Finite Group Databasebeta

← #14816933

Subgroups — #14816933

Order 2816.

932 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622504C211yesmaximal, characteristic, complemented
2C2×C4×#4323C211yesmaximal, characteristic
3#13072482C211yesmaximal, characteristic, complemented
4#13071517C211yesmaximal, characteristic, complemented
5#13070147C211yesmaximal, characteristic, complemented
6#13070090C211yesmaximal, characteristic, complemented
7#13069986C211yesmaximal, characteristic, complemented
8#13069953C211yesmaximal, characteristic, complemented
9#13069341C211yesmaximal, characteristic, complemented
10#13069171C211yesmaximal, characteristic, complemented
11#13068961C211yesmaximal, characteristic
12#13068961C211yesmaximal, characteristic
13#13068880C211yesmaximal, characteristic, complemented
14#13068878C211yesmaximal, characteristic, complemented
15C11×#1862C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C22×#4323C2211yescharacteristic
18C2×#66946C2211yescharacteristic
19C2×#66946C2211yescharacteristic
20C2×C4⋊C4×D11—21no—
21C2×#66943C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C11×#389C2211yescharacteristic
27#10622834C2211yescharacteristic
28#10622834C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30#10622825—21no—
31#10622823—21no—
32C2×#66885C2211yescharacteristic
33C2×#66885C2211yescharacteristic
34C2×#66881C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36C4×#4323—24no—
37#10622602—21no—
38#10622598C2211yescharacteristic
39#10622598C2211yescharacteristic
40#10622589C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622562—21no—
46#10622561—21no—
47C4×Dic11⋊C4C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4×C11⋊C8C2211yescharacteristic
50#10622504—24no—
51#10622281—21no—
52#10622280—21no—
53C11×#340C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×C4×D11—21no—
66C22×C4×D11—21no—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C4×D4×C11—22no—
70C4×D4×C11—41no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C42×C11C2311yescharacteristic
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×#4323—22no—
82C2×#4323—22no—
83C2×#4323Q814yes—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4D411yescharacteristic
98C2×Dic11⋊C4D411yescharacteristic
99C2×C4×Dic11C2311yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103#66946—22no—
104#66946—22no—
105#66946—22no—
106#66946—41no—
107C4⋊C4×D11—44no—
108#66943—22no—
109#66943—41no—
110C4×D44—22no—
111C4×D44—41no—
112C11×#107—22no—
113C11×#102—22no—
114C11×#102—41no—
115C11×#95—21no—
116#66896—22no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95D411yescharacteristic
121C11⋊#95D411yescharacteristic
122#66885—22no—
123#66885—22no—
124#66881—41no—
125Dic11⋊C8—22no—
126#66873D414yes—
127#66872—22no—
128#66872—22no—
129#66871—22no—
130C4×C11⋊C8—22no—
131#26382—111nomaximal, Sylow
132C24×C11—21no—
133C23×D11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11C2×Q812yes—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—42no—
144C22×C4×C11—42no—
145C22×C4×C11—81no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2411yescharacteristic
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44C2×D412yes—
160C2×D44C2×Q812yes—
161C2×D44#4112yes—
162C2×C4×D11—24no—
163C2×C4×D11—42no—
164C2×C4×D11—42no—
165C2×C4×D11—42no—
166C2×C4×D11—42no—
167C2×C4×D11—42no—
168C2×C4×D11—42no—
169C2×C4×D11—81no—
170C2×C4×D11—81no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—42no—
182C11×C4⋊C4C2×D412yes—
183C11×C4⋊C4#4112yes—
184C11×C22⋊C4—42no—
185C42×C11—21no—
186C42×C11—21no—
187C22⋊Dic11—42no—
188C22⋊Dic11—81no—
189C22⋊Dic11—81no—
190C22⋊Dic11—81no—
191#4323—28no—
192(C2×D11)⋊C4—24no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—42no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—42no—
202C4⋊Dic11—42no—
203C4⋊Dic11—81no—
204Dic11⋊C4—22no—
205Dic11⋊C4—22no—
206Dic11⋊C4—42no—
207Dic11⋊C4—42no—
208Dic11⋊C4—81no—
209Dic11⋊C4—81no—
210C4×Dic11—21no—
211C4×Dic11—21no—
212C4×Dic11—21no—
213C4×Dic11—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8C2×D412yes—
219C2×C11⋊C8C2×Q812yes—
220C2×#478—111no—
