Finite Group Databasebeta

← #15870239

Subgroups — #15870239

Order 3328.

900 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718696C211yesmaximal, characteristic
2#13117531C211yesmaximal, characteristic
3#13117193C211yesmaximal, characteristic, complemented
4#13115466C211yesmaximal, characteristic, complemented
5#13115466C211yesmaximal, characteristic, complemented
6#13115424C211yesmaximal, characteristic, complemented
7#13115410C211yesmaximal, characteristic, complemented
8#13115029C211yesmaximal, characteristic, complemented
9#13114932C211yesmaximal, characteristic, complemented
10#13114732C211yesmaximal, characteristic, complemented
11#13114724C211yesmaximal, characteristic, complemented
12#13114663C211yesmaximal, characteristic, complemented
13#102×Dic13C211yesmaximal, characteristic, complemented
14#13114604C211yesmaximal, characteristic, complemented
15C13×#1874C211yesmaximal, characteristic
16C2×C13×#121C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C2×D4×Dic13C2211yescharacteristic
19C2×#88180C2211yescharacteristic
20C2×#88180C2211yescharacteristic
21C2×C13×#102C2211yescharacteristic
22C2×C13×#102C2211yescharacteristic
23C2×C13×C22⋊C8C2211yescharacteristic
24#11718882—21no—
25#11718882C2211yescharacteristic
26#11718881—21no—
27C2×#88072C2211yescharacteristic
28C2×#88072C2211yescharacteristic
29#11718873C2211yescharacteristic
30C4×C22⋊Dic13—21no—
31C4×C22⋊Dic13—21no—
32C2×C22⋊#1055C2211yescharacteristic
33C2×#88055C2211yescharacteristic
34C2×C8×Dic13C2211yescharacteristic
35#11718696C418yescomplemented
36#11718646C2211yescharacteristic
37C4⋊C4×Dic13—21no—
38C4⋊C4×Dic13—21no—
39C4⋊C4×Dic13C2211yescharacteristic
40C4⋊C4×Dic13C2211yescharacteristic
41C4⋊C4×Dic13C2211yescharacteristic
42C4⋊C4×Dic13C2211yescharacteristic
43C4⋊C4×Dic13C2211yescharacteristic
44C2×#88048C2211yescharacteristic
45C2×#88048C2211yescharacteristic
46C2×#88048C2211yescharacteristic
47C2×#88047C2211yescharacteristic
48#11718612—21no—
49#11718611—21no—
50C13×#340C2211yescharacteristic
51C13×#340C2211yescharacteristic
52#11718143C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718142C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60C22×D4×C13—21no—
61C22×D4×C13C2311yescharacteristic
62C23×C4×C13—21no—
63C23×C4×C13C2311yescharacteristic
64C23×Dic13—21no—
65C22×C8×C13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C13×#121—22no—
68C13×#121C2×C414yes—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—22no—
71C2×C13×C4⋊C4—22no—
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C22⋊C4—21no—
76C2×C22⋊Dic13—21no—
77C2×C22⋊Dic13—21no—
78C2×C22⋊Dic13—21no—
79C2×C22⋊Dic13—21no—
80C2×C22⋊Dic13—21no—
81C2×C22⋊Dic13D411yescharacteristic
82C2×C22⋊Dic13D411yescharacteristic
83D4×Dic13—22no—
84D4×Dic13—22no—
85#88180—22no—
86#88180—22no—
87#88180—22no—
88#88180C2×C414yescomplemented
89C2×C4⋊Dic13—21no—
90C2×C4⋊Dic13D411yescharacteristic
91C2×C4⋊Dic13D411yescharacteristic
92C2×C4⋊Dic13C2311yescharacteristic
93C2×C4⋊Dic13C2311yescharacteristic
94C2×C4⋊Dic13C2311yescharacteristic
95C2×C4⋊Dic13C2311yescharacteristic
96C2×C4×Dic13—21no—
97C2×C4×Dic13—21no—
98C2×C4×Dic13—21no—
99C2×C4×Dic13—21no—
100C2×C4×Dic13—21no—
101C2×C4×Dic13—21no—
102C2×C4×Dic13C2311yescharacteristic
103C2×C4×Dic13C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106C13×#102—22no—
107C13×#102—22no—
108C13×C22⋊C8—22no—
109#88072C2×C414yescomplemented
110#88072C2×C414yescomplemented
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88071—21no—
118C22⋊#1055C2×C414yescomplemented
119#88055—22no—
120C8×Dic13—22no—
