Finite Group Databasebeta

← #14767597

Subgroups — #14767597

Order 2816.

922 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622768C211yesmaximal, characteristic
2#13071328C211yesmaximal, characteristic, complemented
3#13071326C211yesmaximal, characteristic, complemented
4#13069431C211yesmaximal, characteristic, complemented
5#13069431C211yesmaximal, characteristic, complemented
6#13068974C211yesmaximal, characteristic, complemented
7#13068968C211yesmaximal, characteristic, complemented
8#13068966C211yesmaximal, characteristic
9#13068958C211yesmaximal, characteristic, complemented
10#13068956C211yesmaximal, characteristic, complemented
11#13068950C211yesmaximal, characteristic, complemented
12#13068948C211yesmaximal, characteristic, complemented
13#13068742C211yesmaximal, characteristic, complemented
14#13068366C211yesmaximal, characteristic, complemented
15C11×#1879C211yesmaximal, characteristic
16C22×C11×D8C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×#66989C2211yescharacteristic
19C2×#66989C2211yescharacteristic
20C2×D4×Dic11C2211yescharacteristic
21C22×#4324C2211yescharacteristic
22C22×#4324C2211yescharacteristic
23C22×Dic44C2211yescharacteristic
24C2×#66940C2211yescharacteristic
25C2×C4×Dic22C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C11×#390C2211yescharacteristic
29#10622834C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32#10622823—21no—
33#10622823—21no—
34#10622768C418yescomplemented
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37C2×#66879C2211yescharacteristic
38C2×C8×Dic11C2211yescharacteristic
39#10622589C2211yescharacteristic
40#10622589C2211yescharacteristic
41#10622587C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43C2×#66874C2211yescharacteristic
44#10622559—21no—
45#10622559—21no—
46#10622558—21no—
47#10622558—21no—
48#10622557—21no—
49#10622557—21no—
50#10622545C2211yescharacteristic
51#10622542C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#336C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×Dic11—21no—
64C22×Dic22C2311yescharacteristic
65C22×Dic22C2311yescharacteristic
66C2×C11×D8—41no—
67C2×C11×D8—41no—
68C2×C11×D8C2×C414yes—
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C4×D4×C11—41no—
72C4×D4×C11—41no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C42×C11C2311yescharacteristic
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86#66989—22no—
87#66989—22no—
88#66989C2×C414yescomplemented
89#66989C2×C414yescomplemented
90D4×Dic11—41no—
91D4×Dic11—41no—
92C2×#4324—41no—
93C2×#4324—41no—
94C2×#4324—41no—
95C2×#4324—41no—
96C2×#4324C2×C414yescomplemented
97C2×#4324C2×C414yescomplemented
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—21no—
105C2×Dic11⋊C4—21no—
106C2×C4×Dic11—21no—
107C2×C4×Dic11—21no—
108C2×C4×Dic11C2311yescharacteristic
109C2×C4×Dic11C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C2×Dic44—41no—
113C2×Dic44—41no—
114C2×Dic44C2×C414yescomplemented
115#66940—41no—
116#66940—41no—
117C4×Dic22—41no—
118C4×Dic22—41no—
119C11×#102—41no—
120C11×#102—41no—
121#66896—41no—
122#66896—41no—
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×C414yescomplemented
135#66874—41no—
136#66874—41no—
137#22274—111nomaximal, Sylow
138C24×C11—21no—
139C24×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×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—
149C2×D4×C11—21no—
150C2×D4×C11C22×C412yes—
151C2×D4×C11C22×C412yes—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—42no—
155C22×C4×C11—81no—
