Finite Group Databasebeta

← #14795172

Subgroups — #14795172

Order 2816.

802 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622697C211yesmaximal, characteristic, complemented
2C2×#10622613C211yesmaximal, characteristic, complemented
3#13071309C211yesmaximal, characteristic
4#13070053C211yesmaximal, characteristic, complemented
5#13070052C211yesmaximal, characteristic, complemented
6#13069805C211yesmaximal, characteristic
7#13069798C211yesmaximal, characteristic
8#13069569C211yesmaximal, characteristic, complemented
9#13069382C211yesmaximal, characteristic, complemented
10#13069351C211yesmaximal, characteristic, complemented
11#13069341C211yesmaximal, characteristic, complemented
12#13069312C211yesmaximal, characteristic, complemented
13#13069298C211yesmaximal, characteristic, complemented
14#13068623C211yesmaximal, characteristic, complemented
15C11×#2628C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×#66983C2211yescharacteristic
19C2×C4×D44C2211yescharacteristic
20C11×#400—21no—
21C11×#399—21no—
22C11×#395—21no—
23C11×#393—21no—
24C11×#389C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C11×#382C2211yescharacteristic
27C11×#380C2211yescharacteristic
28C11×#380C2211yescharacteristic
29#10622825C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32#10622697—24no—
33#10622613—24no—
34#10622603—21no—
35#10622602—21no—
36C2×#66873C2211yescharacteristic
37C2×#66873C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44#10622570—21no—
45#10622569—21no—
46#10622552C2211yescharacteristic
47C4×C4⋊Dic11C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51C2×#66867C2211yescharacteristic
52C2×C4×C11⋊C8C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11—21no—
64C22×D44C2311yescharacteristic
65C22×C4×D11—21no—
66C11×C4⋊Q8—22no—
67C11×C4⋊Q8—22no—
68C11×#117—22no—
69C11×#117—22no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4D411yescharacteristic
82C2×C11×C22⋊C4D411yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C22⋊Dic11—21no—
86#66983—22no—
87#66983—22no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C4×D44—22no—
102C4×D44—22no—
103C11×#95—21no—
104C11×#95—21no—
105C11×#95—21no—
106C11×#95—21no—
107C11×#95—21no—
108C11×#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C22⋊(C11⋊C8)—22no—
113C22⋊(C11⋊C8)—22no—
114#66873—22no—
115#66873—22no—
116#66873—22no—
117#66873—22no—
118#66872—22no—
119#66872—22no—
120#66872—22no—
121#66871—22no—
122C4⋊(C11⋊C8)—22no—
123C4⋊(C11⋊C8)D414yescomplemented
124#66867—22no—
125C4×C11⋊C8—22no—
126#24716—111nomaximal, Sylow
127C24×C11C2×D411yescharacteristic
128C23×D11—21no—
129C2×Q8×C11—42no—
130C2×Q8×C11—81no—
131C2×Q8×C11—81no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2411yescharacteristic
148C2×C22⋊D11—24no—
149C2×C22⋊D11—81no—
150C2×C22⋊D11—81no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44#4112yes—
160C2×C4×D11—42no—
161C2×C4×D11—81no—
162C2×C4×D11—81no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—42no—
174C11×C4⋊C4—81no—
175C11×C4⋊C4—81no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—81no—
179C11×C22⋊C4—81no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11C2×D412yes—
183C42×C11#4112yes—
184C22⋊Dic11—81no—
185(C2×D11)⋊C4—24no—
186(C2×D11)⋊C4—42no—
187(C2×D11)⋊C4—81no—
188(C2×D11)⋊C4—81no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11#4112yes—
195Dic11⋊C4—81no—
196C4×Dic11—81no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8C2×D412yes—
208C2×C11⋊C8C2×D412yes—
209C2×#476—111no—
210C2×#433—111no—
211#2628D1111yescharacteristic, complemented
212#2324—111no—
213#2077—111no—
214#2077—111no—
215#2034—111no—
216#2033—111no—
217#1988—111no—
218#1949—111no—
219#1943—111no—
220#1941—111no—
