Finite Group Databasebeta

← #15880531

Subgroups — #15880531

Order 3328.

686 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123490C211yesmaximal, characteristic
2#13123425C211yesmaximal, characteristic
3#13115586C211yesmaximal, characteristic, complemented
4#13115581C211yesmaximal, characteristic, complemented
5#13115435C211yesmaximal, characteristic, complemented
6#13115435C211yesmaximal, characteristic, complemented
7#13115432C211yesmaximal, characteristic, complemented
8#13115432C211yesmaximal, characteristic, complemented
9#13114935C211yesmaximal, characteristic
10#13114933C211yesmaximal, characteristic
11#13114876C211yesmaximal, characteristic
12#13114721C211yesmaximal, characteristic, complemented
13#13114716C211yesmaximal, characteristic, complemented
14#13114622C211yesmaximal, characteristic
15C13×#2924C211yesmaximal, characteristic
16C2×C13×#117C2211yescharacteristic
17C2×#88180C2211yescharacteristic
18C22×#6099C2211yescharacteristic
19C13×#433—21no—
20C13×#433—21no—
21C13×#432—21no—
22C13×#431—21no—
23C13×#424C2211yescharacteristic
24C13×#424C2211yescharacteristic
25C13×#407C2211yescharacteristic
26C2×C13×C22⋊C8C2211yescharacteristic
27C13×#405C2211yescharacteristic
28C13×#405C2211yescharacteristic
29C4×C22⋊Dic13C2211yescharacteristic
30#11718868C2211yescharacteristic
31C2×#88062C2211yescharacteristic
32C2×#88062C2211yescharacteristic
33#11718763C2211yescharacteristic
34#11718763C2211yescharacteristic
35#11718762C2211yescharacteristic
36#11718762C2211yescharacteristic
37C2×#88055C2211yescharacteristic
38C2×C8×Dic13C2211yescharacteristic
39#11718659C2211yescharacteristic
40#11718659C2211yescharacteristic
41#11718659C2211yescharacteristic
42#11718659C2211yescharacteristic
43#11718656C411yescharacteristic, complemented
44#11718656C411yescharacteristic, complemented
45#11718656C411yescharacteristic, complemented
46#11718656C411yescharacteristic, complemented
47#11718625C411yescharacteristic, complemented
48#11718625C411yescharacteristic, complemented
49#11718625C411yescharacteristic, complemented
50#11718625C411yescharacteristic, complemented
51#11718381—21no—
52#11718381—21no—
53#11718380—21no—
54#11718379—21no—
55#11718150C2211yescharacteristic
56#11718150C2211yescharacteristic
57#11718147C2211yescharacteristic
58#11718147C2211yescharacteristic
59#11718147C2211yescharacteristic
60#11718147C2211yescharacteristic
61#11718142C2211yescharacteristic
62#11718142C2211yescharacteristic
63#11718124C2211yescharacteristic
64#11718124C2211yescharacteristic
65#11718124C2211yescharacteristic
66#11718124C2211yescharacteristic
67C23×C4×C13C2311yescharacteristic
68C2×C13×M16C2311yescharacteristic
69C2×C13×M16C2311yescharacteristic
70C22×C8×C13C2311yescharacteristic
71C22×C8×C13C2311yescharacteristic
72C13×#117—21no—
73C13×#117—21no—
74C13×#117C2×C411yescharacteristic
75C13×#117C2×C411yescharacteristic
76C13×#117C2311yescharacteristic
77C13×#117C2311yescharacteristic
78C2×C13×C4⋊C4C2×C411yescharacteristic
79C2×C13×C4⋊C4C2×C411yescharacteristic
80C2×C13×C22⋊C4—21no—
81C2×C42×C13—21no—
82C2×C22⋊Dic13—21no—
