Finite Group Databasebeta

← #15871172

Subgroups — #15871172

Order 3328.

712 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#88133C211yesmaximal, characteristic
2#13115452C211yesmaximal, characteristic
3#13115439C211yesmaximal, characteristic
4#13115400C211yesmaximal, characteristic, complemented
5#13115399C211yesmaximal, characteristic, complemented
6#13115390C211yesmaximal, characteristic, complemented
7#13114978C211yesmaximal, characteristic, complemented
8#13114709C211yesmaximal, characteristic, complemented
9#13114706C211yesmaximal, characteristic, complemented
10#13114697C211yesmaximal, characteristic, complemented
11#13114622C211yesmaximal, characteristic
12#13114622C211yesmaximal, characteristic
13#13114620C211yesmaximal, characteristic
14#97×Dic13C211yesmaximal, characteristic, complemented
15C13×#1924C211yesmaximal, characteristic
16C22×#6099C2211yescharacteristic
17C2×#88133C411yescharacteristic
18C2×C13×C4⋊C8C2211yescharacteristic
19C2×C13×C22⋊C8C2211yescharacteristic
20C2×C13×C22⋊C8C2211yescharacteristic
21C2×C13×#97C2211yescharacteristic
22C4×C13×C22⋊C4C2211yescharacteristic
23C4×C22⋊Dic13C2211yescharacteristic
24C4×C22⋊Dic13C2211yescharacteristic
25C2×C22⋊#1055C2211yescharacteristic
26C2×#88055C2211yescharacteristic
27C2×#88055C2211yescharacteristic
28C2×#88055C2211yescharacteristic
29C2×#88054C2211yescharacteristic
30C2×#88054C2211yescharacteristic
31C2×C8×Dic13C2211yescharacteristic
32C2×C8×Dic13C2211yescharacteristic
33C2×C8×Dic13C2211yescharacteristic
34#11718612C411yescharacteristic
35#11718606C411yescharacteristic
36#11718605C411yescharacteristic
37C4×C4⋊Dic13C2211yescharacteristic
38C4×#6101C2211yescharacteristic
39C4×#6101C2211yescharacteristic
40C42×Dic13C2211yescharacteristic
41C2×#88043C2211yescharacteristic
42C2×C4×#1055C2211yescharacteristic
43#11718316C411yescharacteristic
44#11718314C411yescharacteristic
45#11718313C411yescharacteristic
46#11718312C411yescharacteristic
47C13×#336C2211yescharacteristic
48C13×#336C2211yescharacteristic
49#11718142C2211yescharacteristic
50#11718142C2211yescharacteristic
51#11718142C2211yescharacteristic
52#11718142C2211yescharacteristic
53#11718142C2211yescharacteristic
54#11718142C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C22×C8×C13C2311yescharacteristic
61C22×C8×C13C2311yescharacteristic
62C22×C8×C13C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C2×C13×C22⋊C4C2×C411yescharacteristic
65C2×C13×C22⋊C4C2×C411yescharacteristic
66C2×C42×C13C2311yescharacteristic
67C2×C42×C13C2311yescharacteristic
68C2×C22⋊Dic13C2×C411yescharacteristic
69C2×C22⋊Dic13C2×C411yescharacteristic
70C2×C22⋊Dic13C2×C411yescharacteristic
71C2×C22⋊Dic13C2×C411yescharacteristic
72C2×C4⋊Dic13C2×C411yescharacteristic
73C2×C4⋊Dic13C2×C411yescharacteristic
74C2×#6101C2×C411yescharacteristic
75C2×#6101C2×C411yescharacteristic
76C2×#6101C2×C411yescharacteristic
77C2×#6101C2×C411yescharacteristic
78C2×C4×Dic13C2×C411yescharacteristic
79C2×C4×Dic13C2×C411yescharacteristic
80C2×C4×Dic13C2×C411yescharacteristic
81C2×C4×Dic13C2×C411yescharacteristic
82C2×C4×Dic13C2311yescharacteristic
83C2×C4×Dic13C2311yescharacteristic
84C2×C4×Dic13C2311yescharacteristic
85C2×C4×Dic13C2311yescharacteristic
86C2×#6099—22no—
87C2×#6099—22no—
88C2×#6099—22no—
89C22×#1055C2311yescharacteristic
90C22×#1055C2311yescharacteristic
91C22×#1055C2311yescharacteristic
92C22×#1055C2311yescharacteristic
93#88133—24no—
94C13×C4⋊C8—22no—
