Finite Group Databasebeta

← #15870774

Subgroups — #15870774

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#13124618C211yesmaximal, characteristic
2#13123777C211yesmaximal, characteristic, complemented
3#13123265C211yesmaximal, characteristic
4#13115611C211yesmaximal, characteristic, complemented
5#13115438C211yesmaximal, characteristic, complemented
6#13115438C211yesmaximal, characteristic, complemented
7#13115112C211yesmaximal, characteristic
8#13115112C211yesmaximal, characteristic
9#13114857C211yesmaximal, characteristic
10#13114719C211yesmaximal, characteristic, complemented
11#13114714C211yesmaximal, characteristic, complemented
12#13114711C211yesmaximal, characteristic, complemented
13#13114677C211yesmaximal, characteristic
14#13114670C211yesmaximal, characteristic
15C13×#1986C211yesmaximal, characteristic, complemented
16C13×#533C2211yescharacteristic
17C2×#88161C2211yescharacteristic
18C2×#88161C2211yescharacteristic
19C4×#6127C2211yescharacteristic
20C4×C13×M16C2211yescharacteristic
21C4×C13×C4⋊C4C2211yescharacteristic
22C2×#88062C2211yescharacteristic
23C2×#88062C2211yescharacteristic
24#11718783C2211yescharacteristic
25#11718783C2211yescharacteristic
26#11718755C411yescharacteristic, complemented
27#11718752C411yescharacteristic, complemented
28#11718748C411yescharacteristic, complemented
29#11718745C411yescharacteristic, complemented
30#11718727C411yescharacteristic, complemented
31#11718727C411yescharacteristic, complemented
32#11718724C411yescharacteristic, complemented
33#11718724C411yescharacteristic, complemented
34#11718685—21no—
35#11718685—21no—
36#11718685—21no—
37#11718685—21no—
38#11718663C2211yescharacteristic
39#11718663C2211yescharacteristic
40#11718660C2211yescharacteristic
41#11718660C2211yescharacteristic
42#11718659C2211yescharacteristic
43#11718659C2211yescharacteristic
44#11718658C2211yescharacteristic
45#11718658C2211yescharacteristic
46C2×#88045C2211yescharacteristic
47C2×#88045C2211yescharacteristic
48#11718585C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C2×#88043C2211yescharacteristic
51C2×#88043C2211yescharacteristic
52C2×C4×#1055C2211yescharacteristic
53#11718368—21no—
54D13×#97—21no—
55#11718350—21no—
56#11718350—21no—
57C13×#339C2211yescharacteristic
58C13×#339C2211yescharacteristic
59C13×#339C2211yescharacteristic
60C13×#339C2211yescharacteristic
61#11718150C2211yescharacteristic
62#11718150C2211yescharacteristic
63#11718116C2211yescharacteristic
64#11718116C2211yescharacteristic
65#11718115C2211yescharacteristic
66#11718115C2211yescharacteristic
67C2×#6127C2311yescharacteristic
68C2×C13×M16C2311yescharacteristic
69C2×C13×M16C2311yescharacteristic
70C13×C4⋊Q8C2×C411yescharacteristic
71C13×C4⋊Q8C2×C411yescharacteristic
72C13×#125C2×C411yescharacteristic
73C13×#125C2×C411yescharacteristic
74C13×C22⋊Q8—21no—
75C13×C22⋊Q8—21no—
76C4×Q8×C13—21no—
77C4×Q8×C13—21no—
78C13×#117C2311yescharacteristic
79C13×#117C2311yescharacteristic
80C2×C13×C4⋊C4—21no—
81C2×C42×C13C2311yescharacteristic
82C2×C42×C13C2311yescharacteristic
83C2×C42×C13C2311yescharacteristic
84C4×C22⋊D13—21no—
85C4×C22⋊D13—21no—
86#88180C2311yescharacteristic
87C2×#6099C2311yescharacteristic
88C2×#6099C2311yescharacteristic
89C22×#1055C2311yescharacteristic
90C22×#1055C2311yescharacteristic
91C22×#1055C2311yescharacteristic
92C22×#1055C2311yescharacteristic
93#88161—22no—
94#88161—22no—
95#88161—22no—
96#88161Q814yescomplemented
97C2×#6094—21no—
98C2×#6094—21no—
99C2×C8×D13—21no—
100C2×C8×D13—21no—
