Finite Group Databasebeta

← #15848383

Subgroups — #15848383

Order 3328.

662 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125961C211yesmaximal, characteristic, complemented
2#13124651C211yesmaximal, characteristic, complemented
3#13123947C211yesmaximal, characteristic, complemented
4#13114250C212yesmaximal, complemented
5#13114243C212yesmaximal, complemented
6#13114216C212yesmaximal, complemented
7#13114209C212yesmaximal, complemented
8#13113606C211yesmaximal, characteristic, complemented
9#13113513C211yesmaximal, characteristic, complemented
10C2×#11718073C211yesmaximal, characteristic, complemented
11C13×#3035C211yesmaximal, characteristic
12C2×C13×#135—21no—
13C13×#532C2211yescharacteristic
14C4×C13×#41C2211yescharacteristic
15C2×#88123C2211yescharacteristic
16C13×#464—21no—
17C13×#463—21no—
18C13×#462C2211yescharacteristic
19C13×#461C2211yescharacteristic
20C13×#460C2211yescharacteristic
21C13×#459C2211yescharacteristic
22C2×C13×C4⋊C8C2211yescharacteristic
23C13×#416—21no—
24#11718893—21no—
25#11718740C2212yes—
26#11718731C2212yes—
27#11718695—22no—
28Q8×#1055C2212yes—
29#11718682C2212yes—
30#11718681—21no—
31D4×#1055—22no—
32D4×#1055C2212yes—
33#11718669—21no—
34#11718669—21no—
35#11718669C2212yes—
36#11718668—21no—
37#11718656—21no—
38#11718586—21no—
39#11718586C2211yescharacteristic
40#11718585C2211yescharacteristic
41C2×C4⋊#1055—21no—
42C2×C4⋊#1055C2211yescharacteristic
43#11718139C2212yes—
44#11718136C2212yes—
45#11718073C2212yes—
46#11718073C2212yes—
47#11718072C2212yes—
48#11718072C2212yes—
49C2×C13×#41—21no—
50C2×C13×#41D411yescharacteristic
51C22×Dic26—21no—
52C13×#135—44no—
53C2×C13×Q16—21no—
54C2×C13×SD16—21no—
55C2×C13×SD16—21no—
56C2×C13×D8—21no—
57C22×C8×C13—21no—
58C13×C4⋊Q8C2311yescharacteristic
59C13×#127C2311yescharacteristic
60C13×#124—21no—
61C13×#121—21no—
62C13×#121—21no—
63C4×Q8×C13D411yescharacteristic
64C4×Q8×C13C2311yescharacteristic
65C4×D4×C13—21no—
66C4×D4×C13—21no—
67C4×D4×C13—21no—
68C4×D4×C13—21no—
69C4×D4×C13D411yescharacteristic
70C4×D4×C13C2311yescharacteristic
71C13×#117—21no—
72C13×#117D411yescharacteristic
73C2×C42×C13—21no—
74C2×C42×C13C2311yescharacteristic
75C2×C4⋊Dic13—21no—
76C2×C4⋊Dic13—21no—
77C2×#6099—21no—
78C22×#1055—21no—
79C22×#1055—22no—
80#88123—21no—
81#88123—21no—
82#88123—21no—
83#88123C2312yes—
84C13×C4⋊C8—21no—
85C13×C4⋊C8C2311yescharacteristic
86C13×C4⋊C8C2311yescharacteristic
87C13×#103—21no—
88C13×#103—21no—
89C13×#102—21no—
90C13×#102—21no—
91#88075—22no—
92#88072—22no—
93#88072—22no—
94#88072—22no—
95C22⋊#1055—22no—
96C22⋊#1055D412yes—
97#88048—22no—
98#88048—22no—
99#88048—22no—
100#88047—22no—
101C4⋊#1055—21no—
102C4⋊#1055—21no—
103C4⋊#1055—22no—
104C4⋊#1055D411yescharacteristic
105C4⋊#1055D411yescharacteristic
106C4⋊#1055C2312yes—
