Finite Group Databasebeta

← #14757025

Subgroups — #14757025

Order 2816.

764 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077387C211yesmaximal, characteristic
2#13077266C211yesmaximal, characteristic, complemented
3#13077043C211yesmaximal, characteristic, complemented
4#13069264C211yesmaximal, characteristic, complemented
5#13069262C211yesmaximal, characteristic, complemented
6#13069217C211yesmaximal, characteristic, complemented
7#13068944C211yesmaximal, characteristic
8#13068942C211yesmaximal, characteristic
9#13068892C211yesmaximal, characteristic, complemented
10#13068890C211yesmaximal, characteristic, complemented
11#13068517C211yesmaximal, characteristic, complemented
12#13068425C211yesmaximal, characteristic, complemented
13#13068425C211yesmaximal, characteristic, complemented
14#13068366C211yesmaximal, characteristic, complemented
15C11×#1922C211yesmaximal, characteristic, complemented
16C2×#66960C2211yescharacteristic
17C2×#66957C2211yescharacteristic
18C2×#66954C2211yescharacteristic
19#10623053C2211yescharacteristic
20#10623053C2211yescharacteristic
21C11×#427C2211yescharacteristic
22C11×#424C2211yescharacteristic
23C11×#405C2211yescharacteristic
24C2×#66889C2211yescharacteristic
25C2×#66889C2211yescharacteristic
26#10622742C2211yescharacteristic
27C2×#66886C2211yescharacteristic
28C2×#66886C2211yescharacteristic
29M16×Dic11C2211yescharacteristic
30M16×Dic11C2211yescharacteristic
31#10622723C2211yescharacteristic
32C2×#66879C2211yescharacteristic
33C2×C8×Dic11C2211yescharacteristic
34#10622615C2211yescharacteristic
35#10622615C2211yescharacteristic
36#10622612C2211yescharacteristic
37#10622610C2211yescharacteristic
38#10622545C2211yescharacteristic
39C2×#66869C2211yescharacteristic
40C2×#66869C2211yescharacteristic
41#10622486C411yescharacteristic, complemented
42#10622486C411yescharacteristic, complemented
43#10622485C411yescharacteristic, complemented
44#10622485C411yescharacteristic, complemented
45#10622465C411yescharacteristic, complemented
46#10622465C411yescharacteristic, complemented
47#10622465C411yescharacteristic, complemented
48#10622465C411yescharacteristic, complemented
49#10622453—21no—
50#10622453—21no—
51#10622448—21no—
52#10622448—21no—
53#10622321—21no—
54D11×#97—21no—
55#10622302—21no—
56C4×#4313—21no—
57C11×#341C2211yescharacteristic
58C11×#339C2211yescharacteristic
59C11×#339C2211yescharacteristic
60C11×#336C2211yescharacteristic
61#10622190C2211yescharacteristic
62#10622188C2211yescharacteristic
63#10622188C2211yescharacteristic
64#10622170C2211yescharacteristic
65#10622170C2211yescharacteristic
66#10622162C2211yescharacteristic
67C2×#4339C2311yescharacteristic
68C2×#4339C2311yescharacteristic
69C2×C11×M16C2311yescharacteristic
70C2×C11×M16C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C11×#117C2311yescharacteristic
