Finite Group Databasebeta

← #14803903

Subgroups — #14803903

Order 2816.

874 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×#10622407C211yesmaximal, characteristic, complemented
2C2×C8×C22⋊D11C211yesmaximal, characteristic
3#13073786C211yesmaximal, characteristic
4#13073535C211yesmaximal, characteristic
5#13070047C211yesmaximal, characteristic, complemented
6#13070046C211yesmaximal, characteristic, complemented
7#13069818C211yesmaximal, characteristic, complemented
8#13069816C211yesmaximal, characteristic, complemented
9#13069575C211yesmaximal, characteristic, complemented
10#13069373C211yesmaximal, characteristic, complemented
11#13069036C211yesmaximal, characteristic, complemented
12#13068645C211yesmaximal, characteristic, complemented
13#13068644C211yesmaximal, characteristic, complemented
14#103×Dic11C211yesmaximal, characteristic, complemented
15C11×#1892C211yesmaximal, characteristic, complemented
16C23×C8×C11C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×#66999C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C2×C4×C22⋊D11C2211yescharacteristic
21C22×C8×D11C2211yescharacteristic
22C2×#66941C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C11×#380C2211yescharacteristic
26C2×#66899C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28#10622825C2211yescharacteristic
29#10622825C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C8×C22⋊D11—24no—
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×#66882C2211yescharacteristic
34C2×#66882C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36C2×C8×Dic11C2211yescharacteristic
37#10622607—21no—
38#10622600C2211yescharacteristic
39#10622600C2211yescharacteristic
40#10622600C2211yescharacteristic
41#10622589C2211yescharacteristic
42C4⋊C4×Dic11C2211yescharacteristic
43#10622585—21no—
44C2×#66871C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622570—21no—
47#10622570—21no—
48#10622561—21no—
49#10622560—21no—
50#10622407—24no—
51#10622286—21no—
52#10622263—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11D411yescharacteristic
64C22×C4×D11C2311yescharacteristic
65C22×Dic22—21no—
66C22×C8×C11—22no—
67C22×C8×C11—22no—
68C22×C8×C11—41no—
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8—41no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11D411yescharacteristic
82#66999—22no—
83#66999—41no—
84Q8×Dic11—22no—
85Q8×Dic11—22no—
86C4×C22⋊D11—22no—
87C4×C22⋊D11—22no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4D411yescharacteristic
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4D411yescharacteristic
103C2×C4×Dic11—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C2×C8×D11—22no—
109C2×C8×D11—22no—
110C2×C8×D11—41no—
111#66941—22no—
112#66941—22no—
113C11×#103—22no—
114C11×#103—22no—
115C11×#95—21no—
116#66899—22no—
117#66899—22no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C22⋊(C11⋊C8)—22no—
125(C2×D11)⋊C8—22no—
126#66882—22no—
127#66882—41no—
128Dic11⋊C8D414yes—
129C8×Dic11—22no—
130#66871—22no—
131#66871—41no—
132#25340—111nomaximal, Sylow
133C24×C11C2×D411yescharacteristic
134C23×D11C2×D411yescharacteristic
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11#4112yes—
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—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C2×C22⋊D11—22no—
154C2×C22⋊D11—22no—
155C2×C22⋊D11Q1614yes—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11C2×D411yescharacteristic
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11—21no—
168C2×C4×D11—21no—
169C2×Dic22—42no—
170C2×Dic22—81no—
171C2×Dic22—81no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—44no—
177C2×C8×C11C2×D412yes—
178C2×C8×C11#4112yes—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—42no—
186C11×C22⋊C4—42no—
187C11×C22⋊C4—81no—
188C22⋊Dic11—22no—
189C22⋊Dic11—81no—
190C22⋊Dic11—81no—
191(C2×D11)⋊C4—22no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—81no—
194(C2×D11)⋊C4—81no—
195(C2×D11)⋊C4—81no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—42no—
205Dic11⋊C4—22no—
206Dic11⋊C4—42no—
207Dic11⋊C4—42no—
208Dic11⋊C4—42no—
209Dic11⋊C4—81no—
210C4×Dic11—42no—
211C4×Dic11—42no—
