Finite Group Databasebeta

← #15870917

Subgroups — #15870917

Order 3328.

818 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×#11718358C211yesmaximal, characteristic
2#13117577C211yesmaximal, characteristic, complemented
3#13117547C211yesmaximal, characteristic
4#13115805C211yesmaximal, characteristic, complemented
5#13115652C211yesmaximal, characteristic
6#13115533C211yesmaximal, characteristic
7#13115526C211yesmaximal, characteristic, complemented
8#13115519C211yesmaximal, characteristic
9#13115512C211yesmaximal, characteristic, complemented
10#13114964C211yesmaximal, characteristic, complemented
11#13114667C211yesmaximal, characteristic, complemented
12#13114662C211yesmaximal, characteristic
13C4×#88056C211yesmaximal, characteristic, complemented
14C4×#88061C211yesmaximal, characteristic
15C13×#1726C211yesmaximal, characteristic, complemented
16C2×#88129C2211yescharacteristic
17C2×C4×D52C2211yescharacteristic
18C2×#88124C2211yescharacteristic
19C2×C4×Dic26C2211yescharacteristic
20C2×C13×#97C2211yescharacteristic
21C2×C13×#97C2211yescharacteristic
22C2×C13×#97C2211yescharacteristic
23C2×C4×C8×C13C2211yescharacteristic
24C2×C4×C8×C13C2211yescharacteristic
25C2×C4×C8×C13C2211yescharacteristic
26C13×#376C2211yescharacteristic
27C2×#88061C2211yescharacteristic
28C2×#88061C2211yescharacteristic
29C2×#88061C2211yescharacteristic
30C2×#88061C2211yescharacteristic
31C2×#88056C2211yescharacteristic
32C2×#88056C2211yescharacteristic
33C2×#88056C2211yescharacteristic
34C2×#88056C2211yescharacteristic
35#11718600C2211yescharacteristic
36#11718596C2211yescharacteristic
37#11718596C2211yescharacteristic
38C4×C4⋊Dic13C2211yescharacteristic
39C4×C4⋊Dic13C2211yescharacteristic
40#11718590C2211yescharacteristic
41#11718589C2211yescharacteristic
42#11718589C2211yescharacteristic
43#11718358C418yescomplemented
44#11718331—21no—
45#11718331—21no—
46#11718329—21no—
47#11718329—21no—
48#11718316—21no—
49#11718316—21no—
50#11718308—21no—
51#11718308—21no—
52#11718143C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718143C2211yescharacteristic
57#11718143C2211yescharacteristic
58#11718143C2211yescharacteristic
59#11718143C2211yescharacteristic
60C22×D52C2311yescharacteristic
61C22×C4×D13—21no—
62C22×Dic26C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C2×C42×C13C2311yescharacteristic
68C2×C42×C13C2311yescharacteristic
69C2×C42×C13C2311yescharacteristic
70C2×#6103—21no—
71C2×#6103—21no—
72C2×#6103—21no—
73C2×#6103—21no—
74C2×#6103—21no—
75C2×C4⋊Dic13—21no—
76C2×C4⋊Dic13—21no—
77C2×C4⋊Dic13—21no—
78C2×C4⋊Dic13—21no—
79C2×C4⋊Dic13C2311yescharacteristic
80C2×C4⋊Dic13C2311yescharacteristic
81C2×C4⋊Dic13C2311yescharacteristic
82C2×C4⋊Dic13C2311yescharacteristic
83C2×C4⋊Dic13C2311yescharacteristic
84C2×C4⋊Dic13C2311yescharacteristic
85C2×#6101—21no—
86C2×#6101—21no—
87C2×#6101—21no—
88C2×#6101—21no—
89C2×#6101—21no—
90C2×C4×Dic13—21no—
91C2×C4×Dic13—21no—
92C2×C4×Dic13—21no—
93#88129—22no—
94#88129C2×C414yes—
95C4×D52—22no—
96C4×D52—22no—
97#88124—22no—
98#88124C2×C414yescomplemented
99C4×Dic26—22no—
100C4×Dic26—22no—
101C13×#97—22no—
102C13×#97—22no—
103C13×#97—22no—
104C4×C8×C13—22no—
105C4×C8×C13—22no—
106C4×C8×C13C2×C414yescomplemented
107C13×#95D411yescharacteristic
108C13×#95D411yescharacteristic
109C13×#95D411yescharacteristic
110C13×#95D411yescharacteristic
