Finite Group Databasebeta

← #15869677

Subgroups — #15869677

Order 3328.

1010 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718703C211yesmaximal, characteristic
2C2×#11718679C211yesmaximal, characteristic, complemented
3C2×#11718658C211yesmaximal, characteristic, complemented
4#13117518C211yesmaximal, characteristic, complemented
5#13115689C211yesmaximal, characteristic, complemented
6#13115566C211yesmaximal, characteristic, complemented
7#13115536C211yesmaximal, characteristic, complemented
8#13115525C211yesmaximal, characteristic, complemented
9#13115265C211yesmaximal, characteristic
10#13115257C211yesmaximal, characteristic, complemented
11#13114867C211yesmaximal, characteristic, complemented
12#13114734C211yesmaximal, characteristic, complemented
13C4×#88050C211yesmaximal, characteristic, complemented
14C4×#88072C211yesmaximal, characteristic, complemented
15C13×#2324C211yesmaximal, characteristic
16C2×C13×#121C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×C13×#117C2211yescharacteristic
19C22×#6105C2211yescharacteristic
20C2×#88178C2211yescharacteristic
21C22×#6099C2211yescharacteristic
22C23×#1055C2211yescharacteristic
23C2×C4×Dic26C2211yescharacteristic
24C13×#390—21no—
25C13×#390C2211yescharacteristic
26C13×#389C2211yescharacteristic
27C13×#388—21no—
28C13×#386—21no—
29C13×#385—21no—
30C13×#380C2211yescharacteristic
31C4×C13×C4⋊C4C2211yescharacteristic
32C2×#88072C2211yescharacteristic
33C2×#88072C2211yescharacteristic
34C2×#88072C2211yescharacteristic
35#11718873C2211yescharacteristic
36#11718703C418yescomplemented
37#11718679—24no—
38#11718658—24no—
39#11718639—21no—
40#11718633—21no—
41C2×#88050C2211yescharacteristic
42C2×#88050C2211yescharacteristic
43C2×#88050C2211yescharacteristic
44C2×#88048C2211yescharacteristic
45C2×#88047C2211yescharacteristic
46C2×#88047C2211yescharacteristic
47#11718606—21no—
48#11718605—21no—
49C4×C4⋊Dic13C2211yescharacteristic
50#11718590C2211yescharacteristic
51#11718589C2211yescharacteristic
52C2×#88043C2211yescharacteristic
53C2×#88043C2211yescharacteristic
54C2×C4×#1055C2211yescharacteristic
55C2×C4×#1055C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62C22×D4×C13—21no—
63C22×D4×C13C2311yescharacteristic
64C23×C4×C13—21no—
65C23×C4×C13C2311yescharacteristic
66C22×Dic26C2311yescharacteristic
67C13×#121—22no—
68C13×#121C2×C414yes—
69C4×D4×C13—22no—
70C4×D4×C13—22no—
71C13×#117—22no—
72C13×#117—22no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4D411yescharacteristic
75C2×C13×C4⋊C4D411yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C22⋊C4—21no—
80C2×C13×C22⋊C4—21no—
81C2×C13×C22⋊C4—21no—
82C2×C13×C22⋊C4—21no—
83C2×C13×C22⋊C4—21no—
84C2×C13×C22⋊C4D411yescharacteristic
85C2×C13×C22⋊C4D411yescharacteristic
86C2×C42×C13—21no—
87C2×C42×C13C2311yescharacteristic
88C2×C42×C13C2311yescharacteristic
89C2×C22⋊Dic13—21no—
90C2×C22⋊Dic13—21no—
91C2×#6105—22no—
92C2×#6105—22no—
93C2×#6105C2×C414yes—
94C2×C4⋊Dic13C2311yescharacteristic
95C2×C4⋊Dic13C2311yescharacteristic
96C2×C4⋊Dic13C2311yescharacteristic
