Finite Group Databasebeta

← #15848195

Subgroups — #15848195

Order 3328.

686 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125779C211yesmaximal, characteristic
2#13124641C211yesmaximal, characteristic, complemented
3C2×#11718688C211yesmaximal, characteristic
4#13114252C214yesmaximal, complemented
5#13114184C214yesmaximal, complemented
6#13113607C211yesmaximal, characteristic, complemented
7#13113503C211yesmaximal, characteristic
8#13113491C211yesmaximal, characteristic, complemented
9C13×#2982C211yesmaximal, characteristic, complemented
10C2×C4×Q8×C13C2211yescharacteristic
11C22×#6106—21no—
12C2×#88128C2211yescharacteristic
13#11719175C2211yescharacteristic
14C8×Q8×C13—22no—
15C8×Q8×C13C2214yescomplemented
16C13×#431—22no—
17C13×#431C2211yescharacteristic
18C13×#431C2211yescharacteristic
19#11718886—21no—
20#11718688—22no—
21#11718688C2214yes—
22#11718683—22no—
23#11718682C2212yescomplemented
24#11718681C2212yescomplemented
25C2×#88049—21no—
26#11718625—21no—
27#11718585C2211yescharacteristic
28C2×C4⋊#1055C2211yescharacteristic
29#11718509—22no—
30#11718392—22no—
31#11718355C2212yes—
32#11718354C2212yes—
33#11718077C2214yes—
34#11718074C2212yescomplemented
35#11718073C2212yescomplemented
36#11718049C2214yescomplemented
37C22×Q8×C13D411yescharacteristic
38C22×D52—21no—
39C22×D52—21no—
40C22×D52—21no—
41C4×Q8×C13—21no—
42C4×Q8×C13—21no—
43C4×Q8×C13D412yes—
44C4×Q8×C13C2312yes—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4D411yescharacteristic
47C2×C42×C13—21no—
48C2×C42×C13C2311yescharacteristic
49C2×#6106—24no—
50C2×#6106—44no—
51#88180—21no—
52#88178—21no—
53#88178—21no—
54C2×#6099—21no—
55C22×#1055—21no—
56C2×#6095—24no—
57#88128—21no—
58#88128—21no—
59#88128—21no—
60#88128C2312yes—
61#88124—21no—
62#88123C2311yescharacteristic
63#88123C2311yescharacteristic
64C4×Dic26—21no—
65C4×Dic26—21no—
66C13×C4⋊C8—24no—
67C13×C4⋊C8D412yes—
68C13×C4⋊C8C2312yes—
69C13×C22⋊C8—21no—
70C13×C22⋊C8D412yes—
71C4×C8×C13—24no—
72C4×C8×C13—21no—
73C4×C8×C13C2312yes—
74#88075—22no—
75#88075—22no—
76#88061—24no—
77#88049—24no—
78#88048—22no—
79#88047—22no—
80C4⋊#1055—21no—
81C4⋊#1055—21no—
82C4⋊#1055C2312yes—
83C4⋊#1055C2312yes—
84#19396—131nomaximal, Sylow
85C23×D13—41no—
86C2×Q8×C13—21no—
87C2×Q8×C13—22no—
88C2×Q8×C13SD1614yescomplemented
89C2×Q8×C13C2×D412yes—
90C22×C4×C13—21no—
91C22×C4×C13—21no—
92C22×C4×C13C2×D411yescharacteristic
93C22×C4×C13C2×D411yescharacteristic
94C22×C4×C13#4111yescharacteristic
95C2×D52—22no—
96C2×D52—22no—
97C2×D52—22no—
98C2×D52—42no—
99C2×D52—42no—
100C2×D52—41no—
101C2×D52—41no—
102C2×D52—41no—
103C2×D52—82no—
104C2×D52—82no—
105C2×Dic26—21no—
106C2×Dic26—21no—
107C2×C8×C13—22no—
108C2×C8×C13C2×D414yes—
109C13×C4⋊C4—22no—
110C13×C4⋊C4—21no—
111C13×C4⋊C4—22no—
112C13×C4⋊C4C2×D412yes—
113C42×C13—22no—
114C42×C13—22no—
115C42×C13C2×D411yescharacteristic
116C42×C13C2×D411yescharacteristic
117C42×C13#4111yescharacteristic
118C42×C13C2411yescharacteristic
119C22⋊Dic13—41no—
120#6106—48no—
121C4⋊Dic13—21no—
122C4⋊Dic13—21no—
123C4⋊Dic13—21no—