83C2×C22⋊Dic13—21no—
84#88180—21no—
85#88180—21no—
86#88180C2×C411yescharacteristic
87#88180C2×C411yescharacteristic
88#88180C2311yescharacteristic
89#88180C2311yescharacteristic
90C2×C4⋊Dic13C2×C411yescharacteristic
91C2×C4⋊Dic13C2×C411yescharacteristic
92C2×C4×Dic13—21no—
93C2×C4×Dic13C2311yescharacteristic
94C2×C4×Dic13C2311yescharacteristic
95C2×#6099—22no—
96C2×#6099—22no—
97C2×#6099C2×C411yescharacteristic
98C2×#6099C2×C411yescharacteristic
99C2×#6099C2×C411yescharacteristic
100C2×#6099C2×C411yescharacteristic
101C2×#6099C2311yescharacteristic
102C2×#6099C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105C13×C4⋊C8—21no—
106C13×C4⋊C8—21no—
107C13×C4⋊C8—21no—
108C13×C4⋊C8—21no—
109C13×C22⋊C8—21no—
110C13×C22⋊C8—21no—
111C13×C22⋊C8D411yescharacteristic
112C13×C22⋊C8D411yescharacteristic
113C13×C22⋊C8D411yescharacteristic
114C13×C22⋊C8D411yescharacteristic
115C13×#97—21no—
116C13×#97—21no—
117C4×C8×C13—21no—
118C4×C8×C13—21no—
119#88071—21no—
120C22⋊#1055—21no—
121C22⋊#1055—21no—
122#88062—22no—
123#88062—22no—
124#88055—21no—
125#88055—21no—
126#88055—22no—
127#88054—21no—
128#88054—21no—
129#88054—21no—
130#88054—21no—
131C8×Dic13—21no—
132C8×Dic13—21no—
133C8×Dic13—22no—
134#88048C2×C411yescharacteristic
135#88048C2×C411yescharacteristic
136#88048C2×C411yescharacteristic
137#88048C2×C411yescharacteristic
138#88048C2×C411yescharacteristic
139#88048C2×C411yescharacteristic
140#88048C2×C411yescharacteristic
141#88048C2×C411yescharacteristic
142#88047C2×C411yescharacteristic
143#88047C2×C411yescharacteristic
144#88047C2×C411yescharacteristic
145#88047C2×C411yescharacteristic
146#88047C2×C411yescharacteristic
147#88047C2×C411yescharacteristic
148#88047C2×C411yescharacteristic
149#88047C2×C411yescharacteristic
150#22608—131nomaximal, Sylow
151C24×C13#4111yescharacteristic
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13C22×C411yescharacteristic
159C22×C4×C13C22×C411yescharacteristic
160C22×C4×C13C2×D411yescharacteristic
161C22×C4×C13C2×D411yescharacteristic
162C22×C4×C13#4111yescharacteristic
163C22×C4×C13C2411yescharacteristic
164C22×Dic13—21no—
165C22×Dic13—21no—
166C22×Dic13—21no—
167C22×Dic13—21no—
168C13×M16—21no—
169C13×M16—21no—
170C13×M16—21no—
171C13×M16—21no—
172C2×C8×C13—21no—
173C2×C8×C13—21no—
174C2×C8×C13—21no—
175C2×C8×C13—21no—
176C2×C8×C13—21no—
177C2×C8×C13—21no—
178C2×C8×C13C2×D411yescharacteristic
179C2×C8×C13C2×D411yescharacteristic
180C2×C8×C13C2×D411yescharacteristic
181C2×C8×C13C2×D411yescharacteristic
182C13×C4⋊C4—21no—
183C13×C4⋊C4—21no—
184C13×C4⋊C4C22×C411yescharacteristic
185C13×C4⋊C4C22×C411yescharacteristic
186C13×C4⋊C4C22×C411yescharacteristic
187C13×C4⋊C4C22×C411yescharacteristic
188C13×C22⋊C4—21no—
189C13×C22⋊C4—21no—
190C13×C22⋊C4—21no—
191C13×C22⋊C4—21no—
192C42×C13—21no—
193C42×C13—21no—
194C42×C13—21no—
195C42×C13—21no—
196C22⋊Dic13—21no—
197C22⋊Dic13—21no—
198C22⋊Dic13—21no—
199C22⋊Dic13—21no—
200C22⋊Dic13—42no—
201C4⋊Dic13—21no—
202C4⋊Dic13—21no—
203C4⋊Dic13C22×C411yescharacteristic
204C4⋊Dic13C22×C411yescharacteristic
205C4⋊Dic13C22×C411yescharacteristic