212C4×Dic11C2×D412yes—
213C4×Dic11#4112yes—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8C2×D412yes—
220C8×D11—44no—
221C2×#477—111no—
222C2×C8×D4—111no—
223#2563—111no—
224#2538—111no—
225#2076—111no—
226#2076—111no—
227#2036—111no—
228#2036—111no—
229#1990—111no—
230#1947—111no—
231#1892—111no—
232#1892D1111yescharacteristic, complemented
233#1808—111no—
234#1808—111no—
235C4×#103—111no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11C2×Q1612yes—
243C23×C11C22×D411yescharacteristic
244C22×D11—21no—
245C22×D11—21no—
246C22×D11—21no—
247C22×D11—21no—
248C22×D11—21no—
249C22×D11—21no—
250C22×D11C2×Q1612yes—
251Q8×C11—22no—
252Q8×C11—22no—
253Q8×C11—41no—
254Q8×C11—41no—
255C2×C4×C11—21no—
256C2×C4×C11—22no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—41no—
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—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11H(5,𝔽2)11yescharacteristic
279C2×C4×C112−1+411yescharacteristic
280C22⋊D11—28no—
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—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11#12112yes—
299C2×Dic11#12112yes—
300C2×Dic11C2×Q1612yes—
301C2×Dic11#13512yes—
302C4×D11—41no—
303C4×D11—41no—
304C4×D11—41no—
305C4×D11—41no—
306Dic22—84no—
307C8×C11—22no—
308C8×C11—22no—
309C11⋊C8—22no—
310C11⋊C8—41no—
311C23×C8—111no—
312C23×C8C2×D1111yescharacteristic
313C2×C4⋊Q8—111no—
314C2×C22⋊Q8—111no—
315C2×C22⋊Q8C2×D1111yescharacteristic
316C2×C4×Q8—111no—
317C2×C4×D4—111no—
318#477—224no—
319C8×D4—224no—
320C2×#107—111no—
321C2×#107—111no—
322C2×#107—111no—
323C2×#107—111no—
324C2×C4⋊C8—111no—
325C2×#103—111no—
326C2×#103—111no—
327C2×#103C2×D1111yescharacteristic
328C2×#103C2×D1111yescharacteristic
329C2×C22⋊C8—111no—
330C2×C22⋊C8—111no—
331C2×C4×C8—111no—
332#396—221no—
333#396—221no—
334#393—221no—
335#393—221no—
336#390—221no—
337#390—221no—
338#389—221no—
339#384—111no—
340#382—221no—
341#380—111no—
342#380—111no—
343#380—111no—
344#380—111no—
345#380—111no—
346#380C2×D1111yescharacteristic
347C4×C4⋊C4—111no—
348#340—111no—
349#340—111no—
350#340—111no—
351#340—111no—
352#340—111no—
353#340—111no—
354#340C2×D1111yescharacteristic
355#340C2×D1111yescharacteristic
356C22×C11—22no—
357C22×C11—22no—
358C22×C11—22no—
359C22×C11—41no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11—41no—
363C22×C11C2×#12111yescharacteristic
364C22×C11#54611yescharacteristic
365C22×C11#54711yescharacteristic
366C22×C11C22×Q1611yescharacteristic
367C22×C11C2×#13511yescharacteristic
368C22×C11#57611yescharacteristic
369C22×C11#57711yescharacteristic
370C2×D11—22no—
371C2×D11—22no—
372C2×D11—22no—
373C2×D11—41no—
374C2×D11—41no—
375C2×D11—41no—
376C2×D11—41no—
377C4×C11—41no—
378C4×C11—42no—
379C4×C11—81no—
380C4×C11—81no—
381C4×C11—81no—
382C4×C11#52911yescharacteristic
383C4×C11#54211yescharacteristic
384C4×C11#54611yescharacteristic
385C4×C11#54811yescharacteristic
386Dic11—22no—
387Dic11—41no—
388Dic11—81no—
389Dic11—81no—
390Dic11—81no—
391Dic11—81no—
392Dic11#46714yes—
393C22×Q8—221no—
394C22×Q8C22×D1111yescharacteristic
395C22×D4—111no—
396C23×C4—111no—
397C23×C4C22×D1111yescharacteristic
398C22×C8—22no—
399C22×C8—22no—
400C22×C8—41no—
401C22×C8—111no—
402C22×C8—111no—
403C22×C8—222no—
404C22×C8—222no—
405C22×C8—441no—
406C22×C8C22×D1111yescharacteristic
407C22×C8C22×D1111yescharacteristic
408C4⋊Q8—222no—
409C4⋊Q8—222no—
410C22⋊Q8—22no—
411C22⋊Q8—41no—
412C22⋊Q8—222no—
413C22⋊Q8—441no—
414C4×Q8—222no—
415C4×Q8—222no—
416C4×D4—222no—
417C4×D4—222no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4C22×D1111yescharacteristic
430C2×C4⋊C4C22×D1111yescharacteristic
431C2×C4⋊C4C22×D1111yescharacteristic
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—111no—
435C2×C22⋊C4—111no—
436C2×C22⋊C4—221no—
437C2×C22⋊C4—221no—
438C2×C22⋊C4—221no—
439C2×C22⋊C4—221no—
440C2×C22⋊C4—221no—
441C2×C22⋊C4—221no—
442C2×C42—111no—
443C2×C42—221no—
444C2×C42—221no—
445#107—222no—
446#107—222no—
447#107—441no—
448#107—441no—
449C4⋊C8—114no—
450#103—22no—
451#103—22no—
452#103—222no—
453#103—222no—
454C22⋊C8—222no—
455C22⋊C8—222no—
456C4×C8—222no—
457#95—21no—
458#95—221no—
