Finite Group Databasebeta

← #15907986

Subgroups — #15907986

Order 3328.

778 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13119758C211yesmaximal, characteristic
2#13116267C211yesmaximal, characteristic, complemented
3#13116262C211yesmaximal, characteristic, complemented
4#13116039C211yesmaximal, characteristic, complemented
5#13116039C211yesmaximal, characteristic, complemented
6#13115635C211yesmaximal, characteristic
7#13115594C211yesmaximal, characteristic, complemented
8#13115148C211yesmaximal, characteristic, complemented
9#13115143C211yesmaximal, characteristic, complemented
10#13114969C211yesmaximal, characteristic, complemented
11#13114931C211yesmaximal, characteristic, complemented
12#13114922C211yesmaximal, characteristic, complemented
13#13114848C211yesmaximal, characteristic, complemented
14#13114669C211yesmaximal, characteristic, complemented
15C13×#2352C211yesmaximal, characteristic
16C2×C4×D4×C13C2211yescharacteristic
17C2×C13×#117C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C2×#88178C2211yescharacteristic
20C2×#88178C2211yescharacteristic
21C2×C4×Dic26C2211yescharacteristic
22C13×#388—21no—
23C13×#387—21no—
24C13×#386—21no—
25C13×#382C2211yescharacteristic
26C13×#380C2211yescharacteristic
27C13×#380C2211yescharacteristic
28C4×C13×C4⋊C4C2211yescharacteristic
29C4×C13×C22⋊C4—21no—
30#11718882—21no—
31#11718873C2211yescharacteristic
32#11718873C2211yescharacteristic
33C2×C22⋊#1055C2211yescharacteristic
34C2×C22⋊#1055C2211yescharacteristic
35C2×C22⋊#1055C2211yescharacteristic
36C2×C22⋊#1055C2211yescharacteristic
37#11718634—21no—
38C2×#88050C2211yescharacteristic
39C2×#88050C2211yescharacteristic
40C2×#88050C2211yescharacteristic
41C2×#88050C2211yescharacteristic
42C2×#88047C2211yescharacteristic
43C2×#88047C2211yescharacteristic
44#11718609—21no—
45#11718609—21no—
46#11718596C2211yescharacteristic
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×C13D411yescharacteristic
60C23×C4×C13—21no—
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C22×Dic26C2311yescharacteristic
64C4×D4×C13—22no—
65C4×D4×C13—22no—
66C13×#117—22no—
67C13×#117—41no—
68C2×C13×C4⋊C4—22no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—41no—
71C2×C13×C4⋊C4D411yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C22⋊C4—21no—
77C2×C13×C22⋊C4—21no—
78C2×C13×C22⋊C4—21no—
79C2×C13×C22⋊C4D411yescharacteristic
80C2×C13×C22⋊C4D411yescharacteristic
81C2×C42×C13—21no—
82C2×C42×C13—21no—
83C2×C42×C13C2311yescharacteristic
84C2×C22⋊Dic13—21no—
85C2×C22⋊Dic13—21no—
86C2×C22⋊Dic13—21no—
87C2×C22⋊Dic13—21no—
88C2×C4⋊Dic13—21no—
89C2×C4⋊Dic13—21no—
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92C2×C4⋊Dic13C2311yescharacteristic
93#88178—22no—
94#88178—22no—
95#88178—41no—
96#88178—41no—
97C2×#6101—21no—
98C2×#6101—21no—
99C2×#6101—21no—
100C2×C4×Dic13—21no—
101C22×#1055C2311yescharacteristic
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105C4×Dic26—22no—
106C4×Dic26—22no—
107C13×#95—21no—
108C13×#95—21no—
109C13×#95—21no—
110C13×#95—21no—
111C13×#95—21no—
112#88071—21no—
113#88071—21no—
114C22⋊#1055—41no—
115C22⋊#1055—41no—
116C22⋊#1055—41no—
117C22⋊#1055—41no—
118#88050—22no—
119#88050—22no—
