Finite Group Databasebeta

← #15832975

Subgroups — #15832975

Order 3328.

648 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124879C211yesmaximal, characteristic
2#13123859C211yesmaximal, characteristic, complemented
3#13113698C211yesmaximal, characteristic, complemented
4#13113691C211yesmaximal, characteristic, complemented
5#13113670C211yesmaximal, characteristic, complemented
6#13113663C211yesmaximal, characteristic, complemented
7#13113658C211yesmaximal, characteristic, complemented
8#13113646C211yesmaximal, characteristic, complemented
9C8×#6106C211yesmaximal, characteristic, complemented
10C8×#6104C211yesmaximal, characteristic, complemented
11#13113627C211yesmaximal, characteristic, complemented
12#13113260C211yesmaximal, characteristic, complemented
13#13113244C211yesmaximal, characteristic, complemented
14#13113136C211yesmaximal, characteristic, complemented
15C13×#2993C211yesmaximal, characteristic, complemented
16C13×#529C2211yescharacteristic
17C2×C4×D52C2211yescharacteristic
18C13×#446C2211yescharacteristic, complemented
19C8×Q8×C13C2211yescharacteristic, complemented
20C13×#436—21no—
21C13×#436C2211yescharacteristic, complemented
22C13×#435—21no—
23C8×D4×C13C2211yescharacteristic, complemented
24C13×#433—21no—
25C13×#431C2211yescharacteristic
26C13×#424—21no—
27C13×#423C2211yescharacteristic
28#11718727C411yescharacteristic
29#11718727C411yescharacteristic
30#11718718C411yescharacteristic
31#11718718C411yescharacteristic
32#11718707C411yescharacteristic
33#11718705C411yescharacteristic
34#11718697C411yescharacteristic
35#11718695C411yescharacteristic
36C4×#6106C2211yescharacteristic
37C4×#6106C2211yescharacteristic
38C4×#6104C2211yescharacteristic
39C4×#6104C2211yescharacteristic
40#11718586C2211yescharacteristic
41#11718586C2211yescharacteristic
42#11718586C2211yescharacteristic
43#11718495—21no—
44#11718495—21no—
45D13×C22⋊C8—21no—
46D13×C22⋊C8—21no—
47C8×D52C2211yescharacteristic
48C8×D52C2211yescharacteristic
49C8×D52C2211yescharacteristic
50C8×D52C2211yescharacteristic
51Q8⋊#1055C2211yescharacteristic, complemented
52Q8⋊#1055C2211yescharacteristic, complemented
53D4⋊#1055C2211yescharacteristic, complemented
54D4⋊#1055C2211yescharacteristic, complemented
55#11718075C2211yescharacteristic
56#11718075C2211yescharacteristic
57#11718075C2211yescharacteristic
58#11718075C2211yescharacteristic
59#11718072C2211yescharacteristic, complemented
60#11718072C2211yescharacteristic, complemented
61#11718071C2211yescharacteristic, complemented
62#11718071C2211yescharacteristic, complemented
63#11718047C2211yescharacteristic, complemented
64#11718046C2211yescharacteristic, complemented
65#11718046C2211yescharacteristic, complemented
66C8×#1055C2211yescharacteristic, complemented
67C22×D52C2×C411yescharacteristic
68C22×C4×D13—21no—
69C2×C13×M16—21no—
70C2×C13×M16—21no—
71C22×C8×C13—21no—
72C13×#126—21no—
73C13×#125C2×C411yescharacteristic
74C13×#124C2×C411yescharacteristic
75C13×#123—21no—
76C13×C22⋊Q8C2×C411yescharacteristic
77C13×#121C2×C411yescharacteristic
78C4×Q8×C13C2311yescharacteristic
79C4×D4×C13—21no—
80C4×D4×C13C2311yescharacteristic
81C13×#117—21no—
82C2×C42×C13C2311yescharacteristic
83C2×#6106C2×C411yescharacteristic
84C2×#6106C2×C411yescharacteristic
85C2×#6104C2×C411yescharacteristic
86C2×#6104C2×C411yescharacteristic
87C2×#6103—21no—
88C2×C4⋊Dic13C2×C411yescharacteristic
89C2×C8×D13—21no—
90C2×C8×D13—21no—
91C2×C8×D13—21no—
92C2×C8×D13—21no—
93C4×D52—21no—
