Finite Group Databasebeta

← #14652910

Subgroups — #14652910

Order 2816.

764 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076959C211yesmaximal, characteristic
2#13068594C211yesmaximal, characteristic, complemented
3C2×#10622108C211yesmaximal, characteristic, complemented
4C2×#10622175C211yesmaximal, characteristic, complemented
5C2×#10622089C211yesmaximal, characteristic, complemented
6#13066841C211yesmaximal, characteristic, complemented
7C2×C11×#327C211yesmaximal, characteristic, complemented
8C2×C11×#121C2211yescharacteristic
9C2×#66993C411yescharacteristic, complemented
10C2×#66992—21no—
11C2×#66992—21no—
12C2×#66983C2211yescharacteristic
13C22×C4×Dic11C2211yescharacteristic
14C2×C11×C22⋊C8C2211yescharacteristic
15C2×C11×#95C2211yescharacteristic
16#10622834C411yescharacteristic, complemented
17C2×C11⋊#95—21no—
18C2×C11⋊#95—21no—
19C2×C11⋊#95C2211yescharacteristic
20C2×C22⋊(C11⋊C8)C2211yescharacteristic
21C2×Dic11⋊C8—21no—
22#10622601C411yescharacteristic, complemented
23#10622589C411yescharacteristic, complemented
24#10622570—21no—
25#10622570—21no—
26C11×#327—22no—
27#10622188—21no—
28#10622175—22no—
29#10622108—22no—
30#10622089—22no—
31C22×D4×C11—21no—
32C22×D4×C11C2×C411yescharacteristic
33C23×C4×C11—21no—
34C23×C4×C11C2311yescharacteristic
35C22×C22⋊D11—21no—
36C22×C22⋊D11—21no—
37C22×C22⋊D11—21no—
38C23×Dic11—21no—
39C23×Dic11D411yescharacteristic
40C23×Dic11D411yescharacteristic
41C22×D44C2×C411yescharacteristic
42C22×C8×C11—21no—
43C11×#121—21no—
44C11×#121—21no—
45C11×#121—21no—
46C11×#121—21no—
47C2×C11×C4⋊C4C2×C411yescharacteristic
48C2×C11×C22⋊C4—21no—
49C2×C22⋊Dic11—21no—
50C2×C22⋊Dic11—21no—
51#66993—42no—
52#66992—42no—
53#66992—42no—
54#66992—42no—
55#66992—42no—
56#66983—21no—
57#66983—21no—
58#66983—21no—
59#66983—21no—
60C2×(C2×D11)⋊C4—21no—
61C2×(C2×D11)⋊C4—21no—
62C2×(C2×D11)⋊C4—21no—
63C2×C4⋊Dic11C2×C411yescharacteristic
64C2×Dic11⋊C4—21no—
65C2×Dic11⋊C4—21no—
66C2×C4×Dic11—42no—
67C2×C4×Dic11C2×C411yescharacteristic
68C2×C4×Dic11C2×C411yescharacteristic
69C2×C4×Dic11D411yescharacteristic
70C2×C4×Dic11D411yescharacteristic
71C22×C11⋊C8—21no—
72C11×C22⋊C8—21no—
73C11×C22⋊C8—21no—
74C11×#95—21no—
75C11×#95D412yescomplemented
76C11⋊#95—21no—
77C11⋊#95—42no—
78C11⋊#95—42no—
79C11⋊#95D412yescomplemented
80C22⋊(C11⋊C8)—21no—
81C22⋊(C11⋊C8)—21no—
82Dic11⋊C8—42no—
83#9715—111nomaximal, Sylow
84C24×C11—21no—
85C24×C11C2×D411yescharacteristic
86C23×D11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—41no—
94C2×D4×C11—41no—
95C2×D4×C11—41no—
96C2×D4×C11—41no—
97C22×C4×C11—21no—
98C22×C4×C11—22no—
99C22×C4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11—41no—
106C22×C4×C11—41no—
107C22×C4×C11C22×C411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11#4111yescharacteristic
112C22×C4×C11#4111yescharacteristic
113C2×C22⋊D11—42no—
114C2×C22⋊D11—42no—
115C2×C22⋊D11—42no—
116C2×C22⋊D11—42no—
117C2×C22⋊D11—42no—
118C2×C22⋊D11—42no—
119C2×C22⋊D11—41no—
120C2×C22⋊D11—41no—
121C2×C22⋊D11—41no—
122C2×C22⋊D11—41no—
123C2×C22⋊D11—41no—
124C2×C22⋊D11—41no—
125C22×Dic11—22no—
126C22×Dic11—21no—
127C22×Dic11—22no—
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—41no—
131C22×Dic11—41no—