101C4×D52C2×C411yescharacteristic
102C4×D52C2×C411yescharacteristic
103#88126—21no—
104C42×D13—21no—
105C4×Dic26C2×C411yescharacteristic
106C4×Dic26C2×C411yescharacteristic
107C13×#97—21no—
108C4×C8×C13—21no—
109C13×#95—21no—
110#88062—22no—
111#88062—22no—
112#88055—21no—
113#88055—21no—
114C8×Dic13—21no—
115C8×Dic13—21no—
116#88050C2×C411yescharacteristic
117#88050C2×C411yescharacteristic
118#88050C2×C411yescharacteristic
119#88050C2×C411yescharacteristic
120#88049C2×C411yescharacteristic
121#88049C2×C411yescharacteristic
122#88049C2×C411yescharacteristic
123#88049C2×C411yescharacteristic
124#88048C2×C411yescharacteristic
125#88048C2×C411yescharacteristic
126#88048C2×C411yescharacteristic
127#88048C2×C411yescharacteristic
128#88047C2×C411yescharacteristic
129#88047C2×C411yescharacteristic
130#88047C2×C411yescharacteristic
131#88047C2×C411yescharacteristic
132#88045—22no—
133#88045—22no—
134C4⋊#1055—21no—
135C4⋊#1055—21no—
136C4⋊#1055—21no—
137C4⋊#1055—21no—
138C4⋊#1055—21no—
139C4⋊#1055—21no—
140C4⋊#1055C2×C411yescharacteristic
141C4⋊#1055C2×C411yescharacteristic
142C4⋊#1055C2×C411yescharacteristic
143C4⋊#1055C2×C411yescharacteristic
144#88043—21no—
145#88043—21no—
146#88043—22no—
147#88043D411yescharacteristic
148#88043D411yescharacteristic
149#88043D411yescharacteristic
150#88043D411yescharacteristic
151C4×#1055—21no—
152C4×#1055—21no—
153C4×#1055—22no—
154#21629—131nomaximal, Sylow
155C2×Q8×C13—21no—
156C2×Q8×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13#4111yescharacteristic
160C22×C4×C13#4111yescharacteristic
161C22×C4×C13C2411yescharacteristic
162C2×C22⋊D13—21no—
163#6127—21no—
164#6127—21no—
165#6127C2×Q812yes—
166#6127#4112yes—
167C2×D52C22×C411yescharacteristic
168C2×C4×D13—21no—
169C2×C4×D13—21no—
170C2×C4×D13—21no—
171C2×Dic26C22×C411yescharacteristic
172C13×M16—21no—
173C13×M16—21no—
174C13×M16C2×Q812yes—
175C13×M16#4112yes—
176C2×C8×C13—21no—
177C2×C8×C13—21no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—21no—
183C13×C4⋊C4—21no—
184C13×C4⋊C4—42no—
185C13×C4⋊C4C22×C411yescharacteristic
186C13×C4⋊C4C22×C411yescharacteristic
187C13×C4⋊C4C22×C411yescharacteristic
188C13×C4⋊C4C22×C411yescharacteristic
189C13×C22⋊C4—21no—
190C13×C22⋊C4—21no—
191C42×C13—21no—
192C42×C13—21no—
193C42×C13—21no—
194C42×C13—21no—
195C42×C13—21no—
196C42×C13—21no—
197C42×C13C22×C411yescharacteristic
198C42×C13C22×C411yescharacteristic
199C42×C13C2×D411yescharacteristic
200C42×C13C2×D411yescharacteristic
201C22⋊Dic13—21no—
202#6103—21no—
203#6103—21no—
204C4⋊Dic13C22×C411yescharacteristic
205C4⋊Dic13C22×C411yescharacteristic
206#6101—21no—
207#6101—21no—
208C4×Dic13—21no—
209C4×Dic13—21no—
210C4×Dic13—21no—
211#6099—21no—
212#6099—21no—
213#6099—21no—
214#6099—21no—
215C2×#1055—21no—
216C2×#1055—21no—
217C2×#1055—21no—
218C2×#1055—21no—
219C2×#1055—21no—
220C2×#1055—21no—
221C2×#1055—21no—
222C2×#1055—21no—
223C2×#1055C22×C411yescharacteristic
224C2×#1055C22×C411yescharacteristic
225C2×#1055C22×C411yescharacteristic
226C2×#1055C22×C411yescharacteristic
227C2×#1055C2×D411yescharacteristic
228C2×#1055C2×D411yescharacteristic
229C2×#1055C2×D411yescharacteristic
230C2×#1055C2×D411yescharacteristic
231C2×#1055C2×Q812yes—
232C2×#1055#4112yes—
233#6094—24no—
234#6094—24no—
235C8×D13—24no—
236C8×D13—24no—
237#3076—131no—
238#2961—131no—
239#2875—131no—
240#1986D1311yescharacteristic, complemented
241#1950—131no—
242#1922—131no—
243#1922—131no—
244#1866—131no—
245#1866—131no—
246#1806—131no—
247#1773—131no—
248#1772—131no—
249#1771—131no—