124C4⋊Dic13—21no—
125#6101—41no—
126#6101—41no—
127C4×Dic13—41no—
128#6099—42no—
129C2×#1055—22no—
130C2×#1055—22no—
131C2×#1055—42no—
132#6095—84no—
133#3208—131no—
134#3078—131no—
135C2×#460—131no—
136#2982D1311yescharacteristic, complemented
137#1678—134no—
138#1666—134no—
139#1570—131no—
140#1545—131no—
141#1542—131no—
142C23×C13#12111yescharacteristic
143C22×D13—42no—
144C22×D13—82no—
145C22×D13—82no—
146C22×D13—82no—
147Q8×C13—22no—
148Q8×C13—24no—
149Q8×C13C2×SD1614yes—
150C2×C4×C13—22no—
151C2×C4×C13—24no—
152C2×C4×C13—22no—
153C2×C4×C13—22no—
154C2×C4×C13—41no—
155C2×C4×C13—81no—
156C2×C4×C13#12111yescharacteristic
157C2×C4×C13#12111yescharacteristic
158C2×C4×C13#12111yescharacteristic
159C2×C4×C13C2×SD1612yes—
160C2×C4×C13#13512yes—
161C2×C4×C13C22×D411yescharacteristic
162C2×C4×C13C22×D411yescharacteristic
163C2×C4×C13C2×#4111yescharacteristic
164C2×Dic13—41no—
165C2×Dic13—41no—
166D52—42no—
167D52—42no—
168D52—44no—
169D52—82no—
170D52—82no—
171D52—82no—
172D52—82no—
173Dic26—42no—
174Dic26—81no—
175C8×C13—24no—
176C8×C13—42no—
177#1055—42no—
178#1055—42no—
179C22×SD16—261no—
180#533—131no—
181C2×#127—131no—
182C2×C4×Q8C2×D1311yescharacteristic
183#492—132no—
184#486—132no—
185#479—262no—
186#477—132no—
187#475—132no—
188#460—134no—
189#460—262no—
190#460—262no—
191#450—262no—
192C8×Q8—22no—
193C8×Q8C2×D1314yescomplemented
194#431—22no—
195#431C2×D1311yescharacteristic
196#431C2×D1311yescharacteristic
197#428—261no—
198#423—131no—
199C2×C4⋊C8—131no—
200#419—261no—
201C2×#102—261no—
202#334—134no—
203#333—132no—
204#332—132no—
205#331—134no—
206C22×C13—21no—
207C22×C13—21no—
208C22×C13#46512yes—
209C22×C13C2×#12111yescharacteristic
210C2×D13—82no—
211C2×D13—82no—
212C2×D13—82no—
213C2×D13—164no—
214C4×C13—21no—
215C4×C13—24no—
216C4×C13—21no—
217C4×C13—21no—
218C4×C13—42no—
219C4×C13#46512yes—
220C4×C13C22×SD1611yescharacteristic
221C4×C13C2×#13511yescharacteristic
222C4×C13#57712yes—
223Dic13—81no—
224Dic13—81no—
225C22×Q8D5211yescharacteristic
226C22×D4—261no—
227C22×D4—261no—
228C22×D4—261no—
229C2×SD16—264no—
230C2×SD16—264no—
231C2×SD16—524no—
232C2×M16—261no—
233C22×C8—261no—
234C4⋊Q8—131no—
235C4⋊Q8—131no—
236#127—132no—
237#127—261no—
238#127—261no—
239#127—261no—
240#125—261no—
241C22⋊Q8—261no—
242C22⋊Q8—261no—
243C4×Q8—21no—
244C4×Q8—21no—
245C4×Q8—261no—
246C4×Q8—261no—
247C4×Q8D5212yes—
248C4×Q8C22×D1312yes—
249#117—261no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4D5211yescharacteristic
252C2×C42—21no—
253C2×C42C22×D1311yescharacteristic
254#107—262no—
255#106—262no—
256C4⋊C8—24no—
257C4⋊C8—132no—
258C4⋊C8—132no—
259C4⋊C8—261no—
260C4⋊C8—261no—
261C4⋊C8C22⋊D1312yes—
262C4⋊C8C22×D1312yes—
263#103—262no—
264#103—262no—
265#102—264no—
266#102—264no—
267C22⋊C8—21no—
268C22⋊C8C22⋊D1312yes—
269C4×C8—24no—
270C4×C8—21no—
271C4×C8C22×D1312yes—
272C2×C13—22no—
273C2×C13#304311yescharacteristic
274C2×C13C2×#46511yescharacteristic
275C2×C13#306811yescharacteristic
276D13—162no—
277C24—521no—
278C2×Q8—22no—
279C2×Q8—21no—
280C2×Q8—261no—
281C2×Q8—261no—
