Finite Group Databasebeta

← #15925414

Subgroups — #15925414

Order 3328.

966 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×#11718669C211yesmaximal, characteristic, complemented
2C22×#88048C211yesmaximal, characteristic, complemented
3#13118538C211yesmaximal, characteristic, complemented
4#13116369C211yesmaximal, characteristic, complemented
5#13116337C211yesmaximal, characteristic, complemented
6#13116210C211yesmaximal, characteristic, complemented
7#13116169C211yesmaximal, characteristic, complemented
8#13115599C211yesmaximal, characteristic, complemented
9#13115421C211yesmaximal, characteristic, complemented
10#13115265C211yesmaximal, characteristic
11#13115154C211yesmaximal, characteristic
12#13115097C211yesmaximal, characteristic, complemented
13#13115029C211yesmaximal, characteristic, complemented
14#13115016C211yesmaximal, characteristic, complemented
15C13×#2361C211yesmaximal, characteristic
16C2×C13×#121C2211yescharacteristic
17C2×C4×D4×C13—21no—
18C2×C4×D4×C13C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C4⋊Dic13C2211yescharacteristic
21C23×#1055C2211yescharacteristic
22C2×#88132—21no—
23C2×#88123C2211yescharacteristic
24C13×#390C2211yescharacteristic
25C13×#389C2211yescharacteristic
26C13×#388—21no—
27C13×#386—21no—
28C13×#385—21no—
29C4×C13×C4⋊C4C2211yescharacteristic
30C4×C13×C22⋊C4C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32C2×#88072C2211yescharacteristic
33C2×#88072C2211yescharacteristic
34C2×#88072C2211yescharacteristic
35#11718873C2211yescharacteristic
36C2×C22⋊#1055C2211yescharacteristic
37#11718669—24no—
38C2×#88048—24no—
39C2×#88048C2211yescharacteristic
40C2×#88048C2211yescharacteristic
41C2×#88048C2211yescharacteristic
42C2×#88048C2211yescharacteristic
43C2×#88048C2211yescharacteristic
44C2×#88048C2211yescharacteristic
45#11718611—21no—
46#11718596C2211yescharacteristic
47#11718589C2211yescharacteristic
48#11718589C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C2×C4⋊#1055C2211yescharacteristic
51#11718322—21no—
52#11718317—21no—
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C22×D4×C13—21no—
62C22×D4×C13C2311yescharacteristic
63C23×C4×C13—21no—
64C23×C4×C13—21no—
65C23×C4×C13C2311yescharacteristic
66C23×Dic13—21no—
67C22×Dic26—21no—
68C13×#121—22no—
69C13×#121Q814yescomplemented
70C4×D4×C13—22no—
71C4×D4×C13—41no—
72C4×D4×C13—44no—
73C2×C13×C4⋊C4—22no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4—41no—
77C2×C13×C4⋊C4C2311yescharacteristic
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⋊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×C4⋊Dic13—22no—
91C2×C4⋊Dic13—21no—
92C2×C4⋊Dic13—21no—
93C2×C4⋊Dic13—21no—
94C2×C4⋊Dic13—21no—
95C2×C4⋊Dic13—41no—
96C2×C4⋊Dic13C2311yescharacteristic
97C2×C4⋊Dic13C2311yescharacteristic
98C2×C4⋊Dic13C2311yescharacteristic
99C2×C4⋊Dic13C2311yescharacteristic
100C2×#6101—21no—
101C2×#6101—21no—
102C22×#1055—22no—
103C22×#1055—22no—
