Finite Group Databasebeta

← #15833011

Subgroups — #15833011

Order 3328.

638 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123947C211yesmaximal, characteristic, complemented
2#13123912C211yesmaximal, characteristic, complemented
3#13113715C211yesmaximal, characteristic, complemented
4#13113701C211yesmaximal, characteristic, complemented
5#13113680C211yesmaximal, characteristic, complemented
6#13113666C211yesmaximal, characteristic, complemented
7#13113660C211yesmaximal, characteristic, complemented
8SD16⋊#1055C211yesmaximal, characteristic, complemented
9SD16×#1055C211yesmaximal, characteristic, complemented
10D8×#1055C211yesmaximal, characteristic, complemented
11#13113621C211yesmaximal, characteristic, complemented
12#13113270C211yesmaximal, characteristic, complemented
13#13113235C211yesmaximal, characteristic, complemented
14#13113136C211yesmaximal, characteristic, complemented
15C13×#3106C211yesmaximal, characteristic
16C13×#532C2211yescharacteristic
17C4×C13×#41C2211yescharacteristic
18C13×#482C411yescharacteristic
19C13×#482C411yescharacteristic
20C13×#477C411yescharacteristic
21C13×#476C411yescharacteristic
22C13×#460C411yescharacteristic
23C13×#459C411yescharacteristic
24C13×#449C411yescharacteristic
25C13×#449C411yescharacteristic
26C4×C13×SD16C2211yescharacteristic
27C4×C13×SD16C2211yescharacteristic
28C4×C13×D8C2211yescharacteristic
29C4×C13×D8C2211yescharacteristic
30C13×#431C2211yescharacteristic
31#11718895—21no—
32#11718895—21no—
33Q8×#1055C2211yescharacteristic
34Q8×#1055C2211yescharacteristic
35#11718673C2211yescharacteristic
36#11718673C2211yescharacteristic
37#11718672—21no—
38#11718672—21no—
39D4×#1055—21no—
40D4×#1055—21no—
41D4×#1055C2211yescharacteristic
42D4×#1055C2211yescharacteristic
43D4×#1055C2211yescharacteristic
44D4×#1055C2211yescharacteristic
45#11718587C2211yescharacteristic
46#11718586—21no—
47#11718586C2211yescharacteristic
48#11718586C2211yescharacteristic
49C2×C4⋊#1055—21no—
50C2×C4⋊#1055C2211yescharacteristic
51Q8⋊#1055C2211yescharacteristic
52Q8⋊#1055C2211yescharacteristic
53D4⋊#1055C2211yescharacteristic
54D4⋊#1055C2211yescharacteristic
55D4⋊#1055C2211yescharacteristic
56D4⋊#1055C2211yescharacteristic
57D4⋊#1055C2211yescharacteristic
58D4⋊#1055C2211yescharacteristic
59#11718050C2211yescharacteristic
60#11718050C2211yescharacteristic
61#11718049C2211yescharacteristic
62#11718049C2211yescharacteristic
63#11718047C2211yescharacteristic
64#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×C13×#41—21no—
68C2×C13×#41C2×C411yescharacteristic
69C2×C13×SD16C2×C411yescharacteristic
70C2×C13×SD16C2×C411yescharacteristic
71C2×C13×D8C2×C411yescharacteristic
72C2×C13×D8C2×C411yescharacteristic
73C13×C4⋊Q8C2×C411yescharacteristic
74C13×#127C2×C411yescharacteristic
75C13×#124—21no—
76C13×#121—21no—
77C13×#121C2×C411yescharacteristic
78C13×#121C2×C411yescharacteristic
79C4×Q8×C13C2×C411yescharacteristic
80C4×Q8×C13C2311yescharacteristic
81C4×D4×C13—21no—
82C4×D4×C13—21no—
83C4×D4×C13—21no—
84C4×D4×C13C2×C411yescharacteristic
85C4×D4×C13C2311yescharacteristic
86C4×D4×C13C2311yescharacteristic
87C4×D4×C13C2311yescharacteristic
88C13×#117—21no—
89C13×#117C2×C411yescharacteristic
90C2×C42×C13—21no—
91C2×C42×C13C2311yescharacteristic
92C2×#6099—21no—
93C2×#6099—21no—
94C22×#1055—21no—
95C22×#1055—21no—
96C22×#1055—21no—
97C22×#1055—21no—
98C22×#1055—21no—
99C13×#107C2×C411yescharacteristic
100C13×#107C2×C411yescharacteristic
101C13×#106C2×C411yescharacteristic
102C13×#106C2×C411yescharacteristic
103C13×C4⋊C8C2×C411yescharacteristic
