Finite Group Databasebeta

← #15920048

Subgroups — #15920048

Order 3328.

990 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718755C211yesmaximal, characteristic, complemented
2C22×#88050C211yesmaximal, characteristic
3C22⋊C4×Dic26C211yesmaximal, characteristic
4#13116380C211yesmaximal, characteristic, complemented
5#13116214C211yesmaximal, characteristic, complemented
6#13116214C211yesmaximal, characteristic, complemented
7#13115974C211yesmaximal, characteristic, complemented
8#13115103C211yesmaximal, characteristic, complemented
9#13115103C211yesmaximal, characteristic, complemented
10#13115029C211yesmaximal, characteristic
11#13115016C211yesmaximal, characteristic
12#13114859C211yesmaximal, characteristic
13#13114838C211yesmaximal, characteristic, complemented
14#13114770C211yesmaximal, characteristic
15C13×#2440C211yesmaximal, characteristic
16C23×Dic26C2211yescharacteristic
17C2×C13×C4⋊Q8C2211yescharacteristic
18C2×C13×C22⋊Q8—21no—
19C22×C13×C4⋊C4C2211yescharacteristic
20C23×#1055C2211yescharacteristic
21C2×C4×Dic26C2211yescharacteristic
22C2×C4×Dic26C2211yescharacteristic
23C13×#398—21no—
24C13×#395—21no—
25C13×#389C2211yescharacteristic
26C13×#389C2211yescharacteristic
27C13×#385—21no—
28C13×#384C2211yescharacteristic
29C13×#380C2211yescharacteristic
30C4×C13×C22⋊C4C2211yescharacteristic
31#11718873C2211yescharacteristic
32C2×C22⋊#1055C2211yescharacteristic
33#11718755—24no—
34C2×#88050—24no—
35C2×#88050C2211yescharacteristic
36C2×#88050C2211yescharacteristic
37C2×#88050C2211yescharacteristic
38C2×#88050C2211yescharacteristic
39C2×#88050C2211yescharacteristic
40C2×#88050C2211yescharacteristic
41C2×#88050C2211yescharacteristic
42C2×#88050C2211yescharacteristic
43C2×#88048C2211yescharacteristic
44C2×#88048C2211yescharacteristic
45C2×#88048C2211yescharacteristic
46C2×#88048C2211yescharacteristic
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
61C22×Q8×C13—21no—
62C23×C4×C13—21no—
63C23×C4×C13C2311yescharacteristic
64C23×Dic13—21no—
65C22×Dic26—22no—
66C22×Dic26—22no—
67C22×Dic26—21no—
68C22×Dic26—22no—
69C22×Dic26—41no—
70C22×Dic26—41no—
71C22×Dic26Q814yescomplemented
72C22×Dic26C2311yescharacteristic
73C22×Dic26C2311yescharacteristic
74C13×C4⋊Q8—22no—
75C13×C4⋊Q8—41no—
76C13×C22⋊Q8—44no—
77C2×C13×C4⋊C4—22no—
78C2×C13×C4⋊C4—21no—
79C2×C13×C4⋊C4—21no—
80C2×C13×C4⋊C4—21no—
81C2×C13×C4⋊C4—21no—
82C2×C13×C4⋊C4—21no—
83C2×C13×C4⋊C4—21no—
84C2×C13×C4⋊C4—41no—
85C2×C13×C4⋊C4C2311yescharacteristic
86C2×C13×C4⋊C4C2311yescharacteristic
87C2×C13×C4⋊C4C2311yescharacteristic
88C2×C13×C4⋊C4C2311yescharacteristic
89C2×C13×C22⋊C4—21no—
90C2×C13×C22⋊C4D411yescharacteristic
91C2×C13×C22⋊C4D411yescharacteristic
92C2×C42×C13C2311yescharacteristic
93C2×C42×C13C2311yescharacteristic
94C2×C22⋊Dic13—21no—
95C2×C4⋊Dic13C2311yescharacteristic
96C2×C4⋊Dic13C2311yescharacteristic
97C2×#6101—21no—
