Finite Group Databasebeta

← #14822291

Subgroups — #14822291

Order 2816.

832 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
1#13073134C211yesmaximal, characteristic, complemented
2#13071678C211yesmaximal, characteristic
3#13070021C211yesmaximal, characteristic, complemented
4#13070001C211yesmaximal, characteristic, complemented
5#13069849C211yesmaximal, characteristic
6#13069849C211yesmaximal, characteristic
7#13069296C211yesmaximal, characteristic, complemented
8#13069239C211yesmaximal, characteristic, complemented
9#13069190C211yesmaximal, characteristic, complemented
10#13069189C211yesmaximal, characteristic, complemented
11#13069176C211yesmaximal, characteristic, complemented
12#13068860C211yesmaximal, characteristic, complemented
13#13068616C211yesmaximal, characteristic, complemented
14#13068430C211yesmaximal, characteristic, complemented
15C11×#1862C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66993C2211yescharacteristic
18C2×C4×C22⋊D11—21no—
19C2×#66946C2211yescharacteristic
20C2×#66943—21no—
21C2×C11×#107C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C11×#389C2211yescharacteristic
25#10622834C2211yescharacteristic
26C2×#66896C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28#10622826—21no—
29C2×#66885C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32#10622599—21no—
33#10622598C2211yescharacteristic
34#10622598C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37#10622586C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41#10622570—21no—
42#10622569—21no—
43#10622552C2211yescharacteristic
44#10622548C2211yescharacteristic
45C4×Dic11⋊C4C2211yescharacteristic
46C2×C4⋊(C11⋊C8)C2211yescharacteristic
47#10622274—21no—
48#10622267—21no—
49C11×#340C2211yescharacteristic
50C11×#336C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C22×C22⋊D11—21no—
62C22×C22⋊D11—21no—
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C4×D4×C11—22no—
68C4×D4×C11—41no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—21no—
74C2×C42×C11C2311yescharacteristic
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77#66993—22no—
78#66993—22no—
79C4×C22⋊D11—44no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4D411yescharacteristic
92C2×Dic11⋊C4D411yescharacteristic
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11C2311yescharacteristic
96C2×C4×Dic11C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99#66946—22no—
100#66946—41no—
101#66943—44no—
102C11×#107—22no—
103C11×#102—22no—
104C11×#102—41no—
105C11×#95—21no—
106#66896—22no—
107#66896—22no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95D411yescharacteristic
114C11⋊#95D411yescharacteristic
115#66885—22no—
116#66885—22no—
117C8×Dic11—41no—
118#66873—22no—
119#66873—41no—
120#66871—22no—
121C4⋊(C11⋊C8)—41no—
122#26752—111nomaximal, Sylow
123C24×C11—21no—
124C23×D11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11#4112yes—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—42no—
135C22×C4×C11—42no—
136C22×C4×C11—81no—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C2×C22⋊D11—24no—
141C2×C22⋊D11—24no—
142C2×C22⋊D11—42no—
143C2×C22⋊D11—42no—
144C2×C22⋊D11—81no—
145C2×C22⋊D11—81no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11C2×D411yescharacteristic
150C22×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44#4112yes—
159C2×C4×D11—42no—
160C2×C4×D11—42no—
161C2×C4×D11—81no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—42no—
173C11×C4⋊C4#4112yes—
174C11×C4⋊C4#4112yes—
175C11×C22⋊C4—42no—
176C42×C11—21no—
177C42×C11—21no—
178C22⋊Dic11—42no—
179C22⋊Dic11—81no—
180(C2×D11)⋊C4—42no—
181(C2×D11)⋊C4—42no—
182(C2×D11)⋊C4—81no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—42no—
190C4⋊Dic11—42no—
191C4⋊Dic11—42no—
192C4⋊Dic11—42no—
193Dic11⋊C4—41no—
194Dic11⋊C4—42no—
195Dic11⋊C4D814yes—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C4×Dic11—42no—
201C4×Dic11—42no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208#2506—111no—
209#2366—111no—
210#2071—111no—