107C4⋊#1055C2312yes—
108C4×#1055—22no—
109C4×#1055C2312yes—
110#19414—131nomaximal, Sylow
111C13×#41—22no—
112C13×#41—42no—
113C13×#41—42no—
114C13×#41SD1614yes—
115C2×Q8×C13—21no—
116C2×Q8×C13C2×D411yescharacteristic
117C2×D4×C13—21no—
118C2×D4×C13—21no—
119C2×D4×C13—21no—
120C2×D4×C13—21no—
121C2×D4×C13—41no—
122C2×D4×C13C2×D411yescharacteristic
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—41no—
127C22×C4×C13C2×D411yescharacteristic
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13#4111yescharacteristic
130C22×Dic13—41no—
131C2×Dic26—22no—
132C2×Dic26—41no—
133C2×Dic26—82no—
134C13×Q16—42no—
135C13×SD16—42no—
136C13×SD16—42no—
137C13×D8—42no—
138C2×C8×C13—21no—
139C2×C8×C13—21no—
140C2×C8×C13—42no—
141C13×C4⋊C4—21no—
142C13×C4⋊C4—21no—
143C13×C4⋊C4—21no—
144C13×C4⋊C4—21no—
145C13×C4⋊C4C2×D411yescharacteristic
146C13×C4⋊C4C2×D411yescharacteristic
147C13×C22⋊C4—21no—
148C13×C22⋊C4—21no—
149C13×C22⋊C4—21no—
150C13×C22⋊C4—41no—
151C13×C22⋊C4—41no—
152C42×C13—21no—
153C42×C13—21no—
154C42×C13—21no—
155C42×C13C2×D411yescharacteristic
156C42×C13C2×D411yescharacteristic
157C42×C13#4111yescharacteristic
158C42×C13C2411yescharacteristic
159C4⋊Dic13—22no—
160C4⋊Dic13—22no—
161C4⋊Dic13—41no—
162C4⋊Dic13—41no—
163#6099—42no—
164C2×#1055—22no—
165C2×#1055—22no—
166C2×#1055—82no—
167C2×#1055—81no—
168C2×#1055C2×D412yes—
169C2×#1055C2×D412yes—
170#3227—131no—
171#3079—131no—
172#3035D1311yescharacteristic
173#2988—131no—
174#1678—132no—
175#1677—132no—
176#1672—132no—
177#1671—132no—
178#1570—131no—
179#1547—131no—
180C2×#333—131no—
181C23×C13—21no—
182C23×C13—41no—
183C23×C13#12111yescharacteristic
184Q8×C13—21no—
185Q8×C13—41no—
186Q8×C13—41no—
187Q8×C13C2×SD1612yes—
188D4×C13—24no—
189D4×C13—21no—
190D4×C13—41no—
191D4×C13—41no—
192D4×C13—41no—
193D4×C13—41no—
194D4×C13—81no—
195D4×C13—82no—
196D4×C13C2×SD1612yes—
197C2×C4×C13—21no—
198C2×C4×C13—21no—
199C2×C4×C13—21no—
200C2×C4×C13—24no—
201C2×C4×C13—21no—
202C2×C4×C13—21no—
203C2×C4×C13—41no—
204C2×C4×C13—41no—
205C2×C4×C13—41no—
206C2×C4×C13—41no—
207C2×C4×C13—81no—
208C2×C4×C13—82no—
209C2×C4×C13#12111yescharacteristic
210C2×C4×C13#12111yescharacteristic
211C2×C4×C13#12111yescharacteristic
212C2×C4×C13C2×SD1612yes—
213C2×C4×C13#13512yes—
214C2×C4×C13C22×D411yescharacteristic
215C2×C4×C13C22×D411yescharacteristic
216C2×C4×C13C2×#4111yescharacteristic
217C2×Dic13—42no—
218C2×Dic13—82no—
219Dic26—82no—
220Dic26—82no—
221C8×C13—41no—
222C8×C13—41no—
223#1055—22no—
224#1055—22no—
225#1055—42no—
226#1055—42no—
227C2×#135—21no—
228#532C2×D1311yescharacteristic
229C2×C4⋊Q8—131no—
230C4×#41C2×D1311yescharacteristic
231#498—132no—
232#486—132no—
233#481—262no—
234#477—132no—
235#476—132no—
236#476—261no—
237#476—261no—
238#475—261no—
239#474—261no—
