Finite Group Databasebeta

← #14795173

Subgroups — #14795173

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×#10622483C211yesmaximal, characteristic, complemented
2C2×#10622333C211yesmaximal, characteristic, complemented
3#13074441C211yesmaximal, characteristic, complemented
4#13071305C211yesmaximal, characteristic
5#13070052C211yesmaximal, characteristic, complemented
6#13069805C211yesmaximal, characteristic
7#13069799C211yesmaximal, characteristic
8#13069566C211yesmaximal, characteristic, complemented
9#13069387C211yesmaximal, characteristic, complemented
10#13069352C211yesmaximal, characteristic, complemented
11#13069343C211yesmaximal, characteristic, complemented
12#13069314C211yesmaximal, characteristic, complemented
13#13069297C211yesmaximal, characteristic, complemented
14#13068625C211yesmaximal, characteristic, complemented
15C11×#2077C211yesmaximal, characteristic, complemented
16C2×#66983C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C2×#66946C2211yescharacteristic
19C2×#66941C2211yescharacteristic
20C2×C11×#106C2211yescharacteristic
21C2×C11×C22⋊C8C2211yescharacteristic
22C11×#380C2211yescharacteristic
23C11×#380C2211yescharacteristic
24#10622825C2211yescharacteristic
25C2×C22⋊(C11⋊C8)C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29C2×#66879C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32C2×C8×Dic11C2211yescharacteristic
33#10622601C2211yescharacteristic
34#10622598C2211yescharacteristic
35#10622590C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37#10622586C2211yescharacteristic
38#10622586C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43#10622570—21no—
44#10622569—21no—
45#10622562—21no—
46#10622560—21no—
47#10622483—24no—
48#10622333—24no—
49#10622283—21no—
50#10622281—21no—
51#10622273—21no—
52#10622269—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×Dic22—21no—
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—21no—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11D411yescharacteristic
76C2×C22⋊Dic11D411yescharacteristic
77#66983—22no—
78#66983—22no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83#66979—22no—
84#66979—22no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11D411yescharacteristic
87C2×C4⋊Dic11D411yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11C2311yescharacteristic
96C2×C4×Dic11C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99#66946—22no—
100#66946—22no—
101#66941—22no—
102#66941—22no—
103C11×#106—22no—
104C11×C22⋊C8—22no—
105C11×#95—21no—
106C11×#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C22⋊(C11⋊C8)—22no—
115#66885—22no—
116#66885—22no—
117#66882—22no—
118#66879—22no—
119Dic11⋊C8—22no—
120Dic11⋊C8D414yescomplemented
121C8×Dic11—22no—
122#66873—22no—
123#66873—22no—
124#66872—22no—
125#66872—22no—
126#24716—111nomaximal, Sylow
127C24×C11C2×D411yescharacteristic
128C23×D11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
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×C11C2×D411yescharacteristic
140C22×C4×C11C2411yescharacteristic
141C2×C22⋊D11—24no—
142C2×C22⋊D11—81no—
143C2×C22⋊D11—81no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11C2×D411yescharacteristic
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C22×Dic11C2×D411yescharacteristic
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44#4112yes—
157C2×C4×D11—42no—
158C2×C4×D11—81no—
159C2×C4×D11—81no—
160C2×Dic22—42no—
161C2×Dic22—81no—
162C2×Dic22—81no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11C2×D412yes—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C22⋊C4—81no—
178C11×C22⋊C4—81no—
179C22⋊Dic11—22no—
180C22⋊Dic11—22no—
181C22⋊Dic11—81no—
182(C2×D11)⋊C4—24no—
183(C2×D11)⋊C4—42no—
184(C2×D11)⋊C4—81no—
185(C2×D11)⋊C4—81no—
186C4⋊Dic11—22no—
187C4⋊Dic11—22no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—81no—
194C4⋊Dic11#4112yes—
195Dic11⋊C4—42no—
196Dic11⋊C4—81no—
197Dic11⋊C4—81no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C4×Dic11—81no—
201C4×Dic11C2×D412yes—
202C4×Dic11#4112yes—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8C2×D412yes—
209C2×#476—111no—
210C2×#433—111no—
211#2628—111no—
212#2324—111no—
213#2077—111no—
214#2077D1111yescharacteristic, complemented
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—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C112−1+411yescharacteristic
263C2×C4×C112−1+411yescharacteristic
264C22⋊D11—84no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—22no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11#12112yes—
285C2×Dic11#12112yes—
286D44—22no—
287D44—22no—
288D44—41no—
289D44—41no—
290C4×D11—84no—
291Dic22—84no—
292C8×C11—22no—
293C8×C11—41no—
294C11⋊C8—22no—
295C11⋊C8—41no—
296C2×C4⋊Q8—111no—
297C2×#121—111no—
298C2×C4×D4—111no—
299C2×#117—111no—
300#476—224no—
301#433—224no—
302C2×#107—111no—
303C2×#106—111no—
304C2×#106—111no—
305C2×#106C2×D1111yescharacteristic
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⋊C8C2×D1111yescharacteristic
314C2×#97—111no—
315C2×C4×C8—111no—
