Finite Group Databasebeta

← #15775843

Subgroups — #15775843

Order 3328.

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

normal subgroups only

This group has 324 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#13116181C211yesmaximal, characteristic
2#13113877C211yesmaximal, characteristic
3#13113843C211yesmaximal, characteristic
4#13112863C211yesmaximal, characteristic
5#13112842C211yesmaximal, characteristic
6#13112782C211yesmaximal, characteristic
7C13×#2794C211yesmaximal, characteristic
8#11719205C2211yescharacteristic
9C13×#400—21no—
10C13×#400—21no—
11C13×#400C2211yescharacteristic
12C13×#398C2211yescharacteristic
13C13×#387—21no—
14C13×#387—21no—
15C13×#387—21no—
16C13×#387—21no—
17C13×#384C2211yescharacteristic
18#11718632—21no—
19#11718631—21no—
20#11718625—21no—
21#11718122C2211yescharacteristic
22#11718120C2211yescharacteristic
23#11718120C2211yescharacteristic
24#11718115—21no—
25#11718044—21no—
26#11718044—21no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C13×C4⋊C4C2311yescharacteristic
35C2×C42×C13—21no—
36C2×C42×C13D411yescharacteristic
37#88180—21no—
38#88178—21no—
39#88178—21no—
40C2×#6099—21no—
41#88144—41no—
42#88142—41no—
43C13×#95—21no—
44C13×#95—21no—
45C13×#95—21no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95D411yescharacteristic
53C13×#95D411yescharacteristic
54C22⋊#1055—21no—
55C22⋊#1055—21no—
56#88050—41no—
57#88050—41no—
58#88048—41no—
59#88048—41no—
60#88047—41no—
61#88047—41no—
62#12236—131nomaximal, Sylow
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C2×Dic26—21no—
73C2×Dic26—21no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—42no—
79C13×C4⋊C4—42no—
80C13×C4⋊C4—42no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C42×C13—21no—
84C42×C13—21no—
85C42×C13—81no—
86C22⋊Dic13—41no—
87C4⋊Dic13—21no—
88C4⋊Dic13—21no—
89C4⋊Dic13—21no—
90C4⋊Dic13—21no—
91#6101—41no—
92#6101—41no—
93C4×Dic13—41no—
94#6099—22no—
95#6099—41no—
96C2×#1055—41no—
97C2×#1055—41no—
98C2×#1055—41no—
99#2794D1311yescharacteristic
100#2060—131no—
101#1617—131no—
102#1611—131no—
103#1353—131no—
104#1346—131no—
105#1325—131no—
106C23×C13#12011yescharacteristic
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—22no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—42no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13#13511yescharacteristic
131C2×C4×C13#13711yescharacteristic
132C2×Dic13—41no—
133C2×Dic13—41no—
134Dic26—81no—
135Dic26—81no—
136#1055—42no—
137#1055—81no—
138#1055—81no—
139#544—131no—
140#484—261no—
141#483—261no—
142#428—261no—
143#400—21no—
144#400—21no—
145#400C2×D1311yescharacteristic
146#398C2×D1311yescharacteristic
147#387—21no—
148#387—21no—
149#387—21no—
150#387—21no—
151#384C2×D1311yescharacteristic
152#343—131no—
153#339—261no—
154#328—261no—
155#328—261no—
156#324—131no—
157#324—131no—
158C22×C13—21no—
159C22×C13—21no—
160C22×C13#45211yescharacteristic
161C22×C13#45611yescharacteristic
162C22×C13B(4,𝔽2)11yescharacteristic
163C4×C13—21no—
164C4×C13—21no—
165C4×C13—42no—
166C4×C13—41no—
167C4×C13—41no—
168C4×C13—81no—
169C4×C13—81no—
170C4×C13—81no—
171C4×C13—81no—
172C4×C13—81no—
173Dic13—81no—
174Dic13—81no—
175C2×M16—261no—
176C4⋊Q8—521no—
177#125—521no—
178C22⋊Q8—261no—
179C22⋊Q8—261no—
180#117—261no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4C22⋊D1311yescharacteristic
186C2×C4⋊C4C22⋊D1311yescharacteristic
187C2×C4⋊C4C22⋊D1311yescharacteristic
188C2×C4⋊C4C22×D1311yescharacteristic
189C2×C42—21no—
190C2×C42C22⋊D1311yescharacteristic
191#107—521no—
192#107—521no—
193#106—521no—
194#106—521no—
195#103—521no—
196#103—521no—
197C22⋊C8—261no—
198C22⋊C8—261no—
199#95—21no—
200#95—21no—
201#95—21no—
202#95—21no—
203#95—21no—
204#95—21no—
205#95—21no—
206#95—21no—
207#95—21no—
208#95C22⋊D1311yescharacteristic
209#95C22⋊D1311yescharacteristic
210C2×C13—21no—
211C2×C13—21no—
212C2×C13#160311yescharacteristic
213C2×C13#219811yescharacteristic
214C2×C13#220311yescharacteristic
215C2×Q8—261no—
216C2×Q8—261no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4C2×C22⋊D1311yescharacteristic
224C22×C4C2×C22⋊D1311yescharacteristic
225C22×C4C2×C22⋊D1311yescharacteristic
226M16—262no—
227M16—521no—
228C2×C8—521no—
229C2×C8—521no—
230C2×C8—521no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—42no—
236C4⋊C4—42no—
237C4⋊C4—42no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—261no—
241C4⋊C4—261no—
242C4⋊C4—261no—
243C4⋊C4—261no—
244C4⋊C4—521no—
245C4⋊C4—521no—
246C22⋊C4—521no—
247C42—21no—
248C42—21no—
249C42—81no—
250C42—521no—
251C13#1223611yescharacteristic, complemented, Sylow
252C23#8820711yescharacteristic
253Q8—1041no—
254Q8—1041no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—42no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—521no—
279C2×C4—521no—
280C2×C4#8820411yescharacteristic
281C2×C4#8820511yescharacteristic
282C8—522no—
283C8—1041no—
284C8—1041no—
285C22—21no—
286C22—21no—
287C22#1171890011yescharacteristic
288C22#1171890511yescharacteristic
289C22#1171890711yescharacteristic
290C4—21no—
291C4—21no—
292C4—42no—
293C4—41no—
294C4—41no—
295C4—81no—
296C4—81no—
297C4—81no—
298C4—81no—
299C4—81no—
300C4—1041no—
301C4—1041no—
302C2—21no—
303C2—21no—
304C2#1311379911yescharacteristic
305C2#1311683211yescharacteristic
306C2#1311685711yescharacteristic
subgroupG/H
centerC22#11718905
commutator, cosocleC2×C13×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2794C2
socleC22×C13B(4,𝔽2)
prime radicalC23×C13#120
hypercenter#2794D13
hypocenterC13#12236
LCSG ▷ C2×C13×C4⋊C4 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2794

Complements

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

NH ≅ G/Ntype
251. C13#12236semidirect

Maximal subgroups

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

subgroupindex
#131161812
#131138772
#131138432
#131128632
#131128422
#131127822
C13×#27942
#1223613