Finite Group Databasebeta

← #16035972

Subgroups — #16035972

Order 3328.

1978 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#13123146C212yesmaximal, complemented
2#13123123C212yesmaximal
3#13120950C211yesmaximal, characteristic, complemented
4#13120950C211yesmaximal, characteristic, complemented
5#13120641C212yesmaximal
6#13120110C214yesmaximal, complemented
7#13119920C214yesmaximal, complemented
8#13119554C214yesmaximal, complemented
9#13118857C214yesmaximal, complemented
10#13117569C212yesmaximal, complemented
11#13117434C212yesmaximal
12C4×#88178C212yesmaximal, complemented
13C2×C4×C13×C22⋊C4C211yesmaximal, characteristic
14C24×C4×C13C2211yescharacteristic
15C22×C13×C22⋊C4C2211yescharacteristic
16C22×C13×C22⋊C4C2211yescharacteristic
17C22×C42×C13C2211yescharacteristic
18C22×C42×C13C2211yescharacteristic
19C2×#88178C2212yes—
20C2×#88178C2212yes—
21C2×#88178C2212yes—
22C2×#88178C2212yes—
23C2×#88124C2212yescomplemented
24C2×C4×Dic26C2212yescomplemented
25C4×C13×C22⋊C4C2214yes—
26C4×C13×C22⋊C4C2214yes—
27C2×C13×#95C2211yescharacteristic
28C2×C13×#95C2211yescharacteristic
29#11718908C2214yes—
30#11718873C2212yes—
31#11718873C2212yes—
32#11718873C2212yes—
33#11718873C2212yes—
34#11718873C2212yes—
35#11718873C2212yes—
36#11718871C2214yes—
37#11718871C2214yes—
38#11718871C2214yes—
39#11718871C2214yes—
40C4×C22⋊Dic13C2214yes—
41#11718612C2214yes—
42#11718612C2214yes—
43#11718612C2214yes—
44#11718612C2214yes—
45#11718610C2214yes—
46#11718609C2214yes—
47#11718609C2214yes—
48#11718608C2214yes—
49#11718597C2212yescomplemented
50C4×C4⋊Dic13C2212yescomplemented
51#11718594C2214yescomplemented
52#11718594C2214yescomplemented
53#11718594C2214yescomplemented
54C4×#6101C2214yescomplemented
55#11718590C2212yescomplemented
56#11718589C2212yescomplemented
57#11718589C2212yescomplemented
58#11718589C2212yescomplemented
59#11718322C2214yescomplemented
60#11718322C2214yescomplemented
61#11718317C2214yescomplemented
62#11718317C2214yescomplemented
63#11718316C2214yescomplemented
64#11718315C2214yescomplemented
65#11718308C2214yescomplemented
66#11718307C2214yescomplemented
67C25×C13C2311yescharacteristic
68C23×C4×C13—24no—
69C23×C4×C13—42no—
70C23×C4×C13—42no—
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2312yes—
73C23×C4×C13C2312yes—
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C22×Dic26C2312yes—
80C22×Dic26C2312yes—
81C2×C13×C22⋊C4—24no—
82C2×C13×C22⋊C4Q818yescomplemented
83C2×C13×C22⋊C4C2314yes—
84C2×C13×C22⋊C4C2314yes—
85C2×C42×C13—42no—
86C2×C42×C13—42no—
87C2×C42×C13C2312yes—
88C2×C42×C13C2312yes—
89C2×C42×C13C2312yes—
90C2×C42×C13C2312yes—
91C2×C22⋊Dic13C2314yes—
92C2×C22⋊Dic13C2314yes—
93C2×C22⋊Dic13C2314yes—
94C2×C22⋊Dic13C2314yes—
95C2×C22⋊Dic13C2314yes—
96C2×C22⋊Dic13C2314yes—
97C2×C4⋊Dic13C2312yes—
98C2×C4⋊Dic13C2312yes—
99C2×C4⋊Dic13C2312yes—
100C2×C4⋊Dic13C2312yes—