104C13×C4⋊C8C2×C411yescharacteristic
105C13×#103C2×C411yescharacteristic
106C13×#103C2×C411yescharacteristic
107C13×#102C2×C411yescharacteristic
108C13×#102C2×C411yescharacteristic
109C13×#102C2×C411yescharacteristic
110C13×#102C2×C411yescharacteristic
111C13×#102C2×C411yescharacteristic
112C13×#102C2×C411yescharacteristic
113C13×C22⋊C8C2×C411yescharacteristic
114C13×C22⋊C8C2×C411yescharacteristic
115C4×C8×C13C2311yescharacteristic
116C4×C8×C13C2311yescharacteristic
117C22⋊#1055—21no—
118C22⋊#1055—21no—
119C22⋊#1055—21no—
120C22⋊#1055—21no—
121C22⋊#1055—21no—
122C22⋊#1055—21no—
123C22⋊#1055—21no—
124C22⋊#1055—21no—
125C22⋊#1055D411yescharacteristic
126C22⋊#1055D411yescharacteristic
127C4⋊#1055—21no—
128C4⋊#1055—21no—
129C4⋊#1055—21no—
130C4⋊#1055—21no—
131C4⋊#1055D411yescharacteristic
132C4⋊#1055D411yescharacteristic
133C4⋊#1055C2311yescharacteristic
134C4⋊#1055C2311yescharacteristic
135C4⋊#1055C2311yescharacteristic
136C4⋊#1055C2311yescharacteristic
137#88043—21no—
138C4×#1055—21no—
139C4×#1055—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#17920—131nomaximal, Sylow
145C13×#41—22no—
146C13×#41—22no—
147C13×#41—81no—
148C13×#41—81no—
149C2×Q8×C13—21no—
150C2×Q8×C13C22×C411yescharacteristic
151C2×D4×C13—21no—
152C2×D4×C13—21no—
153C2×D4×C13—21no—
154C2×D4×C13—21no—
155C2×D4×C13—21no—
156C2×D4×C13C22×C411yescharacteristic
157C2×D4×C13C22×C411yescharacteristic
158C2×D4×C13C22×C411yescharacteristic
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13C22×C411yescharacteristic
165C22×C4×C13C2×D411yescharacteristic
166C22×C4×C13#4111yescharacteristic
167C13×SD16—22no—
168C13×SD16—22no—
169C13×D8—22no—
170C13×D8—22no—
171C2×C8×C13C22×C411yescharacteristic
172C2×C8×C13C22×C411yescharacteristic
173C2×C8×C13C22×C411yescharacteristic
174C2×C8×C13C22×C411yescharacteristic
175C13×C4⋊C4—21no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4C22×C411yescharacteristic
179C13×C4⋊C4C22×C411yescharacteristic
180C13×C4⋊C4C22×C411yescharacteristic
181C13×C4⋊C4C22×C411yescharacteristic
182C13×C22⋊C4—21no—
183C13×C22⋊C4—21no—
184C13×C22⋊C4—21no—
185C13×C22⋊C4—21no—
186C13×C22⋊C4—21no—
187C13×C22⋊C4—21no—
188C13×C22⋊C4—21no—
189C42×C13—21no—
190C42×C13—21no—
191C42×C13—21no—
192C42×C13C22×C411yescharacteristic
193C42×C13C2×D411yescharacteristic
194C42×C13#4111yescharacteristic
195C42×C13C2411yescharacteristic
196#6099—81no—
197#6099—81no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—81no—
205C2×#1055—81no—
206C2×#1055—81no—
207C2×#1055—81no—
208C2×#1055—81no—
209C2×#1055C2×D411yescharacteristic
210C2×#1055C2×D411yescharacteristic
211C2×#1055C2×D411yescharacteristic
212C2×#1055C2×D411yescharacteristic
213#3106D1311yescharacteristic
214#2988—131no—
215#2981—131no—
216#1588—131no—
217#1586—131no—
218#1583—131no—
219#1581—131no—
220#1580—131no—
221SD16⋊C8—131no—
222C8×SD16—131no—
223C8×D8—131no—
224#1573—131no—
225#1488—131no—
226#1480—131no—
227#1454—131no—
228C23×C13—21no—
229C23×C13—21no—
230C23×C13—21no—
231C23×C13C4×D411yescharacteristic
232Q8×C13—21no—
233Q8×C13—81no—
234Q8×C13#13112yes—
235D4×C13—24no—
236D4×C13—21no—
237D4×C13—21no—
238D4×C13—21no—
239D4×C13—21no—
240D4×C13—21no—
241D4×C13—81no—
242D4×C13—81no—
243D4×C13—81no—
244D4×C13—81no—
245D4×C13#13112yes—
246C2×C4×C13—24no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13—81no—
264C2×C4×C13C4×D411yescharacteristic
265C2×C4×C13C4×D411yescharacteristic
266C2×C4×C13C4×D411yescharacteristic
267C2×C4×C13C23×C411yescharacteristic
268C2×C4×C13C22×D411yescharacteristic
269C2×C4×C13C2×#4111yescharacteristic
270C8×C13—21no—
