Finite Group Databasebeta

← #15834151

Subgroups — #15834151

Order 3328.

642 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123996C211yesmaximal, characteristic, complemented
2#13123871C211yesmaximal, characteristic, complemented
3#13113750C211yesmaximal, characteristic, complemented
4#13113739C211yesmaximal, characteristic, complemented
5#13113680C211yesmaximal, characteristic, complemented
6#13113673C211yesmaximal, characteristic, complemented
7#13113666C211yesmaximal, characteristic, complemented
8#13113666C211yesmaximal, characteristic, complemented
9#13113660C211yesmaximal, characteristic, complemented
10SD16⋊#1055C211yesmaximal, characteristic, complemented
11#13113621C211yesmaximal, characteristic, complemented
12#13113296C211yesmaximal, characteristic, complemented
13C2×D4⋊#1055C211yesmaximal, characteristic, complemented
14#13113129C211yesmaximal, characteristic, complemented
15C13×#3105C211yesmaximal, characteristic
16C13×#529C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C13×#484C411yescharacteristic
19C13×#481C411yescharacteristic
20C13×#478C411yescharacteristic
21C13×#478C411yescharacteristic
22C13×#463C411yescharacteristic
23C13×#463C411yescharacteristic
24C13×#450C411yescharacteristic
25C13×#447C411yescharacteristic
26C4×C13×SD16C2211yescharacteristic
27C4×C13×SD16C2211yescharacteristic
28C4×C13×D8C2211yescharacteristic
29C4×C13×D8C2211yescharacteristic
30C13×#431C2211yescharacteristic
31#11718868—21no—
32C2×C22⋊#1055—21no—
33#11718685C2211yescharacteristic, complemented
34Q8×#1055C2211yescharacteristic, complemented
35#11718673C2211yescharacteristic
36#11718673C2211yescharacteristic
37#11718673C2211yescharacteristic, complemented
38#11718672—21no—
39#11718672—21no—
40#11718672—21no—
41D4×#1055—21no—
42D4×#1055C2211yescharacteristic
43D4×#1055C2211yescharacteristic
44D4×#1055C2211yescharacteristic, complemented
45#11718661—21no—
46#11718660—21no—
47#11718587C2211yescharacteristic
48#11718586C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C2×C4×#1055C2211yescharacteristic
51Q8⋊#1055C2211yescharacteristic, complemented
52Q8⋊#1055C2211yescharacteristic, complemented
53D4⋊#1055C2211yescharacteristic
54D4⋊#1055C2211yescharacteristic
55D4⋊#1055C2211yescharacteristic
56D4⋊#1055C2211yescharacteristic
57D4⋊#1055C2211yescharacteristic, complemented
58D4⋊#1055C2211yescharacteristic, complemented
59#11718050C2211yescharacteristic, complemented
60#11718050C2211yescharacteristic, complemented
61#11718049C2211yescharacteristic, complemented
62#11718049C2211yescharacteristic, complemented
63#11718047C2211yescharacteristic, complemented
64#11718047C2211yescharacteristic, complemented
65#11718046C2211yescharacteristic, complemented
66#11718046C2211yescharacteristic, complemented
67C22×D4×C13C2×C411yescharacteristic
68C23×C4×C13—21no—
69C2×C13×SD16C2×C411yescharacteristic
70C2×C13×SD16C2×C411yescharacteristic
71C2×C13×D8C2×C411yescharacteristic
72C2×C13×D8C2×C411yescharacteristic
73C13×#126—21no—
74C13×#125C2×C411yescharacteristic
75C13×#124C2×C411yescharacteristic
76C13×#123—21no—
77C13×C22⋊Q8C2×C411yescharacteristic
78C13×#121C2×C411yescharacteristic
79C4×Q8×C13C2311yescharacteristic
80C4×D4×C13—21no—
81C4×D4×C13—21no—
82C4×D4×C13—21no—
83C4×D4×C13C2×C411yescharacteristic
84C4×D4×C13C2×C411yescharacteristic
85C4×D4×C13C2311yescharacteristic
86C4×D4×C13C2311yescharacteristic