97#88178—22no—
98#88178C2×C414yescomplemented
99C2×#6101—21no—
100C2×#6101—21no—
101C2×#6101—21no—
102C2×C4×Dic13—21no—
103C2×C4×Dic13—21no—
104C2×#6099—22no—
105C2×#6099—22no—
106C2×#6099C2×C414yescomplemented
107C22×#1055—22no—
108C22×#1055—22no—
109C22×#1055—22no—
110C22×#1055C2311yescharacteristic
111C22×#1055C2311yescharacteristic
112C22×#1055C2311yescharacteristic
113C22×#1055C2311yescharacteristic
114C4×Dic26—22no—
115C4×Dic26—22no—
116C13×#95—21no—
117C13×#95—21no—
118C13×#95—21no—
119#88072—22no—
120#88072—22no—
121#88072C2×C414yes—
122#88071—21no—
123#88071—21no—
124#88071—21no—
125#88071—21no—
126#88071—21no—
127#88050—22no—
128#88050—22no—
129#88050C2×C414yescomplemented
130#88048—22no—
131#88047—22no—
132#88047C2×C414yescomplemented
133#88043—22no—
134#88043D414yescomplemented
135C4×#1055—22no—
136C4×#1055—22no—
137#21543—131nomaximal, Sylow
138C24×C13—21no—
139C24×C13C2×D411yescharacteristic
140C2×D4×C13—24no—
141C2×D4×C13—21no—
142C2×D4×C13—21no—
143C2×D4×C13—21no—
144C2×D4×C13—21no—
145C2×D4×C13—21no—
146C2×D4×C13—81no—
147C2×D4×C13—81no—
148C2×D4×C13C22×C412yes—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—42no—
157C22×C4×C13—81no—
158C22×C4×C13—81no—
159C22×C4×C13C22×C412yes—
160C22×C4×C13C2×D411yescharacteristic
161C22×C4×C13C2×D411yescharacteristic
162C22×C4×C13C2×D411yescharacteristic
163C22×C4×C13C2×D411yescharacteristic
164C22×C4×C13C2×D411yescharacteristic
165C22×C4×C13#4112yes—
166C22×C4×C13C2411yescharacteristic
167C22×Dic13—21no—
168C22×Dic13—21no—
169C22×Dic13—21no—
170C22×Dic13—21no—
171C2×Dic26—21no—
172C2×Dic26—21no—
173C2×Dic26—21no—
174C2×Dic26—21no—
175C2×Dic26—21no—
176C2×Dic26C22×C412yes—
177C13×C4⋊C4—22no—
178C13×C4⋊C4—22no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—21no—
183C13×C4⋊C4—21no—
184C13×C4⋊C4—81no—
185C13×C4⋊C4C22×C412yes—
186C13×C22⋊C4—24no—
187C13×C22⋊C4—22no—
188C13×C22⋊C4—22no—
189C13×C22⋊C4—42no—
190C13×C22⋊C4—81no—
191C13×C22⋊C4—81no—
192C13×C22⋊C4—81no—
193C42×C13—21no—
194C42×C13—21no—
195C42×C13—81no—
196C42×C13C2×D412yes—
197C42×C13#4112yes—
198C22⋊Dic13—24no—
199C22⋊Dic13—81no—
200#6105—28no—
201C4⋊Dic13—21no—
202C4⋊Dic13—21no—
203C4⋊Dic13—21no—
204C4⋊Dic13—21no—
205C4⋊Dic13—21no—
206C4⋊Dic13C22×C412yes—
207#6101—24no—
208#6101—42no—
209#6101—81no—
210C4×Dic13—42no—
211C4×Dic13—81no—
212#6099—28no—
213C2×#1055—28no—
214C2×#1055—21no—
215C2×#1055—21no—
216C2×#1055—21no—
217C2×#1055—21no—
218C2×#1055—21no—
219C2×#1055—21no—
220C2×#1055C22×C412yes—
221C2×#1055C22×C412yes—
222C2×#1055C2×D412yes—
223C2×#1055C2×D412yes—
224C2×#1055#4112yes—
225C2×#1055#4112yes—
226C2×#468—131no—
227C2×#440—131no—
228C2×#405—131no—
229#2324D1311yescharacteristic
230#2323—131no—
231#1968—131no—
232#1942—131no—
233#1936—131no—
234#1935—131no—
235#1893—131no—
236#1892—131no—
237#1809—131no—
238#1776—131no—
239C4×#103—131no—
240C4×#102—131no—
241C23×C13—21no—
242C23×C13—21no—
243C23×C13—21no—
244C23×C13—21no—
245C23×C13—21no—
246C23×C13—21no—
247C23×C13—22no—
248C23×C13—41no—
249C23×C13—41no—
