Finite Group Databasebeta

← #15833885

Subgroups — #15833885

Order 3328.

740 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124834C211yesmaximal, characteristic
2#13123575C211yesmaximal, characteristic, complemented
3D4×#6094C211yesmaximal, characteristic, complemented
4#13113751C211yesmaximal, characteristic, complemented
5#13113747C211yesmaximal, characteristic, complemented
6#13113701C211yesmaximal, characteristic, complemented
7#13113700C211yesmaximal, characteristic, complemented
8#13113700C211yesmaximal, characteristic, complemented
9#13113699C211yesmaximal, characteristic, complemented
10#13113657C211yesmaximal, characteristic, complemented
11#13113605C211yesmaximal, characteristic, complemented
12#13113285C211yesmaximal, characteristic, complemented
13D13×D4⋊C8C211yesmaximal, characteristic, complemented
14#13113124C211yesmaximal, characteristic, complemented
15C13×#1580C211yesmaximal, characteristic, complemented
16C2×#88155—21no—
17C22×#6094—21no—
18#11719253C2211yescharacteristic
19C4×D4×D13C2211yescharacteristic
20C4×C13×D8C2211yescharacteristic
21C8×D4×C13C2211yescharacteristic
22C8×D4×C13C2211yescharacteristic, complemented
23#11718817C411yescharacteristic
24#11718811C411yescharacteristic
25#11718772—21no—
26#11718772—21no—
27C4×#6104C2211yescharacteristic
28C4×#6104C2211yescharacteristic
29#11718673C2211yescharacteristic, complemented
30D4×#1055C2211yescharacteristic
31#11718551C411yescharacteristic
32#11718543C411yescharacteristic
33#11718499C2211yescharacteristic
34#11718498C2211yescharacteristic
35#11718495C2211yescharacteristic, complemented
36D13×C4⋊C8C2211yescharacteristic
37#11718447C411yescharacteristic
38#11718435C411yescharacteristic
39#11718434C411yescharacteristic
40#11718420C411yescharacteristic
41#11718391—21no—
42#11718389—21no—
43#11718388—21no—
44#11718387—21no—
45C4×D104C2211yescharacteristic
46#11718349C2211yescharacteristic
47#11718349C2211yescharacteristic, complemented
48C4×#6094C2211yescharacteristic
49#11718346C2211yescharacteristic
50C4×C8×D13C2211yescharacteristic
51C13×#334C2211yescharacteristic, complemented
52C13×D4⋊C8C2211yescharacteristic
53C13×D4⋊C8C2211yescharacteristic, complemented
54C13×#322C2211yescharacteristic, complemented
55D4⋊#1055C2211yescharacteristic
56D4⋊#1055C2211yescharacteristic, complemented
57#11718075C2211yescharacteristic
58#11718075C2211yescharacteristic, complemented
59#11718072C2211yescharacteristic, complemented
60#11718072C2211yescharacteristic, complemented
61#11718051C2211yescharacteristic
62#11718051C2211yescharacteristic, complemented
63#11718049C2211yescharacteristic, complemented
64#11718046C2211yescharacteristic, complemented
65#11718046C2211yescharacteristic, complemented
66#11718046C2211yescharacteristic, complemented
67C2×D4×D13C2×C411yescharacteristic
68C2×#6127—21no—
69C22×C4×D13—21no—
70C2×C13×D8C2×C411yescharacteristic
71C22×C8×C13—21no—
72C22×C8×C13—21no—
73C4×D4×C13C2311yescharacteristic
74C4×D4×C13C2311yescharacteristic
75#88194C2×C411yescharacteristic
76#88192C2×C411yescharacteristic
77D4×Dic13C2×C411yescharacteristic
78C2×#6104C2×C411yescharacteristic
79C2×#6104C2×C411yescharacteristic
80C4×C22⋊D13—21no—
81C4×C22⋊D13—21no—
82C2×#6099—21no—
83C22×#1055—21no—
84C2×D104C2×C411yescharacteristic
85#88155—44no—
86C2×#6094—21no—
87C2×#6094—21no—
88C2×#6094—21no—
89C2×#6094—21no—
90C2×#6094—44no—
91C2×#6094D411yescharacteristic
92C2×#6094D411yescharacteristic
93C2×C8×D13—21no—
94C2×C8×D13—21no—
95C2×C8×D13—21no—
96#88149C2×C411yescharacteristic
97#88147C2×C411yescharacteristic
98C4⋊C4×D13C2×C411yescharacteristic
99#88142C2×C411yescharacteristic
100#88139—21no—