94C4×D52—21no—
95C4×D52C2×C411yescharacteristic
96C4×D52C2×C411yescharacteristic
97C4×D52C2311yescharacteristic
98C4×D52C2311yescharacteristic
99C13×C4⋊C8—21no—
100C13×C4⋊C8—21no—
101C13×C4⋊C8—21no—
102C13×C4⋊C8D411yescharacteristic
103C13×C4⋊C8D411yescharacteristic
104C13×C4⋊C8C2311yescharacteristic
105C13×C4⋊C8C2311yescharacteristic
106C13×C22⋊C8—21no—
107C13×C22⋊C8—21no—
108C13×C22⋊C8D411yescharacteristic
109C13×C22⋊C8D411yescharacteristic
110C13×#97—21no—
111C4×C8×C13—21no—
112C4×C8×C13C2311yescharacteristic
113C4×C8×C13C2311yescharacteristic
114#88075C2×C411yescharacteristic
115#88075C2×C411yescharacteristic
116#88072C2×C411yescharacteristic
117#88072C2×C411yescharacteristic
118C22⋊#1055—21no—
119C22⋊#1055—21no—
120C22⋊#1055C2×C411yescharacteristic
121C22⋊#1055C2×C411yescharacteristic
122#88060—21no—
123#88060—21no—
124#88060—21no—
125#88060—21no—
126#88049C2×C411yescharacteristic
127#88049C2×C411yescharacteristic
128#88049C2×C411yescharacteristic
129#88049C2×C411yescharacteristic
130#88048C2×C411yescharacteristic
131#88048C2×C411yescharacteristic
132#88047C2×C411yescharacteristic
133#88047C2×C411yescharacteristic
134C4⋊#1055—21no—
135C4⋊#1055C2×C411yescharacteristic
136C4⋊#1055C2×C411yescharacteristic
137C4⋊#1055C2311yescharacteristic
138C4⋊#1055C2311yescharacteristic
139C4×#1055—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#17918—131nomaximal, Sylow
145C23×D13—21no—
146C2×Q8×C13C22×C411yescharacteristic
147C2×D4×C13—21no—
148C2×D4×C13C22×C411yescharacteristic
149C22×C4×C13—21no—
150C22×C4×C13C22×C411yescharacteristic
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13#4111yescharacteristic
153C22×Dic13—21no—
154C2×D52—21no—
155C2×D52—22no—
156C2×D52—22no—
157C2×D52C22×C411yescharacteristic
158C2×D52C22×C411yescharacteristic
159C2×C4×D13—21no—
160C2×C4×D13—21no—
161C2×C4×D13—21no—
162C2×C4×D13—21no—
163C2×C4×D13—81no—
164C2×C4×D13—81no—
165C13×M16—81no—
166C13×M16—81no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—81no—
170C2×C8×C13C2×D411yescharacteristic
171C2×C8×C13C2×D411yescharacteristic
172C2×C8×C13C2×D411yescharacteristic
173C2×C8×C13C2×D411yescharacteristic
174C13×C4⋊C4—21no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4C22×C411yescharacteristic
179C13×C4⋊C4C22×C411yescharacteristic
180C13×C22⋊C4—21no—
181C13×C22⋊C4—21no—
182C13×C22⋊C4—21no—
183C13×C22⋊C4—21no—
184C13×C22⋊C4—21no—
185C42×C13—21no—
186C42×C13C22×C411yescharacteristic
187C42×C13C2×D411yescharacteristic
188C42×C13#4111yescharacteristic
189C42×C13C2411yescharacteristic
190#6106—22no—
191#6106—22no—
192#6104—22no—
193#6104—22no—
194#6103—21no—
195#6103—21no—
196#6103—21no—
197#6103—21no—
198C4⋊Dic13—21no—
199C4⋊Dic13C22×C411yescharacteristic
200C4⋊Dic13C22×C411yescharacteristic
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055C22×C411yescharacteristic
206C2×#1055C22×C411yescharacteristic
207C2×#1055C22×C411yescharacteristic
208C2×#1055C22×C411yescharacteristic
209C8×D13—81no—
210C8×D13—81no—
211C8×D13—81no—
212C8×D13—81no—
213#3105—131no—
214#2993D1311yescharacteristic, complemented
215#2972—131no—
216#1586—131no—
217#1585—131no—
218#1582—131no—
219#1581—131no—
220#1580—131no—
221SD16⋊C8—131no—
222C8×SD16—131no—
223C8×D8—131no—
224#1574—131no—
225#1486—131no—
226#1482—131no—
227#1454—131no—
228C23×C13—21no—
229C23×C13C4×D411yescharacteristic
230C22×D13—21no—
231C22×D13—21no—
232C22×D13—24no—
233C22×D13—81no—
234C22×D13—81no—
235Q8×C13—21no—
236Q8×C13—21no—
237D4×C13—21no—
