Finite Group Databasebeta

← #15767248

Subgroups — #15767248

Order 3328.

364 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 103 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#13125382C211yesmaximal, characteristic
2#13113527C211yesmaximal, characteristic
3#13113522C211yesmaximal, characteristic
4C2×#11718073C211yesmaximal, characteristic
5#13113238C211yesmaximal, characteristic
6#13112687C211yesmaximal, characteristic
7C13×#1950C211yesmaximal, characteristic
8#11719175C2211yescharacteristic
9C2×#88123C2211yescharacteristic
10C2×C13×#108—21no—
11C13×#423C2211yescharacteristic
12C2×C13×C4⋊C8C2211yescharacteristic
13C4×C13×M16C2211yescharacteristic
14#11718782—21no—
15#11718782—21no—
16#11718586C2211yescharacteristic
17C2×C4⋊#1055C2211yescharacteristic
18#11718363—22no—
19#11718343—21no—
20#11718341—21no—
21C13×#341—21no—
22#11718078—22no—
23#11718078—21no—
24#11718076—22no—
25#11718073—21no—
26#11718073—22no—
27C22×Dic26—21no—
28C2×C13×M16—21no—
29C2×C13×M16D411yescharacteristic
30C2×C13×M16D411yescharacteristic
31C22×C8×C13—21no—
32C2×C42×C13C2311yescharacteristic
33#88180—21no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13—21no—
36#88178—21no—
37#88178—21no—
38C22×#1055—21no—
39#88124—21no—
40#88123—21no—
41#88123—21no—
42#88123—21no—
43#88123D412yes—
44#88123D411yescharacteristic
45#88123D411yescharacteristic
46C4×Dic26—21no—
47C4×Dic26—21no—
48C13×#108—42no—
49C13×C4⋊C8—21no—
50C13×C4⋊C8—21no—
51C13×C4⋊C8—21no—
52C13×C4⋊C8D412yes—
53C13×#97—21no—
54C4×C8×C13—21no—
55C22⋊#1055—21no—
56#88058—22no—
57#88058—22no—
58#88057—22no—
59#88057—22no—
60C4⋊#1055—21no—
61C4⋊#1055—21no—
62C4⋊#1055—21no—
63C4×#1055—21no—
64#10555—131nomaximal, Sylow
65C22×C4×C13C2×D411yescharacteristic
66C22×C4×C13#4111yescharacteristic
67C22×C4×C13#4111yescharacteristic
68C22×Dic13—41no—
69C2×Dic26—21no—
70C2×Dic26—22no—
71C2×Dic26—21no—
72C2×Dic26—41no—
73C2×Dic26—82no—
74C13×M16—21no—
75C13×M16—21no—
76C13×M16—41no—
77C13×M16—41no—
78C13×M16SD1612yes—
79C13×M16Q1612yes—
80C2×C8×C13—21no—
81C2×C8×C13—21no—
82C2×C8×C13—22no—
83C2×C8×C13—41no—
84C2×C8×C13—41no—
85C2×C8×C13—41no—
86C42×C13C2×D411yescharacteristic
87C42×C13C2×D411yescharacteristic
88C42×C13C2×D411yescharacteristic
89C42×C13#4111yescharacteristic
90C22⋊Dic13—41no—
91C4⋊Dic13—22no—
92C4⋊Dic13—21no—
93C4⋊Dic13—21no—
94C4⋊Dic13—21no—
95C4⋊Dic13—21no—
96C4⋊Dic13—22no—
97C4⋊Dic13—41no—
98C4⋊Dic13—41no—
99#6101—41no—
100#6101—41no—
101C4×Dic13—41no—
102C2×#1055—41no—
103C2×#1055—41no—
104C2×#1055—81no—
105#3165—131no—
106#1950D1311yescharacteristic
107#1550—131no—
108#1549—131no—
109C2×#333—131no—
110#1481—131no—
111#1283—131no—
112C23×C13#12411yescharacteristic
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—41no—
116C2×C4×C13#12011yescharacteristic
117C2×C4×C13#12111yescharacteristic
118C2×C4×C13#12111yescharacteristic
119C2×C4×C13#12111yescharacteristic
120C2×C4×C13#12311yescharacteristic
121C2×C4×C13#12311yescharacteristic
122C2×C4×C13C2×SD1611yescharacteristic
123C2×C4×C13C2×Q1611yescharacteristic
124C2×C4×C13#13711yescharacteristic
125C2×C4×C13#13711yescharacteristic
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13—42no—
129C2×Dic13—82no—
130Dic26—41no—
131Dic26—41no—
132Dic26—82no—
133Dic26—81no—
134Dic26—82no—
135C8×C13—22no—
136C8×C13—22no—
137C8×C13—42no—
138C8×C13—81no—
139#1055—81no—
140#1055—81no—
141#533—131no—
142C2×C4⋊Q8—131no—
143#501—262no—
144#500—261no—
145#498—261no—
146#431—131no—
147C2×#108—21no—
148#428—261no—
149#428—261no—
150#423C2×D1311yescharacteristic
151C2×C4⋊C8—131no—
152C2×C4⋊C8C2×D1311yescharacteristic
153C4×M16C2×D1311yescharacteristic
154#341—21no—
155#333—261no—
156#333—262no—
157#332—262no—
158#332—261no—
