Finite Group Databasebeta

← #15912371

Subgroups — #15912371

Order 3328.

792 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718743C211yesmaximal, characteristic, complemented
2C2×#11718670C211yesmaximal, characteristic
3#13117930C211yesmaximal, characteristic, complemented
4#13116231C211yesmaximal, characteristic, complemented
5#13116217C211yesmaximal, characteristic, complemented
6#13116072C211yesmaximal, characteristic
7#13116072C211yesmaximal, characteristic
8#13115769C211yesmaximal, characteristic
9#13115769C211yesmaximal, characteristic
10#13115760C211yesmaximal, characteristic, complemented
11#13115560C211yesmaximal, characteristic, complemented
12#13115474C211yesmaximal, characteristic, complemented
13#13115467C211yesmaximal, characteristic, complemented
14#13114661C211yesmaximal, characteristic
15C13×#2547C211yesmaximal, characteristic
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C13×#124C2211yescharacteristic
18C2×C13×#124C2211yescharacteristic
19C2×C4×D4×C13C2211yescharacteristic
20C2×#88124C2211yescharacteristic
21C13×#397—21no—
22C13×#397—21no—
23C13×#391C2211yescharacteristic
24C13×#391C2211yescharacteristic
25C13×#380—21no—
26C13×#380—21no—
27C4×C13×C4⋊C4C2211yescharacteristic
28C2×#88075C2211yescharacteristic
29C2×#88075C2211yescharacteristic
30C2×#88075C2211yescharacteristic
31C2×#88075C2211yescharacteristic
32C2×#88075C2211yescharacteristic
33C2×#88075C2211yescharacteristic
34C2×#88075C2211yescharacteristic
35C2×#88075C2211yescharacteristic
36C2×#88072C2211yescharacteristic
37C2×#88072C2211yescharacteristic
38C2×#88072C2211yescharacteristic
39C2×#88072C2211yescharacteristic
40#11718743—24no—
41#11718670—24no—
42#11718639—21no—
43#11718633—21no—
44C2×#88048C2211yescharacteristic
45C2×#88047C2211yescharacteristic
46C4×C4⋊Dic13C2211yescharacteristic
47C4×C4⋊Dic13C2211yescharacteristic
48C4×C4⋊Dic13C2211yescharacteristic
49#11718589C2211yescharacteristic
50#11718589C2211yescharacteristic
51C2×C4⋊#1055C2211yescharacteristic
52C2×C4⋊#1055C2211yescharacteristic
53C2×C4⋊#1055C2211yescharacteristic
54C2×#88043C2211yescharacteristic
55#11718313—21no—
56#11718310—21no—
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C22×Q8×C13C2311yescharacteristic
62C22×Q8×C13C2311yescharacteristic
63C22×D4×C13C2311yescharacteristic
64C23×C4×C13—21no—
65C13×C4⋊Q8—22no—
66C13×C4⋊Q8—22no—
67C13×#124—22no—
68C13×#124—22no—
69C13×#124—41no—
70C13×#124—41no—
71C4×D4×C13—22no—
72C4×D4×C13—22no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4D411yescharacteristic
76C2×C13×C4⋊C4D411yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C22⋊C4—21no—
79C2×C13×C22⋊C4—21no—
80C2×C13×C22⋊C4—21no—
81C2×C13×C22⋊C4—21no—
82C2×C13×C22⋊C4—21no—
83C2×C42×C13C2311yescharacteristic
84C2×C42×C13C2311yescharacteristic
85C2×C42×C13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×#6101—21no—
91C2×#6101—21no—
92C2×#6101—21no—
93C2×#6101—21no—
94C2×C4×Dic13—21no—
95C2×C4×Dic13—21no—
96C2×C4×Dic13—21no—
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99C22×#1055C2311yescharacteristic
100C22×#1055C2311yescharacteristic
101#88124—22no—
102#88124D414yes—
103C13×#95—21no—
104C13×#95—21no—
105C13×#95—21no—
106C13×#95—21no—
107C13×#95D411yescharacteristic
108C13×#95D411yescharacteristic
109#88075—22no—
110#88075—22no—
111#88075—22no—
112#88075—22no—
113#88075—22no—
114#88075—22no—