104C22×#1055—22no—
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107C22×#1055C2311yescharacteristic
108C22×#1055C2311yescharacteristic
109#88132—44no—
110#88123—22no—
111#88123—41no—
112C13×#95—21no—
113C13×#95—21no—
114C13×#95D411yescharacteristic
115C13×#95D411yescharacteristic
116#88072—22no—
117#88072—22no—
118#88072—22no—
119#88072—41no—
120#88071—21no—
121#88071—21no—
122#88071—21no—
123C22⋊#1055—22no—
124#88048—22no—
125#88048—22no—
126#88048—22no—
127#88048—22no—
128#88048—41no—
129#88048D414yescomplemented
130C4⋊#1055—22no—
131C4⋊#1055—22no—
132#26338—131nomaximal, Sylow
133C24×C13—21no—
134C24×C13C2×D411yescharacteristic
135C2×D4×C13—24no—
136C2×D4×C13—21no—
137C2×D4×C13—21no—
138C2×D4×C13—21no—
139C2×D4×C13—21no—
140C2×D4×C13—21no—
141C2×D4×C13—42no—
142C2×D4×C13—42no—
143C2×D4×C13C2×Q812yes—
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—21no—
151C22×C4×C13—42no—
152C22×C4×C13—42no—
153C22×C4×C13—42no—
154C22×C4×C13—42no—
155C22×C4×C13—81no—
156C22×C4×C13—81no—
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13C2×D411yescharacteristic
159C22×C4×C13C2×D411yescharacteristic
160C22×C4×C13C2×D411yescharacteristic
161C22×C4×C13C2×D411yescharacteristic
162C22×C4×C13C2×Q812yes—
163C22×C4×C13#4112yes—
164C22×C4×C13C2411yescharacteristic
165C22×Dic13—21no—
166C22×Dic13—21no—
167C22×Dic13—21no—
168C22×Dic13—21no—
169C22×Dic13—42no—
170C22×Dic13—42no—
171C22×Dic13—81no—
172C2×Dic26—42no—
173C2×Dic26—42no—
174C2×Dic26—81no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—42no—
180C13×C4⋊C4—42no—
181C13×C4⋊C4C2×D412yes—
182C13×C4⋊C4C2×Q812yes—
183C13×C22⋊C4—22no—
184C13×C22⋊C4—24no—
185C13×C22⋊C4—42no—
186C13×C22⋊C4—42no—
187C13×C22⋊C4—81no—
188C13×C22⋊C4SD1614yes—
189C42×C13—21no—
190C42×C13—21no—
191C42×C13—21no—
192C42×C13—21no—
193C42×C13—42no—
194C22⋊Dic13—42no—
195C4⋊Dic13—21no—
196C4⋊Dic13—21no—
197C4⋊Dic13—21no—
198C4⋊Dic13—21no—
199C4⋊Dic13—21no—
200C4⋊Dic13—21no—
201C4⋊Dic13—21no—
202C4⋊Dic13—42no—
203C4⋊Dic13—42no—
204C4⋊Dic13—42no—
205C4⋊Dic13—81no—
206C4⋊Dic13C2×D412yes—
207#6101—42no—
208#6101—42no—
209C2×#1055—28no—
210C2×#1055—21no—
211C2×#1055—21no—
212C2×#1055—21no—
213C2×#1055—21no—
214C2×#1055—21no—
215C2×#1055—21no—
216C2×#1055—21no—
217C2×#1055—21no—
218C2×#1055—21no—
219C2×#1055—21no—
220C2×#1055C2×D412yes—
221C2×#1055#4112yes—
222C2×#476—131no—
223C22×#106—131no—
224#2440—131no—
225#2361D1311yescharacteristic
226#2094—131no—
227#2088—131no—
228#2065—131no—
229#2058—131no—
230#1948—131no—
231#1920—131no—
232#1893—131no—
233#1874—131no—
234#1864—131no—
235#1853—131no—
236#1850—131no—
237C23×C13—21no—
238C23×C13—21no—
239C23×C13—21no—
240C23×C13—21no—
241C23×C13—22no—
242C23×C13—41no—
243C23×C13—41no—
244C23×C13—41no—
245C23×C13—41no—
246C23×C13—41no—
247C23×C13—41no—
248C23×C13C22⋊Q812yes—
249C23×C13C2×SD1612yes—
250C23×C13AGL(1,ℤ/8)12yes—
251C23×C13C22×D411yescharacteristic
252D4×C13—22no—
253D4×C13—22no—
254D4×C13—48no—
