Finite Group Databasebeta

← #15870764

Subgroups — #15870764

Order 3328.

730 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124624C211yesmaximal, characteristic
2#13123773C211yesmaximal, characteristic, complemented
3#13123264C211yesmaximal, characteristic
4#13115779C211yesmaximal, characteristic, complemented
5#13115609C211yesmaximal, characteristic, complemented
6#13115433C211yesmaximal, characteristic, complemented
7#13115433C211yesmaximal, characteristic, complemented
8#13115109C211yesmaximal, characteristic
9#13115109C211yesmaximal, characteristic
10#13114719C211yesmaximal, characteristic, complemented
11#13114714C211yesmaximal, characteristic, complemented
12#13114711C211yesmaximal, characteristic, complemented
13#13114681C211yesmaximal, characteristic
14#13114674C211yesmaximal, characteristic
15C13×#1806C211yesmaximal, characteristic
16C4×C13×#41C2211yescharacteristic
17C2×#88202C2211yescharacteristic
18C2×#88202C2211yescharacteristic
19#11719175C2211yescharacteristic
20C13×#423C2211yescharacteristic
21C2×C13×#104C2211yescharacteristic
22C2×C13×#104C2211yescharacteristic
23C4×C13×C4⋊C4C2211yescharacteristic
24#11718894C2211yescharacteristic
25#11718894C2211yescharacteristic
26C2×#88062C2211yescharacteristic
27C2×#88062C2211yescharacteristic
28#11718783C2211yescharacteristic
29#11718783C2211yescharacteristic
30#11718780C2211yescharacteristic
31#11718780C2211yescharacteristic
32#11718683C411yescharacteristic, complemented
33#11718683C411yescharacteristic, complemented
34#11718682C411yescharacteristic, complemented
35#11718681C411yescharacteristic, complemented
36#11718670C411yescharacteristic, complemented
37#11718670C411yescharacteristic, complemented
38#11718669C411yescharacteristic, complemented
39#11718668C411yescharacteristic, complemented
40#11718659C2211yescharacteristic
41#11718659C2211yescharacteristic
42#11718658—21no—
43#11718658—21no—
44#11718658C2211yescharacteristic
45#11718658C2211yescharacteristic
46C2×C4⋊#1055C2211yescharacteristic
47C4×#6099—21no—
48C4×#6099C2211yescharacteristic
49C2×#88043—21no—
50C2×#88043C2211yescharacteristic
51C2×#88043C2211yescharacteristic
52C2×C4×#1055C2211yescharacteristic
53#11718489—21no—
54#11718489—21no—
55#11718489—21no—
56#11718489—21no—
57C13×#339C2211yescharacteristic
58C13×#339C2211yescharacteristic
59#11718150C2211yescharacteristic
60#11718150C2211yescharacteristic
61#11718116C2211yescharacteristic
62#11718116C2211yescharacteristic
63#11718115C2211yescharacteristic
64#11718115C2211yescharacteristic
65#11718115C2211yescharacteristic
66#11718115C2211yescharacteristic
67C2×C13×#41C2311yescharacteristic
68C2×C13×M16C2311yescharacteristic
69C2×C13×M16C2311yescharacteristic
70C4×Q8×C13C2×C411yescharacteristic
71C4×Q8×C13C2×C411yescharacteristic
72C4×D4×C13—21no—
73C4×D4×C13—21no—
74C4×D4×C13C2×C411yescharacteristic
75C4×D4×C13C2×C411yescharacteristic
76C13×#117—21no—
77C13×#117C2311yescharacteristic
78C2×C13×C4⋊C4—21no—
79C2×C42×C13—21no—
80C2×C42×C13C2311yescharacteristic
81C2×C42×C13C2311yescharacteristic