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88061—22no—
118#88061—22no—
119#88061C2×C414yes—
120#88061C2×C414yes—
121#88056—22no—
122#88056—22no—
123#88056C2×C414yescomplemented
124#88056C2×C414yescomplemented
125#21643—131nomaximal, Sylow
126C23×D13—21no—
127C22×C4×C13C2×D411yescharacteristic
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2411yescharacteristic
134C22×Dic13—21no—
135C22×Dic13—21no—
136C22×Dic13—21no—
137C22×Dic13—21no—
138C22×Dic13—21no—
139C22×Dic13—21no—
140C22×Dic13—21no—
141C2×D52—21no—
142C2×D52—21no—
143C2×D52—21no—
144C2×D52—21no—
145C2×D52—21no—
146C2×D52C22×C412yes—
147C2×C4×D13—42no—
148C2×C4×D13—81no—
149C2×C4×D13—81no—
150C2×Dic26—21no—
151C2×Dic26—21no—
152C2×Dic26—21no—
153C2×Dic26—21no—
154C2×Dic26—21no—
155C2×Dic26C22×C412yes—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13—21no—
164C2×C8×C13C22×C412yes—
165C2×C8×C13C22×C412yes—
166C2×C8×C13#4112yes—
167C2×C8×C13#4112yes—
168C42×C13—21no—
169C42×C13—21no—
170C42×C13C22×C412yes—
171C42×C13#4112yes—
172C42×C13#4112yes—
173C42×C13#4112yes—
174#6103—24no—
175#6103—24no—
176#6103—42no—
177#6103—81no—
178#6103—81no—
179C4⋊Dic13—21no—
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—21no—
189C4⋊Dic13—81no—
190C4⋊Dic13—81no—
191C4⋊Dic13—81no—
192C4⋊Dic13—81no—
193C4⋊Dic13C22×C412yes—
194C4⋊Dic13C22×C412yes—
195#6101—24no—
196#6101—24no—
197#6101—42no—
198#6101—81no—
199#6101—81no—
200C4×Dic13—42no—
201C4×Dic13—81no—
202C4×Dic13—81no—
203C2×#488—131no—
204#2330—131no—
205#2326—131no—
206#1992—131no—
207#1959—131no—
208#1936—131no—
209#1935—131no—
210#1934—131no—
211#1933—131no—
212#1834—131no—
213#1763—131no—
214#1762—131no—
215C4×#103—131no—
216C4×#102—131no—
217#1726D1311yescharacteristic, complemented
218C23×C13C22×D411yescharacteristic
219C22×D13—22no—
220C22×D13—41no—
221C22×D13—41no—
222C22×D13—41no—
223C22×D13—41no—
224C22×D13—41no—
225C22×D13—41no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
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—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13C4×D412yes—
241C2×C4×C13C4×D412yes—
242C2×C4×C13#12412yes—
243C2×C4×C13#12412yes—
244C2×C4×C13C23×C411yescharacteristic
245C2×C4×C13C2×#4111yescharacteristic
246C2×C4×C13C2×#4111yescharacteristic
247C2×C4×C13C2×#4111yescharacteristic
248C2×C4×C13C2×#4111yescharacteristic
249C2×C4×C13C2×#4111yescharacteristic
250C2×Dic13—22no—
251C2×Dic13—22no—
252C2×Dic13—22no—
253C2×Dic13—41no—
254C2×Dic13—41no—
255C2×Dic13—41no—
256C2×Dic13—41no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271D52—22no—
272D52—22no—
273D52—41no—
274D52—41no—
275C4×D13—84no—
276Dic26—22no—
277Dic26—22no—
278Dic26—41no—
279Dic26—41no—
280C8×C13—22no—
281C8×C13—22no—
282C8×C13—22no—
283C8×C13—22no—
284C2×#125—131no—
285C2×#124—131no—
286C2×C4×Q8—131no—
287C2×C4×D4—131no—
288#488—138no—
289C2×#103—131no—
290C2×#103—131no—
291C2×#103—131no—
292C2×#103—131no—
293C2×#102—131no—
294C2×#102—131no—
295C2×#102—131no—
296C2×#102—131no—
297C2×#97C2×D1311yescharacteristic
298C2×#97C2×D1311yescharacteristic
299C2×#97C2×D1311yescharacteristic
300C2×C4×C8C2×D1311yescharacteristic
301C2×C4×C8C2×D1311yescharacteristic
302C2×C4×C8C2×D1311yescharacteristic
303#391—131no—
304#390—131no—
305#389—131no—
306#389—131no—
307#389—261no—
308#389—261no—
309#388—261no—
310#388—261no—
311#387—261no—
312#387—261no—
313#385—261no—
314#385—261no—