95C13×C22⋊C8—22no—
96C13×C22⋊C8—22no—
97C13×#97—22no—
98C13×#95C2×C411yescharacteristic
99C13×#95C2×C411yescharacteristic
100#88071C2×C411yescharacteristic
101#88071C2×C411yescharacteristic
102#88071C2×C411yescharacteristic
103#88071C2×C411yescharacteristic
104#88071C2×C411yescharacteristic
105#88071C2×C411yescharacteristic
106#88071C2×C411yescharacteristic
107#88071C2×C411yescharacteristic
108#88071C2×C411yescharacteristic
109#88071C2×C411yescharacteristic
110C22⋊#1055—22no—
111#88055—22no—
112#88055—22no—
113#88055—22no—
114#88054—22no—
115#88054—22no—
116C8×Dic13—22no—
117C8×Dic13—22no—
118C8×Dic13—22no—
119#88043—22no—
120C4×#1055—22no—
121#21667—131nomaximal, Sylow
122C24×C13C22×C411yescharacteristic
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13C22×C411yescharacteristic
130C22×C4×C13C22×C411yescharacteristic
131C22×C4×C13C22×C411yescharacteristic
132C22×C4×C13C22×C411yescharacteristic
133C22×C4×C13C22×C411yescharacteristic
134C22×C4×C13C2411yescharacteristic
135C22×Dic13C22×C411yescharacteristic
136C22×Dic13C22×C411yescharacteristic
137C22×Dic13C22×C411yescharacteristic
138C22×Dic13C22×C411yescharacteristic
139C22×Dic13C22×C411yescharacteristic
140C22×Dic13C22×C411yescharacteristic
141C22×Dic13C22×C411yescharacteristic
142C22×Dic13C22×C411yescharacteristic
143C2×C8×C13—21no—
144C2×C8×C13—21no—
145C2×C8×C13—21no—
146C2×C8×C13—21no—
147C2×C8×C13—21no—
148C2×C8×C13—21no—
149C2×C8×C13—21no—
150C2×C8×C13—21no—
151C2×C8×C13—21no—
152C2×C8×C13—21no—
153C2×C8×C13#4112yes—
154C2×C8×C13#4112yes—
155C13×C22⋊C4—22no—
156C13×C22⋊C4—41no—
157C42×C13—21no—
158C42×C13—21no—
159C42×C13—21no—
160C42×C13—21no—
161C22⋊Dic13—22no—
162C22⋊Dic13—22no—
163C22⋊Dic13—22no—
164C22⋊Dic13—41no—
165C4⋊Dic13—22no—
166C4⋊Dic13—41no—
167#6101—22no—
168#6101—22no—
169#6101—41no—
170#6101M1614yescomplemented
171C4×Dic13—21no—
172C4×Dic13—21no—
173C4×Dic13—21no—
174C4×Dic13—21no—
175C4×Dic13—21no—
176C4×Dic13—21no—
177C4×Dic13—21no—
178C4×Dic13—21no—
179C4×Dic13—22no—
180C4×Dic13—22no—
181C4×Dic13—41no—
182C4×Dic13—41no—
183#6099—44no—
184C2×#1055—21no—
185C2×#1055—21no—
186C2×#1055—21no—
187C2×#1055—21no—
188C2×#1055—21no—
189C2×#1055—21no—
190C2×#1055—21no—
191C2×#1055—21no—
192C2×#1055#4112yes—
193C2×#1055#4112yes—
194C2×#1055#4112yes—
195C2×#1055#4112yes—
196C4×#126—131no—
197#1924—131no—
198#1924D1311yescharacteristic
199#1923—131no—
200#1917—131no—
201#1917—131no—
202#1916—131no—
203#1839—131no—
204#1771—131no—
205#1770—131no—
206C8×C4⋊C4—131no—
207#1753—131no—
208#1753—131no—
209#1753—131no—
210C4×#97—131no—
211C23×C13—21no—
212C23×C13—21no—
213C23×C13—21no—
214C23×C13—21no—
215C23×C13—21no—
216C23×C13—21no—
217C23×C13—21no—
218C23×C13C23×C411yescharacteristic
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
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—41no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13C2×M1612yes—
238C2×C4×C13C2×#4111yescharacteristic
239C2×C4×C13C2×#4111yescharacteristic
240C2×C4×C13C2×#4111yescharacteristic
241C2×C4×C13C2×#4111yescharacteristic
242C2×C4×C13C2×#4111yescharacteristic
243C2×C4×C13C2×#4111yescharacteristic
244C2×Dic13—21no—
245C2×Dic13—21no—
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—21no—
258C2×Dic13—21no—
259C2×Dic13—21no—
260C2×Dic13—21no—
261C2×Dic13—21no—
262C2×Dic13—21no—
263C2×Dic13—21no—
264C2×Dic13—21no—
265C2×Dic13C2×M1612yes—
266C2×Dic13C2×M1612yes—
267C2×Dic13#13112yes—
268C8×C13—22no—
269C8×C13—22no—
