Finite Group Databasebeta

← #14823146

Subgroups — #14823146

Order 2816.

776 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622480C211yesmaximal, characteristic
2#13072960C211yesmaximal, characteristic
3#13071639C211yesmaximal, characteristic
4#13070010C211yesmaximal, characteristic, complemented
5#13069951C211yesmaximal, characteristic, complemented
6#13069818C211yesmaximal, characteristic
7#13069625C211yesmaximal, characteristic
8#13069484C211yesmaximal, characteristic, complemented
9#13069260C211yesmaximal, characteristic, complemented
10#13069256C211yesmaximal, characteristic, complemented
11#13069228C211yesmaximal, characteristic
12#13068957C211yesmaximal, characteristic, complemented
13#13068812C211yesmaximal, characteristic
14#13068516C211yesmaximal, characteristic, complemented
15C2×C11×#479C211yesmaximal, characteristic, complemented
16C2×C11×#125C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×#66999C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C2×#66950C2211yescharacteristic
21C2×#66945C2211yescharacteristic
22C11×#479—24no—
23C2×C11×#107C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28#10622843C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66879C2211yescharacteristic
36#10622606—21no—
37#10622603—21no—
38#10622603—21no—
39#10622600C2211yescharacteristic
40#10622599—21no—
41#10622591—21no—
42#10622590—21no—
43C4⋊C4×Dic11C2211yescharacteristic
44C4⋊C4×Dic11C2211yescharacteristic
45#10622587C2211yescharacteristic
46C2×#66874C2211yescharacteristic
47C2×#66872C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49#10622553—21no—
50C4×(C2×D11)⋊C4C2211yescharacteristic
51C4×Dic11⋊C4—21no—
52#10622542C2211yescharacteristic
53#10622541C2211yescharacteristic
54#10622480—24no—
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×C4×D11C2311yescharacteristic
63C22×Dic22C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C11×#125—22no—
67C11×#125—41no—
68C4×Q8×C11—22no—
69C4×Q8×C11—41no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C42×C11—21no—
77C2×C42×C11C2311yescharacteristic
78#66999—22no—
79#66999—22no—
80C2×#4326—22no—
81C2×#4326—22no—
82C2×#4326—41no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4D411yescharacteristic
88C2×(C2×D11)⋊C4D411yescharacteristic
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101#66950—22no—
102#66950—41no—
103#66945—22no—
104#66945—41no—
105C11×#107—22no—
106C11×#106D414yes—
107C11×C4⋊C8—22no—
108C11×#103—22no—
109C11×#103—22no—
110#66899—22no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95D411yescharacteristic
122C11⋊#95D411yescharacteristic
123(C2×D11)⋊C8—22no—
124(C2×D11)⋊C8—22no—
125#66882—22no—
126#66880—22no—
127#66880—22no—
128#66879—22no—
129#66874—22no—
130#66872—41no—
131#66871—22no—
132#26809—111nomaximal, Sylow
133C23×D11C2×D411yescharacteristic
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11#4112yes—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C2×C4×D11—21no—
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11C2×D412yes—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—42no—
177C11×C4⋊C4—42no—
178C11×C4⋊C4—42no—
179C11×C4⋊C4C2×D412yes—
180C11×C4⋊C4C2×D412yes—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—42no—
184#4326—44no—
185(C2×D11)⋊C4—24no—
186(C2×D11)⋊C4—41no—
187(C2×D11)⋊C4—41no—
188(C2×D11)⋊C4—42no—
189(C2×D11)⋊C4—42no—
190(C2×D11)⋊C4—42no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—42no—
197C4⋊Dic11#4112yes—
198Dic11⋊C4—24no—
199Dic11⋊C4—42no—
200C4×Dic11—21no—
201C4×Dic11—21no—
202C4×Dic11—42no—
203C4×Dic11—42no—
204C4×Dic11—42no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8#4112yes—
211C2×#485—111no—
212C2×#479D1111yescharacteristic, complemented
213#2489—111no—
