Finite Group Databasebeta

← #15901359

Subgroups — #15901359

Order 3328.

954 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718706C211yesmaximal, characteristic, complemented
2C2×#11718894C211yesmaximal, characteristic
3#13117727C211yesmaximal, characteristic, complemented
4#13116231C211yesmaximal, characteristic, complemented
5#13116224C211yesmaximal, characteristic, complemented
6#13116079C211yesmaximal, characteristic, complemented
7#13116072C211yesmaximal, characteristic, complemented
8#13115769C211yesmaximal, characteristic, complemented
9#13115760C211yesmaximal, characteristic, complemented
10#13115467C211yesmaximal, characteristic, complemented
11#13115460C211yesmaximal, characteristic, complemented
12#13115260C211yesmaximal, characteristic, complemented
13#13115016C211yesmaximal, characteristic, complemented
14#13114776C211yesmaximal, characteristic
15C13×#2432C211yesmaximal, characteristic
16C22×C13×#41C2211yescharacteristic
17C2×C13×C4⋊Q8C2211yescharacteristic
18C2×C13×#124C2211yescharacteristic
19C2×C13×C22⋊Q8C2211yescharacteristic
20C2×#88180C2211yescharacteristic
21C23×#1055C2211yescharacteristic
22C13×#394—21no—
23C13×#394—21no—
24C13×#391C2211yescharacteristic
25C13×#390C2211yescharacteristic
26C13×#385—21no—
27C13×#385—21no—
28C4×C13×C22⋊C4C2211yescharacteristic
29#11718894—24no—
30C2×#88075C2211yescharacteristic
31C2×#88075C2211yescharacteristic
32C2×#88075C2211yescharacteristic
33C2×#88075C2211yescharacteristic
34C2×#88075C2211yescharacteristic
35C2×#88075C2211yescharacteristic
36C2×#88075C2211yescharacteristic
37C2×#88075C2211yescharacteristic
38C2×#88072C2211yescharacteristic
39C2×#88072C2211yescharacteristic
40C2×#88072C2211yescharacteristic
41C2×#88072C2211yescharacteristic
42#11718873C2211yescharacteristic
43C2×C22⋊#1055C2211yescharacteristic
44#11718706—24no—
45C2×#88048C2211yescharacteristic
46C2×#88047C2211yescharacteristic
47#11718606—21no—
48#11718606—21no—
49C4×C4⋊Dic13C2211yescharacteristic
50C4×C4⋊Dic13C2211yescharacteristic
51#11718589C2211yescharacteristic
52#11718589C2211yescharacteristic
53C2×C4⋊#1055C2211yescharacteristic
54C2×C4⋊#1055C2211yescharacteristic
55#11718312—21no—
56#11718310—21no—
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C2×C13×#41—22no—
62C2×C13×#41—22no—
63C2×C13×#41—22no—
64C2×C13×#41—22no—
65C2×C13×#41—41no—
66C2×C13×#41—41no—
67C22×Q8×C13C2311yescharacteristic
68C22×Q8×C13C2311yescharacteristic
69C22×D4×C13—21no—
70C22×D4×C13C2311yescharacteristic
71C23×C4×C13—21no—
72C23×C4×C13C2311yescharacteristic
73C13×C4⋊Q8—22no—
74C13×C4⋊Q8—41no—
75C13×#124—22no—
76C13×#124—41no—
77C13×C22⋊Q8—22no—
78C13×C22⋊Q8—22no—
79C2×C13×C4⋊C4—21no—
80C2×C13×C4⋊C4—21no—
81C2×C13×C4⋊C4—21no—
82C2×C13×C4⋊C4C2311yescharacteristic
83C2×C13×C22⋊C4—21no—
84C2×C13×C22⋊C4—21no—
85C2×C13×C22⋊C4—21no—
86C2×C13×C22⋊C4—21no—
87C2×C13×C22⋊C4—21no—
88C2×C13×C22⋊C4D411yescharacteristic
89C2×C13×C22⋊C4D411yescharacteristic
90C2×C42×C13C2311yescharacteristic
91C2×C42×C13C2311yescharacteristic
92C2×C22⋊Dic13—21no—
