Finite Group Databasebeta

← #14823540

Subgroups — #14823540

Order 2816.

842 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622430C211yesmaximal, characteristic
2#13072462C211yesmaximal, characteristic
3#13072388C211yesmaximal, characteristic, complemented
4#13070007C211yesmaximal, characteristic, complemented
5#13069941C211yesmaximal, characteristic, complemented
6#13069930C211yesmaximal, characteristic
7#13069699C211yesmaximal, characteristic
8#13069494C211yesmaximal, characteristic
9#13069308C211yesmaximal, characteristic, complemented
10#13069303C211yesmaximal, characteristic, complemented
11#13069299C211yesmaximal, characteristic
12#13068947C211yesmaximal, characteristic
13#13068868C211yesmaximal, characteristic, complemented
14#13068490C211yesmaximal, characteristic, complemented
15C2×C11×#487C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×#66999—21no—
19C2×Q8×Dic11C2211yescharacteristic
20C22×#4325C2211yescharacteristic
21C22×#4325C2211yescharacteristic
22C2×#66946C2211yescharacteristic
23C11×#487—24no—
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×C4×C8×C11C2211yescharacteristic
29#10622844—21no—
30#10622843C2211yescharacteristic
31#10622843C2211yescharacteristic
32#10622843C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66885C2211yescharacteristic
36C2×#66885C2211yescharacteristic
37C2×#66879C2211yescharacteristic
38C2×#66879C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40#10622607—21no—
41#10622602—21no—
42#10622601C2211yescharacteristic
43#10622599—21no—
44#10622598C2211yescharacteristic
45#10622596—21no—
46#10622591—21no—
47#10622591—21no—
48#10622586C2211yescharacteristic
49C2×#66871C2211yescharacteristic
50C2×#66871C2211yescharacteristic
51#10622552C2211yescharacteristic
52C4×Dic11⋊C4C2211yescharacteristic
53#10622541C2211yescharacteristic
54#10622430—24no—
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11—21no—
62C22×Q8×C11C2311yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×D44C2311yescharacteristic
65C22×C4×D11—21no—
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×C4⋊Q8—22no—
69C11×C4⋊Q8—22no—
70C11×C4⋊Q8—41no—
71C11×C4⋊Q8—41no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C42×C11C2311yescharacteristic
78#66999—44no—
79Q8×Dic11—22no—
80Q8×Dic11—41no—
81C2×#4325—22no—
82C2×#4325—22no—
83C2×#4325—22no—
84C2×#4325—22no—
85C2×#4325—22no—
86C2×#4325—41no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4D411yescharacteristic
100C2×Dic11⋊C4D411yescharacteristic
101C2×C4×Dic11—21no—
102C2×C4×Dic11C2311yescharacteristic
103C2×C4×Dic11C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106#66946—22no—
107#66946—41no—
108C11×#103—22no—
109C11×#103—22no—
110C11×#103—22no—
111C11×#103D414yes—
112C4×C8×C11—22no—
113#66899—22no—
114#66899—22no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95D411yescharacteristic
125C11⋊#95D411yescharacteristic
126#66885—22no—
127#66885—22no—
128#66879—22no—
129#66879—22no—
130Dic11⋊C8—22no—
131#66871—22no—
132#66871—41no—
133#26836—111nomaximal, Sylow
134C23×D11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
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×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—42no—
147C2×Q8×C11—42no—
148C2×Q8×C11—81no—
149C2×Q8×C11C2×D412yes—
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×Dic11C2×D411yescharacteristic
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44—21no—
169C2×D44#4112yes—
170C2×C4×D11—42no—
171C2×C4×D11—42no—
172C2×C4×D11—81no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11C2×D412yes—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—42no—
183C11×C4⋊C4—42no—
184C11×C4⋊C4—42no—
185C11×C4⋊C4C2×D412yes—
186C42×C11—21no—
187C42×C11—21no—
188#4325—28no—
189#4325—44no—
190(C2×D11)⋊C4—42no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—81no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—42no—
202C4⋊Dic11—42no—
