Finite Group Databasebeta

← #15904286

Subgroups — #15904286

Order 3328.

746 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718682C211yesmaximal, characteristic, complemented
2C2×#11718661C211yesmaximal, characteristic
3#13120657C211yesmaximal, characteristic
4#13116267C211yesmaximal, characteristic
5#13116262C211yesmaximal, characteristic
6#13116036C211yesmaximal, characteristic
7#13116029C211yesmaximal, characteristic
8#13115788C211yesmaximal, characteristic, complemented
9#13115604C211yesmaximal, characteristic, complemented
10#13115576C211yesmaximal, characteristic, complemented
11#13115566C211yesmaximal, characteristic, complemented
12#13115529C211yesmaximal, characteristic, complemented
13#13115515C211yesmaximal, characteristic, complemented
14#13114851C211yesmaximal, characteristic, complemented
15C13×#2323C211yesmaximal, characteristic
16C2×C13×C22⋊Q8C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C2×C13×#117C2211yescharacteristic
19C2×#88123C2211yescharacteristic
20C13×#391C2211yescharacteristic
21C13×#389—21no—
22C13×#389C2211yescharacteristic
23C13×#388—21no—
24C13×#388—21no—
25C13×#387—21no—
26C13×#380C2211yescharacteristic
27C4×C13×C4⋊C4C2211yescharacteristic
28C2×#88075C2211yescharacteristic
29C2×#88075C2211yescharacteristic
30C2×#88075C2211yescharacteristic
31C2×#88075C2211yescharacteristic
32#11718873C2211yescharacteristic
33#11718873C2211yescharacteristic
34C2×C22⋊#1055C2211yescharacteristic
35C2×C22⋊#1055C2211yescharacteristic
36#11718682—24no—
37#11718661—24no—
38#11718647—21no—
39#11718640—21no—
40C2×#88048C2211yescharacteristic
41C2×#88047C2211yescharacteristic
42C2×#88047C2211yescharacteristic
43C2×#88047C2211yescharacteristic
44#11718610—21no—
45#11718608—21no—
46#11718597C2211yescharacteristic
47#11718589C2211yescharacteristic
48#11718589C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C2×C4⋊#1055C2211yescharacteristic
51C2×#88043C2211yescharacteristic
52C2×C4×#1055C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61C22×Q8×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C22×Dic26—21no—
64C13×C22⋊Q8—22no—
65C13×C22⋊Q8—22no—
66C4×Q8×C13—22no—
67C4×Q8×C13—22no—
68C13×#117—22no—
69C13×#117—22no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4D411yescharacteristic
74C2×C13×C4⋊C4D411yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C22⋊C4—21no—
79C2×C13×C22⋊C4—21no—
80C2×C13×C22⋊C4D411yescharacteristic
81C2×C13×C22⋊C4D411yescharacteristic
82C2×C42×C13—21no—
83C2×C42×C13—21no—
84C2×C42×C13C2311yescharacteristic
85C2×C42×C13C2311yescharacteristic
86C2×C22⋊Dic13—21no—
87C2×C22⋊Dic13—21no—
88C2×C4⋊Dic13—21no—
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92C2×C4⋊Dic13C2311yescharacteristic
93C2×#6101—21no—
94C2×#6101—21no—
95C22×#1055C2311yescharacteristic
96C22×#1055C2311yescharacteristic
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99#88123—22no—
100#88123—22no—
101C13×#95—21no—
102C13×#95—21no—
103C13×#95—21no—
104C13×#95—21no—
105C13×#95—21no—
106#88075—22no—