132C22×Dic11—41no—
133C22×Dic11—41no—
134C22×Dic11—41no—
135C22×Dic11—41no—
136C22×Dic11—41no—
137C22×Dic11—41no—
138C22×Dic11—41no—
139C22×Dic11C22⋊C411yescharacteristic
140C22×Dic11C22⋊C411yescharacteristic
141C22×Dic11C22⋊C411yescharacteristic
142C22×Dic11C22⋊C411yescharacteristic
143C22×Dic11D812yes—
144C22×Dic11SD1612yes—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—41no—
148C2×D44—41no—
149C2×C8×C11—41no—
150C2×C8×C11—41no—
151C2×C8×C11—41no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C22⋊C4—41no—
155C11×C22⋊C4—41no—
156C22⋊Dic11—42no—
157C22⋊Dic11—42no—
158(C2×D11)⋊C4—42no—
159(C2×D11)⋊C4—42no—
160(C2×D11)⋊C4—41no—
161(C2×D11)⋊C4—41no—
162C4⋊Dic11—21no—
163C4⋊Dic11—21no—
164Dic11⋊C4—42no—
165Dic11⋊C4—42no—
166C4×Dic11—22no—
167C4×Dic11—22no—
168C4×Dic11—41no—
169C4×Dic11—41no—
170C2×C11⋊C8—41no—
171C2×C11⋊C8—41no—
172C2×C11⋊C8—41no—
173#2856—111no—
174#1797—111no—
175C2×#327—111no—
176C2×#327—111no—
177C2×#327—111no—
178C2×#327D1111yescharacteristic, complemented
179#1434—111no—
180C23×C11—21no—
181C23×C11—21no—
182C23×C11—21no—
183C23×C11—21no—
184C23×C11—41no—
185C23×C11—41no—
186C23×C11—41no—
187C23×C11—41no—
188C23×C11—41no—
189C23×C11—41no—
190C23×C11—41no—
191C23×C11C2×C22⋊C411yescharacteristic
192C23×C11#12111yescharacteristic
193C23×C11#12111yescharacteristic
194C23×C11C2×D811yescharacteristic
195C23×C11C2×SD1611yescharacteristic
196C23×C11AGL(1,ℤ/8)11yescharacteristic
197C23×C11AGL(1,ℤ/8)11yescharacteristic
198C22×D11—41no—
199C22×D11—41no—
200C22×D11—41no—
201C22×D11—41no—
202C22×D11—41no—
203C22×D11—41no—
204C22×D11—41no—
205D4×C11—81no—
206D4×C11—81no—
207D4×C11—81no—
208D4×C11—81no—
209D4×C11—81no—
210D4×C11—81no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—42no—
225C2×C4×C11—81no—
226C2×C4×C11—81no—
227C2×C4×C11—81no—
228C2×C4×C11—81no—
229C2×C4×C11C4×D411yescharacteristic
230C2×C4×C11C4×D411yescharacteristic
231C2×C4×C11#12411yescharacteristic
232C2×C4×C11#12711yescharacteristic
233C22⋊D11—84no—
234C22⋊D11—84no—
235C22⋊D11—81no—
236C22⋊D11—81no—
237C22⋊D11—81no—
238C22⋊D11—81no—
239C2×Dic11—21no—
240C2×Dic11—21no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—42no—
258C2×Dic11—81no—
259C2×Dic11—81no—
260C2×Dic11—81no—
261C2×Dic11—81no—
262C2×Dic11#9912yes—
263C2×Dic11#10212yes—
264C2×Dic11#10212yes—
265D44—81no—
266D44—81no—
267C8×C11—81no—
268C11⋊C8—81no—
269C2×#127—111no—
270C2×#121—111no—
271C2×#121—221no—
272C2×#121—221no—
273C2×#121C2×D1111yescharacteristic
274C22×C42—111no—
275C2×C4⋊C8—221no—
276C2×C22⋊C8—111no—
277C2×C22⋊C8C2×D1111yescharacteristic
278#390—111no—
279#390—111no—
280#390—221no—
281#390—221no—
282#384—111no—
283C2×#95—111no—
284C2×#95—221no—
285C2×#95—221no—
286C2×#95C2×D1111yescharacteristic
287#336—221no—
288#327—22no—
289#327—222no—
290#327—222no—
291#327—222no—
292C22×C11—21no—
293C22×C11—21no—
294C22×C11—21no—
295C22×C11—21no—
296C22×C11—21no—
297C22×C11—21no—
298C22×C11—21no—
299C22×C11—21no—
300C22×C11—21no—
301C22×C11—21no—
302C22×C11—21no—
303C22×C11—21no—
304C22×C11—81no—
305C22×C11—81no—
306C22×C11—81no—
307C22×C11—81no—
308C22×C11—81no—
309C22×C11—81no—
310C22×C11—81no—
311C22×C11#39011yescharacteristic
312C22×C11C2×#9911yescharacteristic
