Finite Group Databasebeta

← #15920066

Subgroups — #15920066

Order 3328.

986 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718670C211yesmaximal, characteristic, complemented
2C2×#11718894C211yesmaximal, characteristic
3#13118549C211yesmaximal, characteristic, complemented
4#13116374C211yesmaximal, characteristic, complemented
5#13116231C211yesmaximal, characteristic, complemented
6#13116217C211yesmaximal, characteristic, complemented
7#13115987C211yesmaximal, characteristic, complemented
8#13115083C211yesmaximal, characteristic, complemented
9#13115083C211yesmaximal, characteristic, complemented
10#13115033C211yesmaximal, characteristic, complemented
11#13115016C211yesmaximal, characteristic, complemented
12#13114863C211yesmaximal, characteristic, complemented
13#13114836C211yesmaximal, characteristic, complemented
14#13114776C211yesmaximal, characteristic
15C13×#2339C211yesmaximal, characteristic
16C22×C13×#41C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×C4×D4×C13C2211yescharacteristic
19C2×#88180C2211yescharacteristic
20C23×#1055C2211yescharacteristic
21C2×#88124C2211yescharacteristic
22C13×#391C2211yescharacteristic
23C13×#391C2211yescharacteristic
24C13×#386—21no—
25C13×#386—21no—
26C13×#381—21no—
27C13×#380C2211yescharacteristic
28C4×C13×C22⋊C4C2211yescharacteristic
29C2×C13×#95—21no—
30#11718894—24no—
31C2×#88075C2211yescharacteristic
32C2×#88075C2211yescharacteristic
33C2×#88075C2211yescharacteristic
34C2×#88075C2211yescharacteristic
35C2×#88072C2211yescharacteristic
36C2×#88072C2211yescharacteristic
37C2×#88072C2211yescharacteristic
38C2×#88072C2211yescharacteristic
39#11718873C2211yescharacteristic
40C2×C22⋊#1055C2211yescharacteristic
41#11718670—24no—
42C2×#88048C2211yescharacteristic
43C2×#88047C2211yescharacteristic
44C2×#88047C2211yescharacteristic
45C2×#88047C2211yescharacteristic
46#11718610—21no—
47#11718609—21no—
48#11718596C2211yescharacteristic
49#11718589C2211yescharacteristic
50#11718589C2211yescharacteristic
51C2×C4⋊#1055C2211yescharacteristic
52C2×C4⋊#1055C2211yescharacteristic
53#11718315—21no—
54#11718308—21no—
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C2×C13×#41—22no—
62C2×C13×#41—22no—
63C2×C13×#41—22no—
64C2×C13×#41—41no—
65C2×C13×#41—41no—
66C2×C13×#41Q814yes—
67C22×Q8×C13C2311yescharacteristic
68C22×D4×C13—21no—
69C22×D4×C13C2311yescharacteristic
70C23×C4×C13—21no—
71C23×C4×C13—21no—
72C23×C4×C13—21no—
73C23×C4×C13C2311yescharacteristic
74C4×D4×C13—22no—
75C4×D4×C13—22no—
76C4×D4×C13—41no—
77C4×D4×C13—41no—
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C22⋊C4—21no—
81C2×C13×C22⋊C4—21no—
82C2×C13×C22⋊C4—21no—
83C2×C13×C22⋊C4D411yescharacteristic
84C2×C13×C22⋊C4D411yescharacteristic
85C2×C42×C13C2311yescharacteristic
86C2×C42×C13C2311yescharacteristic
87C2×C22⋊Dic13—21no—
88C2×C22⋊Dic13—21no—
89#88180—22no—
90#88180—41no—
91C2×C4⋊Dic13—21no—
92C2×C4⋊Dic13—21no—
93C2×C4⋊Dic13C2311yescharacteristic
94C2×C4⋊Dic13C2311yescharacteristic
95C2×C4⋊Dic13C2311yescharacteristic
