355

Subgroups — #15775355

Order 3328.

372 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 63 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#13116065C211yesmaximal, characteristic
2#13113838C212yesmaximal
3#13112842C212yesmaximal, complemented
4#13112780C211yesmaximal, characteristic, complemented
5C13×#2822C211yesmaximal, characteristic, complemented
6C2×C13×#125—21no—
7#11719215C2211yescharacteristic
8C13×#400—22no—
9C13×#398—21no—
10C13×#398—22no—
11C13×#398C2212yes—
12C13×#382C2211yescharacteristic
13#11718628—22no—
14#11718627—21no—
15C2×#88045—21no—
16#11718122C2211yescharacteristic
17#11718120C2212yes—
18#11718043—22no—
19C2×#6127—21no—
20C13×#125—42no—
21C13×#125—42no—
22C2×C13×C4⋊C4—21no—
23C2×C13×C4⋊C4—22no—
24C2×C13×C4⋊C4—21no—
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4D411yescharacteristic
28C2×C13×C4⋊C4D412yes—
29C2×C13×C4⋊C4C2311yescharacteristic
30C2×C42×C13D411yescharacteristic
31#88184—22no—
32C2×#6099—21no—
33#88151—41no—
34#88149—41no—
35C13×#95—22no—
36C13×#95—21no—
37C13×#95—22no—
38C13×#95—22no—
39C13×#95D412yes—
40C22⋊#1055—22no—
41#88050—41no—
42#88049—41no—
43#88049—42no—
44#88047—42no—
45#88045—42no—
46#12157—131nomaximal, Sylow
47C22×C4×C13—21no—
48C22×C4×C13—21no—
49C22×C4×C13—22no—
50C22×C4×C13—22no—
51C22×C4×C13C2×D411yescharacteristic
52C22×C4×C13C2×D412yes—
53C2×C22⋊D13—41no—
54#6127—41no—
55#6127—41no—
56#6127—41no—
57#6127—41no—
58C2×D52—21no—
59C2×D52—22no—
60C2×C4×D13—41no—
61C2×Dic26—21no—
62C13×C4⋊C4—41no—
63C13×C4⋊C4—42no—
64C13×C4⋊C4—41no—
65C13×C4⋊C4—42no—
66C13×C4⋊C4—44no—
67C13×C4⋊C4—42no—
68C13×C4⋊C4—42no—
69C13×C4⋊C4—42no—
70C13×C4⋊C4—81no—
71C42×C13—21no—
72C42×C13D812yes—
73#6103—42no—
74C4⋊Dic13—22no—
75#6099—41no—
76#6099—41no—
77C2×#1055—42no—
78C2×#1055—41no—
79#2822D1311yescharacteristic, complemented
80#2040—131no—
81#1610—132no—
82#1346—132no—
83#1324—131no—
84C23×C13#12011yescharacteristic
85C22×D13—41no—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—22no—
89C2×C4×C13—22no—
90C2×C4×C13—41no—
91C2×C4×C13—41no—
92C2×C4×C13—42no—
93C2×C4×C13—42no—
94C2×C4×C13—42no—
95C2×C4×C13—42no—
96C2×C4×C13—42no—
97C2×C4×C13—42no—
98C2×C4×C13—42no—
99C2×C4×C13—42no—
100C2×C4×C13—41no—
101C2×C4×C13C2×D811yescharacteristic
102C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
103C22⋊D13—81no—
104C22⋊D13—81no—
105C2×Dic13—41no—
106D52—41no—
107D52—41no—
108D52—82no—
109C4×D13—81no—
110C4×D13—81no—
111Dic26—41no—
112Dic26—41no—
113#1055—81no—
114#1055—82no—
115#537—131no—
116C2×#125—21no—
117#480—262no—
118C2×#104—261no—
119#417—261no—
120#400—22no—
121#398—21no—
122#398—22no—
123#398C2×D1312yes—
124#382C2×D1311yescharacteristic
125#343—131no—
126#327—262no—
127#324—132no—
128C22×C13—21no—
129C22×C13—21no—
130C22×C13#44711yescharacteristic
131C22×C13#45411yescharacteristic
132C22×C13B(4,𝔽2)11yescharacteristic