238D4×C13—21no—
239D4×C13—81no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13C4×D411yescharacteristic
251C2×C4×C13C4×D411yescharacteristic
252C2×C4×C13C4×D411yescharacteristic
253C2×C4×C13C23×C411yescharacteristic
254C2×C4×C13C22×D411yescharacteristic
255C2×C4×C13C2×#4111yescharacteristic
256C2×Dic13—21no—
257C2×Dic13—21no—
258C2×Dic13—81no—
259D52—24no—
260D52—21no—
261D52—21no—
262D52#13112yes—
263D52#13112yes—
264C4×D13—41no—
265C4×D13—41no—
266C4×D13—41no—
267C4×D13—41no—
268C4×D13—81no—
269C4×D13—81no—
270C8×C13—21no—
271C8×C13—21no—
272C8×C13—21no—
273C8×C13—21no—
274C8×C13—41no—
275C8×C13—41no—
276#1055—21no—
277#1055—21no—
278#1055—21no—
279#1055—21no—
280#1055—41no—
281#1055—41no—
282#1055—41no—
283#1055—41no—
284#529C2×D1311yescharacteristic
285C2×C4×D4—131no—
286#484—131no—
287#481—131no—
288#478—131no—
289#478—131no—
290#463—131no—
291#463—131no—
292#450—131no—
293#447—131no—
294#446C2×D1311yescharacteristic, complemented
295C8×Q8C2×D1311yescharacteristic, complemented
296C4×SD16—131no—
297C4×SD16—131no—
298C4×D8—131no—
299C4×D8—131no—
300#436—21no—
301#436C2×D1311yescharacteristic, complemented
302#435—21no—
303C8×D4—131no—
304C8×D4—131no—
305C8×D4—131no—
306C8×D4—131no—
307C8×D4—261no—
308C8×D4—261no—
309C8×D4C2×D1311yescharacteristic, complemented
310#433—21no—
311#431—131no—
312#431—131no—
313#431—131no—
314#431C2×D1311yescharacteristic
315#424—21no—
316#423C2×D1311yescharacteristic
317C2×C22⋊C8—261no—
318C2×C22⋊C8—261no—
319#335—131no—
320#335—131no—
321#334—131no—
322#334—131no—
323Q8⋊C8—131no—
324Q8⋊C8—131no—
325D4⋊C8—131no—
326D4⋊C8—131no—
327D4⋊C8—131no—
328D4⋊C8—131no—
329D4⋊C8—131no—
330D4⋊C8—131no—
331#322—131no—
332#322—131no—
333#322—131no—
334C82—131no—
335C22×C13—21no—
336C22×C13—21no—
337C22×C13—21no—
338C22×C13—41no—
339C22×C13—41no—
340C22×C13—41no—
341C22×C13C2×C4×D411yescharacteristic
342C2×D13—22no—
343C2×D13—22no—
344C2×D13—41no—
345C2×D13—41no—
346C2×D13—41no—
347C2×D13—41no—
348C2×D13—84no—
349C4×C13—21no—
350C4×C13—21no—
351C4×C13—21no—
352C4×C13—21no—
353C4×C13—41no—
354C4×C13—41no—
355C4×C13—41no—
356C4×C13C2×#13111yescharacteristic
357C4×C13C2×#13111yescharacteristic
358C4×C13#57611yescharacteristic
359C4×C13#57711yescharacteristic
360Dic13—41no—
361Dic13—41no—
362C22×D4—131no—
363C23×C4—261no—
364C2×SD16—131no—
365C2×SD16—131no—
366C2×D8—131no—
367C2×D8—131no—
368C2×M16—21no—
369C2×M16—21no—
370C22×C8—21no—
371C22×C8—261no—
372C22×C8—261no—
373C22×C8—261no—
374C22×C8—261no—
375#126—21no—
376#125C4×D1311yescharacteristic
377#124C4×D1311yescharacteristic
378#123—21no—
379C22⋊Q8C4×D1311yescharacteristic
380#121C4×D1311yescharacteristic
381C4×Q8C22×D1311yescharacteristic
382C4×D4—21no—
383C4×D4—131no—
384C4×D4—131no—
385C4×D4—131no—
386C4×D4—131no—
387C4×D4—261no—
388C4×D4—261no—
389C4×D4C22×D1311yescharacteristic
390#117—21no—
391C2×C4⋊C4—131no—
392C2×C22⋊C4—261no—
393C2×C42C22×D1311yescharacteristic
394#107—131no—
395#107—131no—
396#106—131no—
397#106—131no—
398C4⋊C8—21no—
399C4⋊C8—21no—
400C4⋊C8—21no—
401C4⋊C8—131no—
402C4⋊C8—131no—
403C4⋊C8—131no—
404C4⋊C8—131no—
405C4⋊C8—261no—
406C4⋊C8C22⋊D1311yescharacteristic
407C4⋊C8C22⋊D1311yescharacteristic
408C4⋊C8C22×D1311yescharacteristic
409C4⋊C8C22×D1311yescharacteristic
410#103—131no—
411#103—131no—
412#102—131no—
413#102—131no—
414#102—131no—
415#102—131no—
416#102—131no—
417#102—131no—
418C22⋊C8—21no—
419C22⋊C8—21no—
420C22⋊C8—131no—
421C22⋊C8—131no—
422C22⋊C8—261no—