250#1765—131no—
251#1764—131no—
252C23×C13C2×#4111yescharacteristic
253C22×D13—21no—
254Q8×C13—81no—
255Q8×C13—81no—
256C2×C4×C13—22no—
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—21no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13—41no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—41no—
268C2×C4×C13C4×D411yescharacteristic
269C2×C4×C13C4×D411yescharacteristic
270C2×C4×C13C4×D411yescharacteristic
271C2×C4×C13C4×D411yescharacteristic
272C2×C4×C13C23×C411yescharacteristic
273C2×C4×C13C22×D411yescharacteristic
274C2×C4×C13C22×Q811yescharacteristic
275C2×C4×C13C2×#4111yescharacteristic
276C2×C4×C13C2×#4111yescharacteristic
277C2×C4×C13C2×#4111yescharacteristic
278C22⋊D13—22no—
279C22⋊D13—22no—
280C2×Dic13—21no—
281C2×Dic13—21no—
282C2×Dic13—21no—
283D52—21no—
284D52C4×Q812yes—
285C4×D13—22no—
286C4×D13—22no—
287C4×D13—81no—
288C4×D13—81no—
289Dic26—21no—
290Dic26C4×Q812yes—
291C8×C13—22no—
292C8×C13—22no—
293#1055—21no—
294#1055—21no—
295#1055—21no—
296#1055—21no—
297#1055—21no—
298#1055—21no—
299#1055—41no—
300#1055—41no—
301#1055C22⋊Q812yes—
302#1055C22⋊Q812yes—
303C2×#131—131no—
304C2×#131—131no—
305#533C2×D1311yescharacteristic
306C4×#41—131no—
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#423—131no—
326C2×C4⋊C8—131no—
327C2×#104—131no—
328C2×#104—131no—
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—261no—
338C4×M16C2×D1311yescharacteristic
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#339C2×D1311yescharacteristic
349#339C2×D1311yescharacteristic
350#339C2×D1311yescharacteristic
351#339C2×D1311yescharacteristic
352#336—131no—
353#336—131no—
354C22×C13—21no—
355C22×C13—21no—
356C22×C13C2×C4×D411yescharacteristic
357C22×C13#52911yescharacteristic
358C22×C13#53311yescharacteristic
359C2×D13—22no—
360C2×D13—41no—
361C2×D13—41no—
362C4×C13—21no—
363C4×C13—21no—
364C4×C13—21no—
365C4×C13—21no—
366C4×C13—42no—
367C4×C13—41no—
368C4×C13—41no—
369C4×C13—41no—
370C4×C13—41no—
371C4×C13—81no—
372C4×C13C2×C4×Q811yescharacteristic
373C4×C13C4×#4111yescharacteristic
374C4×C13C2×C22⋊Q811yescharacteristic
375C4×C13#52511yescharacteristic
376Dic13—22no—
377Dic13—41no—
378Dic13—41no—
379C2×#41—131no—
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⋊Q8C4×D1311yescharacteristic
397C4⋊Q8C4×D1311yescharacteristic
398#125C4×D1311yescharacteristic
399#125C4×D1311yescharacteristic
400C22⋊Q8—21no—
401C22⋊Q8—21no—
402C4×Q8—21no—
403C4×Q8—21no—
404C4×Q8—131no—
405C4×Q8—131no—
406C4×D4—131no—
407C4×D4—131no—
408C4×D4—261no—
409C4×D4—261no—
410#117—131no—
411#117—261no—
412#117C22×D1311yescharacteristic
413#117C22×D1311yescharacteristic
414C2×C4⋊C4—21no—
415C2×C42—261no—
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—131no—
430C4⋊C8—131no—
431C4⋊C8—131no—
432C4⋊C8—131no—
433C4⋊C8—261no—
434C4⋊C8—261no—
435C4⋊C8—261no—
436C4⋊C8—261no—
437C4⋊C8—261no—
438C4⋊C8—261no—
439#104—262no—
440#104—262no—
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—21no—
450#97—131no—
451#97—131no—
452#97—131no—
453#97—131no—
454#97—262no—
455#97—261no—
456#97—261no—
457#97—261no—
458#97—261no—
459C4×C8—21no—
460C4×C8—262no—
461C4×C8—261no—
462C4×C8—261no—
463C4×C8—261no—
464C4×C8—261no—
465#95—21no—
466C2×C13—21no—
467C2×C13—21no—
468C2×C13C4×C22⋊Q811yescharacteristic
469C2×C13#295611yescharacteristic
470C2×C13#295711yescharacteristic
471D13—42no—
472#41—132no—
473#41—132no—
474#41—261no—
475#41—261no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—131no—
479C2×D4—131no—