87C4×D4×C13C2311yescharacteristic
88C13×#117—21no—
89C2×C13×C4⋊C4C2×C411yescharacteristic
90C2×C13×C22⋊C4—21no—
91C2×C42×C13C2311yescharacteristic
92C2×#6099—21no—
93C2×#6099—21no—
94C2×#6099—21no—
95C22×#1055—21no—
96C22×#1055—21no—
97C22×#1055—21no—
98C22×#1055—21no—
99C22×#1055—21no—
100C13×#107C2×C411yescharacteristic
101C13×#107C2×C411yescharacteristic
102C13×#106C2×C411yescharacteristic
103C13×#106C2×C411yescharacteristic
104C13×C4⋊C8C2×C411yescharacteristic
105C13×C4⋊C8C2×C411yescharacteristic
106C13×#103C2×C411yescharacteristic
107C13×#103C2×C411yescharacteristic
108C13×#102C2×C411yescharacteristic
109C13×#102C2×C411yescharacteristic
110C13×#102C2×C411yescharacteristic
111C13×#102C2×C411yescharacteristic
112C13×#102C2×C411yescharacteristic
113C13×#102C2×C411yescharacteristic
114C13×C22⋊C8C2×C411yescharacteristic
115C13×C22⋊C8C2×C411yescharacteristic
116C4×C8×C13C2311yescharacteristic
117C4×C8×C13C2311yescharacteristic
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⋊#1055D411yescharacteristic
131C4⋊#1055D411yescharacteristic
132C4⋊#1055C2311yescharacteristic
133C4⋊#1055C2311yescharacteristic
134C4⋊#1055C2311yescharacteristic
135C4⋊#1055C2311yescharacteristic
136#88043—21no—
137#88043—21no—
138C4×#1055—21no—
139C4×#1055—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18020—131nomaximal, Sylow
145C24×C13—21no—
146C2×Q8×C13C22×C411yescharacteristic
147C2×D4×C13—22no—
148C2×D4×C13—21no—
149C2×D4×C13—21no—
150C2×D4×C13—41no—
151C2×D4×C13C22×C411yescharacteristic
152C2×D4×C13C22×C411yescharacteristic
153C2×D4×C13C22×C411yescharacteristic
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—81no—
161C22×C4×C13—81no—
162C22×C4×C13C22×C411yescharacteristic
163C22×C4×C13C2×D411yescharacteristic
164C22×C4×C13#4111yescharacteristic
165C13×SD16—22no—
166C13×SD16—41no—
167C13×D8—22no—
168C13×D8—41no—
169C2×C8×C13C22×C411yescharacteristic
170C2×C8×C13C22×C411yescharacteristic
171C2×C8×C13C22×C411yescharacteristic
172C2×C8×C13C22×C411yescharacteristic
173C13×C4⋊C4—21no—
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×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—
189C13×C22⋊C4—21no—
190C13×C22⋊C4—21no—
191C42×C13—21no—
192C42×C13C22×C411yescharacteristic
193C42×C13C2×D411yescharacteristic
194C42×C13#4111yescharacteristic
195C42×C13C2411yescharacteristic
196#6099—81no—
197#6099—81no—
198#6099—81no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—42no—
206C2×#1055—81no—
207C2×#1055—81no—
208C2×#1055—81no—
209C2×#1055—81no—
210C2×#1055C2×D411yescharacteristic
211C2×#1055C2×D411yescharacteristic
212C2×#1055C2×D411yescharacteristic
213C2×#1055C2×D411yescharacteristic
214#3105D1311yescharacteristic
215#2994—131no—
216#2974—131no—
217#1594—131no—
218#1592—131no—
219#1583—131no—
220#1582—131no—
221#1581—131no—
222#1581—131no—
223#1580—131no—
224SD16⋊C8—131no—
225#1573—131no—
226#1494—131no—
227C2×D4⋊C8—131no—
228#1452—131no—
229C23×C13—21no—
230C23×C13—21no—
231C23×C13—21no—
232C23×C13—42no—
233C23×C13—42no—
234C23×C13—81no—
235C23×C13C4×D411yescharacteristic
236Q8×C13—21no—
237Q8×C13—21no—
238D4×C13—21no—
239D4×C13—21no—
240D4×C13—21no—
241D4×C13—21no—
242D4×C13—21no—
243D4×C13—42no—
244D4×C13—42no—
245D4×C13#13112yes—
246C2×C4×C13—22no—
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—81no—
263C2×C4×C13—81no—
264C2×C4×C13—81no—
265C2×C4×C13C4×D411yescharacteristic
266C2×C4×C13C4×D411yescharacteristic
