Finite Group Databasebeta

← #14789985

Subgroups — #14789985

Order 2816.

1012 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623050C211yesmaximal, characteristic
2C2×#10622442C211yesmaximal, characteristic, complemented
3C2×#10622463C211yesmaximal, characteristic, complemented
4#13071298C211yesmaximal, characteristic
5#13069955C211yesmaximal, characteristic, complemented
6#13069945C211yesmaximal, characteristic, complemented
7#13069768C211yesmaximal, characteristic, complemented
8#13069758C211yesmaximal, characteristic, complemented
9#13069571C211yesmaximal, characteristic, complemented
10#13069567C211yesmaximal, characteristic, complemented
11#13068926C211yesmaximal, characteristic
12#13068921C211yesmaximal, characteristic
13#13068817C211yesmaximal, characteristic
14#13068806C211yesmaximal, characteristic
15C11×#1798C211yesmaximal, characteristic
16C2×C11×#117C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C2×#66977C2211yescharacteristic
20#10623050—24no—
21#10623050—24no—
22C2×#66943—21no—
23C2×#66941—21no—
24C2×#66931—21no—
25C2×#66931—21no—
26C2×#66923C2211yescharacteristic
27C2×#66923C2211yescharacteristic
28C2×#66922C2211yescharacteristic
29C2×#66922C2211yescharacteristic
30C2×C4×Dic22C2211yescharacteristic
31C2×C11×C4⋊C8C2211yescharacteristic
32C2×C11×C4⋊C8C2211yescharacteristic
33C2×C11×C22⋊C8C2211yescharacteristic
34C2×C11×C22⋊C8C2211yescharacteristic
35#10622825C2211yescharacteristic
36C2×#66882C2211yescharacteristic
37C2×#66882C2211yescharacteristic
38C2×#66882C2211yescharacteristic
39C2×#66881C2211yescharacteristic
40C2×#66880C2211yescharacteristic
41C2×#66880C2211yescharacteristic
42C2×#66880C2211yescharacteristic
43C2×#66880C2211yescharacteristic
44#10622591—21no—
45#10622585—21no—
46#10622558—21no—
47#10622557—21no—
48C4×C4⋊Dic11C2211yescharacteristic
49#10622542C2211yescharacteristic
50#10622541C2211yescharacteristic
51#10622463—24no—
52#10622442—24no—
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61#10622189C2211yescharacteristic
62#10622189C2211yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×Dic11—21no—
65C22×Dic22—21no—
66C22×Dic22—21no—
67C22×Dic22C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C11×#117—22no—
73C11×#117—22no—
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C22⋊C4D411yescharacteristic
77C2×C11×C22⋊C4D411yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83#66979—22no—
84#66979—22no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11—22no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97#66977—22no—
98#66977Q814yescomplemented
99C2×Dic11⋊C4—21no—
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×Dic11—21no—
109#66943—28no—
110#66941—28no—
111#66931—28no—
112#66931—28no—
113#66923—22no—
114#66923—22no—
115#66923—22no—
116#66923D414yes—
117#66922—22no—
118#66922—22no—
119#66922—22no—
120#66922D414yes—
121C4×Dic22—22no—
122C4×Dic22—22no—
123C11×C4⋊C8—22no—
124C11×C4⋊C8—22no—
125C11×C22⋊C8—22no—
126C11×C22⋊C8—22no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130C11⋊#95—21no—
131C11⋊#95—21no—
132#66882—22no—
133#66882—22no—
134#66882—22no—
135#66881—22no—
136#66880—22no—
137#66880—22no—
138#66880—22no—
139#66880—22no—
140#24311—111nomaximal, Sylow
141C24×C11C2×D411yescharacteristic
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
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—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—81no—
164C22×Dic11—81no—
165C2×Dic22—24no—
166C2×Dic22—24no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22—81no—
173C2×Dic22—81no—
174C2×Dic22—81no—
175C2×Dic22—81no—
176C2×Dic22C2×Q812yes—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—22no—
191C11×C22⋊C4—22no—
192C11×C22⋊C4—22no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11C2×D412yes—
196C42×C11C2×D412yes—
197C22⋊Dic11—24no—
198C22⋊Dic11—24no—
199C22⋊Dic11—81no—
200C4⋊Dic11—24no—
201C4⋊Dic11—24no—
202C4⋊Dic11—24no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11—21no—
212C4⋊Dic11C2×D412yes—
213C4⋊Dic11C2×D412yes—
214C4⋊Dic11C2×D412yes—