156C22×C4×C11—81no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2411yescharacteristic
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—42no—
165C22×Dic11—81no—
166C22×Dic11—81no—
167C22×Dic11C2×D411yescharacteristic
168C22×Dic11C2×D411yescharacteristic
169C22×Dic11C2×D411yescharacteristic
170C22×Dic11C2×D411yescharacteristic
171C2×Dic22—21no—
172C2×Dic22—21no—
173C2×Dic22—21no—
174C2×Dic22—21no—
175C2×Dic22—21no—
176C2×Dic22—21no—
177C2×Dic22—21no—
178C2×Dic22—21no—
179C2×Dic22—21no—
180C2×Dic22—21no—
181C2×Dic22C22×C412yes—
182C2×Dic22C22×C412yes—
183C11×D8—44no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11C22×C412yes—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C22⋊C4—42no—
195C11×C22⋊C4—81no—
196C11×C22⋊C4—81no—
197C42×C11—21no—
198C42×C11—21no—
199C22⋊Dic11—24no—
200C22⋊Dic11—24no—
201C22⋊Dic11—24no—
202C22⋊Dic11—24no—
203C22⋊Dic11—42no—
204C22⋊Dic11—81no—
205C22⋊Dic11—81no—
206#4324—44no—
207#4324—44no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11—21no—
212Dic11⋊C4—42no—
213Dic11⋊C4—42no—
214Dic11⋊C4—81no—
215Dic11⋊C4—81no—
216Dic11⋊C4—81no—
217Dic11⋊C4—81no—
218C4×Dic11—21no—
219C4×Dic11—21no—
220C4×Dic11—42no—
221C4×Dic11—42no—
222C4×Dic11C22×C412yes—
223C4×Dic11#4112yes—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8C22×C412yes—
230Dic44—44no—
231C2×#495—111no—
232#2326—111no—
233#2326—111no—
234#1959—111no—
235#1959—111no—
236#1880—111no—
237#1880—111no—
238#1879—111no—
239#1879D1111yescharacteristic
240#1878—111no—
241#1878—111no—
242#1877—111no—
243#1877—111no—
244#1834—111no—
245#1746—111no—
246C23×C11—22no—
247C23×C11—22no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11—41no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11—41no—
257C23×C11—41no—
258C23×C11—41no—
259C23×C11—41no—
260C23×C11C22×D411yescharacteristic
261D4×C11—22no—
262D4×C11—22no—
263D4×C11—22no—
264D4×C11—22no—
265D4×C11—41no—
266D4×C11—41no—
267D4×C11—41no—
268D4×C11—41no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—84no—
282C2×C4×C11C23×C411yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C11H(5,𝔽2)11yescharacteristic
285C2×C4×C11H(5,𝔽2)11yescharacteristic
286C2×C4×C11H(5,𝔽2)11yescharacteristic
287C2×C4×C11H(5,𝔽2)11yescharacteristic
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—22no—
293C2×Dic11—22no—
294C2×Dic11—21no—
295C2×Dic11—21no—
296C2×Dic11—21no—
297C2×Dic11—21no—
298C2×Dic11—21no—
299C2×Dic11—21no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11—41no—
306C2×Dic11—41no—
307C2×Dic11—41no—
308C2×Dic11—41no—
309C2×Dic11—41no—
310C2×Dic11—84no—
311C2×Dic11C4×D412yes—
312C2×Dic11C4×D412yes—
313Dic22—22no—
314Dic22—22no—
315Dic22—22no—
316Dic22—22no—
317Dic22—41no—
318Dic22—41no—
319Dic22—41no—
320Dic22—41no—
321C8×C11—22no—
322C8×C11—41no—
323C11⋊C8—22no—
324C11⋊C8—41no—
325C22×Q16—111no—
326C22×SD16—111no—
327C22×SD16—111no—
328C22×D8C2×D1111yescharacteristic
329C2×#124—111no—
330C2×#124—111no—
331C2×C4×Q8—111no—
332C2×C4×Q8—111no—
333C2×C4×D4—111no—
334C2×C4×D4C2×D1111yescharacteristic
335#495—118no—
336C2×#103—111no—
337C2×#103—111no—
338C2×#103—111no—
339C2×#103—111no—
340C2×#102—111no—
341C2×#102—111no—
342C2×#102C2×D1111yescharacteristic
343C2×#102C2×D1111yescharacteristic
344C2×#97—111no—
345C2×C4×C8—111no—
346#391—111no—
347#391—111no—
348#390—111no—
349#390C2×D1111yescharacteristic
350#388—221no—
351#388—221no—
352#388—221no—
353#388—221no—
354#385—221no—
355#385—221no—
356#385—221no—
357#385—221no—
358#384—111no—
359#384—111no—
360#376—111no—
361#340—111no—
362#340—111no—