480C2×D4—261no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—261no—
484C22×C4—261no—
485C22×C4—261no—
486C22×C4#612911yescharacteristic
487C22×C4#612911yescharacteristic
488C22×C4C23×D1311yescharacteristic
489M16—21no—
490M16—21no—
491M16—264no—
492M16—264no—
493M16—261no—
494M16—261no—
495M16—261no—
496M16—261no—
497M16Q8×D1312yes—
498M16#613112yes—
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—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—42no—
528C4⋊C4—131no—
529C4⋊C4—131no—
530C4⋊C4—261no—
531C4⋊C4—261no—
532C4⋊C4C2×C4×D1311yescharacteristic
533C4⋊C4C2×C4×D1311yescharacteristic
534C4⋊C4C2×C4×D1311yescharacteristic
535C4⋊C4C2×C4×D1311yescharacteristic
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—261no—
539C22⋊C4—261no—
540C22⋊C4—261no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—261no—
548C42—261no—
549C42—261no—
550C42C2×C4×D1311yescharacteristic
551C42C2×C4×D1311yescharacteristic
552C42D4×D1311yescharacteristic
553C42D4×D1311yescharacteristic
554C13#2162911yescharacteristic, complemented, Sylow
555C23—261no—
556C23C2×#612911yescharacteristic
557Q8—81no—
558Q8—81no—
559Q8—132no—
560Q8—261no—
561D4—132no—
562D4—262no—
563D4—262no—
564D4—261no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—261no—
578C2×C4—262no—
579C2×C4—262no—
580C2×C4—261no—
581C2×C4—261no—
582C2×C4—1041no—
583C2×C4—1041no—
584C2×C4#8813511yescharacteristic
585C2×C4#8813511yescharacteristic
586C2×C4#8813511yescharacteristic
587C2×C4#8813511yescharacteristic
588C2×C4C22×C4×D1311yescharacteristic
589C2×C4C2×D4×D1311yescharacteristic
590C2×C4C2×Q8×D1311yescharacteristic
591C2×C4C2×#613111yescharacteristic
592C2×C4#41×D1311yescharacteristic
593C2×C4#41×D1311yescharacteristic
594C8—22no—
595C8—22no—
596C8—132no—
597C8—132no—
598C8—261no—
599C8—261no—
600C8—261no—
601C8—261no—
602C8—261no—
603C8—261no—
604C8—521no—
605C8—521no—
606C22—21no—
607C22—21no—
608C22—262no—
609C22—521no—
610C22—521no—
611C22C2×#8813511yescharacteristic
612C22#1171938511yescharacteristic
613C22#1171943311yescharacteristic
614C4—21no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—42no—
619C4—41no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—81no—
624C4—262no—
625C4—521no—
626C4—521no—
627C4C4×Q8×D1311yescharacteristic
628C4C4×#613111yescharacteristic
629C4D13×C22⋊Q811yescharacteristic
630C4#1171933211yescharacteristic
631C2—21no—
632C2—21no—
633C2—522no—
634C2#1311737411yescharacteristic
635C2#1312374211yescharacteristic
636C2#1312374911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1986C2
socleC22×C13C2×C4×D4
prime radicalC2×#6127C23
cosocleC22×C4×C13C24
hypercenter#1986D13
hypocenterC13#21629
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1986

Complements

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

NH ≅ G/Ntype
2. #13123777C2semidirect
4. #13115611C2semidirect
5. #13115438C2semidirect
6. #13115438C2semidirect
10. #13114719C2semidirect
11. #13114714C2semidirect
12. #13114711C2semidirect
15. C13×#1986C2semidirect
26. #11718755C4semidirect
27. #11718752C4semidirect
28. #11718748C4semidirect
29. #11718745C4semidirect
30. #11718727C4semidirect
31. #11718727C4semidirect
32. #11718724C4semidirect
33. #11718724C4semidirect
96. #88161Q8semidirect
240. #1986D13semidirect
554. C13#21629semidirect

Maximal subgroups

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

subgroupindex
#131246182
#131237772
#131232652
#131156112
#131154382
#131151122
#131148572
#131147192
#131147142
#131147112
#131146772
#131146702
C13×#19862
#2162913