107#88075—22no—
108#88075—22no—
109#88075—22no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88071—21no—
116C22⋊#1055—22no—
117C22⋊#1055—22no—
118#88048—22no—
119#88047—22no—
120#88047—22no—
121#88047—22no—
122C4⋊#1055—22no—
123C4⋊#1055D414yes—
124#88043—22no—
125C4×#1055—22no—
126#24714—131nomaximal, Sylow
127C24×C13C2×D411yescharacteristic
128C2×Q8×C13—21no—
129C2×Q8×C13—21no—
130C2×Q8×C13—21no—
131C2×Q8×C13—21no—
132C2×Q8×C13—21no—
133C2×Q8×C13#4112yes—
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×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2411yescharacteristic
150C22×Dic13—21no—
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13—21no—
154C2×Dic26—42no—
155C2×Dic26—81no—
156C2×Dic26—81no—
157C13×C4⋊C4—24no—
158C13×C4⋊C4—22no—
159C13×C4⋊C4—22no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—42no—
166C13×C4⋊C4—81no—
167C13×C4⋊C4#4112yes—
168C13×C22⋊C4—24no—
169C13×C22⋊C4—22no—
170C13×C22⋊C4—22no—
171C13×C22⋊C4—81no—
172C42×C13—21no—
173C42×C13—21no—
174C42×C13—42no—
175C42×C13—81no—
176C42×C13C2×D412yes—
177C42×C13#4112yes—
178C22⋊Dic13—81no—
179C22⋊Dic13—81no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13—42no—
189#6101—81no—
190#6101—81no—
191C2×#1055—21no—
192C2×#1055—21no—
193C2×#1055—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055C2×D412yes—
202C2×#1055C2×D412yes—
203C2×#477—131no—
204C2×#433—131no—
205#2628—131no—
206#2323D1311yescharacteristic
207#2076—131no—
208#2075—131no—
209#2036—131no—
210#2035—131no—
211#1988—131no—
212#1949—131no—
213#1944—131no—
214#1942—131no—
215#1935—131no—
216#1933—131no—
217#1805—131no—
218C23×C13—21no—
219C23×C13—21no—
220C23×C13—21no—
221C23×C13—21no—
222C23×C13—21no—
223C23×C13—21no—
224C23×C13—21no—
225C23×C13C22×D411yescharacteristic
226Q8×C13—22no—
227Q8×C13—22no—
228Q8×C13—41no—
229Q8×C13—41no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—22no—
238C2×C4×C13—22no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13#12112yes—
260C2×C4×C13#12112yes—
261C2×C4×C13C22×D411yescharacteristic
262C2×C4×C13C2×#4111yescharacteristic
263C2×C4×C13C2×#4111yescharacteristic
264C2×C4×C13C2×#4111yescharacteristic
265C2×C4×C132−1+411yescharacteristic
266C2×C4×C132−1+411yescharacteristic
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278C2×Dic13—41no—
279Dic26—84no—
280#1055—22no—
281#1055—22no—
282#1055—41no—
283#1055—41no—
284C2×C4⋊Q8—131no—
285C2×C22⋊Q8C2×D1311yescharacteristic
286C2×C4×Q8C2×D1311yescharacteristic
287C2×#117C2×D1311yescharacteristic
288#477—264no—
289#433—264no—
290C2×#107—131no—
291C2×#107—131no—
292C2×#107—131no—
293C2×#106—131no—
294C2×C4⋊C8—131no—
295C2×C4⋊C8—131no—
296C2×#103—131no—
297C2×#103—131no—
298C2×#103—131no—
299C2×#103—131no—
300C2×C22⋊C8—131no—
301C2×C22⋊C8—131no—
302C2×#97—131no—
303C2×C4×C8—131no—
304#400—261no—
305#399—261no—
306#395—261no—
307#393—261no—
308#391C2×D1311yescharacteristic
309#389—21no—
310#389—131no—
311#389—131no—
312#389C2×D1311yescharacteristic
313#388—21no—
314#388—21no—