315#384—131no—
316#384—131no—
317C4×C4⋊C4—131no—
318C4×C4⋊C4—131no—
319#376C2×D1311yescharacteristic
320#340—131no—
321#340—131no—
322#340—131no—
323#340—131no—
324#340—131no—
325#340—131no—
326#340—131no—
327#340—131no—
328C22×C13C2×C4×D411yescharacteristic
329C22×C13C2×#12411yescharacteristic
330C22×C13#53211yescharacteristic
331C22×C13#57611yescharacteristic
332C22×C13#57711yescharacteristic
333C22×C13#57711yescharacteristic
334C22×C13#57811yescharacteristic
335C2×D13—42no—
336C2×D13—42no—
337C2×D13—42no—
338C2×D13—81no—
339C2×D13—81no—
340C2×D13—81no—
341C2×D13—81no—
342C4×C13—22no—
343C4×C13—22no—
344C4×C13—22no—
345C4×C13—22no—
346C4×C13—41no—
347C4×C13—41no—
348C4×C13C4×#4111yescharacteristic
349C4×C13C4×#4111yescharacteristic
350C4×C13#52911yescharacteristic
351C4×C13#52911yescharacteristic
352Dic13—42no—
353Dic13—42no—
354Dic13—42no—
355Dic13—81no—
356Dic13—81no—
357Dic13—81no—
358Dic13—81no—
359C22×Q8—131no—
360C22×D4—131no—
361C23×C4—261no—
362C22×C8C22×D1311yescharacteristic
363C22×C8C22×D1311yescharacteristic
364C22×C8C22×D1311yescharacteristic
365C22×C8C22×D1311yescharacteristic
366#125—134no—
367#125—262no—
368#124—134no—
369#124—262no—
370C4×Q8—262no—
371C4×Q8—262no—
372C4×D4—262no—
373C4×D4—262no—
374C2×C4⋊C4—131no—
375C2×C4⋊C4—131no—
376C2×C4⋊C4—131no—
377C2×C4⋊C4—131no—
378C2×C4⋊C4—131no—
379C2×C4⋊C4—131no—
380C2×C4⋊C4—261no—
381C2×C4⋊C4—261no—
382C2×C4⋊C4—261no—
383C2×C4⋊C4—261no—
384C2×C4⋊C4—261no—
385C2×C4⋊C4—261no—
386C2×C4⋊C4—261no—
387C2×C4⋊C4—261no—
388C2×C4⋊C4—261no—
389C2×C22⋊C4—261no—
390C2×C22⋊C4—261no—
391C2×C22⋊C4—261no—
392C2×C22⋊C4—261no—
393C2×C22⋊C4—261no—
394C2×C42—261no—
395C2×C42—261no—
396C2×C42—261no—
397C2×C42C22×D1311yescharacteristic
398C2×C42C22×D1311yescharacteristic
399C2×C42C22×D1311yescharacteristic
400#103—134no—
401#103—134no—
402#103—262no—
403#103—262no—
404#102—134no—
405#102—134no—
406#102—262no—
407#102—262no—
408#97—22no—
409#97—22no—
410#97—22no—
411C4×C8—22no—
412C4×C8—22no—
413C4×C8C4×D1314yescomplemented
414#95—261no—
415#95—261no—
416#95—261no—
417#95—261no—
418#95—261no—
419#95—261no—
420#95D5211yescharacteristic
421#95D5211yescharacteristic
422#95D5211yescharacteristic
423#95D5211yescharacteristic
424C2×C13C4×#12411yescharacteristic
425C2×C13#295111yescharacteristic
426C2×C13#295211yescharacteristic
427C2×C13#313611yescharacteristic
428C2×C13#313711yescharacteristic
429C2×C13#317811yescharacteristic
430C2×C13#317911yescharacteristic
431D13—82no—
432C24—261no—
433C2×Q8—132no—
434C2×Q8—261no—
435C2×Q8—261no—
436C2×Q8—261no—
437C2×Q8—261no—
438C2×Q8—261no—
439C2×D4—132no—
440C2×D4—261no—
441C2×D4—261no—
442C2×D4—261no—
443C2×D4—261no—
444C2×D4—261no—
445C22×C4—261no—
446C22×C4—261no—
447C22×C4—261no—
448C22×C4—261no—
449C22×C4—261no—
450C22×C4—261no—
451C22×C4—261no—
452C22×C4—522no—
453C22×C4—1041no—
454C22×C4—1041no—
455C22×C4C2×D5211yescharacteristic
456C22×C4C2×D5211yescharacteristic
457C22×C4C2×D5211yescharacteristic
458C22×C4C2×D5211yescharacteristic
459C22×C4C2×D5211yescharacteristic
460C22×C4C2×D5211yescharacteristic
461C22×C4C23×D1311yescharacteristic
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8C2×C4×D1312yes—
471C2×C8C2×C4×D1312yes—
472C2×C8#612712yes—
473C2×C8#612712yes—
474C4⋊C4—132no—
475C4⋊C4—132no—
476C4⋊C4—264no—
477C4⋊C4—264no—
478C4⋊C4—261no—
479C4⋊C4—261no—
480C4⋊C4—261no—
481C4⋊C4—261no—
