Finite Group Databasebeta

← #15919991

Subgroups — #15919991

Order 3328.

966 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718681C211yesmaximal, characteristic, complemented
2C2×#11718894C211yesmaximal, characteristic
3#13118527C211yesmaximal, characteristic, complemented
4#13116357C211yesmaximal, characteristic, complemented
5#13116210C211yesmaximal, characteristic, complemented
6#13116210C211yesmaximal, characteristic, complemented
7#13115972C211yesmaximal, characteristic, complemented
8#13115104C211yesmaximal, characteristic, complemented
9#13115090C211yesmaximal, characteristic, complemented
10#13115033C211yesmaximal, characteristic, complemented
11#13115016C211yesmaximal, characteristic, complemented
12#13114859C211yesmaximal, characteristic, complemented
13#13114851C211yesmaximal, characteristic, complemented
14#13114776C211yesmaximal, characteristic
15C13×#2341C211yesmaximal, characteristic
16C22×C13×#41C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C2×C4×Q8×C13C2211yescharacteristic
19C2×#88180C2211yescharacteristic
20C23×#1055C2211yescharacteristic
21C2×#88123C2211yescharacteristic
22C13×#390—21no—
23C13×#390—21no—
24C13×#390C2211yescharacteristic
25C13×#390C2211yescharacteristic
26C13×#380—21no—
27C13×#380C2211yescharacteristic
28C4×C13×C22⋊C4—21no—
29C4×C13×C22⋊C4C2211yescharacteristic
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#11718681—24no—
42C2×#88048C2211yescharacteristic
43C2×#88048C2211yescharacteristic
44C2×#88048C2211yescharacteristic
45C2×#88047C2211yescharacteristic
46#11718609—21no—
47#11718608—21no—
48#11718597C2211yescharacteristic
49#11718589C2211yescharacteristic
50#11718589C2211yescharacteristic
51C2×C4⋊#1055C2211yescharacteristic
52C2×C4⋊#1055C2211yescharacteristic
53#11718316—21no—
54#11718307—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×#41Q814yescomplemented
67C22×Q8×C13C2311yescharacteristic
68C22×D4×C13—21no—
69C22×D4×C13C2311yescharacteristic
70C23×C4×C13—21no—
71C23×C4×C13C2311yescharacteristic
72C22×Dic26—21no—
73C4×Q8×C13—22no—
74C4×Q8×C13—22no—
75C4×Q8×C13—41no—
76C4×Q8×C13—41no—
77C2×C13×C4⋊C4—21no—
78C2×C13×C4⋊C4—21no—
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C22⋊C4—21no—
82C2×C13×C22⋊C4—21no—
83C2×C13×C22⋊C4—21no—
84C2×C13×C22⋊C4—21no—
85C2×C13×C22⋊C4—21no—
86C2×C13×C22⋊C4D411yescharacteristic
87C2×C13×C22⋊C4D411yescharacteristic
88C2×C42×C13—21no—
89C2×C42×C13—21no—
90C2×C42×C13C2311yescharacteristic
91C2×C42×C13C2311yescharacteristic
92C2×C22⋊Dic13—21no—
93C2×C22⋊Dic13—21no—
94#88180—22no—
95#88180—41no—
96C2×C4⋊Dic13—21no—
97C2×C4⋊Dic13C2311yescharacteristic
98C2×C4⋊Dic13C2311yescharacteristic
99C2×C4⋊Dic13C2311yescharacteristic
100C2×C4⋊Dic13C2311yescharacteristic
101C2×#6101—21no—
102C2×#6101—21no—
103C2×C4×Dic13—21no—
104C22×#1055—22no—
105C22×#1055—22no—
106C22×#1055—41no—
107C22×#1055C2311yescharacteristic
108C22×#1055C2311yescharacteristic
109C22×#1055C2311yescharacteristic
110C22×#1055C2311yescharacteristic
111#88123—22no—
112#88123—41no—
113C13×#95—21no—
114C13×#95D411yescharacteristic
115C13×#95D411yescharacteristic
116#88075—22no—
117#88075—22no—
118#88075—22no—
119#88075D414yes—
120#88072—22no—
121#88072—22no—
122#88072—41no—
123#88072—41no—
124#88071—21no—
125#88071—21no—
126#88071—21no—
127#88071—21no—
128#88071—21no—
129C22⋊#1055—22no—
130#88048—22no—
131#88048—22no—
132#88048—41no—
133#88047—41no—
134C4⋊#1055—22no—
135C4⋊#1055—41no—
