Finite Group Databasebeta

← #14767619

Subgroups — #14767619

Order 2816.

826 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622794C211yesmaximal, characteristic
2#13071334C211yesmaximal, characteristic
3#13071332C211yesmaximal, characteristic
4#13069434C211yesmaximal, characteristic
5#13069434C211yesmaximal, characteristic
6#13068960C211yesmaximal, characteristic
7#13068959C211yesmaximal, characteristic
8#13068958C211yesmaximal, characteristic
9#13068957C211yesmaximal, characteristic
10#13068956C211yesmaximal, characteristic
11#13068955C211yesmaximal, characteristic
12#13068954C211yesmaximal, characteristic
13#13068745C211yesmaximal, characteristic
14#13068366C211yesmaximal, characteristic
15C11×#1878C211yesmaximal, characteristic
16C22×C11×Q16C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C2×#66997C2211yescharacteristic
20C2×#66997C2211yescharacteristic
21C22×#4326C2211yescharacteristic
22C22×#4326C2211yescharacteristic
23C22×Dic44C2211yescharacteristic
24C2×#66940C2211yescharacteristic
25C2×C4×Dic22C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C11×#391C2211yescharacteristic
29#10622843C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32#10622794C418yescomplemented
33C2×#66880C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66879C2211yescharacteristic
36C2×C8×Dic11C2211yescharacteristic
37#10622591—21no—
38#10622591—21no—
39#10622590C2211yescharacteristic
40#10622590C2211yescharacteristic
41#10622587C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43C2×#66874C2211yescharacteristic
44#10622546—21no—
45#10622546—21no—
46#10622545C2211yescharacteristic
47#10622542C2211yescharacteristic
48#10622268—21no—
49#10622268—21no—
50#10622265—21no—
51#10622265—21no—
52C11×#340C2211yescharacteristic
53C11×#336C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×Dic22C2311yescharacteristic
63C22×Dic22C2311yescharacteristic
64C2×C11×Q16—41no—
65C2×C11×Q16—41no—
66C2×C11×Q16C2×C414yes—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C4×Q8×C11—41no—
70C4×Q8×C11—41no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C42×C11—21no—
75C2×C42×C11C2311yescharacteristic
76Q8×Dic11—41no—
77Q8×Dic11—41no—
78#66997—22no—
79#66997—22no—
80#66997C2×C414yes—
81#66997C2×C414yes—
82C2×#4326—41no—
83C2×#4326—41no—
84C2×#4326—41no—
85C2×#4326—41no—
86C2×#4326C2×C414yes—
87C2×#4326C2×C414yes—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11C2311yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C2×Dic44—41no—
105C2×Dic44—41no—
106C2×Dic44C2×C414yes—
107#66940—41no—
108#66940—41no—
109C4×Dic22—41no—
110C4×Dic22—41no—
111C11×#103—41no—
112C11×#103—41no—
113C11×#95—21no—
114C11×#95—21no—
115#66899—41no—
116#66899—41no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95D411yescharacteristic
128C11⋊#95D411yescharacteristic
129C11⋊#95D411yescharacteristic
130C11⋊#95D411yescharacteristic
131#66880—41no—
132#66880—41no—
133#66879—22no—
134C8×Dic11C2×C414yes—
135#66874—41no—
136#66874—41no—
137#22277—111nomaximal, Sylow
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11C22×C412yes—
149C2×Q8×C11C22×C412yes—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2411yescharacteristic
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22—21no—
173C2×Dic22—21no—
174C2×Dic22—21no—
175C2×Dic22C22×C412yes—
176C2×Dic22C22×C412yes—
177C11×Q16—44no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11C22×C412yes—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—42no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—42no—
192#4326—44no—
193#4326—44no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—42no—
199Dic11⋊C4—24no—
200Dic11⋊C4—24no—
201Dic11⋊C4—24no—
202Dic11⋊C4—24no—
203Dic11⋊C4—42no—
204Dic11⋊C4—42no—
205C4×Dic11—21no—
206C4×Dic11—21no—