221C2×C4×D8—111no—
222#2454—111no—
223D4×C4⋊C4—111no—
224#2094—111no—
225#2083—111no—
226#2065—111no—
227#2059—111no—
228#1941—111no—
229#1916—111no—
230#1879—111no—
231#1879—111no—
232#1864—111no—
233#1864—111no—
234#1862D1111yescharacteristic, complemented
235C23×C11—22no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11C22×D411yescharacteristic
243C22×D11—22no—
244C22×D11—22no—
245C22×D11—22no—
246C22×D11—41no—
247C22×D11—41no—
248C22×D11—41no—
249C22×D11—41no—
250D4×C11—22no—
251D4×C11—22no—
252D4×C11—41no—
253D4×C11—41no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
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—84no—
269C2×C4×C11AGL(1,ℤ/8)12yes—
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C22×Q811yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11H(5,𝔽2)11yescharacteristic
275C2×C4×C112−1+411yescharacteristic
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—21no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11#13512yes—
297D44—22no—
298D44—22no—
299D44—22no—
300D44C22⋊Q814yes—
301C4×D11—48no—
302C4×D11—84no—
303C4×D11—84no—
304C8×C11—41no—
305C8×C11—41no—
306C11⋊C8—22no—
307C11⋊C8—22no—
308C22×D8—111no—
309C2×#125—111no—
310C2×C4×D4—111no—
311C2×C4×D4—111no—
312C2×C4×D4—111no—
313C2×C4×D4C2×D1111yescharacteristic
314C22×C4⋊C4—221no—
315#478—224no—
316C4×D8—224no—
317C2×#107—111no—
318C2×#107C2×D1111yescharacteristic
319C2×#106—111no—
320C2×#106—111no—
321C2×#106—111no—
322C2×C4⋊C8—111no—
323C2×#102—111no—
324C2×#102—111no—
325C2×#102—111no—
326C2×#102—111no—
327C2×#102C2×D1111yescharacteristic
328C2×#102C2×D1111yescharacteristic
329C2×C4×C8—111no—
330#399—221no—
331#396—221no—
332#390—111no—
333#390—111no—
334#389—111no—
335#389—111no—
336#389—111no—
337#389C2×D1111yescharacteristic
338#385—221no—
339#385—221no—
340#385—221no—
341#384—111no—
342#380—221no—
343#380—221no—
344C4×C4⋊C4—111no—
345#340—111no—
346#340—111no—
347#340—111no—
348#340C2×D1111yescharacteristic
349#336—111no—
350#336—111no—
351#336—111no—
352#336C2×D1111yescharacteristic
353C22×C11—42no—
354C22×C11—42no—
355C22×C11—42no—
356C22×C11—81no—
357C22×C11—81no—
358C22×C11—81no—
359C22×C11—81no—
360C22×C11#52511yescharacteristic
361C22×C11D4211yescharacteristic
362C22×C11D4×Q811yescharacteristic
363C22×C11C2×#13511yescharacteristic
364C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
365C22×C11#57611yescharacteristic
366C22×C11#57711yescharacteristic
367C2×D11—24no—
368C2×D11—42no—
369C2×D11—42no—
370C2×D11—42no—
371C2×D11—42no—
372C2×D11—42no—
373C2×D11—42no—
374C4×C11—22no—
375C4×C11—42no—
376C4×C11—42no—
377C4×C11—41no—
378C4×C11—81no—
379C4×C11C2×C22⋊Q811yescharacteristic
380C4×C11#53911yescharacteristic
381C4×C11#54711yescharacteristic
382C4×C11#55411yescharacteristic
383Dic11—22no—
384Dic11—41no—
385Dic11—41no—
386Dic11—41no—
387Dic11—81no—
388Dic11—81no—
389Dic11—81no—
390C22×D4—111no—
391C22×D4C22×D1111yescharacteristic
392C23×C4—21no—
393C23×C4—221no—
394C23×C4—221no—
395C23×C4—221no—
396C2×D8—114no—
397C2×D8—222no—
398C2×D8—222no—
399C22×C8—111no—
400C22×C8—111no—
401C22×C8C22×D1111yescharacteristic
402C22×C8C22×D1111yescharacteristic
403#125—222no—
404#125—441no—
405C4×D4—22no—
406C4×D4—41no—
407C4×D4—222no—
408C4×D4—222no—
409C4×D4—222no—
410C4×D4—222no—
411C4×D4—441no—
412C4×D4—441no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4—444no—
427C2×C4⋊C4C22×D1111yescharacteristic
428C2×C4⋊C4C22×D1111yescharacteristic
429C2×C4⋊C4C22×D1111yescharacteristic
430C2×C22⋊C4—21no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C22⋊C4—221no—
437C2×C22⋊C4—221no—
438C2×C42—111no—
439C2×C42—111no—
440C2×C42C22×D1111yescharacteristic
441#107—22no—
442#107—222no—
443#106—222no—
444#106—222no—
445#106—441no—
446C4⋊C8—222no—
447#102—22no—
448#102—41no—
449#102—114no—
450#102—222no—
451#102—222no—
452#102—222no—
453C4×C8—222no—
454#95—21no—
455#95—111no—
456#95—111no—
457#95—221no—
458#95—221no—
459#95—221no—
460C2×C11—82no—
461C2×C11#244911yescharacteristic
462C2×C11#310511yescharacteristic
463C2×C11#311911yescharacteristic
464C2×C11#326411yescharacteristic
465C2×C11#328411yescharacteristic