115#88075—41no—
116#88075—41no—
117#88072—22no—
118#88072—22no—
119#88072—22no—
120#88072—22no—
121#88071—21no—
122#88071—21no—
123#88071—21no—
124#88071—21no—
125#88071—21no—
126#88048—22no—
127#88047—22no—
128C4⋊#1055—22no—
129C4⋊#1055—41no—
130C4⋊#1055—41no—
131#88043—22no—
132#25289—131nomaximal, Sylow
133C24×C13—21no—
134C2×Q8×C13—21no—
135C2×Q8×C13—21no—
136C2×Q8×C13—21no—
137C2×Q8×C13—21no—
138C2×Q8×C13—21no—
139C2×Q8×C13—21no—
140C2×Q8×C13—21no—
141C2×Q8×C13—21no—
142C2×Q8×C13—21no—
143C2×Q8×C13—21no—
144C2×Q8×C13—21no—
145C2×Q8×C13—21no—
146C2×D4×C13—21no—
147C2×D4×C13—21no—
148C2×D4×C13—21no—
149C2×D4×C13—21no—
150C2×D4×C13—21no—
151C2×D4×C13#4112yes—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—42no—
156C22×C4×C13—42no—
157C22×C4×C13—42no—
158C22×C4×C13C2×D411yescharacteristic
159C22×C4×C13C2×D411yescharacteristic
160C22×C4×C13C2×D411yescharacteristic
161C22×C4×C13C2×D411yescharacteristic
162C22×C4×C13C2×D411yescharacteristic
163C22×C4×C13C2×D411yescharacteristic
164C22×C4×C13C2411yescharacteristic
165C22×Dic13—21no—
166C22×Dic13—21no—
167C22×Dic13—21no—
168C22×Dic13—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—41no—
172C13×C4⋊C4—41no—
173C13×C4⋊C4—42no—
174C13×C4⋊C4—42no—
175C13×C22⋊C4—42no—
176C13×C22⋊C4—42no—
177C13×C22⋊C4—42no—
178C13×C22⋊C4—42no—
179C13×C22⋊C4—42no—
180C42×C13—21no—
181C42×C13—21no—
182C42×C13—21no—
183C42×C13—21no—
184C42×C13C2×D412yes—
185C42×C13#4112yes—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13C2×D412yes—
192C4⋊Dic13C2×D412yes—
193C4⋊Dic13#4112yes—
194#6101—24no—
195#6101—24no—
196#6101—42no—
197#6101—81no—
198C4×Dic13—42no—
199C4×Dic13—81no—
200C4×Dic13—81no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—21no—
209C2×#1055—21no—
210C2×#1055—21no—
211C2×#1055—21no—
212C2×#1055—21no—
213C2×#491—131no—
214C2×#478—131no—
215#2547D1311yescharacteristic
216#2370—131no—
217#2068—131no—
218#2066—131no—
219#2042—131no—
220#2042—131no—
221#1983—131no—
222#1983—131no—
223#1981—131no—
224#1940—131no—
225#1928—131no—
226#1927—131no—
227#1762—131no—
228C23×C13—22no—
229C23×C13—41no—
230C23×C13—41no—
231C23×C13—41no—
232C23×C13—41no—
233C23×C13—41no—
234C23×C13—41no—
235C23×C13C22×D411yescharacteristic
236Q8×C13—41no—
237Q8×C13—41no—
238Q8×C13—41no—
239Q8×C13—41no—
240Q8×C13—41no—
241Q8×C13—41no—
242Q8×C13—41no—
243Q8×C13—41no—
244D4×C13—22no—
245D4×C13—22no—
246D4×C13—41no—
247D4×C13—41no—
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—21no—
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—21no—
261C2×C4×C13—21no—
262C2×C4×C13—21no—
263C2×C4×C13—21no—
264C2×C4×C13—41no—
265C2×C4×C13—41no—
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—84no—
274C2×C4×C13#12112yes—
275C2×C4×C13#12112yes—
276C2×C4×C13C22×D411yescharacteristic
277C2×C4×C13C2×#4111yescharacteristic
278C2×C4×C13C2×#4111yescharacteristic
279C2×C4×C13C2×#4111yescharacteristic
280C2×C4×C13H(5,𝔽2)11yescharacteristic
281C2×C4×C132−1+411yescharacteristic
282C2×Dic13—22no—
283C2×Dic13—22no—
284C2×Dic13—22no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291C2×Dic13—41no—
292C2×Dic13—41no—
293C2×Dic13—41no—
294#1055—41no—
295#1055—41no—
296#1055—41no—
297#1055—41no—
298C2×C4⋊Q8C2×D1311yescharacteristic
299C2×#125—131no—
300C2×#124C2×D1311yescharacteristic
301C2×#124C2×D1311yescharacteristic
302C2×C4×D4C2×D1311yescharacteristic