136#25951—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×C13C2×D412yes—
147C2×Q8×C13C2×Q812yes—
148C2×Q8×C13#4112yes—
149C2×D4×C13—24no—
150C2×D4×C13—21no—
151C2×D4×C13—21no—
152C2×D4×C13—21no—
153C2×D4×C13—21no—
154C2×D4×C13—21no—
155C2×D4×C13—42no—
156C2×D4×C13—42no—
157C2×D4×C13C2×Q812yes—
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×C13C2×D411yescharacteristic
169C22×C4×C13C2×D411yescharacteristic
170C22×C4×C13C2×D411yescharacteristic
171C22×C4×C13C2×D411yescharacteristic
172C22×C4×C13C2×D411yescharacteristic
173C22×C4×C13C2×Q812yes—
174C22×C4×C13#4112yes—
175C22×C4×C13C2411yescharacteristic
176C22×Dic13—21no—
177C22×Dic13—21no—
178C22×Dic13—21no—
179C22×Dic13—21no—
180C2×Dic26—42no—
181C2×Dic26—42no—
182C2×Dic26—81no—
183C13×C4⋊C4—21no—
184C13×C4⋊C4—21no—
185C13×C4⋊C4—21no—
186C13×C4⋊C4—21no—
187C13×C4⋊C4—42no—
188C13×C4⋊C4—42no—
189C13×C22⋊C4—22no—
190C13×C22⋊C4—41no—
191C13×C22⋊C4—42no—
192C13×C22⋊C4—42no—
193C13×C22⋊C4—81no—
194C13×C22⋊C4—81no—
195C13×C22⋊C4—81no—
196C42×C13—21no—
197C42×C13—21no—
198C42×C13—21no—
199C42×C13—21no—
200C42×C13—42no—
201C42×C13—42no—
202C22⋊Dic13—42no—
203C22⋊Dic13—81no—
204C4⋊Dic13—21no—
205C4⋊Dic13—21no—
206C4⋊Dic13—21no—
207C4⋊Dic13—21no—
208C4⋊Dic13—21no—
209C4⋊Dic13—21no—
210C4⋊Dic13—21no—
211C4⋊Dic13—42no—
212C4⋊Dic13C2×D412yes—
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×#475—131no—
230C2×#416—131no—
231#2439—131no—
232#2341D1311yescharacteristic
233#2092—131no—
234#2065—131no—
235#2065—131no—
236#2023—131no—
237#1865—131no—
238#1863—131no—
239#1854—131no—
240#1850—131no—
241#1807—131no—
242#1805—131no—
243#1788—131no—
244C23×C13—21no—
245C23×C13—21no—
246C23×C13—21no—
247C23×C13—21no—
248C23×C13—21no—
249C23×C13—21no—
250C23×C13—22no—
251C23×C13—41no—
252C23×C13—41no—
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—22no—
262Q8×C13C22⋊Q814yes—
263D4×C13—22no—
264D4×C13—22no—
265D4×C13—48no—
266D4×C13—41no—
267D4×C13—41no—
268C2×C4×C13—22no—
269C2×C4×C13—21no—
270C2×C4×C13—21no—
271C2×C4×C13—22no—
272C2×C4×C13—22no—
273C2×C4×C13—21no—
274C2×C4×C13—21no—
275C2×C4×C13—22no—
276C2×C4×C13—22no—
277C2×C4×C13—22no—
278C2×C4×C13—22no—
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—21no—
287C2×C4×C13—21no—
288C2×C4×C13—48no—
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×C13C22⋊Q812yes—
296C2×C4×C13#13512yes—
297C2×C4×C13C22×D411yescharacteristic
298C2×C4×C13C22×Q811yescharacteristic
299C2×C4×C13C2×#4111yescharacteristic
300C2×C4×C13C2×#4111yescharacteristic
301C2×C4×C13H(5,𝔽2)11yescharacteristic
302C2×C4×C13H(5,𝔽2)11yescharacteristic
303C2×Dic13—22no—
304C2×Dic13—41no—
305C2×Dic13—41no—
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—
315Dic26—84no—
316#1055—22no—
317#1055—41no—
318#1055—41no—
319#1055—41no—
320C22×#41C2×D1311yescharacteristic
321C23×C8—131no—
322C2×C4⋊Q8—131no—
323C2×C4×Q8C2×D1311yescharacteristic
324C2×C4×Q8C2×D1311yescharacteristic
325C2×#117—131no—
326#475—264no—
327C2×#107—131no—
328C2×#106—131no—
329C2×#106—131no—
330C2×#106—131no—
331C2×C4⋊C8—131no—
332C2×C4⋊C8—131no—
333#416—264no—
334C2×#103—131no—
335C2×#103—131no—
336C2×#103—131no—
337C2×#103—131no—
338C2×#102—131no—
339C2×#102—131no—
340C2×#102—131no—
341C2×#102—131no—
342C2×C22⋊C8—131no—
343#396—261no—
344#393—261no—
345#391—261no—
346#390—21no—
347#390—21no—
348#390C2×D1311yescharacteristic
349#390C2×D1311yescharacteristic
350#389—131no—
351#389—131no—
352#387—261no—
353#382—131no—
354#380—21no—
355#380—131no—
356#380C2×D1311yescharacteristic
