Finite Group Databasebeta

← #15833543

Subgroups — #15833543

Order 3328.

622 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125425C211yesmaximal, characteristic
2#13123981C211yesmaximal, characteristic, complemented
3#13123912C211yesmaximal, characteristic, complemented
4#13113747C211yesmaximal, characteristic, complemented
5#13113735C211yesmaximal, characteristic, complemented
6#13113729C211yesmaximal, characteristic, complemented
7#13113718C211yesmaximal, characteristic, complemented
8#13113657C211yesmaximal, characteristic, complemented
9#13113645C211yesmaximal, characteristic, complemented
10#13113639C211yesmaximal, characteristic, complemented
11#13113628C211yesmaximal, characteristic, complemented
12#13113601C211yesmaximal, characteristic, complemented
13#13113297C211yesmaximal, characteristic, complemented
14C8×#6099C211yesmaximal, characteristic, complemented
15C13×#1492C211yesmaximal, characteristic, complemented
16C13×#532C2211yescharacteristic
17#11719184C2211yescharacteristic
18C13×#423C2211yescharacteristic
19C2×C4×C8×C13C2211yescharacteristic
20#11718895—21no—
21#11718895—21no—
22#11718789—21no—
23#11718788—21no—
24#11718750C411yescharacteristic
25#11718741C411yescharacteristic
26#11718735C411yescharacteristic
27#11718732C411yescharacteristic
28#11718703C411yescharacteristic
29#11718703C411yescharacteristic
30#11718700C411yescharacteristic
31#11718700C411yescharacteristic
32C4×#6105C2211yescharacteristic
33C4×#6105C2211yescharacteristic
34C4×#6104C2211yescharacteristic
35C4×#6104C2211yescharacteristic
36#11718673C2211yescharacteristic
37#11718673C2211yescharacteristic
38#11718672—21no—
39#11718672—21no—
40D4×#1055C2211yescharacteristic
41D4×#1055C2211yescharacteristic
42#11718587C2211yescharacteristic
43#11718586C2211yescharacteristic
44C4×#6099C2211yescharacteristic
45#11718501—21no—
46#11718500—21no—
47#11718499C2211yescharacteristic
48#11718495C2211yescharacteristic
49#11718492C2211yescharacteristic
50#11718491C2211yescharacteristic
51C13×D4⋊C8C2211yescharacteristic
52C13×D4⋊C8C2211yescharacteristic
53C13×D4⋊C8C2211yescharacteristic
54C13×D4⋊C8C2211yescharacteristic
55#11718072C2211yescharacteristic
56#11718072C2211yescharacteristic
57#11718071C2211yescharacteristic
58#11718071C2211yescharacteristic
59#11718051C2211yescharacteristic
60#11718051C2211yescharacteristic
61#11718048C2211yescharacteristic
62#11718048C2211yescharacteristic
63#11718046C2211yescharacteristic
64#11718046C2211yescharacteristic
65C8×#1055C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×C13×#41—21no—
68C2×C13×M16—21no—
69C22×C8×C13—21no—
70C13×C4⋊Q8C2×C411yescharacteristic
71C13×#127C2×C411yescharacteristic
72C13×#124—21no—
73C13×#121—21no—
74C13×#121C2×C411yescharacteristic
75C13×#121C2×C411yescharacteristic
76C4×D4×C13—21no—
77C4×D4×C13C2311yescharacteristic
78C4×D4×C13C2311yescharacteristic
79C2×C42×C13C2311yescharacteristic
80C2×#6105C2×C411yescharacteristic
81C2×#6105C2×C411yescharacteristic
82C2×#6104C2×C411yescharacteristic
83C2×#6104C2×C411yescharacteristic
84#88184C2×C411yescharacteristic
85#88183—21no—
86C4×C22⋊D13—21no—
87#88178C2×C411yescharacteristic
88C2×#6099—21no—
89C2×#6099—21no—
90C2×#6099C2×C411yescharacteristic
91C2×#6099C2×C411yescharacteristic
92C22×#1055—21no—
93C22×#1055—21no—
94C2×#6094—21no—
95C2×C8×D13—21no—
96#88130—21no—
97#88129C2×C411yescharacteristic
98C4×D52C2311yescharacteristic
99#88126—21no—
100#88124C2×C411yescharacteristic
101C4×Dic26C2311yescharacteristic
102C13×C4⋊C8—21no—
