Finite Group Databasebeta

← #15880525

Subgroups — #15880525

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#13123496C211yesmaximal, characteristic
2#13123494C211yesmaximal, characteristic
3#13123425C211yesmaximal, characteristic
4#13115588C211yesmaximal, characteristic, complemented
5#13115583C211yesmaximal, characteristic, complemented
6#13115438C211yesmaximal, characteristic, complemented
7#13115438C211yesmaximal, characteristic, complemented
8#13115433C211yesmaximal, characteristic, complemented
9#13115433C211yesmaximal, characteristic, complemented
10#13114936C211yesmaximal, characteristic
11#13114876C211yesmaximal, characteristic
12#13114719C211yesmaximal, characteristic, complemented
13#13114714C211yesmaximal, characteristic, complemented
14#13114620C211yesmaximal, characteristic
15C13×#1826C211yesmaximal, characteristic
16C2×C13×#117C2211yescharacteristic
17C2×#88180C2211yescharacteristic
18C22×#6099C2211yescharacteristic
19C13×#407C2211yescharacteristic
20C4×C13×C22⋊C4C2211yescharacteristic
21#11718868C2211yescharacteristic
22C2×C22⋊#1055C2211yescharacteristic
23C2×#88062C2211yescharacteristic
24C2×#88062C2211yescharacteristic
25#11718783C2211yescharacteristic
26#11718783C2211yescharacteristic
27#11718780C2211yescharacteristic
28#11718780C2211yescharacteristic
29#11718661—21no—
30#11718661—21no—
31#11718660C2211yescharacteristic
32#11718660C2211yescharacteristic
33#11718659C2211yescharacteristic
34#11718659C2211yescharacteristic
35#11718659C2211yescharacteristic
36#11718659C2211yescharacteristic
37#11718658C2211yescharacteristic
38#11718658C2211yescharacteristic
39#11718656C411yescharacteristic, complemented
40#11718656C411yescharacteristic, complemented
41#11718656C411yescharacteristic, complemented
42#11718656C411yescharacteristic, complemented
43#11718625C411yescharacteristic, complemented
44#11718625C411yescharacteristic, complemented
45#11718625C411yescharacteristic, complemented
46#11718625C411yescharacteristic, complemented
47#11718587—21no—
48#11718586—21no—
49C2×#88043C2211yescharacteristic
50C2×C4×#1055C2211yescharacteristic
51#11718381—21no—
52#11718381—21no—
53#11718380—21no—
54#11718379—21no—
55C13×#339C2211yescharacteristic
56C13×#339C2211yescharacteristic
57C13×#339C2211yescharacteristic
58C13×#339C2211yescharacteristic
59#11718150C2211yescharacteristic
60#11718150C2211yescharacteristic
61#11718116C2211yescharacteristic
62#11718116C2211yescharacteristic
63#11718115C2211yescharacteristic
64#11718115C2211yescharacteristic
65#11718115C2211yescharacteristic
66#11718115C2211yescharacteristic
67C23×C4×C13C2311yescharacteristic
68C2×C13×M16C2311yescharacteristic
69C2×C13×M16C2311yescharacteristic
70C13×#117—21no—
71C13×#117—21no—
72C13×#117C2×C411yescharacteristic
73C13×#117C2×C411yescharacteristic
74C13×#117C2311yescharacteristic
75C13×#117C2311yescharacteristic
76C2×C13×C4⋊C4C2×C411yescharacteristic
77C2×C13×C4⋊C4C2×C411yescharacteristic
78C2×C13×C22⋊C4—21no—
79C2×C13×C22⋊C4—21no—
80C2×C42×C13—21no—
81C2×C42×C13C2311yescharacteristic
82C2×C42×C13C2311yescharacteristic
