Finite Group Databasebeta

← #15920438

Subgroups — #15920438

Order 3328.

920 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718724C211yesmaximal, characteristic, complemented
2C2×#11718665C211yesmaximal, characteristic
3C22⋊C4×Dic26C211yesmaximal, characteristic
4#13116375C211yesmaximal, characteristic, complemented
5#13116214C211yesmaximal, characteristic, complemented
6#13116214C211yesmaximal, characteristic, complemented
7#13115984C211yesmaximal, characteristic, complemented
8#13115103C211yesmaximal, characteristic, complemented
9#13115089C211yesmaximal, characteristic, complemented
10#13115035C211yesmaximal, characteristic
11#13115021C211yesmaximal, characteristic
12#13114867C211yesmaximal, characteristic
13#13114838C211yesmaximal, characteristic, complemented
14#13114770C211yesmaximal, characteristic
15C13×#2441C211yesmaximal, characteristic
16C23×Dic26C2211yescharacteristic
17C2×C13×#125C2211yescharacteristic
18C2×C13×#117C2211yescharacteristic
19C22×#6099C2211yescharacteristic
20C2×C4×Dic26C2211yescharacteristic
21C2×C4×Dic26C2211yescharacteristic
22C13×#399—21no—
23C13×#396—21no—
24C13×#389—21no—
25C13×#389C2211yescharacteristic
26C13×#389C2211yescharacteristic
27C13×#387—21no—
28C13×#384C2211yescharacteristic
29C13×#380C2211yescharacteristic
30C4×C13×C22⋊C4C2211yescharacteristic
31#11718873C2211yescharacteristic
32C2×C22⋊#1055C2211yescharacteristic
33#11718724—24no—
34#11718665—24no—
35C2×#88050C2211yescharacteristic
36C2×#88050C2211yescharacteristic
37C2×#88050C2211yescharacteristic
38C2×#88050C2211yescharacteristic
39C2×#88050C2211yescharacteristic
40C2×#88050C2211yescharacteristic
41C2×#88050C2211yescharacteristic
42C2×#88050C2211yescharacteristic
43C2×#88048C2211yescharacteristic
44C2×#88048C2211yescharacteristic
45C2×#88047C2211yescharacteristic
46C2×#88047C2211yescharacteristic
47#11718603—21no—
48C22⋊C4×Dic13—21no—
49#11718590C2211yescharacteristic
50#11718590C2211yescharacteristic
51C2×C4⋊#1055C2211yescharacteristic
52C2×C4⋊#1055C2211yescharacteristic
53#11718307—21no—
54#11718307—21no—
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×Dic13—21no—
63C22×Dic26—22no—
64C22×Dic26—22no—
65C22×Dic26—21no—
66C22×Dic26—22no—
67C22×Dic26—41no—
68C22×Dic26—41no—
69C22×Dic26Q814yes—
70C22×Dic26C2311yescharacteristic
71C22×Dic26C2311yescharacteristic
72C13×#125—22no—
73C13×#125—41no—
74C13×#117—22no—
75C13×#117—41no—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4—21no—
78C2×C13×C4⋊C4—21no—
79C2×C13×C4⋊C4—21no—
80C2×C13×C4⋊C4—21no—
81C2×C13×C4⋊C4—21no—
82C2×C13×C4⋊C4C2311yescharacteristic
83C2×C13×C4⋊C4C2311yescharacteristic
84C2×C13×C4⋊C4C2311yescharacteristic
85C2×C13×C4⋊C4C2311yescharacteristic
86C2×C13×C22⋊C4—21no—
87C2×C13×C22⋊C4—21no—
