Finite Group Databasebeta

← #14803339

Subgroups — #14803339

Order 2816.

800 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622667C211yesmaximal, characteristic
2C2×Q8×C11⋊C8C211yesmaximal, characteristic, complemented
3#13073982C211yesmaximal, characteristic, complemented
4#13070004C211yesmaximal, characteristic
5#13069997C211yesmaximal, characteristic, complemented
6#13069938C211yesmaximal, characteristic, complemented
7#13069933C211yesmaximal, characteristic
8#13069476C211yesmaximal, characteristic, complemented
9#13069469C211yesmaximal, characteristic
10#13069428C211yesmaximal, characteristic
11#13069384C211yesmaximal, characteristic, complemented
12#13069302C211yesmaximal, characteristic
13#13069295C211yesmaximal, characteristic, complemented
14C4×#66874C211yesmaximal, characteristic, complemented
15C11×#2592C211yesmaximal, characteristic
16C2×C11×#124C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C22×#4326C2211yescharacteristic
19C22×#4324C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C11×#397—21no—
22C11×#393—21no—
23C11×#391C2211yescharacteristic
24C11×#391C2211yescharacteristic
25C11×#390C2211yescharacteristic
26C11×#390C2211yescharacteristic
27C11×#388—21no—
28C11×#388—21no—
29C4×C11×C4⋊C4C2211yescharacteristic
30#10622842—21no—
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37#10622667—24no—
38Q8×C11⋊C8—24no—
39#10622595—21no—
40#10622591—21no—
41#10622591—21no—
42C2×#66874C2211yescharacteristic
43C2×#66874C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622549C2211yescharacteristic
47#10622542C2211yescharacteristic
48#10622542C2211yescharacteristic
49#10622541C2211yescharacteristic
50#10622541C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×C4×C11⋊C8C2211yescharacteristic
55C2×C4×C11⋊C8C2211yescharacteristic
56C2×C4×C11⋊C8C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11D411yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D4×C11C2311yescharacteristic
64C22×Dic22C2311yescharacteristic
65C11×#124—22no—
66C11×#124—22no—
67C4×Q8×C11—22no—
68C4×Q8×C11—22no—
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×#4326—22no—
85C2×#4326—22no—
86C2×#4326—41no—
87C2×#4324—22no—
88C2×#4324—22no—
89C2×#4324—41no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C4×Dic22—22no—
102C4×Dic22—22no—
103C11×#95—21no—
104C11×#95—21no—
105C11×#95—21no—
106C11×#95—21no—
107C11×#95—21no—
108#66899—22no—
109#66899—22no—
110#66899—41no—
111#66896—22no—
112#66896—22no—
113#66896—41no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122#66874—22no—
123#66874—22no—
124#66872—41no—
125#66871—41no—
126C4⋊(C11⋊C8)—22no—
127C4⋊(C11⋊C8)—22no—
128C4⋊(C11⋊C8)D414yes—
129C4×C11⋊C8—22no—
130C4×C11⋊C8—22no—
131C4×C11⋊C8—22no—
132#25297—111nomaximal, Sylow
133C24×C11—21no—
134C2×Q8×C11—22no—
135C2×Q8×C11—22no—
136C2×Q8×C11—22no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2411yescharacteristic
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22#4112yes—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C22⋊C4—42no—
177C11×C22⋊C4—42no—
178C11×C22⋊C4—42no—
179C11×C22⋊C4—42no—
180C11×C22⋊C4—81no—
181C11×C22⋊C4—81no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—81no—
187C42×C11C2×D412yes—
188C42×C11#4112yes—
189#4326—44no—
190#4324—44no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197Dic11⋊C4—42no—
198Dic11⋊C4—42no—
199Dic11⋊C4—42no—
200C4×Dic11—42no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8C2×D412yes—
211C2×C11⋊C8C2×D412yes—
212C2×C11⋊C8#4112yes—
213C2×#464—111no—
214C2×C8×Q8—111no—
215#2592D1111yescharacteristic
216#2581—111no—
217#2067—111no—
