Finite Group Databasebeta

← #15848201

Subgroups — #15848201

Order 3328.

656 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125761C211yesmaximal, characteristic
2#13124308C211yesmaximal, characteristic
3#13123917C211yesmaximal, characteristic, complemented
4#13114264C214yesmaximal, complemented
5#13114186C214yesmaximal, complemented
6#13113606C211yesmaximal, characteristic, complemented
7#13113521C211yesmaximal, characteristic, complemented
8#13113486C211yesmaximal, characteristic
9C2×C13×#475C211yesmaximal, characteristic, complemented
10C2×C13×C4⋊Q8C2211yescharacteristic
11C2×C4×Q8×C13C2211yescharacteristic
12C2×#88196—21no—
13#11719182C2211yescharacteristic
14C13×#475—22no—
15C13×#475C2214yes—
16C2×C13×#106—21no—
17C2×C13×C4⋊C8C2211yescharacteristic
18C2×C13×#103—21no—
19#11718888—22no—
20#11718746C2212yes—
21#11718744—22no—
22#11718742C2212yes—
23#11718692C2212yes—
24#11718689—22no—
25#11718688C2212yes—
26Q8×#1055—22no—
27Q8×#1055C2214yes—
28#11718627—21no—
29#11718586—22no—
30#11718586C2211yescharacteristic
31#11718586C2211yescharacteristic
32#11718585C2211yescharacteristic
33#11718139C2214yes—
34#11718077C2212yes—
35#11718074C2212yes—
36#11718072C2214yes—
37C22×Q8×C13—21no—
38C22×Q8×C13D411yescharacteristic
39C2×#6127—21no—
40C22×C8×C13—21no—
41C13×C4⋊Q8—21no—
42C13×C4⋊Q8—21no—
43C13×C4⋊Q8—21no—
44C13×C4⋊Q8C2312yes—
45C4×Q8×C13—21no—
46C4×Q8×C13—21no—
47C4×Q8×C13D412yes—
48C4×Q8×C13C2312yes—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4D411yescharacteristic
53C2×C42×C13—21no—
54C2×C42×C13C2311yescharacteristic
55C2×#6107—22no—
56#88196—44no—
57C2×#6106—22no—
58C2×#6106—24no—
59#88184—21no—
60#88184—21no—
61C2×#6099—21no—
62#88129—21no—
63#88128C2311yescharacteristic
64C4×D52—21no—
65C4×D52—21no—
66#88123C2311yescharacteristic
67C13×#106—24no—
68C13×C4⋊C8—21no—
69C13×C4⋊C8C2312yes—
70C13×#103—24no—
71#88075—24no—
72C22⋊#1055—21no—
73C22⋊#1055D412yes—
74#88050—22no—
75#88049—22no—
76C4⋊#1055—21no—
77C4⋊#1055—24no—
78C4⋊#1055D412yes—
79C4⋊#1055C2312yes—
80C4⋊#1055C2312yes—
81C4×#1055—21no—
82C4×#1055—24no—
83C4×#1055C2312yes—
84#19397—131nomaximal, Sylow
85C2×Q8×C13—21no—
86C2×Q8×C13—22no—
87C2×Q8×C13—22no—
88C2×Q8×C13—41no—
89C2×Q8×C13—82no—
90C2×Q8×C13SD1614yescomplemented
91C2×Q8×C13C2×D412yes—
92C22×C4×C13—21no—
93C22×C4×C13—21no—
94C22×C4×C13—41no—
95C22×C4×C13C2×D411yescharacteristic
96C22×C4×C13C2×D411yescharacteristic
97C22×C4×C13#4111yescharacteristic
98C2×C22⋊D13—41no—
99#6127—42no—
100#6127—42no—
101C2×D52—21no—
102C2×D52—21no—
103C2×D52—21no—
104C2×C4×D13—41no—
105C2×Dic26—21no—
106C2×C8×C13—22no—
107C2×C8×C13—42no—
108C13×C4⋊C4—22no—
109C13×C4⋊C4—21no—
110C13×C4⋊C4—22no—
111C13×C4⋊C4—22no—
112C13×C4⋊C4—22no—
113C13×C4⋊C4—41no—
114C13×C4⋊C4—41no—
115C13×C4⋊C4C2×D412yes—
116C42×C13—22no—
117C42×C13—22no—
118C42×C13C2×D411yescharacteristic
119C42×C13C2×D411yescharacteristic
