Finite Group Databasebeta

← #14816902

Subgroups — #14816902

Order 2816.

932 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622374C211yesmaximal, characteristic, complemented
2C2×#10622369C211yesmaximal, characteristic
3#13072464C211yesmaximal, characteristic, complemented
4#13071526C211yesmaximal, characteristic, complemented
5#13070136C211yesmaximal, characteristic, complemented
6#13070097C211yesmaximal, characteristic, complemented
7#13069985C211yesmaximal, characteristic, complemented
8#13069943C211yesmaximal, characteristic, complemented
9#13069345C211yesmaximal, characteristic, complemented
10#13069174C211yesmaximal, characteristic, complemented
11#13068964C211yesmaximal, characteristic
12#13068962C211yesmaximal, characteristic
13#13068878C211yesmaximal, characteristic, complemented
14#13068865C211yesmaximal, characteristic, complemented
15C11×#1864C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C2×D4×Dic11C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C22×#4323C2211yescharacteristic
20C2×#66950—21no—
21C2×#66946C2211yescharacteristic
22C2×#66941C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28#10622825—21no—
29C2×C11⋊#95—21no—
30C2×#66885C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36#10622607—21no—
37#10622601C2211yescharacteristic
38#10622598C2211yescharacteristic
39#10622598C2211yescharacteristic
40#10622598C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44#10622563—21no—
45#10622563—21no—
46#10622552C2211yescharacteristic
47#10622549C2211yescharacteristic
48C4×C4⋊Dic11C2211yescharacteristic
49#10622374—24no—
50#10622369—24no—
51#10622286—21no—
52#10622281—21no—
53C11×#340C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×Dic11—21no—
64C23×Dic11—21no—
65C22×D44C2311yescharacteristic
66C22×C4×D11—21no—
67C22×Dic22—21no—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C4×D4×C11—22no—
71C4×D4×C11—22no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C42×C11C2311yescharacteristic
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80D4×Dic11—22no—
81D4×Dic11—22no—
82D4×Dic11—41no—
83D4×Dic11—41no—
84C2×#4323—22no—
85C2×#4323—22no—
86C2×#4323Q814yescomplemented
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⋊Dic11—21no—
95C2×C4⋊Dic11D411yescharacteristic
96C2×C4⋊Dic11D411yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×Dic11⋊C4—21no—
101C2×C4×Dic11C2311yescharacteristic
102C2×C4×Dic11C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105#66950—44no—
106#66946—22no—
107#66946—41no—
108#66941—22no—
109#66941—41no—
110C11×#106—22no—
111C11×#102—22no—
112C11×#102D414yes—
113C11×#95—21no—
114#66896—22no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95D411yescharacteristic
121C11⋊#95D411yescharacteristic
122#66885—22no—
123#66885—41no—
124#66882—41no—
125#66881—22no—
126Dic11⋊C8—22no—
127C8×Dic11—22no—
128#66873—22no—
129#66872—22no—
130#66871—22no—
131#26380—111nomaximal, Sylow
132C24×C11—21no—
133C23×D11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11C2×D412yes—
138C2×D4×C11C2×Q812yes—
139C2×D4×C11#4112yes—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—24no—
143C22×C4×C11—21no—
144C22×C4×C11—81no—
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×Dic11—42no—
153C22×Dic11—42no—
154C22×Dic11—42no—
155C22×Dic11—42no—
156C22×Dic11—81no—
157C22×Dic11—81no—
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161C22×Dic11C2×D411yescharacteristic
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44C2×Q812yes—
168C2×C4×D11—42no—
169C2×C4×D11—42no—
170C2×C4×D11—81no—
171C2×Dic22—42no—
172C2×Dic22—42no—
173C2×Dic22—81no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11C2×D412yes—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—42no—
185C11×C4⋊C4C2×D412yes—
186C11×C4⋊C4#4112yes—
187C11×C22⋊C4—24no—
188C42×C11—21no—
189C42×C11—21no—
190C22⋊Dic11—42no—
191C22⋊Dic11—42no—
192#4323—28no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—42no—
195(C2×D11)⋊C4—42no—
196(C2×D11)⋊C4—42no—
197(C2×D11)⋊C4—81no—
198C4⋊Dic11—22no—
199C4⋊Dic11—22no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—42no—
207C4⋊Dic11—81no—
208C4⋊Dic11—81no—
209Dic11⋊C4—42no—
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⋊C8—21no—
219C2×C11⋊C8C2×Q812yes—
220C2×#476—111no—
