Finite Group Databasebeta

← #16036800

Subgroups — #16036800

Order 3328.

2286 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123124C212yesmaximal
2#13123120C212yesmaximal
3#13120950C211yesmaximal, characteristic, complemented
4#13120809C212yesmaximal, complemented
5#13120054C214yesmaximal, complemented
6#13119841C214yesmaximal, complemented
7#13118513C214yesmaximal, complemented
8#13118505C214yesmaximal, complemented
9#13117571C212yesmaximal, complemented
10#13117566C212yesmaximal, complemented
11#13117218C212yesmaximal
12C2×D13×#95C211yesmaximal, characteristic
13C13×#2659C211yesmaximal, characteristic, complemented
14C23×C4×D13C2211yescharacteristic
15C23×C4×D13C2211yescharacteristic
16C23×C4×D13C2211yescharacteristic
17C2×C13×C22⋊Q8C2212yes—
18C2×#88200C2212yes—
19C2×#88200C2212yes—
20C2×#88178C2212yes—
21C2×#88151C2212yes—
22C2×#88151C2212yes—
23C2×#88146C2212yes—
24C2×#88146C2212yes—
25C13×#398C2214yescomplemented
26C13×#395C2214yescomplemented
27C13×#380C2212yes—
28C13×#380C2212yes—
29C2×C13×#95C2211yescharacteristic
30#11718891C2214yescomplemented
31#11718873C2212yes—
32#11718873C2212yes—
33C2×#88071C2211yescharacteristic
34C2×#88071C2211yescharacteristic
35C2×#88071C2211yescharacteristic
36#11718650C2214yes—
37#11718650C2214yes—
38#11718648C2212yes—
39#11718648C2212yes—
40#11718648C2212yes—
41#11718648C2212yes—
42#11718648C2212yes—
43#11718648C2212yes—
44#11718647C2214yescomplemented
45#11718646C2214yescomplemented
46#11718645C2214yescomplemented
47#11718642C2214yescomplemented
48#11718642C2214yescomplemented
49#11718639C2214yescomplemented
50#11718633C2214yescomplemented
51#11718616C2214yes—
52#11718611C2214yes—
53#11718607C2214yes—
54C22⋊C4×Dic13C2214yes—
55#11718329C2214yes—
56#11718329C2214yes—
57#11718327C2214yes—
58#11718325C2214yes—
59D13×#95C2214yes—
60D13×#95C2214yes—
61#11718322C2214yescomplemented
62#11718322C2214yescomplemented
63#11718321C2214yescomplemented
64#11718317C2214yescomplemented
65#11718314C2214yescomplemented
66#11718307C2214yescomplemented
67C24×D13C2311yescharacteristic
68C22×Q8×C13C2312yes—
69C23×C4×C13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C23×Dic13C2311yescharacteristic
75C22×C4×D13—24no—
76C22×C4×D13—24no—
77C22×C4×D13—42no—
78C22×C4×D13—42no—
79C22×C4×D13—42no—
80C22×C4×D13—42no—
81C22×C4×D13—42no—
82C22×C4×D13—42no—
83C22×C4×D13Q818yescomplemented
84C22×C4×D13C2312yes—
85C22×C4×D13C2312yes—
86C22×C4×D13C2312yes—
87C22×C4×D13C2312yes—
88C22×C4×D13C2312yes—
89C22×C4×D13C2312yes—
90C22×Dic26C2312yes—
91C13×C22⋊Q8—28no—
92C2×C13×C4⋊C4C2314yes—
93C2×C13×C4⋊C4C2312yes—
94C2×C13×C4⋊C4C2312yes—
95C2×C13×C4⋊C4C2312yes—
96C2×C13×C4⋊C4C2312yes—
97C2×C13×C4⋊C4C2312yes—
98C2×C13×C22⋊C4C2314yes—
99C2×C22⋊Dic13C2314yes—
100#88200—44no—
101#88200—44no—
102C2×#6103C2314yes—
103C2×#6103C2314yes—
104C2×#6103C2314yes—
105C2×#6103C2314yes—
106C2×C4⋊Dic13C2312yes—
107C2×C4⋊Dic13C2312yes—
108C2×C4⋊Dic13C2312yes—
109C2×C4⋊Dic13C2314yes—
110C2×C4⋊Dic13C2314yes—
111C2×C4⋊Dic13C2312yes—
112C2×C4⋊Dic13C2312yes—