271C8×C13—21no—
272C8×C13—21no—
273C8×C13—21no—
274#1055—21no—
275#1055—21no—
276#1055—21no—
277#1055—21no—
278#1055—41no—
279#1055—41no—
280#1055—41no—
281#1055—41no—
282#1055—41no—
283#1055—41no—
284#532C2×D1311yescharacteristic
285C4×#41C2×D1311yescharacteristic
286#482Dic1311yescharacteristic
287#482Dic1311yescharacteristic
288#477Dic1311yescharacteristic
289#476Dic1311yescharacteristic
290#460Dic1311yescharacteristic
291#459Dic1311yescharacteristic
292#449Dic1311yescharacteristic
293#449Dic1311yescharacteristic
294C8×Q8—131no—
295C8×Q8—131no—
296C4×SD16C2×D1311yescharacteristic
297C4×SD16C2×D1311yescharacteristic
298C4×D8C2×D1311yescharacteristic
299C4×D8C2×D1311yescharacteristic
300#436—131no—
301#436—131no—
302#435—261no—
303#435—261no—
304C8×D4—131no—
305C8×D4—131no—
306C8×D4—131no—
307C8×D4—131no—
308C8×D4—261no—
309C8×D4—261no—
310#432—131no—
311#431—131no—
312#431—131no—
313#431—261no—
314#431C2×D1311yescharacteristic
315C2×C4⋊C8—131no—
316C2×C4⋊C8—261no—
317#408—261no—
318#408—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—22no—
337C22×C13—21no—
338C22×C13—21no—
339C22×C13—41no—
340C22×C13—41no—
341C22×C13—41no—
342C22×C13—41no—
343C22×C13—41no—
344C22×C13—41no—
345C22×C13—41no—
346C22×C13—41no—
347C22×C13C2×C4×D411yescharacteristic
348C4×C13—21no—
349C4×C13—22no—
350C4×C13—21no—
351C4×C13—21no—
352C4×C13—21no—
353C4×C13—41no—
354C4×C13—41no—
355C4×C13—41no—
356C4×C13—41no—
357C4×C13C2×#13111yescharacteristic
358C4×C13C2×#13111yescharacteristic
359C4×C13#57611yescharacteristic
360C4×C13#57711yescharacteristic
361C2×#41—21no—
362C2×#41C2×Dic1311yescharacteristic
363C2×SD16C2×Dic1311yescharacteristic
364C2×SD16C2×Dic1311yescharacteristic
365C2×D8C2×Dic1311yescharacteristic
366C2×D8C2×Dic1311yescharacteristic
367C2×M16—261no—
368C2×M16—261no—
369C22×C8—261no—
370C22×C8—261no—
371C22×C8—261no—
372C22×C8—261no—
373C22×C8—261no—
374C4⋊Q8C2×Dic1311yescharacteristic
375#127C2×Dic1311yescharacteristic
376#124—21no—
377#121—21no—
378#121C2×Dic1311yescharacteristic
379#121C2×Dic1311yescharacteristic
380C4×Q8C2×Dic1311yescharacteristic
381C4×Q8C22×D1311yescharacteristic
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4C2×Dic1311yescharacteristic
386C4×D4C22×D1311yescharacteristic
387C4×D4C22×D1311yescharacteristic
388C4×D4C22×D1311yescharacteristic
389#117—21no—
390#117C2×Dic1311yescharacteristic
391C2×C42—21no—
392C2×C42C22×D1311yescharacteristic
393#107C2×Dic1311yescharacteristic
394#107C2×Dic1311yescharacteristic
395#106C2×Dic1311yescharacteristic
396#106C2×Dic1311yescharacteristic
397C4⋊C8—131no—
398C4⋊C8—131no—
399C4⋊C8—131no—
400C4⋊C8—131no—
401C4⋊C8—131no—
402C4⋊C8—131no—
403C4⋊C8—261no—
404C4⋊C8—261no—
405C4⋊C8—261no—
406C4⋊C8—261no—
407C4⋊C8C2×Dic1311yescharacteristic
408C4⋊C8C2×Dic1311yescharacteristic
409#103C2×Dic1311yescharacteristic
410#103C2×Dic1311yescharacteristic
411#102C2×Dic1311yescharacteristic
412#102C2×Dic1311yescharacteristic
413#102C2×Dic1311yescharacteristic
414#102C2×Dic1311yescharacteristic
415#102C2×Dic1311yescharacteristic
416#102C2×Dic1311yescharacteristic
417C22⋊C8—131no—
418C22⋊C8—131no—
419C22⋊C8—261no—
420C22⋊C8—261no—
421C22⋊C8—261no—
422C22⋊C8—261no—
423C22⋊C8—261no—
424C22⋊C8—261no—
425C22⋊C8—261no—
426C22⋊C8—261no—
427C22⋊C8C2×Dic1311yescharacteristic
428C22⋊C8C2×Dic1311yescharacteristic
429#97—261no—
430C4×C8—131no—
431C4×C8—131no—
432C4×C8—131no—
433C4×C8—131no—
434C4×C8—261no—
435C4×C8—261no—
436C4×C8C22×D1311yescharacteristic
437C4×C8C22×D1311yescharacteristic
438C2×C13—41no—
439C2×C13—42no—
440C2×C13—81no—
441C2×C13—81no—