120#88050—41no—
121#88050—41no—
122#88047—41no—
123#88047—41no—
124C4⋊#1055—22no—
125#88043—22no—
126#24984—131nomaximal, Sylow
127C24×C13C2×D411yescharacteristic
128C24×C13C2×D411yescharacteristic
129C2×D4×C13—22no—
130C2×D4×C13—22no—
131C2×D4×C13—41no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
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—21no—
147C22×C4×C13—21no—
148C22×C4×C13—42no—
149C22×C4×C13—42no—
150C22×C4×C13—81no—
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2411yescharacteristic
156C22×Dic13—21no—
157C22×Dic13—21no—
158C22×Dic13—21no—
159C22×Dic13—21no—
160C2×Dic26—21no—
161C2×Dic26—21no—
162C2×Dic26—21no—
163C2×Dic26—21no—
164C2×Dic26—21no—
165C2×Dic26#4112yes—
166C13×C4⋊C4—22no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—42no—
175C13×C4⋊C4#4112yes—
176C13×C22⋊C4—22no—
177C13×C22⋊C4—22no—
178C13×C22⋊C4—42no—
179C13×C22⋊C4—42no—
180C13×C22⋊C4—81no—
181C42×C13—42no—
182C42×C13—81no—
183C42×C13#4112yes—
184C42×C13#4112yes—
185C22⋊Dic13—42no—
186C22⋊Dic13—42no—
187C22⋊Dic13—81no—
188C22⋊Dic13—81no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13—42no—
196C4⋊Dic13—81no—
197#6101—42no—
198#6101—42no—
199#6101—42no—
200C4×Dic13—42no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—21no—
209C2×#1055—21no—
210C2×#1055—21no—
211C2×#1055—21no—
212C2×#1055—21no—
213#2538—131no—
214#2352D1311yescharacteristic
215#2076—131no—
216#2075—131no—
217#2036—131no—
218#2036—131no—
219#1955—131no—
220#1947—131no—
221#1873—131no—
222#1872—131no—
223#1836—131no—
224#1825—131no—
225#1823—131no—
226#1805—131no—
227#1763—131no—
228C23×C13—21no—
229C23×C13—21no—
230C23×C13—21no—
231C23×C13—21no—
232C23×C13—21no—
233C23×C13—21no—
234C23×C13—21no—
235C23×C13—21no—
236C23×C13—21no—
237C23×C13—21no—
238C23×C13—21no—
239C23×C13—21no—
240C23×C13—21no—
241C23×C13#13712yes—
242C23×C13C22×D411yescharacteristic
243D4×C13—44no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—22no—
254C2×C4×C13—21no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13—41no—
265C2×C4×C13—41no—
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—84no—
275C2×C4×C13#12312yes—
276C2×C4×C13#12312yes—
277C2×C4×C13C2×#4111yescharacteristic
278C2×C4×C13C2×#4111yescharacteristic
279C2×C4×C13C2×#4111yescharacteristic
280C2×C4×C13C2×#4111yescharacteristic
281C2×C4×C13H(5,𝔽2)11yescharacteristic
282C2×C4×C13H(5,𝔽2)11yescharacteristic
283C2×Dic13—22no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291C2×Dic13—41no—
292C2×Dic13—41no—
293C2×Dic13—41no—
294C2×Dic13—41no—
295Dic26—22no—
296Dic26—22no—
297Dic26—41no—
298Dic26—41no—
299#1055—41no—
300#1055—41no—
301#1055—41no—
302#1055—41no—
303C2×C22⋊Q8—131no—
304C2×C22⋊Q8—131no—
305C2×C4×Q8—131no—
306C2×C4×D4C2×D1311yescharacteristic
307C2×#117C2×D1311yescharacteristic
308C22×C4⋊C4C2×D1311yescharacteristic
309C2×#107—131no—
310C2×#107—131no—
311C2×C4⋊C8—131no—
312C2×#103—131no—
313C2×#103—131no—
314C2×#103—131no—
315C2×#103—131no—
316C2×C22⋊C8—131no—
317C2×C22⋊C8—131no—
318C2×C22⋊C8—131no—
319C2×C22⋊C8—131no—
320C2×#97—131no—
321#396—261no—
322#396—261no—
323#390—261no—
324#389—261no—
325#388—21no—
326#387—21no—
327#386—21no—
328#384—131no—
329#382C2×D1311yescharacteristic