93C2×C22⋊Dic13—21no—
94#88180—22no—
95#88180D414yes—
96C2×C4⋊Dic13C2311yescharacteristic
97C2×C4⋊Dic13C2311yescharacteristic
98C2×C4⋊Dic13C2311yescharacteristic
99C2×C4⋊Dic13C2311yescharacteristic
100C2×#6101—21no—
101C2×#6101—21no—
102C2×C4×Dic13—21no—
103C2×C4×Dic13—21no—
104C2×C4×Dic13—21no—
105C22×#1055—22no—
106C22×#1055—41no—
107C22×#1055—41no—
108C22×#1055C2311yescharacteristic
109C22×#1055C2311yescharacteristic
110C22×#1055C2311yescharacteristic
111C22×#1055C2311yescharacteristic
112C13×#95—21no—
113C13×#95—21no—
114C13×#95D411yescharacteristic
115C13×#95D411yescharacteristic
116#88075—22no—
117#88075—22no—
118#88075—22no—
119#88075—22no—
120#88075—22no—
121#88075—41no—
122#88075—41no—
123#88075—41no—
124#88072—22no—
125#88072—22no—
126#88072—22no—
127#88072—41no—
128#88071—21no—
129#88071—21no—
130#88071—21no—
131#88071—21no—
132#88071—21no—
133C22⋊#1055—22no—
134#88048—22no—
135#88047—22no—
136C4⋊#1055—41no—
137C4⋊#1055—41no—
138#24485—131nomaximal, Sylow
139C24×C13—21no—
140C24×C13C2×D411yescharacteristic
141C13×#41—28no—
142C13×#41—44no—
143C13×#41—44no—
144C13×#41—44no—
145C2×Q8×C13—21no—
146C2×Q8×C13—21no—
147C2×Q8×C13—21no—
148C2×Q8×C13—21no—
149C2×Q8×C13—21no—
150C2×Q8×C13—21no—
151C2×Q8×C13—21no—
152C2×Q8×C13—21no—
153C2×Q8×C13—21no—
154C2×Q8×C13—21no—
155C2×Q8×C13—21no—
156C2×Q8×C13#4112yes—
157C2×D4×C13—21no—
158C2×D4×C13—21no—
159C2×D4×C13—21no—
160C2×D4×C13—21no—
161C2×D4×C13—21no—
162C2×D4×C13—42no—
163C2×D4×C13—42no—
164C2×D4×C13—42no—
165C2×D4×C13#4112yes—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13—42no—
174C22×C4×C13—42no—
175C22×C4×C13—42no—
176C22×C4×C13C2×D412yes—
177C22×C4×C13C2×D411yescharacteristic
178C22×C4×C13C2×D411yescharacteristic
179C22×C4×C13C2×D411yescharacteristic
180C22×C4×C13C2×D411yescharacteristic
181C22×C4×C13C2×D411yescharacteristic
182C22×C4×C13#4112yes—
183C22×C4×C13C2411yescharacteristic
184C22×Dic13—21no—
185C22×Dic13—21no—
186C22×Dic13—21no—
187C22×Dic13—21no—
188C13×C4⋊C4—21no—
189C13×C4⋊C4—21no—
190C13×C4⋊C4—42no—
191C13×C4⋊C4—42no—
192C13×C4⋊C4—42no—
193C13×C22⋊C4—22no—
194C13×C22⋊C4—41no—
195C13×C22⋊C4—42no—
196C13×C22⋊C4—42no—
197C13×C22⋊C4—42no—
198C13×C22⋊C4—42no—
199C13×C22⋊C4—42no—
200C42×C13—21no—
201C42×C13—21no—
202C42×C13—21no—
203C42×C13—21no—
204C22⋊Dic13—24no—
205C22⋊Dic13—81no—
206C4⋊Dic13—21no—
207C4⋊Dic13—21no—
208C4⋊Dic13—21no—
209C4⋊Dic13—21no—
210C4⋊Dic13—21no—
211C4⋊Dic13—21no—
212C4⋊Dic13C2×D412yes—
213C4⋊Dic13C2×D412yes—
214#6101—42no—
215#6101—42no—
216C4×Dic13—24no—
217C4×Dic13—81no—
218C4×Dic13—81no—
219C2×#1055—21no—
220C2×#1055—21no—
221C2×#1055—21no—
222C2×#1055—21no—
223C2×#1055—21no—
224C2×#1055—21no—
225C2×#1055—21no—
226C2×#1055—21no—
227C2×#1055—21no—
228C2×#1055—21no—
229C2×#1055—21no—
230C2×#1055—21no—
231C2×#1055—44no—
232C2×#485—131no—
233C2×#416—131no—
234#2432D1311yescharacteristic
235#2347—131no—
236#2068—131no—
237#2067—131no—
238#2043—131no—
239#2042—131no—
240#1983—131no—
241#1981—131no—
242#1927—131no—
243#1926—131no—
244#1892—131no—
245#1850—131no—
