Finite Group Databasebeta

← #15907943

Subgroups — #15907943

Order 3328.

862 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117765C211yesmaximal, characteristic, complemented
2#13116267C211yesmaximal, characteristic, complemented
3#13116262C211yesmaximal, characteristic, complemented
4#13116015C211yesmaximal, characteristic, complemented
5#13116015C211yesmaximal, characteristic, complemented
6#13115635C211yesmaximal, characteristic, complemented
7#13115592C211yesmaximal, characteristic, complemented
8#13115159C211yesmaximal, characteristic, complemented
9#13115154C211yesmaximal, characteristic, complemented
10#13114971C211yesmaximal, characteristic, complemented
11#13114928C211yesmaximal, characteristic, complemented
12#13114924C211yesmaximal, characteristic, complemented
13#13114846C211yesmaximal, characteristic, complemented
14#13114661C211yesmaximal, characteristic, complemented
15C13×#2537C211yesmaximal, characteristic
16C2×C13×#121—21no—
17C2×C13×#121C2211yescharacteristic
18C2×C13×#121C2211yescharacteristic
19C2×C4×D4×C13C2211yescharacteristic
20C2×C4×D4×C13C2211yescharacteristic
21C2×#88180C2211yescharacteristic
22C22×C4⋊Dic13C2211yescharacteristic
23C13×#394—21no—
24C13×#394—21no—
25C13×#384C2211yescharacteristic
26C13×#380—21no—
27C13×#380C2211yescharacteristic
28C13×#380C2211yescharacteristic
29#11718881—21no—
30C2×#88072C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32C2×#88072C2211yescharacteristic
33C2×#88072C2211yescharacteristic
34#11718873C2211yescharacteristic
35#11718873C2211yescharacteristic
36C2×C22⋊#1055C2211yescharacteristic
37C2×C22⋊#1055C2211yescharacteristic
38C2×C22⋊#1055C2211yescharacteristic
39C2×C22⋊#1055C2211yescharacteristic
40#11718642—21no—
41C2×#88047C2211yescharacteristic
42C2×#88047C2211yescharacteristic
43#11718612—21no—
44C22⋊C4×Dic13—21no—
45#11718597C2211yescharacteristic
46C4×C4⋊Dic13C2211yescharacteristic
47C2×C4⋊#1055C2211yescharacteristic
48C2×#88043C2211yescharacteristic
49#11718121C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59C22×D4×C13—21no—
60C22×D4×C13—21no—
61C22×D4×C13D411yescharacteristic
62C22×D4×C13C2311yescharacteristic
63C23×C4×C13—21no—
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C23×Dic13—21no—
67C13×#121—22no—
68C13×#121—22no—
69C13×#121—41no—
70C13×#121—41no—
71C13×#121—44no—
72C4×D4×C13—22no—
73C4×D4×C13—22no—
74C4×D4×C13—22no—
75C4×D4×C13—22no—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4—21no—
78C2×C13×C4⋊C4D411yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C4⋊C4C2311yescharacteristic
82C2×C13×C22⋊C4—21no—
83C2×C13×C22⋊C4—21no—
84C2×C13×C22⋊C4—21no—
85C2×C13×C22⋊C4—21no—
86C2×C13×C22⋊C4—21no—
87C2×C13×C22⋊C4D411yescharacteristic
88C2×C13×C22⋊C4D411yescharacteristic
89C2×C42×C13C2311yescharacteristic
90C2×C22⋊Dic13—21no—
91C2×C22⋊Dic13—21no—
92C2×C22⋊Dic13—21no—
93#88180—22no—
94#88180—41no—
95C2×C4⋊Dic13—22no—
96C2×C4⋊Dic13—21no—
97C2×C4⋊Dic13—41no—
98C2×C4⋊Dic13C2311yescharacteristic
99C2×C4⋊Dic13C2311yescharacteristic
100C2×C4⋊Dic13C2311yescharacteristic
101C2×C4⋊Dic13C2311yescharacteristic
102C2×C4×Dic13—21no—
103C2×C4×Dic13—21no—
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107C22×#1055C2311yescharacteristic
108C13×#95—21no—
109C13×#95—21no—
110#88072—22no—
111#88072—22no—
112#88072—41no—
113#88072—41no—
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88071—21no—
118#88071—21no—
119C22⋊#1055—41no—
120C22⋊#1055—41no—
121C22⋊#1055—41no—
122C22⋊#1055—41no—
123#88047—41no—
124#88047—41no—
125C4⋊#1055—22no—
126#88043—22no—
127#24981—131nomaximal, Sylow