267C2×C4×C13C4×D411yescharacteristic
268C2×C4×C13C23×C411yescharacteristic
269C2×C4×C13C22×D411yescharacteristic
270C2×C4×C13C2×#4111yescharacteristic
271C8×C13—21no—
272C8×C13—21no—
273C8×C13—21no—
274C8×C13—21no—
275#1055—21no—
276#1055—21no—
277#1055—21no—
278#1055—21no—
279#1055—41no—
280#1055—41no—
281#1055—41no—
282#1055—41no—
283#1055—41no—
284#1055—41no—
285#529C2×D1311yescharacteristic
286C2×C4×D4C2×D1311yescharacteristic
287#484Dic1311yescharacteristic
288#481Dic1311yescharacteristic
289#478Dic1311yescharacteristic
290#478Dic1311yescharacteristic
291#463Dic1311yescharacteristic
292#463Dic1311yescharacteristic
293#450Dic1311yescharacteristic
294#447Dic1311yescharacteristic
295#446—131no—
296C8×Q8—131no—
297C4×SD16C2×D1311yescharacteristic
298C4×SD16C2×D1311yescharacteristic
299C4×D8C2×D1311yescharacteristic
300C4×D8C2×D1311yescharacteristic
301#436—131no—
302#436—131no—
303#436—131no—
304#435—261no—
305#435—261no—
306#435—261no—
307C8×D4—131no—
308C8×D4—131no—
309C8×D4—131no—
310C8×D4—261no—
311#433—261no—
312#432—131no—
313#431—131no—
314#431C2×D1311yescharacteristic
315#424—261no—
316C2×C4⋊C8—131no—
317#407—261no—
318C2×C22⋊C8—261no—
319C2×C4×C8—131no—
320#335—131no—
321#335—131no—
322#334—131no—
323#334—131no—
324Q8⋊C8—131no—
325Q8⋊C8—131no—
326D4⋊C8—131no—
327D4⋊C8—131no—
328D4⋊C8—131no—
329D4⋊C8—131no—
330D4⋊C8—131no—
331D4⋊C8—131no—
332#322—131no—
333#322—131no—
334#322—131no—
335#322—131no—
336C22×C13—21no—
337C22×C13—21no—
338C22×C13—22no—
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×C13—84no—
348C22×C13#44412yes—
349C22×C13C2×C4×D411yescharacteristic
350C4×C13—21no—
351C4×C13—21no—
352C4×C13—21no—
353C4×C13—21no—
354C4×C13—41no—
355C4×C13—41no—
356C4×C13—41no—
357C4×C13—41no—
358C4×C13—41no—
359C4×C13C2×#13111yescharacteristic
360C4×C13#56811yescharacteristic
361C4×C13#57611yescharacteristic
362C4×C13#57711yescharacteristic
363C22×D4C2×Dic1311yescharacteristic
364C23×C4—21no—
365C2×SD16C2×Dic1311yescharacteristic
366C2×SD16C2×Dic1311yescharacteristic
367C2×D8C2×Dic1311yescharacteristic
368C2×D8C2×Dic1311yescharacteristic
369C2×M16—261no—
370C2×M16—261no—
371C2×M16—261no—
372C22×C8—261no—
373C22×C8—261no—
374C22×C8—261no—
375C22×C8—261no—
376C22×C8—261no—
377#126—21no—
378#125C2×Dic1311yescharacteristic
379#124C2×Dic1311yescharacteristic
380#123—21no—
381C22⋊Q8C2×Dic1311yescharacteristic
382#121C2×Dic1311yescharacteristic
383C4×Q8C22×D1311yescharacteristic
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4C2×Dic1311yescharacteristic
388C4×D4C2×Dic1311yescharacteristic
389C4×D4C22×D1311yescharacteristic
390C4×D4C22×D1311yescharacteristic
391C4×D4C22×D1311yescharacteristic
392#117—21no—
393C2×C4⋊C4C2×Dic1311yescharacteristic
394C2×C22⋊C4—21no—
395C2×C42C22×D1311yescharacteristic
396#107C2×Dic1311yescharacteristic
397#107C2×Dic1311yescharacteristic
398#106C2×Dic1311yescharacteristic
399#106C2×Dic1311yescharacteristic
400C4⋊C8—131no—
401C4⋊C8—131no—
402C4⋊C8—131no—
403C4⋊C8—131no—
404C4⋊C8—131no—
405C4⋊C8—131no—
406C4⋊C8—261no—
407C4⋊C8—261no—
408C4⋊C8—261no—
409C4⋊C8C2×Dic1311yescharacteristic
410C4⋊C8C2×Dic1311yescharacteristic
411#103C2×Dic1311yescharacteristic
412#103C2×Dic1311yescharacteristic
413#102C2×Dic1311yescharacteristic
414#102C2×Dic1311yescharacteristic
415#102C2×Dic1311yescharacteristic
416#102C2×Dic1311yescharacteristic
417#102C2×Dic1311yescharacteristic