482C4⋊C4—261no—
483C4⋊C4—261no—
484C4⋊C4—261no—
485C4⋊C4—261no—
486C4⋊C4—261no—
487C4⋊C4—261no—
488C4⋊C4—522no—
489C4⋊C4—1041no—
490C4⋊C4—1041no—
491C4⋊C4—1041no—
492C4⋊C4—1041no—
493C4⋊C4—1041no—
494C4⋊C4—1041no—
495C22⋊C4—264no—
496C22⋊C4—264no—
497C22⋊C4—522no—
498C22⋊C4—1041no—
499C22⋊C4—1041no—
500C42—21no—
501C42—21no—
502C42—522no—
503C42—1041no—
504C42—1041no—
505C42C2×C4×D1312yes—
506C42#612712yes—
507C42#612712yes—
508C42#612712yes—
509C13#2164311yescharacteristic, complemented, Sylow
510C23—262no—
511C23—521no—
512C23—521no—
513C23—521no—
514C23—521no—
515C23—521no—
516C23—521no—
517C23C22×D5211yescharacteristic
518Q8—262no—
519Q8—262no—
520Q8—521no—
521Q8—521no—
522D4—262no—
523D4—262no—
524D4—521no—
525D4—521no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
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—21no—
539C2×C4—21no—
540C2×C4—262no—
541C2×C4—262no—
542C2×C4—262no—
543C2×C4—521no—
544C2×C4—521no—
545C2×C4—521no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4—521no—
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—1044no—
562C2×C4C4×D5212yes—
563C2×C4C4×D5212yes—
564C2×C4#8812912yes—
565C2×C4#8812912yes—
566C2×C4C22×C4×D1311yescharacteristic
567C2×C4C2×#612711yescharacteristic
568C2×C4C2×#612711yescharacteristic
569C2×C4C2×#612711yescharacteristic
570C2×C4C2×#612711yescharacteristic
571C2×C4C2×#612711yescharacteristic
572C8—22no—
573C8—22no—
574C8—22no—
575C8—22no—
576C22—522no—
577C22—522no—
578C22—522no—
579C22—1041no—
580C22—1041no—
581C22—1041no—
582C22—1041no—
583C22C2×C4×D5211yescharacteristic
584C22C2×#8812911yescharacteristic
585C22#1171918211yescharacteristic
586C22#1171945611yescharacteristic
587C22#1171945611yescharacteristic
588C22#1171945711yescharacteristic
589C22#1171945811yescharacteristic
590C4—22no—
591C4—22no—
592C4—22no—
593C4—22no—
594C4—41no—
595C4—41no—
596C4—522no—
597C4—522no—
598C4—522no—
599C4—1041no—
600C4—1041no—
601C4—1041no—
602C4—1041no—
603C4C4×#612711yescharacteristic
604C4C4×#612711yescharacteristic
605C4#1171918411yescharacteristic
606C4#1171918411yescharacteristic
607C2—1042no—
608C2C4×#8812911yescharacteristic
609C2#1312371311yescharacteristic
610C2#1312372111yescharacteristic
611C2#1312519211yescharacteristic
612C2#1312520311yescharacteristic
613C2#1312550411yescharacteristic
614C2#1312551911yescharacteristic
subgroupG/H
centerC23C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1726C2
socleC23×C13C22×D4
prime radicalC22×D52C23
cosocleC22×C4×C13C24
hypercenter#1726D13
hypocenterC13#21643
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ #376 ◁ #1726

Complements

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

NH ≅ G/Ntype
2. #13117577C2semidirect
4. #13115805C2semidirect
7. #13115526C2semidirect
9. #13115512C2semidirect
10. #13114964C2semidirect
11. #13114667C2semidirect
13. C4×#88056C2semidirect
15. C13×#1726C2semidirect
43. #11718358C4semidirect
98. #88124C2×C4semidirect
106. C4×C8×C13C2×C4semidirect
123. #88056C2×C4semidirect
124. #88056C2×C4semidirect
217. #1726D13semidirect
413. C4×C8C4×D13semidirect
509. C13#21643semidirect

Maximal subgroups

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

subgroupindex
C2×#117183582
#131175772
#131175472
#131158052
#131156522
#131155332
#131155262
#131155192
#131155122
#131149642
#131146672
#131146622
C4×#880562
C4×#880612
C13×#17262
#2164313