103C13×C4⋊C8C2311yescharacteristic
104C13×C4⋊C8C2311yescharacteristic
105C4×C8×C13—21no—
106C4×C8×C13C2311yescharacteristic
107C4×C8×C13C2311yescharacteristic
108#88072C2×C411yescharacteristic
109#88072C2×C411yescharacteristic
110#88072C2×C411yescharacteristic
111#88072C2×C411yescharacteristic
112C22⋊#1055—21no—
113C22⋊#1055—21no—
114C22⋊#1055—21no—
115C22⋊#1055—21no—
116C22⋊#1055—21no—
117C22⋊#1055D411yescharacteristic
118C22⋊#1055D411yescharacteristic
119#88060—21no—
120#88060—21no—
121#88055—21no—
122#88054—21no—
123#88054—21no—
124C8×Dic13—21no—
125#88050C2×C411yescharacteristic
126#88050C2×C411yescharacteristic
127#88049C2×C411yescharacteristic
128#88049C2×C411yescharacteristic
129#88048C2×C411yescharacteristic
130#88048C2×C411yescharacteristic
131#88047C2×C411yescharacteristic
132#88047C2×C411yescharacteristic
133C4⋊#1055D411yescharacteristic
134C4⋊#1055D411yescharacteristic
135C4⋊#1055C2311yescharacteristic
136C4⋊#1055C2311yescharacteristic
137#88043—21no—
138#88043C2×C411yescharacteristic
139#88043C2×C411yescharacteristic
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#17968—131nomaximal, Sylow
145C13×#41—81no—
146C13×#41—81no—
147C2×Q8×C13—21no—
148C2×D4×C13—21no—
149C2×D4×C13—21no—
150C2×D4×C13—21no—
151C2×D4×C13—21no—
152C2×D4×C13C22×C411yescharacteristic
153C2×D4×C13C22×C411yescharacteristic
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13C22×C411yescharacteristic
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13#4111yescharacteristic
159C2×C22⋊D13—21no—
160C2×D52C22×C411yescharacteristic
161C2×C4×D13—21no—
162C2×Dic26C22×C411yescharacteristic
163C13×M16—81no—
164C2×C8×C13—21no—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13—42no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4C22×C411yescharacteristic
171C13×C4⋊C4C22×C411yescharacteristic
172C13×C22⋊C4—21no—
173C13×C22⋊C4—21no—
174C13×C22⋊C4—21no—
175C13×C22⋊C4—21no—
176C42×C13C22×C411yescharacteristic
177C42×C13C2×D411yescharacteristic
178C42×C13#4111yescharacteristic
179C42×C13C2411yescharacteristic
180C22⋊Dic13—21no—
181#6105—22no—
182#6105—22no—
183#6104—22no—
184#6104—22no—
185#6103—21no—
186#6103—21no—
187#6103—21no—
188#6103—21no—
189C4⋊Dic13C22×C411yescharacteristic
190C4⋊Dic13C22×C411yescharacteristic
191#6101—21no—
192#6101—21no—
193#6101—21no—
194#6101—21no—
195C4×Dic13—21no—
196#6099—22no—
197#6099—22no—
198#6099—81no—
199#6099—81no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—81no—
203C2×#1055—81no—
204C2×#1055C22×C411yescharacteristic
205C2×#1055C22×C411yescharacteristic
206C2×#1055C22×C411yescharacteristic
207C2×#1055C22×C411yescharacteristic
208C2×#1055C2×D411yescharacteristic
209C2×#1055C2×D411yescharacteristic
210C2×#1055C2×D411yescharacteristic
211C2×#1055C2×D411yescharacteristic
212#6094—81no—
213C8×D13—81no—
214#3171—131no—
215#2993—131no—
216#2981—131no—
217#1594—131no—
218#1592—131no—
219#1590—131no—
220#1589—131no—
221#1580—131no—
222SD16⋊C8—131no—
223C8×SD16—131no—
224C8×D8—131no—
225#1569—131no—
226#1494—131no—
227#1492D1311yescharacteristic, complemented
228C8×M16—131no—
229C23×C13—21no—
230C23×C13—21no—
231C23×C13C4×D411yescharacteristic
232C22×D13—21no—
233Q8×C13—81no—
234D4×C13—21no—
235D4×C13—21no—
236D4×C13—21no—
237D4×C13—21no—
238D4×C13—81no—
239D4×C13—81no—
240D4×C13—81no—
241D4×C13—81no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13C4×D411yescharacteristic
254C2×C4×C13C4×D411yescharacteristic
255C2×C4×C13C4×D411yescharacteristic
256C2×C4×C13C23×C411yescharacteristic