121#88048—22no—
122#88048—22no—
123#88048C2×C414yescomplemented
124#88047C2×C414yescomplemented
125#21588—131nomaximal, Sylow
126C24×C13—21no—
127C24×C13C2×D411yescharacteristic
128C2×D4×C13—24no—
129C2×D4×C13—21no—
130C2×D4×C13—21no—
131C2×D4×C13—21no—
132C2×D4×C13—21no—
133C2×D4×C13—21no—
134C2×D4×C13—81no—
135C2×D4×C13—81no—
136C2×D4×C13C22×C412yes—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—24no—
145C22×C4×C13—81no—
146C22×C4×C13—81no—
147C22×C4×C13C22×C412yes—
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13#4112yes—
150C22×C4×C13C2411yescharacteristic
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13—21no—
154C22×Dic13—21no—
155C22×Dic13—42no—
156C22×Dic13—81no—
157C22×Dic13—81no—
158C22×Dic13C2×D411yescharacteristic
159C22×Dic13C2×D411yescharacteristic
160C22×Dic13C2×D411yescharacteristic
161C22×Dic13C2×D411yescharacteristic
162C2×C8×C13—21no—
163C2×C8×C13—21no—
164C2×C8×C13—21no—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C13×C4⋊C4—24no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4C22×C412yes—
173C13×C4⋊C4#4112yes—
174C13×C4⋊C4#4112yes—
175C13×C22⋊C4—24no—
176C22⋊Dic13—24no—
177C22⋊Dic13—22no—
178C22⋊Dic13—22no—
179C22⋊Dic13—42no—
180C22⋊Dic13—81no—
181C22⋊Dic13—81no—
182C22⋊Dic13—81no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—22no—
186C4⋊Dic13—22no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13—81no—
192C4⋊Dic13C22×C412yes—
193C4⋊Dic13C22×C412yes—
194C4×Dic13—24no—
195C4×Dic13—21no—
196C4×Dic13—21no—
197C4×Dic13—81no—
198C4×Dic13—81no—
199C4×Dic13—81no—
200C4×Dic13—81no—
201C4×Dic13—81no—
202C4×Dic13#4112yes—
203C4×Dic13#4112yes—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055C22×C412yes—
209C2×#1055C22×C412yes—
210C2×#482—131no—
211#2324—131no—
212#2274—131no—
213#1926—131no—
214#1926—131no—
215#1920—131no—
216#1918—131no—
217#1874D1311yescharacteristic
218#1853—131no—
219#1825—131no—
220#1776—131no—
221C4×#106—131no—
222#1762—131no—
223C4×#102—131no—
224#1750—131no—
225C23×C13—21no—
226C23×C13—21no—
227C23×C13—21no—
228C23×C13—21no—
229C23×C13—21no—
230C23×C13—21no—
231C23×C13—22no—
232C23×C13—41no—
233C23×C13—41no—
234C23×C13—41no—
235C23×C13—41no—
236C23×C13—41no—
237C23×C13—41no—
238C23×C13C4×D412yes—
239C23×C13C22×D411yescharacteristic
240D4×C13—22no—
241D4×C13—22no—
242D4×C13—41no—
243D4×C13—41no—
244D4×C13—84no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—22no—
248C2×C4×C13—22no—
249C2×C4×C13—22no—
250C2×C4×C13—22no—
251C2×C4×C13—22no—
252C2×C4×C13—22no—
253C2×C4×C13—22no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13—84no—
261C2×C4×C13C4×D412yes—
262C2×C4×C13C23×C411yescharacteristic
263C2×C4×C13C2×#4111yescharacteristic
264C2×C4×C13C2×#4111yescharacteristic
265C2×C4×C13C2×#4111yescharacteristic
266C2×C4×C13C2×#4111yescharacteristic
267C2×C4×C13C2×#4111yescharacteristic
268C2×Dic13—21no—
269C2×Dic13—21no—
270C2×Dic13—21no—
271C2×Dic13—21no—
272C2×Dic13—22no—
273C2×Dic13—22no—
274C2×Dic13—21no—
275C2×Dic13—21no—
276C2×Dic13—21no—
277C2×Dic13—21no—
278C2×Dic13—21no—
279C2×Dic13—21no—
280C2×Dic13—41no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—84no—
291C2×Dic13#12312yes—
292C2×Dic13#12312yes—
293C8×C13—41no—
294C8×C13—41no—
295#1055—22no—
296#1055—22no—
297C2×#121C2×D1311yescharacteristic
298C2×C4×D4—131no—
299C2×#117—131no—
300C2×#117—131no—
301C22×C4⋊C4C2×D1311yescharacteristic
302#482—138no—
303C2×#107—131no—
304C2×#106—131no—
305C2×#106—131no—
306C2×#106—131no—
307C2×#102—131no—
308C2×#102—131no—
309C2×#102C2×D1311yescharacteristic
310C2×#102C2×D1311yescharacteristic
