Finite Group Databasebeta

← #15830764

Subgroups — #15830764

Order 3328.

1010 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123865C211yesmaximal, characteristic, complemented
2#13117776C211yesmaximal, characteristic, complemented
3#13113392C212yesmaximal, complemented
4#13113387C211yesmaximal, characteristic, complemented
5#13113383C211yesmaximal, characteristic, complemented
6#13113379C212yesmaximal, complemented
7#13113348C211yesmaximal, characteristic, complemented
8#13113344C211yesmaximal, characteristic, complemented
9#13113340C212yesmaximal, complemented
10#13113327C212yesmaximal, complemented
11C13×#3506C211yesmaximal, characteristic
12C13×#559—22no—
13C13×#556C412yescomplemented
14C13×#555C412yescomplemented
15C13×#553—22no—
16C13×#550C412yescomplemented
17C13×#547C412yescomplemented
18C13×#538—21no—
19C13×#538—21no—
20C13×#535—21no—
21C13×#533C2211yescharacteristic
22C13×#532C2211yescharacteristic
23C13×#525C2212yes—
24C13×#525C2212yes—
25C13×#520—21no—
26C2×C4×D4×C13C2211yescharacteristic
27#11718881—21no—
28#11718873C2211yescharacteristic
29#11718872C2211yescharacteristic
30C4×C22⋊Dic13C2211yescharacteristic
31C2×#88071C2211yescharacteristic
32#11718868C2212yes—
33C2×C22⋊#1055C2212yes—
34#11718672—22no—
35#11718672—22no—
36#11718642—21no—
37#11718612—21no—
38C22⋊C4×Dic13—21no—
39#11718598C2211yescharacteristic
40#11718593C2211yescharacteristic
41#11718587C2211yescharacteristic
42#11718587C2211yescharacteristic
43#11718130C2212yes—
44#11718130C2212yes—
45#11718130C2212yes—
46#11718130C2212yes—
47#11718129C2212yes—
48#11718129C2212yes—
49#11718129C2212yes—
50#11718129C2212yes—
51C2×C13×#41—21no—
52C2×C13×#41C2×C412yes—
53C2×C13×#41C2×C412yescomplemented
54C22×D4×C13D411yescharacteristic
55C23×C4×C13C2311yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×Dic13—21no—
58C13×C4⋊Q8C2×C411yescharacteristic, complemented
59C13×C4⋊Q8C2×C411yescharacteristic, complemented
60C13×C4⋊Q8C2×C411yescharacteristic, complemented
61C13×#127—22no—
62C13×#127C2×C411yescharacteristic, complemented
63C13×#126—22no—
64C13×#126—22no—
65C13×#125—21no—
66C13×#124—22no—
67C13×#124—22no—
68C13×#124—22no—
69C13×#124—21no—
70C13×#123—22no—
71C13×#123—22no—
72C13×#123—22no—
73C13×#123—22no—
74C13×C22⋊Q8—21no—
75C13×C22⋊Q8C2×C412yes—
76C13×C22⋊Q8C2×C412yescomplemented
77C13×C22⋊Q8C2312yes—
78C13×#121—22no—
79C13×#121—22no—
80C13×#121—21no—
81C13×#121—22no—
82C13×#121—22no—
83C13×#121C2×C412yes—
84C13×#121C2×C412yescomplemented
85C13×#121C2312yes—
86C13×#120—22no—
87C13×#120—22no—
88C4×Q8×C13—22no—
89C4×Q8×C13—21no—
90C4×Q8×C13C2×C412yescomplemented
91C4×D4×C13—22no—
92C4×D4×C13—22no—
93C4×D4×C13—22no—
94C4×D4×C13—22no—
95C4×D4×C13—22no—
96C4×D4×C13—21no—
97C4×D4×C13C2×C412yes—
98C4×D4×C13C2×C412yes—
99C4×D4×C13C2×C412yescomplemented
100C4×D4×C13D412yes—
101C4×D4×C13D412yes—
102C13×#117—21no—
103C13×#117—22no—
104C13×#117C2×C412yes—
105C13×#117C2×C412yescomplemented
106C2×C13×C4⋊C4—22no—
107C2×C13×C4⋊C4D411yescharacteristic
108C2×C13×C22⋊C4D411yescharacteristic
109C2×C13×C22⋊C4D411yescharacteristic
110C2×C42×C13C2311yescharacteristic
111C2×C22⋊Dic13—21no—
112C2×C22⋊Dic13—21no—
113C2×C22⋊Dic13—21no—
114C2×C4⋊Dic13—21no—
115C2×C4×Dic13—21no—
116C2×C4×Dic13—21no—
117C2×#6099—22no—
118C22×#1055—22no—
119#88071—21no—
120#88071—21no—
121#88071—21no—
122#88071—21no—
123#88071—21no—
124#88071C2311yescharacteristic
125#88071C2311yescharacteristic
126#88071C2311yescharacteristic