203Dic11⋊C4—22no—
204Dic11⋊C4—22no—
205Dic11⋊C4—42no—
206Dic11⋊C4—42no—
207C4×Dic11—21no—
208C4×Dic11—21no—
209C4×Dic11—21no—
210C4×Dic11—21no—
211C4×Dic11—42no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8#4112yes—
217C2×C11⋊C8#4112yes—
218C2×#487D1111yescharacteristic, complemented
219C2×#440—111no—
220#2452—111no—
221#2446—111no—
222#2068—111no—
223#2057—111no—
224#2055—111no—
225#2013—111no—
226#1973—111no—
227#1935—111no—
228#1935—111no—
229#1934—111no—
230#1877—111no—
231#1863—111no—
232#1771—111no—
233C23×C11C22×D411yescharacteristic
234C22×D11—22no—
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—41no—
240C22×D11—41no—
241Q8×C11—22no—
242Q8×C11—22no—
243Q8×C11—41no—
244Q8×C11—41no—
245Q8×C11—41no—
246Q8×C11—41no—
247Q8×C11—41no—
248Q8×C11—41no—
249Q8×C11—84no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
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×C11AGL(1,ℤ/8)12yes—
267C2×C4×C11#13712yes—
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11H(5,𝔽2)11yescharacteristic
273C2×C4×C112−1+411yescharacteristic
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295D44—22no—
296D44—22no—
297D44—41no—
298D44—41no—
299C4×D11—84no—
300C8×C11—22no—
301C8×C11—41no—
302C11⋊C8—22no—
303C11⋊C8—22no—
304C22×SD16—111no—
305C22×SD16—111no—
306C2×C4⋊Q8C2×D1111yescharacteristic
307C2×C4⋊Q8C2×D1111yescharacteristic
308C2×C22⋊Q8—221no—
309C2×C4×Q8—111no—
310C2×C4×D4—111no—
311#487—24no—
312#440—224no—
313C2×#107—111no—
314C2×#107—111no—
315C2×C4⋊C8—111no—
316C2×#103—111no—
317C2×#103—111no—
318C2×#103C2×D1111yescharacteristic
319C2×#103C2×D1111yescharacteristic
320C2×#103C2×D1111yescharacteristic
321C2×#103C2×D1111yescharacteristic
322C2×#102—111no—
323C2×#102—111no—
324C2×#97—111no—
325C2×#97—111no—
326C2×C4×C8C2×D1111yescharacteristic
327#400—221no—
328#398—221no—
329#396—221no—
330#393—221no—
331#391—111no—
332#391—111no—
333#391—111no—
334#390—111no—
335#390—111no—
336#389—111no—
337#389—111no—
338#389—111no—
339#387—221no—
340#387—221no—
341#385—221no—
342C4×C4⋊C4—111no—
343#340—111no—
344#340—111no—
345#340—111no—
346#340—111no—
347#336—111no—
348#336—111no—
349C22×C11#53211yescharacteristic
350C22×C11D4211yescharacteristic
351C22×C11#54811yescharacteristic
352C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
353C22×C11C2×#13711yescharacteristic
354C22×C11#57711yescharacteristic
355C22×C11#57811yescharacteristic
356C2×D11—42no—
357C2×D11—42no—
358C2×D11—42no—
359C2×D11—81no—
360C2×D11—81no—
361C2×D11—81no—
362C2×D11—81no—
363C4×C11—22no—
364C4×C11—22no—
365C4×C11—42no—
366C4×C11—42no—
367C4×C11—81no—
368C4×C11—81no—
369C4×C11#52511yescharacteristic
370C4×C11#54211yescharacteristic
371C4×C11#54711yescharacteristic
372C4×C11#55111yescharacteristic
373Dic11—41no—
374Dic11—41no—
375Dic11—41no—
376Dic11—41no—
377Dic11—81no—
378Dic11—81no—
379Dic11—81no—
380C22×Q8—21no—
381C22×Q8C22×D1111yescharacteristic
382C22×Q8C22×D1111yescharacteristic
383C22×D4—111no—
384C23×C4—221no—
385C2×SD16—222no—
386C2×SD16—222no—
387C2×SD16—222no—
388C2×SD16—222no—
389C2×SD16—222no—
390C2×SD16—441no—
391C22×C8—111no—
392C22×C8—111no—
393C22×C8C22×D1111yescharacteristic
394C22×C8C22×D1111yescharacteristic
395C4⋊Q8—22no—
396C4⋊Q8—22no—
397C4⋊Q8—41no—
398C4⋊Q8—41no—
399C22⋊Q8—444no—
400C4×Q8—222no—
401C4×Q8—441no—
402C4×D4—222no—
403C4×D4—441no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4C22×D1111yescharacteristic
417C2×C4⋊C4C22×D1111yescharacteristic
418C2×C22⋊C4—221no—
419C2×C22⋊C4—221no—
420C2×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C22⋊C4—221no—
423C2×C42—111no—
424C2×C42—111no—
425C2×C42—221no—
426C2×C42C22×D1111yescharacteristic
427#107—222no—
428#107—441no—
429C4⋊C8—222no—
430#103—22no—
431#103—22no—
432#103—22no—
433#103—222no—
434#103—222no—
435#103C22⋊D1114yes—
436#102—222no—
437#102—222no—
438#97—222no—
439#97—222no—
440C4×C8—22no—
441#95—111no—