257C2×C4×C13C22×D411yescharacteristic
258C2×C4×C13C2×#4111yescharacteristic
259C22⋊D13—81no—
260C2×Dic13—21no—
261C2×Dic13—21no—
262C2×Dic13—21no—
263D52—21no—
264D52—21no—
265C4×D13—41no—
266C4×D13—41no—
267Dic26—21no—
268Dic26—21no—
269C8×C13—22no—
270C8×C13—41no—
271C8×C13—41no—
272C8×C13—41no—
273#1055—21no—
274#1055—21no—
275#1055—21no—
276#1055—21no—
277#1055—21no—
278#1055—21no—
279#1055—41no—
280#1055—41no—
281#1055#13112yes—
282#1055#13112yes—
283#532C2×D1311yescharacteristic
284#529—131no—
285#501—131no—
286#496—131no—
287#490—131no—
288#489—131no—
289#469—131no—
290#469—131no—
291#468—131no—
292#468—131no—
293#446—131no—
294C8×Q8—131no—
295C4×SD16—131no—
296C4×SD16—131no—
297C4×D8—131no—
298C4×D8—131no—
299#436—131no—
300#436—131no—
301#436—131no—
302#436—261no—
303#435—261no—
304#435—261no—
305#435—261no—
306C8×D4—131no—
307C8×D4—131no—
308C8×D4—131no—
309#433—261no—
310#432—131no—
311#431—131no—
312#424—261no—
313#423C2×D1311yescharacteristic
314#408—261no—
315#408—261no—
316C4×M16—131no—
317C2×C4×C8C2×D1311yescharacteristic
318#335—131no—
319#335—131no—
320#334—131no—
321#334—131no—
322Q8⋊C8—131no—
323Q8⋊C8—131no—
324D4⋊C8—131no—
325D4⋊C8—131no—
326D4⋊C8C2×D1311yescharacteristic
327D4⋊C8C2×D1311yescharacteristic
328D4⋊C8C2×D1311yescharacteristic
329D4⋊C8C2×D1311yescharacteristic
330#322—131no—
331#322—131no—
332C82—131no—
333C82—131no—
334C22×C13—21no—
335C22×C13—21no—
336C22×C13—21no—
337C22×C13—41no—
338C22×C13—41no—
339C22×C13—41no—
340C22×C13—41no—
341C22×C13—41no—
342C22×C13—41no—
343C22×C13C2×C4×D411yescharacteristic
344C2×D13—41no—
345C2×D13—41no—
346C2×D13—41no—
347C4×C13—21no—
348C4×C13—21no—
349C4×C13—21no—
350C4×C13—21no—
351C4×C13—41no—
352C4×C13—41no—
353C4×C13C2×#13111yescharacteristic
354C4×C13C2×#13111yescharacteristic
355C4×C13#57611yescharacteristic
356C4×C13#57711yescharacteristic
357Dic13—41no—
358Dic13—41no—
359Dic13—41no—
360C2×#41—21no—
361C2×SD16—131no—
362C2×SD16—131no—
363C2×D8—131no—
364C2×D8—131no—
365C2×M16—21no—
366C2×M16—131no—
367C2×M16—131no—
368C2×M16—261no—
369C2×M16—261no—
370C2×M16—261no—
371C22×C8—21no—
372C22×C8—261no—
373C22×C8—261no—
374C22×C8—261no—
375C4⋊Q8C4×D1311yescharacteristic
376#127C4×D1311yescharacteristic
377#126—261no—
378#125—131no—
379#124—21no—
380#124—131no—
381#123—261no—
382C22⋊Q8—131no—
383#121—21no—
384#121—131no—
385#121C4×D1311yescharacteristic
386#121C4×D1311yescharacteristic
387C4×Q8—131no—
388C4×D4—21no—
389C4×D4—131no—
390C4×D4—261no—
391C4×D4C22×D1311yescharacteristic
392C4×D4C22×D1311yescharacteristic
393#117—261no—
394C2×C42C22×D1311yescharacteristic
395#107—131no—
396#107—131no—
397#106—131no—
398#106—131no—
399C4⋊C8—21no—
400C4⋊C8—131no—
401C4⋊C8—131no—
402C4⋊C8—131no—
403C4⋊C8—131no—
404C4⋊C8—261no—
405C4⋊C8—261no—
406C4⋊C8C22×D1311yescharacteristic
407C4⋊C8C22×D1311yescharacteristic
408#103—131no—
409#103—131no—
410#102—131no—
411#102—131no—
412#102—131no—
413#102—131no—
414#102—131no—
415#102—131no—
416C22⋊C8—131no—
417C22⋊C8—131no—
418C22⋊C8—261no—
419C22⋊C8—261no—
420C22⋊C8—261no—
421C22⋊C8—261no—
422C22⋊C8—261no—
423C22⋊C8—261no—
424C22⋊C8—261no—
425#97—131no—
426#97—131no—
427#97—261no—
428#97—261no—
429C4×C8—21no—
430C4×C8—131no—
431C4×C8—131no—
432C4×C8—131no—
433C4×C8—131no—
434C4×C8—261no—
435C4×C8C22×D1311yescharacteristic
436C4×C8C22×D1311yescharacteristic
437C2×C13—41no—
438C2×C13—81no—
439C2×C13—81no—
440C2×C13#293111yescharacteristic
441C2×C13#294611yescharacteristic
442C2×C13#295611yescharacteristic
443D13—81no—
444#41—81no—