98C2×#6101—21no—
99C2×C4×Dic13—21no—
100C2×C4×Dic13—21no—
101C22×#1055—22no—
102C22×#1055—22no—
103C22×#1055—41no—
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107C22×#1055C2311yescharacteristic
108C4×Dic26—22no—
109C4×Dic26—22no—
110C4×Dic26—41no—
111C4×Dic26—41no—
112C13×#95—21no—
113C13×#95—21no—
114C13×#95—21no—
115C13×#95D411yescharacteristic
116C13×#95D411yescharacteristic
117#88071—21no—
118#88071—21no—
119#88071—21no—
120#88071—21no—
121#88071—21no—
122C22⋊#1055—22no—
123#88050—22no—
124#88050—22no—
125#88050—22no—
126#88050—22no—
127#88050—22no—
128#88050—41no—
129#88050—41no—
130#88050D414yes—
131#88048—22no—
132#88048—22no—
133#88048—41no—
134#88048—41no—
135C4⋊#1055—22no—
136C4⋊#1055—41no—
137#25955—131nomaximal, Sylow
138C24×C13C2×D411yescharacteristic
139C2×Q8×C13—42no—
140C2×Q8×C13—42no—
141C2×Q8×C13—81no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—42no—
151C22×C4×C13—42no—
152C22×C4×C13—81no—
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13C2×D411yescharacteristic
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13C2×Q812yes—
159C22×C4×C13#4112yes—
160C22×C4×C13C2411yescharacteristic
161C22×Dic13—21no—
162C22×Dic13—24no—
163C22×Dic13—21no—
164C22×Dic13—21no—
165C22×Dic13—21no—
166C22×Dic13—42no—
167C22×Dic13—42no—
168C2×Dic26—21no—
169C2×Dic26—21no—
170C2×Dic26—21no—
171C2×Dic26—21no—
172C2×Dic26—21no—
173C2×Dic26—21no—
174C2×Dic26—21no—
175C2×Dic26—28no—
176C2×Dic26—24no—
177C2×Dic26—21no—
178C2×Dic26—44no—
179C2×Dic26—44no—
180C2×Dic26—44no—
181C2×Dic26—42no—
182C2×Dic26—42no—
183C2×Dic26C2×D412yes—
184C2×Dic26C2×Q812yes—
185C2×Dic26C2×Q812yes—
186C2×Dic26#4112yes—
187C13×C4⋊C4—21no—
188C13×C4⋊C4—21no—
189C13×C4⋊C4—21no—
190C13×C4⋊C4—21no—
191C13×C4⋊C4—21no—
192C13×C4⋊C4—21no—
193C13×C4⋊C4—21no—
194C13×C4⋊C4—42no—
195C13×C4⋊C4—42no—
196C13×C4⋊C4—42no—
197C13×C4⋊C4—42no—
198C13×C4⋊C4—42no—
199C13×C4⋊C4—81no—
200C13×C4⋊C4C2×D412yes—
201C13×C22⋊C4—22no—
202C13×C22⋊C4—42no—
203C13×C22⋊C4SD1614yes—
204C42×C13—21no—
205C42×C13—21no—
206C42×C13—21no—
207C42×C13—21no—
208C22⋊Dic13—42no—
209C4⋊Dic13—21no—
210C4⋊Dic13—21no—
211C4⋊Dic13—21no—
212C4⋊Dic13—21no—
213#6101—42no—
214#6101—42no—
215C4×Dic13—42no—
216C4×Dic13—42no—
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—21no—
228C2×#1055—44no—
229C2×#1055C2×D412yes—
230C2×#475—131no—
231C22×#103—131no—
232#2440D1311yescharacteristic
233Q8×C22⋊C4—131no—
234#2096—131no—
235#2066—131no—
236#2066—131no—
237#2024—131no—
238#1865—131no—
239#1865—131no—
240#1853—131no—
241#1850—131no—
242#1807—131no—
243#1803—131no—
244#1787—131no—
245C23×C13—21no—
246C23×C13—21no—
247C23×C13—21no—
248C23×C13—21no—
249C23×C13C22⋊Q812yes—
250C23×C13C2×SD1612yes—
251C23×C13#13712yes—
252C23×C13C22×D411yescharacteristic
253Q8×C13—84no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—22no—
261C2×C4×C13—22no—
262C2×C4×C13—22no—