101#88138—21no—
102#88135—21no—
103C22⋊C4×D13—21no—
104C4×D52C2311yescharacteristic
105C4×D52C2311yescharacteristic
106C42×D13C2311yescharacteristic
107C13×#107C2×C411yescharacteristic
108C13×C4⋊C8C2311yescharacteristic
109C13×C4⋊C8C2311yescharacteristic
110C13×#102C2×C411yescharacteristic
111C13×#102C2×C411yescharacteristic
112C13×C22⋊C8—21no—
113C13×C22⋊C8—21no—
114C4×C8×C13C2311yescharacteristic
115C4×C8×C13C2311yescharacteristic
116C4×C8×C13C2311yescharacteristic
117#88072C2×C411yescharacteristic
118#88072C2×C411yescharacteristic
119C22⋊#1055—21no—
120C22⋊#1055—21no—
121#88061C2×C411yescharacteristic
122#88061C2×C411yescharacteristic
123#88060—21no—
124#88060—21no—
125#88060—21no—
126#88060—21no—
127#88060C2×C411yescharacteristic
128#88060C2×C411yescharacteristic
129#88058C2×C411yescharacteristic
130#88055D411yescharacteristic
131#88055D411yescharacteristic
132#88054—21no—
133#88054—21no—
134#88054C2×C411yescharacteristic
135#88054C2×C411yescharacteristic
136C8×Dic13—21no—
137#88049C2×C411yescharacteristic
138#88049C2×C411yescharacteristic
139#88047C2×C411yescharacteristic
140#88047C2×C411yescharacteristic
141C4⋊#1055C2311yescharacteristic
142C4⋊#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144C4×#1055C2311yescharacteristic
145C4×#1055C2311yescharacteristic
146#18001—131nomaximal, Sylow
147C23×D13—21no—
148C2×D4×C13C22×C411yescharacteristic
149C2×D4×C13C22×C411yescharacteristic
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C2×C22⋊D13—21no—
153C2×C22⋊D13—21no—
154C2×C22⋊D13—21no—
155C2×C22⋊D13—21no—
156C22×Dic13—21no—
157D4×D13—22no—
158D4×D13—41no—
159#6127—42no—
160#6127—42no—
161C2×D52—21no—
162C2×D52C22×C411yescharacteristic
163C2×D52C22×C411yescharacteristic
164C2×C4×D13—21no—
165C2×C4×D13—21no—
166C2×C4×D13—21no—
167C2×C4×D13—21no—
168C2×C4×D13—42no—
169C2×C4×D13—42no—
170C2×C4×D13C22×C411yescharacteristic
171C2×C4×D13C2×D411yescharacteristic
172C2×C4×D13#4111yescharacteristic
173C2×Dic26—21no—
174C13×D8—22no—
175C2×C8×C13—21no—
176C2×C8×C13—21no—
177C2×C8×C13—21no—
178C2×C8×C13—42no—
179C2×C8×C13—42no—
180C2×C8×C13C22×C411yescharacteristic
181C2×C8×C13C22×C411yescharacteristic
182C2×C8×C13C2×D411yescharacteristic
183C2×C8×C13C2×D411yescharacteristic
184C13×C4⋊C4C22×C411yescharacteristic
185C13×C4⋊C4C22×C411yescharacteristic
186C13×C22⋊C4—21no—
187C13×C22⋊C4—21no—
188C42×C13C2411yescharacteristic
189C22⋊Dic13—21no—
190C22⋊Dic13—21no—
191#6104—22no—
192#6104—41no—
193#6103—21no—
194#6103—21no—
195#6103—21no—
196#6103—21no—
197C4⋊Dic13C22×C411yescharacteristic
198C4⋊Dic13C22×C411yescharacteristic
199#6101—21no—
200#6101—21no—
201C4×Dic13C22×C411yescharacteristic
202C4×Dic13C2×D411yescharacteristic
203C4×Dic13#4111yescharacteristic
204#6099—42no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—42no—
209C2×#1055C22×C411yescharacteristic
210C2×#1055C22×C411yescharacteristic
211C2×#1055C2×D411yescharacteristic
212C2×#1055C2×D411yescharacteristic
213D104—41no—
214#6094—22no—
215#6094—22no—
216#6094—42no—
217#6094—42no—
218#6094—42no—
219#6094—42no—
220C8×D13—42no—
221C8×D13—42no—
222C8×D13—42no—
223#3100—131no—
224#2935—131no—
225D4×M16—131no—
226#1594—131no—
227#1594—131no—
228#1586—131no—
229#1586—131no—
230#1586—131no—
231#1586—131no—
232#1580—131no—
233#1580D1311yescharacteristic, complemented
234#1570—131no—
235#1492—131no—
236C2×D4⋊C8—131no—
237#1451—131no—
238C23×C13—21no—
239C23×C13—21no—
240C22×D13—21no—
241C22×D13—21no—
242C22×D13—42no—
243C22×D13—42no—
244C22×D13—81no—
245C22×D13C4×D411yescharacteristic
246D4×C13—21no—
247D4×C13—21no—
248D4×C13—21no—
249D4×C13#13112yescomplemented
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13C23×C411yescharacteristic