128C24×C13—21no—
129C24×C13C2×D411yescharacteristic
130C24×C13C2×D411yescharacteristic
131C2×D4×C13—22no—
132C2×D4×C13—22no—
133C2×D4×C13—21no—
134C2×D4×C13—21no—
135C2×D4×C13—21no—
136C2×D4×C13—21no—
137C2×D4×C13—21no—
138C2×D4×C13—41no—
139C2×D4×C13—42no—
140C2×D4×C13—42no—
141C2×D4×C13—42no—
142C2×D4×C13—42no—
143C2×D4×C13—81no—
144C2×D4×C13—81no—
145C2×D4×C13#4112yes—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
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—21no—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—42no—
162C22×C4×C13—42no—
163C22×C4×C13—42no—
164C22×C4×C13C2×D411yescharacteristic
165C22×C4×C13C2×D411yescharacteristic
166C22×C4×C13C2×D411yescharacteristic
167C22×C4×C13C2×D411yescharacteristic
168C22×C4×C13C2411yescharacteristic
169C22×Dic13—21no—
170C22×Dic13—21no—
171C22×Dic13—21no—
172C22×Dic13—21no—
173C22×Dic13—42no—
174C22×Dic13—42no—
175C22×Dic13—81no—
176C13×C4⋊C4—22no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—21no—
183C13×C4⋊C4—42no—
184C13×C4⋊C4—81no—
185C13×C22⋊C4—22no—
186C13×C22⋊C4—22no—
187C13×C22⋊C4—42no—
188C13×C22⋊C4—42no—
189C13×C22⋊C4—42no—
190C13×C22⋊C4—42no—
191C13×C22⋊C4—42no—
192C42×C13#4112yes—
193C42×C13#4112yes—
194C22⋊Dic13—42no—
195C22⋊Dic13—42no—
196C22⋊Dic13—81no—
197C4⋊Dic13—21no—
198C4⋊Dic13—21no—
199C4⋊Dic13—21no—
200C4⋊Dic13—21no—
201C4⋊Dic13—21no—
202C4⋊Dic13—21no—
203C4⋊Dic13—21no—
204C4⋊Dic13—42no—
205C4⋊Dic13#4112yes—
206C4×Dic13—42no—
207C4×Dic13—81no—
208C2×#1055—21no—
209C2×#1055—21no—
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—
220#2537D1311yescharacteristic
221#2352—131no—
222#2076—131no—
223#2075—131no—
224#2033—131no—
225#2033—131no—
226#1955—131no—
227#1947—131no—
228#1875—131no—
229#1874—131no—
230#1836—131no—
231#1825—131no—
232#1824—131no—
233#1804—131no—
234#1762—131no—
235C23×C13—21no—
236C23×C13—21no—
237C23×C13—21no—
238C23×C13—21no—
239C23×C13—21no—
240C23×C13—21no—
241C23×C13—21no—
242C23×C13—21no—
243C23×C13—22no—
244C23×C13—21no—
245C23×C13—21no—
246C23×C13—21no—
247C23×C13—21no—
248C23×C13—21no—
249C23×C13—41no—
250C23×C13—41no—
251C23×C13—41no—
252C23×C13—41no—
253C23×C13—41no—
254C23×C13—41no—
255C23×C13AGL(1,ℤ/8)12yes—
256C23×C13C22×D411yescharacteristic
257D4×C13—22no—
258D4×C13—22no—
259D4×C13—44no—
260D4×C13—41no—
261D4×C13—41no—
262D4×C13—84no—
263D4×C13—84no—
264C2×C4×C13—21no—
265C2×C4×C13—21no—
266C2×C4×C13—21no—
267C2×C4×C13—21no—
268C2×C4×C13—21no—
269C2×C4×C13—21no—
270C2×C4×C13—21no—
271C2×C4×C13—21no—
272C2×C4×C13—21no—
273C2×C4×C13—21no—
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—41no—
283C2×C4×C13—41no—
284C2×C4×C13—41no—
285C2×C4×C13—41no—
286C2×C4×C13—41no—
287C2×C4×C13—41no—
288C2×C4×C13—41no—
289C2×C4×C13—41no—
290C2×C4×C13—41no—
291C2×C4×C13—84no—
292C2×C4×C13#12312yes—
293C2×C4×C13#12312yes—
294C2×C4×C13C2×#4111yescharacteristic
295C2×C4×C13C2×#4111yescharacteristic
296C2×C4×C13C2×#4111yescharacteristic
297C2×C4×C13C2×#4111yescharacteristic
298C2×C4×C13H(5,𝔽2)11yescharacteristic
299C2×C4×C13H(5,𝔽2)11yescharacteristic
300C2×Dic13—22no—
301C2×Dic13—41no—
302C2×Dic13—41no—
303C2×Dic13—41no—
304C2×Dic13—41no—
305C2×Dic13—41no—
306C2×Dic13—41no—
307C2×Dic13—41no—
308C2×Dic13—41no—
309C2×Dic13—41no—
310C2×Dic13—41no—
311C2×Dic13—41no—
312C2×Dic13—84no—
313#1055—41no—
314#1055—41no—
315#1055—41no—
316#1055—41no—
317C2×#121—21no—
318C2×#121C2×D1311yescharacteristic
319C2×#121C2×D1311yescharacteristic
320C2×C4×D4C2×D1311yescharacteristic
321C2×C4×D4C2×D1311yescharacteristic
322C2×#117—131no—
323C22×C4⋊C4—131no—
