Finite Group Databasebeta

← #15925416

Subgroups — #15925416

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×#11718745C211yesmaximal, characteristic, complemented
2C22×#88048C211yesmaximal, characteristic, complemented
3#13117850C211yesmaximal, characteristic
4#13116370C211yesmaximal, characteristic, complemented
5#13116338C211yesmaximal, characteristic, complemented
6#13116207C211yesmaximal, characteristic, complemented
7#13116166C211yesmaximal, characteristic, complemented
8#13115597C211yesmaximal, characteristic, complemented
9#13115418C211yesmaximal, characteristic, complemented
10#13115262C211yesmaximal, characteristic
11#13115153C211yesmaximal, characteristic
12#13115096C211yesmaximal, characteristic, complemented
13#13115028C211yesmaximal, characteristic, complemented
14#13115016C211yesmaximal, characteristic, complemented
15C13×#2440C211yesmaximal, characteristic, complemented
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C13×C22⋊Q8—21no—
18C22×C13×C4⋊C4C2211yescharacteristic
19C2×#88184C2211yescharacteristic
20C22×C4⋊Dic13C2211yescharacteristic
21C23×#1055C2211yescharacteristic
22C2×#88135—21no—
23C2×C4×D52C2211yescharacteristic
24C13×#398—21no—
25C13×#395—21no—
26C13×#389C2211yescharacteristic
27C13×#389C2211yescharacteristic
28C13×#385—21no—
29C13×#384C2211yescharacteristic
30C13×#380C2211yescharacteristic
31C4×C13×C22⋊C4C2211yescharacteristic
32C2×C22⋊#1055C2211yescharacteristic
33#11718745—24no—
34C2×#88049C2211yescharacteristic
35C2×#88049C2211yescharacteristic
36C2×#88049C2211yescharacteristic
37C2×#88049C2211yescharacteristic
38C2×#88048—24no—
39C2×#88048C2211yescharacteristic
40C2×#88048C2211yescharacteristic
41C2×#88048C2211yescharacteristic
42C2×#88048C2211yescharacteristic
43C2×#88048C2211yescharacteristic
44C2×#88048C2211yescharacteristic
45#11718619—21no—
46#11718600C2211yescharacteristic
47C4×C4⋊Dic13C2211yescharacteristic
48#11718589C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C2×C4⋊#1055C2211yescharacteristic
51#11718331—21no—
52#11718329—21no—
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C22×Q8×C13—21no—
62C23×C4×C13—21no—
63C23×C4×C13C2311yescharacteristic
64C22×C22⋊D13—21no—
65C23×Dic13—21no—
66C22×D52C2311yescharacteristic
67C22×C4×D13—21no—
68C13×C4⋊Q8—22no—
69C13×C4⋊Q8—41no—
70C13×C22⋊Q8—44no—
71C2×C13×C4⋊C4—22no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4—21no—
78C2×C13×C4⋊C4—41no—
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C4⋊C4C2311yescharacteristic
82C2×C13×C4⋊C4C2311yescharacteristic
83C2×C13×C22⋊C4—21no—
84C2×C13×C22⋊C4D411yescharacteristic
85C2×C13×C22⋊C4D411yescharacteristic
86C2×C42×C13C2311yescharacteristic
87C2×C42×C13C2311yescharacteristic
88#88184—22no—
89#88184Q814yescomplemented
90C2×#6103—21no—
91C2×#6103—21no—
92C2×#6103—21no—
93C2×#6103—21no—
94C2×C4⋊Dic13—22no—
95C2×C4⋊Dic13—21no—
96C2×C4⋊Dic13—41no—
97C2×C4⋊Dic13C2311yescharacteristic
98C2×C4⋊Dic13C2311yescharacteristic
99C2×C4⋊Dic13C2311yescharacteristic
100C2×#6101—21no—
101C2×C4×Dic13—21no—
102C22×#1055—22no—
103C22×#1055—22no—
104C22×#1055—22no—