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×#6099—22no—
94C2×#6099—22no—
95C2×#6099C2×C411yescharacteristic
96C2×#6099C2×C411yescharacteristic
97C2×#6099C2×C411yescharacteristic
98C2×#6099C2×C411yescharacteristic
99C2×#6099C2311yescharacteristic
100C2×#6099C2311yescharacteristic
101C22×#1055C2311yescharacteristic
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105C13×C22⋊C8—21no—
106C13×C22⋊C8—21no—
107C13×#95—21no—
108C22⋊#1055—21no—
109C22⋊#1055—21no—
110C22⋊#1055D411yescharacteristic
111C22⋊#1055D411yescharacteristic
112C22⋊#1055D411yescharacteristic
113C22⋊#1055D411yescharacteristic
114#88062—22no—
115#88062—22no—
116#88055—21no—
117#88055—21no—
118#88054—21no—
119#88054—21no—
120#88054—21no—
121#88054—21no—
122C8×Dic13—21no—
123C8×Dic13—21no—
124#88048C2×C411yescharacteristic
125#88048C2×C411yescharacteristic
126#88048C2×C411yescharacteristic
127#88048C2×C411yescharacteristic
128#88048C2×C411yescharacteristic
129#88048C2×C411yescharacteristic
130#88048C2×C411yescharacteristic
131#88048C2×C411yescharacteristic
132#88047C2×C411yescharacteristic
133#88047C2×C411yescharacteristic
134#88047C2×C411yescharacteristic
135#88047C2×C411yescharacteristic
136#88047C2×C411yescharacteristic
137#88047C2×C411yescharacteristic
138#88047C2×C411yescharacteristic
139#88047C2×C411yescharacteristic
140C4⋊#1055—21no—
141C4⋊#1055—21no—
142C4⋊#1055—21no—
143C4⋊#1055—21no—
144#88043—21no—
145#88043—21no—
146#88043—22no—
147C4×#1055—21no—
148C4×#1055—21no—
149C4×#1055—22no—
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×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13C22×C411yescharacteristic
161C22×C4×C13C22×C411yescharacteristic
162C22×C4×C13C2×D411yescharacteristic
163C22×C4×C13C2×D411yescharacteristic
164C22×C4×C13#4111yescharacteristic
165C22×C4×C13C2411yescharacteristic
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—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4C22×C411yescharacteristic
177C13×C4⋊C4C22×C411yescharacteristic
178C13×C4⋊C4C22×C411yescharacteristic
179C13×C4⋊C4C22×C411yescharacteristic
180C13×C22⋊C4—21no—
181C13×C22⋊C4—21no—
182C13×C22⋊C4—21no—
183C13×C22⋊C4—21no—
184C13×C22⋊C4—42no—
185C42×C13—21no—
186C42×C13—21no—
187C42×C13—21no—
188C42×C13—21no—
189C42×C13—21no—
190C42×C13—21no—
191C42×C13—21no—
192C42×C13—21no—
193C22⋊Dic13—21no—
194C22⋊Dic13—21no—
195C22⋊Dic13—21no—
196C22⋊Dic13—21no—
197C4⋊Dic13—21no—
198C4⋊Dic13—21no—
199C4⋊Dic13C22×C411yescharacteristic
200C4⋊Dic13C22×C411yescharacteristic
201C4⋊Dic13C22×C411yescharacteristic
202C4⋊Dic13C22×C411yescharacteristic
203C4×Dic13—21no—
204C4×Dic13—21no—
205C4×Dic13—21no—
206C4×Dic13—21no—
207#6099—22no—
208#6099—22no—
209#6099—22no—
210#6099—22no—
211#6099—21no—
212#6099—21no—
213#6099—21no—
214#6099—21no—
215C2×#1055—21no—
216C2×#1055—21no—
217C2×#1055—21no—
218C2×#1055—21no—
219C2×#1055—21no—
220C2×#1055—21no—
221C2×#1055—21no—
222C2×#1055—21no—
223C2×#1055C22×C411yescharacteristic
224C2×#1055C22×C411yescharacteristic
225C2×#1055C22×C411yescharacteristic
226C2×#1055C22×C411yescharacteristic
227C2×#1055C2×D411yescharacteristic