257C2×C4×C13C22×D411yescharacteristic
258C2×C4×C13C2×#4111yescharacteristic
259C22⋊D13—42no—
260C22⋊D13—42no—
261C22⋊D13—42no—
262C22⋊D13—81no—
263C2×Dic13—21no—
264C2×Dic13—21no—
265C2×Dic13—42no—
266C2×Dic13C4×D411yescharacteristic
267C2×Dic13C4×D411yescharacteristic
268C2×Dic13C4×D411yescharacteristic
269D52—21no—
270D52—21no—
271D52—21no—
272D52—21no—
273D52—42no—
274C4×D13—21no—
275C4×D13—21no—
276C4×D13—41no—
277C4×D13—42no—
278C4×D13—41no—
279C4×D13—41no—
280C4×D13—41no—
281C4×D13—41no—
282C4×D13—42no—
283C4×D13AGL(1,ℤ/8)12yes—
284C4×D13AGL(1,ℤ/8)12yes—
285Dic26—42no—
286C8×C13—21no—
287C8×C13—21no—
288C8×C13—21no—
289C8×C13—21no—
290C8×C13—41no—
291C8×C13—41no—
292C8×C13—41no—
293#1055—22no—
294#1055—21no—
295#1055—21no—
296#1055—21no—
297#1055—21no—
298#1055—41no—
299#1055—41no—
300C2×#131—261no—
301C22×M16—261no—
302#532—131no—
303C2×C4×D4—131no—
304#480—131no—
305#480—131no—
306#474—131no—
307#474—131no—
308#459—131no—
309#459—131no—
310#447—131no—
311#447—131no—
312C4×D8—131no—
313C4×D8—131no—
314C4×D8—131no—
315C4×D8C2×D1311yescharacteristic
316#436—131no—
317#436—131no—
318#436—131no—
319#436—131no—
320#435—261no—
321#435—261no—
322#435—261no—
323#435—261no—
324C8×D4—131no—
325C8×D4—131no—
326C8×D4C2×D1311yescharacteristic
327C8×D4C2×D1311yescharacteristic, complemented
328#431—131no—
329#423—131no—
330C2×C4⋊C8—131no—
331#408—261no—
332#407—261no—
333C4×M16—131no—
334C2×C4×C8—131no—
335#334—131no—
336#334—131no—
337#334—131no—
338#334C2×D1311yescharacteristic, complemented
339D4⋊C8—131no—
340D4⋊C8—131no—
341D4⋊C8—131no—
342D4⋊C8—131no—
343D4⋊C8—131no—
344D4⋊C8—131no—
345D4⋊C8C2×D1311yescharacteristic
346D4⋊C8C2×D1311yescharacteristic, complemented
347#322—131no—
348#322—131no—
349#322—131no—
350#322C2×D1311yescharacteristic, complemented
351C22×C13—22no—
352C22×C13—41no—
353C22×C13—41no—
354C22×C13—41no—
355C22×C13—41no—
356C22×C13—41no—
357C22×C13C2×C4×D411yescharacteristic
358C2×D13—21no—
359C2×D13—21no—
360C2×D13—41no—
361C2×D13—41no—
362C2×D13—41no—
363C2×D13—41no—
364C2×D13—41no—
365C2×D13—41no—
366C2×D13—84no—
367C2×D13#44212yes—
368C4×C13—21no—
369C4×C13—41no—
370C4×C13—41no—
371C4×C13C2×#13111yescharacteristic
372C4×C13#56811yescharacteristic
373C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
374C4×C13C2×AGL(1,ℤ/8)11yescharacteristic
375Dic13—21no—
376Dic13—21no—
377Dic13—41no—
378Dic13—41no—
379Dic13#44212yes—
380C2×#41—261no—
381C22×D4—131no—
382C23×C4—261no—
383C2×D8—131no—
384C2×D8—131no—
385C2×D8—131no—
386C2×D8C4×D1311yescharacteristic
387#131—524no—
388C2×M16—131no—
389C2×M16—131no—
390C2×M16—261no—
391C2×M16—261no—
392C2×M16—261no—
393C2×M16—261no—
394C2×M16—261no—
395C2×M16—524no—
396C22×C8—21no—
397C22×C8—21no—
398C22×C8—261no—
399C22×C8—261no—
400C22×C8—261no—
401C22×C8—261no—
402C4⋊Q8—131no—
403#127—131no—
404#124—261no—
405#121—131no—
406#121—131no—
407#121—261no—
408C4×D4—131no—
409C4×D4—131no—
410C4×D4—131no—
411C4×D4—131no—
412C4×D4—261no—
413C4×D4—261no—
414C4×D4—261no—
415C4×D4C22×D1311yescharacteristic
416C4×D4C22×D1311yescharacteristic
417C2×C4⋊C4—131no—
418C2×C22⋊C4—261no—
419C2×C42—131no—
420#107—131no—
421#107—131no—
422#107—131no—
423#107C4×D1311yescharacteristic
424C4⋊C8—131no—
425C4⋊C8—131no—
426C4⋊C8—131no—
427C4⋊C8—131no—
428C4⋊C8—261no—
429C4⋊C8—261no—
430C4⋊C8C22×D1311yescharacteristic
431C4⋊C8C22×D1311yescharacteristic
432#102—131no—
433#102—131no—
434#102—131no—
435#102—131no—
436#102—131no—
437#102—131no—
438#102C4×D1311yescharacteristic
439#102C4×D1311yescharacteristic
440C22⋊C8—21no—
441C22⋊C8—21no—
442C22⋊C8—131no—
443C22⋊C8—131no—
444C22⋊C8—261no—
445C22⋊C8—261no—