255D4×C13—41no—
256D4×C13—41no—
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—21no—
261C2×C4×C13—21no—
262C2×C4×C13—21no—
263C2×C4×C13—22no—
264C2×C4×C13—22no—
265C2×C4×C13—22no—
266C2×C4×C13—22no—
267C2×C4×C13—22no—
268C2×C4×C13—21no—
269C2×C4×C13—22no—
270C2×C4×C13—21no—
271C2×C4×C13—21no—
272C2×C4×C13—21no—
273C2×C4×C13—21no—
274C2×C4×C13—21no—
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×C13—84no—
284C2×C4×C13C22⋊Q812yes—
285C2×C4×C13C2×SD1612yes—
286C2×C4×C13C2×SD1612yes—
287C2×C4×C13C22×D411yescharacteristic
288C2×C4×C13C22×Q811yescharacteristic
289C2×C4×C13C2×#4111yescharacteristic
290C2×C4×C13C2×#4111yescharacteristic
291C2×C4×C13H(5,𝔽2)11yescharacteristic
292C2×C4×C132−1+411yescharacteristic
293C2×Dic13—22no—
294C2×Dic13—41no—
295C2×Dic13—41no—
296C2×Dic13—41no—
297C2×Dic13—41no—
298C2×Dic13—41no—
299C2×Dic13—41no—
300C2×Dic13—41no—
301C2×Dic13—41no—
302C2×Dic13—41no—
303C2×Dic13—41no—
304C2×Dic13—41no—
305C2×Dic13—84no—
306Dic26—84no—
307#1055—22no—
308#1055—22no—
309#1055—41no—
310#1055—41no—
311C23×C8—131no—
312C2×C4⋊Q8—131no—
313C2×C22⋊Q8—261no—
314C2×#121C2×D1311yescharacteristic
315C2×C4×D4—21no—
316C2×C4×D4C2×D1311yescharacteristic
317C22×C4⋊C4—131no—
318C22×C4⋊C4C2×D1311yescharacteristic
319#476—264no—
320C2×#106—131no—
321C2×#106—131no—
322C2×#106—131no—
323C2×#106—131no—
324C2×#106—131no—
325C2×#106—131no—
326C2×#106—264no—
327C2×C4⋊C8—131no—
328C2×C4⋊C8—131no—
329C2×#102—131no—
330C2×#102—131no—
331C2×#102—131no—
332C2×#102—131no—
333C2×C22⋊C8—131no—
334#398—261no—
335#395—261no—
336#390C2×D1311yescharacteristic
337#389—131no—
338#389—131no—
339#389C2×D1311yescharacteristic
340#388—21no—
341#386—21no—
342#385—21no—
343#385—261no—
344#384—131no—
345#380—131no—
346C4×C4⋊C4C2×D1311yescharacteristic
347C4×C22⋊C4C2×D1311yescharacteristic
348#340—131no—
349#340—131no—
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—22no—
360C22×C13—22no—
361C22×C13—22no—
362C22×C13—42no—
363C22×C13—42no—
364C22×C13—42no—
365C22×C13—81no—
366C22×C13—81no—
367C22×C13—81no—
368C22×C13—81no—
369C22×C13#47614yescomplemented
370C22×C13C2×C22⋊Q811yescharacteristic
371C22×C13D4211yescharacteristic
372C22×C13#54711yescharacteristic
373C22×C13C22×SD1611yescharacteristic
374C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
375C22×C13#57711yescharacteristic
376C22×C13#57711yescharacteristic
377C4×C13—22no—
378C4×C13—22no—
379C4×C13—22no—
380C4×C13—41no—
381C4×C13—41no—
382C4×C13—42no—
383C4×C13—42no—
384C4×C13—81no—
385C4×C13#52511yescharacteristic
386C4×C13#53911yescharacteristic
387C4×C13D4×Q811yescharacteristic
388C4×C13#55411yescharacteristic
389Dic13—42no—
390Dic13—81no—
391Dic13—81no—
392Dic13—81no—
393C22×Q8—261no—
394C22×D4—21no—
395C22×D4C22×D1311yescharacteristic
396C23×C4—21no—
397C23×C4—21no—
398C23×C4—261no—
399C23×C4C22×D1311yescharacteristic
400C22×C8—131no—
401C22×C8—131no—
402C22×C8—131no—
403C22×C8—131no—
404C22×C8—262no—