459#95—221no—
460#95—221no—
461#95—221no—
462#95—221no—
463#95—221no—
464C2×C11—42no—
465C2×C11#242711yescharacteristic
466C2×C11C2×#46711yescharacteristic
467C2×C11#306211yescharacteristic
468C2×C11#329911yescharacteristic
469C2×C11#330511yescharacteristic
470C2×C11#333811yescharacteristic
471C2×C11#334011yescharacteristic
472D11—42no—
473C24—111no—
474C24D4×D1111yescharacteristic
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—442no—
481C2×Q8—881no—
482C2×Q8—881no—
483C2×Q8#433912yes—
484C2×D4—114no—
485C2×D4—222no—
486C2×D4—222no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—111no—
498C22×C4—111no—
499C22×C4—111no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—221no—
508C22×C4—221no—
509C22×C4—221no—
510C22×C4D4×D1111yescharacteristic
511C22×C4C23×D1111yescharacteristic
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—44no—
517C2×C8—112no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8—221no—
523C2×C8—444no—
524C2×C8D4×D1112yes—
525C2×C8#434112yes—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—42no—
533C4⋊C4—222no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—221no—
540C4⋊C4—221no—
541C4⋊C4—221no—
542C4⋊C4—442no—
543C4⋊C4—442no—
544C4⋊C4—442no—
545C4⋊C4—442no—
546C4⋊C4—881no—
547C22⋊C4—42no—
548C22⋊C4—81no—
549C22⋊C4—222no—
550C22⋊C4—222no—
551C22⋊C4—442no—
552C22⋊C4—881no—
553C22⋊C4—881no—
554C22⋊C4—881no—
555C22⋊C4—881no—
556C22⋊C4—881no—
557C42—112no—
558C42—112no—
559C42—442no—
560C42—442no—
561C11#2534011yescharacteristic, complemented, Sylow
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—112no—
569C23—221no—
570C23—221no—
571C23—221no—
572C23—221no—
573C23—221no—
574C23—221no—
575C23Q16×D1112yes—
576C23C2×D4×D1111yescharacteristic
577Q8—22no—
578Q8—22no—
579Q8—41no—
580Q8—41no—
581Q8—884no—
582D4—228no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—112no—
603C2×C4—112no—
604C2×C4—112no—
605C2×C4—112no—
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—441no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4C2×#433911yescharacteristic
628C2×C4C2×D4×D1111yescharacteristic
629C2×C4C2×#434111yescharacteristic
630C2×C4#6703711yescharacteristic
631C2×C4#41×D1111yescharacteristic
632C2×C4#6704311yescharacteristic
633C8—22no—
634C8—22no—
635C8—222no—
636C8—441no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—222no—
645C22—222no—
646C22—222no—
647C22—441no—
648C22—441no—
649C22—441no—
650C22—441no—
651C22#1062302111yescharacteristic
652C22D11×#12111yescharacteristic
653C22#1062314211yescharacteristic
654C22#1062329311yescharacteristic
655C22C2×Q16×D1111yescharacteristic
656C22D11×#13511yescharacteristic
657C22#1062330011yescharacteristic
658C4—41no—
659C4—42no—
660C4—81no—
661C4—81no—
662C4—81no—
663C4—114no—
664C4—222no—
665C4—441no—
666C4—881no—
667C4—881no—
668C4—881no—
669C4—881no—
670C4#1062306911yescharacteristic
671C4#1062308311yescharacteristic
672C4#1062312211yescharacteristic
673C4#1062319311yescharacteristic
674C2—42no—
675C2—442no—
676C2#1307219011yescharacteristic
677C2D11×#46711yescharacteristic
678C2#1307828911yescharacteristic
679C2#1308048811yescharacteristic
680C2#1308056211yescharacteristic
681C2#1308100511yescharacteristic
682C2#1308102411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1892C2
socleC23×C11C22×D4
prime radicalC22×C22⋊D11D4
hypercenter#1892D11
hypocenterC11#25340
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1892

Complements

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

NH ≅ G/Ntype
1. C2×#10622407C2semidirect
5. #13070047C2semidirect
6. #13070046C2semidirect
7. #13069818C2semidirect
8. #13069816C2semidirect
9. #13069575C2semidirect
10. #13069373C2semidirect
11. #13069036C2semidirect
12. #13068645C2semidirect
13. #13068644C2semidirect
14. #103×Dic11C2semidirect
15. C11×#1892C2semidirect
232. #1892D11semidirect
561. C11#25340semidirect

Maximal subgroups

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

subgroupindex
C2×#106224072
C2×C8×C22⋊D112
#130737862
#130735352
#130700472
#130700462
#130698182
#130698162
#130695752
#130693732
#130690362
#130686452
#130686442
#103×Dic112
C11×#18922
#2534011