Finite Group Databasebeta

← #14817343

Subgroups — #14817343

Order 2816.

802 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072301C211yesmaximal, characteristic, complemented
2#13071658C211yesmaximal, characteristic
3#13070189C211yesmaximal, characteristic, complemented
4#13070116C211yesmaximal, characteristic, complemented
5#13069988C211yesmaximal, characteristic, complemented
6#13069750C211yesmaximal, characteristic, complemented
7#13069566C211yesmaximal, characteristic, complemented
8#13069207C211yesmaximal, characteristic, complemented
9#13069045C211yesmaximal, characteristic
10#13068865C211yesmaximal, characteristic, complemented
11#13068817C211yesmaximal, characteristic, complemented
12#13068793C211yesmaximal, characteristic, complemented
13#13068624C211yesmaximal, characteristic, complemented
14#13068332C211yesmaximal, characteristic, complemented
15C11×#1875C211yesmaximal, characteristic
16C2×C11×#121C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C23×C11⋊C8C2211yescharacteristic
21C2×#66941C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25#10622834—21no—
26#10622834C2211yescharacteristic
27#10622833—21no—
28C2×#66896C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30#10622825C2211yescharacteristic
31C4×C22⋊Dic11C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36#10622598C2211yescharacteristic
37#10622598C2211yescharacteristic
38#10622590C2211yescharacteristic
39C4⋊C4×Dic11C2211yescharacteristic
40#10622586C2211yescharacteristic
41#10622564—21no—
42#10622561—21no—
43#10622560—21no—
44C22⋊C4×Dic11—21no—
45#10622546—21no—
46#10622542—21no—
47C11×#340C2211yescharacteristic
48C11×#340C2211yescharacteristic
49#10622189C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×D4×C11—21no—
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×Dic11—21no—
63C22×Dic22—21no—
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C11×#121—22no—
67C11×#121Q814yescomplemented
68C11×#117—22no—
69C11×#117—41no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C42×C11—21no—
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11D411yescharacteristic
82C2×C22⋊Dic11D411yescharacteristic
83D4×Dic11—22no—
84D4×Dic11—41no—
85#66979—22no—
86#66979—41no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11C2311yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8—22no—
100C22×C11⋊C8—41no—
101C22×C11⋊C8—41no—
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104#66941—22no—
105#66941—41no—
106C11×#102—22no—
107C11×#102—41no—
108C11×C22⋊C8—22no—
109#66896—41no—
110#66896—41no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95D411yescharacteristic
119C11⋊#95D411yescharacteristic
120#66882—22no—
121#66881—41no—
122Dic11⋊C8—41no—
123Dic11⋊C8—41no—
124#26409—111nomaximal, Sylow
125C24×C11—21no—
126C24×C11C2×D411yescharacteristic
127C2×D4×C11—24no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—81no—
134C2×D4×C11—81no—
135C2×D4×C11C2×Q812yes—
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×C11—21no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×Q812yes—
145C22×C4×C11#4112yes—
146C22×C4×C11C2411yescharacteristic
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—42no—
152C22×Dic11—42no—
153C22×Dic11—81no—
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C2×Dic22—42no—
159C2×Dic22—42no—
160C2×Dic22—81no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4C2×Q812yes—
172C11×C4⋊C4#4112yes—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—42no—
175C42×C11—42no—
176C22⋊Dic11—22no—
177C22⋊Dic11—41no—
178C22⋊Dic11—42no—
179C22⋊Dic11—42no—
180C22⋊Dic11—42no—
181C22⋊Dic11—81no—
182C22⋊Dic11—81no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—81no—
191C4⋊Dic11—81no—
192C4⋊Dic11#4112yes—
193Dic11⋊C4—42no—
194Dic11⋊C4—42no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11—21no—
199C4×Dic11—42no—
200C4×Dic11—81no—