405C22×C8—262no—
406C22×C8—262no—
407C4⋊Q8—262no—
408C4⋊Q8—521no—
409C22⋊Q8—524no—
410#121—22no—
411#121Dic2614yescomplemented
412C4×D4—22no—
413C4×D4—41no—
414C4×D4—44no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—41no—
419C2×C4⋊C4—131no—
420C2×C4⋊C4—131no—
421C2×C4⋊C4—131no—
422C2×C4⋊C4—131no—
423C2×C4⋊C4—262no—
424C2×C4⋊C4—261no—
425C2×C4⋊C4—261no—
426C2×C4⋊C4—261no—
427C2×C4⋊C4—261no—
428C2×C4⋊C4—261no—
429C2×C4⋊C4—261no—
430C2×C4⋊C4—521no—
431C2×C4⋊C4C22×D1311yescharacteristic
432C2×C4⋊C4C22×D1311yescharacteristic
433C2×C4⋊C4C22×D1311yescharacteristic
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—261no—
439C2×C22⋊C4C22⋊D1311yescharacteristic
440C2×C22⋊C4C22⋊D1311yescharacteristic
441C2×C42—21no—
442C2×C42C22×D1311yescharacteristic
443C2×C42C22×D1311yescharacteristic
444#106—134no—
445#106—262no—
446#106—262no—
447#106—262no—
448#106—262no—
449#106—521no—
450C4⋊C8—262no—
451C4⋊C8—262no—
452#102—262no—
453#102—262no—
454#102—262no—
455#102—521no—
456C22⋊C8—262no—
457#95—21no—
458#95—21no—
459#95—261no—
460#95—261no—
461#95—261no—
462#95C22⋊D1311yescharacteristic
463#95C22⋊D1311yescharacteristic
464C2×C13—24no—
465C2×C13—82no—
466C2×C13#244911yescharacteristic
467C2×C13C2×#47611yescharacteristic
468C2×C13#308411yescharacteristic
469C2×C13#326511yescharacteristic
470C2×C13D4×SD1611yescharacteristic
471C2×C13#333511yescharacteristic
472C2×C13#334511yescharacteristic
473C24—21no—
474C24C2×C22⋊D1311yescharacteristic
475C2×Q8—522no—
476C2×Q8—522no—
477C2×Q8—1041no—
478C2×D4—24no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—42no—
485C2×D4—42no—
486C2×D4C2×Dic2612yes—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—81no—
499C22×C4—81no—
500C22×C4—261no—
501C22×C4—261no—
502C22×C4—261no—
503C22×C4—261no—
504C22×C4—522no—
505C22×C4—522no—
506C22×C4—1041no—
507C22×C4C2×Dic2612yes—
508C22×C4#612712yes—
509C22×C4C2×C22⋊D1311yescharacteristic
510C22×C4C2×C22⋊D1311yescharacteristic
511C22×C4C2×C22⋊D1311yescharacteristic
512C22×C4C2×C22⋊D1311yescharacteristic
513C22×C4C2×C22⋊D1311yescharacteristic
514C22×C4C23×D1311yescharacteristic
515C2×C8—132no—
516C2×C8—132no—
517C2×C8—268no—
518C2×C8—261no—
519C2×C8—261no—
520C2×C8—261no—
521C2×C8—261no—
522C2×C8—261no—
523C2×C8—261no—
524C2×C8—261no—
525C2×C8—261no—
526C2×C8—261no—
527C2×C8—261no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—42no—
533C4⋊C4—42no—
534C4⋊C4—132no—
535C4⋊C4—261no—
536C4⋊C4—261no—
537C4⋊C4—261no—
538C4⋊C4—261no—
539C4⋊C4—261no—
540C4⋊C4—261no—
541C4⋊C4—261no—
542C4⋊C4—522no—
543C4⋊C4—522no—
544C4⋊C4—522no—
545C4⋊C4—522no—
546C4⋊C4—522no—
547C4⋊C4—1041no—
548C4⋊C4C2×Dic2612yes—
549C4⋊C4D4×D1312yes—
550C22⋊C4—22no—
551C22⋊C4—24no—
552C22⋊C4—42no—
553C22⋊C4—42no—
554C22⋊C4—81no—
555C22⋊C4—522no—
556C22⋊C4#610514yes—
557C42—21no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—42no—
562C13#2633811yescharacteristic, complemented, Sylow
