Finite Group Databasebeta

← #15767247

Subgroups — #15767247

Order 3328.

364 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 99 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#13115612C211yesmaximal, characteristic
3#13113524C211yesmaximal, characteristic
4#13113521C211yesmaximal, characteristic
5#13113238C211yesmaximal, characteristic
6#13112686C211yesmaximal, characteristic
7C2×C13×#333C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9#11719175C2211yescharacteristic
10C2×C13×C4⋊C8C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×#88059—21no—
13#11718741—22no—
14#11718740—21no—
15#11718739—21no—
16#11718625—21no—
17#11718625—21no—
18#11718586C2211yescharacteristic
19#11718585C2211yescharacteristic
20C4×#6099C2211yescharacteristic
21C13×#333—22no—
22#11718144—21no—
23#11718139—22no—
24#11718076—22no—
25#11718074—21no—
26#11718073—21no—
27C22×Q8×C13—21no—
28C22×C8×C13—21no—
29C22×C8×C13—21no—
30C13×C4⋊Q8—21no—
31C13×C4⋊Q8—21no—
32C13×C4⋊Q8—21no—
33C13×C4⋊Q8D412yes—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C42×C13C2311yescharacteristic
37#88180—21no—
38#88178—21no—
39#88178—21no—
40C2×#6099—21no—
41C2×#6099D411yescharacteristic
42C2×#6099D411yescharacteristic
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×C4⋊C8D412yes—
52C22⋊#1055—21no—
53#88059—42no—
54#88048—22no—
55#88048—22no—
56#88047—22no—
57#88047—22no—
58C4⋊#1055—21no—
59C4⋊#1055—21no—
60C4⋊#1055—21no—
61#88043—21no—
62C4×#1055—21no—
63C4×#1055—21no—
64#10555—131nomaximal, Sylow
65C2×Q8×C13—22no—
66C2×Q8×C13—41no—
67C2×Q8×C13—82no—
68C22×C4×C13—41no—
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13#4111yescharacteristic
71C22×C4×C13#4111yescharacteristic
72C2×Dic26—21no—
73C2×Dic26—21no—
74C2×C8×C13—22no—
75C2×C8×C13—41no—
76C2×C8×C13—41no—
77C2×C8×C13—41no—
78C2×C8×C13—81no—
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#6099—41no—
98#6099—41no—
99#6099SD1612yes—
100#6099Q1612yes—
101C2×#1055—21no—
102C2×#1055—21no—
103C2×#1055—41no—
104C2×#1055—41no—
105#3165—131no—
106#1950—131no—
107#1550—131no—
108#1549—131no—
109C2×#333D1311yescharacteristic
110#1481—131no—
111#1283—131no—
112C23×C13#12411yescharacteristic
113Q8×C13—82no—
114Q8×C13—82no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—41no—
118C2×C4×C13—42no—
119C2×C4×C13—82no—
120C2×C4×C13#12011yescharacteristic
121C2×C4×C13#12111yescharacteristic
122C2×C4×C13#12111yescharacteristic
123C2×C4×C13#12111yescharacteristic
124C2×C4×C13#12311yescharacteristic
125C2×C4×C13#12311yescharacteristic
126C2×C4×C13C2×SD1611yescharacteristic
127C2×C4×C13C2×Q1611yescharacteristic
128C2×C4×C13#13711yescharacteristic
129C2×C4×C13#13711yescharacteristic
130C2×Dic13—41no—
131C2×Dic13—41no—
132Dic26—41no—
133Dic26—41no—
134Dic26—81no—
135C8×C13—42no—
136C8×C13—81no—
137#1055—22no—
138#1055—22no—
139#1055—81no—
140#1055—81no—
141#533—131no—
142C2×C4⋊Q8C2×D1311yescharacteristic
143#501—262no—
144#500—261no—
145#498—261no—
146#431—131no—
147C2×#108—261no—
148#428—261no—
149#428—261no—
150#423—131no—
151C2×C4⋊C8C2×D1311yescharacteristic
152C2×C4⋊C8C2×D1311yescharacteristic
153C4×M16—131no—
154#341—261no—
155#333—22no—
156#333—261no—
157#332—261no—
158#332—262no—
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—82no—