74C11×#117C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C4×Dic11C2311yescharacteristic
77C2×C4×Dic11C2311yescharacteristic
78C2×#4318C2311yescharacteristic
79C2×#4318C2311yescharacteristic
80C22×C11⋊C8C2311yescharacteristic
81C22×C11⋊C8C2311yescharacteristic
82#66960—22no—
83#66960—22no—
84C2×Dic44C2×C411yescharacteristic
85#66957—22no—
86#66957—22no—
87C2×D88C2×C411yescharacteristic
88C2×#4314C2×C411yescharacteristic
89C2×#4314C2×C411yescharacteristic
90#66954—22no—
91#66954—22no—
92C2×#4313—21no—
93C2×#4313—21no—
94C2×C8×D11—21no—
95C2×C8×D11—21no—
96#66946C2×C411yescharacteristic
97#66946C2×C411yescharacteristic
98#66946C2×C411yescharacteristic
99#66946C2×C411yescharacteristic
100#66940C2×C411yescharacteristic
101#66940C2×C411yescharacteristic
102#66940C2×C411yescharacteristic
103#66940C2×C411yescharacteristic
104(C22⋊D11)⋊C4—21no—
105(C22⋊D11)⋊C4—21no—
106(C22⋊D11)⋊C4—21no—
107(C22⋊D11)⋊C4—21no—
108#66925—21no—
109#66925—21no—
110C42×D11—21no—
111C42×D11—21no—
112C11×#107C2×C411yescharacteristic
113C11×#107C2×C411yescharacteristic
114C11×#106C2×C411yescharacteristic
115C11×#106C2×C411yescharacteristic
116C11×C4⋊C8—21no—
117C11×C4⋊C8—21no—
118C11×#97—21no—
119C4×C8×C11—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122#66889—22no—
123#66889—22no—
124#66886—22no—
125#66886—22no—
126(C2×D11)⋊C8—21no—
127(C2×D11)⋊C8—21no—
128(C2×D11)⋊C8—21no—
129(C2×D11)⋊C8—21no—
130#66879—21no—
131#66879—21no—
132#66879D411yescharacteristic
133#66879D411yescharacteristic
134#66879D411yescharacteristic
135#66879D411yescharacteristic
136C8×Dic11—21no—
137C8×Dic11—21no—
138C8×Dic11C2×C411yescharacteristic
139C8×Dic11C2×C411yescharacteristic
140C8×Dic11C2×C411yescharacteristic
141C8×Dic11C2×C411yescharacteristic
142#66874C2×C411yescharacteristic
143#66874C2×C411yescharacteristic
144#66874C2×C411yescharacteristic
145#66874C2×C411yescharacteristic
146#66873C2×C411yescharacteristic
147#66873C2×C411yescharacteristic
148#66873C2×C411yescharacteristic
149#66873C2×C411yescharacteristic
150#66869—22no—
151#66869—22no—
152C4⋊(C11⋊C8)—21no—
153C4⋊(C11⋊C8)—21no—
154#66867—21no—
155C4×C11⋊C8—21no—
156#21140—111nomaximal, Sylow
157C22×C4×C11—21no—
158C22×C4×C11C2411yescharacteristic
159C2×C22⋊D11—21no—
160C2×C22⋊D11—21no—
161C22×Dic11—21no—
162C22×Dic11#4111yescharacteristic
163C22×Dic11#4111yescharacteristic
164#4339—21no—
165#4339—21no—
166#4339—21no—
167#4339—21no—
168#4339—21no—
169#4339—21no—
170#4339#4112yes—
171#4339#4112yes—
172C2×D44C22×C411yescharacteristic
173C2×D44C22×C411yescharacteristic
174C2×C4×D11—21no—
175C2×C4×D11—21no—
176C2×C4×D11—21no—
177C2×C4×D11—21no—
178C2×C4×D11—21no—
179C2×C4×D11—21no—
180C2×Dic22C22×C411yescharacteristic
181C2×Dic22C22×C411yescharacteristic
182C11×M16—21no—
183C11×M16—21no—
184C11×M16—21no—