315#387—21no—
316#382—131no—
317#380—131no—
318#380—131no—
319#380C2×D1311yescharacteristic
320C4×C4⋊C4C2×D1311yescharacteristic
321#340—131no—
322#340—131no—
323#340—131no—
324#340—131no—
325#340—131no—
326#340—131no—
327#340—131no—
328#340—131no—
329C22×C13—41no—
330C22×C13—41no—
331C22×C13—41no—
332C22×C13—41no—
333C22×C13—41no—
334C22×C13—41no—
335C22×C13—41no—
336C22×C13C2×#12111yescharacteristic
337C22×C13#52511yescharacteristic
338C22×C13#53611yescharacteristic
339C22×C13#57611yescharacteristic
340C22×C13#57711yescharacteristic
341C22×C13#57811yescharacteristic
342C22×C13#57811yescharacteristic
343C4×C13—22no—
344C4×C13—22no—
345C4×C13—42no—
346C4×C13—41no—
347C4×C13—42no—
348C4×C13—41no—
349C4×C13—41no—
350C4×C13—81no—
351C4×C13—81no—
352C4×C13#54711yescharacteristic
353C4×C13#54811yescharacteristic
354C4×C13#55211yescharacteristic
355C4×C13#55611yescharacteristic
356Dic13—81no—
357Dic13—81no—
358Dic13—81no—
359Dic13—81no—
360C22×Q8—261no—
361C22×Q8C22×D1311yescharacteristic
362C23×C4C22×D1311yescharacteristic
363C22×C8—131no—
364C22×C8—131no—
365C22×C8—131no—
366C22×C8—131no—
367C4⋊Q8—262no—
368C4⋊Q8—262no—
369C22⋊Q8—22no—
370C22⋊Q8—22no—
371C4×Q8—22no—
372C4×Q8—22no—
373#117—22no—
374#117—22no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—131no—
379C2×C4⋊C4—131no—
380C2×C4⋊C4—131no—
381C2×C4⋊C4—131no—
382C2×C4⋊C4—261no—
383C2×C4⋊C4—261no—
384C2×C4⋊C4—261no—
385C2×C4⋊C4C22⋊D1311yescharacteristic
386C2×C4⋊C4C22⋊D1311yescharacteristic
387C2×C4⋊C4C22×D1311yescharacteristic
388C2×C4⋊C4C22×D1311yescharacteristic
389C2×C4⋊C4C22×D1311yescharacteristic
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—261no—
393C2×C22⋊C4—261no—
394C2×C22⋊C4C22⋊D1311yescharacteristic
395C2×C22⋊C4C22⋊D1311yescharacteristic
396C2×C42—21no—
397C2×C42—21no—
398C2×C42C22×D1311yescharacteristic
399C2×C42C22×D1311yescharacteristic
400#107—262no—
401#107—262no—
402#107—262no—
403#106—262no—
404C4⋊C8—134no—
405C4⋊C8—262no—
406#103—262no—
407#103—262no—
408#103—262no—
409#103—262no—
410C22⋊C8—262no—
411C22⋊C8—262no—
412#97—262no—
413C4×C8—262no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—261no—
420#95—261no—
421#95—261no—
422#95—261no—
423#95—261no—
424#95—261no—
425C2×C13—81no—
426C2×C13#241511yescharacteristic
427C2×C13#305911yescharacteristic
428C2×C13#306211yescharacteristic
429C2×C13#312111yescharacteristic
430C2×C13#312411yescharacteristic
431C2×C13#324211yescharacteristic
432C2×C13#324311yescharacteristic
433C24C2×C22⋊D1311yescharacteristic
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—522no—
440C2×Q8—1041no—
441C2×Q8—1041no—
442C2×Q8#612712yes—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—261no—
454C22×C4—261no—
455C22×C4—261no—
456C22×C4—261no—
457C22×C4C2×C22⋊D1311yescharacteristic
458C22×C4C2×C22⋊D1311yescharacteristic
459C22×C4C2×C22⋊D1311yescharacteristic
460C22×C4C2×C22⋊D1311yescharacteristic
461C22×C4C2×C22⋊D1311yescharacteristic
462C22×C4C23×D1311yescharacteristic
463C2×C8—132no—
464C2×C8—132no—
465C2×C8—261no—
