Finite Group Databasebeta

← #15767253

Subgroups — #15767253

Order 3328.

364 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 97 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#13125378C211yesmaximal, characteristic
2#13115609C211yesmaximal, characteristic
3#13113527C211yesmaximal, characteristic
4C2×#11718139C211yesmaximal, characteristic
5#13113240C211yesmaximal, characteristic
6#13112685C211yesmaximal, characteristic
7C13×#1548C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9#11719175C2211yescharacteristic
10C13×#431C2211yescharacteristic
11C13×#423C2211yescharacteristic
12C2×#88062—21no—
13#11718741—22no—
14#11718740—21no—
15#11718739—21no—
16#11718625—21no—
17#11718625—21no—
18C2×C4⋊#1055C2211yescharacteristic
19C2×C4⋊#1055C2211yescharacteristic
20C4×#6099C2211yescharacteristic
21C13×#333—22no—
22#11718150—21no—
23#11718139—22no—
24#11718078—21no—
25#11718073—21no—
26#11718048—22no—
27C22×Q8×C13—21no—
28C2×C13×M16—21no—
29C13×C4⋊Q8—21no—
30C13×C4⋊Q8—21no—
31C13×C4⋊Q8—21no—
32C13×C4⋊Q8D412yes—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C42×C13C2311yescharacteristic
36#88180—21no—
37#88178—21no—
38#88178—21no—
39C2×#6099D411yescharacteristic
40C2×#6099D411yescharacteristic
41C22×#1055—21no—
42C22×#1055—21no—
43#88124—21no—
44#88123D411yescharacteristic
45#88123D411yescharacteristic
46C4×Dic26—21no—
47C4×Dic26—21no—
48C13×C4⋊C8—21no—
49C13×C4⋊C8—21no—
50C13×C4⋊C8—21no—
51C13×C22⋊C8—21no—
52C4×C8×C13—21no—
53#88062—42no—
54#88048—22no—
55#88048—22no—
56#88047—22no—
57#88047—22no—
58C4⋊#1055—21no—
59C4⋊#1055—21no—
60C4⋊#1055—21no—
61C4⋊#1055D412yes—
62#88043—21no—
63C4×#1055—21no—
64#10556—131nomaximal, Sylow
65C2×Q8×C13—22no—
66C2×Q8×C13—41no—
67C2×Q8×C13—81no—
68C2×Q8×C13—81no—
69C22×C4×C13—41no—
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13#4111yescharacteristic
72C22×C4×C13#4111yescharacteristic
73C2×Dic26—21no—
74C2×Dic26—21no—
75C13×M16—41no—
76C13×M16—41no—
77C2×C8×C13—41no—
78C2×C8×C13—41no—
79C13×C4⋊C4—22no—
80C13×C4⋊C4—22no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C42×C13C2×D411yescharacteristic
84C42×C13C2×D411yescharacteristic
85C42×C13C2×D411yescharacteristic
86C42×C13#4111yescharacteristic
87C22⋊Dic13—41no—
88C4⋊Dic13—21no—
89C4⋊Dic13—21no—
90C4⋊Dic13—21no—
91C4⋊Dic13—21no—
92#6101—41no—
93#6101—41no—
94C4×Dic13—41no—
95#6099—21no—
96#6099—21no—
97#6099SD1612yes—
98#6099Q1612yes—
99C2×#1055—21no—
100C2×#1055—21no—
101C2×#1055—22no—
102C2×#1055—41no—
103C2×#1055—41no—
104C2×#1055—41no—
105C2×#1055—81no—
106#3165—131no—
107#1950—131no—
108#1550—131no—
109#1548D1311yescharacteristic
110C2×#332—131no—
111#1481—131no—
112#1283—131no—
113C23×C13#12411yescharacteristic
114Q8×C13—82no—
115Q8×C13—81no—
116Q8×C13—81no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—41no—
120C2×C4×C13—42no—
121C2×C4×C13—82no—
122C2×C4×C13#12011yescharacteristic
123C2×C4×C13#12111yescharacteristic
124C2×C4×C13#12111yescharacteristic
125C2×C4×C13#12111yescharacteristic
126C2×C4×C13#12311yescharacteristic
127C2×C4×C13#12311yescharacteristic
128C2×C4×C13C2×SD1611yescharacteristic
129C2×C4×C13C2×Q1611yescharacteristic
130C2×C4×C13#13711yescharacteristic
131C2×C4×C13#13711yescharacteristic
132C2×Dic13—41no—
133C2×Dic13—41no—
134Dic26—41no—
135Dic26—41no—
136Dic26—81no—
137C8×C13—81no—
138C8×C13—81no—
139#1055—22no—
140#1055—22no—
141#1055—42no—
142#1055—81no—
143#533—131no—
144C2×C4⋊Q8C2×D1311yescharacteristic
145#501—262no—
146#500—261no—
147#498—261no—
148#431C2×D1311yescharacteristic
149C2×#108—261no—
150#428—261no—
151#428—261no—
152#423C2×D1311yescharacteristic
153C2×C4⋊C8—131no—
154C2×C4⋊C8—131no—
155C4×M16—131no—
156#341—261no—
157#333—22no—
158#333—261no—