446C22⋊C8—261no—
447C22⋊C8—261no—
448C22⋊C8—261no—
449C22⋊C8—261no—
450#97—131no—
451#97—131no—
452C4×C8—131no—
453C4×C8—131no—
454C4×C8—131no—
455C4×C8—261no—
456C4×C8C22×D1311yescharacteristic
457C4×C8C22×D1311yescharacteristic
458C4×C8C22×D1311yescharacteristic
459C2×C13—42no—
460C2×C13—81no—
461C2×C13#293311yescharacteristic
462C2×C13C2×#44211yescharacteristic
463C2×C13#295611yescharacteristic
464D13—22no—
465D13—81no—
466D13—81no—
467C24—261no—
468#41—522no—
469#41—522no—
470C2×Q8—261no—
471C2×D4—131no—
472C2×D4—131no—
473C2×D4—261no—
474C2×D4—261no—
475C2×D4—261no—
476C2×D4—261no—
477C2×D4—262no—
478C2×D4—261no—
479C2×D4—521no—
480C2×D4C2×C4×D1311yescharacteristic
481C2×D4C2×C4×D1311yescharacteristic
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—131no—
485C22×C4—131no—
486C22×C4—131no—
487C22×C4—261no—
488C22×C4—261no—
489C22×C4—261no—
490C22×C4—261no—
491C22×C4—261no—
492C22×C4—522no—
493C22×C4—522no—
494D8—22no—
495D8—262no—
496D8—521no—
497D8—521no—
498M16—262no—
499M16—262no—
500M16—522no—
501M16—522no—
502M16—522no—
503M16—522no—
504M16—522no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—42no—
509C2×C8—42no—
510C2×C8—131no—
511C2×C8—131no—
512C2×C8—131no—
513C2×C8—131no—
514C2×C8—261no—
515C2×C8—261no—
516C2×C8—261no—
517C2×C8—522no—
518C2×C8—522no—
519C2×C8—522no—
520C2×C8—522no—
521C2×C8C2×C4×D1311yescharacteristic
522C2×C8C2×C4×D1311yescharacteristic
523C2×C8D4×D1311yescharacteristic
524C2×C8D4×D1311yescharacteristic
525C4⋊C4—131no—
526C4⋊C4—131no—
527C4⋊C4—261no—
528C4⋊C4—261no—
529C4⋊C4C2×C4×D1311yescharacteristic
530C4⋊C4C2×C4×D1311yescharacteristic
531C22⋊C4—21no—
532C22⋊C4—21no—
533C22⋊C4—261no—
534C22⋊C4—261no—
535C22⋊C4—261no—
536C22⋊C4—261no—
537C22⋊C4—261no—
538C22⋊C4—261no—
539C42—131no—
540C42—131no—
541C42—131no—
542C42C23×D1311yescharacteristic
543C13#1800111yescharacteristic, complemented, Sylow
544C23—21no—
545C23—21no—
546C23—131no—
547C23—261no—
548C23—261no—
549C23—522no—
550C23—522no—
551C23—1041no—
552Q8—522no—
553D4—21no—
554D4—21no—
555D4—21no—
556D4—261no—
557D4—261no—
558D4—261no—
559D4—261no—
560D4—522no—
561D4—522no—
562D4—522no—
563D4—522no—
564D4—1041no—
565D4#8815512yescomplemented
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—131no—
573C2×C4—132no—
574C2×C4—132no—
575C2×C4—131no—
576C2×C4—131no—
577C2×C4—261no—
578C2×C4—261no—
579C2×C4—261no—
580C2×C4—261no—
581C2×C4—521no—
582C2×C4—522no—
583C2×C4—522no—
584C2×C4—522no—
585C2×C4—521no—
586C2×C4—521no—
587C2×C4—521no—
588C2×C4—521no—
589C2×C4C22×C4×D1311yescharacteristic
590C2×C4C2×D4×D1311yescharacteristic
591C2×C4#41×D1311yescharacteristic
592C8—21no—
593C8—21no—
594C8—21no—
595C8—21no—
596C8—41no—
597C8—41no—
598C8—41no—
599C8—262no—
600C8—261no—
601C8—261no—
602C8—261no—
603C8—261no—
604C8—521no—
605C8—521no—
606C22—22no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—132no—
613C22—261no—
614C22—261no—
615C22—521no—
616C22—521no—
617C22—521no—
618C22—521no—
619C22—521no—
620C22—521no—
621C22—1044no—
622C22C4×D4×D1311yescharacteristic
623C4—21no—
624C4—41no—
625C4—41no—
626C4—132no—
627C4—261no—
628C4—261no—
629C4—521no—
630C4—521no—
631C4C2×#8815511yescharacteristic
632C4#1171945511yescharacteristic
633C4D13×AGL(1,ℤ/8)11yescharacteristic
634C4D13×AGL(1,ℤ/8)11yescharacteristic
635C2—42no—
636C2—81no—
637C2—262no—
638C2—1041no—
639C2—1041no—
640C2#1312355611yescharacteristic
641C2D13×#44211yescharacteristic
642C2#1312374411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1580C2
socleC22×C13C2×C4×D4
prime radical#13124834C2
cosocleC42×C13C24
hypercenter#1580D13
hypocenterC13#18001
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1580