363#340—111no—
364#340C2×D1111yescharacteristic
365#336—111no—
366#336—111no—
367#336—111no—
368#336C2×D1111yescharacteristic
369C22×C11—42no—
370C22×C11—42no—
371C22×C11—42no—
372C22×C11—42no—
373C22×C11—42no—
374C22×C11—42no—
375C22×C11—81no—
376C22×C11—81no—
377C22×C11—81no—
378C22×C11—81no—
379C22×C11—81no—
380C22×C11—81no—
381C22×C11—81no—
382C22×C11—81no—
383C22×C11C2×C4×D411yescharacteristic
384C22×C11#53511yescharacteristic
385C22×C11#53511yescharacteristic
386C22×C11#57611yescharacteristic
387C22×C11#57711yescharacteristic
388C22×C11#57711yescharacteristic
389C22×C11#57811yescharacteristic
390C4×C11—41no—
391C4×C11—41no—
392C4×C11—81no—
393C4×C11—81no—
394C4×C11#51811yescharacteristic
395C4×C11#51811yescharacteristic
396C4×C11#54011yescharacteristic
397C4×C11#54011yescharacteristic
398Dic11—22no—
399Dic11—22no—
400Dic11—42no—
401Dic11—42no—
402Dic11—41no—
403Dic11—41no—
404Dic11—81no—
405Dic11—81no—
406C22×Q8—111no—
407C22×Q8—111no—
408C22×D4C22×D1111yescharacteristic
409C22×D4C22×D1111yescharacteristic
410C23×C4—21no—
411C23×C4—221no—
412C2×Q16—114no—
413C2×Q16—441no—
414C2×Q16—441no—
415C2×SD16—114no—
416C2×SD16—114no—
417C2×SD16—441no—
418C2×SD16—441no—
419C2×SD16—441no—
420C2×SD16—441no—
421C2×D8—41no—
422C2×D8—41no—
423C2×D8C4×D1114yes—
424C22×C8—111no—
425C22×C8—111no—
426C22×C8C22×D1111yescharacteristic
427C22×C8C22×D1111yescharacteristic
428#124—114no—
429#124—114no—
430#124—222no—
431#124—222no—
432C4×Q8—441no—
433C4×Q8—441no—
434C4×Q8—441no—
435C4×Q8—441no—
436C4×D4—41no—
437C4×D4—41no—
438C4×D4—441no—
439C4×D4—441no—
440C2×C4⋊C4—111no—
441C2×C4⋊C4—111no—
442C2×C4⋊C4—221no—
443C2×C4⋊C4—221no—
444C2×C4⋊C4—221no—
445C2×C4⋊C4—221no—
446C2×C4⋊C4—221no—
447C2×C4⋊C4—221no—
448C2×C4⋊C4C22×D1111yescharacteristic
449C2×C4⋊C4C22×D1111yescharacteristic
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—221no—
454C2×C22⋊C4—221no—
455C2×C22⋊C4—221no—
456C2×C22⋊C4—221no—
457C2×C22⋊C4—221no—
458C2×C22⋊C4—221no—
459C2×C22⋊C4—221no—
460C2×C42—111no—
461C2×C42—111no—
462C2×C42—221no—
463C2×C42—221no—
464C2×C42C22×D1111yescharacteristic
465#103—441no—
466#103—441no—
467#103—441no—
468#103—441no—
469#102—41no—
470#102—41no—
471#102—441no—
472#102—441no—
473#97—222no—
474C4×C8—114no—
475#95—111no—
476#95—111no—
477#95—111no—
478#95—111no—
479#95—221no—
480#95—221no—
481#95—221no—
482#95—221no—
483C2×C11—82no—
484C2×C11—82no—
485C2×C11#232811yescharacteristic
486C2×C11#295111yescharacteristic
487C2×C11#295211yescharacteristic
488C2×C11#322411yescharacteristic
489C2×C11#322411yescharacteristic
490C2×C11#322511yescharacteristic
491C2×C11#322511yescharacteristic
492C24—21no—
493C24—21no—
494C2×Q8—112no—
495C2×Q8—112no—
496C2×Q8—221no—
497C2×Q8—221no—
498C2×Q8—221no—
499C2×Q8—221no—
500C2×Q8—221no—
501C2×Q8—221no—
502C2×Q8—221no—
503C2×Q8—221no—
504C2×Q8—221no—
505C2×Q8—221no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4C2×C4×D1112yes—
517C2×D4C2×C4×D1112yes—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—42no—
521C22×C4—81no—
522C22×C4—81no—
523C22×C4—111no—
524C22×C4—111no—
525C22×C4—111no—
526C22×C4—111no—
527C22×C4—221no—
528C22×C4—221no—
529C22×C4—221no—
530C22×C4—221no—
531C22×C4—442no—
532C22×C4—881no—
533C22×C4—881no—
534C22×C4D4×D1111yescharacteristic
535C22×C4D4×D1111yescharacteristic
536C22×C4C23×D1111yescharacteristic
537Q16—444no—
538SD16—444no—
539SD16—444no—
540D8—44no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—112no—
547C2×C8—221no—
548C2×C8—221no—
549C2×C8—221no—
550C2×C8—221no—
