Finite Group Databasebeta

← #15760271

Subgroups — #15760271

Order 3328.

538 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 117 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#13123859C211yesmaximal, characteristic
2#13120010C211yesmaximal, characteristic
3#13114825C211yesmaximal, characteristic
4#13113517C211yesmaximal, characteristic, complemented
5#13112738C211yesmaximal, characteristic, complemented
6#13112737C211yesmaximal, characteristic, complemented
7C13×#1548C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C4×D52C2211yescharacteristic
10C13×#431C2211yescharacteristic
11C13×#423C2211yescharacteristic
12#11718892C414yes—
13C2×#88063—21no—
14#11718649—21no—
15#11718648—22no—
16#11718638—21no—
17C4×C4⋊Dic13C2211yescharacteristic
18#11718586C2211yescharacteristic
19#11718585C2211yescharacteristic
20#11718495—22no—
21D13×C22⋊C8—22no—
22C8×D52—22no—
23C13×#333—22no—
24#11718146—21no—
25#11718138—22no—
26C22×Q8×C13C2×C412yes—
27C22×D52D411yescharacteristic
28C22×C4×D13D412yes—
29C2×C13×M16—21no—
30C13×C4⋊Q8—21no—
31C13×C4⋊Q8—21no—
32C13×C4⋊Q8—21no—
33C13×C4⋊Q8—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C42×C13C2311yescharacteristic
37C2×#6103—24no—
38C2×#6103C2×C412yes—
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13D411yescharacteristic
41C2×C4×Dic13—21no—
42C2×#6099—21no—
43C2×C8×D13—24no—
44C4×D52—21no—
45C4×D52—21no—
46C4×D52—21no—
47C4×D52—21no—
48C13×C4⋊C8—21no—
49C13×C4⋊C8—21no—
50C13×C4⋊C8D412yes—
51C13×C22⋊C8—21no—
52C4×C8×C13—21no—
53#88071—24no—
54#88071C2×C412yes—
55C22⋊#1055—21no—
56#88063—42no—
57#88060—24no—
58C4⋊#1055—21no—
59C4⋊#1055—21no—
60C4⋊#1055D412yes—
61C4×#1055—21no—
62#9391—131nomaximal, Sylow
63C23×D13C22⋊C412yes—
64C2×Q8×C13—22no—
65C2×Q8×C13—22no—
66C2×Q8×C13—82no—
67C22×C4×C13—22no—
68C22×C4×C13C22×C411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×Dic13—22no—
72C22×Dic13C22⋊C412yes—
73C2×D52—21no—
74C2×D52—21no—
75C2×D52—21no—
76C2×D52—21no—
77C2×D52SD1612yes—
78C2×D52Q1612yes—
79C2×C4×D13—22no—
80C2×C4×D13—22no—
81C2×C4×D13—44no—
82C13×M16—41no—
83C13×M16—41no—
84C2×C8×C13—22no—
85C2×C8×C13—41no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—41no—
90C42×C13C2×D411yescharacteristic
91C42×C13C2×D411yescharacteristic
92C42×C13#4111yescharacteristic
93C42×C13#4111yescharacteristic
94#6103—22no—
95#6103—22no—
96#6103—84no—
97C4⋊Dic13—21no—
98C4⋊Dic13—21no—
99C4⋊Dic13—42no—
100C4×Dic13—41no—
101C4×Dic13—41no—
102#6099—41no—
103#6099—41no—
104C2×#1055—22no—
105C2×#1055—41no—
106C8×D13—84no—
107#2972—131no—
108#2563—131no—
109#1800—131no—
110#1548—131no—
111#1548D1311yescharacteristic, complemented
112#1303—131no—
113#1303—131no—
114C23×C13C2×C22⋊C411yescharacteristic
115C22×D13—22no—
116C22×D13—22no—
117C22×D13—42no—
118C22×D13—42no—
119C22×D13#10314yes—
120Q8×C13—82no—
121Q8×C13—82no—
122C2×C4×C13—22no—
123C2×C4×C13—41no—
124C2×C4×C13—44no—
125C2×C4×C13—42no—
126C2×C4×C13C4×D411yescharacteristic
127C2×C4×C13C4×D411yescharacteristic
128C2×C4×C13#12011yescharacteristic
129C2×C4×C13#12111yescharacteristic
130C2×C4×C13#12111yescharacteristic
131C2×C4×C13#12311yescharacteristic
132C2×C4×C13C2×SD1611yescharacteristic
133C2×C4×C13C2×Q1611yescharacteristic
134C2×C4×C13#13511yescharacteristic
135C2×C4×C13#13511yescharacteristic
136C2×Dic13—22no—
137C2×Dic13—42no—
138C2×Dic13—42no—
139C2×Dic13—42no—
140C2×Dic13—42no—
141D52—22no—
142D52—22no—
143D52—22no—
144D52—22no—
145C4×D13—44no—
146C4×D13—82no—
147C8×C13—42no—
148C8×C13—81no—
149#1055—42no—
150#1055—81no—
151C2×C4⋊Q8C2×D1311yescharacteristic
152C2×C4×D4—131no—
153C8×D4—262no—
154C8×D4—262no—
155#431—131no—
156#431C2×D1311yescharacteristic
157#423—131no—
158#423C2×D1311yescharacteristic
159C2×#100—261no—
160C2×C22⋊C8—262no—
161#393—134no—
162#390—261no—
163#382—261no—
164#380—262no—
165C4×C4⋊C4—131no—
166#343—261no—
167#333—22no—
168#333—262no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13#38611yescharacteristic