263C2×C4×C13—22no—
264C2×C4×C13—21no—
265C2×C4×C13—22no—
266C2×C4×C13—21no—
267C2×C4×C13—21no—
268C2×C4×C13—21no—
269C2×C4×C13—21no—
270C2×C4×C13—21no—
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×C13—41no—
278C2×C4×C13—41no—
279C2×C4×C13—41no—
280C2×C4×C13—41no—
281C2×C4×C13—41no—
282C2×C4×C13—84no—
283C2×C4×C13C22⋊Q812yes—
284C2×C4×C13C2×SD1612yes—
285C2×C4×C13C2×SD1612yes—
286C2×C4×C13C22×D411yescharacteristic
287C2×C4×C13C22×Q811yescharacteristic
288C2×C4×C13C2×#4111yescharacteristic
289C2×C4×C13C2×#4111yescharacteristic
290C2×C4×C13H(5,𝔽2)11yescharacteristic
291C2×C4×C13H(5,𝔽2)11yescharacteristic
292C2×Dic13—22no—
293C2×Dic13—22no—
294C2×Dic13—22no—
295C2×Dic13—22no—
296C2×Dic13—48no—
297C2×Dic13—41no—
298C2×Dic13—41no—
299C2×Dic13—41no—
300C2×Dic13—41no—
301C2×Dic13—41no—
302C2×Dic13—41no—
303C2×Dic13—41no—
304C2×Dic13—41no—
305Dic26—22no—
306Dic26—22no—
307Dic26—22no—
308Dic26—22no—
309Dic26—22no—
310Dic26—48no—
311Dic26—41no—
312Dic26—41no—
313Dic26C22⋊Q814yescomplemented
314#1055—22no—
315#1055—41no—
316#1055—41no—
317#1055—41no—
318C23×Q8—131no—
319C23×C8—131no—
320C2×C4⋊Q8C2×D1311yescharacteristic
321C2×C22⋊Q8—21no—
322C2×C4×Q8—131no—
323C2×C4×Q8—131no—
324C22×C4⋊C4C2×D1311yescharacteristic
325#475—264no—
326C2×#106—131no—
327C2×#106—131no—
328C2×#106—131no—
329C2×#106—131no—
330C2×C4⋊C8—131no—
331C2×C4⋊C8—131no—
332C2×#103—131no—
333C2×#103—131no—
334C2×#103—131no—
335C2×#103—131no—
336C2×#103—131no—
337C2×#103—131no—
338C2×#103—131no—
339C2×#103—131no—
340C2×#103—264no—
341C2×C22⋊C8—131no—
342#398—21no—
343#395—21no—
344#391—131no—
345#391—131no—
346#391—261no—
347#391—261no—
348#389C2×D1311yescharacteristic
349#389C2×D1311yescharacteristic
350#385—21no—
351#384C2×D1311yescharacteristic
352#380—131no—
353#380—261no—
354#380C2×D1311yescharacteristic
355C4×C22⋊C4—261no—
356C4×C22⋊C4C2×D1311yescharacteristic
357#340—131no—
358#340—131no—
359#340—131no—
360#340—131no—
361#336—131no—
362#336—131no—
363C22×C13—22no—
364C22×C13—22no—
365C22×C13—22no—
366C22×C13—22no—
367C22×C13—22no—
368C22×C13—22no—
369C22×C13#47514yescomplemented
370C22×C13C2×C22⋊Q811yescharacteristic
371C22×C13D4211yescharacteristic
372C22×C13#54611yescharacteristic
373C22×C13C22×SD1611yescharacteristic
374C22×C13C2×#13711yescharacteristic
375C22×C13#57711yescharacteristic
376C22×C13#57811yescharacteristic
377C4×C13—22no—
378C4×C13—22no—
379C4×C13—22no—
380C4×C13—41no—
381C4×C13—42no—
382C4×C13—41no—
383C4×C13—81no—
384C4×C13—81no—
385C4×C13—81no—
386C4×C13C2×C22⋊Q811yescharacteristic
387C4×C13#54311yescharacteristic
388C4×C13#54611yescharacteristic
389C4×C13#55111yescharacteristic
390Dic13—24no—
391Dic13—42no—
392Dic13—81no—
393Dic13—81no—
394C22×Q8—21no—
395C22×Q8—134no—
396C22×Q8—131no—
397C22×Q8—131no—
398C22×Q8—262no—
399C22×Q8—262no—
400C22×Q8—262no—
401C22×Q8—261no—
402C22×Q8—521no—
403C22×Q8—521no—