240#464—21no—
241#463—21no—
242#462C2×D1311yescharacteristic
243#461C2×D1311yescharacteristic
244#460C2×D1311yescharacteristic
245#459C2×D1311yescharacteristic
246C8×Q8—132no—
247C8×D4—132no—
248C8×D4—262no—
249#431—131no—
250#431—261no—
251#428—261no—
252#423—131no—
253C2×C4⋊C8—131no—
254C2×C4⋊C8—261no—
255C2×C4⋊C8C2×D1311yescharacteristic
256#417—261no—
257#416—21no—
258#334—132no—
259#334—132no—
260#333—132no—
261#333—132no—
262#332—132no—
263#331—132no—
264C22×C13—21no—
265C22×C13—21no—
266C22×C13—22no—
267C22×C13—41no—
268C22×C13—41no—
269C22×C13—81no—
270C22×C13—81no—
271C22×C13—81no—
272C22×C13#46512yes—
273C22×C13C2×#12111yescharacteristic
274C4×C13—21no—
275C4×C13—22no—
276C4×C13—21no—
277C4×C13—21no—
278C4×C13—41no—
279C4×C13—41no—
280C4×C13—81no—
281C4×C13#46512yes—
282C4×C13C22×SD1611yescharacteristic
283C4×C13C2×#13511yescharacteristic
284C4×C13#57711yescharacteristic
285C4×C13#57811yescharacteristic
286Dic13—82no—
287C2×#41—21no—
288C2×#41C22⋊D1311yescharacteristic
289C22×Q8—261no—
290#135—44no—
291C2×Q16—21no—
292C2×SD16—21no—
293C2×SD16—21no—
294C2×D8—21no—
295C2×M16—261no—
296C22×C8—21no—
297C22×C8—262no—
298C22×C8—261no—
299C4⋊Q8—132no—
300C4⋊Q8—261no—
301C4⋊Q8—261no—
302C4⋊Q8—261no—
303C4⋊Q8C22×D1311yescharacteristic
304#127C22×D1311yescharacteristic
305#124—21no—
306#121—21no—
307#121—21no—
308C4×Q8C22⋊D1311yescharacteristic
309C4×Q8C22×D1311yescharacteristic
310C4×D4—21no—
311C4×D4—21no—
312C4×D4—21no—
313C4×D4—21no—
314C4×D4C22⋊D1311yescharacteristic
315C4×D4C22×D1311yescharacteristic
316#117—21no—
317#117C22⋊D1311yescharacteristic
318C2×C4⋊C4—261no—
319C2×C4⋊C4—261no—
320C2×C42—21no—
321C2×C42C22×D1311yescharacteristic
322#107—262no—
323#106—262no—
324#106—262no—
325#106—262no—
326C4⋊C8—21no—
327C4⋊C8—131no—
328C4⋊C8—131no—
329C4⋊C8—132no—
330C4⋊C8—132no—
331C4⋊C8—262no—
332C4⋊C8—261no—
333C4⋊C8—261no—
334C4⋊C8C22×D1311yescharacteristic
335C4⋊C8C22×D1311yescharacteristic
336#103—21no—
337#103—21no—
338#103—262no—
339#102—21no—
340#102—21no—
341#102—262no—
342#102—262no—
343#102—262no—
344C22⋊C8—132no—
345C22⋊C8—262no—
346C4×C8—132no—
347C4×C8—262no—
348C2×C13—22no—
349C2×C13—42no—
350C2×C13—161no—
351C2×C13#304611yescharacteristic
352C2×C13C2×#46511yescharacteristic
353C2×C13#306811yescharacteristic
354#41—22no—
355#41—42no—
356#41—42no—
357#41#610514yes—
358C2×Q8—21no—
359C2×Q8—262no—
360C2×Q8—521no—
361C2×Q8—1042no—
362C2×Q8C2×C22⋊D1311yescharacteristic
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—41no—
368C2×D4C2×C22⋊D1311yescharacteristic
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—41no—
373C22×C4—521no—
374C22×C4D4×D1311yescharacteristic
375C22×C4#612911yescharacteristic
376C22×C4C2×C22⋊D1311yescharacteristic
377Q16—42no—
378SD16—42no—
379SD16—42no—
380D8—42no—