127#88071C2311yescharacteristic
128C22⋊#1055—22no—
129C22⋊#1055—22no—
130C22⋊#1055C2312yes—
131C22⋊#1055C2312yes—
132C4⋊#1055—21no—
133C4⋊#1055—21no—
134#88043—21no—
135#88043—21no—
136#17629—131nomaximal, Sylow
137C24×C13C2×D411yescharacteristic
138C24×C13C2×D411yescharacteristic
139C13×#41—42no—
140C13×#41—42no—
141C13×#41—82no—
142C13×#41—82no—
143C2×Q8×C13—21no—
144C2×Q8×C13—21no—
145C2×Q8×C13C22×C412yes—
146C2×D4×C13—22no—
147C2×D4×C13—22no—
148C2×D4×C13—22no—
149C2×D4×C13—22no—
150C2×D4×C13—22no—
151C2×D4×C13—21no—
152C2×D4×C13—21no—
153C2×D4×C13—41no—
154C2×D4×C13—41no—
155C2×D4×C13C22⋊C412yes—
156C2×D4×C13C22⋊C412yes—
157C2×D4×C13C22×C412yes—
158C22×C4×C13—22no—
159C22×C4×C13—22no—
160C22×C4×C13—22no—
161C22×C4×C13—81no—
162C22×C4×C13—81no—
163C22×C4×C13C22×C412yes—
164C22×C4×C13C22×C412yes—
165C22×C4×C13C2×D411yescharacteristic
166C22×C4×C13C2×D411yescharacteristic
167C22×C4×C13C2×D411yescharacteristic
168C22×C4×C13C2×D411yescharacteristic
169C22×C4×C13C2×D412yes—
170C22×C4×C13C2×D412yes—
171C22×C4×C13C2411yescharacteristic
172C22×Dic13—21no—
173C22×Dic13—21no—
174C22×Dic13—21no—
175C22×Dic13—21no—
176C22×Dic13—42no—
177C22×Dic13—42no—
178C22×Dic13—81no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—22no—
181C13×C4⋊C4—22no—
182C13×C4⋊C4—21no—
183C13×C4⋊C4—21no—
184C13×C4⋊C4—21no—
185C13×C4⋊C4—22no—
186C13×C4⋊C4—22no—
187C13×C4⋊C4C22⋊C412yes—
188C13×C4⋊C4C22⋊C412yes—
189C13×C4⋊C4C22×C412yes—
190C13×C4⋊C4C22×C412yes—
191C13×C22⋊C4—22no—
192C13×C22⋊C4—22no—
193C13×C22⋊C4—22no—
194C13×C22⋊C4—22no—
195C13×C22⋊C4—22no—
196C13×C22⋊C4—22no—
197C13×C22⋊C4—22no—
198C13×C22⋊C4—22no—
199C13×C22⋊C4—22no—
200C13×C22⋊C4C22⋊C412yes—
201C13×C22⋊C4C22⋊C412yes—
202C13×C22⋊C4C22⋊C412yes—
203C13×C22⋊C4C22⋊C412yes—
204C42×C13—22no—
205C42×C13—22no—
206C42×C13—22no—
207C42×C13C22×C411yescharacteristic
208C42×C13C22×C411yescharacteristic
209C42×C13C2×D411yescharacteristic
210C42×C13C2×D411yescharacteristic
211C22⋊Dic13—42no—
212C22⋊Dic13—42no—
213C22⋊Dic13—81no—
214C4⋊Dic13—81no—
215C4×Dic13—42no—
216C4×Dic13—81no—
217#6099—82no—
218C2×#1055—22no—
219C2×#1055—22no—
220C2×#1055—82no—
221#3506D1311yescharacteristic
222#2973—131no—
223#2353—131no—
224#1516—132no—
225#1515—131no—
226#1514—131no—
227#1513—132no—
228#1506—131no—
229#1505—131no—
230#1504—132no—
231#1501—132no—
232C23×C13—21no—
233C23×C13—21no—
234C23×C13—21no—
235C23×C13—21no—
236C23×C13—22no—
237C23×C13—41no—
238C23×C13—41no—
239C23×C13—41no—
240C23×C13—41no—
241C23×C13C2×C22⋊C412yes—
242C23×C13C2×C22⋊C412yes—
243C23×C13C22×D411yescharacteristic
244Q8×C13—42no—
245Q8×C13—42no—
246Q8×C13—81no—
247D4×C13—42no—
248D4×C13—42no—
249D4×C13—42no—
250D4×C13—42no—
251D4×C13—42no—
252D4×C13—42no—
253D4×C13—81no—
254D4×C13—82no—
255D4×C13—82no—
256D4×C13—82no—
257D4×C13—82no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—22no—
261C2×C4×C13—22no—
262C2×C4×C13—22no—
263C2×C4×C13—42no—
264C2×C4×C13—42no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—41no—
268C2×C4×C13—41no—
269C2×C4×C13—42no—
270C2×C4×C13—42no—
271C2×C4×C13—44no—
272C2×C4×C13—82no—
273C2×C4×C13—82no—
274C2×C4×C13C2×C22⋊C411yescharacteristic
275C2×C4×C13C2×C22⋊C412yes—
276C2×C4×C13C2×C22⋊C412yes—
277C2×C4×C13C2×C22⋊C411yescharacteristic
278C2×C4×C13C2×C22⋊C411yescharacteristic
279C2×C4×C13C2×C22⋊C411yescharacteristic
280C2×C4×C13C23×C411yescharacteristic
281C2×C4×C13C22×D411yescharacteristic
