Finite Group Databasebeta

← #15936110

Subgroups — #15936110

Order 3328.

762 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13119422C211yesmaximal, characteristic
2#13116379C211yesmaximal, characteristic, complemented
3#13116151C211yesmaximal, characteristic
4#13116079C211yesmaximal, characteristic, complemented
5#13115919C211yesmaximal, characteristic
6#13115693C211yesmaximal, characteristic
7#13115467C211yesmaximal, characteristic, complemented
8#13115463C211yesmaximal, characteristic
9#13115414C211yesmaximal, characteristic, complemented
10#13115395C211yesmaximal, characteristic, complemented
11#13115191C211yesmaximal, characteristic
12#13115191C211yesmaximal, characteristic
13#13114841C211yesmaximal, characteristic, complemented
14C4×#88075C211yesmaximal, characteristic, complemented
15C13×#2365C211yesmaximal, characteristic, complemented
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C2×C4×Q8×C13C2211yescharacteristic
19C22×#6106C2211yescharacteristic
20C22×#6106C2211yescharacteristic
21C2×#88152—21no—
22C13×#391C2211yescharacteristic
23C13×#391C2211yescharacteristic
24C13×#389—21no—
25C13×#387—21no—
26C13×#387—21no—
27C4×C13×C4⋊C4—21no—
28C4×C13×C4⋊C4C2211yescharacteristic
29C4×C13×C4⋊C4C2211yescharacteristic
30C2×#88075C2211yescharacteristic
31C2×#88075C2211yescharacteristic
32C2×#88075C2211yescharacteristic
33C2×#88075C2211yescharacteristic
34C2×#88075C2211yescharacteristic
35C2×#88075C2211yescharacteristic
36#11718655—21no—
37C2×#88049C2211yescharacteristic
38C2×#88049C2211yescharacteristic
39C2×#88048C2211yescharacteristic
40C2×#88048C2211yescharacteristic
41#11718600C2211yescharacteristic
42#11718600C2211yescharacteristic
43#11718600C2211yescharacteristic
44#11718596C2211yescharacteristic
45C4×C4⋊Dic13C2211yescharacteristic
46#11718589C2211yescharacteristic
47C2×C4⋊#1055C2211yescharacteristic
48C2×C4×#1055C2211yescharacteristic
49#11718335—21no—
50#11718331—21no—
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718116C2211yescharacteristic
56#11718116C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×Q8×C13C2311yescharacteristic
60C22×Q8×C13C2311yescharacteristic
61C22×D52C2311yescharacteristic
62C13×C4⋊Q8—22no—
63C13×C4⋊Q8—22no—
64C4×Q8×C13—22no—
65C4×Q8×C13—22no—
66C4×Q8×C13—41no—
67C4×Q8×C13—41no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4D411yescharacteristic
73C2×C13×C4⋊C4D411yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C42×C13—21no—
77C2×C42×C13—21no—
78C2×C42×C13—21no—
79C2×C42×C13C2311yescharacteristic
80C2×C42×C13C2311yescharacteristic
81C2×C42×C13C2311yescharacteristic
82C2×#6106—22no—
83C2×#6106—22no—
84C2×#6106—22no—
85C2×#6106—41no—
86C2×#6106—41no—
87C2×#6106—41no—
88C2×#6103—21no—
89C2×#6103—21no—
90C2×#6103—21no—
91C2×#6103—21no—
92C2×#6103—21no—
93C2×#6103—21no—
94C2×C4⋊Dic13—21no—
95C2×C4⋊Dic13—21no—
96C2×C4⋊Dic13C2311yescharacteristic
97C2×C4⋊Dic13C2311yescharacteristic
98C2×C4⋊Dic13C2311yescharacteristic
99C2×#6101—21no—
100C2×C4×Dic13—21no—
101C22×#1055C2311yescharacteristic
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105#88152—44no—
106C13×#95—21no—
107C13×#95—21no—
108C13×#95—21no—
109C13×#95—21no—
110C13×#95—21no—
111C13×#95D411yescharacteristic
112C13×#95D411yescharacteristic
113#88075—22no—
