Finite Group Databasebeta

← #14853533

Subgroups — #14853533

Order 2816.

754 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074595C211yesmaximal, characteristic, complemented
2#13071338C211yesmaximal, characteristic
3#13070189C211yesmaximal, characteristic, complemented
4#13070187C211yesmaximal, characteristic, complemented
5#13069849C211yesmaximal, characteristic
6#13069849C211yesmaximal, characteristic
7#13069311C211yesmaximal, characteristic, complemented
8#13069310C211yesmaximal, characteristic, complemented
9#13069297C211yesmaximal, characteristic, complemented
10#13069296C211yesmaximal, characteristic, complemented
11#13068623C211yesmaximal, characteristic, complemented
12#13068617C211yesmaximal, characteristic, complemented
13#13068616C211yesmaximal, characteristic, complemented
14#13068475C211yesmaximal, characteristic, complemented
15C11×#1804C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66993C2211yescharacteristic
18C2×C4×D44C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×#102C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C11×#382C2211yescharacteristic
23#10622834C2211yescharacteristic
24C2×#66896C2211yescharacteristic
25C2×#66896C2211yescharacteristic
26#10622826—21no—
27#10622826—21no—
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66879C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32#10622601C2211yescharacteristic
33#10622598C2211yescharacteristic
34#10622598C2211yescharacteristic
35#10622590C2211yescharacteristic
36#10622586C2211yescharacteristic
37#10622586C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40#10622569—21no—
41#10622569—21no—
42#10622548C2211yescharacteristic
43#10622545C2211yescharacteristic
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45#10622274—21no—
46#10622274—21no—
47#10622273—21no—
48#10622273—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
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—22no—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C22⋊C4—21no—
73C2×C42×C11C2311yescharacteristic
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76#66993—22no—
77#66993—22no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×C4×Dic11C2311yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C4×D44—22no—
95C4×D44—22no—
96C11×C4⋊C8—22no—
97C11×#102—41no—
98C11×#102—41no—
99C11×#95—21no—
100C11×#95—21no—
101#66896—22no—
102#66896—22no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95D411yescharacteristic
110C11⋊#95D411yescharacteristic
111C11⋊#95D411yescharacteristic
112C11⋊#95D411yescharacteristic
113#66885—22no—
114#66885—22no—
115#66879—41no—
116C8×Dic11—41no—
117#66873—41no—
118#66873—41no—
119C4⋊(C11⋊C8)—22no—
120#29133—111nomaximal, Sylow
121C24×C11—21no—
122C23×D11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11#4112yes—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—42no—
133C22×C4×C11—81no—
134C22×C4×C11—81no—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2411yescharacteristic
138C2×C22⋊D11—24no—
139C2×C22⋊D11—24no—
140C2×C22⋊D11—81no—
141C2×C22⋊D11—81no—
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×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—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×C22⋊C4—42no—
173C42×C11#4112yes—
174C42×C11#4112yes—
175C22⋊Dic11—81no—
176C22⋊Dic11—81no—
177(C2×D11)⋊C4—42no—
178(C2×D11)⋊C4—81no—
179(C2×D11)⋊C4—81no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—81no—
187C4⋊Dic11—81no—
188C4⋊Dic11—81no—
189C4⋊Dic11—81no—
190Dic11⋊C4—81no—
191Dic11⋊C4—81no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202#2647—111no—
203#2328—111no—
204#2101—111no—
205#2101—111no—
206#2041—111no—
207#2041—111no—
208#1936—111no—
209#1936—111no—
210#1934—111no—
211#1934—111no—
212#1804—111no—