250C23×C13—41no—
251C23×C13—41no—
252C23×C13—41no—
253C23×C13—41no—
254C23×C13C4×D412yes—
255C23×C13C22×D411yescharacteristic
256D4×C13—22no—
257D4×C13—22no—
258D4×C13—41no—
259D4×C13—41no—
260D4×C13—84no—
261C2×C4×C13—21no—
262C2×C4×C13—21no—
263C2×C4×C13—21no—
264C2×C4×C13—21no—
265C2×C4×C13—21no—
266C2×C4×C13—21no—
267C2×C4×C13—22no—
268C2×C4×C13—22no—
269C2×C4×C13—22no—
270C2×C4×C13—22no—
271C2×C4×C13—22no—
272C2×C4×C13—21no—
273C2×C4×C13—21no—
274C2×C4×C13—21no—
275C2×C4×C13—21no—
276C2×C4×C13—21no—
277C2×C4×C13—21no—
278C2×C4×C13—41no—
279C2×C4×C13—41no—
280C2×C4×C13—41no—
281C2×C4×C13—41no—
282C2×C4×C13—41no—
283C2×C4×C13—41no—
284C2×C4×C13—41no—
285C2×C4×C13—41no—
286C2×C4×C13—84no—
287C2×C4×C13C4×D412yes—
288C2×C4×C13#12112yes—
289C2×C4×C13#12112yes—
290C2×C4×C13C23×C411yescharacteristic
291C2×C4×C13C22×D411yescharacteristic
292C2×C4×C13C2×#4111yescharacteristic
293C2×C4×C13C2×#4111yescharacteristic
294C2×C4×C13C2×#4111yescharacteristic
295C2×C4×C13C2×#4111yescharacteristic
296C2×Dic13—22no—
297C2×Dic13—22no—
298C2×Dic13—41no—
299C2×Dic13—41no—
300C2×Dic13—41no—
301C2×Dic13—41no—
302C2×Dic13—41no—
303C2×Dic13—41no—
304C2×Dic13—41no—
305C2×Dic13—41no—
306C2×Dic13—41no—
307C2×Dic13—41no—
308Dic26—22no—
309Dic26—22no—
310Dic26—41no—
311Dic26—41no—
312#1055—22no—
313#1055—22no—
314#1055—22no—
315#1055C4×D414yes—
316C22×SD16—131no—
317C22×M16—131no—
318C23×C8—131no—
319C2×C22⋊Q8—131no—
320C2×#121C2×D1311yescharacteristic
321C2×C4×Q8—131no—
322C2×C4×D4C2×D1311yescharacteristic
323C2×#117C2×D1311yescharacteristic
324#468—138no—
325#440—264no—
326C2×#107—131no—
327C2×#107—131no—
328C2×#106—131no—
329C2×#103—131no—
330C2×#103—131no—
331C2×#103—131no—
332C2×#102—131no—
333C2×#102—131no—
334C2×#102—131no—
335#405—264no—
336C2×#97—131no—
337C2×#97—131no—
338C2×C4×C8—131no—
339C2×C4×C8—131no—
340#391—131no—
341#390—21no—
342#390C2×D1311yescharacteristic
343#389—131no—
344#389—261no—
345#389C2×D1311yescharacteristic
346#388—21no—
347#388—261no—
348#388—261no—
349#387—261no—
350#386—21no—
351#385—21no—
352#380—131no—
353#380C2×D1311yescharacteristic
354C4×C4⋊C4—131no—
355C4×C4⋊C4C2×D1311yescharacteristic
356#340—131no—
357#340—131no—
358#340—131no—
359#340—131no—
360#340—131no—
361#340—131no—
362C22×C13—22no—
363C22×C13—22no—
364C22×C13—22no—
365C22×C13—41no—
366C22×C13—41no—
367C22×C13—41no—
368C22×C13—41no—
369C22×C13—42no—
370C22×C13—42no—
371C22×C13—42no—
372C22×C13—81no—
373C22×C13—81no—
374C22×C13—81no—
375C22×C13—81no—
376C22×C13C2×C4×D411yescharacteristic
377C22×C13C2×#12111yescharacteristic
378C22×C13#53211yescharacteristic
379C22×C13#57611yescharacteristic
380C22×C13#57711yescharacteristic
381C22×C13#57711yescharacteristic
382C22×C13#57811yescharacteristic
383C4×C13—22no—
384C4×C13—22no—
385C4×C13—22no—
386C4×C13—42no—
387C4×C13—41no—
388C4×C13—41no—
389C4×C13—81no—
390C4×C13—81no—
391C4×C13C2×C4×D411yescharacteristic
392C4×C13C4×#4111yescharacteristic
393C4×C13#52511yescharacteristic
394C4×C13#52911yescharacteristic
395Dic13—42no—
396Dic13—42no—