113#88178—28no—
114C2×#6101C2314yes—
115C2×#6101C2314yes—
116C2×#6101C2314yes—
117C2×C4×Dic13C2314yes—
118C2×C4×Dic13C2314yes—
119#88151—44no—
120#88151—44no—
121#88146—44no—
122#88146—44no—
123C13×#95C2314yes—
124C13×#95C2314yes—
125C13×#95C2314yes—
126#88071C2314yes—
127#88071C2314yes—
128#88071C2314yes—
129#88071C2314yes—
130#88071C2314yes—
131#88071C2314yes—
132#88071C2314yes—
133#88071C2314yes—
134#88071C2314yes—
135#88071C2314yes—
136#88071C2314yes—
137#35052—131nomaximal, Sylow
138C24×C13C2411yescharacteristic
139C23×D13—22no—
140C23×D13—22no—
141C23×D13—22no—
142C23×D13—22no—
143C23×D13—22no—
144C23×D13—22no—
145C23×D13C2×Q814yes—
146C23×D13C2411yescharacteristic
147C23×D13C2411yescharacteristic
148C2×Q8×C13—24no—
149C2×Q8×C13—42no—
150C2×Q8×C13—42no—
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×C13C2×Q814yes—
158C22×C4×C13#4114yes—
159C22×C4×C13#4114yes—
160C22×C4×C13C2414yes—
161C22×C4×C13C2414yes—
162C22×C4×C13C2412yes—
163C22×C4×C13C2412yes—
164C22×C4×C13C2412yes—
165C22×Dic13—22no—
166C22×Dic13—22no—
167C22×Dic13—41no—
168C22×Dic13—41no—
169C22×Dic13—41no—
170C22×Dic13—41no—
171C22×Dic13—41no—
172C22×Dic13—41no—
173C22×Dic13C2×Q814yes—
174C22×Dic13C2412yes—
175C22×Dic13C2412yes—
176C22×Dic13C2414yes—
177C22×Dic13C2414yes—
178C22×Dic13C2412yes—
179C2×C4×D13—24no—
180C2×C4×D13—24no—
181C2×C4×D13—24no—
182C2×C4×D13—24no—
183C2×C4×D13—24no—
184C2×C4×D13—24no—
185C2×C4×D13—24no—
186C2×C4×D13—24no—
187C2×C4×D13—24no—
188C2×C4×D13—24no—
189C2×C4×D13—416no—
190C2×C4×D13—42no—
191C2×C4×D13—42no—
192C2×C4×D13—42no—
193C2×C4×D13—42no—
194C2×C4×D13—42no—
195C2×C4×D13—42no—
196C2×C4×D13—416no—
197C2×C4×D13—416no—
198C2×C4×D13C2×Q818yes—
199C2×C4×D13C2×Q818yes—
200C2×Dic26—24no—
201C2×Dic26—42no—
202C2×Dic26—42no—
203C13×C4⋊C4—24no—
204C13×C4⋊C4—28no—
205C13×C4⋊C4—42no—
206C13×C4⋊C4—42no—
207C13×C4⋊C4—42no—
208C13×C4⋊C4—42no—
209C13×C22⋊C4—28no—
210C22⋊Dic13—28no—
211#6103—28no—
212#6103—28no—
213#6103—28no—
214#6103—28no—
215C4⋊Dic13—24no—
216C4⋊Dic13—42no—
217C4⋊Dic13—42no—
218C4⋊Dic13—44no—
219C4⋊Dic13—44no—
220C4⋊Dic13—42no—
221C4⋊Dic13—42no—
222#6101—28no—
223#6101—44no—
224#6101—44no—
225C4×Dic13—44no—
226C4×Dic13—44no—
227#2848—132no—
228#2848—132no—
229#2659—131no—
230#2659D1311yescharacteristic, complemented
231#2646—132no—
232#2569—134no—
233#2549—134no—
234#2438—134no—
235#2438—134no—
236#2329—132no—
237#2329—132no—
238#2280—132no—
239C22×#95—131no—
240C23×C13—21no—
241C23×C13—21no—
242C23×C13—21no—
243C23×C13—21no—
244C23×C13C22×Q812yes—
245C23×C13C2×#4112yes—
246C23×C13C2×#4112yes—
247C23×C13C2511yescharacteristic
248C22×D13—28no—
249C22×D13—28no—
250C22×D13—28no—
251C22×D13—28no—
252C22×D13—28no—
253C22×D13—21no—
254C22×D13—21no—
255C22×D13—21no—
256C22×D13—21no—
257C22×D13—21no—
258C22×D13—21no—
259C22×D13—21no—
260C22×D13—21no—
261C22×D13—28no—
262C22×D13—28no—
263C22×D13C22×Q812yes—
264C22×D13C22×Q812yes—
265C22×D13H(5,𝔽2)12yes—
266C22×D13H(5,𝔽2)12yes—
267C22×D13H(5,𝔽2)12yes—
268C22×D132−1+412yes—
269Q8×C13—84no—