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107C22×#1055C2311yescharacteristic
108C22×#1055C2311yescharacteristic
109#88135—44no—
110C4×D52—22no—
111C4×D52—41no—
112C13×#95—21no—
113C13×#95—21no—
114C13×#95—21no—
115C13×#95D411yescharacteristic
116C13×#95D411yescharacteristic
117#88071—21no—
118#88071—21no—
119C22⋊#1055—22no—
120#88049—22no—
121#88049—22no—
122#88049—22no—
123#88049—41no—
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×C13C2×D411yescharacteristic
134C23×D13—21no—
135C2×Q8×C13—42no—
136C2×Q8×C13—42no—
137C2×Q8×C13—81no—
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×C13—42no—
147C22×C4×C13—42no—
148C22×C4×C13—81no—
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×Q812yes—
155C22×C4×C13#4112yes—
156C22×C4×C13C2411yescharacteristic
157C2×C22⋊D13—24no—
158C2×C22⋊D13—42no—
159C2×C22⋊D13—42no—
160C22×Dic13—21no—
161C22×Dic13—21no—
162C22×Dic13—21no—
163C22×Dic13—42no—
164C22×Dic13—42no—
165C22×Dic13—81no—
166C2×D52—21no—
167C2×D52—21no—
168C2×D52—21no—
169C2×D52—21no—
170C2×D52—21no—
171C2×D52C2×Q812yes—
172C2×C4×D13—42no—
173C2×C4×D13—42no—
174C2×C4×D13—81no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—42no—
183C13×C4⋊C4—42no—
184C13×C4⋊C4—42no—
185C13×C4⋊C4—42no—
186C13×C4⋊C4—42no—
187C13×C4⋊C4—81no—
188C13×C4⋊C4C2×D412yes—
189C13×C22⋊C4—22no—
190C13×C22⋊C4—42no—
191C13×C22⋊C4SD1614yes—
192C42×C13—21no—
193C42×C13—21no—
194C42×C13—21no—
195C42×C13—21no—
196#6103—24no—
197#6103—42no—
198#6103—42no—
199#6103—81no—
200C4⋊Dic13—21no—
201C4⋊Dic13—21no—
202C4⋊Dic13—21no—
203C4⋊Dic13—21no—
204C4⋊Dic13—42no—
205C4⋊Dic13C2×D412yes—
206C4⋊Dic13C2×Q812yes—
207#6101—42no—
208C4×Dic13—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#2440D1311yescharacteristic, complemented
225#2361—131no—
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×C13C22⋊Q812yes—
242C23×C13C2×SD1612yes—
243C23×C13AGL(1,ℤ/8)12yes—
244C23×C13C22×D411yescharacteristic
245C22×D13—22no—
246C22×D13—41no—
247C22×D13—41no—
248C22×D13—41no—
249C22×D13—41no—
250C22×D13—41no—
251C22×D13—41no—
252Q8×C13—84no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—22no—
260C2×C4×C13—22no—
261C2×C4×C13—22no—
262C2×C4×C13—22no—
263C2×C4×C13—21no—
264C2×C4×C13—22no—
265C2×C4×C13—21no—
266C2×C4×C13—21no—
267C2×C4×C13—21no—
268C2×C4×C13—21no—
269C2×C4×C13—21no—
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×C13—41no—
278C2×C4×C13—41no—
279C2×C4×C13—41no—
280C2×C4×C13—41no—
281C2×C4×C13—84no—
282C2×C4×C13C22⋊Q812yes—
283C2×C4×C13C2×SD1612yes—
284C2×C4×C13C2×SD1612yes—
285C2×C4×C13C22×D411yescharacteristic
286C2×C4×C13C22×Q811yescharacteristic
287C2×C4×C13C2×#4111yescharacteristic
288C2×C4×C13C2×#4111yescharacteristic
289C2×C4×C13H(5,𝔽2)11yescharacteristic
290C2×C4×C132−1+411yescharacteristic
291C22⋊D13—48no—
292C2×Dic13—22no—
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—84no—
302D52—22no—
303D52—22no—
304D52—41no—
305D52—41no—
306C4×D13—84no—
307#1055—22no—
308#1055—22no—
309#1055—41no—
310#1055—41no—
311C23×C8—131no—
312C2×C4⋊Q8C2×D1311yescharacteristic
313C2×C22⋊Q8—21no—
314C2×#121—131no—