215C4⋊Dic11C2×D412yes—
216C4⋊Dic11C2×Q812yes—
217Dic11⋊C4—24no—
218Dic11⋊C4—24no—
219Dic11⋊C4—24no—
220Dic11⋊C4—24no—
221Dic11⋊C4—24no—
222Dic11⋊C4—42no—
223Dic11⋊C4—81no—
224C4×Dic11—24no—
225C4×Dic11—42no—
226C4×Dic11—81no—
227C2×#544—111no—
228C2×#479—111no—
229C2×#477—111no—
230#2323—111no—
231#2059—111no—
232#2057—111no—
233#2026—111no—
234#2024—111no—
235#1989—111no—
236#1988—111no—
237#1873—111no—
238#1872—111no—
239#1854—111no—
240#1852—111no—
241#1798D1111yescharacteristic
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11C22⋊Q812yes—
249C23×C11C22×D411yescharacteristic
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11#12012yes—
267C2×C4×C11#12012yes—
268C2×C4×C11C22⋊Q812yes—
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C22×Q811yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C112−1+411yescharacteristic
274C2×C4×C112−1+411yescharacteristic
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
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—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—84no—
300Dic22—22no—
301Dic22—22no—
302Dic22—41no—
303Dic22—41no—
304Dic22—84no—
305Dic22—84no—
306C8×C11—41no—
307C8×C11—41no—
308C8×C11—41no—
309C8×C11—41no—
310#544—224no—
311#544—224no—
312C2×C4⋊Q8—111no—
313C2×C4⋊Q8—111no—
314C2×C4⋊Q8—221no—
315C2×#125—111no—
316C2×#125—111no—
317C2×#125—221no—
318C2×C22⋊Q8—111no—
319C2×C22⋊Q8—221no—
320C2×C22⋊Q8—221no—
321C2×C4×Q8—111no—
322C2×#117—111no—
323C2×#117C2×D1111yescharacteristic
324C22×C4⋊C4—111no—
325#479—224no—
326#477—224no—
327C2×#107—111no—
328C2×#107—111no—
329C2×#107—111no—
330C2×#106—111no—
331C2×C4⋊C8C2×D1111yescharacteristic
332C2×C4⋊C8C2×D1111yescharacteristic
333C2×#103—111no—
334C2×#103—111no—
335C2×#103—111no—
336C2×#103—111no—
337C2×C22⋊C8C2×D1111yescharacteristic
338C2×C22⋊C8C2×D1111yescharacteristic
339#391—111no—
340#389—111no—
341#389—221no—
342#388—221no—
343#388—221no—
344#387—221no—
345#380—111no—
346C4×C4⋊C4—111no—
347#340—111no—
348#340—111no—
349#340—111no—
350#340—111no—
351#340—111no—
352#340—111no—
353#340—111no—
354#340—111no—
355#336C2×D1111yescharacteristic
356#336C2×D1111yescharacteristic
357C22×C11—22no—
358C22×C11—22no—
359C22×C11—22no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11—41no—
363C22×C11—41no—
364C22×C11C2×#12011yescharacteristic
365C22×C11C2×C22⋊Q811yescharacteristic
366C22×C11#53611yescharacteristic
367C22×C11#57611yescharacteristic
368C22×C11#57711yescharacteristic
369C22×C11#57811yescharacteristic
370C22×C11#57811yescharacteristic
371C4×C11—22no—
372C4×C11—22no—
373C4×C11—22no—
374C4×C11—41no—
375C4×C11—41no—
376C4×C11#54811yescharacteristic
377C4×C11#54811yescharacteristic
378C4×C11D4×Q811yescharacteristic
379C4×C11D4×Q811yescharacteristic
380Dic11—42no—
381Dic11—42no—
382Dic11—42no—
383Dic11—42no—
384Dic11—42no—
385Dic11—42no—
386Dic11—81no—
387Dic11—81no—
388C22×Q8—111no—
389C22×Q8—221no—
390C22×Q8—221no—
391C23×C4—221no—
392C23×C4C22×D1111yescharacteristic
393C22×C8C22×D1111yescharacteristic
394C22×C8C22×D1111yescharacteristic
395C22×C8C22×D1111yescharacteristic
396C22×C8C22×D1111yescharacteristic
397C4⋊Q8—114no—
398C4⋊Q8—222no—
399C4⋊Q8—222no—
400C4⋊Q8—228no—
401C4⋊Q8—222no—
402#125—114no—
403#125—222no—
404#125—222no—
405#125—228no—
406#125—222no—
407C22⋊Q8—114no—
408C22⋊Q8—228no—
409C22⋊Q8—228no—
410C22⋊Q8—222no—
411C4×Q8—222no—
412C4×Q8—222no—
413#117—22no—
414#117—22no—
415#117—222no—
416#117—222no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—222no—
425C2×C4⋊C4—222no—
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⋊C4—221no—
434C2×C4⋊C4—221no—
435C2×C4⋊C4—221no—
436C2×C4⋊C4D4411yescharacteristic
437C2×C4⋊C4D4411yescharacteristic
438C2×C22⋊C4—221no—
439C2×C22⋊C4—221no—
440C2×C22⋊C4—221no—
441C2×C22⋊C4D4411yescharacteristic
442C2×C22⋊C4D4411yescharacteristic
443C2×C42—221no—
444C2×C42—221no—
445C2×C42—221no—
446C2×C42C22×D1111yescharacteristic
447C2×C42C22×D1111yescharacteristic
448#107—222no—
449#107—222no—
450#107—222no—
451#106—222no—
452C4⋊C8—22no—
453C4⋊C8—22no—
454#103—222no—