101C2×C4⋊Dic13C2312yes—
102C2×C4⋊Dic13C2312yes—
103C2×C4⋊Dic13C2312yes—
104C2×C4⋊Dic13C2312yes—
105C2×C4⋊Dic13C2312yes—
106C2×C4⋊Dic13C2312yes—
107#88178—28no—
108#88178—28no—
109#88178—44no—
110#88178—44no—
111C2×#6101C2314yes—
112C2×#6101C2314yes—
113C2×#6101C2314yes—
114C2×#6101C2314yes—
115C2×#6101C2314yes—
116C2×#6101C2314yes—
117C2×C4×Dic13C2314yes—
118C2×C4×Dic13C2314yes—
119#88124—44no—
120C4×Dic26—44no—
121C13×#95C2314yes—
122C13×#95C2314yes—
123#88071C2314yes—
124#88071C2314yes—
125#88071C2314yes—
126#88071C2314yes—
127#88071C2314yes—
128#88071C2314yes—
129#88071C2314yes—
130#88071C2314yes—
131#88071C2314yes—
132#88071C2314yes—
133#35012—131nomaximal, Sylow
134C24×C13—22no—
135C24×C13—22no—
136C24×C13—41no—
137C24×C13—41no—
138C24×C13—41no—
139C24×C13—41no—
140C24×C13C2×Q814yes—
141C24×C13C2412yes—
142C24×C13C2411yescharacteristic
143C22×C4×C13—22no—
144C22×C4×C13—22no—
145C22×C4×C13—22no—
146C22×C4×C13—22no—
147C22×C4×C13—24no—
148C22×C4×C13—24no—
149C22×C4×C13—24no—
150C22×C4×C13—24no—
151C22×C4×C13—41no—
152C22×C4×C13—41no—
153C22×C4×C13—41no—
154C22×C4×C13—41no—
155C22×C4×C13—41no—
156C22×C4×C13—41no—
157C22×C4×C13—42no—
158C22×C4×C13—42no—
159C22×C4×C13—41no—
160C22×C4×C13—41no—
161C22×C4×C13—41no—
162C22×C4×C13—41no—
163C22×C4×C13—416no—
164C22×C4×C13C2×Q814yes—
165C22×C4×C13C2×Q814yes—
166C22×C4×C13#4114yes—
167C22×C4×C13#4114yes—
168C22×C4×C13C2412yes—
169C22×C4×C13C2412yes—
170C22×C4×C13C2412yes—
171C22×C4×C13C2412yes—
172C22×C4×C13C2412yes—
173C22×C4×C13C2411yescharacteristic
174C22×C4×C13C2411yescharacteristic
175C22×Dic13C2414yes—
176C22×Dic13C2414yes—
177C22×Dic13C2414yes—
178C22×Dic13C2414yes—
179C2×Dic26—24no—
180C2×Dic26—24no—
181C2×Dic26—42no—
182C2×Dic26—42no—
183C2×Dic26—42no—
184C2×Dic26—42no—
185C13×C22⋊C4—28no—
186C13×C22⋊C4C2×Q8116yes—
187C42×C13—24no—
188C42×C13—24no—
189C42×C13—42no—
190C42×C13—42no—
191C22⋊Dic13—28no—
192C22⋊Dic13—28no—
193C22⋊Dic13—44no—
194C22⋊Dic13—44no—
195C22⋊Dic13—44no—
196C22⋊Dic13—44no—
197C4⋊Dic13—24no—
198C4⋊Dic13—24no—
199C4⋊Dic13—42no—
200C4⋊Dic13—42no—
201C4⋊Dic13—42no—
202C4⋊Dic13—42no—
203C4⋊Dic13—42no—
204C4⋊Dic13—42no—
205C4⋊Dic13—42no—
206C4⋊Dic13—42no—
207#6101—28no—
208#6101—28no—
209#6101—28no—
210#6101—28no—
211#6101—44no—
212#6101—44no—
213C4×Dic13—44no—
214C4×Dic13—44no—
215#2851—132no—
216#2848—132no—
217#2659—131no—
218#2659—131no—
219#2626—132no—
220#2574—134no—
221#2556—134no—
222#2522—134no—
223#2465—134no—
224#2329—132no—
225#2312—132no—
226C4×C22⋊Q8—132no—
227C2×C4×C22⋊C4D1311yescharacteristic
228C23×C13—21no—
229C23×C13—21no—
230C23×C13—21no—
231C23×C13—21no—
232C23×C13—28no—
233C23×C13—22no—
234C23×C13—22no—
235C23×C13—22no—
236C23×C13—22no—
237C23×C13—22no—
238C23×C13—22no—
239C23×C13—44no—
240C23×C13—44no—
241C23×C13—44no—
242C23×C13—44no—
243C23×C13—44no—
244C23×C13—44no—
