Finite Group Databasebeta

← #14811024

Subgroups — #14811024

Order 2816.

990 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622488C211yesmaximal, characteristic, complemented
2C22×#66874C211yesmaximal, characteristic
3#13072312C211yesmaximal, characteristic
4#13071448C211yesmaximal, characteristic
5#13070151C211yesmaximal, characteristic, complemented
6#13070012C211yesmaximal, characteristic, complemented
7#13070006C211yesmaximal, characteristic, complemented
8#13069756C211yesmaximal, characteristic, complemented
9#13068871C211yesmaximal, characteristic, complemented
10#13068867C211yesmaximal, characteristic, complemented
11#13068793C211yesmaximal, characteristic
12#13068643C211yesmaximal, characteristic
13#13068620C211yesmaximal, characteristic, complemented
14#13068552C211yesmaximal, characteristic
15C11×#1852C211yesmaximal, characteristic
16C23×Dic22C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C2×#66977—21no—
19C23×C11⋊C8C2211yescharacteristic
20C2×#66941C2211yescharacteristic
21C2×#66940C2211yescharacteristic
22C2×#66940C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×#107C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C11×#380C2211yescharacteristic
27#10622825C2211yescharacteristic
28#10622823—21no—
29C4×C22⋊Dic11C2211yescharacteristic
30C2×#66880C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36#10622598C2211yescharacteristic
37#10622597—21no—
38#10622592—21no—
39#10622589C2211yescharacteristic
40#10622587C2211yescharacteristic
41#10622587C2211yescharacteristic
42#10622586C2211yescharacteristic
43C2×#66874—24no—
44C2×#66874C2211yescharacteristic
45C2×#66874C2211yescharacteristic
46C2×#66874C2211yescharacteristic
47C2×#66874C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49C2×#66871C2211yescharacteristic
50#10622555—21no—
51C22⋊C4×Dic11—21no—
52#10622488—24no—
53#10622259—21no—
54#10622259—21no—
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C23×Dic11—21no—
64C22×Dic22—22no—
65C22×Dic22—22no—
66C22×Dic22—21no—
67C22×Dic22—22no—
68C22×Dic22—21no—
69C22×Dic22—41no—
70C22×Dic22—41no—
71C22×Dic22Q814yescomplemented
72C22×Dic22C2311yescharacteristic
73C22×Dic22C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—41no—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C22⋊C4—21no—
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11D411yescharacteristic
86C2×C22⋊Dic11D411yescharacteristic
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90#66977—44no—
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×Dic11C2311yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C22×C11⋊C8—22no—
102C22×C11⋊C8—22no—
103C22×C11⋊C8—41no—
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106#66941—22no—
107#66941—41no—
108#66940—22no—
109#66940—22no—
110#66940—41no—
111#66940—41no—
112C11×#107—22no—
113C11×#107—41no—
114C11×C22⋊C8—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⋊#95D411yescharacteristic
124C11⋊#95D411yescharacteristic
125#66880—22no—
126#66880—22no—
127#66880—41no—
128#66880—41no—
129Dic11⋊C8—22no—
130Dic11⋊C8—41no—
131#66874—22no—
132#66874—22no—
133#66874—22no—
134#66874D414yes—
135#66871—22no—
136#66871—41no—
137#25963—111nomaximal, Sylow
138C24×C11C2×D411yescharacteristic
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—42no—