185C11×M16#4112yes—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11C22×C411yescharacteristic
193C2×C8×C11C22×C411yescharacteristic
194C2×C8×C11C2×D411yescharacteristic
195C2×C8×C11C2×D411yescharacteristic
196C11×C4⋊C4C22×C411yescharacteristic
197C11×C4⋊C4C22×C411yescharacteristic
198C11×C4⋊C4C22×C411yescharacteristic
199C11×C4⋊C4C22×C411yescharacteristic
200C11×C22⋊C4—21no—
201C11×C22⋊C4—21no—
202C42×C11—21no—
203C42×C11—21no—
204C42×C11—21no—
205C42×C11—21no—
206(C2×D11)⋊C4—21no—
207(C2×D11)⋊C4—21no—
208(C2×D11)⋊C4—21no—
209(C2×D11)⋊C4—21no—
210Dic11⋊C4—21no—
211Dic11⋊C4—21no—
212Dic11⋊C4—21no—
213Dic11⋊C4—21no—
214C4×Dic11—21no—
215C4×Dic11—21no—
216C4×Dic11—21no—
217C4×Dic11—21no—
218C4×Dic11—21no—
219C4×Dic11—21no—
220C4×Dic11C22×C411yescharacteristic
221C4×Dic11C22×C411yescharacteristic
222C4×Dic11C2×D411yescharacteristic
223C4×Dic11C2×D411yescharacteristic
224#4318—21no—
225#4318—21no—
226#4318—21no—
227#4318#4112yes—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—21no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8C22×C411yescharacteristic
235C2×C11⋊C8C22×C411yescharacteristic
236C2×C11⋊C8C2×D411yescharacteristic
237C2×C11⋊C8C2×D411yescharacteristic
238Dic44—22no—
239D88—22no—
240#4314—22no—
241#4314—22no—
242#4313—24no—
243#4313—24no—
244C8×D11—24no—
245C8×D11—24no—
246C4×#135—111no—
247#2923—111no—
248#2875—111no—
249#1929—111no—
250#1929—111no—
251#1922—111no—
252#1922D1111yescharacteristic, complemented
253#1876—111no—
254#1876—111no—
255#1866—111no—
256#1866—111no—
257C4×#108—111no—
258#1759—111no—
259#1759—111no—
260#1746—111no—
261C23×C11C2×#4111yescharacteristic
262C22×D11—21no—
263C22×D11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11C23×C411yescharacteristic
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C22⋊D11—22no—
278C22⋊D11—22no—
279C22⋊D11—41no—
280C22⋊D11—41no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11C4×D411yescharacteristic
289C2×Dic11C4×D411yescharacteristic
290C2×Dic11C4×D411yescharacteristic
291C2×Dic11C4×D411yescharacteristic
292D44—21no—
293D44—21no—
294D44—21no—
295D44#11712yes—
296C4×D11—22no—
297C4×D11—22no—
298C4×D11—41no—
299C4×D11—41no—
300C4×D11—81no—
301C4×D11—81no—
302C4×D11—81no—
303C4×D11—81no—
304Dic22—21no—
305Dic22—21no—
306Dic22—21no—
307Dic22#11712yes—
308C8×C11—21no—
309C8×C11—21no—
310C8×C11—21no—
311C8×C11—22no—
312C8×C11—21no—
313C8×C11—41no—
314C11⋊C8—21no—
315C11⋊C8—21no—
316C11⋊C8—21no—
317C11⋊C8—22no—
318C11⋊C8—21no—
319C11⋊C8—41no—
320C2×#135—111no—
321C2×#131—111no—
322C2×#131—111no—
323C4×#41—111no—
324C4×#41—111no—
325C4×Q16—111no—
326C4×Q16—111no—
327C4×SD16—111no—
328C4×SD16—111no—
329C4×SD16—111no—
330C4×SD16—111no—
331C4×D8—111no—
332C4×D8—111no—
333#433—221no—
334#433—221no—
335#432—221no—
336#432—221no—
337C2×#108—111no—
338C2×#108—111no—
339#427C2×D1111yescharacteristic