466C2×C8—261no—
467C2×C8—261no—
468C2×C8—261no—
469C2×C8—261no—
470C2×C8—261no—
471C2×C8—261no—
472C2×C8—261no—
473C2×C8—261no—
474C2×C8—261no—
475C4⋊C4—24no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—42no—
484C4⋊C4—81no—
485C4⋊C4—261no—
486C4⋊C4—261no—
487C4⋊C4—261no—
488C4⋊C4—261no—
489C4⋊C4—261no—
490C4⋊C4—261no—
491C4⋊C4—261no—
492C4⋊C4—261no—
493C4⋊C4—522no—
494C4⋊C4—1041no—
495C4⋊C4—1041no—
496C4⋊C4#612712yes—
497C22⋊C4—24no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—81no—
501C22⋊C4—1041no—
502C22⋊C4—1041no—
503C42—21no—
504C42—21no—
505C42—42no—
506C42—81no—
507C42D4×D1312yes—
508C42#612912yes—
509C13#2471411yescharacteristic, complemented, Sylow
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23C22×C22⋊D1311yescharacteristic
518Q8—22no—
519Q8—22no—
520Q8—41no—
521Q8—41no—
522Q8—1044no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—521no—
553C2×C4—521no—
554C2×C4—521no—
555C2×C4—521no—
556C2×C4—521no—
557C2×C4—521no—
558C2×C4—521no—
559C2×C4—521no—
560C2×C4—521no—
561C2×C4—521no—
562C2×C4—521no—
563C2×C4—521no—
564C2×C4#8819312yes—
565C2×C4#8819312yes—
566C2×C4C2×#612711yescharacteristic
567C2×C4C2×#612711yescharacteristic
568C2×C4C2×D4×D1311yescharacteristic
569C2×C4C2×#612911yescharacteristic
570C2×C4#8825711yescharacteristic
571C2×C4#8825711yescharacteristic
572C8—262no—
573C8—262no—
574C8—521no—
575C8—521no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22#1171949611yescharacteristic
584C22C2×#8819311yescharacteristic
585C22#1171953011yescharacteristic
586C22#1171954011yescharacteristic
587C22#1171954211yescharacteristic
588C22#1171954311yescharacteristic
589C22#1171954311yescharacteristic
590C4—22no—
591C4—22no—
592C4—41no—
593C4—42no—
594C4—41no—
595C4—41no—
596C4—42no—
597C4—81no—
598C4—81no—
599C4—1041no—
600C4—1041no—
601C4—1041no—
602C4—1041no—
603C4#1171924611yescharacteristic
604C4#1171924711yescharacteristic
605C4#1171925611yescharacteristic
606C4#1171925711yescharacteristic
607C2—81no—
608C2#1311826511yescharacteristic
609C2#1312448811yescharacteristic
610C2#1312451811yescharacteristic
611C2#1312506511yescharacteristic
612C2#1312509811yescharacteristic
613C2#1312609811yescharacteristic
614C2#1312611311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2323C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#2323D13
hypocenterC13#24714
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2323

Complements

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

NH ≅ G/Ntype
1. C2×#11718682C2semidirect
8. #13115788C2semidirect
9. #13115604C2semidirect
10. #13115576C2semidirect
11. #13115566C2semidirect
12. #13115529C2semidirect
13. #13115515C2semidirect
14. #13114851C2semidirect
509. C13#24714semidirect

Maximal subgroups

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

subgroupindex
C2×#117186822
C2×#117186612
#131206572
#131162672
#131162622
#131160362
#131160292
#131157882
#131156042
#131155762
#131155662
#131155292
#131155152
#131148512
C13×#23232
#2471413