Finite Group Databasebeta

← #14826968

Subgroups — #14826968

Order 2816.

762 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073202C211yesmaximal, characteristic
2#13071672C211yesmaximal, characteristic, complemented
3#13070158C211yesmaximal, characteristic, complemented
4#13069934C211yesmaximal, characteristic
5#13069863C211yesmaximal, characteristic, complemented
6#13069701C211yesmaximal, characteristic
7#13069470C211yesmaximal, characteristic
8#13069251C211yesmaximal, characteristic, complemented
9#13069244C211yesmaximal, characteristic
10#13069195C211yesmaximal, characteristic, complemented
11#13068970C211yesmaximal, characteristic
12#13068970C211yesmaximal, characteristic
13#13068622C211yesmaximal, characteristic, complemented
14C4×#66880C211yesmaximal, characteristic, complemented
15C11×#1916C211yesmaximal, characteristic, complemented
16C22×#4314C2211yescharacteristic
17C22×#4314C2211yescharacteristic
18C2×#66951—21no—
19C2×#66922C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×#66881C2211yescharacteristic
28C2×#66881C2211yescharacteristic
29C2×#66880C2211yescharacteristic
30C2×#66880C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35#10622607—21no—
36C4⋊C4×Dic11—21no—
37#10622586—21no—
38#10622552C2211yescharacteristic
39#10622552C2211yescharacteristic
40#10622552C2211yescharacteristic
41#10622548C2211yescharacteristic
42C4×C4⋊Dic11C2211yescharacteristic
43C4×C4⋊Dic11C2211yescharacteristic
44#10622542C2211yescharacteristic
45#10622542C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622287—21no—
48#10622283—21no—
49#10622267—21no—
50#10622267—21no—
51C11×#336C2211yescharacteristic
52C11×#336C2211yescharacteristic
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59C22×D44C2311yescharacteristic
60C22×Dic22C2311yescharacteristic
61C22×Dic22C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C2×C11×C4⋊C4D411yescharacteristic
67C2×C11×C4⋊C4D411yescharacteristic
68C2×C42×C11C2311yescharacteristic
69C2×C42×C11C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×#4314—22no—
94C2×#4314—22no—
95C2×#4314—22no—
96C2×#4314—41no—
97C2×#4314—41no—
98C2×#4314—41no—
99#66951—44no—
100#66922—22no—
101#66922—22no—
102C4×Dic22—22no—
103C4×Dic22—22no—
104C4×Dic22—41no—
105C4×Dic22—41no—
106C11×C4⋊C8—41no—
107C4×C8×C11—41no—
108C11×#95D411yescharacteristic
109C11×#95D411yescharacteristic
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—41no—
119#66881—22no—
120#66881—41no—
121#66880—22no—
122#66880—22no—
123#66880—22no—
124#66880—41no—
125#66880—41no—
126#66880—41no—
127#27066—111nomaximal, Sylow
128C23×D11—21no—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2411yescharacteristic
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44—21no—
149C2×Dic22—21no—
150C2×Dic22—21no—
151C2×Dic22—21no—
152C2×Dic22—21no—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22#4112yes—
160C2×Dic22#4112yes—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11#4112yes—
173C11×C4⋊C4—41no—
174C11×C4⋊C4SD1614yescomplemented
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—21no—
181(C2×D11)⋊C4—42no—
182(C2×D11)⋊C4—42no—
183(C2×D11)⋊C4—42no—
184(C2×D11)⋊C4—42no—
185(C2×D11)⋊C4—81no—
186(C2×D11)⋊C4—81no—
187C4⋊Dic11—24no—
188C4⋊Dic11—24no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—42no—
199C4⋊Dic11—81no—
200C4⋊Dic11#4112yes—
201Dic11⋊C4—42no—
202Dic11⋊C4—42no—
203Dic11⋊C4—42no—
204C4×Dic11—42no—
205C4×Dic11—42no—
206C4×Dic11—42no—
207C4×Dic11—42no—
208#4314—44no—
209#4314—44no—
210#2512—111no—
211#2365—111no—
212#2096—111no—
213#2055—111no—
214#2043—111no—
215#2013—111no—
216#1968—111no—
217#1927—111no—
218#1926—111no—
219#1919—111no—
220#1916D1111yescharacteristic, complemented
221#1880—111no—