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⋊C8—44no—
208#2439—111no—
209#2363—111no—
210#2101—111no—
211#2088—111no—
212#2065—111no—
213#2023—111no—
214#1988—111no—
215#1921—111no—
216#1893—111no—
217#1875D1111yescharacteristic
218#1862—111no—
219#1854—111no—
220#1850—111no—
221#1804—111no—
222#1735—111no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—22no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11C22⋊Q812yes—
237C23×C11C22×D411yescharacteristic
238D4×C11—22no—
239D4×C11—22no—
240D4×C11—41no—
241D4×C11—41no—
242D4×C11—84no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
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⋊Q812yes—
259C2×C4×C11C22×Q811yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11H(5,𝔽2)11yescharacteristic
264C2×C4×C11H(5,𝔽2)11yescharacteristic
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—22no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—84no—
289C2×Dic11#13512yes—
290Dic22—84no—
291C8×C11—41no—
292C8×C11—41no—
293C11⋊C8—41no—
294C11⋊C8—41no—
295C23×C8—111no—
296C2×C4⋊Q8—111no—
297C2×#121C2×D1111yescharacteristic
298C2×C4×D4—111no—
299C2×#117—111no—
300C2×#117C2×D1111yescharacteristic
301C2×#107—111no—
302C2×#106—111no—
303C2×C4⋊C8—111no—
304C2×C4⋊C8—111no—
305C2×#102—111no—
306C2×#102—111no—
307C2×#102C2×D1111yescharacteristic
308C2×#102C2×D1111yescharacteristic
309C2×C22⋊C8C2×D1111yescharacteristic
310#396—221no—
311#393—221no—
312#391—221no—
313#390—111no—
314#390—221no—
315#389—111no—
316#389—111no—
317#389—111no—
318#388—221no—
319#387—221no—
320#386—221no—
321#382—111no—
322#380—111no—
323C4×C4⋊C4—111no—
324C4×C22⋊C4—111no—
325C4×C22⋊C4—221no—
326#340—111no—
327#340—111no—
328#340—111no—
329#340—111no—
330#340—111no—
331#340—111no—
332#340—111no—
333#340—111no—
334#340C2×D1111yescharacteristic
335#340C2×D1111yescharacteristic
336#336—111no—
337#336—111no—
338C22×C11—22no—
339C22×C11—22no—
340C22×C11—22no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11—42no—
346C22×C11—42no—
347C22×C11—42no—
348C22×C11—81no—
349C22×C11—81no—
350C22×C11—81no—
351C22×C11—81no—
352C22×C11C2×C22⋊Q811yescharacteristic
353C22×C11#54611yescharacteristic
354C22×C11#54611yescharacteristic
355C22×C11C2×#13511yescharacteristic
356C22×C11#57511yescharacteristic
357C22×C11#57611yescharacteristic
358C22×C11#57711yescharacteristic
359C4×C11—22no—
360C4×C11—42no—
361C4×C11—42no—
362C4×C11—81no—
363C4×C11#52911yescharacteristic
364C4×C11#53811yescharacteristic
365C4×C11#55411yescharacteristic
366C4×C11#55411yescharacteristic
367Dic11—22no—
368Dic11—41no—
369Dic11—41no—
370Dic11—42no—
371Dic11—41no—
372Dic11—81no—
373Dic11—81no—
374Dic11—81no—
375C22×Q8—221no—
376C22×D4—21no—
377C22×D4C22×D1111yescharacteristic
378C23×C4—221no—
379C23×C4C22×D1111yescharacteristic
380C22×C8—111no—
381C22×C8—111no—
382C22×C8—222no—
383C22×C8—441no—
384C22×C8—441no—
385C22×C8C22×D1111yescharacteristic
386C22×C8C22×D1111yescharacteristic
387C4⋊Q8—222no—
388C4⋊Q8—441no—
389#121—22no—
390#121Dic2214yescomplemented
391C4×D4—222no—
392C4×D4—441no—
393#117—22no—
394#117—41no—
395#117—222no—
396#117—441no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
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—21no—
418C2×C42—111no—
419C2×C42—111no—
420C2×C42—221no—
421C2×C42—221no—
422#107—222no—
423#106—441no—
424C4⋊C8—441no—
425C4⋊C8—441no—
426#102—22no—
427#102—41no—
428#102—441no—
429#102—441no—
430C22⋊C8—22no—
431#95—111no—
432#95—111no—
433#95—221no—
434#95—221no—
435#95—221no—
436#95—221no—
437#95—221no—
438#95—221no—
439#95—221no—
440C2×C11—42no—
441C2×C11—82no—
442C2×C11#245011yescharacteristic
443C2×C11#307611yescharacteristic
444C2×C11#308111yescharacteristic
445C2×C11#329711yescharacteristic
446C2×C11#330411yescharacteristic
447C2×C11#331911yescharacteristic
448C2×C11#332111yescharacteristic
449C24—21no—