330#380—131no—
331#380—131no—
332#380C2×D1311yescharacteristic
333#380C2×D1311yescharacteristic
334C4×C4⋊C4C2×D1311yescharacteristic
335C4×C22⋊C4—21no—
336#340—131no—
337#340—131no—
338#340—131no—
339#340—131no—
340#340—131no—
341#340—131no—
342#340—131no—
343#340—131no—
344#340—131no—
345#340—131no—
346C22×C13—22no—
347C22×C13—22no—
348C22×C13—22no—
349C22×C13—41no—
350C22×C13—41no—
351C22×C13—41no—
352C22×C13—41no—
353C22×C13—41no—
354C22×C13—41no—
355C22×C13—41no—
356C22×C13—41no—
357C22×C13—41no—
358C22×C13—41no—
359C22×C13—41no—
360C22×C13C2×#12311yescharacteristic
361C22×C13#54611yescharacteristic
362C22×C13#54611yescharacteristic
363C22×C13C2×#13711yescharacteristic
364C22×C13#57511yescharacteristic
365C22×C13#57611yescharacteristic
366C22×C13#57811yescharacteristic
367C4×C13—22no—
368C4×C13—22no—
369C4×C13—41no—
370C4×C13—41no—
371C4×C13—42no—
372C4×C13—81no—
373C4×C13—81no—
374C4×C13—81no—
375C4×C13#52911yescharacteristic
376C4×C13#54011yescharacteristic
377C4×C13#55311yescharacteristic
378C4×C13#55511yescharacteristic
379Dic13—42no—
380Dic13—81no—
381Dic13—81no—
382Dic13—81no—
383C22×Q8—131no—
384C22×D4C22⋊D1311yescharacteristic
385C23×C4—21no—
386C23×C4C22×D1311yescharacteristic
387C23×C4C22×D1311yescharacteristic
388C22×C8—131no—
389C22×C8—131no—
390C22×C8—131no—
391C22×C8—131no—
392C22⋊Q8—262no—
393C22⋊Q8—262no—
394C22⋊Q8—521no—
395C22⋊Q8—521no—
396C4×Q8—262no—
397C4×Q8—262no—
398C4×D4—22no—
399C4×D4—22no—
400#117—22no—
401#117—41no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—41no—
405C2×C4⋊C4—131no—
406C2×C4⋊C4—131no—
407C2×C4⋊C4—131no—
408C2×C4⋊C4—261no—
409C2×C4⋊C4—261no—
410C2×C4⋊C4—261no—
411C2×C4⋊C4—261no—
412C2×C4⋊C4—261no—
413C2×C4⋊C4C22⋊D1311yescharacteristic
414C2×C4⋊C4C22×D1311yescharacteristic
415C2×C4⋊C4C22×D1311yescharacteristic
416C2×C4⋊C4C22×D1311yescharacteristic
417C2×C4⋊C4C22×D1311yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—261no—
422C2×C22⋊C4—261no—
423C2×C22⋊C4—261no—
424C2×C22⋊C4—261no—
425C2×C22⋊C4C22⋊D1311yescharacteristic
426C2×C22⋊C4C22⋊D1311yescharacteristic
427C2×C42—21no—
428C2×C42—21no—
429C2×C42—261no—
430C2×C42C22×D1311yescharacteristic
431#107—521no—
432#107—521no—
433C4⋊C8—262no—
434#103—262no—
435#103—262no—
436#103—521no—
437#103—521no—
438C22⋊C8—521no—
439C22⋊C8—521no—
440C22⋊C8—521no—
441C22⋊C8—521no—
442#97—262no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—261no—
449#95—261no—
450C2×C13—42no—
451C2×C13—81no—
452C2×C13#242011yescharacteristic
453C2×C13#309511yescharacteristic
454C2×C13#309811yescharacteristic
455C2×C13#330911yescharacteristic
456C2×C13#331211yescharacteristic
457C2×C13#331311yescharacteristic
458C2×C13#331411yescharacteristic
459C24C2×C22⋊D1311yescharacteristic
460C24C2×C22⋊D1311yescharacteristic
461C2×Q8—132no—
462C2×Q8—261no—
463C2×Q8—261no—
464C2×Q8—261no—
465C2×Q8—261no—
466C2×Q8—261no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—41no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—81no—
489C22×C4—261no—
490C22×C4—261no—
491C22×C4—261no—
492C22×C4—261no—
493C22×C4C2×C22⋊D1311yescharacteristic
494C22×C4C2×C22⋊D1311yescharacteristic
495C22×C4C2×C22⋊D1311yescharacteristic
496C22×C4C2×C22⋊D1311yescharacteristic