245C23×C13C22×Q814yes—
246C23×C13C22×Q812yes—
247C23×C13C2×#4112yes—
248C23×C13C2×#4112yes—
249C23×C13C2511yescharacteristic
250C2×C4×C13—28no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—22no—
254C2×C4×C13—22no—
255C2×C4×C13—22no—
256C2×C4×C13—22no—
257C2×C4×C13—22no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—22no—
261C2×C4×C13—22no—
262C2×C4×C13—22no—
263C2×C4×C13—22no—
264C2×C4×C13—22no—
265C2×C4×C13—22no—
266C2×C4×C13—44no—
267C2×C4×C13—44no—
268C2×C4×C13—44no—
269C2×C4×C13—44no—
270C2×C4×C13—48no—
271C2×C4×C13—48no—
272C2×C4×C13—44no—
273C2×C4×C13C22×Q814yes—
274C2×C4×C13C22×Q814yes—
275C2×C4×C13C2×#4114yes—
276C2×C4×C13C2×#4114yes—
277C2×C4×C13H(5,𝔽2)12yes—
278C2×C4×C13H(5,𝔽2)12yes—
279C2×Dic13—24no—
280C2×Dic13—24no—
281C2×Dic13—24no—
282C2×Dic13—24no—
283C2×Dic13—24no—
284C2×Dic13—24no—
285C2×Dic13—24no—
286C2×Dic13—24no—
287C2×Dic13—24no—
288C2×Dic13—24no—
289C2×Dic13—24no—
290C2×Dic13—24no—
291Dic26—48no—
292Dic26—84no—
293C24×C4C2×D1311yescharacteristic
294C2×#125—132no—
295C2×C22⋊Q8—132no—
296C2×C22⋊Q8—132no—
297C2×C22⋊Q8—132no—
298C2×C22⋊Q8—132no—
299C2×C4×Q8—132no—
300C22×C22⋊C4C2×D1311yescharacteristic
301C22×C22⋊C4C2×D1311yescharacteristic
302C22×C42C2×D1311yescharacteristic
303C22×C42C2×D1311yescharacteristic
304#399—134no—
305#398—134no—
306#398—134no—
307#396—134no—
308#396—134no—
309#395—134no—
310#395—134no—
311#393—134no—
312#391—132no—
313#391—134no—
314#389—132no—
315#389—132no—
316#389—132no—
317#389—134no—
318#388—134no—
319#388—134no—
320#388—134no—
321#388—134no—
322#387—134no—
323#387—134no—
324#387—134no—
325#387—134no—
326#387—134no—
327#385—134no—
328#385—134no—
329#385—134no—
330#385—134no—
331#382—132no—
332#380—132no—
333#380—132no—
334#380—132no—
335#380—132no—
336#380—132no—
337#380—132no—
338#379—134no—
339C4×C4⋊C4—134no—
340C4×C4⋊C4—132no—
341C4×C22⋊C4—134no—
342C4×C22⋊C4C2×D1314yes—
343C4×C22⋊C4C2×D1314yes—
344C2×#95C2×D1311yescharacteristic
345C2×#95C2×D1311yescharacteristic
346C22×C13—22no—
347C22×C13—22no—
348C22×C13—22no—
349C22×C13—22no—
350C22×C13—22no—
351C22×C13—22no—
352C22×C13—24no—
353C22×C13—24no—
354C22×C13—24no—
355C22×C13—416no—
356C22×C13—42no—
357C22×C13—42no—
358C22×C13—42no—
359C22×C13—42no—
360C22×C13#53314yes—
361C22×C13C23×Q811yescharacteristic
362C22×C13C22×#4111yescharacteristic
363C22×C13C22×#4111yescharacteristic
364C22×C13C2×H(5,𝔽2)11yescharacteristic
365C22×C13C2×H(5,𝔽2)11yescharacteristic
366C22×C13#58511yescharacteristic
367C22×C13#58511yescharacteristic
368C4×C13—24no—
369C4×C13—24no—
370C4×C13—22no—
371C4×C13—22no—
372C4×C13—24no—
373C4×C13—24no—
374C4×C13—42no—
375Dic13—44no—
376Dic13—44no—
377Dic13—44no—
378Dic13—44no—
379C25C22×D1311yescharacteristic
380C22×Q8—132no—
381C22×Q8—132no—
382C23×C4—24no—
383C23×C4—42no—
384C23×C4—42no—
385C23×C4C22×D1311yescharacteristic
386C23×C4C22×D1312yes—