114#88075—22no—
115#88075—22no—
116#88075—41no—
117#88075—41no—
118#88075—41no—
119#88071—21no—
120#88071—21no—
121#88049—22no—
122#88049—41no—
123#88048—22no—
124#88048—41no—
125C4⋊#1055—41no—
126C4×#1055—41no—
127#27066—131nomaximal, Sylow
128C23×D13—21no—
129C2×Q8×C13—21no—
130C2×Q8×C13—21no—
131C2×Q8×C13—21no—
132C2×Q8×C13—21no—
133C2×Q8×C13—21no—
134C2×Q8×C13—21no—
135C2×Q8×C13—21no—
136C2×Q8×C13—21no—
137C2×Q8×C13—21no—
138C2×Q8×C13—21no—
139C2×Q8×C13#4112yes—
140C2×Q8×C13#4112yes—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2411yescharacteristic
152C22×Dic13—21no—
153C22×Dic13—21no—
154C22×Dic13—21no—
155C2×D52—21no—
156C2×D52—21no—
157C2×D52—21no—
158C2×D52—21no—
159C2×D52—21no—
160C2×D52—21no—
161C13×C4⋊C4—24no—
162C13×C4⋊C4—24no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—41no—
167C13×C4⋊C4—42no—
168C13×C4⋊C4—42no—
169C13×C4⋊C4SD1614yescomplemented
170C13×C4⋊C4#4112yes—
171C42×C13—21no—
172C42×C13—21no—
173C42×C13—21no—
174C42×C13—21no—
175C42×C13—21no—
176C42×C13—21no—
177C42×C13—42no—
178C42×C13—42no—
179C42×C13—42no—
180#6106—44no—
181#6106—44no—
182#6103—42no—
183#6103—42no—
184#6103—42no—
185#6103—42no—
186#6103—81no—
187#6103—81no—
188C4⋊Dic13—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13—42no—
195C4⋊Dic13—81no—
196#6101—42no—
197C4×Dic13—42no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
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#4112yes—
210#2512—131no—
211#2365D1311yescharacteristic, complemented
212#2096—131no—
213#2055—131no—
214#2043—131no—
215#2013—131no—
216#1968—131no—
217#1927—131no—
218#1926—131no—
219#1919—131no—
220#1916—131no—
221#1880—131no—
222#1880—131no—
223#1803—131no—
224C4×#103—131no—
225C23×C13C22×D411yescharacteristic
226C22×D13—41no—
227C22×D13—41no—
228C22×D13—41no—
229C22×D13—41no—
230C22×D13—41no—
231C22×D13—41no—
232C22×D13—41no—
233Q8×C13—22no—
234Q8×C13—22no—
235Q8×C13—22no—
236Q8×C13—22no—
237Q8×C13—41no—
238Q8×C13—41no—
239Q8×C13—41no—
240Q8×C13—41no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—22no—
249C2×C4×C13—22no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—22no—
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—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×C13C2×SD1612yes—
269C2×C4×C13C2×SD1612yes—
270C2×C4×C13C2×SD1612yes—
271C2×C4×C13C2×#4111yescharacteristic
272C2×C4×C13C2×#4111yescharacteristic
273C2×C4×C13C2×#4111yescharacteristic
274C2×C4×C13C2×#4111yescharacteristic
275C2×C4×C13H(5,𝔽2)11yescharacteristic
276C2×C4×C13H(5,𝔽2)11yescharacteristic
277C2×Dic13—41no—
278C2×Dic13—41no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286D52—41no—
287D52—41no—
288D52—41no—
289D52—41no—
290#1055—22no—
291#1055—41no—
292#1055—41no—
293#1055—41no—
294C22×SD16—131no—
295C22×SD16—131no—
296C2×C4⋊Q8C2×D1311yescharacteristic
297C2×#126—261no—
298C2×C4×Q8C2×D1311yescharacteristic
299C2×C4×Q8C2×D1311yescharacteristic
300C2×#106—131no—
301C2×#106—131no—
302C2×C4⋊C8—131no—
303C2×#103—131no—
304C2×#103—131no—
305C2×#103—131no—
306C2×#103—131no—
307C2×#103—131no—
308C2×#103—131no—
309C2×#102—131no—
310C2×#102—131no—
311C2×C4×C8—131no—
312#397—261no—
313#396—261no—
314#391C2×D1311yescharacteristic
315#391C2×D1311yescharacteristic
316#390—131no—
317#390—131no—