381M16—522no—
382C2×C8—21no—
383C2×C8—21no—
384C2×C8—42no—
385C2×C8—132no—
386C2×C8—132no—
387C2×C8—262no—
388C2×C8—262no—
389C2×C8—1042no—
390C2×C8—1041no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—262no—
396C4⋊C4—262no—
397C4⋊C4—521no—
398C4⋊C4—521no—
399C4⋊C4C2×C22⋊D1311yescharacteristic
400C4⋊C4C2×C22⋊D1311yescharacteristic
401C22⋊C4—21no—
402C22⋊C4—21no—
403C22⋊C4—21no—
404C22⋊C4—41no—
405C22⋊C4—41no—
406C42—21no—
407C42—21no—
408C42—21no—
409C42D4×D1311yescharacteristic
410C42#612911yescharacteristic
411C42C2×C22⋊D1311yescharacteristic
412C42C23×D1311yescharacteristic
413C13#1941411yescharacteristic, complemented, Sylow
414C23—21no—
415C23—41no—
416C23#8819311yescharacteristic
417Q8—21no—
418Q8—41no—
419Q8—41no—
420Q8—1042no—
421Q8—1042no—
422Q8C2×#610512yes—
423D4—24no—
424D4—21no—
425D4—41no—
426D4—41no—
427D4—41no—
428D4—41no—
429D4—81no—
430D4—82no—
431D4C2×#610512yes—
432C2×C4—21no—
433C2×C4—24no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—81no—
443C2×C4—82no—
444C2×C4—522no—
445C2×C4—1042no—
446C2×C4C2×#610512yes—
447C2×C4#8819311yescharacteristic
448C2×C4#8819311yescharacteristic
449C2×C4#8819311yescharacteristic
450C2×C4#8820412yes—
451C2×C4C2×D4×D1311yescharacteristic
452C2×C4C2×#612911yescharacteristic
453C2×C4C22×C22⋊D1311yescharacteristic
454C8—41no—
455C8—41no—
456C8—262no—
457C8—262no—
458C8—522no—
459C8—522no—
460C22—21no—
461C22—21no—
462C22—22no—
463C22—41no—
464C22—41no—
465C22—81no—
466C22—81no—
467C22—81no—
468C22#1171870212yes—
469C22C2×#8819311yescharacteristic
470C4—21no—
471C4—22no—
472C4—21no—
473C4—21no—
474C4—41no—
475C4—41no—
476C4—81no—
477C4—1042no—
478C4#1171870212yes—
479C4#1171947511yescharacteristic
480C4#1171947611yescharacteristic
481C4C22×#610511yescharacteristic
482C4C2×#8820411yescharacteristic
483C2—22no—
484C2—42no—
485C2—161no—
486C2#1312438411yescharacteristic
487C2C2×#1171870211yescharacteristic
488C2#1312456611yescharacteristic
subgroupG/H
centerC22C2×#88193
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
Fitting, prime radicalC13×#3035C2
socleC22×C13C2×#121
hypercenter#3035D13
hypocenterC13#19414
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3035

Complements

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

NH ≅ G/Ntype
1. #13125961C2semidirect
2. #13124651C2semidirect
3. #13123947C2semidirect
4. #13114250C2semidirect
5. #13114243C2semidirect
6. #13114216C2semidirect
7. #13114209C2semidirect
8. #13113606C2semidirect
9. #13113513C2semidirect
10. C2×#11718073C2semidirect
413. C13#19414semidirect

Maximal subgroups

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

subgroupindex
#131259612
#131246512
#131239472
#131142502
#131142432
#131142162
#131142092
#131136062
#131135132
C2×#117180732
C13×#30352
#1941413