270C8×C13—41no—
271C8×C13—41no—
272#1055—22no—
273#1055—41no—
274#1055—41no—
275#1055#12614yescomplemented
276C22×M16—131no—
277C2×#126—131no—
278C2×C4⋊C8—131no—
279C2×C4⋊C8—131no—
280C2×C4⋊C8C2×D1311yescharacteristic
281C2×C22⋊C8—131no—
282C2×C22⋊C8C2×D1311yescharacteristic
283C2×C22⋊C8C2×D1311yescharacteristic
284C2×#97—131no—
285C2×#97—131no—
286C2×#97—131no—
287C2×#97—131no—
288C2×#97C2×D1311yescharacteristic
289C2×C4×C8—131no—
290C2×C4×C8—131no—
291C2×C4×C8—131no—
292C2×C4×C8—131no—
293#388—131no—
294#388—131no—
295#388—131no—
296#387—131no—
297#387—131no—
298#387—131no—
299#383—131no—
300C4×C4⋊C4—131no—
301C4×C4⋊C4—131no—
302C4×C4⋊C4—131no—
303C4×C22⋊C4—131no—
304C4×C22⋊C4—131no—
305C4×C22⋊C4C2×D1311yescharacteristic
306C43—131no—
307#336—131no—
308#336—131no—
309#336—131no—
310#336—131no—
311#336—131no—
312#336—131no—
313#336—131no—
314#336—131no—
315#336—131no—
316#336—131no—
317#336C2×D1311yescharacteristic
318#336C2×D1311yescharacteristic
319C22×C13—41no—
320C22×C13—41no—
321C22×C13—41no—
322C22×C13—41no—
323C22×C13—41no—
324C22×C13—41no—
325C22×C13—41no—
326C22×C13C4×#4111yescharacteristic
327C22×C13C4×#4111yescharacteristic
328C22×C13C4×#4111yescharacteristic
329C22×C13C22×M1611yescharacteristic
330C22×C13C2×#13111yescharacteristic
331C22×C13#56811yescharacteristic
332C22×C13#56811yescharacteristic
333C4×C13—22no—
334C4×C13—41no—
335C4×C13—41no—
336C4×C13—41no—
337C4×C13—41no—
338C4×C13C2×#12611yescharacteristic
339C4×C13#52911yescharacteristic
340C4×C13#52911yescharacteristic
341C4×C13#52911yescharacteristic
342Dic13—22no—
343Dic13—22no—
344Dic13—22no—
345Dic13—41no—
346Dic13—41no—
347Dic13—41no—
348Dic13—41no—
349Dic13—41no—
350C23×C4C22×D1311yescharacteristic
351C2×M16—262no—
352C2×M16—262no—
353C2×M16—262no—
354C22×C8—131no—
355C22×C8—131no—
356C22×C8—131no—
357C22×C8—131no—
358C22×C8C22×D1311yescharacteristic
359C22×C8C22×D1311yescharacteristic
360C22×C8C22×D1311yescharacteristic
361C22×C8C22×D1311yescharacteristic
362#126—264no—
363C2×C4⋊C4—131no—
364C2×C4⋊C4—131no—
365C2×C4⋊C4—131no—
366C2×C4⋊C4—131no—
367C2×C4⋊C4—131no—
368C2×C4⋊C4—131no—
369C2×C22⋊C4—131no—
370C2×C22⋊C4—131no—
371C2×C22⋊C4—131no—
372C2×C22⋊C4—131no—
373C2×C22⋊C4C4×D1311yescharacteristic
374C2×C22⋊C4C4×D1311yescharacteristic
375C2×C42—131no—
376C2×C42—131no—
377C2×C42—131no—
378C2×C42—131no—
379C2×C42—131no—
380C2×C42—131no—
381C2×C42—131no—
382C2×C42—131no—
383C2×C42C22×D1311yescharacteristic
384C2×C42C22×D1311yescharacteristic
385C4⋊C8—22no—
386C4⋊C8—262no—
387C4⋊C8—262no—
388C22⋊C8—22no—
389C22⋊C8—22no—
390C22⋊C8—262no—
391#97—22no—
392#97—262no—
393#97—262no—
394#97—262no—
395#97—262no—
396C4×C8—262no—
397C4×C8—262no—
398C4×C8—262no—
399C4×C8—262no—
400#95—131no—
401#95—131no—
402#95—131no—
403#95—131no—
404#95—131no—
405#95—131no—
406#95—131no—
407#95—131no—
408#95—131no—
409#95—131no—
410#95C4×D1311yescharacteristic
411#95C4×D1311yescharacteristic
412C2×C13—81no—
413C2×C13C4×#12611yescharacteristic
414C2×C13#296511yescharacteristic
415C2×C13#296711yescharacteristic
416C2×C13#296811yescharacteristic
417C2×C13#296911yescharacteristic
418C2×C13#297011yescharacteristic
419C2×C13#297111yescharacteristic
420C24C2×C4×D1311yescharacteristic
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—131no—
428C22×C4—131no—
429C22×C4—131no—
430C22×C4—131no—
431C22×C4—131no—
432C22×C4—131no—
433C22×C4—131no—
434C22×C4—131no—
435C22×C4C2×C4×D1311yescharacteristic
436C22×C4C2×C4×D1311yescharacteristic