246#1788—131no—
247C23×C13—21no—
248C23×C13—21no—
249C23×C13—21no—
250C23×C13—21no—
251C23×C13—21no—
252C23×C13—21no—
253C23×C13—22no—
254C23×C13—41no—
255C23×C13—41no—
256C23×C13—41no—
257C23×C13—41no—
258C23×C13—41no—
259C23×C13—41no—
260C23×C13#12112yes—
261C23×C13C22×D411yescharacteristic
262Q8×C13—22no—
263Q8×C13—22no—
264Q8×C13—41no—
265Q8×C13—41no—
266Q8×C13—41no—
267Q8×C13—41no—
268Q8×C13—41no—
269Q8×C13—41no—
270D4×C13—22no—
271D4×C13—22no—
272D4×C13—48no—
273D4×C13—41no—
274D4×C13—41no—
275C2×C4×C13—21no—
276C2×C4×C13—21no—
277C2×C4×C13—21no—
278C2×C4×C13—21no—
279C2×C4×C13—22no—
280C2×C4×C13—22no—
281C2×C4×C13—22no—
282C2×C4×C13—22no—
283C2×C4×C13—21no—
284C2×C4×C13—21no—
285C2×C4×C13—21no—
286C2×C4×C13—22no—
287C2×C4×C13—21no—
288C2×C4×C13—21no—
289C2×C4×C13—21no—
290C2×C4×C13—21no—
291C2×C4×C13—21no—
292C2×C4×C13—21no—
293C2×C4×C13—48no—
294C2×C4×C13—41no—
295C2×C4×C13—41no—
296C2×C4×C13—41no—
297C2×C4×C13—41no—
298C2×C4×C13—41no—
299C2×C4×C13—41no—
300C2×C4×C13—41no—
301C2×C4×C13—41no—
302C2×C4×C13#12112yes—
303C2×C4×C13#13512yes—
304C2×C4×C13C22×D411yescharacteristic
305C2×C4×C13C2×#4111yescharacteristic
306C2×C4×C13C2×#4111yescharacteristic
307C2×C4×C13C2×#4111yescharacteristic
308C2×C4×C13H(5,𝔽2)11yescharacteristic
309C2×C4×C13H(5,𝔽2)11yescharacteristic
310C2×Dic13—22no—
311C2×Dic13—22no—
312C2×Dic13—41no—
313C2×Dic13—41no—
314C2×Dic13—41no—
315C2×Dic13—41no—
316C2×Dic13—41no—
317C2×Dic13—41no—
318C2×Dic13—41no—
319C2×Dic13—41no—
320C2×Dic13—41no—
321C2×Dic13—41no—
322#1055—41no—
323#1055—41no—
324#1055—41no—
325#1055—41no—
326C22×#41C2×D1311yescharacteristic
327C23×C8—131no—
328C2×C4⋊Q8C2×D1311yescharacteristic
329C2×#124C2×D1311yescharacteristic
330C2×C22⋊Q8C2×D1311yescharacteristic
331C2×#117—131no—
332#485—264no—
333C2×#107—131no—
334C2×#106—131no—
335C2×C4⋊C8—131no—
336C2×C4⋊C8—131no—
337#416—264no—
338C2×#103—131no—
339C2×#103—131no—
340C2×#103—131no—
341C2×#103—131no—
342C2×#103—131no—
343C2×#103—131no—
344C2×#103—131no—
345C2×#103—131no—
346C2×#102—131no—
347C2×#102—131no—
348C2×#102—131no—
349C2×#102—131no—
350C2×C22⋊C8—131no—
351#394—21no—
352#394—21no—
353#391C2×D1311yescharacteristic
354#390C2×D1311yescharacteristic
355#389—131no—
356#389—131no—
357#388—261no—
358#388—261no—
359#385—21no—
360#385—21no—
361#383—261no—
362#380—131no—
363C4×C4⋊C4—131no—
364C4×C4⋊C4—131no—
365C4×C4⋊C4—261no—
366C4×C22⋊C4C2×D1311yescharacteristic
367#340—131no—
368#340—131no—
369#336—131no—
370#336—131no—
371C22×C13—22no—
372C22×C13—22no—
373C22×C13—22no—
374C22×C13—41no—
375C22×C13—41no—
376C22×C13—41no—
377C22×C13—41no—
378C22×C13—42no—
379C22×C13—42no—
380C22×C13—42no—
381C22×C13—81no—
382C22×C13—81no—
383C22×C13—81no—
384C22×C13—81no—
385C22×C13C2×#12111yescharacteristic
386C22×C13#54611yescharacteristic
387C22×C13#54611yescharacteristic
388C22×C13C2×#13511yescharacteristic
389C22×C13#57511yescharacteristic
390C22×C13#57711yescharacteristic
391C22×C13#57811yescharacteristic
392C4×C13—22no—
393C4×C13—22no—
394C4×C13—42no—
395C4×C13—41no—