207C4×Dic11—42no—
208C4×Dic11—42no—
209C4×Dic11—42no—
210C4×Dic11C22×C412yes—
211C4×Dic11#4112yes—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8C22×C412yes—
218Dic44—44no—
219C2×#494—111no—
220#2327—111no—
221#2327—111no—
222#1960—111no—
223#1960—111no—
224#1878—111no—
225#1878—111no—
226#1878—111no—
227#1878—111no—
228#1878—111no—
229#1878—111no—
230#1878—111no—
231#1878D1111yescharacteristic
232#1835—111no—
233#1746—111no—
234C23×C11C22×D411yescharacteristic
235Q8×C11—22no—
236Q8×C11—22no—
237Q8×C11—22no—
238Q8×C11—22no—
239Q8×C11—41no—
240Q8×C11—41no—
241Q8×C11—41no—
242Q8×C11—41no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
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—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11C23×C411yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11H(5,𝔽2)11yescharacteristic
264C2×C4×C11H(5,𝔽2)11yescharacteristic
265C2×C4×C11H(5,𝔽2)11yescharacteristic
266C2×C4×C11H(5,𝔽2)11yescharacteristic
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
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×Dic11C4×D412yes—
290C2×Dic11C4×D412yes—
291Dic22—22no—
292Dic22—22no—
293Dic22—22no—
294Dic22—22no—
295Dic22—41no—
296Dic22—41no—
297Dic22—41no—
298Dic22—41no—
299C8×C11—22no—
300C8×C11—41no—
301C11⋊C8—22no—
302C11⋊C8—41no—
303C22×Q16—111no—
304C22×Q16—111no—
305C22×Q16—111no—
306C22×Q16C2×D1111yescharacteristic
307C2×C4⋊Q8—111no—
308C2×C4⋊Q8—111no—
309C2×C4×Q8—111no—
310C2×C4×Q8—111no—
311C2×C4×Q8—111no—
312C2×C4×Q8C2×D1111yescharacteristic
313#494—118no—
314C2×#103—111no—
315C2×#103—111no—
316C2×#103—111no—
317C2×#103—111no—
318C2×#103—111no—
319C2×#103—111no—
320C2×#103C2×D1111yescharacteristic
321C2×#103C2×D1111yescharacteristic
322C2×#97—111no—
323C2×C4×C8—111no—
324#391—111no—
325#391—111no—
326#391—111no—
327#391C2×D1111yescharacteristic
328#387—221no—
329#387—221no—
330#387—221no—
331#387—221no—
332#387—221no—
333#387—221no—
334#387—221no—
335#387—221no—
336#382—111no—
337#382—111no—
338#376—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#340C2×D1111yescharacteristic
343#336—111no—
344#336—111no—
345#336—111no—
346#336C2×D1111yescharacteristic
347C22×C11C2×C4×D411yescharacteristic
348C22×C11#53511yescharacteristic
349C22×C11#53511yescharacteristic
350C22×C11#57811yescharacteristic
351C22×C11#57811yescharacteristic
352C22×C11#57811yescharacteristic
353C22×C11#57811yescharacteristic
354C4×C11—42no—
355C4×C11—42no—
356C4×C11—41no—
357C4×C11—41no—
358C4×C11—81no—
359C4×C11—81no—
360C4×C11#51811yescharacteristic
361C4×C11#51811yescharacteristic
362C4×C11#54011yescharacteristic
363C4×C11#54011yescharacteristic
364Dic11—22no—
365Dic11—22no—
366Dic11—42no—
367Dic11—42no—
368Dic11—41no—
369Dic11—41no—
370Dic11—81no—
371Dic11—81no—
372C22×Q8—111no—
373C22×Q8—111no—
374C22×Q8C22×D1111yescharacteristic
375C22×Q8C22×D1111yescharacteristic
376C2×Q16—41no—
377C2×Q16—41no—
378C2×Q16—114no—
379C2×Q16—114no—
380C2×Q16—114no—
381C2×Q16—441no—
382C2×Q16—441no—
383C2×Q16—441no—
384C2×Q16—441no—
385C2×Q16—441no—
386C2×Q16—441no—
387C2×Q16C4×D1114yes—
388C22×C8—111no—
389C22×C8—111no—
390C22×C8C22×D1111yescharacteristic
391C22×C8C22×D1111yescharacteristic
392C4⋊Q8—114no—
393C4⋊Q8—114no—
394C4⋊Q8—222no—
395C4⋊Q8—222no—
396C4×Q8—41no—
397C4×Q8—41no—
398C4×Q8—441no—
399C4×Q8—441no—
400C4×Q8—441no—
401C4×Q8—441no—
402C4×Q8—441no—
403C4×Q8—441no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4C22×D1111yescharacteristic
415C2×C4⋊C4C22×D1111yescharacteristic
416C2×C42—21no—
417C2×C42—111no—
418C2×C42—111no—
419C2×C42—221no—
420C2×C42—221no—
421C2×C42—221no—
422C2×C42C22×D1111yescharacteristic
423#103—41no—
424#103—41no—
425#103—441no—
426#103—441no—
427#103—441no—
428#103—441no—
429#103—441no—
430#103—441no—
431#97—222no—