423C22⋊C8—261no—
424C22⋊C8—261no—
425C22⋊C8—261no—
426C22⋊C8—261no—
427C22⋊C8—261no—
428C22⋊C8C22⋊D1311yescharacteristic
429C22⋊C8C22⋊D1311yescharacteristic
430#97—21no—
431C4×C8—21no—
432C4×C8—131no—
433C4×C8—131no—
434C4×C8—131no—
435C4×C8—131no—
436C4×C8—261no—
437C4×C8C22×D1311yescharacteristic
438C4×C8C22×D1311yescharacteristic
439C2×C13—41no—
440C2×C13—81no—
441C2×C13#292911yescharacteristic
442C2×C13#294611yescharacteristic
443C2×C13#295711yescharacteristic
444D13—42no—
445D13—42no—
446C24—261no—
447C2×Q8C2×C4×D1311yescharacteristic
448C2×D4—21no—
449C2×D4—131no—
450C2×D4—131no—
451C2×D4—262no—
452C2×D4—262no—
453C2×D4—261no—
454C2×D4C2×C4×D1311yescharacteristic
455C22×C4—21no—
456C22×C4—261no—
457C22×C4—261no—
458C22×C4—261no—
459C22×C4—261no—
460C22×C4—261no—
461C22×C4—1041no—
462C22×C4—1041no—
463C22×C4C2×C4×D1311yescharacteristic
464C22×C4#612711yescharacteristic
465C22×C4C2×C22⋊D1311yescharacteristic
466SD16—262no—
467SD16—262no—
468D8—262no—
469D8—262no—
470M16—81no—
471M16—81no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—81no—
475C2×C8—131no—
476C2×C8—131no—
477C2×C8—131no—
478C2×C8—131no—
479C2×C8—261no—
480C2×C8—261no—
481C2×C8—261no—
482C2×C8—261no—
483C2×C8—1041no—
484C2×C8—1041no—
485C2×C8—1041no—
486C2×C8—1041no—
487C2×C8C2×C22⋊D1311yescharacteristic
488C2×C8C2×C22⋊D1311yescharacteristic
489C2×C8C2×C22⋊D1311yescharacteristic
490C2×C8C2×C22⋊D1311yescharacteristic
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—131no—
496C4⋊C4—131no—
497C4⋊C4—261no—
498C4⋊C4C2×C4×D1311yescharacteristic
499C4⋊C4C2×C4×D1311yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—261no—
506C22⋊C4—261no—
507C22⋊C4—261no—
508C22⋊C4—261no—
509C42—21no—
510C42C2×C4×D1311yescharacteristic
511C42#612711yescharacteristic
512C42C2×C22⋊D1311yescharacteristic
513C42C23×D1311yescharacteristic
514C13#1791811yescharacteristic, complemented, Sylow
515C23—21no—
516C23—264no—
517C23—261no—
518C23—261no—
519C23—1041no—
520C23—1041no—
521C23C4×C22⋊D1311yescharacteristic
522Q8—21no—
523Q8—21no—
524D4—21no—
525D4—21no—
526D4—81no—
527D4—132no—
528D4—132no—
529D4—264no—
530D4—261no—
531D4—261no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—261no—
543C2×C4—261no—
544C2×C4—521no—
545C2×C4—521no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4—1041no—
549C2×C4—1041no—
550C2×C4—1041no—
551C2×C4C4×C22⋊D1311yescharacteristic
552C2×C4C4×C22⋊D1311yescharacteristic
553C2×C4C4×C22⋊D1311yescharacteristic
554C2×C4C22×C4×D1311yescharacteristic
555C2×C4C2×#612711yescharacteristic
556C2×C4C22×C22⋊D1311yescharacteristic
557C8—21no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—261no—
564C8—261no—
565C8—261no—
566C8—261no—
567C8—521no—
568C8—521no—
569C8—521no—
570C8—521no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—262no—
578C22—262no—
579C22—521no—
580C22—521no—
581C22—521no—
582C22—521no—
583C22—1044no—
584C22C2×C4×C22⋊D1311yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—521no—
593C4—521no—
594C4D13×#13111yescharacteristic
595C4D13×#13111yescharacteristic
596C4#1171954011yescharacteristic
597C4#1171954211yescharacteristic
598C2—41no—
599C2—81no—
600C2—522no—
601C2—522no—
602C2#1312352811yescharacteristic
603C2#1312366411yescharacteristic
604C2#1312375111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#2993C2
socleC22×C13C2×C4×D4
prime radical#11718697C4
cosocleC42×C13C24
hypercenter#2993D13
hypocenterC13#17918
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2993

