Finite Group Databasebeta

← #15912339

Subgroups — #15912339

Order 3328.

794 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718750C211yesmaximal, characteristic
2C2×#11718755C211yesmaximal, characteristic, complemented
3#13119816C211yesmaximal, characteristic
4#13116214C211yesmaximal, characteristic, complemented
5#13116207C211yesmaximal, characteristic
6#13116082C211yesmaximal, characteristic, complemented
7#13116077C211yesmaximal, characteristic
8#13115768C211yesmaximal, characteristic
9#13115768C211yesmaximal, characteristic
10#13115759C211yesmaximal, characteristic, complemented
11#13115560C211yesmaximal, characteristic, complemented
12#13115470C211yesmaximal, characteristic, complemented
13#13115463C211yesmaximal, characteristic
14#13114669C211yesmaximal, characteristic, complemented
15C13×#2369C211yesmaximal, characteristic, complemented
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×#88129C2211yescharacteristic
18C2×#88129C2211yescharacteristic
19C2×#88123C2211yescharacteristic
20C2×C4×Dic26C2211yescharacteristic
21C13×#391—21no—
22C13×#391—21no—
23C13×#389—21no—
24C13×#389C2211yescharacteristic
25C13×#389C2211yescharacteristic
26C4×C13×C4⋊C4—21no—
27C4×C13×C4⋊C4C2211yescharacteristic
28C4×C13×C4⋊C4C2211yescharacteristic
29C4×C13×C4⋊C4C2211yescharacteristic
30C4×C13×C4⋊C4C2211yescharacteristic
31#11718755—24no—
32#11718750—24no—
33#11718655—21no—
34#11718655—21no—
35C2×#88050C2211yescharacteristic
36C2×#88050C2211yescharacteristic
37C2×#88050C2211yescharacteristic
38C2×#88050C2211yescharacteristic
39C2×#88050C2211yescharacteristic
40C2×#88050C2211yescharacteristic
41C2×#88050C2211yescharacteristic
42C2×#88050C2211yescharacteristic
43C2×#88049C2211yescharacteristic
44C2×#88049C2211yescharacteristic
45C2×#88049C2211yescharacteristic
46C2×#88049C2211yescharacteristic
47C2×#88048C2211yescharacteristic
48C2×#88048C2211yescharacteristic
49#11718600C2211yescharacteristic
50#11718590C2211yescharacteristic
51C2×C4⋊#1055C2211yescharacteristic
52C2×C4⋊#1055C2211yescharacteristic
53C2×C4⋊#1055C2211yescharacteristic
54C2×#88043C2211yescharacteristic
55#11718331—21no—
56#11718331—21no—
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C22×Q8×C13—21no—
62C22×D52C2311yescharacteristic
63C22×Dic26C2311yescharacteristic
64C22×Dic26C2311yescharacteristic
65C13×C4⋊Q8—22no—
66C13×C4⋊Q8D414yes—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4D411yescharacteristic
71C2×C13×C4⋊C4D411yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
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×#6103—21no—
83C2×#6103—21no—
84C2×#6103—21no—
85C2×#6103—21no—
86C2×#6103—21no—
87C2×#6103—21no—
88C2×C4⋊Dic13—21no—
89C2×C4⋊Dic13—21no—
90C2×C4⋊Dic13C2311yescharacteristic
91C2×#6101—21no—
92C2×C4×Dic13—21no—
93C22×#1055C2311yescharacteristic
94C22×#1055C2311yescharacteristic
95C22×#1055C2311yescharacteristic
96C22×#1055C2311yescharacteristic
97#88129—22no—
98#88129—22no—
99#88129—22no—
100#88129—41no—
101#88123—22no—
102#88123—41no—
103C4×Dic26—22no—
104C4×Dic26—22no—
105C13×#95—21no—
106C13×#95—21no—
107C13×#95—21no—
108C13×#95—21no—
109C13×#95—21no—
110C13×#95D411yescharacteristic
111C13×#95D411yescharacteristic
112#88071—21no—
113#88071—21no—
114#88050—22no—
115#88050—22no—
116#88050—22no—
117#88050—22no—
118#88050—22no—
119#88050—22no—