397Dic13—81no—
398Dic13—81no—
399C22×Q8—131no—
400C22×D4—21no—
401C22×D4C22×D1311yescharacteristic
402C23×C4—21no—
403C23×C4C22×D1311yescharacteristic
404C2×SD16—134no—
405C2×SD16—262no—
406C2×SD16—262no—
407C2×M16—134no—
408C2×M16—262no—
409C2×M16—262no—
410C22×C8—131no—
411C22×C8—131no—
412C22×C8—131no—
413C22×C8—131no—
414C22×C8—262no—
415C22×C8—262no—
416C22×C8—262no—
417C22⋊Q8—134no—
418C22⋊Q8—262no—
419#121—22no—
420#121C4×D1314yes—
421C4×Q8—262no—
422C4×Q8—262no—
423C4×D4—22no—
424C4×D4—22no—
425#117—22no—
426#117—22no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—131no—
429C2×C4⋊C4—131no—
430C2×C4⋊C4—131no—
431C2×C4⋊C4—261no—
432C2×C4⋊C4—261no—
433C2×C4⋊C4—261no—
434C2×C4⋊C4C22⋊D1311yescharacteristic
435C2×C4⋊C4C22⋊D1311yescharacteristic
436C2×C4⋊C4C22×D1311yescharacteristic
437C2×C4⋊C4C22×D1311yescharacteristic
438C2×C4⋊C4C22×D1311yescharacteristic
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—261no—
445C2×C22⋊C4—261no—
446C2×C22⋊C4C22⋊D1311yescharacteristic
447C2×C22⋊C4C22⋊D1311yescharacteristic
448C2×C42—21no—
449C2×C42—261no—
450C2×C42—261no—
451C2×C42C22×D1311yescharacteristic
452C2×C42C22×D1311yescharacteristic
453#107—134no—
454#107—262no—
455#106—262no—
456#103—134no—
457#103—262no—
458#103—262no—
459#102—134no—
460#102—262no—
461#102—262no—
462#97—134no—
463#97—262no—
464C4×C8—262no—
465C4×C8—262no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—261no—
470#95—261no—
471#95—261no—
472#95—261no—
473#95—261no—
474C2×C13—42no—
475C2×C13—82no—
476C2×C13C4×#12111yescharacteristic
477C2×C13#294611yescharacteristic
478C2×C13#294711yescharacteristic
479C2×C13#306211yescharacteristic
480C2×C13#306311yescharacteristic
481C2×C13#317411yescharacteristic
482C2×C13#317511yescharacteristic
483C24—21no—
484C24C2×C22⋊D1311yescharacteristic
485C2×Q8—132no—
486C2×Q8—261no—
487C2×Q8—261no—
488C2×Q8—261no—
489C2×Q8—261no—
490C2×Q8—261no—
491C2×D4—24no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—81no—
498C2×D4—81no—
499C2×D4C2×C4×D1312yes—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—42no—
508C22×C4—81no—
509C22×C4—81no—
510C22×C4—261no—
511C22×C4—261no—
512C22×C4—261no—
513C22×C4—261no—
514C22×C4C2×C4×D1312yes—
515C22×C4#612712yes—
516C22×C4C2×C22⋊D1311yescharacteristic
517C22×C4C2×C22⋊D1311yescharacteristic
518C22×C4C2×C22⋊D1311yescharacteristic
519C22×C4C2×C22⋊D1311yescharacteristic
520C22×C4C2×C22⋊D1311yescharacteristic
521C22×C4C23×D1311yescharacteristic
522SD16—268no—
523M16—268no—
524C2×C8—132no—
525C2×C8—132no—
526C2×C8—132no—
527C2×C8—132no—
528C2×C8—132no—
529C2×C8—132no—
530C2×C8—268no—
531C2×C8—261no—
532C2×C8—261no—
533C2×C8—261no—
534C2×C8—261no—
535C2×C8—261no—
536C2×C8—261no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—81no—
545C4⋊C4—132no—
546C4⋊C4—264no—
547C4⋊C4—261no—
548C4⋊C4—261no—
549C4⋊C4—261no—
550C4⋊C4—261no—
551C4⋊C4—261no—
552C4⋊C4—522no—
553C4⋊C4—1041no—
554C4⋊C4C2×C4×D1312yes—
555C22⋊C4—24no—
556C22⋊C4—22no—
557C22⋊C4—22no—
558C22⋊C4—42no—
559C22⋊C4—81no—
560C22⋊C4—81no—