313C22×C11#41011yescharacteristic
314C22×C11C2×#10211yescharacteristic
315C22×C11#41811yescharacteristic
316C22×C11#42111yescharacteristic
317C22×C11#42111yescharacteristic
318C22×C11#45911yescharacteristic
319C22×C11#45911yescharacteristic
320C22×C11#46011yescharacteristic
321C22×C11#46011yescharacteristic
322C2×D11—81no—
323C2×D11—81no—
324C2×D11—81no—
325C2×D11—81no—
326C2×D11—81no—
327C2×D11—81no—
328C2×D11—81no—
329C4×C11—21no—
330C4×C11—21no—
331C4×C11—21no—
332C4×C11—21no—
333C4×C11—82no—
334C4×C11—81no—
335Dic11—22no—
336Dic11—22no—
337Dic11—22no—
338Dic11—41no—
339Dic11—82no—
340Dic11—81no—
341C22×D4—21no—
342C22×D4—111no—
343C22×D4—221no—
344C22×D4—221no—
345C22×D4—221no—
346C22×D4C4×D1111yescharacteristic
347C23×C4—21no—
348C23×C4—111no—
349C23×C4—111no—
350C23×C4—221no—
351C23×C4C22×D1111yescharacteristic
352C22×C8—21no—
353C22×C8—221no—
354#127—442no—
355#121—21no—
356#121—21no—
357#121—21no—
358#121—21no—
359#121—221no—
360#121—221no—
361#121—221no—
362#121—221no—
363#121—442no—
364#121—442no—
365#121—442no—
366#121—442no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4C4×D1111yescharacteristic
371C2×C22⋊C4—21no—
372C2×C22⋊C4—221no—
373C2×C22⋊C4—221no—
374C2×C22⋊C4—221no—
375C2×C22⋊C4—221no—
376C2×C22⋊C4—221no—
377C2×C42—111no—
378C2×C42—111no—
379C2×C42—111no—
380C2×C42—111no—
381C2×C42—442no—
382C4⋊C8—442no—
383C22⋊C8—21no—
384C22⋊C8—21no—
385C22⋊C8—221no—
386C22⋊C8—221no—
387#95—21no—
388#95—112no—
389#95—221no—
390#95—442no—
391#95—442no—
392#95C22⋊D1112yescomplemented
393C2×C11—21no—
394C2×C11—21no—
395C2×C11—21no—
396C2×C11—21no—
397C2×C11—161no—
398C2×C11#151011yescharacteristic
399C2×C11#151411yescharacteristic
400C2×C11#151711yescharacteristic
401C2×C11#151911yescharacteristic
402C2×C11#196311yescharacteristic
403C2×C11#196411yescharacteristic
404C2×C11#198211yescharacteristic
405D11—161no—
406C24—21no—
407C24—221no—
408C24D4×D1111yescharacteristic
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—41no—
414C2×D4—41no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4—221no—
420C2×D4—221no—
421C2×D4—441no—
422C2×D4—441no—
423C2×D4—442no—
424C2×D4—442no—
425C2×D4—442no—
426C2×D4—442no—
427C2×D4—442no—
428C2×D4—442no—
429C2×D4—441no—
430C2×D4—441no—
431C2×D4—441no—
432C2×D4—441no—
433C2×D4—441no—
434C2×D4—441no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—111no—
446C22×C4—111no—
447C22×C4—111no—
448C22×C4—112no—
449C22×C4—112no—
450C22×C4—111no—
451C22×C4—222no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4—222no—
456C22×C4—441no—
457C22×C4—441no—
458C22×C4—441no—
459C22×C4—441no—
460C22×C4—441no—
461C22×C4—441no—
462C22×C4—441no—
463C22×C4—441no—
464C22×C4—441no—
465C22×C4C2×C4×D1111yescharacteristic
466C22×C4#433911yescharacteristic
467C22×C4D4×D1111yescharacteristic
468C22×C4D4×D1111yescharacteristic
469C22×C4#434111yescharacteristic
470C22×C4C2×C22⋊D1111yescharacteristic
471C2×C8—41no—
472C2×C8—41no—
473C2×C8—41no—
474C2×C8—441no—
475C2×C8—441no—
476C2×C8—441no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—442no—
482C4⋊C4—442no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C22⋊C4—442no—
486C22⋊C4—442no—
487C22⋊C4—442no—
488C22⋊C4—442no—
489C22⋊C4—441no—
