Finite Group Databasebeta

← #14826938

Subgroups — #14826938

Order 2816.

848 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073191C211yesmaximal, characteristic, complemented
2#13071680C211yesmaximal, characteristic
3#13070148C211yesmaximal, characteristic, complemented
4#13069934C211yesmaximal, characteristic, complemented
5#13069851C211yesmaximal, characteristic
6#13069706C211yesmaximal, characteristic
7#13069470C211yesmaximal, characteristic, complemented
8#13069251C211yesmaximal, characteristic, complemented
9#13069244C211yesmaximal, characteristic, complemented
10#13069202C211yesmaximal, characteristic, complemented
11#13068949C211yesmaximal, characteristic, complemented
12#13068949C211yesmaximal, characteristic, complemented
13#13068617C211yesmaximal, characteristic, complemented
14C4×#66885C211yesmaximal, characteristic, complemented
15C11×#1916C211yesmaximal, characteristic, complemented
16C22×#4314C2211yescharacteristic
17C22×#4314C2211yescharacteristic
18C2×#66946—21no—
19C2×#66927C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C2×C4×D44C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66881C2211yescharacteristic
32C2×#66881C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35#10622601—21no—
36#10622599—21no—
37#10622594—21no—
38#10622552C2211yescharacteristic
39#10622552C2211yescharacteristic
40#10622548C2211yescharacteristic
41C4×C4⋊Dic11C2211yescharacteristic
42C4×C4⋊Dic11C2211yescharacteristic
43#10622542C2211yescharacteristic
44#10622542C2211yescharacteristic
45#10622542C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622278—21no—
48#10622278—21no—
49#10622273—21no—
50#10622267—21no—
51C11×#336C2211yescharacteristic
52C11×#336C2211yescharacteristic
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59C22×D44—21no—
60C22×D44—21no—
61C22×D44C2311yescharacteristic
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×C4×D11—21no—
65C22×Dic22C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×Dic11⋊C4—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×#4314—22no—
92C2×#4314—22no—
93C2×#4314—22no—
94C2×#4314—41no—
95C2×#4314—41no—
96C2×#4314—41no—
97#66946—44no—
98#66927—22no—
99#66927—22no—
100C4×D44—22no—
101C4×D44—22no—
102C4×D44—41no—
103C4×D44—41no—
104C11×C4⋊C8—41no—
105C4×C8×C11—41no—
106C11×#95D411yescharacteristic
107C11×#95D411yescharacteristic
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117#66885—22no—
118#66885—22no—
119#66885—22no—
120#66885—41no—
121#66885—41no—
122#66885—41no—
123#66881—22no—
124#66881—41no—
125#66880—22no—
126#66880—41no—
127#27064—111nomaximal, Sylow
128C23×D11—21no—
129C23×D11—21no—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2411yescharacteristic
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C2×D44—24no—
144C2×D44—24no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—42no—
156C2×D44—42no—
157C2×D44—81no—
158C2×D44—81no—
159C2×D44#4112yes—
160C2×D44#4112yes—
161C2×C4×D11—42no—
162C2×C4×D11—42no—
163C2×C4×D11—42no—
164C2×C4×D11—42no—
165C2×C4×D11—81no—
166C2×C4×D11—81no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11#4112yes—
185C11×C4⋊C4—41no—
186C11×C4⋊C4SD1614yescomplemented
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—21no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—42no—
195(C2×D11)⋊C4—42no—
196(C2×D11)⋊C4—42no—
197(C2×D11)⋊C4—81no—
198(C2×D11)⋊C4—81no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—42no—
209C4⋊Dic11—81no—
210C4⋊Dic11#4112yes—
211Dic11⋊C4—81no—
212C4×Dic11—42no—
213C4×Dic11—81no—
214#4314—44no—
215#4314—44no—
216#2511—111no—
217#2366—111no—
218#2094—111no—
219#2055—111no—
220#2041—111no—
221#2014—111no—
222#1968—111no—
223#1927—111no—
224#1926—111no—
225#1920—111no—
226#1916D1111yescharacteristic, complemented
227#1877—111no—
228#1877—111no—
229#1802—111no—
230C4×#102—111no—
231C23×C11C22×D411yescharacteristic
232C22×D11—22no—
233C22×D11—22no—
234C22×D11—41no—
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—41no—