282C2×Dic13—22no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291C2×Dic13—41no—
292C2×Dic13—41no—
293C2×Dic13—41no—
294C2×Dic13—84no—
295#1055—42no—
296#1055—42no—
297#559—22no—
298#556Dic1312yescomplemented
299#555Dic1312yescomplemented
300#553—22no—
301#550Dic1312yescomplemented
302#547Dic1312yescomplemented
303#538—21no—
304#538—21no—
305#535—21no—
306#533C2×D1311yescharacteristic
307#532C2×D1311yescharacteristic
308#525C2×D1312yes—
309#525C2×D1312yes—
310#520—21no—
311C2×C4×D4C2×D1311yescharacteristic
312#435—262no—
313#435—262no—
314#432—131no—
315#432—131no—
316#407—132no—
317C2×C22⋊C8—132no—
318#388—261no—
319#387—261no—
320#386—261no—
321#383—131no—
322#381—131no—
323#380—131no—
324C4×C22⋊C4—131no—
325C4×C22⋊C4—261no—
326#376—131no—
327C2×#95—131no—
328#328—132no—
329#328—132no—
330#328—132no—
331#328—132no—
332#327—132no—
333#327—132no—
334#327—132no—
335#327—132no—
336C22×C13—21no—
337C22×C13—21no—
338C22×C13—22no—
339C22×C13—22no—
340C22×C13—22no—
341C22×C13—22no—
342C22×C13—22no—
343C22×C13—22no—
344C22×C13—42no—
345C22×C13—42no—
346C22×C13—42no—
347C22×C13—42no—
348C22×C13—42no—
349C22×C13—81no—
350C22×C13—81no—
351C22×C13C22×C22⋊C411yescharacteristic
352C22×C13#57511yescharacteristic
353C22×C13#57511yescharacteristic
354C4×C13—21no—
355C4×C13—21no—
356C4×C13—22no—
357C4×C13—22no—
358C4×C13—21no—
359C4×C13—21no—
360C4×C13—21no—
361C4×C13—21no—
362C4×C13—42no—
363C4×C13—42no—
364C4×C13—42no—
365Dic13—42no—
366Dic13—81no—
367Dic13—81no—
368Dic13—81no—
369C2×#41—21no—
370C2×#41C2×Dic1312yes—
371C2×#41C2×Dic1312yescomplemented
372C22×D4C22⋊D1311yescharacteristic
373C23×C4—261no—
374C23×C4C22×D1311yescharacteristic
375C23×C4C22×D1311yescharacteristic
376C2×M16—262no—
377C22×C8—262no—
378C4⋊Q8C2×Dic1311yescharacteristic, complemented
379C4⋊Q8C2×Dic1311yescharacteristic, complemented
380C4⋊Q8C2×Dic1311yescharacteristic, complemented
381#127—22no—
382#127C2×Dic1311yescharacteristic, complemented
383#126—22no—
384#126—22no—
385#125—21no—
386#124—22no—
387#124—22no—
388#124—22no—
389#124—21no—
390#123—22no—
391#123—22no—
392#123—22no—
393#123—22no—
394C22⋊Q8—21no—
395C22⋊Q8C2×Dic1312yes—
396C22⋊Q8C2×Dic1312yescomplemented
397C22⋊Q8C22×D1312yes—
398#121—22no—
399#121—22no—
400#121—21no—
401#121—22no—
402#121—22no—
403#121C2×Dic1312yes—
404#121C2×Dic1312yescomplemented
405#121C22×D1312yes—
406#120—22no—
407#120—22no—
408C4×Q8—22no—
409C4×Q8—21no—
410C4×Q8C2×Dic1312yescomplemented
411C4×D4—22no—
412C4×D4—22no—
413C4×D4—22no—
414C4×D4—22no—
415C4×D4—22no—
416C4×D4—21no—
417C4×D4C2×Dic1312yes—
418C4×D4C2×Dic1312yes—
419C4×D4C2×Dic1312yescomplemented
420C4×D4C22⋊D1312yes—
421C4×D4C22⋊D1312yes—
422#117—21no—
423#117—22no—
424#117C2×Dic1312yes—
425#117C2×Dic1312yescomplemented
426C2×C4⋊C4—22no—
427C2×C4⋊C4—261no—
428C2×C4⋊C4C22⋊D1311yescharacteristic
429C2×C22⋊C4—261no—
430C2×C22⋊C4—261no—
431C2×C22⋊C4—261no—
432C2×C22⋊C4C22⋊D1311yescharacteristic
433C2×C22⋊C4C22⋊D1311yescharacteristic
434C2×C42—261no—
435C2×C42—261no—
436C2×C42C22×D1311yescharacteristic
437C4⋊C8—261no—
438C4⋊C8—261no—
439C22⋊C8—132no—
440C22⋊C8—132no—
441C22⋊C8—262no—
442C22⋊C8—262no—
443#97—261no—
444#97—261no—
445#95—131no—
446#95—131no—
447#95—131no—
448#95—131no—
449#95—261no—
450#95—261no—
451#95—261no—
452#95—261no—
453#95—261no—
454C2×C13—21no—
455C2×C13—21no—
456C2×C13—42no—
457C2×C13—42no—
458C2×C13—82no—
459C2×C13#288311yescharacteristic
460C2×C13#289611yescharacteristic
461C2×C13#290111yescharacteristic
