Finite Group Databasebeta

← #15775878

Subgroups — #15775878

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#13116186C211yesmaximal, characteristic
2#13113877C211yesmaximal, characteristic
3#13113843C211yesmaximal, characteristic
4#13112863C211yesmaximal, characteristic
5#13112842C211yesmaximal, characteristic
6#13112780C211yesmaximal, characteristic
7C13×#2769C211yesmaximal, characteristic
8#11719205C2211yescharacteristic
9C13×#400—21no—
10C13×#400C2211yescharacteristic
11C13×#398—21no—
12C13×#398C2211yescharacteristic
13C13×#389—21no—
14C13×#387—21no—
15C13×#387—21no—
16C13×#383—21no—
17C13×#382C2211yescharacteristic
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#12241—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—41no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—81no—
83C42×C13—21no—
84C42×C13—21no—
85C42×C13—42no—
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#2769D1311yescharacteristic
100#2061—131no—
101#1617—131no—
102#1611—131no—
103#1353—131no—
104#1346—131no—
105#1324—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—41no—
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—41no—
131C2×C4×C13#13511yescharacteristic
132C2×C4×C13#13711yescharacteristic
133C2×Dic13—41no—
134C2×Dic13—41no—
135Dic26—81no—
136Dic26—81no—
137#1055—42no—
138#1055—81no—
139#1055—81no—
140#544—131no—
141#484—261no—
142#483—261no—
143#428—261no—
144#400—21no—
145#400C2×D1311yescharacteristic
146#398—21no—
147#398C2×D1311yescharacteristic
148#389—21no—
149#387—21no—
150#387—21no—
151#383—21no—
152#382C2×D1311yescharacteristic
153#343—131no—
154#339—261no—
155#328—261no—
156#328—261no—
157#324—131no—
158#324—131no—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13#45211yescharacteristic
162C22×C13#45611yescharacteristic
163C22×C13B(4,𝔽2)11yescharacteristic
164C4×C13—21no—
165C4×C13—21no—
166C4×C13—42no—
167C4×C13—41no—
168C4×C13—41no—
169C4×C13—81no—
170C4×C13—81no—
171C4×C13—81no—
172C4×C13—81no—
173C4×C13—81no—
174Dic13—81no—
175Dic13—81no—
176C2×M16—261no—
177C4⋊Q8—521no—
178#125—521no—
179C22⋊Q8—261no—
180C22⋊Q8—261no—
181#117—261no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4C22⋊D1311yescharacteristic
187C2×C4⋊C4C22⋊D1311yescharacteristic
188C2×C4⋊C4C22⋊D1311yescharacteristic
189C2×C4⋊C4C22×D1311yescharacteristic
190C2×C42—21no—
191C2×C42C22⋊D1311yescharacteristic
192#107—521no—
193#107—521no—
194#106—521no—
195#106—521no—
196#103—521no—
197#103—521no—
198C22⋊C8—261no—
199C22⋊C8—261no—
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#95—21no—
209#95C22⋊D1311yescharacteristic
210#95C22⋊D1311yescharacteristic
211C2×C13—21no—
212C2×C13—21no—
213C2×C13#160311yescharacteristic
214C2×C13#220111yescharacteristic
215C2×C13#220411yescharacteristic
216C2×Q8—261no—
217C2×Q8—261no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4C2×C22⋊D1311yescharacteristic
225C22×C4C2×C22⋊D1311yescharacteristic
226C22×C4C2×C22⋊D1311yescharacteristic
227M16—262no—
228M16—521no—
229C2×C8—521no—
230C2×C8—521no—
231C2×C8—521no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—42no—
237C4⋊C4—42no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—81no—
241C4⋊C4—261no—
242C4⋊C4—261no—
243C4⋊C4—261no—
244C4⋊C4—261no—
245C4⋊C4—521no—
246C4⋊C4—521no—
247C22⋊C4—521no—
248C42—21no—
249C42—21no—
250C42—42no—
251C42—521no—
252C13#1224111yescharacteristic, complemented, Sylow
253C23#8820711yescharacteristic
254Q8—1041no—
255Q8—1041no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—21no—
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—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—521no—
281C2×C4—521no—
282C2×C4#8820411yescharacteristic
283C2×C4#8820511yescharacteristic
284C8—522no—
285C8—1041no—
286C8—1041no—
287C22—21no—
288C22—21no—
289C22#1171890011yescharacteristic
290C22#1171890511yescharacteristic
291C22#1171890711yescharacteristic
292C4—21no—
293C4—21no—
294C4—42no—
295C4—41no—
296C4—41no—
297C4—81no—
298C4—81no—
299C4—81no—
300C4—81no—
301C4—81no—
302C4—1041no—
303C4—1041no—
304C2—21no—
305C2—21no—
306C2#1311379911yescharacteristic
307C2#1311684911yescharacteristic
308C2#1311686211yescharacteristic
subgroupG/H
centerC22#11718905
commutator, cosocleC2×C13×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2769C2
socleC22×C13B(4,𝔽2)
prime radicalC23×C13#120
hypercenter#2769D13
hypocenterC13#12241
LCSG ▷ C2×C13×C4⋊C4 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2769

Complements

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

NH ≅ G/Ntype
252. C13#12241semidirect

Maximal subgroups

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

subgroupindex
#131161862
#131138772
#131138432
#131128632
#131128422
#131127802
C13×#27692
#1224113