213#1804D1111yescharacteristic, complemented
214#1802—111no—
215#1802—111no—
216#1768—111no—
217C23×C11—22no—
218C23×C11—41no—
219C23×C11—41no—
220C23×C11—41no—
221C23×C11—41no—
222C23×C11—41no—
223C23×C11—41no—
224C23×C11C22×D411yescharacteristic
225C22×D11—22no—
226C22×D11—41no—
227C22×D11—41no—
228C22×D11—41no—
229C22×D11—41no—
230C22×D11—41no—
231C22×D11—41no—
232D4×C11—22no—
233D4×C11—22no—
234D4×C11—41no—
235D4×C11—41no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
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—84no—
250C2×C4×C11#12412yes—
251C2×C4×C11#12412yes—
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11H(5,𝔽2)11yescharacteristic
257C2×C4×C112−1+411yescharacteristic
258C22⋊D11—84no—
259C22⋊D11—84no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281D44—22no—
282D44—22no—
283D44—41no—
284D44—41no—
285C4×D11—84no—
286C8×C11—41no—
287C8×C11—41no—
288C11⋊C8—41no—
289C11⋊C8—41no—
290C2×#127—111no—
291C2×C4×D4—111no—
292C2×C4×D4C2×D1111yescharacteristic
293C2×C4⋊C8—111no—
294C2×C4⋊C8C2×D1111yescharacteristic
295C2×#102—111no—
296C2×#102—111no—
297C2×#102—111no—
298C2×#102—111no—
299C2×#102—111no—
300C2×#102—111no—
301C2×#102C2×D1111yescharacteristic
302C2×#102C2×D1111yescharacteristic
303C2×#97—111no—
304C2×C4×C8—111no—
305#400—221no—
306#400—221no—
307#398—221no—
308#398—221no—
309#390—111no—
310#390—111no—
311#389—111no—
312#389—111no—
313#389—111no—
314#389—111no—
315#386—221no—
316#386—221no—
317#386—221no—
318#386—221no—
319#384—111no—
320#382—111no—
321#382C2×D1111yescharacteristic
322#376—111no—
323#340—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#340—111no—
328#340—111no—
329#340C2×D1111yescharacteristic
330#340C2×D1111yescharacteristic
331#336—111no—
332#336—111no—
333C22×C11—42no—
334C22×C11—42no—
335C22×C11—42no—
336C22×C11—81no—
337C22×C11—81no—
338C22×C11—81no—
339C22×C11—81no—
340C22×C11#52511yescharacteristic
341C22×C11C2×#12411yescharacteristic
342C22×C11#53711yescharacteristic
343C22×C11#57611yescharacteristic
344C22×C11#57611yescharacteristic
345C22×C11#57711yescharacteristic
346C22×C11#57711yescharacteristic
347C2×D11—42no—
348C2×D11—42no—
349C2×D11—42no—
350C2×D11—81no—
351C2×D11—81no—
352C2×D11—81no—
353C2×D11—81no—
354C4×C11—22no—
355C4×C11—22no—
356C4×C11—81no—
357C4×C11—81no—
358C4×C11—81no—
359C4×C11#55211yescharacteristic
360C4×C11#55211yescharacteristic
361C4×C11#55311yescharacteristic
362C4×C11#55311yescharacteristic
363Dic11—41no—
364Dic11—41no—
365Dic11—41no—
366Dic11—41no—
367Dic11—81no—
368Dic11—81no—
369Dic11—81no—
370C22×D4—111no—
371C22×D4—221no—
372C22×D4—221no—
373C22×D4C22×D1111yescharacteristic
374C23×C4—21no—
375C23×C4—221no—
376C22×C8—111no—
377C22×C8—111no—
378C22×C8C22×D1111yescharacteristic
379C22×C8C22×D1111yescharacteristic
380#127—222no—
381#127—222no—
382C4×D4—22no—
383C4×D4—22no—
384C4×D4—222no—
385C4×D4—222no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4C22×D1111yescharacteristic
396C2×C4⋊C4C22×D1111yescharacteristic
397C2×C4⋊C4C22×D1111yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—221no—
400C2×C22⋊C4—221no—
401C2×C22⋊C4—221no—
402C2×C22⋊C4—221no—
403C2×C22⋊C4—221no—
404C2×C42—111no—
405C2×C42—111no—
406C2×C42C22×D1111yescharacteristic
407C4⋊C8—22no—
408C4⋊C8—222no—
409#102—41no—
410#102—41no—
411#102—222no—
412#102—222no—
413#102—222no—
414#102—222no—
415#102—441no—
416#102—441no—
417#97—441no—
418C4×C8—441no—
419#95—21no—
420#95—21no—
421#95—111no—
422#95—111no—
423#95—111no—
424#95—111no—
425#95—221no—
426#95—221no—
427#95—221no—
428#95—221no—
429#95—221no—
430#95—221no—
431C2×C11—82no—
432C2×C11#256211yescharacteristic
433C2×C11#312211yescharacteristic
434C2×C11#312311yescharacteristic
435C2×C11#313611yescharacteristic
436C2×C11#313611yescharacteristic
437C2×C11#325711yescharacteristic