88C2×C13×C22⋊C4D411yescharacteristic
89C2×C13×C22⋊C4D411yescharacteristic
90C2×C42×C13—21no—
91C2×C42×C13C2311yescharacteristic
92C2×C42×C13C2311yescharacteristic
93C2×C22⋊Dic13—21no—
94C2×C4⋊Dic13C2311yescharacteristic
95C2×C4⋊Dic13C2311yescharacteristic
96C2×#6101—21no—
97C2×#6101—21no—
98C2×C4×Dic13—21no—
99C2×C4×Dic13—21no—
100C2×#6099—22no—
101C2×#6099—22no—
102C2×#6099—41no—
103C22×#1055C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107C4×Dic26—22no—
108C4×Dic26—22no—
109C4×Dic26—41no—
110C4×Dic26—41no—
111C13×#95—21no—
112C13×#95—21no—
113C13×#95—21no—
114C13×#95D411yescharacteristic
115C13×#95D411yescharacteristic
116#88071—21no—
117#88071—21no—
118#88071—21no—
119#88071—21no—
120#88071—21no—
121C22⋊#1055—22no—
122#88050—22no—
123#88050—22no—
124#88050—22no—
125#88050—22no—
126#88050—22no—
127#88050—41no—
128#88050—41no—
129#88050D414yes—
130#88048—22no—
131#88048—41no—
132#88047—22no—
133#88047—41no—
134C4⋊#1055—22no—
135C4⋊#1055—41no—
136#25981—131nomaximal, Sylow
137C24×C13C2×D411yescharacteristic
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×Q812yes—
152C22×C4×C13#4112yes—
153C22×C4×C13C2411yescharacteristic
154C22×Dic13—21no—
155C22×Dic13—24no—
156C22×Dic13—21no—
157C22×Dic13—21no—
158C22×Dic13—21no—
159C22×Dic13—42no—
160C22×Dic13—42no—
161C2×Dic26—21no—
162C2×Dic26—21no—
163C2×Dic26—21no—
164C2×Dic26—21no—
165C2×Dic26—21no—
166C2×Dic26—21no—
167C2×Dic26—21no—
168C2×Dic26—28no—
169C2×Dic26—24no—
170C2×Dic26—21no—
171C2×Dic26—44no—
172C2×Dic26—44no—
173C2×Dic26—44no—
174C2×Dic26—42no—
175C2×Dic26—42no—
176C2×Dic26C2×D412yes—
177C2×Dic26C2×Q812yes—
178C2×Dic26C2×Q812yes—
179C2×Dic26#4112yes—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—21no—
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×C4⋊C4—42no—
190C13×C4⋊C4—42no—
191C13×C4⋊C4—81no—
192C13×C4⋊C4—81no—
193C13×C4⋊C4C2×D412yes—
194C13×C22⋊C4—22no—
195C13×C22⋊C4—41no—
196C13×C22⋊C4—42no—
197C13×C22⋊C4—81no—
198C42×C13—21no—
199C42×C13—21no—
200C42×C13—21no—
201C42×C13—21no—
202C42×C13—42no—
203C22⋊Dic13—42no—
204C4⋊Dic13—21no—
205C4⋊Dic13—21no—
206C4⋊Dic13—21no—
207C4⋊Dic13—21no—
208#6101—42no—
209#6101—42no—
210C4×Dic13—42no—
211C4×Dic13—42no—
212#6099—44no—
213C2×#1055—21no—
214C2×#1055—21no—
215C2×#1055—21no—
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×#1055C2×D412yes—
225C2×#479—131no—
226C2×#419—131no—
227#2441D1311yescharacteristic
228Q8×C22⋊C4—131no—
229#2095—131no—
230#2066—131no—
231#2066—131no—
232#2026—131no—
233#1865—131no—
234#1863—131no—
235#1854—131no—
236#1851—131no—
237#1809—131no—
238#1803—131no—
239#1787—131no—
240C23×C13—21no—
241C23×C13—21no—
242C23×C13—21no—
243C23×C13—21no—
244C23×C13—21no—
245C23×C13—21no—
246C23×C13C22⋊Q812yes—
247C23×C13C22×D411yescharacteristic