82C2×C42×C13C2311yescharacteristic
83#88202—22no—
84#88202—22no—
85#88202—22no—
86#88202Q814yescomplemented
87#88180C2311yescharacteristic
88#88180C2311yescharacteristic
89#88178—21no—
90#88178—21no—
91C2×#6099—21no—
92C2×#6099—21no—
93C2×#6099C2311yescharacteristic
94C2×#6099C2311yescharacteristic
95C22×#1055—21no—
96C22×#1055—21no—
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99C22×#1055C2311yescharacteristic
100C22×#1055C2311yescharacteristic
101#88124C2×C411yescharacteristic
102#88124C2×C411yescharacteristic
103#88123C2×C411yescharacteristic
104#88123C2×C411yescharacteristic
105C4×Dic26—21no—
106C4×Dic26—21no—
107C13×C4⋊C8—21no—
108C13×C4⋊C8—21no—
109C13×#104—22no—
110C13×#104—22no—
111C13×#95—21no—
112#88075C2×C411yescharacteristic
113#88075C2×C411yescharacteristic
114#88075C2×C411yescharacteristic
115#88075C2×C411yescharacteristic
116#88072C2×C411yescharacteristic
117#88072C2×C411yescharacteristic
118#88072C2×C411yescharacteristic
119#88072C2×C411yescharacteristic
120#88062—22no—
121#88062—22no—
122#88055—21no—
123#88055—21no—
124#88054—21no—
125#88054—21no—
126#88054—21no—
127#88054—21no—
128C8×Dic13—21no—
129C8×Dic13—21no—
130#88048C2×C411yescharacteristic
131#88048C2×C411yescharacteristic
132#88048C2×C411yescharacteristic
133#88048C2×C411yescharacteristic
134#88047C2×C411yescharacteristic
135#88047C2×C411yescharacteristic
136#88047C2×C411yescharacteristic
137#88047C2×C411yescharacteristic
138C4⋊#1055C2×C411yescharacteristic
139C4⋊#1055C2×C411yescharacteristic
140C4⋊#1055C2×C411yescharacteristic
141C4⋊#1055C2×C411yescharacteristic
142#88043—21no—
143#88043—21no—
144#88043—21no—
145#88043—22no—
146#88043D411yescharacteristic
147#88043D411yescharacteristic
148#88043D411yescharacteristic
149#88043D411yescharacteristic
150C4×#1055—21no—
151C4×#1055—21no—
152C4×#1055—21no—
153C4×#1055—22no—
154#21629—131nomaximal, Sylow
155C13×#41—21no—
156C13×#41—21no—
157C13×#41C2×Q812yes—
158C13×#41#4112yes—
159C2×Q8×C13C22×C411yescharacteristic
160C2×D4×C13—21no—
161C2×D4×C13C22×C411yescharacteristic
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13#4111yescharacteristic
168C22×C4×C13#4111yescharacteristic
169C22×C4×C13C2411yescharacteristic
170C2×Dic26—21no—
171C2×Dic26—21no—
172C13×M16—21no—
173C13×M16—21no—
174C13×M16—21no—
175C13×M16—21no—
176C2×C8×C13—21no—
177C2×C8×C13—21no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—42no—
181C13×C4⋊C4C22×C411yescharacteristic
182C13×C4⋊C4C22×C411yescharacteristic
183C13×C22⋊C4—21no—
184C13×C22⋊C4—21no—
185C13×C22⋊C4—21no—
186C42×C13—21no—
187C42×C13—21no—
188C42×C13—21no—
189C42×C13—21no—
190C42×C13—21no—
191C42×C13—21no—
192C42×C13—21no—
193C42×C13C22×C411yescharacteristic
194C42×C13C22×C411yescharacteristic
195C42×C13C2×D411yescharacteristic
196C42×C13C2×D411yescharacteristic
197C22⋊Dic13—21no—
198C22⋊Dic13—21no—
199C4⋊Dic13—21no—
200C4⋊Dic13—21no—
201C4⋊Dic13C22×C411yescharacteristic
202C4⋊Dic13C22×C411yescharacteristic
203C4⋊Dic13C22×C411yescharacteristic
204C4⋊Dic13C22×C411yescharacteristic