442#95—111no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447#95—221no—
448#95—221no—
449#95—221no—
450#95—221no—
451#95—221no—
452C2×C11#246111yescharacteristic
453C2×C11#317811yescharacteristic
454C2×C11#318211yescharacteristic
455C2×C11#326511yescharacteristic
456C2×C11#327011yescharacteristic
457C2×C11#336711yescharacteristic
458C2×C11#337211yescharacteristic
459D11—82no—
460C24—221no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—42no—
473C2×Q8—42no—
474C2×Q8—81no—
475C2×Q8C2×C22⋊D1112yes—
476C2×D4—112no—
477C2×D4—221no—
478C2×D4—221no—
479C2×D4—221no—
480C2×D4—221no—
481C2×D4—221no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—111no—
487C22×C4—111no—
488C22×C4—111no—
489C22×C4—111no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—442no—
494C22×C4—442no—
495C22×C4—881no—
496C22×C4D4×D1111yescharacteristic
497C22×C4D4×D1111yescharacteristic
498C22×C4C23×D1111yescharacteristic
499SD16—228no—
500SD16—444no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—112no—
507C2×C8—112no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8C2×C22⋊D1112yes—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—42no—
517C4⋊C4—42no—
518C4⋊C4—42no—
519C4⋊C4—222no—
520C4⋊C4—222no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—442no—
528C4⋊C4—442no—
529C4⋊C4—442no—
530C4⋊C4—442no—
531C4⋊C4C2×C22⋊D1112yes—
532C22⋊C4—442no—
533C22⋊C4—442no—
534C22⋊C4—442no—
535C22⋊C4—442no—
536C22⋊C4—881no—
537C42—21no—
538C42—21no—
539C42—221no—
540C42—221no—
541C42—221no—
542C42—221no—
543C42—442no—
544C11#2683611yescharacteristic, complemented, Sylow
545C23—222no—
546C23—441no—
547C23—441no—
548C23—441no—
549C23—441no—
550C23—441no—
551C23—441no—
552C23C2×D4×D1111yescharacteristic
553Q8—22no—
554Q8—22no—
555Q8—41no—
556Q8—41no—
557Q8—41no—
558Q8—41no—
559Q8—41no—
560Q8—41no—
561Q8—84no—
562D4—222no—
563D4—222no—
564D4—441no—
565D4—441no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—221no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—884no—
604C2×C4#6696712yes—
605C2×C4#6697112yes—
606C2×C4#6703711yescharacteristic
607C2×C4#41×D1111yescharacteristic
608C2×C4#41×D1111yescharacteristic
609C2×C4#41×D1111yescharacteristic
610C2×C4#6704311yescharacteristic
611C2×C4C22×C22⋊D1111yescharacteristic
612C8—22no—
613C8—41no—
614C8—222no—
615C8—222no—
616C22—442no—
617C22—442no—
618C22—442no—
619C22—881no—
620C22—881no—
621C22—881no—
622C22—881no—
623C22#1062319911yescharacteristic
624C22#1062320811yescharacteristic
625C22C2×#6696711yescharacteristic
626C22#1062329311yescharacteristic
627C22C2×#6697111yescharacteristic
628C22#1062329711yescharacteristic
629C22D4×C22⋊D1111yescharacteristic
630C4—22no—
631C4—22no—
632C4—42no—
633C4—42no—
634C4—81no—
635C4—81no—
636C4—441no—
637C4—441no—
638C4—441no—
639C4—441no—
640C4—881no—
641C4—881no—
642C4—881no—
643C4#1062320011yescharacteristic
644C4#1062321011yescharacteristic
645C4#1062335511yescharacteristic
646C4#1062335911yescharacteristic
647C2—882no—
648C2#1307257911yescharacteristic
649C2#1307929111yescharacteristic
650C2#1307933711yescharacteristic
651C2#1308011111yescharacteristic
652C2#1308018611yescharacteristic
653C2#1308133911yescharacteristic
654C2#1308140211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#487C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenterC2×#487D11
hypocenterC11#26836
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
3. #13072388C2semidirect
4. #13070007C2semidirect
5. #13069941C2semidirect
9. #13069308C2semidirect
10. #13069303C2semidirect
13. #13068868C2semidirect
14. #13068490C2semidirect
15. C2×C11×#487C2semidirect
218. C2×#487D11semidirect
544. C11#26836semidirect

Maximal subgroups

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

subgroupindex
C2×#106224302
#130724622
#130723882
#130700072
#130699412
#130699302
#130696992
#130694942
#130693082
#130693032
#130692992
#130689472
#130688682
#130684902
C2×C11×#4872
#2683611