133C2×D13—81no—
134C2×D13—81no—
135C2×D13—81no—
136C4×C13—21no—
137C4×C13—21no—
138C4×C13—42no—
139C4×C13—42no—
140C4×C13—82no—
141C4×C13—82no—
142C4×C13—81no—
143Dic13—81no—
144C2×#41—261no—
145C2×M16—261no—
146#125—42no—
147#125—42no—
148C22⋊Q8—521no—
149#121—262no—
150#121—521no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4C22⋊D1311yescharacteristic
157C2×C4⋊C4C22⋊D1312yes—
158C2×C4⋊C4C22×D1311yescharacteristic
159C2×C42C22⋊D1311yescharacteristic
160#107—522no—
161#104—522no—
162#103—521no—
163#102—521no—
164#102—522no—
165C22⋊C8—262no—
166#95—22no—
167#95—21no—
168#95—22no—
169#95—22no—
170#95C22⋊D1312yes—
171C2×C13—21no—
172C2×C13—21no—
173C2×C13#159811yescharacteristic
174C2×C13#220111yescharacteristic
175C2×C13#220311yescharacteristic
176D13—161no—
177#41—521no—
178#41—521no—
179#41—521no—
180#41—521no—
181C2×Q8—261no—
182C2×D4—261no—
183C2×D4—262no—
184C2×D4—521no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—22no—
188C22×C4—22no—
189C22×C4—521no—
190C22×C4C2×C22⋊D1311yescharacteristic
191C22×C4C2×C22⋊D1312yes—
192M16—521no—
193M16—521no—
194C2×C8—522no—
195C2×C8—521no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—42no—
199C4⋊C4—42no—
200C4⋊C4—44no—
201C4⋊C4—42no—
202C4⋊C4—42no—
203C4⋊C4—42no—
204C4⋊C4—81no—
205C4⋊C4—262no—
206C22⋊C4—522no—
207C42—21no—
208C42#610412yes—
209C13#1215711yescharacteristic, complemented, Sylow
210C23—521no—
211C23#8820711yescharacteristic
212Q8—521no—
213Q8—521no—
214D4—521no—
215D4—521no—
216D4—1042no—
217D4—1041no—
218D4—1041no—
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—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—41no—
233C2×C4—42no—
234C2×C4—521no—
235C2×C4—1041no—
236C2×C4—1041no—
237C2×C4C2×#610411yescharacteristic
238C2×C4#8818611yescharacteristic
239C8—1041no—
240C8—1042no—
241C22—21no—
242C22—21no—
243C22—1041no—
244C22—1041no—
245C22—1041no—
246C22#1171887811yescharacteristic
247C22#1171890511yescharacteristic
248C22#1171890611yescharacteristic
249C4—21no—
250C4—21no—
251C4—42no—
252C4—42no—
253C4—82no—
254C4—82no—
255C4—81no—
256C4—1041no—
257C2—21no—
258C2—21no—
259C2—2081no—
260C2#1311377111yescharacteristic
261C2#1311684911yescharacteristic
262C2#1311685711yescharacteristic
subgroupG/H
centerC22#11718905
commutator, cosocleC2×C13×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2822C2
socleC22×C13B(4,𝔽2)
prime radical#11719215C22
hypercenter#2822D13
hypocenterC13#12157
LCSG ▷ C2×C13×C4⋊C4 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2822

Complements

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

NH ≅ G/Ntype
3. #13112842C2semidirect
4. #13112780C2semidirect
5. C13×#2822C2semidirect
79. #2822D13semidirect
209. C13#12157semidirect

Maximal subgroups

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

subgroupindex
#131160652
#131138382
#131128422
#131127802
C13×#28222
#1215713