218#2066—111no—
219#2056—111no—
220#2055—111no—
221#1969—111no—
222#1968—111no—
223#1958—111no—
224#1949—111no—
225#1934—111no—
226#1933—111no—
227C4×#103—111no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11C22×D411yescharacteristic
236Q8×C11—28no—
237Q8×C11—41no—
238Q8×C11—41no—
239Q8×C11—41no—
240Q8×C11—41no—
241D4×C11—41no—
242D4×C11—41no—
243D4×C11—41no—
244D4×C11—41no—
245C2×C4×C11—21no—
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—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11#12112yes—
269C2×C4×C11#12112yes—
270C2×C4×C11#13512yes—
271C2×C4×C11#13512yes—
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11H(5,𝔽2)11yescharacteristic
277C2×C4×C112−1+411yescharacteristic
278C2×Dic11—22no—
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—
288C2×Dic11—41no—
289C2×Dic11—41no—
290Dic22—22no—
291Dic22—22no—
292Dic22—41no—
293Dic22—41no—
294C11⋊C8—22no—
295C11⋊C8—22no—
296C11⋊C8—22no—
297C11⋊C8—41no—
298C22×Q16—111no—
299C22×SD16—111no—
300C2×#124C2×D1111yescharacteristic
301C2×C4×Q8—111no—
302C2×C4×Q8C2×D1111yescharacteristic
303#464—224no—
304C8×Q8—224no—
305C2×#107—111no—
306C2×#106—111no—
307C2×C4⋊C8—111no—
308C2×C4⋊C8—111no—
309C2×C4⋊C8—111no—
310C2×#103—111no—
311C2×#103—111no—
312C2×#103—111no—
313C2×#103—111no—
314C2×#103—111no—
315C2×#102—111no—
316C2×#102—111no—
317C2×#102—111no—
318C2×C4×C8—111no—
319C2×C4×C8—111no—
320C2×C4×C8—111no—
321#400—221no—
322#397—21no—
323#395—221no—
324#393—21no—
325#391—111no—
326#391—111no—
327#391C2×D1111yescharacteristic
328#391C2×D1111yescharacteristic
329#390C2×D1111yescharacteristic
330#390C2×D1111yescharacteristic
331#389—111no—
332#389—111no—
333#388—21no—
334#388—21no—
335#387—221no—
336#387—221no—
337#382—111no—
338C4×C4⋊C4C2×D1111yescharacteristic
339#340—111no—
340#340—111no—
341#340—111no—
342#340—111no—
343C22×C11—81no—
344C22×C11—81no—
345C22×C11—81no—
346C22×C11—81no—
347C22×C11—81no—
348C22×C11—81no—
349C22×C11—81no—
350C22×C11C2×#12111yescharacteristic
351C22×C11#54811yescharacteristic
352C22×C11#55011yescharacteristic
353C22×C11C2×#13511yescharacteristic
354C22×C11C2×#13511yescharacteristic
355C22×C11#57711yescharacteristic
356C22×C11#57811yescharacteristic
357C4×C11—22no—
358C4×C11—22no—
359C4×C11—22no—
360C4×C11—22no—
361C4×C11—41no—
362C4×C11—41no—
363C4×C11—81no—
364C4×C11—81no—
365C4×C11—81no—
366C4×C11#52911yescharacteristic
367C4×C11#54211yescharacteristic
368C4×C11#54611yescharacteristic
369C4×C11#54811yescharacteristic
370Dic11—42no—
371Dic11—81no—
372Dic11—81no—
373Dic11—81no—
374C22×Q8—111no—
375C22×Q8C22⋊D1111yescharacteristic
376C22×Q8C22×D1111yescharacteristic
377C22×D4C22×D1111yescharacteristic
378C2×Q16—222no—
379C2×Q16—222no—
380C2×Q16—441no—
381C2×SD16—222no—
382C2×SD16—222no—
383C2×SD16—441no—
384C22×C8—111no—
385C22×C8—111no—
386C22×C8—111no—
387C22×C8—111no—
388#124—22no—
389#124—22no—
390C4×Q8—22no—
391C4×Q8—22no—
392C4×Q8—222no—
393C4×Q8—222no—
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×C4⋊C4C22×D1111yescharacteristic
404C2×C4⋊C4C22×D1111yescharacteristic
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C42—21no—
412C2×C42—221no—
413C2×C42C22×D1111yescharacteristic
414C2×C42C22×D1111yescharacteristic
415C2×C42C22×D1111yescharacteristic
416#107—441no—
417#106—441no—
418C4⋊C8—114no—
419C4⋊C8—222no—
420C4⋊C8—222no—
421#103—222no—
422#103—222no—
423#103—222no—
424#103—222no—
425#103—441no—
426#102—222no—
427#102—222no—
428#102—441no—
429C4×C8—222no—
430C4×C8—222no—
431C4×C8—222no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—221no—
438#95—221no—
439#95—221no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445C2×C11—161no—