214#2362—111no—
215#2068—111no—
216#2059—111no—
217#2036—111no—
218#2001—111no—
219#1971—111no—
220#1928—111no—
221#1928—111no—
222#1924—111no—
223#1878—111no—
224#1854—111no—
225#1776—111no—
226C23×C11C22×D411yescharacteristic
227C22×D11—21no—
228C22×D11—21no—
229C22×D11—21no—
230C22×D11—21no—
231C22×D11—21no—
232C22×D11—21no—
233C22×D11—21no—
234Q8×C11—22no—
235Q8×C11—22no—
236Q8×C11—41no—
237Q8×C11—41no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
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—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11H(5,𝔽2)11yescharacteristic
261C2×C4×C112−1+411yescharacteristic
262C2×Dic11—21no—
263C2×Dic11—22no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
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—
283C4×D11—41no—
284C4×D11—41no—
285C4×D11—41no—
286C4×D11—41no—
287Dic22—41no—
288Dic22—41no—
289Dic22—41no—
290Dic22—41no—
291C8×C11—22no—
292C8×C11—41no—
293C11⋊C8—22no—
294C11⋊C8—41no—
295C22×Q16—111no—
296C2×#125C2×D1111yescharacteristic
297C2×C22⋊Q8—111no—
298C2×C22⋊Q8—111no—
299C2×C4×Q8C2×D1111yescharacteristic
300C2×#117—111no—
301#485—224no—
302#479—24no—
303C2×#107—111no—
304C2×#107—111no—
305C2×#107C2×D1111yescharacteristic
306C2×#106—111no—
307C2×#106C2×D1111yescharacteristic
308C2×C4⋊C8C2×D1111yescharacteristic
309C2×#103—111no—
310C2×#103—111no—
311C2×#103—111no—
312C2×#103—111no—
313C2×#103C2×D1111yescharacteristic
314C2×#103C2×D1111yescharacteristic
315C2×C22⋊C8—111no—
316C2×C22⋊C8—111no—
317C2×#97—111no—
318#400—221no—
319#397—221no—
320#391—111no—
321#391—111no—
322#391—111no—
323#389—111no—
324#388—221no—
325#388—221no—
326#388—221no—
327#387—221no—
328#382—221no—
329#380—111no—
330C4×C4⋊C4—111no—
331C4×C4⋊C4—111no—
332C4×C4⋊C4—221no—
333C4×C22⋊C4—111no—
334#340—111no—
335#340—111no—
336#340—111no—
337#340—111no—
338#336—111no—
339#336—111no—
340C22×C11#52511yescharacteristic
341C22×C11D4211yescharacteristic
342C22×C11#54711yescharacteristic
343C22×C11#57511yescharacteristic
344C22×C11#57511yescharacteristic
345C22×C11#57811yescharacteristic
346C22×C11#57811yescharacteristic
347C2×D11—41no—
348C2×D11—41no—
349C2×D11—41no—
350C2×D11—41no—
351C2×D11—41no—
352C2×D11—41no—
353C2×D11—41no—
354C4×C11—42no—
355C4×C11—41no—
356C4×C11—41no—
357C4×C11—42no—
358C4×C11—42no—
359C4×C11—81no—
360C4×C11#53211yescharacteristic
361C4×C11#54211yescharacteristic
362C4×C11#54811yescharacteristic
363C4×C11#55111yescharacteristic
364Dic11—41no—
365Dic11—41no—
366Dic11—42no—
367Dic11—41no—
368Dic11—81no—
369Dic11—81no—
370Dic11—81no—
371C22×Q8—111no—
372C22×Q8C22×D1111yescharacteristic
373C23×C4—111no—
374C2×Q16—222no—
375C2×Q16—222no—
376C2×Q16—441no—
377C22×C8—111no—
378C22×C8—111no—
379C22×C8C22×D1111yescharacteristic
380C22×C8C22×D1111yescharacteristic
381#125—22no—
382#125—41no—
383C22⋊Q8—222no—
384C22⋊Q8—222no—
385C22⋊Q8—222no—
386C22⋊Q8—441no—
387C4×Q8—22no—
388C4×Q8—41no—
389#117—222no—
390#117—441no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4C22×D1111yescharacteristic
401C2×C4⋊C4C22×D1111yescharacteristic
402C2×C4⋊C4C22×D1111yescharacteristic
403C2×C22⋊C4—111no—
404C2×C22⋊C4—111no—
405C2×C22⋊C4—221no—
406C2×C22⋊C4—221no—
407C2×C22⋊C4—221no—
408C2×C22⋊C4—221no—
409C2×C42—21no—
410C2×C42—111no—
411C2×C42—221no—
412C2×C42—221no—
413C2×C42—221no—
414C2×C42C22×D1111yescharacteristic
415#107—22no—
416#107—222no—
417#107—222no—
418#106—441no—
419#106C22⋊D1114yes—
420C4⋊C8—22no—
421#103—22no—
422#103—22no—
423#103—222no—
424#103—222no—
425#103—222no—
426#103—222no—
427C22⋊C8—222no—
428C22⋊C8—222no—
429#97—222no—
430#95—111no—
431#95—111no—
432#95—221no—
433#95—221no—
434#95—221no—
435#95—221no—
436#95—221no—
437#95—221no—
438#95—221no—
439#95—221no—
440#95—221no—