311C2×C22⋊C8—131no—
312C2×C22⋊C8C2×D1311yescharacteristic
313C2×#97—131no—
314C2×C4×C8—131no—
315#390—131no—
316#390—261no—
317#389—131no—
318#388—261no—
319#386—261no—
320#385—261no—
321#380—131no—
322C4×C4⋊C4—131no—
323C4×C4⋊C4—131no—
324C4×C4⋊C4—131no—
325C4×C4⋊C4—131no—
326C4×C4⋊C4—131no—
327C4×C4⋊C4—261no—
328C4×C4⋊C4—261no—
329C4×C22⋊C4—261no—
330C4×C22⋊C4—261no—
331#340—131no—
332#340—131no—
333#340—131no—
334#340—131no—
335#340—131no—
336#340—131no—
337#340C2×D1311yescharacteristic
338#340C2×D1311yescharacteristic
339#336—131no—
340#336—131no—
341C22×C13—22no—
342C22×C13—22no—
343C22×C13—22no—
344C22×C13—41no—
345C22×C13—41no—
346C22×C13—41no—
347C22×C13—41no—
348C22×C13—42no—
349C22×C13—42no—
350C22×C13—42no—
351C22×C13—81no—
352C22×C13—81no—
353C22×C13—81no—
354C22×C13—81no—
355C22×C13C2×C4×D411yescharacteristic
356C22×C13C2×#12311yescharacteristic
357C22×C13#52511yescharacteristic
358C22×C13#57611yescharacteristic
359C22×C13#57711yescharacteristic
360C22×C13#57711yescharacteristic
361C22×C13#57711yescharacteristic
362C4×C13—22no—
363C4×C13—42no—
364C4×C13—42no—
365C4×C13—42no—
366C4×C13C4×#4111yescharacteristic
367C4×C13C4×#4111yescharacteristic
368C4×C13#52911yescharacteristic
369C4×C13#52911yescharacteristic
370Dic13—22no—
371Dic13—22no—
372Dic13—41no—
373Dic13—41no—
374Dic13—42no—
375Dic13—42no—
376Dic13—81no—
377Dic13—81no—
378C22×D4—21no—
379C22×D4C22×D1311yescharacteristic
380C23×C4—21no—
381C23×C4—261no—
382C23×C4C22×D1311yescharacteristic
383C22×C8—131no—
384C22×C8—131no—
385C22×C8C22×D1311yescharacteristic
386C22×C8C22×D1311yescharacteristic
387#121—22no—
388#121C4×D1314yes—
389C4×D4—262no—
390C4×D4—262no—
391#117—134no—
392#117—262no—
393#117—262no—
394#117—262no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—131no—
399C2×C4⋊C4—131no—
400C2×C4⋊C4—131no—
401C2×C4⋊C4—131no—
402C2×C4⋊C4—131no—
403C2×C4⋊C4—131no—
404C2×C4⋊C4—261no—
405C2×C4⋊C4C22×D1311yescharacteristic
406C2×C4⋊C4C22×D1311yescharacteristic
407C2×C4⋊C4C22×D1311yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—131no—
410C2×C22⋊C4—131no—
411C2×C22⋊C4—261no—
412C2×C22⋊C4—261no—
413C2×C22⋊C4—261no—
414C2×C22⋊C4—261no—
415C2×C22⋊C4—261no—
416C2×C42—131no—
417C2×C42—131no—
418C2×C42—261no—
419C2×C42—261no—
420C2×C42—261no—
421C2×C42—261no—
422C2×C42—261no—
423C2×C42—261no—
424#107—134no—
425#106—134no—
426#106—262no—
427#106—262no—
428#102—22no—
429#102—22no—
430#102—134no—
431#102—134no—
432C22⋊C8—22no—
433C22⋊C8—134no—
434#97—262no—
435C4×C8—262no—
436#95—261no—
437#95—261no—
438#95—261no—
439#95—261no—
440#95—261no—
441#95—261no—
442#95—261no—
443C2×C13—42no—
444C2×C13—82no—
445C2×C13C4×#12311yescharacteristic
446C2×C13#294611yescharacteristic
447C2×C13#295211yescharacteristic
448C2×C13#309611yescharacteristic
449C2×C13#309911yescharacteristic
450C2×C13#311811yescharacteristic
451C2×C13#312611yescharacteristic
452C24—21no—
453C24D4×D1311yescharacteristic
454C2×D4—24no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—81no—
461C2×D4—81no—
462C2×D4C2×C4×D1312yes—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—24no—
471C22×C4—81no—
472C22×C4—81no—
473C22×C4—131no—
474C22×C4—131no—
475C22×C4—131no—
476C22×C4—131no—
477C22×C4—261no—
478C22×C4—261no—
479C22×C4—261no—
480C22×C4—261no—
481C22×C4—522no—
482C22×C4—1041no—
483C22×C4—1041no—
484C22×C4C2×C4×D1312yes—
485C22×C4D4×D1311yescharacteristic
486C22×C4#612912yes—
487C22×C4C23×D1311yescharacteristic
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—132no—
495C2×C8—132no—
496C2×C8—261no—
497C2×C8—261no—
498C2×C8—261no—