315C2×C4×D4—131no—
316C2×C4×D4—261no—
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—21no—
335#395—21no—
336#390—131no—
337#389—131no—
338#389C2×D1311yescharacteristic
339#389C2×D1311yescharacteristic
340#388—261no—
341#386—261no—
342#385—21no—
343#385—261no—
344#384C2×D1311yescharacteristic
345#380C2×D1311yescharacteristic
346C4×C4⋊C4—131no—
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#47614yescomplemented
363C22×C13C2×C22⋊Q811yescharacteristic
364C22×C13D4211yescharacteristic
365C22×C13#54711yescharacteristic
366C22×C13C22×SD1611yescharacteristic
367C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
368C22×C13#57711yescharacteristic
369C22×C13#57711yescharacteristic
370C2×D13—42no—
371C2×D13—42no—
372C2×D13—42no—
373C2×D13—81no—
374C2×D13—81no—
375C2×D13—81no—
376C2×D13—81no—
377C4×C13—22no—
378C4×C13—22no—
379C4×C13—22no—
380C4×C13—41no—
381C4×C13—41no—
382C4×C13—42no—
383C4×C13—81no—
384C4×C13—81no—
385C4×C13—81no—
386C4×C13#52511yescharacteristic
387C4×C13#53911yescharacteristic
388C4×C13D4×Q811yescharacteristic
389C4×C13#55411yescharacteristic
390Dic13—42no—
391Dic13—42no—
392Dic13—81no—
393C22×Q8—21no—
394C22×D4—131no—
395C22×D4—261no—
396C23×C4—21no—
397C23×C4—261no—
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—22no—
408C4⋊Q8—41no—
409C22⋊Q8—44no—
410#121—134no—
411#121—262no—
412C4×D4—262no—
413C4×D4—521no—
414C4×D4—524no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—41no—
423C2×C4⋊C4—131no—
424C2×C4⋊C4—131no—
425C2×C4⋊C4—131no—
426C2×C4⋊C4—262no—
427C2×C4⋊C4—261no—
428C2×C4⋊C4—261no—
429C2×C4⋊C4—521no—
430C2×C4⋊C4C22×D1311yescharacteristic
431C2×C4⋊C4C22×D1311yescharacteristic
432C2×C4⋊C4C22×D1311yescharacteristic
433C2×C4⋊C4C22×D1311yescharacteristic
434C2×C22⋊C4—21no—
435C2×C22⋊C4—261no—
436C2×C22⋊C4—261no—
437C2×C22⋊C4—261no—
438C2×C22⋊C4—261no—
439C2×C22⋊C4C22⋊D1311yescharacteristic
440C2×C22⋊C4C22⋊D1311yescharacteristic
441C2×C42—261no—
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—21no—
460#95—261no—
461#95—261no—
462#95C22⋊D1311yescharacteristic
463#95C22⋊D1311yescharacteristic
464C2×C13—24no—
465C2×C13#244911yescharacteristic
466C2×C13C2×#47611yescharacteristic
467C2×C13#308411yescharacteristic
468C2×C13#326511yescharacteristic
469C2×C13D4×SD1611yescharacteristic
470C2×C13#333511yescharacteristic
471C2×C13#334511yescharacteristic
472D13—82no—
473C24—261no—
474C24C2×C22⋊D1311yescharacteristic
475C2×Q8—42no—
476C2×Q8—42no—
477C2×Q8—81no—
478C2×D4—132no—
479C2×D4—264no—
480C2×D4—261no—
481C2×D4—261no—
482C2×D4—261no—
483C2×D4—261no—
484C2×D4—261no—
485C2×D4—522no—
486C2×D4—522no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—81no—
498C22×C4—261no—
499C22×C4—261no—
500C22×C4—261no—
501C22×C4—522no—
502C22×C4—522no—
503C22×C4—522no—
504C22×C4—522no—
505C22×C4—1041no—
506C22×C4—1041no—
507C22×C4Q8×D1312yes—
508C22×C4#613112yes—
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—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—42no—
536C4⋊C4—42no—
537C4⋊C4—42no—
538C4⋊C4—42no—
539C4⋊C4—42no—
540C4⋊C4—81no—
541C4⋊C4—132no—
542C4⋊C4—132no—