357C4×C22⋊C4—21no—
358C4×C22⋊C4C2×D1311yescharacteristic
359#340—131no—
360#340—131no—
361#340—131no—
362#340—131no—
363#336—131no—
364#336—131no—
365C22×C13—22no—
366C22×C13—22no—
367C22×C13—22no—
368C22×C13—41no—
369C22×C13—41no—
370C22×C13—41no—
371C22×C13—41no—
372C22×C13—42no—
373C22×C13—42no—
374C22×C13—42no—
375C22×C13—81no—
376C22×C13—81no—
377C22×C13—81no—
378C22×C13—81no—
379C22×C13C2×C22⋊Q811yescharacteristic
380C22×C13D4211yescharacteristic
381C22×C13#54611yescharacteristic
382C22×C13C2×#13511yescharacteristic
383C22×C13#57511yescharacteristic
384C22×C13#57711yescharacteristic
385C22×C13#57711yescharacteristic
386C4×C13—22no—
387C4×C13—24no—
388C4×C13—22no—
389C4×C13—41no—
390C4×C13—41no—
391C4×C13—41no—
392C4×C13—81no—
393C4×C13—81no—
394C4×C13C2×C22⋊Q811yescharacteristic
395C4×C13#54311yescharacteristic
396C4×C13#54611yescharacteristic
397C4×C13#55111yescharacteristic
398Dic13—42no—
399Dic13—81no—
400Dic13—81no—
401Dic13—81no—
402C2×#41—22no—
403C2×#41—22no—
404C2×#41—22no—
405C2×#41—41no—
406C2×#41—41no—
407C2×#41Dic2614yescomplemented
408C22×Q8—261no—
409C22×Q8C22×D1311yescharacteristic
410C22×D4—21no—
411C22×D4C22×D1311yescharacteristic
412C23×C4—21no—
413C23×C4C22×D1311yescharacteristic
414C22×C8—131no—
415C22×C8—131no—
416C22×C8—131no—
417C22×C8—131no—
418C22×C8—262no—
419C22×C8—262no—
420C22×C8—521no—
421C4⋊Q8—262no—
422C4⋊Q8—521no—
423C4×Q8—22no—
424C4×Q8—22no—
425C4×Q8—41no—
426C4×Q8—41no—
427#117—262no—
428#117—521no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
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⋊C4C22×D1311yescharacteristic
439C2×C4⋊C4C22×D1311yescharacteristic
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—261no—
446C2×C22⋊C4—261no—
447C2×C22⋊C4C22⋊D1311yescharacteristic
448C2×C22⋊C4C22⋊D1311yescharacteristic
449C2×C42—21no—
450C2×C42—21no—
451C2×C42—261no—
452C2×C42C22×D1311yescharacteristic
453C2×C42C22×D1311yescharacteristic
454#107—521no—
455#106—262no—
456#106—262no—
457#106—521no—
458C4⋊C8—262no—
459C4⋊C8—521no—
460#103—134no—
461#103—262no—
462#103—262no—
463#103—262no—
464#102—262no—
465#102—262no—
466#102—521no—
467#102—521no—
468C22⋊C8—262no—
469#95—21no—
470#95—261no—
471#95—261no—
472#95—261no—
473#95—261no—
474#95—261no—
475#95C22⋊D1311yescharacteristic
476#95C22⋊D1311yescharacteristic
477C2×C13—42no—
478C2×C13—82no—
479C2×C13#243711yescharacteristic
480C2×C13#307611yescharacteristic
481C2×C13#308411yescharacteristic
482C2×C13#327111yescharacteristic
483C2×C13#328211yescharacteristic
484C2×C13#330411yescharacteristic
485C2×C13#332111yescharacteristic
486C24—21no—
487C24C2×C22⋊D1311yescharacteristic
488#41—28no—
489#41—44no—
490#41—44no—
491#41—44no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—522no—
496C2×Q8—522no—
497C2×Q8—1041no—
498C2×Q8C2×Dic2612yes—
499C2×Q8D4×D1312yes—
500C2×Q8#612912yes—
501C2×D4—24no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—42no—
508C2×D4—42no—
509C2×D4C2×Dic2612yes—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—24no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—261no—
521C22×C4—261no—
522C22×C4—261no—
523C22×C4—261no—
524C22×C4C2×Dic2612yes—
525C22×C4#612712yes—
526C22×C4C2×C22⋊D1311yescharacteristic
527C22×C4C2×C22⋊D1311yescharacteristic
528C22×C4C2×C22⋊D1311yescharacteristic
529C22×C4C2×C22⋊D1311yescharacteristic
530C22×C4C2×C22⋊D1311yescharacteristic
531C22×C4C23×D1311yescharacteristic
532C2×C8—132no—
533C2×C8—261no—
534C2×C8—261no—