96C2×C4⋊Dic13C2311yescharacteristic
97C2×#6101—21no—
98C2×#6101—21no—
99C2×#6101—21no—
100C2×#6101—21no—
101C2×C4×Dic13—21no—
102C22×#1055—22no—
103C22×#1055—22no—
104C22×#1055—41no—
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107C22×#1055C2311yescharacteristic
108C22×#1055C2311yescharacteristic
109#88124—22no—
110#88124—41no—
111C13×#95—21no—
112C13×#95—21no—
113C13×#95—21no—
114C13×#95—21no—
115C13×#95—21no—
116C13×#95D411yescharacteristic
117C13×#95D411yescharacteristic
118#88075—22no—
119#88075—22no—
120#88075—41no—
121#88075—41no—
122#88072—22no—
123#88072—22no—
124#88072—22no—
125#88072D414yes—
126#88071—21no—
127#88071—21no—
128#88071—21no—
129C22⋊#1055—22no—
130#88048—22no—
131#88047—22no—
132#88047—41no—
133#88047—41no—
134C4⋊#1055—22no—
135C4⋊#1055—41no—
136#25956—131nomaximal, Sylow
137C24×C13—21no—
138C24×C13C2×D411yescharacteristic
139C13×#41—28no—
140C13×#41—44no—
141C13×#41—44no—
142C13×#41—44no—
143C2×Q8×C13—21no—
144C2×Q8×C13—21no—
145C2×Q8×C13—21no—
146C2×Q8×C13—21no—
147C2×Q8×C13—21no—
148C2×Q8×C13C2×Q812yes—
149C2×D4×C13—24no—
150C2×D4×C13—21no—
151C2×D4×C13—21no—
152C2×D4×C13—21no—
153C2×D4×C13—42no—
154C2×D4×C13—42no—
155C2×D4×C13C2×D412yes—
156C2×D4×C13C2×Q812yes—
157C2×D4×C13#4112yes—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—24no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—42no—
167C22×C4×C13—42no—
168C22×C4×C13—42no—
169C22×C4×C13—42no—
170C22×C4×C13—42no—
171C22×C4×C13—42no—
172C22×C4×C13—81no—
173C22×C4×C13—81no—
174C22×C4×C13C2×D411yescharacteristic
175C22×C4×C13C2×D411yescharacteristic
176C22×C4×C13C2×D411yescharacteristic
177C22×C4×C13C2×D411yescharacteristic
178C22×C4×C13C2×D411yescharacteristic
179C22×C4×C13C2×Q812yes—
180C22×C4×C13#4112yes—
181C22×C4×C13C2411yescharacteristic
182C22×Dic13—21no—
183C22×Dic13—21no—
184C22×Dic13—21no—
185C22×Dic13—21no—
186C13×C4⋊C4—21no—
187C13×C4⋊C4—21no—
188C13×C4⋊C4—21no—
189C13×C4⋊C4—21no—
190C13×C22⋊C4—22no—
191C13×C22⋊C4—41no—
192C13×C22⋊C4—42no—
193C13×C22⋊C4—42no—
194C13×C22⋊C4—81no—
195C42×C13—21no—
196C42×C13—21no—
197C42×C13—21no—
198C42×C13—21no—
199C22⋊Dic13—42no—
200C22⋊Dic13—81no—
201C4⋊Dic13—21no—
202C4⋊Dic13—21no—
203C4⋊Dic13—21no—
204C4⋊Dic13—21no—
205C4⋊Dic13—21no—
206C4⋊Dic13—21no—
207C4⋊Dic13—21no—
208C4⋊Dic13—42no—
209C4⋊Dic13—81no—
210C4⋊Dic13C2×D412yes—
211#6101—42no—
212#6101—42no—
213#6101—42no—
214#6101—81no—
215C4×Dic13—42no—
216C2×#1055—21no—
217C2×#1055—21no—
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—21no—
227C2×#1055—44no—
228C2×#1055C2×D412yes—
229C2×#478—131no—
230C2×#416—131no—
231#2441—131no—
232#2339D1311yescharacteristic
233#2095—131no—
234#2068—131no—
235#2066—131no—
236#2026—131no—
237#1862—131no—
238#1862—131no—
239#1854—131no—
240#1850—131no—
241#1808—131no—
242#1802—131no—
243#1788—131no—
244C23×C13—22no—
245C23×C13—21no—
246C23×C13—22no—
247C23×C13—22no—
248C23×C13—21no—
249C23×C13—21no—
250C23×C13—21no—
251C23×C13—21no—
252C23×C13—21no—
253C23×C13—41no—
254C23×C13—41no—