172C22×C13C2×#10311yescharacteristic
173C22×C13#41611yescharacteristic
174C2×D13—24no—
175C2×D13—42no—
176C2×D13—42no—
177C2×D13—44no—
178C2×D13—82no—
179C4×C13—21no—
180C4×C13—21no—
181C4×C13—21no—
182C4×C13—82no—
183C4×C13#45512yes—
184C4×C13#46511yescharacteristic
185C4×C13#46511yescharacteristic
186C4×C13#46711yescharacteristic
187C4×C13#46711yescharacteristic
188Dic13—42no—
189Dic13—82no—
190C22×Q8C4×D1312yes—
191C22×D4—131no—
192C23×C4—132no—
193C2×M16—21no—
194C2×M16—261no—
195C22×C8—264no—
196C4⋊Q8—21no—
197C4⋊Q8—21no—
198C4⋊Q8—21no—
199C4⋊Q8—21no—
200C4×D4—261no—
201C4×D4—261no—
202C4×D4—261no—
203C4×D4—261no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—131no—
207C2×C4⋊C4—261no—
208C2×C22⋊C4—132no—
209C2×C22⋊C4—264no—
210C2×C42—261no—
211C2×C42C22×D1311yescharacteristic
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8—132no—
215C4⋊C8—261no—
216C4⋊C8—261no—
217C4⋊C8C22⋊D1312yes—
218#100—522no—
219C22⋊C8—21no—
220C22⋊C8—264no—
221C22⋊C8—261no—
222C4×C8—21no—
223C4×C8—261no—
224#95—132no—
225#95—264no—
226C2×C13—21no—
227C2×C13—21no—
228C2×C13#188511yescharacteristic
229C2×C13#189211yescharacteristic
230C2×C13#191411yescharacteristic
231D13—44no—
232C24—132no—
233C2×Q8—22no—
234C2×Q8—22no—
235C2×Q8—82no—
236C2×D4—132no—
237C2×D4—132no—
238C2×D4—261no—
239C2×D4—261no—
240C2×D4—261no—
241C2×D4—261no—
242C22×C4—22no—
243C22×C4—132no—
244C22×C4—262no—
245C22×C4—262no—
246C22×C4—262no—
247C22×C4—524no—
248C22×C4C2×C4×D1311yescharacteristic
249C22×C4D4×D1311yescharacteristic
250C22×C4D4×D1311yescharacteristic
251M16—41no—
252M16—41no—
253M16—521no—
254M16—521no—
255C2×C8—22no—
256C2×C8—41no—
257C2×C8—262no—
258C2×C8—521no—
259C2×C8—1044no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—261no—
265C4⋊C4—261no—
266C4⋊C4—522no—
267C22⋊C4—262no—
268C22⋊C4—262no—
269C22⋊C4—1044no—
270C42—521no—
271C42—521no—
272C42#612711yescharacteristic
273C42D4×D1311yescharacteristic
274C42#612911yescharacteristic
275C42C2×C22⋊D1311yescharacteristic
276C13#939111yescharacteristic, complemented, Sylow
277C23—134no—
278C23—262no—
279C23—262no—
280C23—522no—
281C23—522no—
282C23C22⋊C4×D1311yescharacteristic
283Q8—82no—
284Q8—82no—
285D4—262no—
286D4—262no—
287D4—262no—
288D4—262no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—44no—
292C2×C4—42no—
293C2×C4—262no—
294C2×C4—524no—
295C2×C4—522no—
296C2×C4—522no—
297C2×C4—522no—
298C2×C4—522no—
299C2×C4—1042no—
300C2×C4#8813511yescharacteristic
301C2×C4#8813711yescharacteristic
302C2×C4#8813811yescharacteristic
303C2×C4SD16×D1311yescharacteristic
304C2×C4#8817011yescharacteristic
305C2×C4Q16×D1311yescharacteristic
306C2×C4#8817311yescharacteristic
307C2×C4C4×C22⋊D1311yescharacteristic
308C2×C4#8819111yescharacteristic
309C2×C4#8819211yescharacteristic
310C8—42no—
311C8—81no—
312C8—522no—
313C8—1041no—
314C22—21no—
315C22—21no—
316C22—264no—
317C22—524no—
318C22—522no—
319C22—522no—
320C22—1042no—
321C22D13×#10311yescharacteristic
322C22#1171846511yescharacteristic
323C22#1171861711yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—82no—
328C4—522no—
329C4—1042no—
330C4#1171846811yescharacteristic
331C4#1171847411yescharacteristic
332C4#1171883211yescharacteristic
333C4#1171884911yescharacteristic
334C4#1171886312yes—
335C2—21no—
336C2—21no—
337C2—524no—
338C2#1311522111yescharacteristic
339C2#1311525611yescharacteristic
340C2#1311538011yescharacteristic
subgroupG/H
centerC22#11718617
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1548C2
socleC22×C13#386
prime radicalC22×D52D4
cosocleC2×C42×C13C23
hypercenter#1548D13
hypocenterC13#9391
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
4. #13113517C2semidirect
5. #13112738C2semidirect
6. #13112737C2semidirect
7. C13×#1548C2semidirect
111. #1548D13semidirect
276. C13#9391semidirect

Maximal subgroups

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

subgroupindex
#131238592
#131200102
#131148252
#131135172
#131127382
#131127372
C13×#15482
#939113