497C22×C4C23×D1311yescharacteristic
498C2×C8—261no—
499C2×C8—261no—
500C2×C8—261no—
501C2×C8—261no—
502C2×C8—261no—
503C2×C8—261no—
504C2×C8—261no—
505C2×C8—261no—
506C2×C8—261no—
507C2×C8—261no—
508C2×C8—261no—
509C2×C8—261no—
510C4⋊C4—22no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—42no—
519C4⋊C4—261no—
520C4⋊C4—261no—
521C4⋊C4—261no—
522C4⋊C4—261no—
523C4⋊C4—261no—
524C4⋊C4—261no—
525C4⋊C4—522no—
526C4⋊C4—522no—
527C4⋊C4—522no—
528C4⋊C4—522no—
529C4⋊C4—1041no—
530C4⋊C4#612912yes—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—42no—
534C22⋊C4—42no—
535C22⋊C4—81no—
536C22⋊C4—522no—
537C22⋊C4—522no—
538C22⋊C4—1041no—
539C22⋊C4—1041no—
540C42—42no—
541C42—81no—
542C42—522no—
543C42#612712yes—
544C42#612712yes—
545C13#2498411yescharacteristic, complemented, Sylow
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23#8820512yes—
560C23C22×C22⋊D1311yescharacteristic
561Q8—262no—
562Q8—262no—
563Q8—521no—
564Q8—521no—
565D4—44no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—84no—
597C2×C4—262no—
598C2×C4—521no—
599C2×C4—521no—
600C2×C4—521no—
601C2×C4—521no—
602C2×C4—521no—
603C2×C4—521no—
604C2×C4—521no—
605C2×C4—521no—
606C2×C4—521no—
607C2×C4—521no—
608C2×C4—521no—
609C2×C4#8818312yes—
610C2×C4#8818312yes—
611C2×C4C2×#612711yescharacteristic
612C2×C4C2×#612711yescharacteristic
613C2×C4C2×#612911yescharacteristic
614C2×C4#8825111yescharacteristic
615C2×C4#41×D1311yescharacteristic
616C2×C4#8825611yescharacteristic
617C8—521no—
618C8—521no—
619C8—521no—
620C8—521no—
621C22—22no—
622C22—22no—
623C22—22no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22C2×#8818311yescharacteristic
636C22#1171951111yescharacteristic
637C22#1171952711yescharacteristic
638C22C2×#8820511yescharacteristic
639C22#1171953411yescharacteristic
640C22#1171954011yescharacteristic
641C22#1171954311yescharacteristic
642C4—22no—
643C4—22no—
644C4—42no—
645C4—41no—
646C4—41no—
647C4—81no—
648C4—81no—
649C4—81no—
650C4—522no—
651C4—1041no—
652C4—1041no—
653C4—1041no—
654C4#1171926211yescharacteristic
655C4#1171926311yescharacteristic
656C4#1171926711yescharacteristic
657C4#1171926811yescharacteristic
658C2—42no—
659C2—81no—
660C2#1311832211yescharacteristic
661C2#1312478411yescharacteristic
662C2#1312481411yescharacteristic
663C2#1312683611yescharacteristic
664C2#1312688111yescharacteristic
665C2#1312690211yescharacteristic
666C2#1312691711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2352C2
socleC23×C13C22×D4
prime radicalC22×D4×C13D4
hypercenter#2352D13
hypocenterC13#24984
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. #13116267C2semidirect
3. #13116262C2semidirect
4. #13116039C2semidirect
5. #13116039C2semidirect
7. #13115594C2semidirect
8. #13115148C2semidirect
9. #13115143C2semidirect
10. #13114969C2semidirect
11. #13114931C2semidirect
12. #13114922C2semidirect
13. #13114848C2semidirect
14. #13114669C2semidirect
545. C13#24984semidirect

Maximal subgroups

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

subgroupindex
#131197582
#131162672
#131162622
#131160392
#131156352
#131155942
#131151482
#131151432
#131149692
#131149312
#131149222
#131148482
#131146692
C13×#23522
#2498413