324C2×#107—131no—
325C2×#107—131no—
326C2×C4⋊C8—131no—
327C2×#102—131no—
328C2×#102—131no—
329C2×#102—131no—
330C2×#102—131no—
331C2×C22⋊C8—131no—
332C2×C22⋊C8—131no—
333C2×C22⋊C8—131no—
334C2×C22⋊C8—131no—
335C2×#97—131no—
336#394—21no—
337#394—21no—
338#388—261no—
339#387—261no—
340#386—261no—
341#384C2×D1311yescharacteristic
342#382—131no—
343#380—21no—
344#380—131no—
345#380—131no—
346#380C2×D1311yescharacteristic
347#380C2×D1311yescharacteristic
348C4×C4⋊C4—131no—
349C4×C22⋊C4—261no—
350#340—131no—
351#340—131no—
352#340—131no—
353#340—131no—
354#340—131no—
355#340—131no—
356#340—131no—
357#340—131no—
358#340—131no—
359#340—131no—
360C22×C13—22no—
361C22×C13—22no—
362C22×C13—22no—
363C22×C13—41no—
364C22×C13—41no—
365C22×C13—41no—
366C22×C13—41no—
367C22×C13—41no—
368C22×C13—41no—
369C22×C13—41no—
370C22×C13—42no—
371C22×C13—41no—
372C22×C13—41no—
373C22×C13—42no—
374C22×C13—41no—
375C22×C13—42no—
376C22×C13—41no—
377C22×C13—81no—
378C22×C13—81no—
379C22×C13—81no—
380C22×C13—81no—
381C22×C13C2×#12311yescharacteristic
382C22×C13#54611yescharacteristic
383C22×C13#54611yescharacteristic
384C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
385C22×C13#57511yescharacteristic
386C22×C13#57611yescharacteristic
387C22×C13#57811yescharacteristic
388C4×C13—22no—
389C4×C13—22no—
390C4×C13—41no—
391C4×C13—41no—
392C4×C13—81no—
393C4×C13—81no—
394C4×C13—81no—
395C4×C13#52911yescharacteristic
396C4×C13#54011yescharacteristic
397C4×C13#55311yescharacteristic
398C4×C13#55511yescharacteristic
399Dic13—42no—
400Dic13—81no—
401Dic13—81no—
402Dic13—81no—
403C22×D4—21no—
404C22×D4—21no—
405C22×D4C22⋊D1311yescharacteristic
406C22×D4C22×D1311yescharacteristic
407C23×C4—21no—
408C23×C4—261no—
409C23×C4C22×D1311yescharacteristic
410C23×C4C22×D1311yescharacteristic
411C22×C8—131no—
412C22×C8—131no—
413C22×C8—131no—
414C22×C8—131no—
415#121—22no—
416#121—22no—
417#121—41no—
418#121—41no—
419#121—44no—
420C4×D4—22no—
421C4×D4—22no—
422C4×D4—22no—
423C4×D4—22no—
424#117—262no—
425#117—521no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—131no—
429C2×C4⋊C4—131no—
430C2×C4⋊C4—131no—
431C2×C4⋊C4—131no—
432C2×C4⋊C4—262no—
433C2×C4⋊C4—261no—
434C2×C4⋊C4—521no—
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⋊C4—261no—
447C2×C22⋊C4C22⋊D1311yescharacteristic
448C2×C22⋊C4C22⋊D1311yescharacteristic
449C2×C42—261no—
450C2×C42—261no—
451C2×C42C22×D1311yescharacteristic
452#107—521no—
453#107—521no—
454C4⋊C8—262no—
455#102—262no—
456#102—262no—
457#102—521no—
458#102—521no—
459C22⋊C8—521no—
460C22⋊C8—521no—
461C22⋊C8—521no—
462C22⋊C8—521no—
463#97—262no—
464#95—21no—
465#95—21no—
466#95—261no—
467#95—261no—
468#95—261no—
469#95—261no—
470#95—261no—
471C2×C13—42no—
472C2×C13—81no—
473C2×C13—82no—
474C2×C13#242011yescharacteristic
475C2×C13#309411yescharacteristic
476C2×C13#309811yescharacteristic
477C2×C13#330811yescharacteristic
478C2×C13#331511yescharacteristic
479C2×C13#331811yescharacteristic
480C2×C13#331911yescharacteristic
481C24—21no—
482C24C2×C22⋊D1311yescharacteristic
483C24C2×C22⋊D1311yescharacteristic
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—41no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—81no—
497C2×D4—81no—
498C2×D4#612912yes—
499C22×C4—21no—
500C22×C4—21no—
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—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—261no—
518C22×C4—261no—
519C22×C4—261no—
520C22×C4—261no—
521C22×C4—522no—
522C22×C4—522no—
523C22×C4—1041no—
524C22×C4C2×C22⋊D1311yescharacteristic
525C22×C4C2×C22⋊D1311yescharacteristic
