Finite Group Databasebeta

← #15767696

Subgroups — #15767696

Order 3328.

292 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 87 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#13115816C211yesmaximal, characteristic
2#13114989C211yesmaximal, characteristic
3#13113494C211yesmaximal, characteristic
4#13113491C211yesmaximal, characteristic
5#13112731C211yesmaximal, characteristic
6#13112664C211yesmaximal, characteristic
7C13×#1301C211yesmaximal, characteristic
8#11719175C2211yescharacteristic
9C13×#431C2211yescharacteristic
10C13×#423C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×#88054—21no—
13C2×#88054—21no—
14#11718593C2211yescharacteristic
15#11718586C2211yescharacteristic
16C2×C4⋊#1055C2211yescharacteristic
17#11718147—21no—
18#11718147—21no—
19#11718078—21no—
20#11718074—21no—
21#11718073—21no—
22#11718073—21no—
23C2×C13×M16—21no—
24C22×C8×C13—21no—
25C2×C42×C13C2311yescharacteristic
26#88180—21no—
27#88178—21no—
28#88178—21no—
29C2×C4×Dic13D411yescharacteristic
30C2×C4×Dic13D411yescharacteristic
31C22×#1055—21no—
32#88124—21no—
33#88123D411yescharacteristic
34#88123D411yescharacteristic
35C4×Dic26—21no—
36C4×Dic26—21no—
37C13×C4⋊C8—21no—
38C13×C4⋊C8—21no—
39C13×C4⋊C8—21no—
40C13×C4⋊C8—21no—
41C13×C4⋊C8—21no—
42C13×C22⋊C8—21no—
43C4×C8×C13—21no—
44#88071—21no—
45#88071—21no—
46C22⋊#1055—21no—
47#88054—42no—
48#88054—42no—
49C4⋊#1055—21no—
50C4⋊#1055—21no—
51C4⋊#1055—21no—
52C4×#1055—21no—
53#10628—131nomaximal, Sylow
54C22×C4×C13C2×D411yescharacteristic
55C22×C4×C13#4111yescharacteristic
56C22×C4×C13#4111yescharacteristic
57C22×Dic13—21no—
58C22×Dic13—21no—
59C2×Dic26—21no—
60C2×Dic26—21no—
61C13×M16—41no—
62C13×M16—41no—
63C2×C8×C13—41no—
64C2×C8×C13—41no—
65C2×C8×C13—41no—
66C2×C8×C13—41no—
67C2×C8×C13—41no—
68C42×C13C2×D411yescharacteristic
69C42×C13#4111yescharacteristic
70C42×C13#4111yescharacteristic
71C42×C13#4111yescharacteristic
72C22⋊Dic13—41no—
73C4⋊Dic13—21no—
74C4⋊Dic13—21no—
75C4⋊Dic13—21no—
76C4⋊Dic13—21no—
77#6101—41no—
78#6101—41no—
79C4×Dic13—21no—
80C4×Dic13—21no—
81C4×Dic13—41no—
82C4×Dic13SD1612yes—
83C4×Dic13Q1612yes—
84C2×#1055—41no—
85C2×#1055—41no—
86C2×#1055—41no—
87C2×#1055—41no—
88#1995—131no—
89#1843—131no—
90#1542—131no—
91#1542—131no—
92#1301—131no—
93#1301D1311yescharacteristic
94#1274—131no—
95C23×C13#12311yescharacteristic
96C2×C4×C13—41no—
97C2×C4×C13—41no—
98C2×C4×C13#12111yescharacteristic
99C2×C4×C13#12311yescharacteristic
100C2×C4×C13#12311yescharacteristic
101C2×C4×C13#12411yescharacteristic
102C2×C4×C13#12611yescharacteristic
103C2×C4×C13#12611yescharacteristic
104C2×C4×C13C2×SD1611yescharacteristic
105C2×C4×C13C2×Q1611yescharacteristic
106C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
107C2×C4×C13#13711yescharacteristic
108C2×Dic13—22no—
109C2×Dic13—22no—
110C2×Dic13—41no—
111C2×Dic13—41no—
112C2×Dic13—41no—
113C2×Dic13—41no—
114C2×Dic13—41no—
115C2×Dic13—41no—
116Dic26—81no—
117Dic26—81no—
118C8×C13—81no—
119C8×C13—81no—
120C8×C13—81no—
121#1055—81no—
122#1055—81no—
123#533—131no—
124#431—131no—
125#431C2×D1311yescharacteristic
126#423C2×D1311yescharacteristic
127C2×C4⋊C8—131no—
128C2×C4⋊C8—261no—
129C2×C4⋊C8—261no—
130C2×C4⋊C8C2×D1311yescharacteristic
131#376—131no—
132#339—261no—
133#339—261no—
134#333—261no—
135#333—261no—
136#332—261no—
137#332—261no—
138C22×C13—21no—
139C22×C13—21no—