120#88050—22no—
121#88050—41no—
122#88049—22no—
123#88049—22no—
124#88049—22no—
125#88049—41no—
126#88048—22no—
127#88048—22no—
128C4⋊#1055—22no—
129C4⋊#1055—41no—
130C4⋊#1055—41no—
131#88043—22no—
132#25287—131nomaximal, Sylow
133C23×D13—21no—
134C2×Q8×C13—24no—
135C2×Q8×C13—81no—
136C2×Q8×C13—81no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2411yescharacteristic
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C2×D52—21no—
152C2×D52—21no—
153C2×D52—21no—
154C2×D52—21no—
155C2×D52—21no—
156C2×D52—21no—
157C2×Dic26—21no—
158C2×Dic26—21no—
159C2×Dic26—21no—
160C2×Dic26—21no—
161C2×Dic26—21no—
162C2×Dic26—21no—
163C2×Dic26—21no—
164C2×Dic26—21no—
165C2×Dic26—21no—
166C2×Dic26—21no—
167C2×Dic26—21no—
168C2×Dic26#4112yes—
169C13×C4⋊C4—24no—
170C13×C4⋊C4—22no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—41no—
177C13×C4⋊C4—81no—
178C13×C4⋊C4—81no—
179C13×C4⋊C4C2×D412yes—
180C13×C4⋊C4C2×D412yes—
181C13×C4⋊C4#4112yes—
182C42×C13—21no—
183C42×C13—21no—
184C42×C13—21no—
185C42×C13—21no—
186C42×C13—42no—
187C42×C13—81no—
188C42×C13—81no—
189C42×C13C2×D412yes—
190C42×C13#4112yes—
191#6103—42no—
192#6103—42no—
193#6103—42no—
194#6103—42no—
195#6103—42no—
196#6103—42no—
197C4⋊Dic13—21no—
198C4⋊Dic13—21no—
199C4⋊Dic13—42no—
200C4⋊Dic13—42no—
201#6101—42no—
202C4×Dic13—42no—
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—
213C2×#1055—21no—
214C2×#1055—21no—
215C2×#489—131no—
216C2×#475—131no—
217#2545—131no—
218#2369D1311yescharacteristic, complemented
219#2066—131no—
220#2065—131no—
221#2043—131no—
222#2042—131no—
223#1983—131no—
224#1983—131no—
225#1981—131no—
226#1940—131no—
227#1927—131no—
228#1926—131no—
229#1763—131no—
230C23×C13C22×D411yescharacteristic
231C22×D13—41no—
232C22×D13—41no—
233C22×D13—41no—
234C22×D13—41no—
235C22×D13—41no—
236C22×D13—41no—
237C22×D13—41no—
238Q8×C13—84no—
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—22no—
246C2×C4×C13—22no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—22no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
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#12112yes—
267C2×C4×C13#12112yes—
268C2×C4×C13#13712yes—
269C2×C4×C13C22×D411yescharacteristic
270C2×C4×C13C2×#4111yescharacteristic
271C2×C4×C13C2×#4111yescharacteristic
272C2×C4×C13C2×#4111yescharacteristic
273C2×C4×C13H(5,𝔽2)11yescharacteristic
274C2×C4×C132−1+411yescharacteristic
275C2×Dic13—22no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278C2×Dic13—41no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284D52—41no—
285D52—41no—
286D52—41no—
287D52—41no—
288Dic26—22no—
289Dic26—22no—
290Dic26—41no—
291Dic26—41no—
292Dic26—41no—
293Dic26—41no—
294Dic26—41no—
295Dic26—41no—
296#1055—41no—
297#1055—41no—
298#1055—41no—
299#1055—41no—
300C2×C4⋊Q8—131no—
301C2×C4⋊Q8C2×D1311yescharacteristic
302C2×#124—131no—
303C2×#124—131no—
304C2×C4×Q8—131no—
305#489—264no—
306#475—264no—
307C2×#106—131no—
308C2×#106—131no—
309C2×C4⋊C8—131no—
310C2×C4⋊C8—131no—
311C2×C4⋊C8—131no—
312C2×#103—131no—
313C2×#103—131no—
314C2×#103—131no—
315C2×#103—131no—
316C2×#103—131no—
317C2×#103—131no—
318C2×#103—131no—
319C2×#103—131no—
320C2×#102—131no—
321C2×#102—131no—
322C2×#102—131no—
323C2×#102—131no—
324C2×#97—131no—
325#396—261no—
326#396—261no—
327#391—21no—
328#391—21no—
329#391—131no—
330#390—131no—
331#389—21no—