169C4×C13#44811yescharacteristic
170C4×C13#45111yescharacteristic
171C4×C13#46111yescharacteristic
172C4×C13#46211yescharacteristic
173C4×C13#47111yescharacteristic
174C4×C13#47311yescharacteristic
175Dic13—81no—
176Dic13—81no—
177C22×Q8—21no—
178C2×M16—131no—
179C2×M16—131no—
180C2×M16—261no—
181C22×C8—21no—
182C22×C8—21no—
183C4⋊Q8—21no—
184C4⋊Q8—21no—
185C4⋊Q8—21no—
186C4⋊Q8—131no—
187C4⋊Q8—131no—
188C4⋊Q8D5212yes—
189#125—261no—
190C22⋊Q8—261no—
191C22⋊Q8—261no—
192C4×Q8—261no—
193C4×Q8—261no—
194#117—261no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C42C22×D1311yescharacteristic
198#108—522no—
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⋊C8C22⋊D1312yes—
210C22⋊C8—261no—
211#97—261no—
212C4×C8—261no—
213C4×C8—261no—
214C2×C13—21no—
215C2×C13—21no—
216C2×C13#204311yescharacteristic
217C2×C13#204811yescharacteristic
218C2×C13#205211yescharacteristic
219C2×Q8—22no—
220C2×Q8—41no—
221C2×Q8—82no—
222C2×Q8—261no—
223C2×Q8—261no—
224C22×C4—41no—
225C22×C4#612711yescharacteristic
226C22×C4D4×D1311yescharacteristic
227C22×C4#612911yescharacteristic
228M16—132no—
229M16—132no—
230M16—261no—
231M16—261no—
232M16—521no—
233M16—521no—
234C2×C8—22no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—81no—
239C2×C8—261no—
240C2×C8—261no—
241C2×C8—521no—
242C2×C8—521no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—261no—
248C4⋊C4—261no—
249C4⋊C4—261no—
250C4⋊C4—261no—
251C4⋊C4—521no—
252C4⋊C4—521no—
253C22⋊C4—521no—
254C42—521no—
255C42C2×D5211yescharacteristic
256C42D4×D1311yescharacteristic
257C42#612911yescharacteristic
258C42C2×C22⋊D1311yescharacteristic
259C13#1055511yescharacteristic, complemented, Sylow
260C23#8813911yescharacteristic
261Q8—82no—
262Q8—82no—
263Q8—521no—
264Q8—521no—
265Q8—1041no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—82no—
271C2×C4—521no—
272C2×C4—521no—
273C2×C4#8813611yescharacteristic
274C2×C4#8813711yescharacteristic
275C2×C4#8814011yescharacteristic
276C2×C4SD16×D1311yescharacteristic
277C2×C4#8816911yescharacteristic
278C2×C4Q16×D1311yescharacteristic
279C2×C4#8817211yescharacteristic
280C2×C4#8818411yescharacteristic
281C2×C4#8819211yescharacteristic
282C2×C4#8819311yescharacteristic
283C8—42no—
284C8—81no—
285C8—262no—
286C8—262no—
287C8—1041no—
288C8—1041no—
289C22—21no—
290C22—21no—
291C22#1171845311yescharacteristic
292C22#1171845811yescharacteristic
293C22#1171862211yescharacteristic
294C4—21no—
295C4—21no—
296C4—21no—
297C4—82no—
298C4—1041no—
299C4—1041no—
300C4#1171846711yescharacteristic
301C4#1171846911yescharacteristic
302C4#1171882311yescharacteristic
303C4#1171883811yescharacteristic
304C4#1171884311yescharacteristic
305C4#1171885311yescharacteristic
306C2—21no—
307C2—21no—
308C2#1311608111yescharacteristic
309C2#1311610811yescharacteristic
310C2#1311613611yescharacteristic
subgroupG/H
centerC22#11718622
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×#333C2
socleC22×C13#394
prime radicalC23×C13#124
hypercenterC2×#333D13
hypocenterC13#10555
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#333

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
#131253782
#131156122
#131135242
#131135212
#131132382
#131126862
C2×C13×#3332
#1055513