418#102C2×Dic1311yescharacteristic
419C22⋊C8—131no—
420C22⋊C8—131no—
421C22⋊C8—261no—
422C22⋊C8—261no—
423C22⋊C8—261no—
424C22⋊C8—261no—
425C22⋊C8—261no—
426C22⋊C8—261no—
427C22⋊C8—261no—
428C22⋊C8C2×Dic1311yescharacteristic
429C22⋊C8C2×Dic1311yescharacteristic
430#97—261no—
431#97—261no—
432C4×C8—131no—
433C4×C8—131no—
434C4×C8—131no—
435C4×C8—131no—
436C4×C8—261no—
437C4×C8—261no—
438C4×C8C22×D1311yescharacteristic
439C4×C8C22×D1311yescharacteristic
440C2×C13—22no—
441C2×C13—42no—
442C2×C13—81no—
443C2×C13—81no—
444C2×C13#293311yescharacteristic
445C2×C13#294611yescharacteristic
446C2×C13C2×#44411yescharacteristic
447C24—21no—
448C2×Q8C22×Dic1311yescharacteristic
449C2×D4—22no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—41no—
453C2×D4C22×Dic1311yescharacteristic
454C2×D4C22×Dic1311yescharacteristic
455C2×D4C22×Dic1311yescharacteristic
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—81no—
463C22×C4—81no—
464C22×C4D4×D1311yescharacteristic
465C22×C4#612911yescharacteristic
466C22×C4C22×Dic1311yescharacteristic
467SD16—22no—
468SD16—41no—
469D8—22no—
470D8—41no—
471M16—1041no—
472M16—1041no—
473M16—1041no—
474C2×C8—131no—
475C2×C8—131no—
476C2×C8—131no—
477C2×C8—131no—
478C2×C8—261no—
479C2×C8—261no—
480C2×C8—261no—
481C2×C8—261no—
482C2×C8—261no—
483C2×C8—261no—
484C2×C8—522no—
485C2×C8—1041no—
486C2×C8—1041no—
487C2×C8—1041no—
488C2×C8—1041no—
489C2×C8C22×Dic1311yescharacteristic
490C2×C8C22×Dic1311yescharacteristic
491C2×C8C22×Dic1311yescharacteristic
492C2×C8C22×Dic1311yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4C22×Dic1311yescharacteristic
499C4⋊C4C22×Dic1311yescharacteristic
500C4⋊C4C22×Dic1311yescharacteristic
501C4⋊C4C22×Dic1311yescharacteristic
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—21no—
511C42—21no—
512C42D4×D1311yescharacteristic
513C42#612911yescharacteristic
514C42C22×Dic1311yescharacteristic
515C42C23×D1311yescharacteristic
516C13#1802011yescharacteristic, complemented, Sylow
517C23—21no—
518C23—21no—
519C23—21no—
520C23—42no—
521C23—42no—
522C23—81no—
523C23D4×Dic1311yescharacteristic
524Q8—21no—
525Q8—21no—
526D4—21no—
527D4—21no—
528D4—21no—
529D4—21no—
530D4—21no—
531D4—42no—
532D4—42no—
533D4#8820212yes—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—81no—
551C2×C4—81no—
552C2×C4—81no—
553C2×C4D4×Dic1311yescharacteristic
554C2×C4D4×Dic1311yescharacteristic
555C2×C4D4×Dic1311yescharacteristic
556C2×C4C2×D4×D1311yescharacteristic
557C2×C4C2×#612911yescharacteristic
558C2×C4C23×Dic1311yescharacteristic
559C8—21no—
560C8—21no—
561C8—21no—
562C8—21no—
563C8—261no—
564C8—261no—
565C8—261no—
566C8—261no—
567C8—521no—
568C8—521no—
569C8—521no—
570C8—521no—
571C8—521no—
572C8—521no—
573C22—21no—
574C22—21no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—84no—
585C22#1171885812yes—
586C22C2×D4×Dic1311yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—41no—
596C4#1171947911yescharacteristic
597C4#1171948011yescharacteristic
598C4C2×#8820211yescharacteristic
599C4#1171952411yescharacteristic
600C2—22no—
601C2—42no—
602C2—81no—
603C2—81no—
604C2#1312356311yescharacteristic
605C2#1312366911yescharacteristic
606C2C2×#1171885811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#3105C2
socleC22×C13C2×C4×D4
prime radicalC13×#447C4
cosocleC42×C13C24
hypercenter#3105D13
hypocenterC13#18020
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3105