303#491—264no—
304#478—264no—
305C2×#107—131no—
306C2×#106—131no—
307C2×C4⋊C8—131no—
308C2×C4⋊C8—131no—
309C2×C4⋊C8—131no—
310C2×#103—131no—
311C2×#103—131no—
312C2×#103—131no—
313C2×#103—131no—
314C2×#103—131no—
315C2×#103—131no—
316C2×#103—131no—
317C2×#103—131no—
318C2×#102—131no—
319C2×#102—131no—
320C2×#102—131no—
321C2×#102—131no—
322C2×#97—131no—
323#397—21no—
324#397—21no—
325#391C2×D1311yescharacteristic
326#391C2×D1311yescharacteristic
327#389—131no—
328#389—131no—
329#389—261no—
330#387—261no—
331#387—261no—
332#380—21no—
333#380—21no—
334C4×C4⋊C4—131no—
335C4×C4⋊C4—131no—
336C4×C4⋊C4—131no—
337C4×C4⋊C4—261no—
338C4×C4⋊C4C2×D1311yescharacteristic
339#340—131no—
340#340—131no—
341#336—131no—
342#336—131no—
343C22×C13—42no—
344C22×C13—42no—
345C22×C13—42no—
346C22×C13—81no—
347C22×C13—81no—
348C22×C13—81no—
349C22×C13—81no—
350C22×C13C2×#12111yescharacteristic
351C22×C13#54611yescharacteristic
352C22×C13#54811yescharacteristic
353C22×C13#57511yescharacteristic
354C22×C13#57511yescharacteristic
355C22×C13#57711yescharacteristic
356C22×C13#57811yescharacteristic
357C4×C13—22no—
358C4×C13—22no—
359C4×C13—41no—
360C4×C13—41no—
361C4×C13—41no—
362C4×C13—41no—
363C4×C13—81no—
364C4×C13—81no—
365C4×C13—81no—
366C4×C13#52911yescharacteristic
367C4×C13#54211yescharacteristic
368C4×C13#54811yescharacteristic
369C4×C13#55011yescharacteristic
370Dic13—42no—
371Dic13—42no—
372Dic13—42no—
373Dic13—81no—
374C22×Q8C22×D1311yescharacteristic
375C22×Q8C22×D1311yescharacteristic
376C22×D4C22×D1311yescharacteristic
377C23×C4—21no—
378C22×C8—131no—
379C22×C8—131no—
380C22×C8—131no—
381C22×C8—131no—
382C4⋊Q8—22no—
383C4⋊Q8—22no—
384#125—134no—
385#125—262no—
386#124—22no—
387#124—22no—
388#124—41no—
389#124—41no—
390C4×D4—22no—
391C4×D4—22no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—131no—
395C2×C4⋊C4—131no—
396C2×C4⋊C4—131no—
397C2×C4⋊C4—131no—
398C2×C4⋊C4—261no—
399C2×C4⋊C4—261no—
400C2×C4⋊C4—261no—
401C2×C4⋊C4—261no—
402C2×C4⋊C4C22⋊D1311yescharacteristic
403C2×C4⋊C4C22⋊D1311yescharacteristic
404C2×C4⋊C4C22×D1311yescharacteristic
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C42—261no—
411C2×C42—261no—
412C2×C42—261no—
413C2×C42C22×D1311yescharacteristic
414C2×C42C22×D1311yescharacteristic
415C2×C42C22×D1311yescharacteristic
416#107—262no—
417#106—262no—
418C4⋊C8—262no—
419C4⋊C8—521no—
420C4⋊C8—521no—
421#103—262no—
422#103—262no—
423#103—262no—
424#103—262no—
425#103—262no—
426#103—262no—
427#103—521no—
428#103—521no—
429#102—262no—
430#102—262no—
431#102—262no—
432#102—262no—
433#97—262no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—261no—
439#95—261no—
440#95—261no—
441#95—261no—
442#95—261no—
443#95C22⋊D1311yescharacteristic
444#95C22⋊D1311yescharacteristic
445C2×C13—82no—
446C2×C13#242611yescharacteristic
447C2×C13#304011yescharacteristic
448C2×C13#304611yescharacteristic
449C2×C13#330711yescharacteristic
450C2×C13#331511yescharacteristic
451C2×C13#337611yescharacteristic
452C2×C13#337711yescharacteristic
453C24—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4#612912yes—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—261no—
479C22×C4—261no—
480C22×C4—261no—
481C22×C4—261no—
482C22×C4C2×C22⋊D1311yescharacteristic
483C22×C4C2×C22⋊D1311yescharacteristic
484C22×C4C2×C22⋊D1311yescharacteristic
485C22×C4C2×C22⋊D1311yescharacteristic