159Q8⋊C8—262no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13#39411yescharacteristic
163C22×C13#48711yescharacteristic
164C22×C13#49111yescharacteristic
165C4×C13—21no—
166C4×C13—21no—
167C4×C13—21no—
168C4×C13#44811yescharacteristic
169C4×C13#45111yescharacteristic
170C4×C13#46111yescharacteristic
171C4×C13#46211yescharacteristic
172C4×C13#47111yescharacteristic
173C4×C13#47311yescharacteristic
174Dic13—82no—
175Dic13—81no—
176Dic13—81no—
177C22×Q8—261no—
178C2×M16—21no—
179C2×M16C22⋊D1311yescharacteristic
180C2×M16C22⋊D1311yescharacteristic
181C22×C8—21no—
182C22×C8—261no—
183C4⋊Q8—132no—
184C4⋊Q8—131no—
185C4⋊Q8—131no—
186C4⋊Q8—261no—
187C4⋊Q8—261no—
188C4⋊Q8—261no—
189#125—261no—
190C22⋊Q8—261no—
191C22⋊Q8—261no—
192C4×Q8—261no—
193C4×Q8—261no—
194#117—261no—
195C2×C4⋊C4—261no—
196C2×C4⋊C4—261no—
197C2×C42C22×D1311yescharacteristic
198#108—42no—
199#107—262no—
200#107—262no—
201#106—262no—
202#106—262no—
203C4⋊C8—21no—
204C4⋊C8—21no—
205C4⋊C8—21no—
206C4⋊C8—261no—
207C4⋊C8—261no—
208C4⋊C8—261no—
209C4⋊C8D5212yes—
210C22⋊C8—261no—
211#97—21no—
212C4×C8—21no—
213C4×C8—261no—
214C2×C13—21no—
215C2×C13—21no—
216C2×C13#204311yescharacteristic
217C2×C13#204811yescharacteristic
218C2×C13#205211yescharacteristic
219C2×Q8—261no—
220C2×Q8—261no—
221C2×Q8—262no—
222C2×Q8—521no—
223C2×Q8—1042no—
224C22×C4—521no—
225C22×C4#613111yescharacteristic
226C22×C4#613111yescharacteristic
227C22×C4C2×C22⋊D1311yescharacteristic
228M16—21no—
229M16—21no—
230M16—41no—
231M16—41no—
232M16#610512yes—
233M16#610712yes—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—22no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—521no—
241C2×C8—521no—
242C2×C8—1041no—
243C4⋊C4—262no—
244C4⋊C4—261no—
245C4⋊C4—261no—
246C4⋊C4—261no—
247C4⋊C4—262no—
248C4⋊C4—261no—
249C4⋊C4—521no—
250C4⋊C4—521no—
251C4⋊C4—521no—
252C4⋊C4—521no—
253C22⋊C4—521no—
254C42—521no—
255C42C2×D5211yescharacteristic
256C42#612711yescharacteristic
257C42D4×D1311yescharacteristic
258C42D4×D1311yescharacteristic
259C13#1055511yescharacteristic, complemented, Sylow
260C23#8820111yescharacteristic
261Q8—521no—
262Q8—521no—
263Q8—1041no—
264Q8—1042no—
265Q8—1042no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—41no—
269C2×C4—521no—
270C2×C4—521no—
271C2×C4—522no—
272C2×C4—1042no—
273C2×C4#8814811yescharacteristic
274C2×C4#8814811yescharacteristic
275C2×C4#8814911yescharacteristic
276C2×C4#8814911yescharacteristic
277C2×C4#8818411yescharacteristic
278C2×C4C2×#610511yescharacteristic
279C2×C4#8819111yescharacteristic
280C2×C4C2×#610711yescharacteristic
281C2×C4#8820511yescharacteristic
282C2×C4#8820511yescharacteristic
283C8—22no—
284C8—22no—
285C8—42no—
286C8—81no—
287C8—1041no—
288C8—1041no—
289C22—21no—
290C22—21no—
291C22#1171865211yescharacteristic
292C22#1171873011yescharacteristic
293C22#1171875411yescharacteristic
294C4—21no—
295C4—21no—
296C4—21no—
297C4—1042no—
298C4—1041no—
299C4—1041no—
300C4#1171855711yescharacteristic
301C4#1171855911yescharacteristic
302C4#1171868011yescharacteristic
303C4#1171869211yescharacteristic
304C4#1171870111yescharacteristic
305C4#1171871111yescharacteristic
306C2—21no—
307C2—21no—
308C2#1311608211yescharacteristic
309C2#1311611111yescharacteristic
310C2#1311613711yescharacteristic
subgroupG/H
centerC22#11718652
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1950C2
socleC22×C13#394
prime radicalC23×C13#124
hypercenter#1950D13
hypocenterC13#10555
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1950

Complements

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

NH ≅ G/Ntype
259. C13#10555semidirect

Maximal subgroups

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

subgroupindex
#131253822
#131135272
#131135222
C2×#117180732
#131132382
#131126872
C13×#19502
#1055513