222#1880—111no—
223#1803—111no—
224C4×#103—111no—
225C23×C11C22×D411yescharacteristic
226C22×D11—41no—
227C22×D11—41no—
228C22×D11—41no—
229C22×D11—41no—
230C22×D11—41no—
231C22×D11—41no—
232C22×D11—41no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11C2×SD1612yes—
249C2×C4×C11C2×SD1612yes—
250C2×C4×C11C2×SD1612yes—
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11H(5,𝔽2)11yescharacteristic
256C2×C4×C11H(5,𝔽2)11yescharacteristic
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278D44—41no—
279D44—41no—
280D44—41no—
281D44—41no—
282Dic22—22no—
283Dic22—22no—
284Dic22—22no—
285Dic22—22no—
286Dic22—41no—
287Dic22—41no—
288Dic22—41no—
289Dic22—41no—
290C8×C11—22no—
291C8×C11—41no—
292C8×C11—41no—
293C8×C11—41no—
294C22×SD16—111no—
295C22×SD16—111no—
296C2×C4⋊Q8—111no—
297C2×#126—221no—
298C2×C4×Q8—111no—
299C2×C4×Q8—111no—
300C2×#106—111no—
301C2×#106—111no—
302C2×C4⋊C8C2×D1111yescharacteristic
303C2×#103—111no—
304C2×#103—111no—
305C2×#103—111no—
306C2×#103—111no—
307C2×#103—111no—
308C2×#103—111no—
309C2×#102—111no—
310C2×#102—111no—
311C2×C4×C8C2×D1111yescharacteristic
312#397—221no—
313#396—221no—
314#391—111no—
315#391—111no—
316#390—111no—
317#390—111no—
318#390—111no—
319#389—111no—
320#389—221no—
321#388—221no—
322#387—221no—
323#387—221no—
324#384—111no—
325C4×C4⋊C4—111no—
326C4×C4⋊C4—111no—
327C4×C4⋊C4—221no—
328C4×C4⋊C4C2×D1111yescharacteristic
329#340—111no—
330#340—111no—
331#340—111no—
332#340—111no—
333#336C2×D1111yescharacteristic
334#336C2×D1111yescharacteristic
335#336C2×D1111yescharacteristic
336#336C2×D1111yescharacteristic
337C22×C11#52511yescharacteristic
338C22×C11#54611yescharacteristic
339C22×C11#55011yescharacteristic
340C22×C11C22×SD1611yescharacteristic
341C22×C11#57511yescharacteristic
342C22×C11#57711yescharacteristic
343C22×C11#57811yescharacteristic
344C2×D11—81no—
345C2×D11—81no—
346C2×D11—81no—
347C2×D11—81no—
348C2×D11—81no—
349C2×D11—81no—
350C2×D11—81no—
351C4×C11—22no—
352C4×C11—22no—
353C4×C11—22no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11—41no—
357C4×C11#52911yescharacteristic
358C4×C11#53811yescharacteristic
359C4×C11#55111yescharacteristic
360C4×C11#55311yescharacteristic
361Dic11—42no—
362Dic11—42no—
363Dic11—42no—
364Dic11—81no—
365Dic11—81no—
366Dic11—81no—
367Dic11—81no—
368C22×Q8—111no—
369C22×Q8—111no—
370C22×D4—111no—
371C2×SD16—222no—
372C2×SD16—222no—
373C2×SD16—222no—
374C2×SD16—441no—
375C2×SD16—441no—
376C2×SD16—441no—
377C22×C8C22×D1111yescharacteristic
378C22×C8C22×D1111yescharacteristic
379C22×C8C22×D1111yescharacteristic
380C22×C8C22×D1111yescharacteristic
381C4⋊Q8—222no—
382C4⋊Q8—222no—
383#126—444no—
384C4×Q8—222no—
385C4×Q8—222no—
386C4×Q8—441no—
387C4×Q8—441no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—111no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4D4411yescharacteristic
401C2×C4⋊C4D4411yescharacteristic
402C2×C22⋊C4—221no—
403C2×C22⋊C4—221no—
404C2×C22⋊C4—221no—
405C2×C22⋊C4—221no—
406C2×C22⋊C4—221no—
407C2×C22⋊C4—221no—
408C2×C42—221no—
409C2×C42—221no—
410C2×C42—221no—
411C2×C42—221no—
412C2×C42C22×D1111yescharacteristic
413C2×C42C22×D1111yescharacteristic
414C2×C42C22×D1111yescharacteristic
415#106—222no—
416#106—441no—
417C4⋊C8—41no—
418#103—222no—
419#103—222no—
420#103—222no—
421#103—441no—
422#103—441no—
423#103—441no—
424#102—222no—
425#102—441no—
426C4×C8—41no—
427#95—221no—
428#95—221no—
429#95—221no—
430#95—221no—
431#95—221no—
432#95—221no—
433#95—221no—
434#95D4411yescharacteristic
435#95D4411yescharacteristic
436C2×C11#246711yescharacteristic
437C2×C11#310311yescharacteristic
438C2×C11#312111yescharacteristic
439C2×C11#329811yescharacteristic
440C2×C11#330711yescharacteristic
441C2×C11#339211yescharacteristic