120C42×C13#4111yescharacteristic
121C42×C13C2411yescharacteristic
122#6107—44no—
123#6106—44no—
124#6106—84no—
125#6103—41no—
126#6103—41no—
127C4⋊Dic13—21no—
128C4⋊Dic13—21no—
129#6099—42no—
130C2×#1055—22no—
131C2×#1055—22no—
132C2×#1055C2×D414yes—
133#3206—131no—
134C2×#475D1311yescharacteristic, complemented
135#3037—131no—
136#2982—131no—
137#1680—134no—
138#1666—134no—
139#1570—131no—
140#1549—131no—
141#1540—131no—
142C23×C13#12111yescharacteristic
143C22×D13—41no—
144Q8×C13—22no—
145Q8×C13—24no—
146Q8×C13—44no—
147Q8×C13—82no—
148Q8×C13C2×SD1614yes—
149C2×C4×C13—22no—
150C2×C4×C13—24no—
151C2×C4×C13—22no—
152C2×C4×C13—22no—
153C2×C4×C13—41no—
154C2×C4×C13—42no—
155C2×C4×C13—81no—
156C2×C4×C13—82no—
157C2×C4×C13#12111yescharacteristic
158C2×C4×C13#12111yescharacteristic
159C2×C4×C13#12111yescharacteristic
160C2×C4×C13C2×SD1612yes—
161C2×C4×C13#13512yes—
162C2×C4×C13C22×D411yescharacteristic
163C2×C4×C13C22×D411yescharacteristic
164C2×C4×C13C2×#4111yescharacteristic
165C22⋊D13—82no—
166C2×Dic13—41no—
167D52—41no—
168D52—41no—
169D52—42no—
170D52—81no—
171C4×D13—82no—
172Dic26—41no—
173Dic26—41no—
174C8×C13—42no—
175#1055—24no—
176#1055—42no—
177#1055—42no—
178C2×#137—261no—
179#532—131no—
180C2×C4⋊Q8C2×D1311yescharacteristic
181C2×C4×Q8C2×D1311yescharacteristic
182#492—132no—
183#487—132no—
184#475—22no—
185#475C2×D1314yes—
186#464—262no—
187#462—132no—
188#461—262no—
189#460—132no—
190#448—262no—
191C8×Q8—134no—
192C8×Q8—262no—
193#431—131no—
194#431—131no—
195#431—262no—
196C2×#106—21no—
197#423—131no—
198C2×C4⋊C8C2×D1311yescharacteristic
199#417—261no—
200C2×#103—21no—
201#334—134no—
202#332—134no—
203#332—132no—
204#331—132no—
205C22×C13—21no—
206C22×C13—21no—
207C22×C13#46512yes—
208C22×C13C2×#12111yescharacteristic
209C2×D13—81no—
210C2×D13—81no—
211C2×D13—81no—
212C4×C13—21no—
213C4×C13—24no—
214C4×C13—21no—
215C4×C13—21no—
216C4×C13—42no—
217C4×C13—82no—
218C4×C13#46512yes—
219C4×C13C22×SD1611yescharacteristic
220C4×C13C2×#13511yescharacteristic
221C4×C13#57712yes—
222Dic13—81no—
223C2×#41—261no—
224C22×Q8—21no—
225C22×Q8C22⋊D1311yescharacteristic
226#137—524no—
227C2×Q16—262no—
228C2×SD16—264no—
229C2×SD16—262no—
230C2×M16—261no—
231C22×C8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8—131no—
236C4⋊Q8C22×D1312yes—
237#127—131no—
238#124—261no—
239#121—261no—
240#121—261no—
241C4×Q8—21no—
242C4×Q8—21no—
243C4×Q8C22⋊D1312yes—
244C4×Q8C22×D1312yes—
245C4×D4—261no—
246C4×D4—261no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4C22⋊D1311yescharacteristic
251C2×C42—21no—
252C2×C42C22×D1311yescharacteristic
253#106—24no—
254C4⋊C8—21no—
255C4⋊C8—132no—
256C4⋊C8—132no—
257C4⋊C8—132no—
258C4⋊C8—264no—
259C4⋊C8—261no—
260C4⋊C8C22×D1312yes—
261#103—24no—
262#103—264no—
263#103—262no—
264#102—262no—
265C22⋊C8—132no—
266C22⋊C8—261no—
267C4×C8—132no—
268C4×C8—264no—
269C4×C8—261no—