396C4×C13—41no—
397C4×C13—41no—
398C4×C13—81no—
399C4×C13—81no—
400C4×C13#52511yescharacteristic
401C4×C13#53511yescharacteristic
402C4×C13#55111yescharacteristic
403C4×C13#55111yescharacteristic
404Dic13—42no—
405Dic13—42no—
406Dic13—81no—
407Dic13—81no—
408C2×#41—22no—
409C2×#41—22no—
410C2×#41—22no—
411C2×#41—22no—
412C2×#41—41no—
413C2×#41—41no—
414C22×Q8C22×D1311yescharacteristic
415C22×Q8C22×D1311yescharacteristic
416C22×D4—21no—
417C22×D4C22×D1311yescharacteristic
418C23×C4—21no—
419C23×C4C22×D1311yescharacteristic
420C22×C8—131no—
421C22×C8—131no—
422C22×C8—131no—
423C22×C8—131no—
424C22×C8—262no—
425C22×C8—521no—
426C22×C8—521no—
427C4⋊Q8—22no—
428C4⋊Q8—41no—
429#124—22no—
430#124—41no—
431C22⋊Q8—22no—
432C22⋊Q8—22no—
433#117—134no—
434#117—262no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—131no—
439C2×C4⋊C4—131no—
440C2×C4⋊C4—131no—
441C2×C4⋊C4—131no—
442C2×C4⋊C4—261no—
443C2×C4⋊C4—261no—
444C2×C4⋊C4C22×D1311yescharacteristic
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—261no—
451C2×C22⋊C4—261no—
452C2×C22⋊C4C22⋊D1311yescharacteristic
453C2×C22⋊C4C22⋊D1311yescharacteristic
454C2×C42—261no—
455C2×C42—261no—
456C2×C42—261no—
457C2×C42C22×D1311yescharacteristic
458C2×C42C22×D1311yescharacteristic
459#107—262no—
460#106—262no—
461C4⋊C8—521no—
462C4⋊C8—521no—
463#103—262no—
464#103—262no—
465#103—262no—
466#103—262no—
467#103—262no—
468#103—521no—
469#103—521no—
470#103—521no—
471#102—262no—
472#102—262no—
473#102—262no—
474#102—521no—
475C22⋊C8—262no—
476#95—21no—
477#95—21no—
478#95—261no—
479#95—261no—
480#95—261no—
481#95—261no—
482#95—261no—
483#95C22⋊D1311yescharacteristic
484#95C22⋊D1311yescharacteristic
485C2×C13—42no—
486C2×C13—82no—
487C2×C13#241111yescharacteristic
488C2×C13#303511yescharacteristic
489C2×C13#304611yescharacteristic
490C2×C13#330111yescharacteristic
491C2×C13#330211yescharacteristic
492C2×C13#330711yescharacteristic
493C2×C13#331311yescharacteristic
494C24—21no—
495C24C2×C22⋊D1311yescharacteristic
496#41—28no—
497#41—44no—
498#41—44no—
499#41—44no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8#612912yes—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—42no—
518C2×D4—42no—
519C2×D4—42no—
520C2×D4#612912yes—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—261no—
532C22×C4—261no—
533C22×C4—261no—
534C22×C4—261no—
535C22×C4D4×D1312yes—
536C22×C4#612912yes—
537C22×C4C2×C22⋊D1311yescharacteristic
538C22×C4C2×C22⋊D1311yescharacteristic
539C22×C4C2×C22⋊D1311yescharacteristic
540C22×C4C2×C22⋊D1311yescharacteristic
541C22×C4C2×C22⋊D1311yescharacteristic
542C22×C4C23×D1311yescharacteristic
543C2×C8—261no—
544C2×C8—261no—
545C2×C8—261no—
546C2×C8—261no—
547C2×C8—261no—
548C2×C8—261no—
549C2×C8—261no—
550C2×C8—261no—
551C2×C8—261no—
552C2×C8—261no—
553C2×C8—261no—
554C2×C8—261no—
555C2×C8—524no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—42no—
559C4⋊C4—42no—
560C4⋊C4—42no—
561C4⋊C4—132no—
562C4⋊C4—132no—
563C4⋊C4—261no—
564C4⋊C4—261no—
565C4⋊C4—261no—
566C4⋊C4—261no—
567C4⋊C4—261no—