140C22×C13#39711yescharacteristic
141C22×C13#48311yescharacteristic
142C22×C13#48411yescharacteristic
143C4×C13—21no—
144C4×C13—21no—
145C4×C13—21no—
146C4×C13—21no—
147C4×C13#46011yescharacteristic
148C4×C13#46211yescharacteristic
149C4×C13#48711yescharacteristic
150C4×C13#48911yescharacteristic
151Dic13—42no—
152Dic13—42no—
153Dic13—81no—
154Dic13—81no—
155C2×M16—21no—
156C22×C8—21no—
157C22×C8—261no—
158C4⋊Q8—131no—
159C4⋊Q8—131no—
160#125—261no—
161C22⋊Q8—261no—
162C22⋊Q8—261no—
163C4×Q8—261no—
164C4×Q8—261no—
165#117—261no—
166C2×C42—131no—
167C2×C42—131no—
168C2×C42C22×D1311yescharacteristic
169C4⋊C8—21no—
170C4⋊C8—21no—
171C4⋊C8—21no—
172C4⋊C8—21no—
173C4⋊C8—21no—
174C4⋊C8—261no—
175C4⋊C8—261no—
176C4⋊C8—261no—
177C4⋊C8—522no—
178C4⋊C8—522no—
179C22⋊C8—21no—
180C22⋊C8—261no—
181C4×C8—21no—
182C4×C8—261no—
183#95—261no—
184#95—261no—
185C2×C13—21no—
186C2×C13—21no—
187C2×C13#207211yescharacteristic
188C2×C13#208011yescharacteristic
189C2×C13#208011yescharacteristic
190C2×Q8—261no—
191C2×Q8—261no—
192C22×C4—261no—
193C22×C4—261no—
194C22×C4#612711yescharacteristic
195C22×C4D4×D1311yescharacteristic
196C22×C4#613111yescharacteristic
197M16—41no—
198M16—41no—
199C2×C8—41no—
200C2×C8—41no—
201C2×C8—41no—
202C2×C8—41no—
203C2×C8—41no—
204C2×C8—521no—
205C2×C8—521no—
206C2×C8—521no—
207C2×C8—521no—
208C4⋊C4—261no—
209C4⋊C4—261no—
210C4⋊C4—261no—
211C4⋊C4—261no—
212C4⋊C4—521no—
213C4⋊C4—521no—
214C22⋊C4—521no—
215C42—132no—
216C42—132no—
217C42—261no—
218C42—261no—
219C42—521no—
220C42#612711yescharacteristic
221C42#612711yescharacteristic
222C42D4×D1311yescharacteristic
223C42#612911yescharacteristic
224C13#1062811yescharacteristic, complemented, Sylow
225C23#8814811yescharacteristic
226Q8—1041no—
227Q8—1041no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—262no—
231C2×C4—262no—
232C2×C4—521no—
233C2×C4—521no—
234C2×C4—521no—
235C2×C4—521no—
236C2×C4—521no—
237C2×C4—521no—
238C2×C4#8813011yescharacteristic
239C2×C4#8813711yescharacteristic
240C2×C4#8813811yescharacteristic
241C2×C4#8813911yescharacteristic
242C2×C4#8814811yescharacteristic
243C2×C4#8815211yescharacteristic
244C2×C4#8816511yescharacteristic
245C2×C4SD16×D1311yescharacteristic
246C2×C4#8816911yescharacteristic
247C2×C4Q16×D1311yescharacteristic
248C8—81no—
249C8—81no—
250C8—81no—
251C8—1041no—
252C8—1041no—
253C22—21no—
254C22—21no—
255C22#1171833611yescharacteristic
256C22#1171852311yescharacteristic
257C22#1171854511yescharacteristic
258C4—21no—
259C4—21no—
260C4—21no—
261C4—21no—
262C4—522no—
263C4—522no—
264C4—1041no—
265C4—1041no—
266C4#1171842311yescharacteristic
267C4#1171842611yescharacteristic
268C4#1171845311yescharacteristic
269C4#1171845411yescharacteristic
270C2—21no—
271C2—21no—
272C2#1311624811yescharacteristic
273C2#1311629111yescharacteristic
274C2#1311629211yescharacteristic
subgroupG/H
centerC2×C4#88139
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1301C2
socleC22×C13#397
prime radicalC23×C13#123
hypercenter#1301D13
hypocenterC13#10628
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1301

Complements

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

NH ≅ G/Ntype
224. C13#10628semidirect

Maximal subgroups

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

subgroupindex
#131158162
#131149892
#131134942
#131134912
#131127312
#131126642
C13×#13012
#1062813