205#6101—21no—
206#6101—21no—
207#6101—21no—
208#6101—21no—
209C4×Dic13—21no—
210C4×Dic13—21no—
211#6099—24no—
212#6099—21no—
213#6099—21no—
214#6099—24no—
215#6099C2×Q812yes—
216#6099#4112yes—
217C2×#1055—24no—
218C2×#1055—21no—
219C2×#1055—21no—
220C2×#1055—21no—
221C2×#1055—21no—
222C2×#1055—21no—
223C2×#1055—21no—
224C2×#1055—21no—
225C2×#1055—21no—
226C2×#1055—24no—
227C2×#1055C22×C411yescharacteristic
228C2×#1055C22×C411yescharacteristic
229C2×#1055C22×C411yescharacteristic
230C2×#1055C22×C411yescharacteristic
231C2×#1055C2×D411yescharacteristic
232C2×#1055C2×D411yescharacteristic
233C2×#1055C2×D411yescharacteristic
234C2×#1055C2×D411yescharacteristic
235C2×#1055C2×Q812yes—
236C2×#1055#4112yes—
237#3076—131no—
238#2961—131no—
239#2875—131no—
240#1986—131no—
241#1950—131no—
242#1922—131no—
243#1922—131no—
244#1866—131no—
245#1866—131no—
246#1806D1311yescharacteristic
247#1773—131no—
248#1772—131no—
249#1771—131no—
250#1765—131no—
251#1764—131no—
252C23×C13—21no—
253C23×C13C2×#4111yescharacteristic
254Q8×C13—21no—
255Q8×C13C4×Q812yes—
256D4×C13—22no—
257D4×C13—22no—
258D4×C13—21no—
259D4×C13C4×Q812yes—
260C2×C4×C13—21no—
261C2×C4×C13—22no—
262C2×C4×C13—22no—
263C2×C4×C13—22no—
264C2×C4×C13—21no—
265C2×C4×C13—21no—
266C2×C4×C13—41no—
267C2×C4×C13—41no—
268C2×C4×C13—41no—
269C2×C4×C13—41no—
270C2×C4×C13—41no—
271C2×C4×C13—41no—
272C2×C4×C13—41no—
273C2×C4×C13—81no—
274C2×C4×C13—81no—
275C2×C4×C13C4×D411yescharacteristic
276C2×C4×C13C4×D411yescharacteristic
277C2×C4×C13C4×D411yescharacteristic
278C2×C4×C13C4×D411yescharacteristic
279C2×C4×C13C23×C411yescharacteristic
280C2×C4×C13C22×D411yescharacteristic
281C2×C4×C13C22×Q811yescharacteristic
282C2×C4×C13C2×#4111yescharacteristic
283C2×C4×C13C2×#4111yescharacteristic
284C2×C4×C13C2×#4111yescharacteristic
285C2×Dic13—21no—
286C2×Dic13—21no—
287C2×Dic13—21no—
288C2×Dic13—21no—
289Dic26—81no—
290Dic26—81no—
291C8×C13—41no—
292C8×C13—41no—
293#1055—21no—
294#1055—21no—
295#1055—21no—
296#1055—21no—
297#1055—22no—
298#1055—21no—
299#1055—22no—
300#1055—21no—
301#1055C22⋊Q812yes—
302#1055C22⋊Q812yes—
303C2×#131—131no—
304C2×#131—131no—
305#533—131no—
306C4×#41C2×D1311yescharacteristic
307#479—131no—
308#479—131no—
309#478—131no—
310#478—131no—
311#477—131no—
312#476—131no—
313#475—131no—
314#474—131no—
315#446—261no—
316#446—261no—
317#446—261no—
318#446—261no—
319C2×#108—131no—
320C2×#108—131no—
321#427—131no—
322#427—131no—
323#424—131no—
324#424—131no—
325#423C2×D1311yescharacteristic
326C2×C4⋊C8—131no—
327C2×#104C2×D1311yescharacteristic
328C2×#104C2×D1311yescharacteristic
329#416—131no—
330#416—131no—
331#405—131no—
332#405—131no—
333#405—131no—
334#405—131no—
335#405—261no—
336#405—261no—
337C4×M16—131no—
338C4×M16—261no—
339C2×#97—131no—
340C2×#97—131no—
341C2×#97—261no—
342C2×C4×C8—131no—
343C4×C4⋊C4C2×D1311yescharacteristic
344#341—131no—
345#341—131no—
346#339—131no—
347#339—131no—
348#339—131no—
349#339—131no—
350#339C2×D1311yescharacteristic
351#339C2×D1311yescharacteristic
352#336—131no—
353#336—131no—
