Finite Group Databasebeta

← #15848309

Subgroups — #15848309

Order 3328.

674 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125758C211yesmaximal, characteristic, complemented
2#13124651C211yesmaximal, characteristic, complemented
3#13123947C211yesmaximal, characteristic, complemented
4#13114268C212yesmaximal, complemented
5#13114261C212yesmaximal, complemented
6#13114182C212yesmaximal, complemented
7#13114175C212yesmaximal, complemented
8#13113606C211yesmaximal, characteristic, complemented
9#13113513C211yesmaximal, characteristic, complemented
10C2×#11718078C211yesmaximal, 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#11718754C2212yes—
26#11718737C2212yes—
27#11718701—22no—
28Q8×#1055C2212yes—
29#11718682—21no—
30#11718681C2212yes—
31#11718680—21no—
32#11718680—21no—
33D4×#1055—22no—
34D4×#1055C2212yes—
35#11718669—21no—
36#11718668C2212yes—
37#11718656—21no—
38#11718586—21no—
39#11718586C2211yescharacteristic
40#11718585C2211yescharacteristic
41C2×C4⋊#1055—21no—
42C2×C4⋊#1055C2211yescharacteristic
43#11718139C2212yes—
44#11718136C2212yes—
45#11718078C2212yes—
46#11718078C2212yes—
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×#6105—22no—
76C2×#6105—22no—
77C2×C4⋊Dic13—21no—
78C2×C4⋊Dic13—21no—
79C2×#6099—21no—
80C22×#1055—21no—
81C22×#1055—22no—
82#88123—21no—
83#88123—21no—
84#88123—21no—
85#88123C2312yes—
86C13×C4⋊C8—21no—
87C13×C4⋊C8C2311yescharacteristic
88C13×C4⋊C8C2311yescharacteristic
89C13×#103—21no—
90C13×#103—21no—
91C13×#102—21no—
92C13×#102—21no—
93#88075—22no—
94#88072—22no—
95C22⋊#1055—22no—
96C22⋊#1055D412yes—
97#88050—22no—
98#88050—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#19408—131nomaximal, Sylow
111C13×#41—22no—
112C13×#41—42no—
113C13×#41—42no—
114C13×#41SD1614yescomplemented
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—81no—
134C2×Dic26—81no—
135C13×Q16—42no—
136C13×SD16—42no—
137C13×SD16—42no—
138C13×D8—42no—
139C2×C8×C13—21no—
140C2×C8×C13—21no—
141C2×C8×C13—42no—
142C13×C4⋊C4—21no—
143C13×C4⋊C4—21no—
144C13×C4⋊C4—21no—
145C13×C4⋊C4—21no—
146C13×C4⋊C4C2×D411yescharacteristic
147C13×C4⋊C4C2×D411yescharacteristic
148C13×C22⋊C4—21no—
149C13×C22⋊C4—21no—
150C13×C22⋊C4—21no—
151C13×C22⋊C4—41no—
152C13×C22⋊C4—41no—
153C42×C13—21no—
154C42×C13—21no—
155C42×C13—21no—
156C42×C13C2×D411yescharacteristic
157C42×C13C2×D411yescharacteristic
158C42×C13#4111yescharacteristic
159C42×C13C2411yescharacteristic
160#6105—82no—
161#6105—82no—
162C4⋊Dic13—22no—
163C4⋊Dic13—22no—
164C4⋊Dic13—41no—
165C4⋊Dic13—41no—
166#6099—42no—
167C2×#1055—22no—
168C2×#1055—22no—
169C2×#1055—82no—
170C2×#1055—81no—
171C2×#1055C2×D412yes—
172C2×#1055C2×D412yes—
173#3206—131no—
174#3079—131no—
175#3035D1311yescharacteristic
176#2988—131no—
177#1680—132no—
178#1679—132no—
179#1666—132no—
180#1665—132no—
181#1570—131no—
182#1547—131no—
183C2×#332—131no—
184C23×C13—21no—
185C23×C13—41no—
186C23×C13#12111yescharacteristic
187Q8×C13—21no—
188Q8×C13—41no—
189Q8×C13—41no—
190Q8×C13C2×SD1612yes—
191D4×C13—24no—
192D4×C13—21no—
193D4×C13—41no—
194D4×C13—41no—
195D4×C13—41no—
196D4×C13—41no—
197D4×C13—81no—
198D4×C13—82no—
199D4×C13C2×SD1612yes—
200C2×C4×C13—21no—
201C2×C4×C13—21no—
202C2×C4×C13—21no—
203C2×C4×C13—24no—