466C2×C11#338011yescharacteristic
467C2×C11#338411yescharacteristic
468D11—44no—
469C24—21no—
470C24—221no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—112no—
477C2×D4—112no—
478C2×D4—112no—
479C2×D4—221no—
480C2×D4—221no—
481C2×D4—221no—
482C2×D4Q8×D1112yes—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—81no—
489C22×C4—111no—
490C22×C4—111no—
491C22×C4—111no—
492C22×C4—111no—
493C22×C4—224no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—442no—
498C22×C4—442no—
499C22×C4—442no—
500C22×C4—442no—
501C22×C4—442no—
502C22×C4—442no—
503C22×C4—881no—
504C22×C4—881no—
505C22×C4D4×D1111yescharacteristic
506C22×C4D4×D1111yescharacteristic
507C22×C4C23×D1111yescharacteristic
508D8—228no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—112no—
516C2×C8—112no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—42no—
526C4⋊C4—222no—
527C4⋊C4—222no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—442no—
535C4⋊C4—442no—
536C4⋊C4—442no—
537C4⋊C4—442no—
538C4⋊C4—881no—
539C4⋊C4—881no—
540C4⋊C4—881no—
541C4⋊C4#433912yes—
542C4⋊C4D4×D1112yes—
543C22⋊C4—42no—
544C22⋊C4—224no—
545C22⋊C4—442no—
546C22⋊C4—442no—
547C22⋊C4—442no—
548C22⋊C4—881no—
549C22⋊C4—881no—
550C22⋊C4—881no—
551C42—21no—
552C42—21no—
553C42—221no—
554C42—221no—
555C42—221no—
556C42—221no—
557C11#2638211yescharacteristic, complemented, Sylow
558C23—22no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—222no—
566C23—222no—
567C23—222no—
568C23—441no—
569C23—441no—
570C23—441no—
571C23—441no—
572C23C2×D4×D1111yescharacteristic
573D4—22no—
574D4—22no—
575D4—41no—
576D4—41no—
577D4—114no—
578D4—222no—
579D4—222no—
580D4—222no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—84no—
596C2×C4—112no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—221no—
603C2×C4—221no—
604C2×C4—221no—
605C2×C4—221no—
606C2×C4—221no—
607C2×C4—221no—
608C2×C4—448no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—884no—
619C2×C4—884no—
620C2×C4#6696412yes—
621C2×C4C2×#433911yescharacteristic
622C2×C4C2×D4×D1111yescharacteristic
623C2×C4#6703711yescharacteristic
624C2×C4C2×Q8×D1111yescharacteristic
625C2×C4#41×D1111yescharacteristic
626C2×C4#6704311yescharacteristic
627C8—41no—
628C8—41no—
629C8—222no—
630C8—222no—
631C22—42no—
632C22—42no—
633C22—42no—
634C22—81no—
635C22—81no—
636C22—81no—
637C22—81no—
638C22—224no—
639C22—442no—
640C22—442no—
641C22—442no—
642C22—442no—
643C22—442no—
644C22—442no—
645C22#1062307811yescharacteristic
646C22#1062312111yescharacteristic
647C22#1062316311yescharacteristic
648C22C2×#6696411yescharacteristic
649C22D11×#13511yescharacteristic
650C22#1062330511yescharacteristic
651C22#1062330911yescharacteristic
652C4—22no—
653C4—41no—
654C4—42no—
655C4—42no—
656C4—81no—
657C4—222no—
658C4—441no—
659C4—441no—
660C4—441no—
661C4—881no—
662C4—881no—
663C4—881no—
664C4#1062304211yescharacteristic
665C4#1062308211yescharacteristic
666C4D11×C22⋊Q811yescharacteristic
667C4#1062319111yescharacteristic
668C2—82no—
669C2—444no—
670C2#1307242411yescharacteristic
671C2#1307866111yescharacteristic
672C2#1307881311yescharacteristic
673C2#1308008911yescharacteristic
674C2#1308033911yescharacteristic
675C2#1308147811yescharacteristic
676C2#1308151911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1862C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenter#1862D11
hypocenterC11#26382
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1862

Complements

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

NH ≅ G/Ntype
1. C2×#10622504C2semidirect
3. #13072482C2semidirect
4. #13071517C2semidirect
5. #13070147C2semidirect
6. #13070090C2semidirect
7. #13069986C2semidirect
8. #13069953C2semidirect
9. #13069341C2semidirect
10. #13069171C2semidirect
13. #13068880C2semidirect
14. #13068878C2semidirect
15. C11×#1862C2semidirect
234. #1862D11semidirect
557. C11#26382semidirect

Maximal subgroups

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

subgroupindex
C2×#106225042
C2×C4×#43232
#130724822
#130715172
#130701472
#130700902
#130699862
#130699532
#130693412
#130691712
#130689612
#130688802
#130688782
C11×#18622
#2638211