462C24C2×C22⋊D1311yescharacteristic
463C24C2×C22⋊D1311yescharacteristic
464#41—42no—
465#41—42no—
466#41—82no—
467#41—82no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8C22×Dic1312yes—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—41no—
479C2×D4—41no—
480C2×D4C22⋊Dic1312yes—
481C2×D4C22⋊Dic1312yes—
482C2×D4C22×Dic1312yes—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—81no—
487C22×C4—81no—
488C22×C4—261no—
489C22×C4—261no—
490C22×C4—261no—
491C22×C4—261no—
492C22×C4—522no—
493C22×C4—522no—
494C22×C4—1041no—
495C22×C4C22×Dic1312yes—
496C22×C4C22×Dic1312yes—
497C22×C4C2×C22⋊D1311yescharacteristic
498C22×C4C2×C22⋊D1311yescharacteristic
499C22×C4C2×C22⋊D1311yescharacteristic
500C22×C4C2×C22⋊D1311yescharacteristic
501C22×C4C2×C22⋊D1312yes—
502C22×C4C2×C22⋊D1312yes—
503C22×C4C23×D1311yescharacteristic
504M16—1042no—
505C2×C8—262no—
506C2×C8—262no—
507C2×C8—1042no—
508C4⋊C4—21no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—1041no—
517C4⋊C4C22⋊Dic1312yes—
518C4⋊C4C22⋊Dic1312yes—
519C4⋊C4C22×Dic1312yes—
520C4⋊C4C22×Dic1312yes—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—522no—
531C22⋊C4—522no—
532C22⋊C4—1041no—
533C22⋊C4C22⋊Dic1312yes—
534C22⋊C4C22⋊Dic1312yes—
535C22⋊C4C22⋊Dic1312yes—
536C22⋊C4C22⋊Dic1312yes—
537C42—22no—
538C42—22no—
539C42—22no—
540C42—522no—
541C42—1041no—
542C42C22×Dic1311yescharacteristic
543C42C22×Dic1311yescharacteristic
544C42C2×C22⋊D1311yescharacteristic
545C42C2×C22⋊D1311yescharacteristic
546C13#1762911yescharacteristic, complemented, Sylow
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—22no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23C2×C22⋊Dic1312yes—
557C23C2×C22⋊Dic1312yes—
558C23C22×C22⋊D1311yescharacteristic
559Q8—42no—
560Q8—42no—
561Q8—81no—
562D4—42no—
563D4—42no—
564D4—42no—
565D4—42no—
566D4—42no—
567D4—42no—
568D4—81no—
569D4—82no—
570D4—82no—
571D4—82no—
572D4—82no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—41no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—44no—
587C2×C4—82no—
588C2×C4—82no—
589C2×C4—262no—
590C2×C4—521no—
591C2×C4—521no—
592C2×C4—521no—
593C2×C4—521no—
594C2×C4—521no—
595C2×C4—521no—
596C2×C4—521no—
597C2×C4—521no—
598C2×C4—521no—
599C2×C4—521no—
600C2×C4—521no—
601C2×C4—1044no—
602C2×C4C2×C22⋊Dic1311yescharacteristic
603C2×C4C2×C22⋊Dic1312yes—
604C2×C4C2×C22⋊Dic1312yes—
605C2×C4C2×C22⋊Dic1311yescharacteristic
606C2×C4C2×C22⋊Dic1311yescharacteristic
607C2×C4C2×C22⋊Dic1311yescharacteristic
608C2×C4C23×Dic1311yescharacteristic
609C2×C4C22×C22⋊D1311yescharacteristic
610C8—522no—
611C8—522no—
612C22—21no—
613C22—21no—
614C22—22no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—42no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—42no—
625C22—81no—
626C22—81no—
627C22#1171952711yescharacteristic
628C22#1171952711yescharacteristic
629C22C22×C22⋊Dic1311yescharacteristic
630C4—21no—
631C4—21no—
632C4—21no—
633C4—21no—
634C4—21no—
635C4—21no—
636C4—22no—
637C4—22no—
638C4—42no—
639C4—42no—
640C4—42no—
641C4—522no—
642C4—1041no—
643C4—1041no—
644C4—1041no—
645C2—21no—
646C2—21no—
647C2—42no—
648C2—42no—
649C2—82no—
650C2#1312329711yescharacteristic
651C2#1312335511yescharacteristic
652C2#1312338311yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
Fitting, prime radicalC13×#3506C2
socleC22×C13C22×C22⋊C4
cosocleC22×C4×C13C24
hypercenter#3506D13
hypocenterC13#17629
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #3506