442C2×C11#340211yescharacteristic
443D11—161no—
444C24—221no—
445C2×Q8—112no—
446C2×Q8—112no—
447C2×Q8—221no—
448C2×Q8—221no—
449C2×Q8—221no—
450C2×Q8—221no—
451C2×Q8—221no—
452C2×Q8—221no—
453C2×Q8—221no—
454C2×Q8—221no—
455C2×Q8—221no—
456C2×Q8—221no—
457C2×D4—221no—
458C2×D4—221no—
459C2×D4—221no—
460C2×D4—221no—
461C2×D4—221no—
462C2×D4—221no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4—221no—
467C22×C4—221no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4C2×D4411yescharacteristic
471C22×C4C2×D4411yescharacteristic
472C22×C4C2×D4411yescharacteristic
473C22×C4C2×D4411yescharacteristic
474C22×C4C2×D4411yescharacteristic
475C22×C4C2×D4411yescharacteristic
476C22×C4C23×D1111yescharacteristic
477SD16—444no—
478SD16—444no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8#434312yes—
491C4⋊C4—41no—
492C4⋊C4—112no—
493C4⋊C4—224no—
494C4⋊C4—224no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—442no—
505C4⋊C4—442no—
506C4⋊C4—442no—
507C4⋊C4—442no—
508C4⋊C4—881no—
509C4⋊C4#431414yescomplemented
510C22⋊C4—442no—
511C22⋊C4—442no—
512C22⋊C4—442no—
513C22⋊C4—442no—
514C22⋊C4—881no—
515C22⋊C4—881no—
516C42—21no—
517C42—21no—
518C42—21no—
519C42—21no—
520C42—21no—
521C42—21no—
522C42—442no—
523C42—442no—
524C42—442no—
525C42—442no—
526C11#2706611yescharacteristic, complemented, Sylow
527C23—441no—
528C23—441no—
529C23—441no—
530C23—441no—
531C23—441no—
532C23—441no—
533C23—441no—
534C23C22×D4411yescharacteristic
535Q8—222no—
536Q8—222no—
537Q8—222no—
538Q8—222no—
539Q8—441no—
540Q8—441no—
541Q8—441no—
542Q8—441no—
543D4—441no—
544D4—441no—
545D4—441no—
546D4—441no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—222no—
563C2×C4—222no—
564C2×C4—222no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4C2×#431412yes—
584C2×C4C2×#431412yes—
585C2×C4C2×#431412yes—
586C2×C4#6703711yescharacteristic
587C2×C4C2×#434311yescharacteristic
588C2×C4#41×D1111yescharacteristic
589C2×C4#41×D1111yescharacteristic
590C2×C4#41×D1111yescharacteristic
591C2×C4#6704211yescharacteristic
592C8—22no—
593C8—41no—
594C8—41no—
595C8—41no—
596C22—881no—
597C22—881no—
598C22—881no—
599C22—881no—
600C22—881no—
601C22—881no—
602C22—881no—
603C22#1062305511yescharacteristic
604C22#1062308511yescharacteristic
605C22#1062310811yescharacteristic
606C22C22×#431411yescharacteristic
607C22#1062327911yescharacteristic
608C22#1062328211yescharacteristic
609C22#1062328411yescharacteristic
610C4—22no—
611C4—22no—
612C4—22no—
613C4—41no—
614C4—41no—
615C4—41no—
616C4—442no—
617C4—442no—
618C4—442no—
619C4—881no—
620C4—881no—
621C4—881no—
622C4—881no—
623C4#1062316811yescharacteristic
624C4#1062318811yescharacteristic
625C4#1062322211yescharacteristic
626C4#1062324011yescharacteristic
627C2—1761no—
628C2#1307266511yescharacteristic
629C2#1307864811yescharacteristic
630C2#1307884711yescharacteristic
631C2#1308048211yescharacteristic
632C2#1308059411yescharacteristic
633C2#1308159811yescharacteristic
634C2#1308169711yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1916C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1916D11
hypocenterC11#27066
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
2. #13071672C2semidirect
3. #13070158C2semidirect
5. #13069863C2semidirect
8. #13069251C2semidirect
10. #13069195C2semidirect
13. #13068622C2semidirect
14. C4×#66880C2semidirect
15. C11×#1916C2semidirect
174. C11×C4⋊C4SD16semidirect
220. #1916D11semidirect
509. C4⋊C4#4314semidirect
526. C11#27066semidirect

Maximal subgroups

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

subgroupindex
#130732022
#130716722
#130701582
#130699342
#130698632
#130697012
#130694702
#130692512
#130692442
#130691952
#130689702
#130686222
C4×#668802
C11×#19162
#2706611