255C23×C13—41no—
256C23×C13—41no—
257C23×C13C22⋊Q812yes—
258C23×C13C22×D411yescharacteristic
259Q8×C13—22no—
260Q8×C13—22no—
261Q8×C13—41no—
262Q8×C13—41no—
263D4×C13—22no—
264D4×C13—22no—
265D4×C13—22no—
266D4×C13—48no—
267D4×C13C22⋊Q814yes—
268C2×C4×C13—21no—
269C2×C4×C13—21no—
270C2×C4×C13—21no—
271C2×C4×C13—21no—
272C2×C4×C13—22no—
273C2×C4×C13—22no—
274C2×C4×C13—22no—
275C2×C4×C13—22no—
276C2×C4×C13—22no—
277C2×C4×C13—21no—
278C2×C4×C13—21no—
279C2×C4×C13—21no—
280C2×C4×C13—21no—
281C2×C4×C13—21no—
282C2×C4×C13—21no—
283C2×C4×C13—21no—
284C2×C4×C13—21no—
285C2×C4×C13—21no—
286C2×C4×C13—48no—
287C2×C4×C13—41no—
288C2×C4×C13—41no—
289C2×C4×C13—41no—
290C2×C4×C13—41no—
291C2×C4×C13—41no—
292C2×C4×C13—41no—
293C2×C4×C13—41no—
294C2×C4×C13—41no—
295C2×C4×C13—84no—
296C2×C4×C13—84no—
297C2×C4×C13C22⋊Q812yes—
298C2×C4×C13#13512yes—
299C2×C4×C13C22×D411yescharacteristic
300C2×C4×C13C22×Q811yescharacteristic
301C2×C4×C13C2×#4111yescharacteristic
302C2×C4×C13C2×#4111yescharacteristic
303C2×C4×C13H(5,𝔽2)11yescharacteristic
304C2×C4×C13H(5,𝔽2)11yescharacteristic
305C2×Dic13—22no—
306C2×Dic13—41no—
307C2×Dic13—41no—
308C2×Dic13—41no—
309C2×Dic13—41no—
310C2×Dic13—41no—
311C2×Dic13—41no—
312C2×Dic13—41no—
313C2×Dic13—41no—
314C2×Dic13—41no—
315C2×Dic13—41no—
316C2×Dic13—41no—
317#1055—22no—
318#1055—41no—
319#1055—41no—
320#1055—41no—
321C22×#41C2×D1311yescharacteristic
322C23×C8—131no—
323C2×#125—131no—
324C2×C4×D4C2×D1311yescharacteristic
325C2×C4×D4C2×D1311yescharacteristic
326C2×#117—131no—
327#478—264no—
328C2×#107—131no—
329C2×#107—131no—
330C2×#107—131no—
331C2×#106—131no—
332C2×C4⋊C8—131no—
333C2×C4⋊C8—131no—
334#416—264no—
335C2×#103—131no—
336C2×#103—131no—
337C2×#103—131no—
338C2×#103—131no—
339C2×#102—131no—
340C2×#102—131no—
341C2×#102—131no—
342C2×#102—131no—
343C2×C22⋊C8—131no—
344#399—261no—
345#396—261no—
346#391C2×D1311yescharacteristic
347#391C2×D1311yescharacteristic
348#389—131no—
349#389—131no—
350#389—261no—
351#387—261no—
352#386—21no—
353#386—21no—
354#384—131no—
355#381—21no—
356#380—131no—
357#380C2×D1311yescharacteristic
358C4×C22⋊C4C2×D1311yescharacteristic
359C2×#95—21no—
360#340—131no—
361#340—131no—
362#340—131no—
363#340—131no—
364#336—131no—
365#336—131no—
366C22×C13—22no—
367C22×C13—22no—
368C22×C13—22no—
369C22×C13—24no—
370C22×C13—42no—
371C22×C13—42no—
372C22×C13—42no—
373C22×C13—41no—
374C22×C13—41no—
375C22×C13—42no—
376C22×C13—42no—
377C22×C13—41no—
378C22×C13—41no—
379C22×C13—42no—
380C22×C13C2×C22⋊Q811yescharacteristic
381C22×C13D4211yescharacteristic
382C22×C13#54611yescharacteristic
383C22×C13C2×#13511yescharacteristic
384C22×C13#57511yescharacteristic
385C22×C13#57611yescharacteristic
386C22×C13#57811yescharacteristic
387C4×C13—22no—
388C4×C13—22no—
389C4×C13—42no—
390C4×C13—41no—
391C4×C13—41no—
392C4×C13—41no—
393C4×C13—81no—
394C4×C13—81no—
395C4×C13C2×C22⋊Q811yescharacteristic
396C4×C13#54311yescharacteristic
397C4×C13#54611yescharacteristic
398C4×C13#55111yescharacteristic
399Dic13—42no—