204C2×C4×C13—21no—
205C2×C4×C13—21no—
206C2×C4×C13—41no—
207C2×C4×C13—41no—
208C2×C4×C13—41no—
209C2×C4×C13—41no—
210C2×C4×C13—81no—
211C2×C4×C13—82no—
212C2×C4×C13#12111yescharacteristic
213C2×C4×C13#12111yescharacteristic
214C2×C4×C13#12111yescharacteristic
215C2×C4×C13C2×SD1612yes—
216C2×C4×C13#13512yes—
217C2×C4×C13C22×D411yescharacteristic
218C2×C4×C13C22×D411yescharacteristic
219C2×C4×C13C2×#4111yescharacteristic
220C2×Dic13—42no—
221C2×Dic13—82no—
222Dic26—42no—
223Dic26—42no—
224Dic26—82no—
225C8×C13—41no—
226C8×C13—41no—
227#1055—22no—
228#1055—22no—
229#1055—42no—
230#1055—42no—
231C2×#135—21no—
232#532C2×D1311yescharacteristic
233C2×C4⋊Q8—131no—
234C4×#41C2×D1311yescharacteristic
235#492—132no—
236#487—132no—
237#477—261no—
238#476—261no—
239#475—132no—
240#474—132no—
241#464—21no—
242#463—21no—
243#462C2×D1311yescharacteristic
244#461—261no—
245#461—261no—
246#461C2×D1311yescharacteristic
247#460C2×D1311yescharacteristic
248#459C2×D1311yescharacteristic
249#448—262no—
250C8×Q8—132no—
251C8×D4—132no—
252C8×D4—262no—
253#431—131no—
254#431—261no—
255#428—261no—
256#423—131no—
257C2×C4⋊C8—131no—
258C2×C4⋊C8—261no—
259C2×C4⋊C8C2×D1311yescharacteristic
260#417—261no—
261#416—21no—
262#334—132no—
263#334—132no—
264#332—132no—
265#332—132no—
266#332—132no—
267#331—132no—
268C22×C13—21no—
269C22×C13—21no—
270C22×C13—22no—
271C22×C13—41no—
272C22×C13—41no—
273C22×C13—81no—
274C22×C13—81no—
275C22×C13—81no—
276C22×C13#46512yes—
277C22×C13C2×#12111yescharacteristic
278C4×C13—21no—
279C4×C13—22no—
280C4×C13—21no—
281C4×C13—21no—
282C4×C13—41no—
283C4×C13—41no—
284C4×C13—81no—
285C4×C13#46512yes—
286C4×C13C22×SD1611yescharacteristic
287C4×C13C2×#13511yescharacteristic
288C4×C13#57611yescharacteristic
289C4×C13#57711yescharacteristic
290Dic13—82no—
291C2×#41—21no—
292C2×#41C22⋊D1311yescharacteristic
293C22×Q8—261no—
294#135—44no—
295C2×Q16—21no—
296C2×SD16—21no—
297C2×SD16—21no—
298C2×SD16—262no—
299C2×SD16—262no—
300C2×D8—21no—
301C2×M16—261no—
302C22×C8—21no—
303C22×C8—262no—
304C22×C8—261no—
305C4⋊Q8—132no—
306C4⋊Q8—261no—
307C4⋊Q8—261no—
308C4⋊Q8—261no—
309C4⋊Q8C22×D1311yescharacteristic
310#127C22×D1311yescharacteristic
311#124—21no—
312#121—21no—
313#121—21no—
314C4×Q8C22⋊D1311yescharacteristic
315C4×Q8C22×D1311yescharacteristic
316C4×D4—21no—
317C4×D4—21no—
318C4×D4—21no—
319C4×D4—21no—
320C4×D4C22⋊D1311yescharacteristic
321C4×D4C22×D1311yescharacteristic
322#117—21no—
323#117C22⋊D1311yescharacteristic
324C2×C4⋊C4—261no—
325C2×C4⋊C4—261no—
326C2×C42—21no—
327C2×C42C22×D1311yescharacteristic
328#107—262no—
329#106—262no—
330C4⋊C8—21no—
331C4⋊C8—131no—
332C4⋊C8—131no—
333C4⋊C8—132no—
334C4⋊C8—132no—
335C4⋊C8—262no—
336C4⋊C8—261no—
337C4⋊C8—261no—
338C4⋊C8C22×D1311yescharacteristic
339C4⋊C8C22×D1311yescharacteristic
340#103—21no—
341#103—21no—
342#103—262no—
343#103—262no—
344#103—262no—
345#102—21no—
346#102—21no—
347#102—262no—
348C22⋊C8—132no—
349C22⋊C8—262no—
350C4×C8—132no—
351C4×C8—262no—
352C2×C13—22no—
353C2×C13—42no—
354C2×C13—161no—
355C2×C13#304511yescharacteristic
356C2×C13C2×#46511yescharacteristic
357C2×C13#306911yescharacteristic
358#41—22no—
359#41—42no—
360#41—42no—
361#41#610514yescomplemented
362C2×Q8—21no—
363C2×Q8—262no—