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—22no—
253C2×C4×C13—22no—
254C2×C4×C13—22no—
255C2×C4×C13—22no—
256C2×C4×C13—21no—
257C2×C4×C13—21no—
258C2×C4×C13—22no—
259C2×C4×C13—21no—
260C2×C4×C13—21no—
261C2×C4×C13—21no—
262C2×C4×C13—21no—
263C2×C4×C13—21no—
264C2×C4×C13—21no—
265C2×C4×C13—21no—
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—41no—
274C2×C4×C13—41no—
275C2×C4×C13—41no—
276C2×C4×C13—41no—
277C2×C4×C13C22⋊Q812yes—
278C2×C4×C13#13712yes—
279C2×C4×C13C22×D411yescharacteristic
280C2×C4×C13C22×Q811yescharacteristic
281C2×C4×C13C2×#4111yescharacteristic
282C2×C4×C13C2×#4111yescharacteristic
283C2×C4×C13H(5,𝔽2)11yescharacteristic
284C2×C4×C13H(5,𝔽2)11yescharacteristic
285C2×Dic13—22no—
286C2×Dic13—22no—
287C2×Dic13—22no—
288C2×Dic13—22no—
289C2×Dic13—48no—
290C2×Dic13—41no—
291C2×Dic13—41no—
292C2×Dic13—41no—
293C2×Dic13—41no—
294C2×Dic13—41no—
295C2×Dic13—41no—
296C2×Dic13—41no—
297C2×Dic13—41no—
298Dic26—22no—
299Dic26—22no—
300Dic26—22no—
301Dic26—22no—
302Dic26—22no—
303Dic26—48no—
304Dic26—41no—
305Dic26—41no—
306Dic26C22⋊Q814yes—
307#1055—22no—
308#1055—41no—
309#1055—41no—
310#1055—41no—
311C23×Q8—131no—
312C22×M16—131no—
313C2×#125C2×D1311yescharacteristic
314C2×C4×Q8—131no—
315C2×C4×Q8—131no—
316C2×#117C2×D1311yescharacteristic
317#479—264no—
318C2×#107—131no—
319C2×#107—131no—
320C2×#106—131no—
321C2×#106—131no—
322C2×C4⋊C8—131no—
323C2×C4⋊C8—131no—
324#419—264no—
325C2×#103—131no—
326C2×#103—131no—
327C2×#103—131no—
328C2×#103—131no—
329C2×#103—131no—
330C2×#103—131no—
331C2×#103—131no—
332C2×#103—131no—
333C2×C22⋊C8—131no—
334#399—21no—
335#396—21no—
336#391—131no—
337#391—131no—
338#391—261no—
339#391—261no—
340#389—21no—
341#389C2×D1311yescharacteristic
342#389C2×D1311yescharacteristic
343#387—21no—
344#384C2×D1311yescharacteristic
345#380—131no—
346#380—261no—
347#380C2×D1311yescharacteristic
348C4×C22⋊C4—261no—
349C4×C22⋊C4C2×D1311yescharacteristic
350#340—131no—
351#340—131no—
352#340—131no—
353#340—131no—
354#336—131no—
355#336—131no—
356C22×C13—22no—
357C22×C13—22no—
358C22×C13—22no—
359C22×C13—41no—
360C22×C13—41no—
361C22×C13—41no—
362C22×C13—41no—
363C22×C13C2×C22⋊Q811yescharacteristic
364C22×C13D4211yescharacteristic
365C22×C13#54611yescharacteristic
366C22×C13C2×#13711yescharacteristic
367C22×C13#57511yescharacteristic
368C22×C13#57711yescharacteristic
369C22×C13#57811yescharacteristic
370C4×C13—22no—
371C4×C13—22no—
372C4×C13—41no—
373C4×C13—41no—
374C4×C13—42no—
375C4×C13—41no—
376C4×C13—81no—
377C4×C13—81no—
378C4×C13—81no—
379C4×C13C2×C22⋊Q811yescharacteristic
380C4×C13#54311yescharacteristic
381C4×C13#54611yescharacteristic
382C4×C13#55111yescharacteristic
383Dic13—24no—
384Dic13—42no—
385Dic13—81no—
386Dic13—81no—
387C22×Q8—134no—