404C23×C4—21no—
405C23×C4—261no—
406C23×C4C22×D1311yescharacteristic
407C22×C8—131no—
408C22×C8—131no—
409C22×C8—131no—
410C22×C8—131no—
411C22×C8—262no—
412C22×C8—262no—
413C22×C8—521no—
414C4⋊Q8—22no—
415C4⋊Q8—41no—
416C22⋊Q8—44no—
417C4×Q8—262no—
418C4×Q8—262no—
419C4×Q8—521no—
420C4×Q8—521no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—41no—
429C2×C4⋊C4—131no—
430C2×C4⋊C4—131no—
431C2×C4⋊C4—261no—
432C2×C4⋊C4—261no—
433C2×C4⋊C4C22×D1311yescharacteristic
434C2×C4⋊C4C22×D1311yescharacteristic
435C2×C4⋊C4C22×D1311yescharacteristic
436C2×C4⋊C4C22×D1311yescharacteristic
437C2×C22⋊C4—21no—
438C2×C22⋊C4—261no—
439C2×C22⋊C4C22⋊D1311yescharacteristic
440C2×C22⋊C4C22⋊D1311yescharacteristic
441C2×C42—261no—
442C2×C42—261no—
443C2×C42C22×D1311yescharacteristic
444C2×C42C22×D1311yescharacteristic
445#106—262no—
446#106—262no—
447#106—521no—
448#106—521no—
449C4⋊C8—262no—
450C4⋊C8—521no—
451#103—134no—
452#103—262no—
453#103—262no—
454#103—262no—
455#103—262no—
456#103—262no—
457#103—521no—
458#103—521no—
459C22⋊C8—262no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—261no—
464#95—261no—
465#95—261no—
466#95—261no—
467#95—261no—
468#95C22⋊D1311yescharacteristic
469#95C22⋊D1311yescharacteristic
470C2×C13—24no—
471C2×C13#243711yescharacteristic
472C2×C13C2×#47511yescharacteristic
473C2×C13#308211yescharacteristic
474C2×C13#327011yescharacteristic
475C2×C13D4×SD1611yescharacteristic
476C2×C13#329811yescharacteristic
477C2×C13#331611yescharacteristic
478C24C2×C22⋊D1311yescharacteristic
479C2×Q8—42no—
480C2×Q8—42no—
481C2×Q8—81no—
482C2×Q8—132no—
483C2×Q8—132no—
484C2×Q8—132no—
485C2×Q8—132no—
486C2×Q8—268no—
487C2×Q8—264no—
488C2×Q8—261no—
489C2×Q8—261no—
490C2×Q8—261no—
491C2×Q8—261no—
492C2×Q8—261no—
493C2×Q8—261no—
494C2×Q8—261no—
495C2×Q8—261no—
496C2×Q8—522no—
497C2×Q8—522no—
498C2×Q8—524no—
499C2×Q8—524no—
500C2×Q8—524no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—81no—
512C22×C4—261no—
513C22×C4—264no—
514C22×C4—261no—
515C22×C4—261no—
516C22×C4—261no—
517C22×C4—522no—
518C22×C4—522no—
519C22×C4Q8×D1312yes—
520C22×C4#613112yes—
521C22×C4C2×C22⋊D1311yescharacteristic
522C22×C4C2×C22⋊D1311yescharacteristic
523C22×C4C2×C22⋊D1311yescharacteristic
524C22×C4C2×C22⋊D1311yescharacteristic
525C22×C4C2×C22⋊D1311yescharacteristic
526C22×C4C23×D1311yescharacteristic
527C2×C8—132no—
528C2×C8—261no—
529C2×C8—261no—
530C2×C8—261no—
531C2×C8—261no—
532C2×C8—261no—
533C2×C8—261no—
534C2×C8—261no—
535C2×C8—261no—
536C2×C8—261no—
537C2×C8—261no—
538C2×C8—261no—
539C2×C8—524no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—42no—
548C4⋊C4—42no—
549C4⋊C4—42no—
550C4⋊C4—42no—
551C4⋊C4—42no—
552C4⋊C4—81no—
553C4⋊C4—261no—
554C4⋊C4—261no—
555C4⋊C4—261no—
556C4⋊C4—261no—
557C4⋊C4—522no—
558C4⋊C4—522no—
559C4⋊C4D4×D1312yes—
560C22⋊C4—22no—
561C22⋊C4—42no—
562C22⋊C4—522no—