240C22×D11—41no—
241C22×D11—41no—
242C22×D11—41no—
243C22×D11—41no—
244C22×D11—41no—
245C22×D11—41no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11C2×SD1612yes—
262C2×C4×C11C2×SD1612yes—
263C2×C4×C11C2×SD1612yes—
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11H(5,𝔽2)11yescharacteristic
269C2×C4×C11H(5,𝔽2)11yescharacteristic
270C2×Dic11—22no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288D44—22no—
289D44—22no—
290D44—22no—
291D44—22no—
292D44—48no—
293D44—41no—
294D44—41no—
295D44—41no—
296D44—41no—
297D44—84no—
298C4×D11—84no—
299C4×D11—84no—
300Dic22—41no—
301Dic22—41no—
302Dic22—41no—
303Dic22—41no—
304C8×C11—22no—
305C8×C11—41no—
306C8×C11—41no—
307C8×C11—41no—
308C22×SD16—111no—
309C22×SD16—111no—
310C2×#127—111no—
311C2×C4×D4—111no—
312C2×C4×D4—111no—
313C2×C4×D4—221no—
314C2×#106—111no—
315C2×#106—111no—
316C2×C4⋊C8C2×D1111yescharacteristic
317C2×#103—111no—
318C2×#103—111no—
319C2×#102—111no—
320C2×#102—111no—
321C2×#102—111no—
322C2×#102—111no—
323C2×#102—111no—
324C2×#102—111no—
325C2×C4×C8C2×D1111yescharacteristic
326#400—221no—
327#400—221no—
328#391—111no—
329#391—111no—
330#391—111no—
331#390—111no—
332#390—111no—
333#390—221no—
334#389—111no—
335#387—221no—
336#387—221no—
337#386—221no—
338#386—221no—
339#384—111no—
340C4×C4⋊C4—111no—
341C4×C4⋊C4—111no—
342C4×C4⋊C4C2×D1111yescharacteristic
343#340—111no—
344#340—111no—
345#340—111no—
346#340—111no—
347#336C2×D1111yescharacteristic
348#336C2×D1111yescharacteristic
349#336C2×D1111yescharacteristic
350#336C2×D1111yescharacteristic
351C22×C11#52511yescharacteristic
352C22×C11#54611yescharacteristic
353C22×C11#55011yescharacteristic
354C22×C11C22×SD1611yescharacteristic
355C22×C11#57511yescharacteristic
356C22×C11#57611yescharacteristic
357C22×C11#57711yescharacteristic
358C2×D11—42no—
359C2×D11—42no—
360C2×D11—42no—
361C2×D11—42no—
362C2×D11—42no—
363C2×D11—42no—
364C2×D11—81no—
365C2×D11—81no—
366C2×D11—81no—
367C2×D11—81no—
368C2×D11—81no—
369C2×D11—81no—
370C2×D11—81no—
371C2×D11—81no—
372C4×C11—22no—
373C4×C11—22no—
374C4×C11—22no—
375C4×C11—41no—
376C4×C11—41no—
377C4×C11—41no—
378C4×C11#52911yescharacteristic
379C4×C11#53811yescharacteristic
380C4×C11#55111yescharacteristic
381C4×C11#55311yescharacteristic
382Dic11—42no—
383Dic11—81no—
384Dic11—81no—
385Dic11—81no—
386Dic11—81no—
387Dic11—81no—
388C22×Q8—111no—
389C22×D4—111no—
390C22×D4—111no—
391C22×D4—221no—
392C22×D4—221no—
393C23×C4—221no—
394C23×C4—221no—
395C2×SD16—222no—
396C2×SD16—222no—
397C2×SD16—222no—
398C2×SD16—441no—
399C2×SD16—441no—
400C2×SD16—441no—
401C22×C8C22×D1111yescharacteristic
402C22×C8C22×D1111yescharacteristic
403C22×C8C22×D1111yescharacteristic
404C22×C8C22×D1111yescharacteristic
405#127—222no—
406#127—222no—
407C4×D4—222no—
408C4×D4—222no—
409C4×D4—441no—
410C4×D4—441no—
411C4×D4—444no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4D4411yescharacteristic
421C2×C4⋊C4D4411yescharacteristic
422C2×C22⋊C4—221no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C22⋊C4—221no—
427C2×C22⋊C4—221no—
428C2×C42—221no—
429C2×C42—221no—
430C2×C42C22×D1111yescharacteristic
431C2×C42C22×D1111yescharacteristic
432C2×C42C22×D1111yescharacteristic
433#106—222no—
434#106—441no—
435C4⋊C8—41no—
436#103—222no—
437#103—441no—
438#102—222no—
439#102—222no—
440#102—222no—
441#102—441no—
442#102—441no—
443#102—441no—
444C4×C8—41no—
445#95—221no—
446#95—221no—
447#95—221no—
448#95—221no—
449#95—221no—
450#95—221no—
451#95—221no—
452#95—221no—
453#95—221no—
454#95D4411yescharacteristic
455#95D4411yescharacteristic
456C2×C11#246711yescharacteristic
457C2×C11#310111yescharacteristic
458C2×C11#311811yescharacteristic
459C2×C11#329511yescharacteristic
460C2×C11#331711yescharacteristic
461C2×C11#339211yescharacteristic
462C2×C11#340311yescharacteristic
463D11—82no—
464D11—82no—
465C24—221no—
466C24—221no—
467C2×Q8—221no—
468C2×Q8—221no—
469C2×Q8—221no—
470C2×Q8—221no—
471C2×Q8—221no—
472C2×Q8—221no—
473C2×D4—112no—