Complements

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

NH ≅ G/Ntype
2. #13123575C2semidirect
3. D4×#6094C2semidirect
4. #13113751C2semidirect
5. #13113747C2semidirect
6. #13113701C2semidirect
7. #13113700C2semidirect
8. #13113700C2semidirect
9. #13113699C2semidirect
10. #13113657C2semidirect
11. #13113605C2semidirect
12. #13113285C2semidirect
13. D13×D4⋊C8C2semidirect
14. #13113124C2semidirect
15. C13×#1580C2semidirect
22. C8×D4×C13C22semidirect
29. #11718673C22semidirect
35. #11718495C22semidirect
47. #11718349C22semidirect
51. C13×#334C22semidirect
53. C13×D4⋊C8C22semidirect
54. C13×#322C22semidirect
56. D4⋊#1055C22semidirect
58. #11718075C22semidirect
59. #11718072C22semidirect
60. #11718072C22semidirect
62. #11718051C22semidirect
63. #11718049C22semidirect
64. #11718046C22semidirect
65. #11718046C22semidirect
66. #11718046C22semidirect
233. #1580D13semidirect
249. D4×C13#131semidirect
327. C8×D4C2×D13semidirect
338. #334C2×D13semidirect
346. D4⋊C8C2×D13semidirect
350. #322C2×D13semidirect
543. C13#18001semidirect
565. D4#88155semidirect

Maximal subgroups

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

subgroupindex
#131248342
#131235752
D4×#60942
#131137512
#131137472
#131137012
#131137002
#131136992
#131136572
#131136052
#131132852
D13×D4⋊C82
#131131242
C13×#15802
#1800113