561C22⋊C4—81no—
562C22⋊C4—264no—
563C22⋊C4—1041no—
564C42—21no—
565C42—21no—
566C42—81no—
567C42—522no—
568C42—1041no—
569C42D4×D1312yes—
570C42#612912yes—
571C13#2154311yescharacteristic, complemented, Sylow
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—22no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23C4×C22⋊D1312yes—
586C23C22×C22⋊D1311yescharacteristic
587Q8—262no—
588Q8—262no—
589Q8—521no—
590Q8—521no—
591D4—22no—
592D4—22no—
593D4—41no—
594D4—41no—
595D4—84no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—84no—
622C2×C4—262no—
623C2×C4—262no—
624C2×C4—521no—
625C2×C4—521no—
626C2×C4—521no—
627C2×C4—521no—
628C2×C4—521no—
629C2×C4—521no—
630C2×C4—521no—
631C2×C4—521no—
632C2×C4—521no—
633C2×C4—521no—
634C2×C4C4×C22⋊D1312yes—
635C2×C4#8819312yes—
636C2×C4#8819312yes—
637C2×C4C22×C4×D1311yescharacteristic
638C2×C4C2×#612711yescharacteristic
639C2×C4C2×D4×D1311yescharacteristic
640C2×C4C2×#612911yescharacteristic
641C2×C4#41×D1311yescharacteristic
642C2×C4#41×D1311yescharacteristic
643C8—134no—
644C8—262no—
645C8—262no—
646C8—262no—
647C22—22no—
648C22—22no—
649C22—22no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22C2×C4×C22⋊D1311yescharacteristic
662C22C2×#8819311yescharacteristic
663C22#1171953711yescharacteristic
664C22#1171954011yescharacteristic
665C22#1171954111yescharacteristic
666C22#1171954111yescharacteristic
667C22#1171954311yescharacteristic
668C4—22no—
669C4—22no—
670C4—22no—
671C4—42no—
672C4—41no—
673C4—41no—
674C4—81no—
675C4—81no—
676C4—522no—
677C4—522no—
678C4—1041no—
679C4—1041no—
680C4C4×#612911yescharacteristic
681C4#1171924311yescharacteristic
682C4C4×D4×D1311yescharacteristic
683C4#1171925211yescharacteristic
684C2—42no—
685C2—82no—
686C2C4×#8819311yescharacteristic
687C2#1312366811yescharacteristic
688C2#1312367511yescharacteristic
689C2#1312451211yescharacteristic
690C2#1312452911yescharacteristic
691C2#1312545811yescharacteristic
692C2#1312546911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2324C2
socleC23×C13C22×D4
prime radicalC2×C13×#121C22
cosocleC22×C4×C13C24
hypercenter#2324D13
hypocenterC13#21543
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2324

Complements

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

NH ≅ G/Ntype
2. C2×#11718679C2semidirect
3. C2×#11718658C2semidirect
4. #13117518C2semidirect
5. #13115689C2semidirect
6. #13115566C2semidirect
7. #13115536C2semidirect
8. #13115525C2semidirect
10. #13115257C2semidirect
11. #13114867C2semidirect
12. #13114734C2semidirect
13. C4×#88050C2semidirect
14. C4×#88072C2semidirect
36. #11718703C4semidirect
98. #88178C2×C4semidirect
106. C2×#6099C2×C4semidirect
129. #88050C2×C4semidirect
132. #88047C2×C4semidirect
134. #88043D4semidirect
571. C13#21543semidirect

Maximal subgroups

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

subgroupindex
C2×#117187032
C2×#117186792
C2×#117186582
#131175182
#131156892
#131155662
#131155362
#131155252
#131152652
#131152572
#131148672
#131147342
C4×#880502
C4×#880722
C13×#23242
#2154313