211#2067—111no—
212#2041—111no—
213#2041—111no—
214#1934—111no—
215#1925—111no—
216#1918—111no—
217#1918—111no—
218#1916—111no—
219#1862—111no—
220#1862D1111yescharacteristic, complemented
221#1802—111no—
222C4×#102—111no—
223C23×C11—22no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11C22×D411yescharacteristic
231C22×D11—22no—
232C22×D11—41no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—41no—
238D4×C11—22no—
239D4×C11—22no—
240D4×C11—41no—
241D4×C11—41no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—22no—
245C2×C4×C11—21no—
246C2×C4×C11—22no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
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—84no—
257C2×C4×C11C2×D812yes—
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11H(5,𝔽2)11yescharacteristic
263C2×C4×C112−1+411yescharacteristic
264C22⋊D11—48no—
265C22⋊D11—84no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
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—41no—
285C2×Dic11C2×D812yes—
286C2×Dic11C2×D812yes—
287D44—22no—
288D44—22no—
289D44—41no—
290D44—41no—
291C4×D11—84no—
292C8×C11—41no—
293C8×C11—41no—
294C11⋊C8—41no—
295C11⋊C8—41no—
296C2×#127—111no—
297C2×#125—221no—
298C2×C4×D4—111no—
299C2×C4×D4—221no—
300C2×C4×D4C2×D1111yescharacteristic
301C2×#107—111no—
302C2×#107C2×D1111yescharacteristic
303C2×C4⋊C8—111no—
304C2×#102—111no—
305C2×#102—111no—
306C2×#102—111no—
307C2×#102—111no—
308C2×#102—111no—
309C2×#102—111no—
310C2×#102C2×D1111yescharacteristic
311C2×#102C2×D1111yescharacteristic
312C2×C4×C8—111no—
313#400—221no—
314#398—221no—
315#390—111no—
316#390—111no—
317#390—221no—
318#389—111no—
319#389—111no—
320#389—111no—
321#389C2×D1111yescharacteristic
322#387—221no—
323#386—221no—
324#386—221no—
325#384—111no—
326C4×C4⋊C4—111no—
327C4×C4⋊C4—111no—
328C4×C4⋊C4—111no—
329#340—111no—
330#340—111no—
331#340—111no—
332#340—111no—
333#340—111no—
334#340C2×D1111yescharacteristic
335#336—111no—
336#336—111no—
337#336—111no—
338#336C2×D1111yescharacteristic
339C22×C11—42no—
340C22×C11—42no—
341C22×C11—42no—
342C22×C11—81no—
343C22×C11—81no—
344C22×C11—81no—
345C22×C11—81no—
346C22×C11#52511yescharacteristic
347C22×C11#54611yescharacteristic
348C22×C11#54811yescharacteristic
349C22×C11C22×D811yescharacteristic
350C22×C11#57511yescharacteristic
351C22×C11#57711yescharacteristic
352C22×C11#57711yescharacteristic
353C2×D11—42no—
354C2×D11—42no—
355C2×D11—42no—
356C2×D11—81no—
357C2×D11—81no—
358C2×D11—81no—
359C2×D11—81no—
360C4×C11—22no—
361C4×C11—42no—
362C4×C11—42no—
363C4×C11—41no—
364C4×C11—81no—
365C4×C11#52911yescharacteristic
366C4×C11#53911yescharacteristic
367C4×C11#55211yescharacteristic
368C4×C11#55311yescharacteristic
369Dic11—22no—
370Dic11—22no—
371Dic11—41no—
372Dic11—41no—
373Dic11—81no—
374Dic11—81no—
375Dic11—81no—
376C22×D4—111no—
377C22×D4—221no—
378C22×D4—221no—
379C22×D4C22×D1111yescharacteristic
380C23×C4—21no—
381C23×C4—221no—
382C22×C8—111no—
383C22×C8—111no—
384C22×C8C22×D1111yescharacteristic
385C22×C8C22×D1111yescharacteristic
386#127—222no—
387#127—222no—
388#125—444no—
389C4×D4—22no—
390C4×D4—41no—
391C4×D4—222no—
392C4×D4—441no—
393C4×D4—444no—
394C2×C4⋊C4—21no—
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⋊C4—221no—
405C2×C4⋊C4C22×D1111yescharacteristic
406C2×C4⋊C4C22×D1111yescharacteristic
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—221no—
410C2×C22⋊C4—221no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C22⋊C4—221no—
414C2×C42—111no—
415C2×C42—111no—
416C2×C42—221no—
417C2×C42—221no—
418C2×C42C22×D1111yescharacteristic
419#107—22no—
420#107—222no—
421C4⋊C8—441no—
422#102—22no—
423#102—41no—
424#102—222no—
425#102—222no—
426#102—222no—
427#102—222no—
428#102—222no—
429#102—441no—
430C4×C8—441no—
431#95—21no—
432#95—111no—
433#95—111no—
434#95—221no—
435#95—221no—
436#95—221no—
437#95—221no—
438#95—221no—
439C2×C11—82no—
440C2×C11#246011yescharacteristic
441C2×C11#310011yescharacteristic
442C2×C11#312311yescharacteristic
443C2×C11#329411yescharacteristic