400Dic13—81no—
401Dic13—81no—
402Dic13—81no—
403C2×#41—22no—
404C2×#41—22no—
405C2×#41—22no—
406C2×#41—41no—
407C2×#41—41no—
408C2×#41Dic2614yes—
409C22×Q8C22×D1311yescharacteristic
410C22×D4—21no—
411C22×D4C22×D1311yescharacteristic
412C23×C4—21no—
413C23×C4—21no—
414C23×C4—21no—
415C23×C4C22×D1311yescharacteristic
416C22×C8—131no—
417C22×C8—131no—
418C22×C8—131no—
419C22×C8—131no—
420C22×C8—262no—
421C22×C8—262no—
422C22×C8—521no—
423#125—262no—
424#125—521no—
425C4×D4—22no—
426C4×D4—22no—
427C4×D4—41no—
428C4×D4—41no—
429#117—262no—
430#117—521no—
431C2×C4⋊C4—131no—
432C2×C4⋊C4—131no—
433C2×C4⋊C4—131no—
434C2×C4⋊C4—131no—
435C2×C4⋊C4—261no—
436C2×C4⋊C4—261no—
437C2×C4⋊C4—261no—
438C2×C4⋊C4—261no—
439C2×C4⋊C4—261no—
440C2×C4⋊C4—261no—
441C2×C4⋊C4C22×D1311yescharacteristic
442C2×C4⋊C4C22×D1311yescharacteristic
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—261no—
447C2×C22⋊C4—261no—
448C2×C22⋊C4C22⋊D1311yescharacteristic
449C2×C22⋊C4C22⋊D1311yescharacteristic
450C2×C42—261no—
451C2×C42C22×D1311yescharacteristic
452C2×C42C22×D1311yescharacteristic
453#107—262no—
454#107—521no—
455#107—521no—
456#106—262no—
457C4⋊C8—262no—
458C4⋊C8—521no—
459#103—262no—
460#103—262no—
461#103—521no—
462#103—521no—
463#102—134no—
464#102—262no—
465#102—262no—
466#102—262no—
467C22⋊C8—262no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—261no—
474#95—261no—
475#95—261no—
476#95C22⋊D1311yescharacteristic
477#95C22⋊D1311yescharacteristic
478C2×C13—42no—
479C2×C13—44no—
480C2×C13#243711yescharacteristic
481C2×C13#307611yescharacteristic
482C2×C13#308311yescharacteristic
483C2×C13#326811yescharacteristic
484C2×C13#328311yescharacteristic
485C2×C13#329711yescharacteristic
486C2×C13#331511yescharacteristic
487C24—21no—
488C24C2×C22⋊D1311yescharacteristic
489#41—28no—
490#41—44no—
491#41—44no—
492#41—44no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8C2×Dic2612yes—
499C2×D4—24no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4C2×Dic2612yes—
506C2×D4D4×D1312yes—
507C2×D4#612912yes—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—24no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—81no—
523C22×C4—81no—
524C22×C4—261no—
525C22×C4—261no—
526C22×C4—261no—
527C22×C4—261no—
528C22×C4C2×Dic2612yes—
529C22×C4#612712yes—
530C22×C4C2×C22⋊D1311yescharacteristic
531C22×C4C2×C22⋊D1311yescharacteristic
532C22×C4C2×C22⋊D1311yescharacteristic
533C22×C4C2×C22⋊D1311yescharacteristic
534C22×C4C2×C22⋊D1311yescharacteristic
535C22×C4C23×D1311yescharacteristic
536C2×C8—132no—
537C2×C8—261no—
538C2×C8—261no—
539C2×C8—261no—
540C2×C8—261no—
541C2×C8—261no—
542C2×C8—261no—
543C2×C8—261no—
544C2×C8—261no—
545C2×C8—261no—
546C2×C8—261no—
547C2×C8—261no—
548C2×C8—524no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—132no—
554C4⋊C4—261no—
555C4⋊C4—261no—
556C4⋊C4—261no—
557C4⋊C4—261no—
558C4⋊C4—261no—
559C4⋊C4—261no—
560C4⋊C4—261no—
561C4⋊C4—522no—
562C4⋊C4—522no—
563C4⋊C4—522no—
564C4⋊C4—522no—
565C4⋊C4—1041no—
566C4⋊C4—1041no—