270C2×C4×C13—22no—
271C2×C4×C13—22no—
272C2×C4×C13—22no—
273C2×C4×C13—22no—
274C2×C4×C13—22no—
275C2×C4×C13—22no—
276C2×C4×C13—24no—
277C2×C4×C13—24no—
278C2×C4×C13—24no—
279C2×C4×C13—24no—
280C2×C4×C13—24no—
281C2×C4×C13—24no—
282C2×C4×C13—44no—
283C2×C4×C13—44no—
284C2×C4×C13—44no—
285C2×C4×C13C22×Q814yes—
286C2×C4×C13C2×#4114yes—
287C2×C4×C13C2×#4114yes—
288C2×Dic13—22no—
289C2×Dic13—22no—
290C2×Dic13—24no—
291C2×Dic13—24no—
292C2×Dic13—22no—
293C2×Dic13—22no—
294C2×Dic13—24no—
295C2×Dic13—24no—
296C2×Dic13—22no—
297C2×Dic13—22no—
298C2×Dic13—24no—
299C2×Dic13—22no—
300C2×Dic13—22no—
301C2×Dic13—24no—
302C2×Dic13—44no—
303C2×Dic13—44no—
304C2×Dic13—44no—
305C2×Dic13C22×Q814yes—
306C4×D13—216no—
307C4×D13—48no—
308C4×D13—48no—
309C4×D13—48no—
310C4×D13—48no—
311C4×D13—48no—
312Dic26—84no—
313C24×C4—131no—
314C24×C4—131no—
315C24×C4—131no—
316C2×C22⋊Q8—132no—
317C2×C22⋊Q8—132no—
318C2×C22⋊Q8—132no—
319C2×C22⋊Q8—132no—
320C2×C22⋊Q8—132no—
321C2×C22⋊Q8C2×D1312yes—
322C2×#117—132no—
323C2×#117—132no—
324#400—134no—
325#400—134no—
326#398—134no—
327#398—134no—
328#398—134no—
329#398C2×D1314yescomplemented
330#395—134no—
331#395C2×D1314yescomplemented
332#391—134no—
333#391—134no—
334#389—134no—
335#389—134no—
336#387—134no—
337#387—134no—
338#387—134no—
339#387—134no—
340#385—134no—
341#385—134no—
342#385—134no—
343#385—134no—
344#385—134no—
345#385—134no—
346#381—134no—
347#380—132no—
348#380—132no—
349#380—132no—
350#380—132no—
351#380—132no—
352#380—132no—
353#380—132no—
354#380—132no—
355#380C2×D1312yes—
356#380C2×D1312yes—
357#379—134no—
358C4×C22⋊C4—134no—
359C4×C22⋊C4—134no—
360C2×#95—131no—
361C2×#95—131no—
362C2×#95—131no—
363C2×#95—134no—
364C2×#95—134no—
365C2×#95C2×D1311yescharacteristic
366C22×C13—22no—
367C22×C13—22no—
368C22×C13—22no—
369C22×C13—22no—
370C22×C13—22no—
371C22×C13—22no—
372C22×C13#53314yes—
373C22×C13C23×Q811yescharacteristic
374C22×C13C22×#4111yescharacteristic
375C22×C13C22×#4111yescharacteristic
376C22×C13C2×H(5,𝔽2)11yescharacteristic
377C22×C13C2×H(5,𝔽2)11yescharacteristic
378C22×C13C2×H(5,𝔽2)11yescharacteristic
379C22×C13C2×2−1+411yescharacteristic
380C2×D13—232no—
381C2×D13—22no—
382C2×D13—22no—
383C2×D13—22no—
384C2×D13—22no—
385C2×D13—22no—
386C2×D13—22no—
387C2×D13—22no—
388C2×D13—22no—
389C2×D13—22no—
390C2×D13—22no—
391C2×D13—22no—
392C2×D13—22no—
393C2×D13#54314yes—
394C2×D13#54414yes—
395C4×C13—24no—
396C4×C13—24no—
397C4×C13—24no—
398C4×C13—44no—
399C4×C13—44no—
400Dic13—24no—
401Dic13—44no—
402Dic13—42no—
403Dic13—42no—
404Dic13—44no—
405C25—131no—
406C22×Q8—132no—
407C22×Q8C22×D1312yes—
408C23×C4—131no—
409C23×C4—132no—
410C23×C4—138no—
411C23×C4—132no—
412C23×C4—131no—
413C23×C4—131no—
414C23×C4—132no—
415C23×C4—132no—
416C23×C4—132no—
417C23×C4—132no—
418C23×C4—264no—
419C23×C4—264no—
420C23×C4—522no—
421C23×C4—522no—
422C23×C4—522no—
423C23×C4—522no—
424C23×C4—522no—
425C23×C4—522no—
426C23×C4C22×D1311yescharacteristic
427C23×C4C22×D1311yescharacteristic
428C23×C4C22×D1311yescharacteristic