221#1936—111no—
222#1934—111no—
223#1804—111no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11C22×D411yescharacteristic
232C22×D11—22no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—41no—
238C22×D11—41no—
239Q8×C11—84no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
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#12112yes—
270C2×C4×C11#12112yes—
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C112−1+411yescharacteristic
276C2×C4×C112−1+411yescharacteristic
277C22⋊D11—84no—
278C2×Dic11—22no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287D44—22no—
288D44—22no—
289D44—41no—
290D44—41no—
291C4×D11—84no—
292C11⋊C8—22no—
293C11⋊C8—22no—
294C11⋊C8—41no—
295C11⋊C8—41no—
296C2×C4⋊Q8C2×D1111yescharacteristic
297C2×#121—111no—
298C2×C4×D4—111no—
299C2×#117C2×D1111yescharacteristic
300#476—224no—
301#433—224no—
302C2×#107—111no—
303C2×#106—111no—
304C2×#106—111no—
305C2×#106—111no—
306C2×C4⋊C8—111no—
307C2×C4⋊C8—111no—
308C2×#102—111no—
309C2×#102—111no—
310C2×#102—111no—
311C2×#102—111no—
312C2×C22⋊C8—111no—
313C2×C22⋊C8—111no—
314C2×#97—111no—
315C2×C4×C8—111no—
316#400—21no—
317#399—21no—
318#395—21no—
319#393—21no—
320#390—111no—
321#390—221no—
322#389—111no—
323#389C2×D1111yescharacteristic
324#389C2×D1111yescharacteristic
325#388—221no—
326#386—221no—
327#385—221no—
328#382C2×D1111yescharacteristic
329#380—111no—
330#380C2×D1111yescharacteristic
331#380C2×D1111yescharacteristic
332C4×C4⋊C4—111no—
333#340—111no—
334#340—111no—
335#340—111no—
336#340—111no—
337#340—111no—
338#340—111no—
339#340—111no—
340#340—111no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11C2×#12111yescharacteristic
349C22×C11#52511yescharacteristic
350C22×C11#53611yescharacteristic
351C22×C11#57611yescharacteristic
352C22×C11#57711yescharacteristic
353C22×C11#57711yescharacteristic
354C22×C11#57711yescharacteristic
355C2×D11—42no—
356C2×D11—42no—
357C2×D11—42no—
358C2×D11—81no—
359C2×D11—81no—
360C2×D11—81no—
361C2×D11—81no—
362C4×C11—22no—
363C4×C11—22no—
364C4×C11—41no—
365C4×C11—41no—
366C4×C11—41no—
367C4×C11—81no—
368C4×C11—81no—
369C4×C11—81no—
370C4×C11—81no—
371C4×C11#54711yescharacteristic
372C4×C11#54811yescharacteristic
373C4×C11#55211yescharacteristic
374C4×C11#55611yescharacteristic
375Dic11—42no—
376Dic11—81no—
377Dic11—81no—
378C22×Q8—21no—
379C22×D4—111no—
380C22×D4—221no—
381C23×C4—221no—
382C23×C4C22×D1111yescharacteristic
383C22×C8—111no—
384C22×C8—111no—
385C22×C8—111no—
386C22×C8—111no—
387C4⋊Q8—22no—
388C4⋊Q8—22no—
389#121—222no—
390#121—222no—
391C4×D4—222no—
392C4×D4—222no—
393#117—22no—
394#117—22no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4C22⋊D1111yescharacteristic
403C2×C4⋊C4C22⋊D1111yescharacteristic
404C2×C4⋊C4C22×D1111yescharacteristic
405C2×C4⋊C4C22×D1111yescharacteristic
406C2×C4⋊C4C22×D1111yescharacteristic
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—221no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4C22⋊D1111yescharacteristic
416C2×C22⋊C4C22⋊D1111yescharacteristic
417C2×C42—221no—
418C2×C42C22×D1111yescharacteristic
419C2×C42C22×D1111yescharacteristic
420#107—222no—
421#106—222no—
422#106—222no—
423#106—222no—
424C4⋊C8—114no—
425C4⋊C8—222no—
426#102—222no—
427#102—222no—
428#102—222no—
429#102—222no—
430C22⋊C8—222no—
431C22⋊C8—222no—
432#97—222no—
433C4×C8—222no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—21no—
440#95—221no—
441#95—221no—
442#95—221no—
443C2×C11—81no—
444C2×C11#241511yescharacteristic
445C2×C11#305711yescharacteristic
446C2×C11#306211yescharacteristic
447C2×C11#311811yescharacteristic
448C2×C11#312511yescharacteristic
449C2×C11#324111yescharacteristic
450C2×C11#324411yescharacteristic
451D11—82no—