282C2×Q8#609514yescomplemented
283C2×Q8C2×D5212yes—
284C2×D4—262no—
285C2×D4—262no—
286C2×D4—262no—
287C2×D4—522no—
288C2×D4—522no—
289C2×D4—521no—
290C2×D4—521no—
291C2×D4—521no—
292C2×D4—1042no—
293C2×D4—1042no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4C2×D5211yescharacteristic
297C22×C4#612711yescharacteristic
298C22×C4C2×C22⋊D1311yescharacteristic
299SD16—528no—
300SD16—1044no—
301M16—522no—
302C2×C8—22no—
303C2×C8—262no—
304C2×C8—262no—
305C2×C8—522no—
306C2×C8C2×C22⋊D1314yes—
307C4⋊C4—22no—
308C4⋊C4—21no—
309C4⋊C4—22no—
310C4⋊C4—261no—
311C4⋊C4—261no—
312C4⋊C4—261no—
313C4⋊C4—261no—
314C4⋊C4—521no—
315C4⋊C4—521no—
316C4⋊C4C2×D5212yes—
317C22⋊C4—521no—
318C42—22no—
319C42—22no—
320C42—521no—
321C42C2×D5211yescharacteristic
322C42#612711yescharacteristic
323C42C2×C22⋊D1311yescharacteristic
324C42C23×D1311yescharacteristic
325C13#1939611yescharacteristic, complemented, Sylow
326C23—522no—
327C23—1042no—
328C23—1042no—
329C23—1042no—
330C23#8818411yescharacteristic
331Q8—22no—
332Q8—24no—
333Q8—522no—
334Q8—1041no—
335Q8C2×#609514yes—
336D4—522no—
337D4—522no—
338D4—524no—
339D4—1042no—
340D4—1042no—
341D4—1042no—
342D4—1042no—
343C2×C4—22no—
344C2×C4—24no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—41no—
348C2×C4—81no—
349C2×C4—521no—
350C2×C4—521no—
351C2×C4C2×#609512yes—
352C2×C4#8815812yes—
353C2×C4#8818411yescharacteristic
354C2×C4#8818411yescharacteristic
355C2×C4#8818411yescharacteristic
356C2×C4C22×D5211yescharacteristic
357C2×C4C2×#612711yescharacteristic
358C2×C4C22×C22⋊D1311yescharacteristic
359C8—24no—
360C8—42no—
361C8—522no—
362C8—522no—
363C22—21no—
364C22—21no—
365C22—1042no—
366C22—1042no—
367C22—1042no—
368C22—2084no—
369C22#1171877512yes—
370C22C2×#8818411yescharacteristic
371C4—21no—
372C4—24no—
373C4—21no—
374C4—21no—
375C4—42no—
376C4—1041no—
377C4—1041no—
378C4#1171877512yes—
379C4C22×#609511yescharacteristic
380C4C2×#8815811yescharacteristic
381C4#1171954212yes—
382C2—22no—
383C2—2082no—
384C2#1312435711yescharacteristic
385C2C2×#1171877511yescharacteristic
386C2#1312456411yescharacteristic
subgroupG/H
centerC22C2×#88184
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC13×#2982C2
socleC22×C13C2×#121
prime radicalC2×#88128C22
hypercenter#2982D13
hypocenterC13#19396
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2982

Complements

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

NH ≅ G/Ntype
2. #13124641C2semidirect
4. #13114252C2semidirect
5. #13114184C2semidirect
6. #13113607C2semidirect
8. #13113491C2semidirect
9. C13×#2982C2semidirect
15. C8×Q8×C13C22semidirect
23. #11718682C22semidirect
24. #11718681C22semidirect
34. #11718074C22semidirect
35. #11718073C22semidirect
36. #11718049C22semidirect
88. C2×Q8×C13SD16semidirect
136. #2982D13semidirect
193. C8×Q8C2×D13semidirect
282. C2×Q8#6095semidirect
325. C13#19396semidirect

Maximal subgroups

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

subgroupindex
#131257792
#131246412
C2×#117186882
#131142522
#131141842
#131136072
#131135032
#131134912
C13×#29822
#1939613