332#389C2×D1311yescharacteristic
333#389C2×D1311yescharacteristic
334#388—261no—
335#388—261no—
336C4×C4⋊C4—21no—
337C4×C4⋊C4C2×D1311yescharacteristic
338C4×C4⋊C4C2×D1311yescharacteristic
339C4×C4⋊C4C2×D1311yescharacteristic
340C4×C4⋊C4C2×D1311yescharacteristic
341#340—131no—
342#340—131no—
343#336—131no—
344#336—131no—
345C22×C13C2×#12111yescharacteristic
346C22×C13#54611yescharacteristic
347C22×C13#54811yescharacteristic
348C22×C13C2×#13711yescharacteristic
349C22×C13#57511yescharacteristic
350C22×C13#57711yescharacteristic
351C22×C13#57711yescharacteristic
352C2×D13—81no—
353C2×D13—81no—
354C2×D13—81no—
355C2×D13—81no—
356C2×D13—81no—
357C2×D13—81no—
358C2×D13—81no—
359C4×C13—22no—
360C4×C13—22no—
361C4×C13—22no—
362C4×C13—42no—
363C4×C13—42no—
364C4×C13—42no—
365C4×C13—41no—
366C4×C13—41no—
367C4×C13—41no—
368C4×C13—81no—
369C4×C13#52911yescharacteristic
370C4×C13#54211yescharacteristic
371C4×C13#54811yescharacteristic
372C4×C13#55011yescharacteristic
373Dic13—42no—
374Dic13—81no—
375Dic13—81no—
376C22×Q8—21no—
377C22×Q8—131no—
378C22×Q8—131no—
379C22×D4—131no—
380C22×C8—131no—
381C22×C8—131no—
382C22×C8—131no—
383C22×C8—131no—
384C4⋊Q8—22no—
385C4⋊Q8—262no—
386C4⋊Q8—521no—
387C4⋊Q8D5214yes—
388#124—262no—
389#124—262no—
390#124—262no—
391#124—521no—
392C4×Q8—262no—
393C4×Q8—262no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—131no—
398C2×C4⋊C4—261no—
399C2×C4⋊C4—261no—
400C2×C4⋊C4—261no—
401C2×C4⋊C4C22⋊D1311yescharacteristic
402C2×C4⋊C4C22⋊D1311yescharacteristic
403C2×C4⋊C4C22×D1311yescharacteristic
404C2×C4⋊C4C22×D1311yescharacteristic
405C2×C4⋊C4C22×D1311yescharacteristic
406C2×C4⋊C4C22×D1311yescharacteristic
407C2×C22⋊C4—261no—
408C2×C22⋊C4—261no—
409C2×C22⋊C4—261no—
410C2×C22⋊C4—261no—
411C2×C22⋊C4—261no—
412C2×C22⋊C4—261no—
413C2×C42—21no—
414C2×C42—21no—
415C2×C42—21no—
416C2×C42—261no—
417C2×C42C22×D1311yescharacteristic
418C2×C42C22×D1311yescharacteristic
419C2×C42C22×D1311yescharacteristic
420#106—262no—
421#106—262no—
422C4⋊C8—262no—
423C4⋊C8—521no—
424C4⋊C8—521no—
425#103—262no—
426#103—262no—
427#103—262no—
428#103—262no—
429#103—262no—
430#103—262no—
431#103—262no—
432#103—521no—
433#102—262no—
434#102—262no—
435#102—262no—
436#102—521no—
437#97—262no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95—261no—
444#95—261no—
445#95C22⋊D1311yescharacteristic
446#95C22⋊D1311yescharacteristic
447C2×C13#242611yescharacteristic
448C2×C13#303711yescharacteristic
449C2×C13#304211yescharacteristic
450C2×C13#331611yescharacteristic
451C2×C13#332111yescharacteristic
452C2×C13#336911yescharacteristic
453C2×C13#337611yescharacteristic
454D13—161no—
455C24—261no—
456C2×Q8—24no—
457C2×Q8—81no—
458C2×Q8—81no—
459C2×Q8—132no—
460C2×Q8—261no—
461C2×Q8—261no—
462C2×Q8—261no—
463C2×Q8—261no—
464C2×Q8—261no—
465C2×Q8—261no—
466C2×Q8—261no—
467C2×Q8—261no—
468C2×Q8—261no—
469C2×Q8—261no—
470C2×Q8—261no—
471C2×D4—261no—
472C2×D4—261no—
473C2×D4—261no—
474C2×D4—261no—
475C2×D4—261no—
476C2×D4—261no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—261no—
482C22×C4—261no—
483C22×C4—261no—
484C22×C4C2×C22⋊D1311yescharacteristic
485C22×C4C2×C22⋊D1311yescharacteristic
486C22×C4C2×C22⋊D1311yescharacteristic
487C22×C4C2×C22⋊D1311yescharacteristic
488C22×C4C2×C22⋊D1311yescharacteristic
489C22×C4C2×C22⋊D1311yescharacteristic
490C22×C4C23×D1311yescharacteristic