228C2×#1055C2×D411yescharacteristic
229C2×#1055C2×D411yescharacteristic
230C2×#1055C2×D411yescharacteristic
231C2×#1055#4112yes—
232C2×#1055#4112yes—
233#2924—131no—
234#2924—131no—
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#1826D1311yescharacteristic
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—22no—
266C2×C4×C13—21no—
267C2×C4×C13—21no—
268C2×C4×C13—21no—
269C2×C4×C13—21no—
270C2×C4×C13—41no—
271C2×C4×C13—42no—
272C2×C4×C13—41no—
273C2×C4×C13—41no—
274C2×C4×C13—41no—
275C2×C4×C13—41no—
276C2×C4×C13—81no—
277C2×C4×C13C4×D411yescharacteristic
278C2×C4×C13C4×D411yescharacteristic
279C2×C4×C13C23×C411yescharacteristic
280C2×C4×C13C22×D411yescharacteristic
281C2×C4×C13C2×#4111yescharacteristic
282C2×C4×C13C2×#4111yescharacteristic
283C2×C4×C132−1+411yescharacteristic
284C2×C4×C132−1+411yescharacteristic
285C2×Dic13—21no—
286C2×Dic13—21no—
287C2×Dic13—21no—
288C2×Dic13—21no—
289C2×Dic13—42no—
290C2×Dic13—81no—
291C8×C13—41no—
292C8×C13—41no—
293#1055—21no—
294#1055—21no—
295#1055—21no—
296#1055—21no—
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—261no—
307#433—261no—
308#433—261no—
309#433—261no—
310#432—261no—
311#432—261no—
312#431—261no—
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#424—131no—
331#424—131no—
332#407—131no—
333#407C2×D1311yescharacteristic
334C2×C22⋊C8—131no—
335#405—131no—
336#405—131no—
337#405—131no—
338#405—131no—
339C2×#97—131no—
340C2×C4×C8—131no—
341C4×C22⋊C4C2×D1311yescharacteristic
342#341—131no—
343#341—131no—
344#339—131no—
345#339—131no—
346#339—131no—
347#339—131no—
348#339C2×D1311yescharacteristic
349#339C2×D1311yescharacteristic
350#339C2×D1311yescharacteristic
351#339C2×D1311yescharacteristic
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—42no—
370C4×C13—41no—
371C4×C13—41no—
372C4×C13—41no—
373C4×C13—41no—
374C4×C13—81no—
375C4×C13C2×#11711yescharacteristic
376C4×C13#51911yescharacteristic
377C4×C13#54711yescharacteristic
378C4×C13#54711yescharacteristic
379Dic13—41no—
380Dic13—41no—
381Dic13—41no—
382Dic13—41no—
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×C8—131no—
397C22×C8—131no—
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—21no—
416C2×C22⋊C4—261no—
417C2×C42—21no—
418C2×C42—261no—
419C2×C42C22×D1311yescharacteristic
420C2×C42C22×D1311yescharacteristic
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—261no—
440C4⋊C8—261no—
441C4⋊C8—261no—
442C4⋊C8—261no—
443C4⋊C8—261no—
444C4⋊C8—261no—
445C4⋊C8—261no—
446C4⋊C8—261no—
447C22⋊C8—21no—
448C22⋊C8—21no—
449C22⋊C8—131no—
450C22⋊C8—131no—
451C22⋊C8—131no—
452C22⋊C8—131no—
453C22⋊C8—261no—
454C22⋊C8—261no—
455#97—262no—
456#97—261no—
457#97—261no—
458#97—261no—
459#97—261no—
460C4×C8—262no—
461C4×C8—261no—
462C4×C8—261no—
463C4×C8—261no—
464C4×C8—261no—
465#95—21no—
466C2×C13—21no—
467C2×C13—21no—
468C2×C13—41no—
469C2×C13—41no—
470C2×C13#234411yescharacteristic
471C2×C13#295511yescharacteristic
472C2×C13#295611yescharacteristic
473C24#612911yescharacteristic
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—261no—
483C22×C4—261no—
484C22×C4C2×C4×D1311yescharacteristic