551C2×C8—221no—
552C2×C8C2×C4×D1112yes—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—221no—
558C4⋊C4—221no—
559C4⋊C4—221no—
560C4⋊C4—221no—
561C4⋊C4—442no—
562C4⋊C4—442no—
563C4⋊C4—881no—
564C4⋊C4—881no—
565C4⋊C4—881no—
566C4⋊C4—881no—
567C22⋊C4—42no—
568C22⋊C4—81no—
569C22⋊C4—81no—
570C22⋊C4—224no—
571C22⋊C4—224no—
572C22⋊C4—224no—
573C22⋊C4—224no—
574C22⋊C4—442no—
575C22⋊C4—881no—
576C22⋊C4—881no—
577C42—21no—
578C42—21no—
579C42—112no—
580C42—112no—
581C42—221no—
582C42—221no—
583C42—442no—
584C42—442no—
585C11#2227411yescharacteristic, complemented, Sylow
586C23—22no—
587C23—22no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23C2×D4×D1111yescharacteristic
601Q8—222no—
602Q8—222no—
603Q8—222no—
604Q8—222no—
605Q8—441no—
606Q8—441no—
607Q8—441no—
608Q8—441no—
609D4—22no—
610D4—22no—
611D4—22no—
612D4—22no—
613D4—41no—
614D4—41no—
615D4—41no—
616D4—41no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—84no—
630C2×C4—112no—
631C2×C4—112no—
632C2×C4—221no—
633C2×C4—221no—
634C2×C4—221no—
635C2×C4—221no—
636C2×C4—221no—
637C2×C4—221no—
638C2×C4—221no—
639C2×C4—221no—
640C2×C4—222no—
641C2×C4—222no—
642C2×C4—221no—
643C2×C4—221no—
644C2×C4—441no—
645C2×C4—441no—
646C2×C4—441no—
647C2×C4—441no—
648C2×C4—441no—
649C2×C4—441no—
650C2×C4—441no—
651C2×C4—441no—
652C2×C4—441no—
653C2×C4—441no—
654C2×C4—884no—
655C2×C4C22×C4×D1111yescharacteristic
656C2×C4#6703711yescharacteristic
657C2×C4#6703711yescharacteristic
658C2×C4#6703711yescharacteristic
659C2×C4#41×D1111yescharacteristic
660C2×C4#6704211yescharacteristic
661C8—22no—
662C8—41no—
663C8—222no—
664C8—441no—
665C22—42no—
666C22—42no—
667C22—42no—
668C22—42no—
669C22—42no—
670C22—42no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22C4×D4×D1111yescharacteristic
680C22#1062312311yescharacteristic
681C22#1062313811yescharacteristic
682C22#1062328811yescharacteristic
683C22#1062330211yescharacteristic
684C22#1062330611yescharacteristic
685C22#1062330611yescharacteristic
686C4—41no—
687C4—41no—
688C4—81no—
689C4—81no—
690C4—222no—
691C4—222no—
692C4—441no—
693C4—441no—
694C4—442no—
695C4—442no—
696C4—881no—
697C4—881no—
698C4#1062301711yescharacteristic
699C4#1062307611yescharacteristic
700C4#1062314611yescharacteristic
701C4#1062319411yescharacteristic
702C2—82no—
703C2—82no—
704C2#1307133711yescharacteristic
705C2#1307748611yescharacteristic
706C2#1307749811yescharacteristic
707C2#1307970611yescharacteristic
708C2#1307970711yescharacteristic
709C2#1307972111yescharacteristic
710C2#1307972211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1879C2
socleC23×C11C22×D4
prime radicalC22×C11×D8C22
cosocleC22×C4×C11C24
hypercenter#1879D11
hypocenterC11#22274
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
2. #13071328C2semidirect
3. #13071326C2semidirect
4. #13069431C2semidirect
5. #13069431C2semidirect
6. #13068974C2semidirect
7. #13068968C2semidirect
9. #13068958C2semidirect
10. #13068956C2semidirect
11. #13068950C2semidirect
12. #13068948C2semidirect
13. #13068742C2semidirect
14. #13068366C2semidirect
34. #10622768C4semidirect
88. #66989C2×C4semidirect
89. #66989C2×C4semidirect
96. C2×#4324C2×C4semidirect
97. C2×#4324C2×C4semidirect
114. C2×Dic44C2×C4semidirect
134. C8×Dic11C2×C4semidirect
585. C11#22274semidirect

Maximal subgroups

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

subgroupindex
C2×#106227682
#130713282
#130713262
#130694312
#130689742
#130689682
#130689662
#130689582
#130689562
#130689502
#130689482
#130687422
#130683662
C11×#18792
#2227411