148C22×C4×C11—42no—
149C22×C4×C11—81no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×Q812yes—
152C22×C4×C11#4112yes—
153C22×C4×C11C2411yescharacteristic
154C22×Dic11—24no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—42no—
160C22×Dic11—42no—
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C2×Dic22—28no—
166C2×Dic22—24no—
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×Dic22—44no—
176C2×Dic22—44no—
177C2×Dic22—44no—
178C2×Dic22—42no—
179C2×Dic22—42no—
180C2×Dic22—42no—
181C2×Dic22—42no—
182C2×Dic22—81no—
183C2×Dic22C2×D412yes—
184C2×Dic22C2×Q812yes—
185C2×Dic22C2×Q812yes—
186C2×Dic22#4112yes—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—42no—
201C11×C4⋊C4C2×D412yes—
202C11×C22⋊C4—42no—
203C22⋊Dic11—22no—
204C22⋊Dic11—42no—
205C22⋊Dic11Q1614yes—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—42no—
211Dic11⋊C4—42no—
212Dic11⋊C4—42no—
213Dic11⋊C4—42no—
214Dic11⋊C4—42no—
215Dic11⋊C4—42no—
216Dic11⋊C4—81no—
217C4×Dic11—21no—
218C4×Dic11—21no—
219C4×Dic11—21no—
220C4×Dic11—21no—
221C4×Dic11—42no—
222C4×Dic11—42no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—44no—
229C2×C11⋊C8C2×D412yes—
230C2×#477—111no—
231C22×#103—111no—
232#2440—111no—
233Q8×C22⋊C4—111no—
234#2095—111no—
235#2068—111no—
236#2068—111no—
237#2024—111no—
238#1863—111no—
239#1863—111no—
240#1852D1111yescharacteristic
241#1850—111no—
242#1808—111no—
243#1803—111no—
244#1787—111no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11C22⋊Q812yes—
250C23×C11C2×Q1612yes—
251C23×C11AGL(1,ℤ/8)12yes—
252C23×C11C22×D411yescharacteristic
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
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—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—84no—
272C2×C4×C11C22⋊Q812yes—
273C2×C4×C11C22×D411yescharacteristic
274C2×C4×C11C22×Q811yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11H(5,𝔽2)11yescharacteristic
278C2×C4×C11H(5,𝔽2)11yescharacteristic
279C2×Dic11—22no—
280C2×Dic11—21no—
281C2×Dic11—22no—
282C2×Dic11—21no—
283C2×Dic11—22no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—22no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—48no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11C2×Q1612yes—
303C2×Dic11C2×Q1612yes—
304Dic22—22no—
305Dic22—22no—
306Dic22—22no—
307Dic22—22no—
308Dic22—22no—
309Dic22—48no—
310Dic22—41no—
311Dic22—41no—
312Dic22—84no—
313Dic22C22⋊Q814yescomplemented
314C8×C11—41no—
315C8×C11—41no—
316C11⋊C8—22no—
317C11⋊C8—41no—
318C23×Q8—111no—
319C23×C8—111no—
320C2×C4⋊Q8—111no—
321C2×C22⋊Q8—221no—
322C2×C4×Q8—111no—
323C2×C4×Q8—111no—
324C22×C4⋊C4C2×D1111yescharacteristic
325#477—224no—
326C2×#107—111no—
327C2×#107—111no—
328C2×#107C2×D1111yescharacteristic
329C2×#107C2×D1111yescharacteristic
330C2×C4⋊C8—111no—
331C2×C4⋊C8—111no—
332C2×#103—111no—
333C2×#103—111no—
334C2×#103—111no—
335C2×#103—111no—
336C2×#103—111no—
337C2×#103—111no—
338C2×#103—111no—
339C2×#103—111no—
340C2×#103—224no—
341C2×C22⋊C8C2×D1111yescharacteristic
342#398—221no—
343#395—221no—
344#391—111no—
345#391—111no—
346#391—221no—
347#391—221no—
348#389—111no—
349#389—111no—
350#385—221no—
351#384—111no—
352#380—111no—
353#380—221no—
354#380C2×D1111yescharacteristic
355C4×C22⋊C4—111no—
356C4×C22⋊C4—221no—