Complements

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

NH ≅ G/Ntype
1. #13123865C2semidirect
2. #13117776C2semidirect
3. #13113392C2semidirect
4. #13113387C2semidirect
5. #13113383C2semidirect
6. #13113379C2semidirect
7. #13113348C2semidirect
8. #13113344C2semidirect
9. #13113340C2semidirect
10. #13113327C2semidirect
13. C13×#556C4semidirect
14. C13×#555C4semidirect
16. C13×#550C4semidirect
17. C13×#547C4semidirect
53. C2×C13×#41C2×C4semidirect
58. C13×C4⋊Q8C2×C4semidirect
59. C13×C4⋊Q8C2×C4semidirect
60. C13×C4⋊Q8C2×C4semidirect
62. C13×#127C2×C4semidirect
76. C13×C22⋊Q8C2×C4semidirect
84. C13×#121C2×C4semidirect
90. C4×Q8×C13C2×C4semidirect
99. C4×D4×C13C2×C4semidirect
105. C13×#117C2×C4semidirect
298. #556Dic13semidirect
299. #555Dic13semidirect
301. #550Dic13semidirect
302. #547Dic13semidirect
371. C2×#41C2×Dic13semidirect
378. C4⋊Q8C2×Dic13semidirect
379. C4⋊Q8C2×Dic13semidirect
380. C4⋊Q8C2×Dic13semidirect
382. #127C2×Dic13semidirect
396. C22⋊Q8C2×Dic13semidirect
404. #121C2×Dic13semidirect
410. C4×Q8C2×Dic13semidirect
419. C4×D4C2×Dic13semidirect
425. #117C2×Dic13semidirect
546. C13#17629semidirect

Maximal subgroups

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

subgroupindex
#131238652
#131177762
#131133922
#131133872
#131133832
#131133792
#131133482
#131133442
#131133402
#131133272
C13×#35062
#1762913