490C22⋊C4—441no—
491C42—222no—
492C42—222no—
493C42—441no—
494C42—441no—
495C11#971511yescharacteristic, complemented, Sylow
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—441no—
508C23—441no—
509C23—441no—
510C23—441no—
511C23—441no—
512C23—441no—
513C23—441no—
514C23C22⋊C4×D1111yescharacteristic
515C23#6693711yescharacteristic
516C23D8×D1111yescharacteristic
517C23#6696411yescharacteristic
518C23SD16×D1111yescharacteristic
519C23#6696711yescharacteristic
520C23#6699211yescharacteristic
521D4—81no—
522D4—81no—
523D4—81no—
524D4—81no—
525D4—81no—
526D4—81no—
527D4—881no—
528D4—881no—
529D4—884no—
530D4—884no—
531D4—881no—
532D4—881no—
533D4—881no—
534D4—881no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—81no—
550C2×C4—81no—
551C2×C4—81no—
552C2×C4—81no—
553C2×C4—112no—
554C2×C4—112no—
555C2×C4—112no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4—221no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—442no—
566C2×C4—442no—
567C2×C4—442no—
568C2×C4—442no—
569C2×C4—442no—
570C2×C4—442no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—442no—
575C2×C4—881no—
576C2×C4—881no—
577C2×C4—881no—
578C2×C4—881no—
579C2×C4(C22⋊D11)⋊C411yescharacteristic
580C2×C4#6693811yescharacteristic
581C2×C4C4×C22⋊D1111yescharacteristic
582C2×C4#6699311yescharacteristic
583C8—81no—
584C8—881no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—21no—
589C22—21no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22—81no—
604C22—881no—
605C22—881no—
606C22—881no—
607C22—881no—
608C22—881no—
609C22—881no—
610C22—881no—
611C22#1062235311yescharacteristic
612C22D11×#9911yescharacteristic
613C22#1062237511yescharacteristic
614C22D11×#10211yescharacteristic
615C22#1062238311yescharacteristic
616C22#1062239911yescharacteristic
617C22#1062243411yescharacteristic
618C22#1062243411yescharacteristic
619C22#1062257011yescharacteristic
620C22#1062276311yescharacteristic
621C22#1062277611yescharacteristic
622C4—21no—
623C4—21no—
624C4—21no—
625C4—21no—
626C4—82no—
627C4—81no—
628C4—222no—
629C4—222no—
630C4—222no—
631C4—441no—
632C4—882no—
633C4—881no—
634C2—21no—
635C2—21no—
636C2—21no—
637C2—21no—
638C2—161no—
639C2—1761no—
640C2#1306714311yescharacteristic
641C2#1306716111yescharacteristic
642C2#1306717411yescharacteristic
643C2#1306718211yescharacteristic
644C2#1306944611yescharacteristic
645C2#1306945011yescharacteristic
646C2#1306954111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#327C2
socleC23×C11C2×C22⋊C4
prime radical#13076959C2
cosocleC23×C4×C11C23
hypercenterC2×#327D11
hypocenterC11#9715
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. #13068594C2semidirect
3. C2×#10622108C2semidirect
4. C2×#10622175C2semidirect
5. C2×#10622089C2semidirect
6. #13066841C2semidirect
7. C2×C11×#327C2semidirect
9. C2×#66993C4semidirect
16. #10622834C4semidirect
22. #10622601C4semidirect
23. #10622589C4semidirect
75. C11×#95D4semidirect
79. C11⋊#95D4semidirect
178. C2×#327D11semidirect
392. #95C22⋊D11semidirect
495. C11#9715semidirect

Maximal subgroups

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

subgroupindex
#130769592
#130685942
C2×#106221082
C2×#106221752
C2×#106220892
#130668412
C2×C11×#3272
#971511