441#95—221no—
442C2×C11#246111yescharacteristic
443C2×C11#311111yescharacteristic
444C2×C11#312711yescharacteristic
445C2×C11#326911yescharacteristic
446C2×C11#326911yescharacteristic
447C2×C11#334911yescharacteristic
448C2×C11#335211yescharacteristic
449D11—81no—
450C24—111no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—221no—
457C2×Q8—221no—
458C2×Q8—221no—
459C2×Q8—221no—
460C2×Q8—221no—
461C2×Q8—221no—
462C2×Q8#434312yes—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—111no—
468C22×C4—111no—
469C22×C4—111no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4D4×D1111yescharacteristic
481C22×C4D4×D1111yescharacteristic
482C22×C4C23×D1111yescharacteristic
483Q16—444no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—112no—
490C2×C8—221no—
491C2×C8—221no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—221no—
495C2×C8C2×C22⋊D1112yes—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—42no—
501C4⋊C4—42no—
502C4⋊C4—42no—
503C4⋊C4—112no—
504C4⋊C4—224no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—442no—
511C4⋊C4—442no—
512C4⋊C4C2×C22⋊D1112yes—
513C4⋊C4C2×C22⋊D1112yes—
514C22⋊C4—224no—
515C22⋊C4—441no—
516C22⋊C4—441no—
517C22⋊C4—442no—
518C22⋊C4—442no—
519C22⋊C4—442no—
520C42—21no—
521C42—21no—
522C42—42no—
523C42—221no—
524C42—221no—
525C42—442no—
526C42—442no—
527C42—442no—
528C11#2680911yescharacteristic, complemented, Sylow
529C23—221no—
530C23—221no—
531C23—221no—
532C23—221no—
533C23—221no—
534C23—221no—
535C23—221no—
536C23C2×D4×D1111yescharacteristic
537Q8—22no—
538Q8—22no—
539Q8—41no—
540Q8—41no—
541Q8—441no—
542Q8—441no—
543Q8—441no—
544Q8—441no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—222no—
569C2×C4—221no—
570C2×C4—221no—
571C2×C4—221no—
572C2×C4—221no—
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×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4#6703711yescharacteristic
589C2×C4C2×#434311yescharacteristic
590C2×C4#6704011yescharacteristic
591C2×C4#41×D1111yescharacteristic
592C2×C4#41×D1111yescharacteristic
593C2×C4C22×C22⋊D1111yescharacteristic
594C8—22no—
595C8—41no—
596C8—222no—
597C8—441no—
598C22—441no—
599C22—441no—
600C22—441no—
601C22—441no—
602C22—441no—
603C22—441no—
604C22—441no—
605C22#1062315811yescharacteristic
606C22#1062316211yescharacteristic
607C22#1062329911yescharacteristic
608C22#1062330211yescharacteristic
609C22#1062330811yescharacteristic
610C22#1062331011yescharacteristic
611C22D4×C22⋊D1111yescharacteristic
612C4—41no—
613C4—42no—
614C4—41no—
615C4—42no—
616C4—42no—
617C4—81no—
618C4—441no—
619C4—441no—
620C4—442no—
621C4—441no—
622C4—881no—
623C4—881no—
624C4—881no—
625C4#1062316811yescharacteristic
626C4#1062317111yescharacteristic
627C4#1062334811yescharacteristic
628C4#1062336311yescharacteristic
629C2—881no—
630C2#1307259011yescharacteristic
631C2#1307873211yescharacteristic
632C2#1307891811yescharacteristic
633C2#1308016511yescharacteristic
634C2#1308017111yescharacteristic
635C2#1308115311yescharacteristic
636C2#1308118811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#479C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenterC2×#479D11
hypocenterC11#26809
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
4. #13070010C2semidirect
5. #13069951C2semidirect
8. #13069484C2semidirect
9. #13069260C2semidirect
10. #13069256C2semidirect
12. #13068957C2semidirect
14. #13068516C2semidirect
15. C2×C11×#479C2semidirect
212. C2×#479D11semidirect
528. C11#26809semidirect

Maximal subgroups

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

subgroupindex
C2×#106224802
#130729602
#130716392
#130700102
#130699512
#130698182
#130696252
#130694842
#130692602
#130692562
#130692282
#130689572
#130688122
#130685162
C2×C11×#4792
#2680911