Complements

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

NH ≅ G/Ntype
1. #13123996C2semidirect
2. #13123871C2semidirect
3. #13113750C2semidirect
4. #13113739C2semidirect
5. #13113680C2semidirect
6. #13113673C2semidirect
7. #13113666C2semidirect
8. #13113666C2semidirect
9. #13113660C2semidirect
10. SD16⋊#1055C2semidirect
11. #13113621C2semidirect
12. #13113296C2semidirect
13. C2×D4⋊#1055C2semidirect
14. #13113129C2semidirect
33. #11718685C22semidirect
34. Q8×#1055C22semidirect
37. #11718673C22semidirect
44. D4×#1055C22semidirect
51. Q8⋊#1055C22semidirect
52. Q8⋊#1055C22semidirect
57. D4⋊#1055C22semidirect
58. D4⋊#1055C22semidirect
59. #11718050C22semidirect
60. #11718050C22semidirect
61. #11718049C22semidirect
62. #11718049C22semidirect
63. #11718047C22semidirect
64. #11718047C22semidirect
65. #11718046C22semidirect
66. #11718046C22semidirect
516. C13#18020semidirect

Maximal subgroups

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

subgroupindex
#131239962
#131238712
#131137502
#131137392
#131136802
#131136732
#131136662
#131136602
SD16⋊#10552
#131136212
#131132962
C2×D4⋊#10552
#131131292
C13×#31052
#1802013