387C23×C4C22×D1312yes—
388C23×C4C22×D1311yescharacteristic
389C23×C4C22×D1311yescharacteristic
390C23×C4C22×D1311yescharacteristic
391C23×C4C22×D1311yescharacteristic
392C23×C4C22×D1311yescharacteristic
393#125—524no—
394C22⋊Q8—268no—
395C22⋊Q8—268no—
396C22⋊Q8—524no—
397C22⋊Q8—524no—
398C4×Q8—524no—
399C2×C4⋊C4—134no—
400C2×C4⋊C4—134no—
401C2×C4⋊C4—134no—
402C2×C4⋊C4—134no—
403C2×C4⋊C4—132no—
404C2×C4⋊C4—132no—
405C2×C4⋊C4—132no—
406C2×C4⋊C4—132no—
407C2×C4⋊C4—132no—
408C2×C4⋊C4—134no—
409C2×C4⋊C4—132no—
410C2×C4⋊C4—132no—
411C2×C4⋊C4—134no—
412C2×C4⋊C4—132no—
413C2×C4⋊C4—132no—
414C2×C4⋊C4—132no—
415C2×C22⋊C4—24no—
416C2×C22⋊C4—134no—
417C2×C22⋊C4—134no—
418C2×C22⋊C4—134no—
419C2×C22⋊C4—134no—
420C2×C22⋊C4—134no—
421C2×C22⋊C4—134no—
422C2×C22⋊C4Dic2618yescomplemented
423C2×C22⋊C4C22×D1314yes—
424C2×C22⋊C4C22×D1314yes—
425C2×C42—42no—
426C2×C42—42no—
427C2×C42—134no—
428C2×C42—134no—
429C2×C42C22×D1312yes—
430C2×C42C22×D1312yes—
431C2×C42C22×D1312yes—
432C2×C42C22×D1312yes—
433#95—134no—
434#95—134no—
435#95—134no—
436#95—134no—
437#95—134no—
438#95—134no—
439#95—134no—
440#95—134no—
441#95—134no—
442#95—134no—
443#95C22×D1314yes—
444#95C22×D1314yes—
445C2×C13—24no—
446C2×C13—44no—
447C2×C13C2×#53311yescharacteristic
448C2×C13#345911yescharacteristic
449C2×C13#346011yescharacteristic
450C2×C13#349011yescharacteristic
451C2×C13#349311yescharacteristic
452C2×C13#350111yescharacteristic
453C2×C13#350111yescharacteristic
454C24—22no—
455C24—22no—
456C24—41no—
457C24—41no—
458C24—41no—
459C24—41no—
460C24C2×Dic2614yes—
461C24C23×D1312yes—
462C24C23×D1311yescharacteristic
463C2×Q8—264no—
464C2×Q8—264no—
465C2×Q8—522no—
466C2×Q8—522no—
467C2×Q8—522no—
468C2×Q8—522no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—416no—
490C22×C4—134no—
491C22×C4—134no—
492C22×C4—134no—
493C22×C4—134no—
494C22×C4C2×Dic2614yes—
495C22×C4C2×Dic2614yes—
496C22×C4#612714yes—
497C22×C4#612714yes—
498C22×C4C23×D1312yes—
499C22×C4C23×D1312yes—
500C22×C4C23×D1312yes—
501C22×C4C23×D1312yes—
502C22×C4C23×D1312yes—
503C22×C4C23×D1311yescharacteristic
504C22×C4C23×D1311yescharacteristic
505C4⋊C4—268no—
506C4⋊C4—268no—
507C4⋊C4—264no—
508C4⋊C4—264no—
509C4⋊C4—268no—
510C4⋊C4—268no—
511C4⋊C4—522no—
512C4⋊C4—522no—
513C4⋊C4—522no—
514C4⋊C4—524no—
515C4⋊C4—522no—
516C4⋊C4—522no—
517C4⋊C4—524no—
518C4⋊C4—522no—
519C4⋊C4—522no—
520C4⋊C4—522no—
521C22⋊C4—28no—
522C22⋊C4—268no—
523C22⋊C4—268no—
524C22⋊C4—524no—
525C22⋊C4—524no—
526C22⋊C4—524no—
527C22⋊C4—524no—
528C22⋊C4C2×Dic26116yes—
529C42—24no—
530C42—24no—
531C42—42no—
532C42—42no—
533C42—524no—
534C42—524no—
535C13#3501211yescharacteristic, complemented, Sylow
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—28no—
541C23—22no—
542C23—22no—
543C23—22no—
544C23—22no—
545C23—22no—
546C23—22no—
547C23—44no—
548C23—44no—
549C23—44no—
550C23—44no—
551C23—44no—