206C4⋊Dic13C22×C411yescharacteristic
207C4×Dic13—21no—
208C4×Dic13—21no—
209C4×Dic13—21no—
210C4×Dic13—21no—
211C4×Dic13—21no—
212C4×Dic13—21no—
213C4×Dic13—21no—
214C4×Dic13—21no—
215#6099—22no—
216#6099—22no—
217#6099—22no—
218#6099—22no—
219#6099—21no—
220#6099—21no—
221#6099—21no—
222#6099—21no—
223C2×#1055—21no—
224C2×#1055—21no—
225C2×#1055—21no—
226C2×#1055—21no—
227C2×#1055C22×C411yescharacteristic
228C2×#1055C22×C411yescharacteristic
229C2×#1055C22×C411yescharacteristic
230C2×#1055C22×C411yescharacteristic
231C2×#1055#4112yes—
232C2×#1055#4112yes—
233#2924—131no—
234#2924D1311yescharacteristic
235#2911—131no—
236#1946—131no—
237#1945—131no—
238#1922—131no—
239#1922—131no—
240#1922—131no—
241#1922—131no—
242#1826—131no—
243#1826—131no—
244#1811—131no—
245#1773—131no—
246#1772—131no—
247#1753—131no—
248C23×C13—21no—
249C23×C13—21no—
250C23×C13—41no—
251C23×C13—41no—
252C23×C13C4×D411yescharacteristic
253C23×C13C4×D411yescharacteristic
254C23×C13C2×#4111yescharacteristic
255C2×C4×C13—21no—
256C2×C4×C13—21no—
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—21no—
261C2×C4×C13—21no—
262C2×C4×C13—21no—
263C2×C4×C13—21no—
264C2×C4×C13—21no—
265C2×C4×C13—21no—
266C2×C4×C13—21no—
267C2×C4×C13—21no—
268C2×C4×C13—21no—
269C2×C4×C13—42no—
270C2×C4×C13—81no—
271C2×C4×C13C4×D411yescharacteristic
272C2×C4×C13C4×D411yescharacteristic
273C2×C4×C13C23×C411yescharacteristic
274C2×C4×C13C22×D411yescharacteristic
275C2×C4×C13C2×#4111yescharacteristic
276C2×C4×C13C2×#4111yescharacteristic
277C2×C4×C132−1+411yescharacteristic
278C2×C4×C132−1+411yescharacteristic
279C2×Dic13—22no—
280C2×Dic13—21no—
281C2×Dic13—21no—
282C2×Dic13—21no—
283C2×Dic13—21no—
284C2×Dic13—41no—
285C2×Dic13—42no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—81no—
291C8×C13—21no—
292C8×C13—21no—
293C8×C13—21no—
294C8×C13—21no—
295C8×C13—41no—
296C8×C13—41no—
297#1055—21no—
298#1055—21no—
299#1055—41no—
300#1055—41no—
301#1055#11712yes—
302#1055#11712yes—
303C22×M16—131no—
304C2×#117—131no—
305C2×#117C2×D1311yescharacteristic
306#433—21no—
307#433—21no—
308#433—261no—
309#433—261no—
310#432—21no—
311#432—261no—
312#431—21no—
313#431—261no—
314C2×#108—131no—
315C2×#108—131no—
316#428—131no—
317#428—131no—
318#428—131no—
319#428—131no—
320#428—131no—
321#428—131no—
322#428—131no—
323#428—131no—
324#427—131no—
325#427—131no—
326#427—131no—
327#427—131no—
328#424—131no—
329#424—131no—
330#424C2×D1311yescharacteristic
331#424C2×D1311yescharacteristic
332#407—131no—
333#407C2×D1311yescharacteristic
334C2×C22⋊C8C2×D1311yescharacteristic
335#405—131no—
336#405—131no—
337#405C2×D1311yescharacteristic
338#405C2×D1311yescharacteristic
339C2×#97—131no—
340C2×C4×C8—131no—
341C4×C22⋊C4—131no—
342#341—131no—
343#341—131no—
344#339—131no—
345#339—131no—
346#339—131no—
347#339—131no—
348#339—131no—
349#339—131no—
350#339—131no—
351#339—131no—
352#336—131no—
353#336—131no—
354C22×C13—21no—
355C22×C13—21no—
356C22×C13—21no—
357C22×C13—21no—
358C22×C13—21no—
359C22×C13—21no—
360C22×C13—21no—
361C22×C13—21no—
362C22×C13—81no—
363C22×C13—81no—
364C22×C13C2×C4×D411yescharacteristic