444C2×C11#331711yescharacteristic
445C2×C11#335811yescharacteristic
446C2×C11#337111yescharacteristic
447D11—82no—
448C24—21no—
449C24—221no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—112no—
456C2×D4—224no—
457C2×D4—224no—
458C2×D4—221no—
459C2×D4—221no—
460C2×D4—221no—
461C2×D4—221no—
462C2×D4—221no—
463C2×D4—442no—
464C2×D4—442no—
465C2×D4—881no—
466C2×D4—881no—
467C2×D4#434312yes—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—81no—
474C22×C4—111no—
475C22×C4—111no—
476C22×C4—111no—
477C22×C4—111no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—442no—
482C22×C4—442no—
483C22×C4—881no—
484C22×C4D4×D1111yescharacteristic
485C22×C4D4×D1111yescharacteristic
486C22×C4C23×D1111yescharacteristic
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—221no—
494C2×C8—221no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—42no—
504C4⋊C4—114no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—441no—
512C4⋊C4—442no—
513C4⋊C4—442no—
514C4⋊C4—442no—
515C4⋊C4—442no—
516C4⋊C4—442no—
517C4⋊C4#433912yes—
518C4⋊C4#434112yes—
519C22⋊C4—42no—
520C22⋊C4—442no—
521C22⋊C4—442no—
522C22⋊C4—442no—
523C22⋊C4—881no—
524C22⋊C4—881no—
525C42—21no—
526C42—21no—
527C42—221no—
528C42—221no—
529C42—221no—
530C42—221no—
531C42—442no—
532C42—442no—
533C11#2675211yescharacteristic, complemented, Sylow
534C23—22no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—222no—
542C23—441no—
543C23—441no—
544C23—441no—
545C23—441no—
546C23—441no—
547C23—441no—
548C23C2×D4×D1111yescharacteristic
549D4—22no—
550D4—22no—
551D4—41no—
552D4—41no—
553D4—222no—
554D4—222no—
555D4—448no—
556D4—441no—
557D4—441no—
558D4—884no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—84no—
574C2×C4—112no—
575C2×C4—112no—
576C2×C4—221no—
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—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—884no—
596C2×C4D8×D1112yes—
597C2×C4C2×#433911yescharacteristic
598C2×C4C2×#434111yescharacteristic
599C2×C4#6703711yescharacteristic
600C2×C4C2×#434311yescharacteristic
601C2×C4#41×D1111yescharacteristic
602C2×C4#6704311yescharacteristic
603C8—41no—
604C8—41no—
605C8—441no—
606C8—441no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—442no—
615C22—442no—
616C22—442no—
617C22—881no—
618C22—881no—
619C22—881no—
620C22—881no—
621C22#1062308311yescharacteristic
622C22#1062312211yescharacteristic
623C22#1062315811yescharacteristic
624C22C2×D8×D1111yescharacteristic
625C22#1062330111yescharacteristic
626C22#1062330611yescharacteristic
627C22#1062330811yescharacteristic
628C4—22no—
629C4—42no—
630C4—41no—
631C4—42no—
632C4—81no—
633C4—222no—
634C4—222no—
635C4—441no—
636C4—441no—
637C4—881no—
638C4—881no—
639C4—881no—
640C4#1062304511yescharacteristic
641C4#1062308811yescharacteristic
642C4#1062317311yescharacteristic
643C4#1062319111yescharacteristic
644C2—82no—
645C2—882no—
646C2#1307257511yescharacteristic
647C2#1307861811yescharacteristic
648C2#1307887011yescharacteristic
649C2#1308042211yescharacteristic
650C2#1308073511yescharacteristic
651C2#1308124911yescharacteristic
652C2#1308138911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1862C2
socleC23×C11C22×D4
prime radicalC2×#66993C22
hypercenter#1862D11
hypocenterC11#26752
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1862

Complements

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

NH ≅ G/Ntype
1. #13073134C2semidirect
3. #13070021C2semidirect
4. #13070001C2semidirect
7. #13069296C2semidirect
8. #13069239C2semidirect
9. #13069190C2semidirect
10. #13069189C2semidirect
11. #13069176C2semidirect
12. #13068860C2semidirect
13. #13068616C2semidirect
14. #13068430C2semidirect
15. C11×#1862C2semidirect
220. #1862D11semidirect
533. C11#26752semidirect

Maximal subgroups

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

subgroupindex
#130731342
#130716782
#130700212
#130700012
#130698492
#130692962
#130692392
#130691902
#130691892
#130691762
#130688602
#130686162
#130684302
C11×#18622
#2675211