357#340—111no—
358#340—111no—
359#340C2×D1111yescharacteristic
360#340C2×D1111yescharacteristic
361#336—111no—
362#336—111no—
363C22×C11—22no—
364C22×C11—22no—
365C22×C11—22no—
366C22×C11—22no—
367C22×C11—22no—
368C22×C11—22no—
369C22×C11#47714yescomplemented
370C22×C11C2×C22⋊Q811yescharacteristic
371C22×C11D4211yescharacteristic
372C22×C11#54611yescharacteristic
373C22×C11C22×Q1611yescharacteristic
374C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
375C22×C11#57711yescharacteristic
376C22×C11#57811yescharacteristic
377C4×C11—22no—
378C4×C11—42no—
379C4×C11—81no—
380C4×C11—81no—
381C4×C11—81no—
382C4×C11C2×C22⋊Q811yescharacteristic
383C4×C11#54311yescharacteristic
384C4×C11#54611yescharacteristic
385C4×C11#55111yescharacteristic
386Dic11—24no—
387Dic11—22no—
388Dic11—22no—
389Dic11—42no—
390Dic11—41no—
391Dic11—41no—
392Dic11—81no—
393Dic11—81no—
394C22×Q8—114no—
395C22×Q8—111no—
396C22×Q8—111no—
397C22×Q8—221no—
398C22×Q8—222no—
399C22×Q8—222no—
400C22×Q8—222no—
401C22×Q8—221no—
402C22×Q8—441no—
403C22×Q8—441no—
404C23×C4—21no—
405C23×C4—221no—
406C23×C4C22×D1111yescharacteristic
407C22×C8—111no—
408C22×C8—111no—
409C22×C8—222no—
410C22×C8—222no—
411C22×C8—441no—
412C22×C8C22×D1111yescharacteristic
413C22×C8C22×D1111yescharacteristic
414C4⋊Q8—222no—
415C4⋊Q8—441no—
416C22⋊Q8—444no—
417C4×Q8—222no—
418C4×Q8—222no—
419C4×Q8—441no—
420C4×Q8—441no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—41no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4C22×D1111yescharacteristic
434C2×C4⋊C4C22×D1111yescharacteristic
435C2×C4⋊C4C22×D1111yescharacteristic
436C2×C4⋊C4C22×D1111yescharacteristic
437C2×C22⋊C4—21no—
438C2×C22⋊C4—111no—
439C2×C22⋊C4—111no—
440C2×C22⋊C4—221no—
441C2×C42—111no—
442C2×C42—111no—
443C2×C42—221no—
444C2×C42—221no—
445#107—22no—
446#107—41no—
447#107—222no—
448#107—441no—
449C4⋊C8—222no—
450C4⋊C8—441no—
451#103—114no—
452#103—222no—
453#103—222no—
454#103—222no—
455#103—222no—
456#103—222no—
457#103—441no—
458#103—441no—
459C22⋊C8—22no—
460#95—21no—
461#95—111no—
462#95—111no—
463#95—221no—
464#95—221no—
465#95—221no—
466#95—221no—
467#95—221no—
468#95—221no—
469#95—221no—
470C2×C11—24no—
471C2×C11#243711yescharacteristic
472C2×C11C2×#47711yescharacteristic
473C2×C11#308211yescharacteristic
474C2×C11#326511yescharacteristic
475C2×C11D4×Q1611yescharacteristic
476C2×C11#329911yescharacteristic
477C2×C11#330811yescharacteristic
478C24D4×D1111yescharacteristic
479C2×Q8—112no—
480C2×Q8—112no—
481C2×Q8—112no—
482C2×Q8—112no—
483C2×Q8—228no—
484C2×Q8—224no—
485C2×Q8—221no—
486C2×Q8—221no—
487C2×Q8—221no—
488C2×Q8—221no—
489C2×Q8—221no—
490C2×Q8—221no—
491C2×Q8—221no—
492C2×Q8—221no—
493C2×Q8—442no—
494C2×Q8—442no—
495C2×Q8—442no—
496C2×Q8—444no—
497C2×Q8—444no—
498C2×Q8—444no—
499C2×Q8—442no—
500C2×Q8—881no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—81no—
512C22×C4—111no—
513C22×C4—111no—
514C22×C4—111no—
515C22×C4—111no—
516C22×C4—221no—
517C22×C4—224no—
518C22×C4—221no—
519C22×C4—221no—
520C22×C4—221no—
521C22×C4—442no—
522C22×C4—442no—
523C22×C4#433912yes—
524C22×C4D4×D1111yescharacteristic
525C22×C4Q8×D1112yes—
526C22×C4C23×D1111yescharacteristic
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—112no—
534C2×C8—221no—
535C2×C8—221no—