438C2×C11#325711yescharacteristic
439D11—82no—
440C24—21no—
441C24—221no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—112no—
448C2×D4—224no—
449C2×D4—224no—
450C2×D4—221no—
451C2×D4—221no—
452C2×D4—221no—
453C2×D4—221no—
454C2×D4—221no—
455C2×D4—881no—
456C2×D4—881no—
457C2×D4—881no—
458C2×D4—881no—
459C2×D4#434312yes—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—42no—
464C22×C4—81no—
465C22×C4—81no—
466C22×C4—111no—
467C22×C4—111no—
468C22×C4—111no—
469C22×C4—111no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—442no—
474C22×C4—881no—
475C22×C4—881no—
476C22×C4D4×D1111yescharacteristic
477C22×C4D4×D1111yescharacteristic
478C22×C4C23×D1111yescharacteristic
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—221no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—881no—
504C4⋊C4—881no—
505C4⋊C4—881no—
506C4⋊C4—881no—
507C4⋊C4—881no—
508C4⋊C4—881no—
509C22⋊C4—42no—
510C22⋊C4—442no—
511C22⋊C4—881no—
512C22⋊C4—881no—
513C22⋊C4—881no—
514C22⋊C4—881no—
515C42—221no—
516C42—221no—
517C42—221no—
518C42—221no—
519C42#433912yes—
520C42#434112yes—
521C11#2913311yescharacteristic, complemented, Sylow
522C23—22no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23—222no—
530C23—441no—
531C23—441no—
532C23—441no—
533C23—441no—
534C23—441no—
535C23—441no—
536C23C2×D4×D1111yescharacteristic
537D4—22no—
538D4—22no—
539D4—41no—
540D4—41no—
541D4—222no—
542D4—222no—
543D4—441no—
544D4—441no—
545D4—884no—
546D4—884no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—84no—
561C2×C4—221no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—221no—
570C2×C4—221no—
571C2×C4—221no—
572C2×C4—221no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—884no—
583C2×C4#6693812yes—
584C2×C4#6693812yes—
585C2×C4C2×#433911yescharacteristic
586C2×C4C2×#434111yescharacteristic
587C2×C4#6703711yescharacteristic
588C2×C4C2×#434311yescharacteristic
589C2×C4#41×D1111yescharacteristic
590C2×C4#6704311yescharacteristic
591C8—41no—
592C8—41no—
593C8—441no—
594C8—441no—
595C22—42no—
596C22—42no—
597C22—42no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—442no—
603C22—442no—
604C22—442no—
605C22—881no—
606C22—881no—
607C22—881no—
608C22—881no—
609C22C2×#6693811yescharacteristic
610C22#1062313911yescharacteristic
611C22#1062315811yescharacteristic
612C22#1062330011yescharacteristic
613C22#1062330111yescharacteristic
614C22#1062330511yescharacteristic
615C22#1062330611yescharacteristic
616C4—22no—
617C4—22no—
618C4—81no—
619C4—81no—
620C4—81no—
621C4—441no—
622C4—441no—
623C4—441no—
624C4—441no—
625C4—881no—
626C4—881no—
627C4—881no—
628C4#1062304511yescharacteristic
629C4#1062306011yescharacteristic
630C4#1062314511yescharacteristic
631C4#1062317311yescharacteristic
632C2—82no—
633C2—882no—
634C2#1307378111yescharacteristic
635C2#1307886111yescharacteristic
636C2#1307887011yescharacteristic
637C2#1307896611yescharacteristic
638C2#1307897411yescharacteristic
639C2#1308002411yescharacteristic
640C2#1308003211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1804C2
socleC23×C11C22×D4
prime radicalC2×#66993C22
hypercenter#1804D11
hypocenterC11#29133
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
1. #13074595C2semidirect
3. #13070189C2semidirect
4. #13070187C2semidirect
7. #13069311C2semidirect
8. #13069310C2semidirect
9. #13069297C2semidirect
10. #13069296C2semidirect
11. #13068623C2semidirect
12. #13068617C2semidirect
13. #13068616C2semidirect
14. #13068475C2semidirect
15. C11×#1804C2semidirect
213. #1804D11semidirect
521. C11#29133semidirect

Maximal subgroups

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

subgroupindex
#130745952
#130713382
#130701892
#130701872
#130698492
#130693112
#130693102
#130692972
#130692962
#130686232
#130686172
#130686162
#130684752
C11×#18042
#2913311