442C2×C13#292911yescharacteristic
443C2×C13#294611yescharacteristic
444C2×C13#295711yescharacteristic
445#41—22no—
446#41—22no—
447#41—81no—
448#41—81no—
449C2×Q8—21no—
450C2×Q8C22×Dic1311yescharacteristic
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4C22×Dic1311yescharacteristic
457C2×D4C22×Dic1311yescharacteristic
458C2×D4C22×Dic1311yescharacteristic
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4D4×D1311yescharacteristic
465C22×C4#612911yescharacteristic
466C22×C4C22×Dic1311yescharacteristic
467SD16—22no—
468SD16—22no—
469D8—22no—
470D8—22no—
471M16—1041no—
472M16—1041no—
473C2×C8—131no—
474C2×C8—131no—
475C2×C8—131no—
476C2×C8—131no—
477C2×C8—261no—
478C2×C8—261no—
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×C8—1041no—
488C2×C8C22×Dic1311yescharacteristic
489C2×C8C22×Dic1311yescharacteristic
490C2×C8C22×Dic1311yescharacteristic
491C2×C8C22×Dic1311yescharacteristic
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4C22×Dic1311yescharacteristic
496C4⋊C4C22×Dic1311yescharacteristic
497C4⋊C4C22×Dic1311yescharacteristic
498C4⋊C4C22×Dic1311yescharacteristic
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42D4×D1311yescharacteristic
510C42#612911yescharacteristic
511C42C22×Dic1311yescharacteristic
512C42C23×D1311yescharacteristic
513C13#1792011yescharacteristic, complemented, Sylow
514C23—21no—
515C23—21no—
516C23—21no—
517C23D4×Dic1311yescharacteristic
518Q8—21no—
519Q8—81no—
520Q8#8820212yes—
521D4—24no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—21no—
527D4—81no—
528D4—81no—
529D4—81no—
530D4—81no—
531D4#8820212yes—
532C2×C4—24no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—81no—
550C2×C4D4×Dic1311yescharacteristic
551C2×C4D4×Dic1311yescharacteristic
552C2×C4D4×Dic1311yescharacteristic
553C2×C4C2×D4×D1311yescharacteristic
554C2×C4C2×#612911yescharacteristic
555C2×C4C23×Dic1311yescharacteristic
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—261no—
561C8—261no—
562C8—261no—
563C8—261no—
564C8—521no—
565C8—521no—
566C8—521no—
567C8—521no—
568C8—521no—
569C8—521no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—22no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22C2×D4×Dic1311yescharacteristic
583C4—21no—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—22no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4#1171947911yescharacteristic
593C4#1171948011yescharacteristic
594C4C2×#8820211yescharacteristic
595C4C2×#8820211yescharacteristic
596C2—41no—
597C2—42no—
598C2—81no—
599C2—81no—
600C2#1312353111yescharacteristic
601C2#1312366911yescharacteristic
602C2#1312375311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
Fitting, prime radicalC13×#3106C2
socleC22×C13C2×C4×D4
cosocleC42×C13C24
hypercenter#3106D13
hypocenterC13#17920
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3106

Complements

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

NH ≅ G/Ntype
1. #13123947C2semidirect
2. #13123912C2semidirect
3. #13113715C2semidirect
4. #13113701C2semidirect
5. #13113680C2semidirect
6. #13113666C2semidirect
7. #13113660C2semidirect
8. SD16⋊#1055C2semidirect
9. SD16×#1055C2semidirect
10. D8×#1055C2semidirect
11. #13113621C2semidirect
12. #13113270C2semidirect
13. #13113235C2semidirect
14. #13113136C2semidirect
513. C13#17920semidirect

Maximal subgroups

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

subgroupindex
#131239472
#131239122
#131137152
#131137012
#131136802
#131136662
#131136602
SD16⋊#10552
SD16×#10552
D8×#10552
#131136212
#131132702
#131132352
#131131362
C13×#31062
#1792013