354C22×C13—21no—
355C22×C13—21no—
356C22×C13—22no—
357C22×C13—41no—
358C22×C13—41no—
359C22×C13C2×C4×D411yescharacteristic
360C22×C13#52911yescharacteristic
361C22×C13#53311yescharacteristic
362C4×C13—21no—
363C4×C13—21no—
364C4×C13—21no—
365C4×C13—21no—
366C4×C13—22no—
367C4×C13—42no—
368C4×C13—41no—
369C4×C13—41no—
370C4×C13—81no—
371C4×C13C2×C4×Q811yescharacteristic
372C4×C13C4×#4111yescharacteristic
373C4×C13C2×C22⋊Q811yescharacteristic
374C4×C13#52511yescharacteristic
375Dic13—41no—
376Dic13—41no—
377Dic13—41no—
378Dic13—41no—
379C2×#41C22×D1311yescharacteristic
380#131—134no—
381#131—262no—
382#131—262no—
383#131—262no—
384C2×M16—131no—
385C2×M16—131no—
386C2×M16—261no—
387C2×M16—261no—
388C2×M16C22×D1311yescharacteristic
389C2×M16C22×D1311yescharacteristic
390C22×C8—131no—
391C22×C8—131no—
392C22×C8—131no—
393C22×C8—131no—
394C22×C8—261no—
395C22×C8—261no—
396C4⋊Q8—131no—
397C4⋊Q8—131no—
398#125—131no—
399#125—131no—
400C22⋊Q8—261no—
401C22⋊Q8—261no—
402C4×Q8—261no—
403C4×Q8—261no—
404C4×Q8C4×D1311yescharacteristic
405C4×Q8C4×D1311yescharacteristic
406C4×D4—21no—
407C4×D4—21no—
408C4×D4C4×D1311yescharacteristic
409C4×D4C4×D1311yescharacteristic
410#117—21no—
411#117—131no—
412#117—131no—
413#117C22×D1311yescharacteristic
414C2×C4⋊C4—21no—
415C2×C42—21no—
416C2×C42C22×D1311yescharacteristic
417C2×C42C22×D1311yescharacteristic
418C2×C42C22×D1311yescharacteristic
419#108—262no—
420#108—262no—
421#107—131no—
422#107—131no—
423#107—131no—
424#107—131no—
425#106—131no—
426#106—131no—
427#106—131no—
428#106—131no—
429C4⋊C8—21no—
430C4⋊C8—21no—
431C4⋊C8—131no—
432C4⋊C8—131no—
433C4⋊C8—131no—
434C4⋊C8—131no—
435C4⋊C8—261no—
436C4⋊C8—261no—
437C4⋊C8—261no—
438C4⋊C8—261no—
439#104—22no—
440#104—22no—
441#103—131no—
442#103—131no—
443#103—131no—
444#103—131no—
445#102—131no—
446#102—131no—
447#102—131no—
448#102—131no—
449#97—131no—
450#97—131no—
451#97—131no—
452#97—131no—
453#97—262no—
454#97—261no—
455#97—261no—
456#97—261no—
457#97—261no—
458#97—261no—
459C4×C8—262no—
460C4×C8—261no—
461C4×C8—261no—
462C4×C8—261no—
463C4×C8—261no—
464C4×C8—261no—
465#95—21no—
466C2×C13—21no—
467C2×C13—21no—
468C2×C13—42no—
469C2×C13C4×C22⋊Q811yescharacteristic
470C2×C13#295611yescharacteristic
471C2×C13#295711yescharacteristic
472#41—21no—
473#41—21no—
474#41#612912yes—
475#41Q8×D1312yes—
476C2×Q8—261no—
477C2×Q8—261no—
478C2×Q8C2×C4×D1311yescharacteristic
479C2×D4—21no—
480C2×D4C2×C4×D1311yescharacteristic
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4#612911yescharacteristic
487C22×C4#612911yescharacteristic
488C22×C4C23×D1311yescharacteristic
489M16—21no—
490M16—21no—
491M16—21no—
492M16—21no—
493M16—132no—
494M16—132no—
495M16—264no—
496M16—264no—
497M16—261no—
498M16—261no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—131no—
502C2×C8—131no—
503C2×C8—132no—
504C2×C8—132no—
505C2×C8—131no—
506C2×C8—131no—
507C2×C8—131no—
508C2×C8—131no—
509C2×C8—131no—
510C2×C8—131no—
511C2×C8—264no—
512C2×C8—264no—
513C2×C8—261no—
514C2×C8—261no—
515C2×C8—261no—
516C2×C8—261no—