159#332—261no—
160#332—262no—
161Q8⋊C8—262no—
162C22×C13—21no—
163C22×C13—21no—
164C22×C13#39411yescharacteristic
165C22×C13#48711yescharacteristic
166C22×C13#49111yescharacteristic
167C4×C13—21no—
168C4×C13—21no—
169C4×C13—21no—
170C4×C13—82no—
171C4×C13#44811yescharacteristic
172C4×C13#45111yescharacteristic
173C4×C13#46111yescharacteristic
174C4×C13#46211yescharacteristic
175C4×C13#47111yescharacteristic
176C4×C13#47211yescharacteristic
177Dic13—81no—
178Dic13—81no—
179C22×Q8—21no—
180C2×M16—21no—
181C2×M16—131no—
182C2×M16—131no—
183C22×C8—261no—
184C22×C8—261no—
185C4⋊Q8—21no—
186C4⋊Q8—21no—
187C4⋊Q8—21no—
188C4⋊Q8—131no—
189C4⋊Q8—131no—
190C4⋊Q8C22⋊D1312yes—
191#125—261no—
192C22⋊Q8—261no—
193C22⋊Q8—261no—
194C4×Q8—261no—
195C4×Q8—261no—
196#117—261no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C42C22×D1311yescharacteristic
200#108—522no—
201#107—262no—
202#107—262no—
203#106—262no—
204#106—262no—
205C4⋊C8—21no—
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—132no—
209C4⋊C8—261no—
210C4⋊C8—261no—
211C4⋊C8—261no—
212C22⋊C8—21no—
213#97—261no—
214C4×C8—21no—
215C4×C8—261no—
216C2×C13—21no—
217C2×C13—21no—
218C2×C13#204311yescharacteristic
219C2×C13#204911yescharacteristic
220C2×C13#205111yescharacteristic
221C2×Q8—22no—
222C2×Q8—41no—
223C2×Q8—81no—
224C2×Q8—81no—
225C2×Q8—261no—
226C2×Q8—261no—
227C22×C4—41no—
228C22×C4#612711yescharacteristic
229C22×C4D4×D1311yescharacteristic
230C22×C4#612911yescharacteristic
231M16—41no—
232M16—41no—
233M16—132no—
234M16—132no—
235M16—261no—
236M16—261no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—261no—
240C2×C8—261no—
241C2×C8—262no—
242C2×C8—521no—
243C2×C8—521no—
244C2×C8—521no—
245C2×C8—1041no—
246C4⋊C4—22no—
247C4⋊C4—22no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—261no—
251C4⋊C4—261no—
252C4⋊C4—261no—
253C4⋊C4—261no—
254C4⋊C4—521no—
255C4⋊C4—521no—
256C22⋊C4—521no—
257C42—521no—
258C42#612711yescharacteristic
259C42D4×D1311yescharacteristic
260C42D4×D1311yescharacteristic
261C42C2×C22⋊D1311yescharacteristic
262C13#1055611yescharacteristic, complemented, Sylow
263C23#8813911yescharacteristic
264Q8—82no—
265Q8—81no—
266Q8—81no—
267Q8—521no—
268Q8—521no—
269Q8—1041no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—42no—
274C2×C4—82no—
275C2×C4—521no—
276C2×C4—521no—
277C2×C4#8813711yescharacteristic
278C2×C4#8813811yescharacteristic
279C2×C4#8813811yescharacteristic
280C2×C4SD16×D1311yescharacteristic
281C2×C4#8816911yescharacteristic
282C2×C4Q16×D1311yescharacteristic
283C2×C4#8817211yescharacteristic
284C2×C4#8818311yescharacteristic
285C2×C4#8819111yescharacteristic
286C2×C4#8819311yescharacteristic
287C8—81no—
288C8—81no—
289C8—262no—
290C8—262no—
291C8—522no—
292C8—1041no—
293C22—21no—
294C22—21no—
295C22#1171845311yescharacteristic
296C22#1171845811yescharacteristic
297C22#1171862011yescharacteristic
298C4—21no—
299C4—21no—
300C4—21no—
301C4—82no—
302C4—1041no—
303C4—1041no—
304C4#1171840911yescharacteristic
305C4#1171841011yescharacteristic
306C4#1171845411yescharacteristic
307C4#1171847911yescharacteristic
308C4#1171883111yescharacteristic
309C4#1171884711yescharacteristic
310C2—21no—
311C2—21no—
312C2#1311608011yescharacteristic
313C2#1311611411yescharacteristic
314C2#1311612811yescharacteristic
subgroupG/H
centerC22#11718620
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1548C2
socleC22×C13#394
prime radicalC23×C13#124
hypercenter#1548D13
hypocenterC13#10556
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
262. C13#10556semidirect

Maximal subgroups

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

subgroupindex
#131253782
#131156092
#131135272
C2×#117181392
#131132402
#131126852
C13×#15482
#1055613