543C4⋊C4—261no—
544C4⋊C4—261no—
545C4⋊C4—261no—
546C4⋊C4—261no—
547C4⋊C4—522no—
548C4⋊C4—522no—
549C4⋊C4D4×D1312yes—
550C22⋊C4—22no—
551C22⋊C4—42no—
552C22⋊C4—264no—
553C22⋊C4—522no—
554C22⋊C4—522no—
555C22⋊C4—1041no—
556C22⋊C4#610614yes—
557C42—21no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—522no—
562C13#2633811yescharacteristic, complemented, Sylow
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—262no—
568C23—521no—
569C23—521no—
570C23—521no—
571C23—521no—
572C23—521no—
573C23—521no—
574C23#8818612yes—
575C23C2×#610612yes—
576C23#8820012yes—
577C23C22×C22⋊D1311yescharacteristic
578Q8—84no—
579D4—262no—
580D4—262no—
581D4—528no—
582D4—521no—
583D4—521no—
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—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—84no—
613C2×C4—262no—
614C2×C4—262no—
615C2×C4—521no—
616C2×C4—521no—
617C2×C4—521no—
618C2×C4—521no—
619C2×C4—521no—
620C2×C4—521no—
621C2×C4—521no—
622C2×C4—1044no—
623C2×C4—1044no—
624C2×C4C2×#610612yes—
625C2×C4C2×#610612yes—
626C2×C4#8820012yes—
627C2×C4C2×D4×D1311yescharacteristic
628C2×C4#8825111yescharacteristic
629C2×C4C2×Q8×D1311yescharacteristic
630C2×C4C2×#613111yescharacteristic
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—522no—
644C22—522no—
645C22—522no—
646C22—1041no—
647C22—1041no—
648C22—1041no—
649C22—1041no—
650C22#1171874514yescomplemented
651C22C2×#8818611yescharacteristic
652C22D4×C22⋊D1311yescharacteristic
653C22C22×#610611yescharacteristic
654C22C2×#8820011yescharacteristic
655C22#1171952911yescharacteristic
656C22#1171954111yescharacteristic
657C22#1171954211yescharacteristic
658C4—22no—
659C4—22no—
660C4—22no—
661C4—41no—
662C4—41no—
663C4—42no—
664C4—81no—
665C4—81no—
666C4—81no—
667C4—522no—
668C4—522no—
669C4—1041no—
670C4#1171933211yescharacteristic
671C4#1171933711yescharacteristic
672C4#1171934111yescharacteristic
673C4#1171935011yescharacteristic
674C2—24no—
675C2—1042no—
676C2#1311864111yescharacteristic
677C2C2×#1171874511yescharacteristic
678C2#1312469411yescharacteristic
679C2#1312632711yescharacteristic
680C2D4×#610611yescharacteristic
681C2#1312718711yescharacteristic
682C2#1312730611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2440C2
socleC23×C13C22×D4
prime radicalC2×#88184C22
hypercenter#2440D13
hypocenterC13#26338
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×#11718745C2semidirect
2. C22×#88048C2semidirect
4. #13116370C2semidirect
5. #13116338C2semidirect
6. #13116207C2semidirect
7. #13116166C2semidirect
8. #13115597C2semidirect
9. #13115418C2semidirect
12. #13115096C2semidirect
13. #13115028C2semidirect
14. #13115016C2semidirect
15. C13×#2440C2semidirect
89. #88184Q8semidirect
129. #88048D4semidirect
224. #2440D13semidirect
362. C22×C13#476semidirect
562. C13#26338semidirect
650. C22#11718745semidirect

Maximal subgroups

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

subgroupindex
C2×#117187452
C22×#880482
#131178502
#131163702
#131163382
#131162072
#131161662
#131155972
#131154182
#131152622
#131151532
#131150962
#131150282
#131150162
C13×#24402
#2633813