316#400—221no—
317#399—221no—
318#395—221no—
319#393—221no—
320#390—111no—
321#390—221no—
322#389—111no—
323#389—111no—
324#389—111no—
325#388—221no—
326#386—221no—
327#385—221no—
328#382—111no—
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#340C2×D1111yescharacteristic
339#340C2×D1111yescharacteristic
340#340C2×D1111yescharacteristic
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—41no—
363C4×C11—81no—
364C4×C11—81no—
365C4×C11—81no—
366C4×C11—81no—
367C4×C11#54711yescharacteristic
368C4×C11#54811yescharacteristic
369C4×C11#55211yescharacteristic
370C4×C11#55611yescharacteristic
371Dic11—22no—
372Dic11—22no—
373Dic11—42no—
374Dic11—41no—
375Dic11—41no—
376Dic11—81no—
377Dic11—81no—
378C22×Q8—221no—
379C22×D4—111no—
380C22×D4—221no—
381C23×C4—221no—
382C23×C4C22×D1111yescharacteristic
383C22×C8—111no—
384C22×C8—111no—
385C22×C8C22×D1111yescharacteristic
386C22×C8C22×D1111yescharacteristic
387C4⋊Q8—222no—
388C4⋊Q8—222no—
389#121—222no—
390#121—222no—
391C4×D4—222no—
392C4×D4—222no—
393#117—222no—
394#117—222no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
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—111no—
411C2×C22⋊C4—111no—
412C2×C22⋊C4—221no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4—221no—
416C2×C22⋊C4—221no—
417C2×C42—111no—
418C2×C42—111no—
419C2×C42—221no—
420#107—222no—
421#106—22no—
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—22no—
431C22⋊C8—222no—
432#97—222no—
433C4×C8—222no—
434#95—21no—
435#95—21no—
436#95—221no—
437#95—221no—
438#95—221no—
439#95—221no—
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—
453C24D4×D1111yescharacteristic
454C2×Q8—442no—
455C2×Q8—881no—
456C2×Q8—881no—
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—111no—
477C22×C4—111no—
478C22×C4—111no—
479C22×C4—111no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—442no—
484C22×C4—881no—
485C22×C4—881no—
486C22×C4D4×D1111yescharacteristic
487C22×C4C23×D1111yescharacteristic
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—112no—
494C2×C8—221no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8D4×D1112yes—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—112no—
509C4⋊C4—222no—
510C4⋊C4—222no—
511C4⋊C4—221no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—442no—
517C4⋊C4—881no—
518C4⋊C4—881no—
519C4⋊C4—881no—
520C22⋊C4—81no—
521C22⋊C4—81no—
522C22⋊C4—224no—
523C22⋊C4—222no—
524C22⋊C4—222no—
525C22⋊C4—442no—
526C22⋊C4—881no—
527C22⋊C4—881no—
528C22⋊C4—881no—
529C42—112no—
530C42—112no—
531C42—221no—
532C42—221no—
533C42—881no—
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—
549C23C2×D4×D1111yescharacteristic
550Q8—884no—
551D4—222no—
552D4—222no—
553D4—441no—
554D4—441no—
555D4—884no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—112no—
576C2×C4—112no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—221no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—221no—
587C2×C4—222no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—884no—
597C2×C4C2×D4×D1111yescharacteristic
598C2×C4#41×D1111yescharacteristic
599C2×C4#41×D1111yescharacteristic
600C2×C4#41×D1111yescharacteristic
601C2×C4#6704311yescharacteristic
602C2×C4#6704311yescharacteristic
603C8—22no—
604C8—41no—
605C8—222no—
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—
621C22D11×#12111yescharacteristic
622C22#1062317911yescharacteristic
623C22#1062318711yescharacteristic
624C22#1062329311yescharacteristic
625C22#1062330011yescharacteristic
626C22#1062330611yescharacteristic
627C22#1062330911yescharacteristic
628C4—41no—
629C4—81no—
630C4—81no—
631C4—81no—
632C4—81no—
633C4—222no—
634C4—222no—
635C4—441no—
636C4—442no—
637C4—441no—
638C4—881no—
639C4—881no—
640C4#1062318611yescharacteristic
641C4#1062320811yescharacteristic
642C4#1062323311yescharacteristic
643C4#1062323911yescharacteristic
644C2—81no—
645C2—882no—
646C2#1307204011yescharacteristic
647C2#1307825311yescharacteristic
648C2#1307828911yescharacteristic
649C2#1307880311yescharacteristic
650C2#1307889611yescharacteristic
651C2#1307987511yescharacteristic
652C2#1307991811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2077C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#2077D11
hypocenterC11#24716
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2077

Complements

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

NH ≅ G/Ntype
1. C2×#10622483C2semidirect
2. C2×#10622333C2semidirect
3. #13074441C2semidirect
5. #13070052C2semidirect
8. #13069566C2semidirect
9. #13069387C2semidirect
10. #13069352C2semidirect
11. #13069343C2semidirect
12. #13069314C2semidirect
13. #13069297C2semidirect
14. #13068625C2semidirect
15. C11×#2077C2semidirect
120. Dic11⋊C8D4semidirect
214. #2077D11semidirect
534. C11#24716semidirect

Maximal subgroups

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

subgroupindex
C2×#106224832
C2×#106223332
#130744412
#130713052
#130700522
#130698052
#130697992
#130695662
#130693872
#130693522
#130693432
#130693142
#130692972
#130686252
C11×#20772
#2471611