429C22⋊Q8—28no—
430C22⋊Q8—268no—
431C22⋊Q8—524no—
432C22⋊Q8—524no—
433C22⋊Q8—524no—
434C22⋊Q8—524no—
435#117—524no—
436#117—524no—
437C2×C4⋊C4—134no—
438C2×C4⋊C4—132no—
439C2×C4⋊C4—132no—
440C2×C4⋊C4—132no—
441C2×C4⋊C4—134no—
442C2×C4⋊C4—134no—
443C2×C4⋊C4—132no—
444C2×C4⋊C4—132no—
445C2×C4⋊C4—134no—
446C2×C4⋊C4—134no—
447C2×C4⋊C4C22×D1312yes—
448C2×C4⋊C4C22×D1314yes—
449C2×C4⋊C4C22×D1312yes—
450C2×C4⋊C4C22×D1312yes—
451C2×C4⋊C4C22×D1312yes—
452C2×C4⋊C4C22×D1312yes—
453C2×C22⋊C4—134no—
454C2×C22⋊C4—134no—
455C2×C22⋊C4—134no—
456C2×C22⋊C4—134no—
457C2×C22⋊C4—134no—
458C2×C22⋊C4C22×D1314yes—
459C2×C42—134no—
460C2×C42—134no—
461#95—134no—
462#95—134no—
463#95—134no—
464#95—134no—
465#95—134no—
466#95—134no—
467#95—134no—
468#95—134no—
469#95—134no—
470#95—134no—
471#95—134no—
472#95C22×D1314yes—
473#95C22×D1314yes—
474#95C22×D1314yes—
475C2×C13—24no—
476C2×C13C2×#53311yescharacteristic
477C2×C13C2×#54311yescharacteristic
478C2×C13C2×#54411yescharacteristic
479C2×C13#349011yescharacteristic
480C2×C13#349011yescharacteristic
481C2×C13#349211yescharacteristic
482C2×C13#349211yescharacteristic
483D13—24no—
484D13—24no—
485C24—131no—
486C24—131no—
487C24—134no—
488C24—262no—
489C24—262no—
490C24—262no—
491C24—262no—
492C24—262no—
493C24—262no—
494C24C23×D1311yescharacteristic
495C2×Q8—24no—
496C2×Q8—42no—
497C2×Q8—42no—
498C2×Q8—264no—
499C2×Q8—522no—
500C2×Q8—522no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—132no—
508C22×C4—134no—
509C22×C4—138no—
510C22×C4—138no—
511C22×C4—132no—
512C22×C4—132no—
513C22×C4—134no—
514C22×C4—134no—
515C22×C4—264no—
516C22×C4—264no—
517C22×C4—264no—
518C22×C4—264no—
519C22×C4—264no—
520C22×C4—264no—
521C22×C4—262no—
522C22×C4—262no—
523C22×C4—264no—
524C22×C4—264no—
525C22×C4—264no—
526C22×C4—264no—
527C22×C4—522no—
528C22×C4—522no—
529C22×C4—522no—
530C22×C4—522no—
531C22×C4—522no—
532C22×C4—522no—
533C22×C4—5216no—
534C22×C4—5216no—
535C22×C4—5216no—
536C22×C4—521no—
537C22×C4—521no—
538C22×C4—521no—
539C22×C4—521no—
540C22×C4—521no—
541C22×C4—521no—
542C22×C4#612914yes—
543C22×C4Q8×D1314yes—
544C22×C4#613114yes—
545C22×C4C23×D1314yes—
546C22×C4C23×D1314yes—
547C22×C4C23×D1312yes—
548C22×C4C23×D1312yes—
549C22×C4C23×D1312yes—
550C4⋊C4—24no—
551C4⋊C4—28no—
552C4⋊C4—42no—
553C4⋊C4—42no—
554C4⋊C4—42no—
555C4⋊C4—42no—
556C4⋊C4—268no—
557C4⋊C4—264no—
558C4⋊C4—522no—
559C4⋊C4—522no—
560C4⋊C4—524no—
561C4⋊C4—524no—
562C4⋊C4—522no—
563C4⋊C4—522no—
564C4⋊C4—524no—
565C4⋊C4—524no—
566C22⋊C4—28no—
567C22⋊C4—268no—
568C22⋊C4—268no—
569C22⋊C4—268no—
570C22⋊C4—268no—
571C22⋊C4—268no—
572C42—524no—
573C42—524no—
574C13#3505211yescharacteristic, complemented, Sylow
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—132no—
580C23—132no—
581C23—132no—
582C23—132no—
583C23—132no—
584C23—132no—
585C23—268no—
586C23—268no—
587C23—268no—
588C23—268no—
589C23—268no—
590C23—268no—
591C23—268no—
592C23—261no—
593C23—261no—
594C23—261no—
595C23—261no—
596C23—261no—
597C23—261no—
598C23—261no—
599C23—261no—
600C23C2×#612912yes—