455#103—222no—
456#103—222no—
457#103—222no—
458C22⋊C8—22no—
459C22⋊C8—22no—
460#95—221no—
461#95—221no—
462#95—221no—
463#95—221no—
464#95—221no—
465C2×C11—42no—
466C2×C11#240911yescharacteristic
467C2×C11#301111yescharacteristic
468C2×C11#301211yescharacteristic
469C2×C11#308211yescharacteristic
470C2×C11#308311yescharacteristic
471C2×C11#324211yescharacteristic
472C2×C11#324311yescharacteristic
473C24C2×D4411yescharacteristic
474C2×Q8—112no—
475C2×Q8—224no—
476C2×Q8—224no—
477C2×Q8—221no—
478C2×Q8—221no—
479C2×Q8—221no—
480C2×Q8—221no—
481C2×Q8—221no—
482C2×Q8—881no—
483C2×Q8—881no—
484C2×Q8—881no—
485C2×Q8—881no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—224no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—881no—
500C22×C4—881no—
501C22×C4C2×D4411yescharacteristic
502C22×C4C2×D4411yescharacteristic
503C22×C4C2×D4411yescharacteristic
504C22×C4C2×D4411yescharacteristic
505C22×C4C2×D4411yescharacteristic
506C22×C4#434112yes—
507C22×C4Q8×D1112yes—
508C22×C4C23×D1111yescharacteristic
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—112no—
524C4⋊C4—112no—
525C4⋊C4—112no—
526C4⋊C4—112no—
527C4⋊C4—112no—
528C4⋊C4—224no—
529C4⋊C4—224no—
530C4⋊C4—224no—
531C4⋊C4—224no—
532C4⋊C4—224no—
533C4⋊C4—224no—
534C4⋊C4—224no—
535C4⋊C4—224no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—221no—
540C4⋊C4—221no—
541C4⋊C4—221no—
542C4⋊C4—221no—
543C4⋊C4—221no—
544C4⋊C4—221no—
545C4⋊C4—442no—
546C4⋊C4—881no—
547C22⋊C4—22no—
548C22⋊C4—22no—
549C22⋊C4—224no—
550C22⋊C4—224no—
551C22⋊C4—881no—
552C42—21no—
553C42—21no—
554C42—224no—
555C42—442no—
556C42—881no—
557C42D4×D1112yes—
558C42D4×D1112yes—
559C11#2431111yescharacteristic, complemented, Sylow
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23#6695012yes—
567C23C22×D4411yescharacteristic
568Q8—222no—
569Q8—222no—
570Q8—441no—
571Q8—441no—
572Q8—884no—
573Q8—884no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—222no—
591C2×C4—222no—
592C2×C4—222no—
593C2×C4—222no—
594C2×C4—222no—
595C2×C4—222no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—884no—
615C2×C4#6693512yes—
616C2×C4#6693512yes—
617C2×C4#6695012yes—
618C2×C4C2×D4×D1111yescharacteristic
619C2×C4C2×D4×D1111yescharacteristic
620C2×C4C2×#434111yescharacteristic
621C2×C4C2×Q8×D1111yescharacteristic
622C2×C4#6704311yescharacteristic
623C2×C4#6704311yescharacteristic
624C8—41no—
625C8—41no—
626C8—41no—
627C8—41no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22C2×#6693511yescharacteristic
636C22C2×#6695011yescharacteristic
637C22#1062305711yescharacteristic
638C22#1062328211yescharacteristic
639C22#1062328311yescharacteristic
640C22#1062328411yescharacteristic
641C22#1062328411yescharacteristic
642C4—22no—
643C4—22no—
644C4—22no—
645C4—41no—
646C4—41no—
647C4—442no—
648C4—442no—
649C4—442no—
650C4—442no—
651C4—442no—
652C4—442no—
653C4—881no—
654C4—881no—
655C4#1062312911yescharacteristic
656C4#1062312911yescharacteristic
657C4#1062316311yescharacteristic
658C4#1062316311yescharacteristic
659C2—42no—
660C2#1307198211yescharacteristic
661C2#1307791311yescharacteristic
662C2#1307792311yescharacteristic
663C2#1307845911yescharacteristic
664C2#1307846911yescharacteristic
665C2#1307988611yescharacteristic
666C2#1307990111yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1798C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1798D11
hypocenterC11#24311
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #1798

Complements

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

NH ≅ G/Ntype
2. C2×#10622442C2semidirect
3. C2×#10622463C2semidirect
5. #13069955C2semidirect
6. #13069945C2semidirect
7. #13069768C2semidirect
8. #13069758C2semidirect
9. #13069571C2semidirect
10. #13069567C2semidirect
98. #66977Q8semidirect
559. C11#24311semidirect

Maximal subgroups

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

subgroupindex
C2×#106230502
C2×#106224422
C2×#106224632
#130712982
#130699552
#130699452
#130697682
#130697582
#130695712
#130695672
#130689262
#130689212
#130688172
#130688062
C11×#17982
#2431111