437C22×C4C2×C4×D1311yescharacteristic
438C22×C4C2×C4×D1311yescharacteristic
439C22×C4C2×C4×D1311yescharacteristic
440C22×C4C23×D1311yescharacteristic
441M16—524no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—132no—
453C2×C8—132no—
454C2×C8—132no—
455C2×C8—132no—
456C2×C8—261no—
457C2×C8—261no—
458C2×C8—261no—
459C2×C8—261no—
460C2×C8—261no—
461C2×C8—261no—
462C2×C8—261no—
463C2×C8—261no—
464C2×C8#612912yes—
465C2×C8#612912yes—
466C4⋊C4—134no—
467C4⋊C4—262no—
468C4⋊C4—262no—
469C4⋊C4—262no—
470C4⋊C4—521no—
471C4⋊C4—521no—
472C22⋊C4—22no—
473C22⋊C4—41no—
474C22⋊C4—262no—
475C22⋊C4—262no—
476C22⋊C4—262no—
477C22⋊C4—521no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—262no—
483C42—262no—
484C42—261no—
485C42—261no—
486C42—261no—
487C42—261no—
488C42—261no—
489C42—261no—
490C42—261no—
491C42—261no—
492C42—521no—
493C42—521no—
494C13#2166711yescharacteristic, complemented, Sylow
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23—21no—
502C23C22×C4×D1311yescharacteristic
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—132no—
522C2×C4—132no—
523C2×C4—132no—
524C2×C4—261no—
525C2×C4—261no—
526C2×C4—261no—
527C2×C4—261no—
528C2×C4—261no—
529C2×C4—261no—
530C2×C4—261no—
531C2×C4—261no—
532C2×C4—261no—
533C2×C4—261no—
534C2×C4—261no—
535C2×C4—261no—
536C2×C4—261no—
537C2×C4—261no—
538C2×C4—261no—
539C2×C4—261no—
540C2×C4—261no—
541C2×C4—261no—
542C2×C4—261no—
543C2×C4—261no—
544C2×C4—261no—
545C2×C4M16×D1312yes—
546C2×C4C2×#612911yescharacteristic
547C2×C4C2×#612911yescharacteristic
548C2×C4#41×D1311yescharacteristic
549C2×C4#41×D1311yescharacteristic
550C2×C4#41×D1311yescharacteristic
551C2×C4#41×D1311yescharacteristic
552C8—22no—
553C8—22no—
554C8—41no—
555C8—41no—
556C8—134no—
557C8—262no—
558C8—521no—
559C8—521no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22#1171922711yescharacteristic
568C22C4×#612911yescharacteristic
569C22C4×#612911yescharacteristic
570C22C2×M16×D1311yescharacteristic
571C22#1171945011yescharacteristic
572C22D13×#13111yescharacteristic
573C22#1171945511yescharacteristic
574C4—22no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—262no—
580C4—262no—
581C4—262no—
582C4—521no—
583C4—521no—
584C4—521no—
585C4—521no—
586C4—521no—
587C4#1171930511yescharacteristic
588C4#1171935411yescharacteristic
589C4#1171938511yescharacteristic
590C4D13×#12611yescharacteristic
591C2—81no—
592C2#1311739011yescharacteristic
593C2#1312379911yescharacteristic
594C2#1312381511yescharacteristic
595C2#1312382711yescharacteristic
596C2#1312383811yescharacteristic
597C2#1312384611yescharacteristic
598C2#1312385311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC13×#1924C2
prime radicalC24×C13C22×C4
cosocleC22×C4×C13C24
hypercenter#1924D13
hypocenterC13#21667
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1924

Complements

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

NH ≅ G/Ntype
4. #13115400C2semidirect
5. #13115399C2semidirect
6. #13115390C2semidirect
7. #13114978C2semidirect
8. #13114709C2semidirect
9. #13114706C2semidirect
10. #13114697C2semidirect
14. #97×Dic13C2semidirect
170. #6101M16semidirect
275. #1055#126semidirect
494. C13#21667semidirect

Maximal subgroups

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

subgroupindex
C4×#881332
#131154522
#131154392
#131154002
#131153992
#131153902
#131149782
#131147092
#131147062
#131146972
#131146222
#131146202
#97×Dic132
C13×#19242
#2166713