388C22×Q8—131no—
389C22×Q8—131no—
390C22×Q8—262no—
391C22×Q8—262no—
392C22×Q8—262no—
393C22×Q8—261no—
394C22×Q8—521no—
395C22×Q8—521no—
396C23×C4—261no—
397C23×C4C22×D1311yescharacteristic
398C2×M16—262no—
399C2×M16—262no—
400C2×M16—521no—
401C22×C8—131no—
402C22×C8—131no—
403C22×C8—131no—
404C22×C8—131no—
405#125—22no—
406#125—41no—
407C4×Q8—262no—
408C4×Q8—262no—
409C4×Q8—521no—
410C4×Q8—521no—
411#117—22no—
412#117—41no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—131no—
420C2×C4⋊C4—131no—
421C2×C4⋊C4—261no—
422C2×C4⋊C4—261no—
423C2×C4⋊C4C22×D1311yescharacteristic
424C2×C4⋊C4C22×D1311yescharacteristic
425C2×C4⋊C4C22×D1311yescharacteristic
426C2×C4⋊C4C22×D1311yescharacteristic
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—261no—
430C2×C22⋊C4C22⋊D1311yescharacteristic
431C2×C22⋊C4C22⋊D1311yescharacteristic
432C2×C42—21no—
433C2×C42—261no—
434C2×C42—261no—
435C2×C42C22×D1311yescharacteristic
436C2×C42C22×D1311yescharacteristic
437#107—262no—
438#107—521no—
439#106—262no—
440#106—521no—
441C4⋊C8—262no—
442C4⋊C8—521no—
443#103—134no—
444#103—262no—
445#103—262no—
446#103—262no—
447#103—262no—
448#103—262no—
449#103—521no—
450#103—521no—
451C22⋊C8—262no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—261no—
456#95—261no—
457#95—261no—
458#95—261no—
459#95—261no—
460#95C22⋊D1311yescharacteristic
461#95C22⋊D1311yescharacteristic
462C2×C13—42no—
463C2×C13#243711yescharacteristic
464C2×C13#307811yescharacteristic
465C2×C13#308211yescharacteristic
466C2×C13#327111yescharacteristic
467C2×C13#327611yescharacteristic
468C2×C13#332011yescharacteristic
469C2×C13#332711yescharacteristic
470C24C2×C22⋊D1311yescharacteristic
471C2×Q8—132no—
472C2×Q8—132no—
473C2×Q8—132no—
474C2×Q8—132no—
475C2×Q8—268no—
476C2×Q8—264no—
477C2×Q8—261no—
478C2×Q8—261no—
479C2×Q8—261no—
480C2×Q8—261no—
481C2×Q8—261no—
482C2×Q8—261no—
483C2×Q8—261no—
484C2×Q8—261no—
485C2×Q8—522no—
486C2×Q8—522no—
487C2×Q8—524no—
488C2×Q8—524no—
489C2×Q8—524no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—261no—
499C22×C4—264no—
500C22×C4—261no—
501C22×C4—261no—
502C22×C4—261no—
503C22×C4—522no—
504C22×C4—522no—
505C22×C4Q8×D1312yes—
506C22×C4#613112yes—
507C22×C4C2×C22⋊D1311yescharacteristic
508C22×C4C2×C22⋊D1311yescharacteristic
509C22×C4C2×C22⋊D1311yescharacteristic
510C22×C4C2×C22⋊D1311yescharacteristic
511C22×C4C2×C22⋊D1311yescharacteristic
512C22×C4C23×D1311yescharacteristic
513M16—524no—
514C2×C8—132no—
515C2×C8—261no—
516C2×C8—261no—
517C2×C8—261no—
518C2×C8—261no—
519C2×C8—261no—
520C2×C8—261no—
521C2×C8—261no—
522C2×C8—261no—
523C2×C8—261no—
524C2×C8—261no—
525C2×C8—261no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—42no—
534C4⋊C4—42no—
535C4⋊C4—42no—
536C4⋊C4—42no—
537C4⋊C4—81no—