445#41—81no—
446C2×Q8—21no—
447C2×Q8—131no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—131no—
453C2×D4—261no—
454C2×D4C2×C4×D1311yescharacteristic
455C2×D4C2×C4×D1311yescharacteristic
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—261no—
459C22×C4C2×C4×D1311yescharacteristic
460C22×C4D4×D1311yescharacteristic
461C22×C4#612911yescharacteristic
462SD16—262no—
463SD16—262no—
464D8—262no—
465D8—262no—
466M16—81no—
467M16—262no—
468M16—262no—
469M16—1041no—
470M16—1041no—
471M16—1041no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—42no—
477C2×C8—131no—
478C2×C8—131no—
479C2×C8—131no—
480C2×C8—131no—
481C2×C8—131no—
482C2×C8—131no—
483C2×C8—131no—
484C2×C8—131no—
485C2×C8—261no—
486C2×C8—261no—
487C2×C8—1041no—
488C2×C8—1041no—
489C2×C8—1041no—
490C4⋊C4—21no—
491C4⋊C4—131no—
492C4⋊C4—131no—
493C4⋊C4—261no—
494C4⋊C4—261no—
495C4⋊C4—261no—
496C4⋊C4—261no—
497C4⋊C4C2×C4×D1311yescharacteristic
498C4⋊C4C2×C4×D1311yescharacteristic
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—261no—
504C22⋊C4—261no—
505C22⋊C4—261no—
506C22⋊C4—261no—
507C22⋊C4—261no—
508C42—261no—
509C42C2×C4×D1311yescharacteristic
510C42D4×D1311yescharacteristic
511C42#612911yescharacteristic
512C42C23×D1311yescharacteristic
513C13#1796811yescharacteristic, complemented, Sylow
514C23—21no—
515C23—21no—
516C23—261no—
517C23#8813511yescharacteristic
518Q8—81no—
519Q8—261no—
520Q8—261no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—81no—
526D4—81no—
527D4—81no—
528D4—81no—
529D4—261no—
530D4—261no—
531D4—1041no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—261no—
544C2×C4—261no—
545C2×C4—261no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4#8813511yescharacteristic
549C2×C4#8813511yescharacteristic
550C2×C4#8813511yescharacteristic
551C2×C4C22×C4×D1311yescharacteristic
552C2×C4C2×D4×D1311yescharacteristic
553C2×C4C2×#612911yescharacteristic
554C8—22no—
555C8—41no—
556C8—41no—
557C8—41no—
558C8—132no—
559C8—132no—
560C8—261no—
561C8—261no—
562C8—261no—
563C8—261no—
564C8—261no—
565C8—261no—
566C8—521no—
567C8—521no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—521no—
578C22—521no—
579C22—521no—
580C22C2×#8813511yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—41no—
586C4—41no—
587C4—521no—
588C4—521no—
589C4—521no—
590C4D13×#13111yescharacteristic
591C4D13×#13111yescharacteristic
592C4#1171946211yescharacteristic
593C4#1171946711yescharacteristic
594C2—41no—
595C2—81no—
596C2—81no—
597C2—1041no—
598C2#1312354411yescharacteristic
599C2#1312366211yescharacteristic
600C2#1312374211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1492C2
socleC22×C13C2×C4×D4
prime radical#13125425C2
cosocleC42×C13C24
hypercenter#1492D13
hypocenterC13#17968
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1492

Complements

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

NH ≅ G/Ntype
2. #13123981C2semidirect
3. #13123912C2semidirect
4. #13113747C2semidirect
5. #13113735C2semidirect
6. #13113729C2semidirect
7. #13113718C2semidirect
8. #13113657C2semidirect
9. #13113645C2semidirect
10. #13113639C2semidirect
11. #13113628C2semidirect
12. #13113601C2semidirect
13. #13113297C2semidirect
14. C8×#6099C2semidirect
15. C13×#1492C2semidirect
227. #1492D13semidirect
513. C13#17968semidirect

Maximal subgroups

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

subgroupindex
#131254252
#131239812
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C13×#14922
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