221C2×C4×D8—111no—
222#2452—111no—
223#2349—111no—
224#2092—111no—
225#2085—111no—
226#2065—111no—
227#2057—111no—
228#1941—111no—
229#1916—111no—
230#1879—111no—
231#1879—111no—
232#1864—111no—
233#1864D1111yescharacteristic, complemented
234#1862—111no—
235C23×C11—22no—
236C23×C11—22no—
237C23×C11—22no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11C22×D411yescharacteristic
243C22×D11—22no—
244C22×D11—41no—
245C22×D11—41no—
246C22×D11—41no—
247C22×D11—41no—
248C22×D11—41no—
249C22×D11—41no—
250D4×C11—22no—
251D4×C11—22no—
252D4×C11—22no—
253D4×C11C22⋊Q814yescomplemented
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—21no—
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—84no—
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—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—
295C2×Dic11—84no—
296C2×Dic11—84no—
297C2×Dic11#13512yes—
298C2×Dic11AGL(1,ℤ/8)12yes—
299D44—22no—
300D44—22no—
301D44—41no—
302D44—41no—
303C4×D11—84no—
304Dic22—84no—
305C8×C11—22no—
306C8×C11—41no—
307C11⋊C8—22no—
308C11⋊C8—41no—
309C22×D8—111no—
310C2×C4⋊Q8—111no—
311C2×C22⋊Q8—221no—
312C2×C4×D4—111no—
313C2×C4×D4—111no—
314C2×C4×D4—111no—
315C2×C4×D4C2×D1111yescharacteristic
316#476—224no—
317C4×D8—224no—
318C2×#107—111no—
319C2×#107—111no—
320C2×#106—111no—
321C2×#106—111no—
322C2×#106C2×D1111yescharacteristic
323C2×C4⋊C8—111no—
324C2×#102—111no—
325C2×#102—111no—
326C2×#102—111no—
327C2×#102—111no—
328C2×#102C2×D1111yescharacteristic
329C2×#102C2×D1111yescharacteristic
330C2×C4×C8—111no—
331#396—221no—
332#393—221no—
333#390—111no—
334#390—111no—
335#389—111no—
336#389—111no—
337#389—111no—
338#389C2×D1111yescharacteristic
339#385—221no—
340#385—221no—
341#385—221no—
342#382—111no—
343#380—221no—
344C4×C4⋊C4—111no—
345C2×#95—221no—
346#340—111no—
347#340—111no—
348#340—111no—
349#340C2×D1111yescharacteristic
350#336—111no—
351#336—111no—
352#336—111no—
353#336C2×D1111yescharacteristic
354C22×C11—24no—
355C22×C11—42no—
356C22×C11—42no—
357C22×C11—42no—
358C22×C11—42no—
359C22×C11—42no—
360C22×C11—42no—
361C22×C11#52511yescharacteristic
362C22×C11D4211yescharacteristic
363C22×C11D4×Q811yescharacteristic
364C22×C11C2×#13511yescharacteristic
365C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
366C22×C11#57611yescharacteristic
367C22×C11#57711yescharacteristic
368C2×D11—42no—
369C2×D11—42no—
370C2×D11—42no—
371C2×D11—81no—
372C2×D11—81no—
373C2×D11—81no—
374C2×D11—81no—
375C4×C11—41no—
376C4×C11—41no—
377C4×C11—42no—
378C4×C11—42no—
379C4×C11—81no—
380C4×C11C2×C22⋊Q811yescharacteristic
381C4×C11#53911yescharacteristic
382C4×C11#54711yescharacteristic
383C4×C11#55411yescharacteristic
384Dic11—22no—
385Dic11—22no—
386Dic11—41no—
387Dic11—41no—
388Dic11—81no—
389Dic11—81no—
390Dic11—81no—
391C22×Q8—221no—
392C22×D4—111no—
393C22×D4C22×D1111yescharacteristic
394C23×C4—21no—
395C23×C4—221no—
396C23×C4—221no—
397C23×C4—221no—
398C2×D8—114no—
399C2×D8—222no—
400C2×D8—222no—
401C22×C8—111no—
402C22×C8—111no—
403C22×C8C22×D1111yescharacteristic
404C22×C8C22×D1111yescharacteristic
405C4⋊Q8—222no—
406C4⋊Q8—441no—
407C22⋊Q8—444no—
408C4×D4—22no—
409C4×D4—22no—
410C4×D4—222no—
411C4×D4—222no—
412C4×D4—222no—
413C4×D4—441no—
414C4×D4—441no—
415C4×D4—441no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4C22×D1111yescharacteristic
427C2×C4⋊C4C22×D1111yescharacteristic
428C2×C4⋊C4C22×D1111yescharacteristic
429C2×C22⋊C4—21no—
430C2×C22⋊C4—221no—
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×C42—111no—
438C2×C42—111no—
439C2×C42C22×D1111yescharacteristic
440#107—222no—
441#107—441no—
442#106—22no—
443#106—222no—
444#106—222no—
445C4⋊C8—222no—
446#102—22no—
447#102—222no—
448#102—222no—
449#102—222no—
450#102—441no—
451#102D4414yes—
452C4×C8—222no—
453#95—21no—
454#95—111no—
455#95—111no—
456#95—221no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461C2×C11—44no—
462C2×C11#244911yescharacteristic
463C2×C11#310611yescharacteristic
464C2×C11#311811yescharacteristic
465C2×C11#326411yescharacteristic
466C2×C11#328211yescharacteristic
467C2×C11#338011yescharacteristic
468C2×C11#338411yescharacteristic
469D11—82no—
470C24—21no—
471C24—221no—
472C2×Q8—442no—
473C2×Q8—442no—
474C2×Q8—881no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—112no—