486C22×C4C2×C22⋊D1311yescharacteristic
487C22×C4C2×C22⋊D1311yescharacteristic
488C22×C4C23×D1311yescharacteristic
489C2×C8—261no—
490C2×C8—261no—
491C2×C8—261no—
492C2×C8—261no—
493C2×C8—261no—
494C2×C8—261no—
495C2×C8—261no—
496C2×C8—261no—
497C2×C8—261no—
498C2×C8—261no—
499C2×C8—261no—
500C2×C8—261no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—41no—
504C4⋊C4—41no—
505C4⋊C4—42no—
506C4⋊C4—42no—
507C4⋊C4—132no—
508C4⋊C4—132no—
509C4⋊C4—132no—
510C4⋊C4—264no—
511C4⋊C4—264no—
512C4⋊C4—261no—
513C4⋊C4—261no—
514C4⋊C4—261no—
515C4⋊C4—261no—
516C4⋊C4—261no—
517C4⋊C4—522no—
518C4⋊C4—1041no—
519C22⋊C4—42no—
520C22⋊C4—42no—
521C22⋊C4—42no—
522C22⋊C4—42no—
523C22⋊C4—42no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—522no—
529C42—1041no—
530C42—1041no—
531C42D4×D1312yes—
532C42#612912yes—
533C13#2528911yescharacteristic, complemented, Sylow
534C23—22no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23C22×C22⋊D1311yescharacteristic
542Q8—41no—
543Q8—41no—
544Q8—41no—
545Q8—41no—
546Q8—41no—
547Q8—41no—
548Q8—41no—
549Q8—41no—
550D4—22no—
551D4—22no—
552D4—41no—
553D4—41no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
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—41no—
578C2×C4—41no—
579C2×C4—84no—
580C2×C4—262no—
581C2×C4—262no—
582C2×C4—262no—
583C2×C4—521no—
584C2×C4—521no—
585C2×C4—521no—
586C2×C4—521no—
587C2×C4—521no—
588C2×C4—521no—
589C2×C4—521no—
590C2×C4—521no—
591C2×C4—521no—
592C2×C4#8819212yes—
593C2×C4#8819212yes—
594C2×C4C2×D4×D1311yescharacteristic
595C2×C4C2×#612911yescharacteristic
596C2×C4C2×#612911yescharacteristic
597C2×C4#8825111yescharacteristic
598C2×C4#41×D1311yescharacteristic
599C2×C4#8825711yescharacteristic
600C8—521no—
601C8—521no—
602C8—521no—
603C8—521no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22C2×#8819211yescharacteristic
612C22#1171951111yescharacteristic
613C22#1171952711yescharacteristic
614C22#1171952711yescharacteristic
615C22#1171953611yescharacteristic
616C22#1171954211yescharacteristic
617C22#1171954311yescharacteristic
618C4—22no—
619C4—22no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—41no—
624C4—81no—
625C4—81no—
626C4—81no—
627C4—522no—
628C4—522no—
629C4—522no—
630C4—1041no—
631C4#1171930311yescharacteristic
632C4#1171930411yescharacteristic
633C4#1171930511yescharacteristic
634C4#1171930811yescharacteristic
635C2—82no—
636C2#1311839811yescharacteristic
637C2#1312432611yescharacteristic
638C2#1312438211yescharacteristic
639C2#1312681211yescharacteristic
640C2#1312693211yescharacteristic
641C2#1312765711yescharacteristic
642C2#1312767211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2547C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
hypercenter#2547D13
hypocenterC13#25289
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2547

Complements

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

NH ≅ G/Ntype
1. C2×#11718743C2semidirect
3. #13117930C2semidirect
4. #13116231C2semidirect
5. #13116217C2semidirect
10. #13115760C2semidirect
11. #13115560C2semidirect
12. #13115474C2semidirect
13. #13115467C2semidirect
533. C13#25289semidirect

Maximal subgroups

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

subgroupindex
C2×#117187432
C2×#117186702
#131179302
#131162312
#131162172
#131160722
#131157692
#131157602
#131155602
#131154742
#131154672
#131146612
C13×#25472
#2528913