538C4⋊C4—81no—
539C4⋊C4—261no—
540C4⋊C4—261no—
541C4⋊C4—261no—
542C4⋊C4—261no—
543C4⋊C4—522no—
544C4⋊C4—522no—
545C4⋊C4D4×D1312yes—
546C22⋊C4—22no—
547C22⋊C4—41no—
548C22⋊C4—42no—
549C22⋊C4—81no—
550C22⋊C4—522no—
551C42—21no—
552C42—21no—
553C42—21no—
554C42—21no—
555C42—42no—
556C42—522no—
557C42—522no—
558C13#2598111yescharacteristic, complemented, Sylow
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23#8820012yes—
566C23C22×C22⋊D1311yescharacteristic
567Q8—134no—
568Q8—262no—
569Q8—262no—
570Q8—262no—
571Q8—262no—
572Q8—262no—
573Q8—528no—
574Q8—521no—
575Q8—521no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—262no—
606C2×C4—262no—
607C2×C4—262no—
608C2×C4—262no—
609C2×C4—528no—
610C2×C4—521no—
611C2×C4—521no—
612C2×C4—521no—
613C2×C4—521no—
614C2×C4—521no—
615C2×C4—521no—
616C2×C4—521no—
617C2×C4—521no—
618C2×C4#8820012yes—
619C2×C4#8820512yes—
620C2×C4C2×D4×D1311yescharacteristic
621C2×C4#8825111yescharacteristic
622C2×C4C2×Q8×D1311yescharacteristic
623C2×C4C2×#613111yescharacteristic
624C2×C4#41×D1311yescharacteristic
625C2×C4#8825611yescharacteristic
626C8—262no—
627C8—521no—
628C8—521no—
629C8—521no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22D4×C22⋊D1311yescharacteristic
638C22C2×#8820011yescharacteristic
639C22#1171952711yescharacteristic
640C22C2×#8820511yescharacteristic
641C22#1171953411yescharacteristic
642C22#1171954111yescharacteristic
643C22#1171954311yescharacteristic
644C4—22no—
645C4—22no—
646C4—41no—
647C4—41no—
648C4—42no—
649C4—41no—
650C4—81no—
651C4—81no—
652C4—81no—
653C4—264no—
654C4—522no—
655C4—1041no—
656C4—1041no—
657C4D13×C22⋊Q811yescharacteristic
658C4#1171933511yescharacteristic
659C4#1171933911yescharacteristic
660C4#1171934211yescharacteristic
661C2—42no—
662C2#1311849911yescharacteristic
663C2#1312463711yescharacteristic
664C2#1312467211yescharacteristic
665C2#1312641711yescharacteristic
666C2#1312647811yescharacteristic
667C2#1312700111yescharacteristic
668C2#1312709811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2441C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#2441D13
hypocenterC13#25981
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2441

Complements

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

NH ≅ G/Ntype
1. C2×#11718724C2semidirect
4. #13116375C2semidirect
5. #13116214C2semidirect
6. #13116214C2semidirect
7. #13115984C2semidirect
8. #13115103C2semidirect
9. #13115089C2semidirect
13. #13114838C2semidirect
558. C13#25981semidirect

Maximal subgroups

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

subgroupindex
C2×#117187242
C2×#117186652
C22⋊C4×Dic262
#131163752
#131162142
#131159842
#131151032
#131150892
#131150352
#131150212
#131148672
#131148382
#131147702
C13×#24412
#2598113