491C2×C8—261no—
492C2×C8—261no—
493C2×C8—261no—
494C2×C8—261no—
495C2×C8—261no—
496C2×C8—261no—
497C2×C8—261no—
498C2×C8—261no—
499C2×C8—261no—
500C2×C8—261no—
501C2×C8—261no—
502C2×C8—261no—
503C4⋊C4—24no—
504C4⋊C4—22no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—41no—
511C4⋊C4—81no—
512C4⋊C4—81no—
513C4⋊C4—261no—
514C4⋊C4—261no—
515C4⋊C4—522no—
516C4⋊C4—522no—
517C4⋊C4—522no—
518C4⋊C4C2×D5212yes—
519C4⋊C4C2×D5212yes—
520C4⋊C4#613112yes—
521C22⋊C4—522no—
522C22⋊C4—522no—
523C22⋊C4—522no—
524C22⋊C4—522no—
525C22⋊C4—522no—
526C22⋊C4—522no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—42no—
532C42—81no—
533C42—81no—
534C42—522no—
535C42C2×D5212yes—
536C42#612712yes—
537C13#2528711yescharacteristic, complemented, Sylow
538C23—521no—
539C23—521no—
540C23—521no—
541C23—521no—
542C23—521no—
543C23—521no—
544C23—521no—
545C23C22×C22⋊D1311yescharacteristic
546Q8—84no—
547Q8—262no—
548Q8—262no—
549Q8—521no—
550Q8—521no—
551Q8—521no—
552Q8—521no—
553Q8—521no—
554Q8—521no—
555D4—521no—
556D4—521no—
557D4—521no—
558D4—521no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
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—262no—
587C2×C4—521no—
588C2×C4—521no—
589C2×C4—521no—
590C2×C4—521no—
591C2×C4—521no—
592C2×C4—521no—
593C2×C4—521no—
594C2×C4—521no—
595C2×C4#8818412yes—
596C2×C4#8818412yes—
597C2×C4#8819612yes—
598C2×C4C22×D5211yescharacteristic
599C2×C4C2×#612711yescharacteristic
600C2×C4C2×#613111yescharacteristic
601C2×C4#8825411yescharacteristic
602C2×C4#41×D1311yescharacteristic
603C2×C4#8825611yescharacteristic
604C8—521no—
605C8—521no—
606C8—521no—
607C8—521no—
608C22—1041no—
609C22—1041no—
610C22—1041no—
611C22—1041no—
612C22—1041no—
613C22—1041no—
614C22—1041no—
615C22C2×#8818411yescharacteristic
616C22C2×#8819611yescharacteristic
617C22#1171952211yescharacteristic
618C22#1171952711yescharacteristic
619C22#1171953411yescharacteristic
620C22#1171954111yescharacteristic
621C22#1171954111yescharacteristic
622C4—22no—
623C4—22no—
624C4—22no—
625C4—41no—
626C4—41no—
627C4—41no—
628C4—42no—
629C4—42no—
630C4—42no—
631C4—81no—
632C4—522no—
633C4—1041no—
634C4—1041no—
635C4#1171928111yescharacteristic
636C4#1171928211yescharacteristic
637C4#1171928511yescharacteristic
638C4#1171928711yescharacteristic
639C2—2081no—
640C2#1311839611yescharacteristic
641C2#1312430811yescharacteristic
642C2#1312434811yescharacteristic
643C2#1312694111yescharacteristic
644C2#1312701611yescharacteristic
645C2#1312757611yescharacteristic
646C2#1312766311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2369C2
socleC23×C13C22×D4
prime radicalC22×D52C23
hypercenter#2369D13
hypocenterC13#25287
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2369

Complements

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

NH ≅ G/Ntype
2. C2×#11718755C2semidirect
4. #13116214C2semidirect
6. #13116082C2semidirect
10. #13115759C2semidirect
11. #13115560C2semidirect
12. #13115470C2semidirect
14. #13114669C2semidirect
15. C13×#2369C2semidirect
218. #2369D13semidirect
537. C13#25287semidirect

Maximal subgroups

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

subgroupindex
C2×#117187502
C2×#117187552
#131198162
#131162142
#131162072
#131160822
#131160772
#131157682
#131157592
#131155602
#131154702
#131154632
#131146692
C13×#23692
#2528713