479C2×D4—221no—
480C2×D4—221no—
481C2×D4—221no—
482C2×D4—221no—
483C2×D4—221no—
484C2×D4C2×D4412yes—
485C2×D4#434112yes—
486C2×D4Q8×D1112yes—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—24no—
490C22×C4—21no—
491C22×C4—81no—
492C22×C4—81no—
493C22×C4—111no—
494C22×C4—111no—
495C22×C4—111no—
496C22×C4—111no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—442no—
501C22×C4—442no—
502C22×C4—442no—
503C22×C4—442no—
504C22×C4—442no—
505C22×C4—442no—
506C22×C4—881no—
507C22×C4—881no—
508C22×C4—881no—
509C22×C4D4×D1111yescharacteristic
510C22×C4D4×D1111yescharacteristic
511C22×C4C23×D1111yescharacteristic
512D8—228no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—112no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8—221no—
523C2×C8—221no—
524C2×C8C2×D4412yes—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—42no—
530C4⋊C4—222no—
531C4⋊C4—222no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—442no—
539C4⋊C4—442no—
540C4⋊C4—881no—
541C4⋊C4—881no—
542C4⋊C4C2×D4412yes—
543C4⋊C4#434112yes—
544C22⋊C4—24no—
545C22⋊C4—442no—
546C22⋊C4—442no—
547C22⋊C4—442no—
548C22⋊C4—442no—
549C22⋊C4—442no—
550C22⋊C4—442no—
551C22⋊C4—881no—
552C42—21no—
553C42—21no—
554C42—221no—
555C42—221no—
556C42—221no—
557C42—221no—
558C11#2638011yescharacteristic, complemented, Sylow
559C23—22no—
560C23—22no—
561C23—22no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—222no—
567C23—441no—
568C23—441no—
569C23—441no—
570C23—441no—
571C23—441no—
572C23—441no—
573C23C2×D4×D1111yescharacteristic
574Q8—884no—
575D4—22no—
576D4—22no—
577D4—22no—
578D4—222no—
579D4—222no—
580D4—441no—
581D4—441no—
582D4#6695014yescomplemented
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—84no—
599C2×C4—112no—
600C2×C4—112no—
601C2×C4—221no—
602C2×C4—221no—
603C2×C4—221no—
604C2×C4—221no—
605C2×C4—221no—
606C2×C4—221no—
607C2×C4—221no—
608C2×C4—221no—
609C2×C4—221no—
610C2×C4—221no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—884no—
621C2×C4—884no—
622C2×C4—884no—
623C2×C4C22×D4411yescharacteristic
624C2×C4C2×#434111yescharacteristic
625C2×C4C2×#434111yescharacteristic
626C2×C4C2×Q8×D1111yescharacteristic
627C2×C4#6704211yescharacteristic
628C2×C4#6704311yescharacteristic
629C8—22no—
630C8—41no—
631C8—222no—
632C8—441no—
633C22—24no—
634C22—42no—
635C22—42no—
636C22—42no—
637C22—42no—
638C22—42no—
639C22—42no—
640C22—442no—
641C22—442no—
642C22—442no—
643C22—881no—
644C22—881no—
645C22—881no—
646C22—881no—
647C22D4×D4411yescharacteristic
648C22#1062311711yescharacteristic
649C22#1062316311yescharacteristic
650C22#1062329311yescharacteristic
651C22D11×#13511yescharacteristic
652C22D11×AGL(1,ℤ/8)11yescharacteristic
653C22#1062330511yescharacteristic
654C4—41no—
655C4—42no—
656C4—42no—
657C4—41no—
658C4—81no—
659C4—222no—
660C4—222no—
661C4—441no—
662C4—441no—
663C4—881no—
664C4—881no—
665C4—881no—
666C4C2×#6695011yescharacteristic
667C4#1062308611yescharacteristic
668C4#1062316611yescharacteristic
669C4#1062319611yescharacteristic
670C2—44no—
671C2—882no—
672C2#1307242311yescharacteristic
673C2#1307866911yescharacteristic
674C2#1307880111yescharacteristic
675C2#1308009811yescharacteristic
676C2#1308032511yescharacteristic
677C2#1308147811yescharacteristic
678C2#1308151011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1864C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenter#1864D11
hypocenterC11#26380
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1864

Complements

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

NH ≅ G/Ntype
1. C2×#10622374C2semidirect
3. #13072464C2semidirect
4. #13071526C2semidirect
5. #13070136C2semidirect
6. #13070097C2semidirect
7. #13069985C2semidirect
8. #13069943C2semidirect
9. #13069345C2semidirect
10. #13069174C2semidirect
13. #13068878C2semidirect
14. #13068865C2semidirect
15. C11×#1864C2semidirect
86. C2×#4323Q8semidirect
233. #1864D11semidirect
253. D4×C11C22⋊Q8semidirect
558. C11#26380semidirect
582. D4#66950semidirect

Maximal subgroups

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

subgroupindex
C2×#106223742
C2×#106223692
#130724642
#130715262
#130701362
#130700972
#130699852
#130699432
#130693452
#130691742
#130689642
#130689622
#130688782
#130688652
C11×#18642
#2638011