552C23—44no—
553C23C22×Dic2614yes—
554C23C22×Dic2612yes—
555C23C2×#612712yes—
556C23C2×#612712yes—
557C23C24×D1311yescharacteristic
558Q8—528no—
559Q8—1044no—
560C2×C4—28no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—44no—
577C2×C4—44no—
578C2×C4—44no—
579C2×C4—44no—
580C2×C4—48no—
581C2×C4—48no—
582C2×C4—44no—
583C2×C4—264no—
584C2×C4—264no—
585C2×C4—264no—
586C2×C4—264no—
587C2×C4—264no—
588C2×C4—264no—
589C2×C4—264no—
590C2×C4—264no—
591C2×C4—264no—
592C2×C4—264no—
593C2×C4—264no—
594C2×C4—264no—
595C2×C4C22×Dic2614yes—
596C2×C4C22×Dic2614yes—
597C2×C4C2×#612714yes—
598C2×C4C2×#612714yes—
599C2×C4#8825112yes—
600C2×C4#8825112yes—
601C22—22no—
602C22—22no—
603C22—22no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—24no—
608C22—24no—
609C22—24no—
610C22—416no—
611C22—42no—
612C22—42no—
613C22—42no—
614C22—42no—
615C22#1171917514yes—
616C22C23×Dic2611yescharacteristic
617C22C22×#612711yescharacteristic
618C22C22×#612711yescharacteristic
619C22C2×#8825111yescharacteristic
620C22C2×#8825111yescharacteristic
621C22#1171964811yescharacteristic
622C22#1171964811yescharacteristic
623C4—24no—
624C4—22no—
625C4—22no—
626C4—24no—
627C4—24no—
628C4—24no—
629C4—42no—
630C4—524no—
631C4—524no—
632C4—524no—
633C4—524no—
634C2—24no—
635C2—44no—
636C2C2×#1171917511yescharacteristic
637C2#1312824511yescharacteristic
638C2#1312825811yescharacteristic
639C2#1312852511yescharacteristic
640C2#1312855611yescharacteristic
641C2#1312863911yescharacteristic
642C2#1312863911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D13
commutator, socle, cosocleC23×C13C25
FittingC2×C4×C13×C22⋊C4C2
prime radicalC25×C13C23
hypercenterC2×C4×C22⋊C4D13
hypocenterC13#35012
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #13123146C2semidirect
3. #13120950C2semidirect
4. #13120950C2semidirect
6. #13120110C2semidirect
7. #13119920C2semidirect
8. #13119554C2semidirect
9. #13118857C2semidirect
10. #13117569C2semidirect
12. C4×#88178C2semidirect
23. C2×#88124C22semidirect
24. C2×C4×Dic26C22semidirect
49. #11718597C22semidirect
50. C4×C4⋊Dic13C22semidirect
51. #11718594C22semidirect
52. #11718594C22semidirect
53. #11718594C22semidirect
54. C4×#6101C22semidirect
55. #11718590C22semidirect
56. #11718589C22semidirect
57. #11718589C22semidirect
58. #11718589C22semidirect
59. #11718322C22semidirect
60. #11718322C22semidirect
61. #11718317C22semidirect
62. #11718317C22semidirect
63. #11718316C22semidirect
64. #11718315C22semidirect
65. #11718308C22semidirect
66. #11718307C22semidirect
82. C2×C13×C22⋊C4Q8semidirect
422. C2×C22⋊C4Dic26semidirect
535. C13#35012semidirect

Maximal subgroups

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

subgroupindex
#131231462
#131231232
#131209502
#131206412
#131201102
#131199202
#131195542
#131188572
#131175692
#131174342
C4×#881782
C2×C4×C13×C22⋊C42
#3501213