270C2×C13—22no—
271C2×C13#304311yescharacteristic
272C2×C13C2×#46511yescharacteristic
273C2×C13#306911yescharacteristic
274D13—161no—
275#41—522no—
276#41—522no—
277C2×Q8—21no—
278C2×Q8—22no—
279C2×Q8—22no—
280C2×Q8—41no—
281C2×Q8—82no—
282C2×Q8—261no—
283C2×Q8#610614yescomplemented
284C2×Q8C2×C22⋊D1312yes—
285C2×D4—261no—
286C2×D4—261no—
287C2×D4—261no—
288C2×D4—521no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—41no—
292C22×C4—521no—
293C22×C4D4×D1311yescharacteristic
294C22×C4#612911yescharacteristic
295C22×C4C2×C22⋊D1311yescharacteristic
296Q16—524no—
297SD16—524no—
298SD16—1044no—
299M16—522no—
300C2×C8—22no—
301C2×C8—42no—
302C2×C8—134no—
303C2×C8—262no—
304C2×C8—262no—
305C4⋊C4—22no—
306C4⋊C4—21no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—261no—
313C4⋊C4—261no—
314C4⋊C4C2×C22⋊D1312yes—
315C22⋊C4—521no—
316C22⋊C4—521no—
317C42—22no—
318C42—22no—
319C42D4×D1311yescharacteristic
320C42#612911yescharacteristic
321C42C2×C22⋊D1311yescharacteristic
322C42C23×D1311yescharacteristic
323C13#1939711yescharacteristic, complemented, Sylow
324C23—521no—
325C23#8819311yescharacteristic
326Q8—24no—
327Q8—22no—
328Q8—44no—
329Q8—82no—
330Q8—521no—
331Q8—521no—
332Q8C2×#610614yes—
333D4—522no—
334D4—521no—
335D4—521no—
336D4—1041no—
337D4—1042no—
338C2×C4—24no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—81no—
345C2×C4—82no—
346C2×C4—521no—
347C2×C4—1042no—
348C2×C4#8819311yescharacteristic
349C2×C4#8819311yescharacteristic
350C2×C4#8819311yescharacteristic
351C2×C4C2×#610612yes—
352C2×C4#8820412yes—
353C2×C4C2×D4×D1311yescharacteristic
354C2×C4C2×#612911yescharacteristic
355C2×C4C22×C22⋊D1311yescharacteristic
356C8—42no—
357C8—264no—
358C8—522no—
359C8—522no—
360C22—21no—
361C22—21no—
362C22—1041no—
363C22—1041no—
364C22—1041no—
365C22#1171870912yes—
366C22C2×#8819311yescharacteristic
367C4—21no—
368C4—24no—
369C4—21no—
370C4—21no—
371C4—42no—
372C4—82no—
373C4—1041no—
374C4#1171870912yes—
375C4#1171946712yes—
376C4C22×#610611yescharacteristic
377C4C2×#8820411yescharacteristic
378C2—22no—
379C2—2081no—
380C2#1312435411yescharacteristic
381C2C2×#1171870911yescharacteristic
382C2#1312457011yescharacteristic
subgroupG/H
centerC22C2×#88193
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC2×C13×#475C2
socleC22×C13C2×#121
prime radical#11719182C22
hypercenterC2×#475D13
hypocenterC13#19397
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
3. #13123917C2semidirect
4. #13114264C2semidirect
5. #13114186C2semidirect
6. #13113606C2semidirect
7. #13113521C2semidirect
9. C2×C13×#475C2semidirect
90. C2×Q8×C13SD16semidirect
134. C2×#475D13semidirect
283. C2×Q8#6106semidirect
323. C13#19397semidirect

Maximal subgroups

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

subgroupindex
#131257612
#131243082
#131239172
#131142642
#131141862
#131136062
#131135212
#131134862
C2×C13×#4752
#1939713