563C22⋊C4#610514yes—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—522no—
569C42—522no—
570C13#2595511yescharacteristic, complemented, Sylow
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23C2×#610512yes—
576C23#8819612yes—
577C23#8820012yes—
578C23C22×C22⋊D1311yescharacteristic
579Q8—84no—
580Q8—134no—
581Q8—262no—
582Q8—262no—
583Q8—262no—
584Q8—262no—
585Q8—262no—
586Q8—528no—
587Q8—521no—
588Q8—521no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—21no—
600C2×C4—22no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—84no—
618C2×C4—262no—
619C2×C4—262no—
620C2×C4—262no—
621C2×C4—262no—
622C2×C4—528no—
623C2×C4—521no—
624C2×C4—521no—
625C2×C4—521no—
626C2×C4—521no—
627C2×C4—521no—
628C2×C4—521no—
629C2×C4—521no—
630C2×C4—521no—
631C2×C4C2×#610512yes—
632C2×C4C2×#610512yes—
633C2×C4#8820012yes—
634C2×C4C2×D4×D1311yescharacteristic
635C2×C4#8825111yescharacteristic
636C2×C4C2×Q8×D1311yescharacteristic
637C2×C4C2×#613111yescharacteristic
638C2×C4#41×D1311yescharacteristic
639C2×C4#8825611yescharacteristic
640C8—262no—
641C8—521no—
642C8—521no—
643C8—521no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—22no—
648C22—22no—
649C22—22no—
650C22#1171875514yescomplemented
651C22C22×#610511yescharacteristic
652C22D4×C22⋊D1311yescharacteristic
653C22C2×#8819611yescharacteristic
654C22C2×#8820011yescharacteristic
655C22#1171953411yescharacteristic
656C22#1171954111yescharacteristic
657C22#1171954311yescharacteristic
658C4—22no—
659C4—22no—
660C4—22no—
661C4—41no—
662C4—41no—
663C4—42no—
664C4—81no—
665C4—81no—
666C4—81no—
667C4—264no—
668C4—522no—
669C4—1041no—
670C4—1041no—
671C4D13×C22⋊Q811yescharacteristic
672C4#1171933511yescharacteristic
673C4#1171933911yescharacteristic
674C4#1171934211yescharacteristic
675C2—24no—
676C2#1311849911yescharacteristic
677C2C2×#1171875511yescharacteristic
678C2#1312467211yescharacteristic
679C2#1312640711yescharacteristic
680C2D4×#610511yescharacteristic
681C2#1312669511yescharacteristic
682C2#1312694111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2440C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#2440D13
hypocenterC13#25955
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2440

Complements

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

NH ≅ G/Ntype
1. C2×#11718755C2semidirect
4. #13116380C2semidirect
5. #13116214C2semidirect
6. #13116214C2semidirect
7. #13115974C2semidirect
8. #13115103C2semidirect
9. #13115103C2semidirect
13. #13114838C2semidirect
71. C22×Dic26Q8semidirect
313. Dic26C22⋊Q8semidirect
369. C22×C13#475semidirect
570. C13#25955semidirect
650. C22#11718755semidirect

Maximal subgroups

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

subgroupindex
C2×#117187552
C22×#880502
C22⋊C4×Dic262
#131163802
#131162142
#131159742
#131151032
#131150292
#131150162
#131148592
#131148382
#131147702
C13×#24402
#2595513