340#424—111no—
341#424C2×D1111yescharacteristic
342C2×#104—111no—
343C2×#104—111no—
344C2×#104—111no—
345C2×#104—111no—
346#416—111no—
347#416—111no—
348#408—111no—
349#408—111no—
350#405—111no—
351#405—221no—
352#405—221no—
353#405C2×D1111yescharacteristic
354C4×M16—111no—
355C4×M16—111no—
356C4×M16—221no—
357C2×#97—111no—
358C2×#97—221no—
359C2×C4×C8—111no—
360#376—111no—
361#341—111no—
362#341C2×D1111yescharacteristic
363#339—111no—
364#339—111no—
365#339C2×D1111yescharacteristic
366#339C2×D1111yescharacteristic
367#336—111no—
368#336—111no—
369#336—111no—
370#336C2×D1111yescharacteristic
371C22×C11—21no—
372C22×C11—21no—
373C22×C11C2×C4×D411yescharacteristic
374C22×C11#52911yescharacteristic
375C22×C11#52911yescharacteristic
376C2×D11—22no—
377C2×D11—41no—
378C2×D11—41no—
379C2×D11—41no—
380C2×D11—41no—
381C2×D11—41no—
382C4×C11—41no—
383C4×C11—41no—
384C4×C11—41no—
385C4×C11—41no—
386C4×C11—81no—
387C4×C11C2×#11711yescharacteristic
388C4×C11C4×#4111yescharacteristic
389C4×C11#52511yescharacteristic
390C4×C11#52511yescharacteristic
391Dic11—21no—
392Dic11—21no—
393Dic11—21no—
394Dic11—21no—
395Dic11—22no—
396Dic11—41no—
397Dic11—81no—
398C2×#41—111no—
399C2×#41—111no—
400#135—222no—
401#135—222no—
402C2×Q16—111no—
403C2×SD16—111no—
404C2×SD16—111no—
405C2×D8—111no—
406#131—222no—
407#131—222no—
408#131—222no—
409#131—222no—
410C2×M16—111no—
411C2×M16—111no—
412C2×M16—221no—
413C2×M16—221no—
414C2×M16C22×D1111yescharacteristic
415C2×M16C22×D1111yescharacteristic
416C22×C8—111no—
417C22×C8—111no—
418C22×C8—221no—
419C22×C8—221no—
420C22×C8C22×D1111yescharacteristic
421C22×C8C22×D1111yescharacteristic
422C4×Q8—111no—
423C4×Q8—111no—
424C4×Q8—111no—
425C4×Q8—111no—
426C4×D4—111no—
427C4×D4—111no—
428C4×D4—111no—
429C4×D4—111no—
430C4×D4—221no—
431C4×D4—221no—
432C4×D4—221no—
433C4×D4—221no—
434#117—221no—
435#117—221no—
436#117C22×D1111yescharacteristic
437#117C22×D1111yescharacteristic
438C2×C42—111no—
439C2×C42—111no—
440C2×C42—221no—
441C2×C42—221no—
442C2×C42C22×D1111yescharacteristic
443#108—222no—
444#108—222no—
445#107C4×D1111yescharacteristic
446#107C4×D1111yescharacteristic
447#106C4×D1111yescharacteristic
448#106C4×D1111yescharacteristic
449C4⋊C8—21no—
450C4⋊C8—21no—
451C4⋊C8—221no—
452C4⋊C8—221no—
453#104—222no—
454#104—222no—
455#104—222no—
456#104—222no—
457#103—111no—
458#103—111no—
459#103—111no—
460#103—111no—
461#102—111no—
462#102—111no—
463#102—111no—
464#102—111no—
465C22⋊C8—221no—
466C22⋊C8—221no—
467C22⋊C8—221no—
468C22⋊C8—221no—
469#97—21no—
470#97—111no—
471#97—111no—
472#97—111no—
473#97—111no—
474#97—221no—
475#97—221no—
476#97—221no—
477C4×C8—21no—
478C4×C8—111no—
479C4×C8—111no—
480C4×C8—111no—
481C4×C8—111no—
482C4×C8—221no—
483C4×C8—221no—
484C4×C8—221no—
485#95—221no—
486#95—221no—
487C2×C11—21no—
488C2×C11—21no—