364C2×Q8—521no—
365C2×Q8—1041no—
366C2×Q8—1041no—
367C2×Q8C2×C22⋊D1311yescharacteristic
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—41no—
373C2×D4C2×C22⋊D1311yescharacteristic
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—41no—
378C22×C4—521no—
379C22×C4D4×D1311yescharacteristic
380C22×C4#612911yescharacteristic
381C22×C4C2×C22⋊D1311yescharacteristic
382Q16—42no—
383SD16—42no—
384SD16—42no—
385SD16—1042no—
386SD16—1042no—
387D8—42no—
388M16—522no—
389C2×C8—21no—
390C2×C8—21no—
391C2×C8—42no—
392C2×C8—132no—
393C2×C8—132no—
394C2×C8—262no—
395C2×C8—262no—
396C2×C8—1042no—
397C2×C8—1041no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—262no—
403C4⋊C4—262no—
404C4⋊C4—521no—
405C4⋊C4—521no—
406C4⋊C4C2×C22⋊D1311yescharacteristic
407C4⋊C4C2×C22⋊D1311yescharacteristic
408C22⋊C4—21no—
409C22⋊C4—21no—
410C22⋊C4—21no—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C42—21no—
414C42—21no—
415C42—21no—
416C42D4×D1311yescharacteristic
417C42#612911yescharacteristic
418C42C2×C22⋊D1311yescharacteristic
419C42C23×D1311yescharacteristic
420C13#1940811yescharacteristic, complemented, Sylow
421C23—21no—
422C23—41no—
423C23#8819311yescharacteristic
424Q8—21no—
425Q8—41no—
426Q8—41no—
427Q8—522no—
428Q8—522no—
429Q8—1042no—
430Q8C2×#610512yes—
431D4—24no—
432D4—21no—
433D4—41no—
434D4—41no—
435D4—41no—
436D4—41no—
437D4—81no—
438D4—82no—
439D4C2×#610512yes—
440C2×C4—21no—
441C2×C4—24no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—81no—
451C2×C4—82no—
452C2×C4—522no—
453C2×C4—1042no—
454C2×C4C2×#610512yes—
455C2×C4#8819311yescharacteristic
456C2×C4#8819311yescharacteristic
457C2×C4#8819311yescharacteristic
458C2×C4#8820412yes—
459C2×C4C2×D4×D1311yescharacteristic
460C2×C4C2×#612911yescharacteristic
461C2×C4C22×C22⋊D1311yescharacteristic
462C8—41no—
463C8—41no—
464C8—262no—
465C8—262no—
466C8—522no—
467C8—522no—
468C22—21no—
469C22—21no—
470C22—22no—
471C22—41no—
472C22—41no—
473C22—81no—
474C22—81no—
475C22—81no—
476C22#1171870212yes—
477C22C2×#8819311yescharacteristic
478C4—21no—
479C4—22no—
480C4—21no—
481C4—21no—
482C4—41no—
483C4—41no—
484C4—81no—
485C4—1042no—
486C4#1171870212yes—
487C4#1171947411yescharacteristic
488C4#1171947511yescharacteristic
489C4C22×#610511yescharacteristic
490C4C2×#8820411yescharacteristic
491C2—22no—
492C2—42no—
493C2—161no—
494C2#1312437311yescharacteristic
495C2C2×#1171870211yescharacteristic
496C2#1312457511yescharacteristic
subgroupG/H
centerC22C2×#88193
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
Fitting, prime radicalC13×#3035C2
socleC22×C13C2×#121
hypercenter#3035D13
hypocenterC13#19408
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. #13125758C2semidirect
2. #13124651C2semidirect
3. #13123947C2semidirect
4. #13114268C2semidirect
5. #13114261C2semidirect
6. #13114182C2semidirect
7. #13114175C2semidirect
8. #13113606C2semidirect
9. #13113513C2semidirect
10. C2×#11718078C2semidirect
114. C13×#41SD16semidirect
361. #41#6105semidirect
420. C13#19408semidirect

Maximal subgroups

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

subgroupindex
#131257582
#131246512
#131239472
#131142682
#131142612
#131141822
#131141752
#131136062
#131135132
C2×#117180782
C13×#30352
#1940813