450C24D4×D1111yescharacteristic
451C2×Q8—442no—
452C2×Q8—442no—
453C2×Q8—881no—
454C2×D4—24no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—81no—
461C2×D4—81no—
462C2×D4C2×Dic2212yes—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—111no—
471C22×C4—111no—
472C22×C4—111no—
473C22×C4—111no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—442no—
479C22×C4—442no—
480C22×C4—881no—
481C22×C4C2×Dic2212yes—
482C22×C4D4×D1111yescharacteristic
483C22×C4#434112yes—
484C22×C4C23×D1111yescharacteristic
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—221no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—221no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8—444no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—112no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—442no—
511C4⋊C4—442no—
512C4⋊C4—881no—
513C4⋊C4—881no—
514C4⋊C4C2×Dic2212yes—
515C4⋊C4#434112yes—
516C22⋊C4—24no—
517C22⋊C4—42no—
518C22⋊C4—222no—
519C22⋊C4—442no—
520C22⋊C4—441no—
521C22⋊C4—442no—
522C22⋊C4—442no—
523C22⋊C4—881no—
524C22⋊C4—881no—
525C42—42no—
526C42—221no—
527C42—221no—
528C42—221no—
529C42—221no—
530C42—442no—
531C42—881no—
532C11#2640911yescharacteristic, complemented, Sylow
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—22no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23#6693112yes—
547C23C2×D4×D1111yescharacteristic
548Q8—884no—
549D4—22no—
550D4—22no—
551D4—41no—
552D4—41no—
553D4—84no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—112no—
570C2×C4—221no—
571C2×C4—221no—
572C2×C4—221no—
573C2×C4—221no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—221no—
581C2×C4—222no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—884no—
594C2×C4#6693112yes—
595C2×C4C22×Dic2211yescharacteristic
596C2×C4C2×#434111yescharacteristic
597C2×C4C2×#434111yescharacteristic
598C2×C4#6703711yescharacteristic
599C2×C4#41×D1111yescharacteristic
600C2×C4#6704211yescharacteristic
601C8—41no—
602C8—41no—
603C8—441no—
604C8—441no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—42no—
613C22—42no—
614C22—42no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—81no—
619C22C2×#6693111yescharacteristic
620C22#1062312211yescharacteristic
621C22#1062318511yescharacteristic
622C22D11×#13511yescharacteristic
623C22#1062329911yescharacteristic
624C22#1062330511yescharacteristic
625C22#1062330611yescharacteristic
626C4—22no—
627C4—42no—
628C4—42no—
629C4—81no—
630C4—222no—
631C4—441no—
632C4—442no—
633C4—441no—
634C4—441no—
635C4—881no—
636C4—881no—
637C4—881no—
638C4#1062307011yescharacteristic
639C4#1062307411yescharacteristic
640C4#1062313111yescharacteristic
641C4#1062314811yescharacteristic
642C2—42no—
643C2—82no—
644C2#1307244411yescharacteristic
645C2#1307840011yescharacteristic
646C2#1307844911yescharacteristic
647C2#1308045911yescharacteristic
648C2#1308055311yescharacteristic
649C2#1308077011yescharacteristic
650C2#1308080611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1875C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenter#1875D11
hypocenterC11#26409
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1875

Complements

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

NH ≅ G/Ntype
1. #13072301C2semidirect
3. #13070189C2semidirect
4. #13070116C2semidirect
5. #13069988C2semidirect
6. #13069750C2semidirect
7. #13069566C2semidirect
8. #13069207C2semidirect
10. #13068865C2semidirect
11. #13068817C2semidirect
12. #13068793C2semidirect
13. #13068624C2semidirect
14. #13068332C2semidirect
67. C11×#121Q8semidirect
390. #121Dic22semidirect
532. C11#26409semidirect

Maximal subgroups

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

subgroupindex
#130723012
#130716582
#130701892
#130701162
#130699882
#130697502
#130695662
#130692072
#130690452
#130688652
#130688172
#130687932
#130686242
#130683322
C11×#18752
#2640911