601C23C2×Q8×D1312yes—
602C23C2×#613112yes—
603C23C24×D1311yescharacteristic
604Q8—84no—
605Q8—1044no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—24no—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—44no—
619C2×C4—44no—
620C2×C4—44no—
621C2×C4—134no—
622C2×C4—2616no—
623C2×C4—262no—
624C2×C4—262no—
625C2×C4—262no—
626C2×C4—264no—
627C2×C4—264no—
628C2×C4—262no—
629C2×C4—264no—
630C2×C4—264no—
631C2×C4—264no—
632C2×C4—262no—
633C2×C4—262no—
634C2×C4—262no—
635C2×C4—262no—
636C2×C4—264no—
637C2×C4—528no—
638C2×C4—528no—
639C2×C4—528no—
640C2×C4—528no—
641C2×C4—528no—
642C2×C4—524no—
643C2×C4—524no—
644C2×C4—524no—
645C2×C4C2×#612914yes—
646C2×C4C2×Q8×D1314yes—
647C2×C4C2×#613114yes—
648C22—22no—
649C22—22no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—134no—
655C22—134no—
656C22—2632no—
657C22—262no—
658C22—262no—
659C22—262no—
660C22—262no—
661C22—262no—
662C22—262no—
663C22—262no—
664C22—262no—
665C22—262no—
666C22—262no—
667C22—262no—
668C22—262no—
669C22#1171943314yes—
670C22C22×#612911yescharacteristic
671C22C22×Q8×D1311yescharacteristic
672C22C22×#613111yescharacteristic
673C22D13×H(5,𝔽2)11yescharacteristic
674C22D13×H(5,𝔽2)11yescharacteristic
675C22D13×H(5,𝔽2)11yescharacteristic
676C22D13×2−1+411yescharacteristic
677C4—24no—
678C4—24no—
679C4—24no—
680C4—44no—
681C4—44no—
682C4—264no—
683C4—522no—
684C4—522no—
685C4—524no—
686C4—524no—
687C2—24no—
688C2—264no—
689C2—264no—
690C2C2×#1171943311yescharacteristic
691C2D13×#54311yescharacteristic
692C2D13×#54411yescharacteristic
693C2#1312852411yescharacteristic
694C2#1312852611yescharacteristic
695C2#1312854311yescharacteristic
696C2#1312854611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D13
commutator, socle, cosocleC23×C13C25
FittingC13×#2659C2
prime radicalC24×D13C23
hypercenter#2659D13
hypocenterC13#35052
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2659

Complements

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

NH ≅ G/Ntype
3. #13120950C2semidirect
4. #13120809C2semidirect
5. #13120054C2semidirect
6. #13119841C2semidirect
7. #13118513C2semidirect
8. #13118505C2semidirect
9. #13117571C2semidirect
10. #13117566C2semidirect
13. C13×#2659C2semidirect
25. C13×#398C22semidirect
26. C13×#395C22semidirect
30. #11718891C22semidirect
44. #11718647C22semidirect
45. #11718646C22semidirect
46. #11718645C22semidirect
47. #11718642C22semidirect
48. #11718642C22semidirect
49. #11718639C22semidirect
50. #11718633C22semidirect
61. #11718322C22semidirect
62. #11718322C22semidirect
63. #11718321C22semidirect
64. #11718317C22semidirect
65. #11718314C22semidirect
66. #11718307C22semidirect
83. C22×C4×D13Q8semidirect
230. #2659D13semidirect
329. #398C2×D13semidirect
331. #395C2×D13semidirect
574. C13#35052semidirect

Maximal subgroups

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

subgroupindex
#131231242
#131231202
#131209502
#131208092
#131200542
#131198412
#131185132
#131185052
#131175712
#131175662
#131172182
C2×D13×#952
C13×#26592
#3505213