Finite Group Databasebeta

← #15775985

Subgroups — #15775985

Order 3328.

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

normal subgroups only

This group has 352 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#13116186C211yesmaximal, characteristic
2#13113877C211yesmaximal, characteristic
3#13113809C211yesmaximal, characteristic
4#13112866C211yesmaximal, characteristic
5#13112863C211yesmaximal, characteristic
6#13112780C211yesmaximal, characteristic
7C13×#2612C211yesmaximal, characteristic
8#11719205C2211yescharacteristic
9C13×#400C2211yescharacteristic
10C13×#398—21no—
11C13×#395C2211yescharacteristic
12C13×#391—21no—
13C13×#389—21no—
14C13×#387—21no—
15C13×#387—21no—
16C13×#382C2211yescharacteristic
17C13×#376—21no—
18#11718889—21no—
19#11718631—21no—
20#11718625—21no—
21#11718122C2211yescharacteristic
22#11718120C2211yescharacteristic
23#11718120C2211yescharacteristic
24#11718115—21no—
25#11718044—21no—
26#11718044—21no—
27C22×Q8×C13D411yescharacteristic
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C13×C4⋊C4C2311yescharacteristic
35C2×C42×C13—21no—
36C2×C42×C13—21no—
37C2×C42×C13D411yescharacteristic
38C2×#6107—41no—
39#88180—21no—
40#88178—21no—
41#88178—21no—
42C2×#6099—21no—
43#88144—41no—
44#88142—41no—
45C13×#95—21no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95D411yescharacteristic
54C13×#95D411yescharacteristic
55#88075—41no—
56C22⋊#1055—21no—
57C22⋊#1055—21no—
58#88050—41no—
59#88048—41no—
60#88047—41no—
61#88047—41no—
62#12258—131nomaximal, Sylow
63C2×Q8×C13—42no—
64C2×Q8×C13—41no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C2×Dic26—21no—
75C2×Dic26—21no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—42no—
80C13×C4⋊C4—42no—
81C13×C4⋊C4—42no—
82C13×C4⋊C4—81no—
83C42×C13—21no—
84C42×C13—42no—
85C42×C13—42no—
86C42×C13Q1612yescomplemented
87C22⋊Dic13—41no—
88#6107—82no—
89C4⋊Dic13—21no—
90C4⋊Dic13—21no—
91C4⋊Dic13—21no—
92C4⋊Dic13—21no—
93#6101—41no—
94#6101—41no—
95C4×Dic13—41no—
96#6099—22no—
97#6099—41no—
98C2×#1055—41no—
99C2×#1055—41no—
100C2×#1055—41no—
101#2612D1311yescharacteristic
102#2061—131no—
103#1617—131no—
104#1605—131no—
105#1354—131no—
106#1353—131no—
107#1324—131no—
108C23×C13#12011yescharacteristic
109Q8×C13—42no—
110Q8×C13—81no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—22no—
114C2×C4×C13—22no—
115C2×C4×C13—22no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
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—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13C2×Q1611yescharacteristic
136C2×C4×C13#13711yescharacteristic
137C2×Dic13—41no—
138C2×Dic13—41no—
139Dic26—81no—
140Dic26—81no—
141#1055—42no—
142#1055—81no—
143#1055—81no—
144#544—131no—
145#484—261no—
146#451—261no—
147#428—261no—
148#400C2×D1311yescharacteristic
149#398—21no—
150#395C2×D1311yescharacteristic
151#391—21no—
152#389—21no—
153#387—21no—
154#387—21no—
155#382C2×D1311yescharacteristic
156#376—21no—
157#343—131no—
158#339—261no—
159#328—261no—
160#328—261no—
161#324—131no—
162#324—131no—
163C22×C13—21no—
164C22×C13—21no—
165C22×C13#45111yescharacteristic
166C22×C13#45611yescharacteristic
167C22×C13B(4,𝔽2)11yescharacteristic
168C4×C13—21no—
169C4×C13—21no—
170C4×C13—42no—
171C4×C13—42no—
172C4×C13—41no—
173C4×C13—41no—
174C4×C13—42no—
175C4×C13—81no—
176C4×C13—81no—
177C4×C13—81no—
178Dic13—81no—
179Dic13—81no—
180C22×Q8C22⋊D1311yescharacteristic
181C2×Q16—521no—
182C2×M16—261no—
183C4⋊Q8—521no—
184#125—521no—
185C22⋊Q8—261no—
186C22⋊Q8—261no—
187#117—261no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4C22⋊D1311yescharacteristic
193C2×C4⋊C4C22⋊D1311yescharacteristic
194C2×C4⋊C4C22×D1311yescharacteristic
195C2×C42—21no—
196C2×C42—21no—
197C2×C42C22⋊D1311yescharacteristic
198#107—521no—
199#107—521no—
200#106—521no—
201#103—521no—
202#103—521no—
203C22⋊C8—261no—
204C22⋊C8—261no—
205#95—21no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95C22⋊D1311yescharacteristic
214#95C22⋊D1311yescharacteristic
215C2×C13—21no—
216C2×C13—21no—
217C2×C13#160511yescharacteristic
218C2×C13#219711yescharacteristic
219C2×C13#220411yescharacteristic
220C2×Q8—42no—
221C2×Q8—41no—
222C2×Q8—261no—
223C2×Q8—261no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4C2×C22⋊D1311yescharacteristic
231C22×C4C2×C22⋊D1311yescharacteristic
232C22×C4C2×C22⋊D1311yescharacteristic
233Q16—1042no—
234M16—262no—
235M16—521no—
236C2×C8—521no—
237C2×C8—521no—
238C2×C8—521no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C4⋊C4—81no—
246C4⋊C4—261no—
247C4⋊C4—261no—
248C4⋊C4—261no—
249C4⋊C4—261no—
250C4⋊C4—521no—
251C4⋊C4—521no—
252C22⋊C4—521no—
253C42—21no—
254C42—42no—
255C42—42no—
256C42—521no—
257C42#610712yescomplemented
258C13#1225811yescharacteristic, complemented, Sylow
259C23#8820711yescharacteristic
260Q8—42no—
261Q8—81no—
262Q8—1041no—
263Q8—1041no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—21no—
270C2×C4—21no—
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—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—521no—
289C2×C4—521no—
290C2×C4#8819611yescharacteristic
291C2×C4C2×#610711yescharacteristic
292C8—522no—
293C8—1041no—
294C8—1041no—
295C22—21no—
296C22—21no—
297C22#1171888911yescharacteristic
298C22#1171890511yescharacteristic
299C22#1171890711yescharacteristic
300C4—21no—
301C4—21no—
302C4—42no—
303C4—42no—
304C4—41no—
305C4—41no—
306C4—42no—
307C4—81no—
308C4—81no—
309C4—81no—
310C4—1041no—
311C4—1041no—
312C2—21no—
313C2—21no—
314C2#1311381011yescharacteristic
315C2#1311682611yescharacteristic
316C2#1311686211yescharacteristic
subgroupG/H
centerC22#11718905
commutator, cosocleC2×C13×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2612C2
socleC22×C13B(4,𝔽2)
prime radicalC23×C13#120
hypercenter#2612D13
hypocenterC13#12258
LCSG ▷ C2×C13×C4⋊C4 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2612

Complements

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

NH ≅ G/Ntype
86. C42×C13Q16semidirect
257. C42#6107semidirect
258. C13#12258semidirect

Maximal subgroups

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

subgroupindex
#131161862
#131138772
#131138092
#131128662
#131128632
#131127802
C13×#26122
#1225813