474C2×D4—112no—
475C2×D4—224no—
476C2×D4—224no—
477C2×D4—221no—
478C2×D4—221no—
479C2×D4—221no—
480C2×D4—221no—
481C2×D4—221no—
482C2×D4—221no—
483C2×D4—221no—
484C2×D4—221no—
485C2×D4—221no—
486C2×D4—221no—
487C2×D4—442no—
488C2×D4—442no—
489C2×D4—881no—
490C2×D4—881no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—442no—
498C22×C4—442no—
499C22×C4—442no—
500C22×C4—442no—
501C22×C4—881no—
502C22×C4—881no—
503C22×C4C2×D4411yescharacteristic
504C22×C4C2×D4411yescharacteristic
505C22×C4C2×D4411yescharacteristic
506C22×C4C2×D4411yescharacteristic
507C22×C4C2×D4411yescharacteristic
508C22×C4C2×D4411yescharacteristic
509C22×C4C23×D1111yescharacteristic
510SD16—444no—
511SD16—444no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8#434312yes—
524C4⋊C4—41no—
525C4⋊C4—112no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—442no—
536C4⋊C4—881no—
537C4⋊C4—881no—
538C4⋊C4#431414yescomplemented
539C22⋊C4—442no—
540C22⋊C4—442no—
541C22⋊C4—442no—
542C22⋊C4—442no—
543C22⋊C4—881no—
544C22⋊C4—881no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42—442no—
552C42—881no—
553C11#2706411yescharacteristic, complemented, Sylow
554C23—222no—
555C23—222no—
556C23—441no—
557C23—441no—
558C23—441no—
559C23—441no—
560C23—441no—
561C23—441no—
562C23—441no—
563C23—441no—
564C23—441no—
565C23—441no—
566C23—441no—
567C23—441no—
568C23C22×D4411yescharacteristic
569Q8—441no—
570Q8—441no—
571Q8—441no—
572Q8—441no—
573D4—222no—
574D4—222no—
575D4—222no—
576D4—222no—
577D4—448no—
578D4—441no—
579D4—441no—
580D4—441no—
581D4—441no—
582D4—884no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—222no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—884no—
617C2×C4—884no—
618C2×C4C2×#431412yes—
619C2×C4C2×#431412yes—
620C2×C4C2×#431412yes—
621C2×C4#6703711yescharacteristic
622C2×C4C2×#434311yescharacteristic
623C2×C4#41×D1111yescharacteristic
624C2×C4#41×D1111yescharacteristic
625C2×C4#41×D1111yescharacteristic
626C2×C4#6704211yescharacteristic
627C8—22no—
628C8—41no—
629C8—41no—
630C8—41no—
631C22—442no—
632C22—442no—
633C22—442no—
634C22—442no—
635C22—442no—
636C22—442no—
637C22—881no—
638C22—881no—
639C22—881no—
640C22—881no—
641C22—881no—
642C22—881no—
643C22—881no—
644C22—881no—
645C22#1062305511yescharacteristic
646C22#1062308511yescharacteristic
647C22#1062310811yescharacteristic
648C22C22×#431411yescharacteristic
649C22#1062327911yescharacteristic
650C22#1062328211yescharacteristic
651C22#1062328311yescharacteristic
652C4—22no—
653C4—22no—
654C4—22no—
655C4—41no—
656C4—41no—
657C4—41no—
658C4—442no—
659C4—881no—
660C4—881no—
661C4—881no—
662C4—881no—
663C4—881no—
664C4#1062316811yescharacteristic
665C4#1062318811yescharacteristic
666C4#1062322211yescharacteristic
667C4#1062324011yescharacteristic
668C2—882no—
669C2—882no—
670C2#1307266511yescharacteristic
671C2#1307862511yescharacteristic
672C2#1307880211yescharacteristic
673C2#1308044111yescharacteristic
674C2#1308074411yescharacteristic
675C2#1308159811yescharacteristic
676C2#1308170611yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1916C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
hypercenter#1916D11
hypocenterC11#27064
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1916

Complements

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

NH ≅ G/Ntype
1. #13073191C2semidirect
3. #13070148C2semidirect
4. #13069934C2semidirect
7. #13069470C2semidirect
8. #13069251C2semidirect
9. #13069244C2semidirect
10. #13069202C2semidirect
11. #13068949C2semidirect
12. #13068949C2semidirect
13. #13068617C2semidirect
14. C4×#66885C2semidirect
15. C11×#1916C2semidirect
186. C11×C4⋊C4SD16semidirect
226. #1916D11semidirect
538. C4⋊C4#4314semidirect
553. C11#27064semidirect

Maximal subgroups

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

subgroupindex
#130731912
#130716802
#130701482
#130699342
#130698512
#130697062
#130694702
#130692512
#130692442
#130692022
#130689492
#130686172
C4×#668852
C11×#19162
#2706411