517C2×C8—261no—
518C2×C8—261no—
519C2×C8—261no—
520C2×C8—261no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—42no—
524C4⋊C4—131no—
525C4⋊C4—131no—
526C4⋊C4—131no—
527C4⋊C4—131no—
528C4⋊C4—261no—
529C4⋊C4—261no—
530C4⋊C4—261no—
531C4⋊C4—261no—
532C4⋊C4—261no—
533C4⋊C4—261no—
534C4⋊C4C2×C4×D1311yescharacteristic
535C4⋊C4C2×C4×D1311yescharacteristic
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—261no—
540C22⋊C4—261no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—261no—
549C42—261no—
550C42C2×C4×D1311yescharacteristic
551C42C2×C4×D1311yescharacteristic
552C42D4×D1311yescharacteristic
553C42D4×D1311yescharacteristic
554C13#2162911yescharacteristic, complemented, Sylow
555C23—21no—
556C23C2×#612911yescharacteristic
557Q8—21no—
558Q8—1041no—
559Q8—1041no—
560Q8#8814112yes—
561D4—22no—
562D4—22no—
563D4—21no—
564D4#8814112yes—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—81no—
579C2×C4—81no—
580C2×C4—261no—
581C2×C4—261no—
582C2×C4—261no—
583C2×C4—261no—
584C2×C4#8813511yescharacteristic
585C2×C4#8813511yescharacteristic
586C2×C4#8813511yescharacteristic
587C2×C4#8813511yescharacteristic
588C2×C4C22×C4×D1311yescharacteristic
589C2×C4C2×D4×D1311yescharacteristic
590C2×C4C2×#612911yescharacteristic
591C2×C4C2×Q8×D1311yescharacteristic
592C2×C4#41×D1311yescharacteristic
593C2×C4#41×D1311yescharacteristic
594C8—41no—
595C8—41no—
596C8—132no—
597C8—132no—
598C8—261no—
599C8—261no—
600C8—261no—
601C8—261no—
602C8—261no—
603C8—261no—
604C8—262no—
605C8—262no—
606C22—21no—
607C22—21no—
608C22—22no—
609C22—41no—
610C22—41no—
611C22C2×#8813511yescharacteristic
612C22#1171930511yescharacteristic
613C22#1171932711yescharacteristic
614C4—21no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—22no—
619C4—42no—
620C4—41no—
621C4—41no—
622C4—81no—
623C4—521no—
624C4—521no—
625C4—521no—
626C4—521no—
627C4C2×#8814111yescharacteristic
628C4#1171922711yescharacteristic
629C4#1171931111yescharacteristic
630C4D13×C22⋊Q811yescharacteristic
631C2—21no—
632C2—21no—
633C2—42no—
634C2#1311736411yescharacteristic
635C2#1312374211yescharacteristic
636C2#1312374911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1806C2
socleC22×C13C2×C4×D4
prime radicalC2×C13×#41C23
cosocleC22×C4×C13C24
hypercenter#1806D13
hypocenterC13#21629
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
2. #13123773C2semidirect
4. #13115779C2semidirect
5. #13115609C2semidirect
6. #13115433C2semidirect
7. #13115433C2semidirect
10. #13114719C2semidirect
11. #13114714C2semidirect
12. #13114711C2semidirect
32. #11718683C4semidirect
33. #11718683C4semidirect
34. #11718682C4semidirect
35. #11718681C4semidirect
36. #11718670C4semidirect
37. #11718670C4semidirect
38. #11718669C4semidirect
39. #11718668C4semidirect
86. #88202Q8semidirect
554. C13#21629semidirect

Maximal subgroups

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

subgroupindex
#131246242
#131237732
#131232642
#131157792
#131156092
#131154332
#131151092
#131147192
#131147142
#131147112
#131146812
#131146742
C13×#18062
#2162913