Complements

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

NH ≅ G/Ntype
2. #13123859C2semidirect
3. #13113698C2semidirect
4. #13113691C2semidirect
5. #13113670C2semidirect
6. #13113663C2semidirect
7. #13113658C2semidirect
8. #13113646C2semidirect
9. C8×#6106C2semidirect
10. C8×#6104C2semidirect
11. #13113627C2semidirect
12. #13113260C2semidirect
13. #13113244C2semidirect
14. #13113136C2semidirect
15. C13×#2993C2semidirect
18. C13×#446C22semidirect
19. C8×Q8×C13C22semidirect
21. C13×#436C22semidirect
23. C8×D4×C13C22semidirect
51. Q8⋊#1055C22semidirect
52. Q8⋊#1055C22semidirect
53. D4⋊#1055C22semidirect
54. D4⋊#1055C22semidirect
59. #11718072C22semidirect
60. #11718072C22semidirect
61. #11718071C22semidirect
62. #11718071C22semidirect
63. #11718047C22semidirect
64. #11718046C22semidirect
65. #11718046C22semidirect
66. C8×#1055C22semidirect
214. #2993D13semidirect
294. #446C2×D13semidirect
295. C8×Q8C2×D13semidirect
301. #436C2×D13semidirect
309. C8×D4C2×D13semidirect
514. C13#17918semidirect

Maximal subgroups

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

subgroupindex
#131248792
#131238592
#131136982
#131136912
#131136702
#131136632
#131136582
#131136462
C8×#61062
C8×#61042
#131136272
#131132602
#131132442
#131131362
C13×#29932
#1791813