485C22×C4C2×C4×D1311yescharacteristic
486C22×C4D4×D1311yescharacteristic
487C22×C4D4×D1311yescharacteristic
488C22×C4#612911yescharacteristic
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—131no—
505C2×C8—131no—
506C2×C8—132no—
507C2×C8—132no—
508C2×C8—131no—
509C2×C8—131no—
510C2×C8—131no—
511C2×C8—131no—
512C2×C8—131no—
513C2×C8—131no—
514C2×C8—261no—
515C2×C8—261no—
516C2×C8—261no—
517C2×C8—261no—
518C2×C8—261no—
519C2×C8—261no—
520C2×C8—261no—
521C2×C8—261no—
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—42no—
539C22⋊C4—261no—
540C22⋊C4—261no—
541C22⋊C4—261no—
542C22⋊C4—261no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42—261no—
552C42—261no—
553C42—261no—
554C42—261no—
555C13#2260811yescharacteristic, complemented, Sylow
556C23—21no—
557C23—21no—
558C23—41no—
559C23—41no—
560C23#8813511yescharacteristic
561C23#8813511yescharacteristic
562C23C2×#612911yescharacteristic
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—22no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—41no—
579C2×C4—42no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—81no—
585C2×C4—261no—
586C2×C4—261no—
587C2×C4—261no—
588C2×C4—261no—
589C2×C4—522no—
590C2×C4—1041no—
591C2×C4#8813511yescharacteristic
592C2×C4#8813511yescharacteristic
593C2×C4C22×C4×D1311yescharacteristic
594C2×C4C2×D4×D1311yescharacteristic
595C2×C4#41×D1311yescharacteristic
596C2×C4#41×D1311yescharacteristic
597C2×C4#8825711yescharacteristic
598C2×C4#8825711yescharacteristic
599C8—41no—
600C8—41no—
601C8—132no—
602C8—132no—
603C8—261no—
604C8—261no—
605C8—261no—
606C8—261no—
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—
621C22C2×#8813511yescharacteristic
622C22#1171935511yescharacteristic
623C22#1171935511yescharacteristic
624C4—21no—
625C4—21no—
626C4—42no—
627C4—41no—
628C4—41no—
629C4—41no—
630C4—41no—
631C4—81no—
632C4—521no—
633C4—521no—
634C4—521no—
635C4—521no—
636C4#1171922111yescharacteristic
637C4D13×#11711yescharacteristic
638C4#1171936011yescharacteristic
639C4#1171936011yescharacteristic
640C2—21no—
641C2—21no—
642C2—41no—
643C2—41no—
644C2#1311770011yescharacteristic
645C2#1312373511yescharacteristic
646C2#1312374211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1826C2
socleC22×C13C2×C4×D4
prime radicalC24×C13#41
cosocleC22×C4×C13C24
hypercenter#1826D13
hypocenterC13#22608
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
4. #13115588C2semidirect
5. #13115583C2semidirect
6. #13115438C2semidirect
7. #13115438C2semidirect
8. #13115433C2semidirect
9. #13115433C2semidirect
12. #13114719C2semidirect
13. #13114714C2semidirect
39. #11718656C4semidirect
40. #11718656C4semidirect
41. #11718656C4semidirect
42. #11718656C4semidirect
43. #11718625C4semidirect
44. #11718625C4semidirect
45. #11718625C4semidirect
46. #11718625C4semidirect
555. C13#22608semidirect

Maximal subgroups

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

subgroupindex
#131234962
#131234942
#131234252
#131155882
#131155832
#131154382
#131154332
#131149362
#131148762
#131147192
#131147142
#131146202
C13×#18262
#2260813