365C22×C13#55211yescharacteristic
366C22×C13#55211yescharacteristic
367C4×C13—21no—
368C4×C13—21no—
369C4×C13—41no—
370C4×C13—41no—
371C4×C13—41no—
372C4×C13—41no—
373C4×C13C2×#11711yescharacteristic
374C4×C13#51911yescharacteristic
375C4×C13#54711yescharacteristic
376C4×C13#54711yescharacteristic
377Dic13—42no—
378Dic13—41no—
379Dic13—41no—
380Dic13—41no—
381Dic13—41no—
382Dic13—81no—
383C23×C4C22×D1311yescharacteristic
384C2×M16—131no—
385C2×M16—131no—
386C2×M16—131no—
387C2×M16—131no—
388C2×M16—131no—
389C2×M16—131no—
390C2×M16—262no—
391C2×M16—262no—
392C2×M16C22×D1311yescharacteristic
393C2×M16C22×D1311yescharacteristic
394C22×C8—131no—
395C22×C8—131no—
396C22×C8C22×D1311yescharacteristic
397C22×C8C22×D1311yescharacteristic
398#117—21no—
399#117—21no—
400#117—131no—
401#117—131no—
402#117—131no—
403#117—131no—
404#117—261no—
405#117—261no—
406#117C4×D1311yescharacteristic
407#117C4×D1311yescharacteristic
408#117C22×D1311yescharacteristic
409#117C22×D1311yescharacteristic
410C2×C4⋊C4—131no—
411C2×C4⋊C4—131no—
412C2×C4⋊C4C4×D1311yescharacteristic
413C2×C4⋊C4C4×D1311yescharacteristic
414C2×C22⋊C4—21no—
415C2×C22⋊C4—261no—
416C2×C22⋊C4—261no—
417C2×C42—21no—
418C2×C42—131no—
419C2×C42—131no—
420C2×C42—261no—
421#108—262no—
422#108—262no—
423#107—131no—
424#107—131no—
425#107—131no—
426#107—131no—
427#107—131no—
428#107—131no—
429#107—131no—
430#107—131no—
431#106—131no—
432#106—131no—
433#106—131no—
434#106—131no—
435#106—131no—
436#106—131no—
437#106—131no—
438#106—131no—
439C4⋊C8—21no—
440C4⋊C8—21no—
441C4⋊C8—21no—
442C4⋊C8—21no—
443C4⋊C8—261no—
444C4⋊C8—261no—
445C4⋊C8—261no—
446C4⋊C8—261no—
447C22⋊C8—21no—
448C22⋊C8—21no—
449C22⋊C8—261no—
450C22⋊C8—261no—
451C22⋊C8C22⋊D1311yescharacteristic
452C22⋊C8C22⋊D1311yescharacteristic
453C22⋊C8C22⋊D1311yescharacteristic
454C22⋊C8C22⋊D1311yescharacteristic
455#97—21no—
456#97—21no—
457#97—262no—
458#97—261no—
459#97—261no—
460C4×C8—21no—
461C4×C8—21no—
462C4×C8—262no—
463C4×C8—261no—
464C4×C8—261no—
465#95—261no—
466C2×C13—21no—
467C2×C13—21no—
468C2×C13—41no—
469C2×C13—41no—
470C2×C13#234411yescharacteristic
471C2×C13#295511yescharacteristic
472C2×C13#295611yescharacteristic
473C24#612711yescharacteristic
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—261no—
481C22×C4—261no—
482C22×C4—261no—
483C22×C4—261no—
484C22×C4C2×C4×D1311yescharacteristic
485C22×C4C2×C4×D1311yescharacteristic
486C22×C4#612711yescharacteristic
487C22×C4C2×C22⋊D1311yescharacteristic
488C22×C4C2×C22⋊D1311yescharacteristic
489C22×C4C23×D1311yescharacteristic
490M16—21no—
491M16—21no—
492M16—21no—
493M16—21no—
494M16—262no—
495M16—262no—
496M16—262no—
497M16—262no—
498M16—261no—
499M16—261no—
500M16—261no—
501M16—261no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—131no—
509C2×C8—131no—
510C2×C8—132no—
511C2×C8—132no—
512C2×C8—131no—
513C2×C8—131no—
514C2×C8—261no—
515C2×C8—261no—
516C2×C8—261no—
517C2×C8—261no—
518C2×C8C2×C22⋊D1311yescharacteristic
519C2×C8C2×C22⋊D1311yescharacteristic
520C2×C8C2×C22⋊D1311yescharacteristic
521C2×C8C2×C22⋊D1311yescharacteristic