499C2×C8—261no—
500C4⋊C4—24no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—132no—
505C4⋊C4—132no—
506C4⋊C4—262no—
507C4⋊C4—262no—
508C4⋊C4—261no—
509C4⋊C4—261no—
510C4⋊C4—261no—
511C4⋊C4—261no—
512C4⋊C4—261no—
513C4⋊C4—261no—
514C4⋊C4—1041no—
515C4⋊C4C2×C4×D1312yes—
516C4⋊C4#612912yes—
517C4⋊C4#612912yes—
518C22⋊C4—24no—
519C22⋊C4—262no—
520C22⋊C4—262no—
521C22⋊C4—264no—
522C22⋊C4—522no—
523C22⋊C4—1041no—
524C22⋊C4—1041no—
525C22⋊C4—1041no—
526C42—132no—
527C42—132no—
528C42—264no—
529C42—261no—
530C42—261no—
531C42—1041no—
532C42—1041no—
533C42—1041no—
534C42—1041no—
535C42—1041no—
536C13#2158811yescharacteristic, complemented, Sylow
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—21no—
543C23—22no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23#8813512yes—
551C23C2×D4×D1311yescharacteristic
552D4—22no—
553D4—22no—
554D4—41no—
555D4—41no—
556D4—84no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—84no—
573C2×C4—132no—
574C2×C4—132no—
575C2×C4—261no—
576C2×C4—261no—
577C2×C4—261no—
578C2×C4—261no—
579C2×C4—262no—
580C2×C4—262no—
581C2×C4—261no—
582C2×C4—261no—
583C2×C4—261no—
584C2×C4—261no—
585C2×C4—261no—
586C2×C4—261no—
587C2×C4—521no—
588C2×C4—521no—
589C2×C4—521no—
590C2×C4—521no—
591C2×C4—521no—
592C2×C4—521no—
593C2×C4—521no—
594C2×C4—521no—
595C2×C4—521no—
596C2×C4—521no—
597C2×C4—1044no—
598C2×C4#8813512yes—
599C2×C4C22×C4×D1311yescharacteristic
600C2×C4C2×#612911yescharacteristic
601C2×C4C2×#612911yescharacteristic
602C2×C4C2×#612911yescharacteristic
603C2×C4#41×D1311yescharacteristic
604C2×C4#41×D1311yescharacteristic
605C8—41no—
606C8—41no—
607C8—262no—
608C8—262no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22—42no—
617C22—42no—
618C22—42no—
619C22—81no—
620C22—81no—
621C22—81no—
622C22—81no—
623C22C2×#8813511yescharacteristic
624C22#1171929111yescharacteristic
625C22D13×#12311yescharacteristic
626C22#1171946211yescharacteristic
627C22#1171946711yescharacteristic
628C22#1171948011yescharacteristic
629C22#1171948311yescharacteristic
630C4—22no—
631C4—42no—
632C4—42no—
633C4—42no—
634C4—262no—
635C4—262no—
636C4—522no—
637C4—522no—
638C4—521no—
639C4—521no—
640C4—1041no—
641C4—1041no—
642C4C4×#612911yescharacteristic
643C4C4×#612911yescharacteristic
644C4#1171930511yescharacteristic
645C4#1171930511yescharacteristic
646C2—42no—
647C2—82no—
648C2#1311736111yescharacteristic
649C2#1312366211yescharacteristic
650C2#1312371511yescharacteristic
651C2#1312478711yescharacteristic
652C2#1312482611yescharacteristic
653C2#1312501311yescharacteristic
654C2#1312512111yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1874C2
socleC23×C13C22×D4
prime radicalC2×C13×#121C22
cosocleC22×C4×C13C24
hypercenter#1874D13
hypocenterC13#21588
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
3. #13117193C2semidirect
4. #13115466C2semidirect
5. #13115466C2semidirect
6. #13115424C2semidirect
7. #13115410C2semidirect
8. #13115029C2semidirect
9. #13114932C2semidirect
10. #13114732C2semidirect
11. #13114724C2semidirect
12. #13114663C2semidirect
13. #102×Dic13C2semidirect
14. #13114604C2semidirect
35. #11718696C4semidirect
88. #88180C2×C4semidirect
109. #88072C2×C4semidirect
110. #88072C2×C4semidirect
118. C22⋊#1055C2×C4semidirect
123. #88048C2×C4semidirect
124. #88047C2×C4semidirect
536. C13#21588semidirect

Maximal subgroups

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

subgroupindex
C2×#117186962
#131175312
#131171932
#131154662
#131154242
#131154102
#131150292
#131149322
#131147322
#131147242
#131146632
#102×Dic132
#131146042
C13×#18742
#2158813