535C2×C8—261no—
536C2×C8—261no—
537C2×C8—261no—
538C2×C8—261no—
539C2×C8—261no—
540C2×C8—261no—
541C2×C8—261no—
542C2×C8—261no—
543C2×C8—261no—
544C2×C8—524no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—42no—
550C4⋊C4—42no—
551C4⋊C4—132no—
552C4⋊C4—261no—
553C4⋊C4—261no—
554C4⋊C4—261no—
555C4⋊C4—261no—
556C4⋊C4—261no—
557C4⋊C4—261no—
558C4⋊C4—261no—
559C4⋊C4—522no—
560C4⋊C4—522no—
561C4⋊C4—1041no—
562C22⋊C4—22no—
563C22⋊C4—41no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—81no—
567C22⋊C4—81no—
568C22⋊C4—81no—
569C22⋊C4—522no—
570C22⋊C4—1041no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—42no—
576C42—42no—
577C42—522no—
578C13#2595111yescharacteristic, complemented, Sylow
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—22no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23#8817812yes—
593C23C22×C22⋊D1311yescharacteristic
594Q8—22no—
595Q8—22no—
596Q8—22no—
597Q8—1044no—
598Q8#8813214yes—
599D4—22no—
600D4—22no—
601D4—48no—
602D4—41no—
603D4—41no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—22no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—48no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—262no—
632C2×C4—521no—
633C2×C4—521no—
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#8817812yes—
644C2×C4#8820412yes—
645C2×C4C22×Dic2611yescharacteristic
646C2×C4C2×#612711yescharacteristic
647C2×C4C2×D4×D1311yescharacteristic
648C2×C4C2×#612911yescharacteristic
649C2×C4#8825111yescharacteristic
650C2×C4#8825111yescharacteristic
651C8—262no—
652C8—521no—
653C8—521no—
654C8—521no—
655C22—22no—
656C22—22no—
657C22—22no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—42no—
663C22—42no—
664C22—42no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22C2×#8817811yescharacteristic
670C22D4×C22⋊D1311yescharacteristic
671C22#1171951111yescharacteristic
672C22C2×#8820411yescharacteristic
673C22#1171952711yescharacteristic
674C22#1171954111yescharacteristic
675C22#1171954211yescharacteristic
676C4—22no—
677C4—24no—
678C4—22no—
679C4—41no—
680C4—41no—
681C4—41no—
682C4—81no—
683C4—81no—
684C4—522no—
685C4—1041no—
686C4—1041no—
687C4—1041no—
688C4C2×#8813211yescharacteristic
689C4#1171918811yescharacteristic
690C4#1171919511yescharacteristic
691C4#1171920011yescharacteristic
692C2—42no—
693C2—82no—
694C2#1311849711yescharacteristic
695C2#1312462411yescharacteristic
696C2#1312469811yescharacteristic
697C2#1312641711yescharacteristic
698C2#1312654411yescharacteristic
699C2#1312677511yescharacteristic
700C2#1312702211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2341C2
socleC23×C13C22×D4
prime radicalC22×C13×#41C22
hypercenter#2341D13
hypocenterC13#25951
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2341

Complements

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

NH ≅ G/Ntype
1. C2×#11718681C2semidirect
3. #13118527C2semidirect
4. #13116357C2semidirect
5. #13116210C2semidirect
6. #13116210C2semidirect
7. #13115972C2semidirect
8. #13115104C2semidirect
9. #13115090C2semidirect
10. #13115033C2semidirect
11. #13115016C2semidirect
12. #13114859C2semidirect
13. #13114851C2semidirect
66. C2×C13×#41Q8semidirect
407. C2×#41Dic26semidirect
578. C13#25951semidirect

Maximal subgroups

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

subgroupindex
C2×#117186812
C2×#117188942
#131185272
#131163572
#131162102
#131159722
#131151042
#131150902
#131150332
#131150162
#131148592
#131148512
#131147762
C13×#23412
#2595113