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—131no—
525C4⋊C4—131no—
526C4⋊C4—131no—
527C4⋊C4—131no—
528C4⋊C4—261no—
529C4⋊C4—261no—
530C4⋊C4C2×C4×D1311yescharacteristic
531C4⋊C4C2×C4×D1311yescharacteristic
532C4⋊C4C2×C4×D1311yescharacteristic
533C4⋊C4C2×C4×D1311yescharacteristic
534C22⋊C4—21no—
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—261no—
539C22⋊C4—261no—
540C22⋊C4—261no—
541C22⋊C4—261no—
542C22⋊C4—522no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—261no—
548C42—261no—
549C42—261no—
550C42—261no—
551C42—261no—
552C42—261no—
553C42—261no—
554C42—261no—
555C13#2260811yescharacteristic, complemented, Sylow
556C23—21no—
557C23—21no—
558C23—41no—
559C23—41no—
560C23C4×C22⋊D1311yescharacteristic
561C23C4×C22⋊D1311yescharacteristic
562C23C2×#612711yescharacteristic
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—42no—
578C2×C4—81no—
579C2×C4—262no—
580C2×C4—261no—
581C2×C4—261no—
582C2×C4—261no—
583C2×C4—261no—
584C2×C4—521no—
585C2×C4—522no—
586C2×C4—521no—
587C2×C4—521no—
588C2×C4—521no—
589C2×C4—521no—
590C2×C4—1041no—
591C2×C4C4×C22⋊D1311yescharacteristic
592C2×C4C4×C22⋊D1311yescharacteristic
593C2×C4C22×C4×D1311yescharacteristic
594C2×C4#41×D1311yescharacteristic
595C2×C4#41×D1311yescharacteristic
596C2×C4#8825711yescharacteristic
597C2×C4#8825711yescharacteristic
598C2×C4C22×C22⋊D1311yescharacteristic
599C8—21no—
600C8—21no—
601C8—21no—
602C8—21no—
603C8—41no—
604C8—41no—
605C8—132no—
606C8—132no—
607C8—261no—
608C8—261no—
609C8—521no—
610C8—521no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—81no—
620C22—81no—
621C22#1171923611yescharacteristic
622C22#1171923611yescharacteristic
623C22C2×C4×C22⋊D1311yescharacteristic
624C4—21no—
625C4—21no—
626C4—41no—
627C4—41no—
628C4—41no—
629C4—41no—
630C4—522no—
631C4—521no—
632C4—521no—
633C4—521no—
634C4—521no—
635C4—1041no—
636C4#1171922111yescharacteristic
637C4D13×#11711yescharacteristic
638C4#1171952911yescharacteristic
639C4#1171952911yescharacteristic
640C2—21no—
641C2—21no—
642C2—41no—
643C2—41no—
644C2#1311770611yescharacteristic
645C2#1312373711yescharacteristic
646C2#1312374311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2924C2
socleC22×C13C2×C4×D4
prime radicalC24×C13#41
cosocleC22×C4×C13C24
hypercenter#2924D13
hypocenterC13#22608
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2924

Complements

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

NH ≅ G/Ntype
3. #13115586C2semidirect
4. #13115581C2semidirect
5. #13115435C2semidirect
6. #13115435C2semidirect
7. #13115432C2semidirect
8. #13115432C2semidirect
12. #13114721C2semidirect
13. #13114716C2semidirect
43. #11718656C4semidirect
44. #11718656C4semidirect
45. #11718656C4semidirect
46. #11718656C4semidirect
47. #11718625C4semidirect
48. #11718625C4semidirect
49. #11718625C4semidirect
50. #11718625C4semidirect
555. C13#22608semidirect

Maximal subgroups

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

subgroupindex
#131234902
#131234252
#131155862
#131155812
#131154352
#131154322
#131149352
#131149332
#131148762
#131147212
#131147162
#131146222
C13×#29242
#2260813