318#390—131no—
319#389—21no—
320#389—131no—
321#388—261no—
322#387—21no—
323#387—21no—
324#384—131no—
325C4×C4⋊C4—21no—
326C4×C4⋊C4—131no—
327C4×C4⋊C4C2×D1311yescharacteristic
328C4×C4⋊C4C2×D1311yescharacteristic
329#340—131no—
330#340—131no—
331#340—131no—
332#340—131no—
333#336—131no—
334#336—131no—
335#336—131no—
336#336—131no—
337C22×C13#52511yescharacteristic
338C22×C13#54611yescharacteristic
339C22×C13#55011yescharacteristic
340C22×C13C22×SD1611yescharacteristic
341C22×C13#57511yescharacteristic
342C22×C13#57711yescharacteristic
343C22×C13#57811yescharacteristic
344C2×D13—81no—
345C2×D13—81no—
346C2×D13—81no—
347C2×D13—81no—
348C2×D13—81no—
349C2×D13—81no—
350C2×D13—81no—
351C4×C13—22no—
352C4×C13—22no—
353C4×C13—22no—
354C4×C13—41no—
355C4×C13—42no—
356C4×C13—42no—
357C4×C13—41no—
358C4×C13—41no—
359C4×C13—42no—
360C4×C13—81no—
361C4×C13#52911yescharacteristic
362C4×C13#53811yescharacteristic
363C4×C13#55111yescharacteristic
364C4×C13#55311yescharacteristic
365Dic13—81no—
366Dic13—81no—
367Dic13—81no—
368C22×Q8C22×D1311yescharacteristic
369C22×Q8C22×D1311yescharacteristic
370C22×D4—131no—
371C2×SD16—262no—
372C2×SD16—262no—
373C2×SD16—262no—
374C2×SD16—521no—
375C2×SD16—521no—
376C2×SD16—521no—
377C22×C8—131no—
378C22×C8—131no—
379C22×C8—131no—
380C22×C8—131no—
381C4⋊Q8—22no—
382C4⋊Q8—22no—
383#126—524no—
384C4×Q8—22no—
385C4×Q8—22no—
386C4×Q8—41no—
387C4×Q8—41no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—131no—
393C2×C4⋊C4—131no—
394C2×C4⋊C4—131no—
395C2×C4⋊C4—261no—
396C2×C4⋊C4—261no—
397C2×C4⋊C4—261no—
398C2×C4⋊C4C22⋊D1311yescharacteristic
399C2×C4⋊C4C22⋊D1311yescharacteristic
400C2×C4⋊C4C22×D1311yescharacteristic
401C2×C4⋊C4C22×D1311yescharacteristic
402C2×C22⋊C4—261no—
403C2×C22⋊C4—261no—
404C2×C22⋊C4—261no—
405C2×C22⋊C4—261no—
406C2×C22⋊C4—261no—
407C2×C22⋊C4—261no—
408C2×C42—21no—
409C2×C42—21no—
410C2×C42—21no—
411C2×C42—261no—
412C2×C42C22×D1311yescharacteristic
413C2×C42C22×D1311yescharacteristic
414C2×C42C22×D1311yescharacteristic
415#106—262no—
416#106—521no—
417C4⋊C8—521no—
418#103—262no—
419#103—262no—
420#103—262no—
421#103—521no—
422#103—521no—
423#103—521no—
424#102—262no—
425#102—521no—
426C4×C8—521no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—261no—
433#95—261no—
434#95C22⋊D1311yescharacteristic
435#95C22⋊D1311yescharacteristic
436C2×C13#246711yescharacteristic
437C2×C13#310311yescharacteristic
438C2×C13#312111yescharacteristic
439C2×C13#329811yescharacteristic
440C2×C13#330711yescharacteristic
441C2×C13#339211yescharacteristic
442C2×C13#340211yescharacteristic
443D13—161no—
444C24—261no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8#612712yes—
456C2×Q8#612712yes—
457C2×D4—261no—
458C2×D4—261no—
459C2×D4—261no—
460C2×D4—261no—
461C2×D4—261no—
462C2×D4—261no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—261no—
468C22×C4—261no—
469C22×C4—261no—
470C22×C4C2×C22⋊D1311yescharacteristic
471C22×C4C2×C22⋊D1311yescharacteristic
472C22×C4C2×C22⋊D1311yescharacteristic
473C22×C4C2×C22⋊D1311yescharacteristic
474C22×C4C2×C22⋊D1311yescharacteristic
475C22×C4C2×C22⋊D1311yescharacteristic
476C22×C4C23×D1311yescharacteristic
477SD16—524no—
478SD16—524no—
479C2×C8—132no—
480C2×C8—261no—
481C2×C8—261no—
482C2×C8—261no—
483C2×C8—261no—