432C4×C8—114no—
433#95—21no—
434#95—21no—
435#95—111no—
436#95—111no—
437#95—111no—
438#95—111no—
439#95—221no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447#95—221no—
448#95—221no—
449C2×C11#232811yescharacteristic
450C2×C11#295011yescharacteristic
451C2×C11#295011yescharacteristic
452C2×C11#322311yescharacteristic
453C2×C11#322311yescharacteristic
454C2×C11#322311yescharacteristic
455C2×C11#322311yescharacteristic
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—112no—
467C2×Q8—112no—
468C2×Q8—221no—
469C2×Q8—221no—
470C2×Q8—221no—
471C2×Q8—221no—
472C2×Q8—221no—
473C2×Q8—221no—
474C2×Q8—221no—
475C2×Q8—221no—
476C2×Q8—221no—
477C2×Q8—221no—
478C2×Q8C2×C4×D1112yes—
479C2×Q8C2×C4×D1112yes—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—111no—
485C22×C4—111no—
486C22×C4—111no—
487C22×C4—111no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4D4×D1111yescharacteristic
493C22×C4D4×D1111yescharacteristic
494C22×C4C23×D1111yescharacteristic
495Q16—44no—
496Q16—444no—
497Q16—444no—
498Q16—444no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—112no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8C2×C4×D1112yes—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—42no—
516C4⋊C4—224no—
517C4⋊C4—224no—
518C4⋊C4—224no—
519C4⋊C4—224no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—221no—
524C4⋊C4—442no—
525C4⋊C4—442no—
526C4⋊C4—442no—
527C42—21no—
528C42—21no—
529C42—42no—
530C42—112no—
531C42—112no—
532C42—221no—
533C42—221no—
534C42—442no—
535C42—442no—
536C42—442no—
537C11#2227711yescharacteristic, complemented, Sylow
538C23C2×D4×D1111yescharacteristic
539Q8—22no—
540Q8—22no—
541Q8—22no—
542Q8—22no—
543Q8—41no—
544Q8—41no—
545Q8—41no—
546Q8—41no—
547Q8—222no—
548Q8—222no—
549Q8—222no—
550Q8—222no—
551Q8—441no—
552Q8—441no—
553Q8—441no—
554Q8—441no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—112no—
574C2×C4—112no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—221no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—222no—
584C2×C4—222no—
585C2×C4—221no—
586C2×C4—221no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4C22×C4×D1111yescharacteristic
598C2×C4#6703711yescharacteristic
599C2×C4#6703711yescharacteristic
600C2×C4#6703711yescharacteristic
601C2×C4#41×D1111yescharacteristic
602C2×C4#6704211yescharacteristic
603C8—22no—
604C8—41no—
605C8—222no—
606C8—441no—
607C22C4×D4×D1111yescharacteristic
608C22#1062312311yescharacteristic
609C22#1062313811yescharacteristic
610C22#1062329711yescharacteristic
611C22#1062330211yescharacteristic
612C22#1062331011yescharacteristic
613C22#1062331011yescharacteristic
614C4—41no—
615C4—41no—
616C4—42no—
617C4—42no—
618C4—81no—
619C4—81no—
620C4—222no—
621C4—222no—
622C4—441no—
623C4—441no—
624C4—442no—
625C4—442no—
626C4—881no—
627C4—881no—
628C4#1062301711yescharacteristic
629C4#1062307611yescharacteristic
630C4#1062314611yescharacteristic
631C4#1062319411yescharacteristic
632C2#1307133711yescharacteristic
633C2#1307747911yescharacteristic
634C2#1307748111yescharacteristic
635C2#1307969511yescharacteristic
636C2#1307969611yescharacteristic
637C2#1307969711yescharacteristic
638C2#1307969811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1878C2
socle, prime radicalC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenter#1878D11
hypocenterC11#22277
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1878

Complements

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

NH ≅ G/Ntype
32. #10622794C4semidirect
537. C11#22277semidirect

Maximal subgroups

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

subgroupindex
C2×#106227942
#130713342
#130713322
#130694342
#130689602
#130689592
#130689582
#130689572
#130689562
#130689552
#130689542
#130687452
#130683662
C11×#18782
#2227711