452C24—221no—
453C24C2×C22⋊D1111yescharacteristic
454C2×Q8—42no—
455C2×Q8—81no—
456C2×Q8—81no—
457C2×D4—112no—
458C2×D4—224no—
459C2×D4—221no—
460C2×D4—221no—
461C2×D4—221no—
462C2×D4—221no—
463C2×D4—221no—
464C2×D4—881no—
465C2×D4—881no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—442no—
480C22×C4—881no—
481C22×C4—881no—
482C22×C4C2×C22⋊D1111yescharacteristic
483C22×C4C2×C22⋊D1111yescharacteristic
484C22×C4C2×C22⋊D1111yescharacteristic
485C22×C4C2×C22⋊D1111yescharacteristic
486C22×C4C2×C22⋊D1111yescharacteristic
487C22×C4C23×D1111yescharacteristic
488C2×C8—112no—
489C2×C8—112no—
490C2×C8—221no—
491C2×C8—221no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—221no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—42no—
511C4⋊C4—81no—
512C4⋊C4—81no—
513C4⋊C4—112no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—881no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—81no—
523C22⋊C4—81no—
524C22⋊C4—224no—
525C22⋊C4—442no—
526C22⋊C4—881no—
527C22⋊C4—881no—
528C22⋊C4—881no—
529C42—21no—
530C42—21no—
531C42—881no—
532C42D4×D1112yes—
533C42#434112yes—
534C11#2471611yescharacteristic, complemented, Sylow
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—222no—
543C23—441no—
544C23—441no—
545C23—441no—
546C23—441no—
547C23—441no—
548C23—441no—
549C23C22×C22⋊D1111yescharacteristic
550Q8—84no—
551D4—222no—
552D4—222no—
553D4—441no—
554D4—441no—
555D4—884no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—222no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—884no—
595C2×C4#6699212yes—
596C2×C4#6699212yes—
597C2×C4C2×D4×D1111yescharacteristic
598C2×C4C2×#434111yescharacteristic
599C2×C4#6704011yescharacteristic
600C2×C4#6704011yescharacteristic
601C2×C4#41×D1111yescharacteristic
602C2×C4#41×D1111yescharacteristic
603C8—222no—
604C8—222no—
605C8—441no—
606C8—441no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—442no—
615C22—442no—
616C22—442no—
617C22—881no—
618C22—881no—
619C22—881no—
620C22—881no—
621C22C2×#6699211yescharacteristic
622C22#1062334711yescharacteristic
623C22#1062335911yescharacteristic
624C22#1062336611yescharacteristic
625C22#1062336711yescharacteristic
626C22#1062336811yescharacteristic
627C22#1062336811yescharacteristic
628C4—22no—
629C4—22no—
630C4—41no—
631C4—41no—
632C4—41no—
633C4—81no—
634C4—81no—
635C4—81no—
636C4—81no—
637C4—442no—
638C4—881no—
639C4—881no—
640C4#1062316211yescharacteristic
641C4#1062316411yescharacteristic
642C4#1062317011yescharacteristic
643C4#1062317211yescharacteristic
644C2—81no—
645C2—882no—
646C2#1307204611yescharacteristic
647C2#1307825711yescharacteristic
648C2#1307829211yescharacteristic
649C2#1307879411yescharacteristic
650C2#1307888711yescharacteristic
651C2#1307986911yescharacteristic
652C2#1307991411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2628C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#2628D11
hypocenterC11#24716
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2628

Complements

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

NH ≅ G/Ntype
1. C2×#10622697C2semidirect
2. C2×#10622613C2semidirect
4. #13070053C2semidirect
5. #13070052C2semidirect
8. #13069569C2semidirect
9. #13069382C2semidirect
10. #13069351C2semidirect
11. #13069341C2semidirect
12. #13069312C2semidirect
13. #13069298C2semidirect
14. #13068623C2semidirect
15. C11×#2628C2semidirect
123. C4⋊(C11⋊C8)D4semidirect
211. #2628D11semidirect
534. C11#24716semidirect

Maximal subgroups

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

subgroupindex
C2×#106226972
C2×#106226132
#130713092
#130700532
#130700522
#130698052
#130697982
#130695692
#130693822
#130693512
#130693412
#130693122
#130692982
#130686232
C11×#26282
#2471611