446C2×C11#242611yescharacteristic
447C2×C11#305011yescharacteristic
448C2×C11#306311yescharacteristic
449C2×C11#336411yescharacteristic
450C2×C11#336511yescharacteristic
451C2×C11#339311yescharacteristic
452C2×C11#339411yescharacteristic
453C24—21no—
454C2×Q8—22no—
455C2×Q8—22no—
456C2×Q8—22no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—112no—
464C2×Q8—221no—
465C2×Q8—221no—
466C2×Q8—221no—
467C2×Q8—221no—
468C2×Q8—221no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4C2×C22⋊D1111yescharacteristic
483C22×C4C2×C22⋊D1111yescharacteristic
484C22×C4C2×C22⋊D1111yescharacteristic
485C22×C4C2×C22⋊D1111yescharacteristic
486C22×C4C2×C22⋊D1111yescharacteristic
487C22×C4C2×C22⋊D1111yescharacteristic
488C22×C4C23×D1111yescharacteristic
489Q16—444no—
490SD16—444no—
491C2×C8—112no—
492C2×C8—112no—
493C2×C8—112no—
494C2×C8—221no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—442no—
517C4⋊C4—442no—
518C4⋊C4—442no—
519C22⋊C4—42no—
520C22⋊C4—42no—
521C22⋊C4—42no—
522C22⋊C4—42no—
523C22⋊C4—81no—
524C22⋊C4—81no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—81no—
530C42—442no—
531C42D4×D1112yes—
532C42#434112yes—
533C11#2529711yescharacteristic, complemented, Sylow
534C23—41no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23C22×C22⋊D1111yescharacteristic
542Q8—28no—
543Q8—41no—
544Q8—41no—
545Q8—41no—
546Q8—41no—
547Q8—222no—
548Q8—222no—
549Q8—441no—
550Q8—441no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—41no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—222no—
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—441no—
589C2×C4—441no—
590C2×C4#6699212yes—
591C2×C4#6699212yes—
592C2×C4#6700312yes—
593C2×C4#6700312yes—
594C2×C4C2×D4×D1111yescharacteristic
595C2×C4C2×#434111yescharacteristic
596C2×C4#41×D1111yescharacteristic
597C2×C4#41×D1111yescharacteristic
598C2×C4#6704211yescharacteristic
599C2×C4#6704311yescharacteristic
600C8—222no—
601C8—222no—
602C8—222no—
603C8—441no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22C2×#6699211yescharacteristic
612C22C2×#6700311yescharacteristic
613C22C2×#6700311yescharacteristic
614C22#1062336211yescharacteristic
615C22#1062336511yescharacteristic
616C22#1062336711yescharacteristic
617C22#1062336911yescharacteristic
618C4—22no—
619C4—22no—
620C4—22no—
621C4—22no—
622C4—41no—
623C4—41no—
624C4—81no—
625C4—81no—
626C4—81no—
627C4—442no—
628C4—881no—
629C4—881no—
630C4—881no—
631C4#1062320711yescharacteristic
632C4#1062320811yescharacteristic
633C4#1062321111yescharacteristic
634C4#1062321311yescharacteristic
635C2—161no—
636C2#1307218511yescharacteristic
637C2#1307819411yescharacteristic
638C2#1307830911yescharacteristic
639C2#1308129711yescharacteristic
640C2#1308130811yescharacteristic
641C2#1308160011yescharacteristic
642C2#1308160811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2592C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2592D11
hypocenterC11#25297
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2592

Complements

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

NH ≅ G/Ntype
2. C2×Q8×C11⋊C8C2semidirect
3. #13073982C2semidirect
5. #13069997C2semidirect
6. #13069938C2semidirect
8. #13069476C2semidirect
11. #13069384C2semidirect
13. #13069295C2semidirect
14. C4×#66874C2semidirect
533. C11#25297semidirect

Maximal subgroups

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

subgroupindex
C2×#106226672
C2×Q8×C11⋊C82
#130739822
#130700042
#130699972
#130699382
#130699332
#130694762
#130694692
#130694282
#130693842
#130693022
#130692952
C4×#668742
C11×#25922
#2529711