536C2×C8—221no—
537C2×C8—221no—
538C2×C8—221no—
539C2×C8—444no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—42no—
548C4⋊C4—221no—
549C4⋊C4—221no—
550C4⋊C4—221no—
551C4⋊C4—221no—
552C4⋊C4—442no—
553C4⋊C4—442no—
554C4⋊C4—442no—
555C4⋊C4—442no—
556C4⋊C4—442no—
557C4⋊C4—442no—
558C4⋊C4—881no—
559C4⋊C4D4×D1112yes—
560C22⋊C4—42no—
561C22⋊C4—114no—
562C22⋊C4—222no—
563C22⋊C4—442no—
564C42—221no—
565C42—221no—
566C42—221no—
567C42—221no—
568C42—442no—
569C42—442no—
570C11#2596311yescharacteristic, complemented, Sylow
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23#6694912yes—
576C23#6696412yes—
577C23Q16×D1112yes—
578C23C2×D4×D1111yescharacteristic
579Q8—114no—
580Q8—222no—
581Q8—222no—
582Q8—222no—
583Q8—222no—
584Q8—222no—
585Q8—448no—
586Q8—441no—
587Q8—441no—
588Q8—884no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—84no—
608C2×C4—112no—
609C2×C4—112no—
610C2×C4—222no—
611C2×C4—221no—
612C2×C4—221no—
613C2×C4—221no—
614C2×C4—222no—
615C2×C4—221no—
616C2×C4—222no—
617C2×C4—221no—
618C2×C4—221no—
619C2×C4—222no—
620C2×C4—221no—
621C2×C4—221no—
622C2×C4—221no—
623C2×C4—221no—
624C2×C4—448no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4#6694912yes—
634C2×C4C2×#433911yescharacteristic
635C2×C4C2×D4×D1111yescharacteristic
636C2×C4#6703711yescharacteristic
637C2×C4C2×Q8×D1111yescharacteristic
638C2×C4#41×D1111yescharacteristic
639C2×C4#6704211yescharacteristic
640C8—41no—
641C8—41no—
642C8—222no—
643C8—441no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—22no—
648C22—22no—
649C22—22no—
650C22#1062248814yescomplemented
651C22C2×#6694911yescharacteristic
652C22#1062312111yescharacteristic
653C22#1062318511yescharacteristic
654C22C2×#6696411yescharacteristic
655C22C2×Q16×D1111yescharacteristic
656C22#1062330611yescharacteristic
657C22#1062331011yescharacteristic
658C4—22no—
659C4—42no—
660C4—81no—
661C4—81no—
662C4—81no—
663C4—222no—
664C4—224no—
665C4—222no—
666C4—441no—
667C4—441no—
668C4—442no—
669C4—881no—
670C4—881no—
671C4#1062308111yescharacteristic
672C4#1062308711yescharacteristic
673C4D11×C22⋊Q811yescharacteristic
674C4#1062316511yescharacteristic
675C2—24no—
676C2#1307228111yescharacteristic
677C2C2×#1062248811yescharacteristic
678C2#1307845611yescharacteristic
679C2#1308011511yescharacteristic
680C2#1308036111yescharacteristic
681C2#1308049011yescharacteristic
682C2#1308060511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1852C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1852D11
hypocenterC11#25963
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1852

Complements

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

NH ≅ G/Ntype
1. C2×#10622488C2semidirect
5. #13070151C2semidirect
6. #13070012C2semidirect
7. #13070006C2semidirect
8. #13069756C2semidirect
9. #13068871C2semidirect
10. #13068867C2semidirect
13. #13068620C2semidirect
71. C22×Dic22Q8semidirect
313. Dic22C22⋊Q8semidirect
369. C22×C11#477semidirect
570. C11#25963semidirect
650. C22#10622488semidirect

Maximal subgroups

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

subgroupindex
C2×#106224882
C22×#668742
#130723122
#130714482
#130701512
#130700122
#130700062
#130697562
#130688712
#130688672
#130687932
#130686432
#130686202
#130685522
C11×#18522
#2596311