526C22×C4C2×C22⋊D1311yescharacteristic
527C22×C4C2×C22⋊D1311yescharacteristic
528C22×C4C23×D1311yescharacteristic
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—261no—
540C2×C8—261no—
541C4⋊C4—22no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—42no—
549C4⋊C4—81no—
550C4⋊C4—132no—
551C4⋊C4—261no—
552C4⋊C4—261no—
553C4⋊C4—261no—
554C4⋊C4—261no—
555C4⋊C4—261no—
556C4⋊C4—261no—
557C4⋊C4—261no—
558C4⋊C4—522no—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—42no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—522no—
567C22⋊C4—522no—
568C22⋊C4—1041no—
569C42—522no—
570C42—1041no—
571C42#612912yes—
572C42#612912yes—
573C13#2498111yescharacteristic, complemented, Sylow
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—22no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23#8818612yes—
595C23C22×C22⋊D1311yescharacteristic
596D4—22no—
597D4—22no—
598D4—44no—
599D4—41no—
600D4—41no—
601D4—84no—
602D4—84no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
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—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—84no—
631C2×C4—262no—
632C2×C4—521no—
633C2×C4—521no—
634C2×C4—521no—
635C2×C4—521no—
636C2×C4—521no—
637C2×C4—521no—
638C2×C4—521no—
639C2×C4—521no—
640C2×C4—521no—
641C2×C4—521no—
642C2×C4—521no—
643C2×C4—1044no—
644C2×C4#8818912yes—
645C2×C4#8818912yes—
646C2×C4C2×#612911yescharacteristic
647C2×C4C2×#612911yescharacteristic
648C2×C4C2×#612911yescharacteristic
649C2×C4#8825111yescharacteristic
650C2×C4#41×D1311yescharacteristic
651C2×C4#8825611yescharacteristic
652C8—521no—
653C8—521no—
654C8—521no—
655C8—521no—
656C22—22no—
657C22—22no—
658C22—22no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—41no—
664C22—42no—
665C22—41no—
666C22—42no—
667C22—41no—
668C22—41no—
669C22—42no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22C2×#8818611yescharacteristic
678C22C2×#8818911yescharacteristic
679C22#1171951111yescharacteristic
680C22#1171952711yescharacteristic
681C22#1171953411yescharacteristic
682C22#1171954011yescharacteristic
683C22#1171954311yescharacteristic
684C4—22no—
685C4—22no—
686C4—41no—
687C4—41no—
688C4—81no—
689C4—81no—
690C4—81no—
691C4—522no—
692C4—1041no—
693C4—1041no—
694C4—1041no—
695C4#1171930511yescharacteristic
696C4#1171932111yescharacteristic
697C4#1171932311yescharacteristic
698C4#1171932411yescharacteristic
699C2—42no—
700C2—81no—
701C2—82no—
702C2#1311832411yescharacteristic
703C2#1312477211yescharacteristic
704C2#1312481011yescharacteristic
705C2#1312682111yescharacteristic
706C2#1312693211yescharacteristic
707C2#1312697711yescharacteristic
708C2#1312698611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
Fitting, prime radicalC13×#2537C2
socleC23×C13C22×D4
hypercenter#2537D13
hypocenterC13#24981
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2537

Complements

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

NH ≅ G/Ntype
1. #13117765C2semidirect
2. #13116267C2semidirect
3. #13116262C2semidirect
4. #13116015C2semidirect
5. #13116015C2semidirect
6. #13115635C2semidirect
7. #13115592C2semidirect
8. #13115159C2semidirect
9. #13115154C2semidirect
10. #13114971C2semidirect
11. #13114928C2semidirect
12. #13114924C2semidirect
13. #13114846C2semidirect
14. #13114661C2semidirect
573. C13#24981semidirect

Maximal subgroups

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

subgroupindex
#131177652
#131162672
#131162622
#131160152
#131156352
#131155922
#131151592
#131151542
#131149712
#131149282
#131149242
#131148462
#131146612
C13×#25372
#2498113