568C4⋊C4—261no—
569C4⋊C4—522no—
570C4⋊C4—522no—
571C22⋊C4—22no—
572C22⋊C4—41no—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C22⋊C4—42no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—264no—
579C22⋊C4—1041no—
580C42—21no—
581C42—21no—
582C42—21no—
583C42—21no—
584C42—264no—
585C42—1041no—
586C42—1041no—
587C13#2448511yescharacteristic, complemented, Sylow
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—22no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23#8819212yes—
602C23C22×C22⋊D1311yescharacteristic
603Q8—22no—
604Q8—22no—
605Q8—41no—
606Q8—41no—
607Q8—41no—
608Q8—41no—
609Q8—41no—
610Q8—41no—
611D4—22no—
612D4—22no—
613D4—48no—
614D4—41no—
615D4—41no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—48no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—262no—
644C2×C4—262no—
645C2×C4—521no—
646C2×C4—521no—
647C2×C4—521no—
648C2×C4—521no—
649C2×C4—521no—
650C2×C4—521no—
651C2×C4—521no—
652C2×C4—521no—
653C2×C4—521no—
654C2×C4—521no—
655C2×C4#8819212yes—
656C2×C4#8820412yes—
657C2×C4C2×D4×D1311yescharacteristic
658C2×C4C2×#612911yescharacteristic
659C2×C4C2×#612911yescharacteristic
660C2×C4C2×#612911yescharacteristic
661C2×C4#8825111yescharacteristic
662C2×C4#8825111yescharacteristic
663C8—521no—
664C8—521no—
665C8—521no—
666C8—521no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22C2×#8819211yescharacteristic
682C22#1171951111yescharacteristic
683C22#1171951111yescharacteristic
684C22C2×#8820411yescharacteristic
685C22#1171952711yescharacteristic
686C22#1171954211yescharacteristic
687C22#1171954311yescharacteristic
688C4—22no—
689C4—22no—
690C4—42no—
691C4—41no—
692C4—41no—
693C4—41no—
694C4—81no—
695C4—81no—
696C4—522no—
697C4—522no—
698C4—1041no—
699C4—1041no—
700C4#1171929111yescharacteristic
701C4#1171929211yescharacteristic
702C4#1171929211yescharacteristic
703C4#1171929711yescharacteristic
704C2—42no—
705C2—82no—
706C2#1311821711yescharacteristic
707C2#1312428511yescharacteristic
708C2#1312438211yescharacteristic
709C2#1312673811yescharacteristic
710C2#1312675311yescharacteristic
711C2#1312681211yescharacteristic
712C2#1312690211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2432C2
socleC23×C13C22×D4
prime radicalC22×C13×#41C22
hypercenter#2432D13
hypocenterC13#24485
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2432

Complements

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

NH ≅ G/Ntype
1. C2×#11718706C2semidirect
3. #13117727C2semidirect
4. #13116231C2semidirect
5. #13116224C2semidirect
6. #13116079C2semidirect
7. #13116072C2semidirect
8. #13115769C2semidirect
9. #13115760C2semidirect
10. #13115467C2semidirect
11. #13115460C2semidirect
12. #13115260C2semidirect
13. #13115016C2semidirect
587. C13#24485semidirect

Maximal subgroups

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

subgroupindex
C2×#117187062
C2×#117188942
#131177272
#131162312
#131162242
#131160792
#131160722
#131157692
#131157602
#131154672
#131154602
#131152602
#131150162
#131147762
C13×#24322
#2448513