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—22no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23#8817812yes—
575C23C2×#610512yes—
576C23#8820312yes—
577C23C22×C22⋊D1311yescharacteristic
578Q8—1044no—
579D4—22no—
580D4—22no—
581D4—48no—
582D4—41no—
583D4—41no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—21no—
596C2×C4—22no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—84no—
610C2×C4—84no—
611C2×C4—262no—
612C2×C4—521no—
613C2×C4—521no—
614C2×C4—521no—
615C2×C4—521no—
616C2×C4—521no—
617C2×C4—521no—
618C2×C4—521no—
619C2×C4—521no—
620C2×C4—521no—
621C2×C4—521no—
622C2×C4—521no—
623C2×C4—1044no—
624C2×C4#8817812yes—
625C2×C4C2×#610512yes—
626C2×C4C2×#610512yes—
627C2×C4C22×Dic2611yescharacteristic
628C2×C4C2×#612711yescharacteristic
629C2×C4C2×D4×D1311yescharacteristic
630C2×C4#8825111yescharacteristic
631C2×C4#41×D1311yescharacteristic
632C2×C4#8825711yescharacteristic
633C8—262no—
634C8—262no—
635C8—521no—
636C8—521no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—42no—
644C22—42no—
645C22—42no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22#1171866914yescomplemented
651C22C2×#8817811yescharacteristic
652C22C22×#610511yescharacteristic
653C22D4×C22⋊D1311yescharacteristic
654C22C2×#8820311yescharacteristic
655C22#1171952911yescharacteristic
656C22#1171954111yescharacteristic
657C22#1171954211yescharacteristic
658C4—22no—
659C4—22no—
660C4—22no—
661C4—42no—
662C4—41no—
663C4—41no—
664C4—42no—
665C4—81no—
666C4—522no—
667C4—1041no—
668C4—1041no—
669C4—1041no—
670C4D4×Dic2611yescharacteristic
671C4#1171924411yescharacteristic
672C4#1171925211yescharacteristic
673C4#1171926911yescharacteristic
674C2—24no—
675C2—82no—
676C2#1311863911yescharacteristic
677C2C2×#1171866911yescharacteristic
678C2#1312469811yescharacteristic
679C2#1312633211yescharacteristic
680C2D4×#610511yescharacteristic
681C2#1312719311yescharacteristic
682C2#1312730011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2361C2
socleC23×C13C22×D4
prime radicalC2×C13×#121C22
hypercenter#2361D13
hypocenterC13#26338
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2361

Complements

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

NH ≅ G/Ntype
1. C2×#11718669C2semidirect
2. C22×#88048C2semidirect
3. #13118538C2semidirect
4. #13116369C2semidirect
5. #13116337C2semidirect
6. #13116210C2semidirect
7. #13116169C2semidirect
8. #13115599C2semidirect
9. #13115421C2semidirect
12. #13115097C2semidirect
13. #13115029C2semidirect
14. #13115016C2semidirect
69. C13×#121Q8semidirect
129. #88048D4semidirect
369. C22×C13#476semidirect
411. #121Dic26semidirect
562. C13#26338semidirect
650. C22#11718669semidirect

Maximal subgroups

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

subgroupindex
C2×#117186692
C22×#880482
#131185382
#131163692
#131163372
#131162102
#131161692
#131155992
#131154212
#131152652
#131151542
#131150972
#131150292
#131150162
C13×#23612
#2633813