567C22⋊C4—22no—
568C22⋊C4—41no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—81no—
572C22⋊C4—522no—
573C22⋊C4—1041no—
574C42—21no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—522no—
579C13#2595611yescharacteristic, complemented, Sylow
580C23—22no—
581C23—22no—
582C23—21no—
583C23—22no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23#8817812yes—
594C23C22×C22⋊D1311yescharacteristic
595Q8—22no—
596Q8—22no—
597Q8—41no—
598Q8—41no—
599D4—22no—
600D4—22no—
601D4—22no—
602D4—48no—
603D4#8813214yes—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—48no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—84no—
632C2×C4—84no—
633C2×C4—262no—
634C2×C4—521no—
635C2×C4—521no—
636C2×C4—521no—
637C2×C4—521no—
638C2×C4—521no—
639C2×C4—521no—
640C2×C4—521no—
641C2×C4—521no—
642C2×C4—521no—
643C2×C4—521no—
644C2×C4—521no—
645C2×C4#8817812yes—
646C2×C4#8820412yes—
647C2×C4C22×Dic2611yescharacteristic
648C2×C4C2×#612711yescharacteristic
649C2×C4C2×D4×D1311yescharacteristic
650C2×C4C2×#612911yescharacteristic
651C2×C4#8825111yescharacteristic
652C2×C4#8825111yescharacteristic
653C8—262no—
654C8—521no—
655C8—521no—
656C8—521no—
657C22—22no—
658C22—22no—
659C22—24no—
660C22—22no—
661C22—42no—
662C22—41no—
663C22—42no—
664C22—42no—
665C22—41no—
666C22—42no—
667C22—41no—
668C22—42no—
669C22—42no—
670C22—41no—
671C22C2×#8817811yescharacteristic
672C22D4×C22⋊D1311yescharacteristic
673C22#1171951111yescharacteristic
674C22C2×#8820411yescharacteristic
675C22#1171952711yescharacteristic
676C22#1171954011yescharacteristic
677C22#1171954311yescharacteristic
678C4—22no—
679C4—22no—
680C4—41no—
681C4—42no—
682C4—41no—
683C4—41no—
684C4—81no—
685C4—81no—
686C4—522no—
687C4—1041no—
688C4—1041no—
689C4—1041no—
690C4C2×#8813211yescharacteristic
691C4#1171918811yescharacteristic
692C4#1171919511yescharacteristic
693C4#1171920011yescharacteristic
694C2—42no—
695C2—44no—
696C2#1311849711yescharacteristic
697C2#1312462411yescharacteristic
698C2#1312468711yescharacteristic
699C2#1312637211yescharacteristic
700C2#1312655411yescharacteristic
701C2#1312668611yescharacteristic
702C2#1312693211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2339C2
socleC23×C13C22×D4
prime radicalC22×C13×#41C22
hypercenter#2339D13
hypocenterC13#25956
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2339

Complements

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

NH ≅ G/Ntype
1. C2×#11718670C2semidirect
3. #13118549C2semidirect
4. #13116374C2semidirect
5. #13116231C2semidirect
6. #13116217C2semidirect
7. #13115987C2semidirect
8. #13115083C2semidirect
9. #13115083C2semidirect
10. #13115033C2semidirect
11. #13115016C2semidirect
12. #13114863C2semidirect
13. #13114836C2semidirect
579. C13#25956semidirect

Maximal subgroups

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

subgroupindex
C2×#117186702
C2×#117188942
#131185492
#131163742
#131162312
#131162172
#131159872
#131150832
#131150332
#131150162
#131148632
#131148362
#131147762
C13×#23392
#2595613