484C2×C8—261no—
485C2×C8—261no—
486C2×C8—261no—
487C2×C8—261no—
488C2×C8—261no—
489C2×C8—261no—
490C2×C8—261no—
491C4⋊C4—24no—
492C4⋊C4—24no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—41no—
497C4⋊C4—42no—
498C4⋊C4—42no—
499C4⋊C4—261no—
500C4⋊C4—261no—
501C4⋊C4—261no—
502C4⋊C4—261no—
503C4⋊C4—261no—
504C4⋊C4—261no—
505C4⋊C4—522no—
506C4⋊C4—522no—
507C4⋊C4—1041no—
508C4⋊C4#610614yescomplemented
509C4⋊C4#612912yes—
510C22⋊C4—522no—
511C22⋊C4—522no—
512C22⋊C4—522no—
513C22⋊C4—522no—
514C22⋊C4—1041no—
515C22⋊C4—1041no—
516C42—21no—
517C42—21no—
518C42—21no—
519C42—21no—
520C42—21no—
521C42—21no—
522C42—42no—
523C42—42no—
524C42—42no—
525C42—522no—
526C13#2706611yescharacteristic, complemented, Sylow
527C23—521no—
528C23—521no—
529C23—521no—
530C23—521no—
531C23—521no—
532C23—521no—
533C23—521no—
534C23C22×C22⋊D1311yescharacteristic
535Q8—22no—
536Q8—22no—
537Q8—22no—
538Q8—22no—
539Q8—41no—
540Q8—41no—
541Q8—41no—
542Q8—41no—
543D4—521no—
544D4—521no—
545D4—521no—
546D4—521no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—521no—
575C2×C4—521no—
576C2×C4—521no—
577C2×C4—521no—
578C2×C4—521no—
579C2×C4—521no—
580C2×C4—521no—
581C2×C4—521no—
582C2×C4—521no—
583C2×C4C2×#610612yes—
584C2×C4C2×#610612yes—
585C2×C4C2×#610612yes—
586C2×C4C2×#612711yescharacteristic
587C2×C4C2×#612711yescharacteristic
588C2×C4C2×#612911yescharacteristic
589C2×C4#8825111yescharacteristic
590C2×C4#41×D1311yescharacteristic
591C2×C4#8825611yescharacteristic
592C8—262no—
593C8—521no—
594C8—521no—
595C8—521no—
596C22—1041no—
597C22—1041no—
598C22—1041no—
599C22—1041no—
600C22—1041no—
601C22—1041no—
602C22—1041no—
603C22#1171949611yescharacteristic
604C22#1171951111yescharacteristic
605C22C22×#610611yescharacteristic
606C22#1171952711yescharacteristic
607C22#1171953911yescharacteristic
608C22#1171954211yescharacteristic
609C22#1171954311yescharacteristic
610C4—22no—
611C4—22no—
612C4—22no—
613C4—41no—
614C4—41no—
615C4—42no—
616C4—42no—
617C4—42no—
618C4—41no—
619C4—81no—
620C4—1041no—
621C4—1041no—
622C4—1041no—
623C4#1171924311yescharacteristic
624C4#1171926111yescharacteristic
625C4#1171926511yescharacteristic
626C4#1171927011yescharacteristic
627C2—2081no—
628C2#1311888111yescharacteristic
629C2#1312486711yescharacteristic
630C2#1312506511yescharacteristic
631C2#1312670111yescharacteristic
632C2#1312681211yescharacteristic
633C2#1312781311yescharacteristic
634C2#1312791111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2365C2
socleC23×C13C22×D4
prime radicalC22×D52C23
hypercenter#2365D13
hypocenterC13#27066
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2365

Complements

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

NH ≅ G/Ntype
2. #13116379C2semidirect
4. #13116079C2semidirect
7. #13115467C2semidirect
9. #13115414C2semidirect
10. #13115395C2semidirect
13. #13114841C2semidirect
14. C4×#88075C2semidirect
15. C13×#2365C2semidirect
169. C13×C4⋊C4SD16semidirect
211. #2365D13semidirect
508. C4⋊C4#6106semidirect
526. C13#27066semidirect

Maximal subgroups

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

subgroupindex
#131194222
#131163792
#131161512
#131160792
#131159192
#131156932
#131154672
#131154632
#131154142
#131153952
#131151912
#131148412
C4×#880752
C13×#23652
#2706613