489C2×C11#229011yescharacteristic
490C2×C11#295711yescharacteristic
491C2×C11#295711yescharacteristic
492D11—42no—
493D11—81no—
494#41—112no—
495#41—112no—
496#41—221no—
497#41—221no—
498#41—221no—
499#41—221no—
500#41—221no—
501#41—221no—
502C2×Q8—111no—
503C2×Q8—111no—
504C2×D4—111no—
505C2×D4—111no—
506C2×D4—221no—
507C2×D4—221no—
508C22×C4—21no—
509C22×C4—111no—
510C22×C4—111no—
511C22×C4—221no—
512C22×C4—221no—
513C22×C4—221no—
514C22×C4—221no—
515C22×C4—221no—
516C22×C4—221no—
517C22×C4—221no—
518C22×C4C23×D1111yescharacteristic
519Q16—222no—
520SD16—222no—
521SD16—222no—
522D8—222no—
523M16—21no—
524M16—21no—
525M16—21no—
526M16—112no—
527M16—224no—
528M16—224no—
529M16—221no—
530M16—221no—
531M16—221no—
532M16#434312yes—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—111no—
540C2×C8—111no—
541C2×C8—111no—
542C2×C8—111no—
543C2×C8—224no—
544C2×C8—224no—
545C2×C8—221no—
546C2×C8—221no—
547C2×C8—221no—
548C2×C8—221no—
549C2×C8—221no—
550C2×C8—221no—
551C2×C8C2×C4×D1111yescharacteristic
552C2×C8C2×C4×D1111yescharacteristic
553C2×C8D4×D1111yescharacteristic
554C2×C8D4×D1111yescharacteristic
555C4⋊C4—221no—
556C4⋊C4—221no—
557C4⋊C4—221no—
558C4⋊C4—221no—
559C4⋊C4C2×C4×D1111yescharacteristic
560C4⋊C4C2×C4×D1111yescharacteristic
561C4⋊C4C2×C4×D1111yescharacteristic
562C4⋊C4C2×C4×D1111yescharacteristic
563C22⋊C4—21no—
564C22⋊C4—21no—
565C22⋊C4—221no—
566C22⋊C4—221no—
567C22⋊C4—221no—
568C22⋊C4—221no—
569C42—21no—
570C42—21no—
571C42—21no—
572C42—21no—
573C42—111no—
574C42—111no—
575C42—111no—
576C42—111no—
577C42—221no—
578C42—221no—
579C42—221no—
580C42—221no—
581C42—221no—
582C42—221no—
583C11#2114011yescharacteristic, complemented, Sylow
584C23—221no—
585C23—221no—
586C23#41×D1111yescharacteristic
587Q8—112no—
588Q8—221no—
589Q8—221no—
590Q8—221no—
591D4—112no—
592D4—222no—
593D4—222no—
594D4—221no—
595D4—221no—
596D4—221no—
597D4—441no—
598D4—441no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—111no—
607C2×C4—111no—
608C2×C4—111no—
609C2×C4—111no—
610C2×C4—221no—
611C2×C4—222no—
612C2×C4—222no—
613C2×C4—221no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4—881no—
622C2×C4—881no—
623C2×C4—881no—
624C2×C4—881no—
625C2×C4C22×C4×D1111yescharacteristic
626C2×C4C2×D4×D1111yescharacteristic
627C2×C4C2×#434311yescharacteristic
628C2×C4#41×D1111yescharacteristic
629C2×C4#41×D1111yescharacteristic
630C2×C4#41×D1111yescharacteristic
631C8—21no—
632C8—21no—
633C8—22no—
634C8—21no—
635C8—21no—
636C8—41no—
637C8—221no—
638C8—221no—
639C8—221no—
640C8—221no—
641C8—222no—
642C8—441no—
643C22—21no—
644C22—21no—
645C22—222no—
646C22—441no—
647C22—441no—
648C22—441no—
649C22—441no—
650C22—441no—
651C22C4×D4×D1111yescharacteristic
652C22#1062322211yescharacteristic
653C22#1062323711yescharacteristic
654C4—41no—
655C4—41no—
656C4—41no—
657C4—41no—
658C4—81no—
659C4—221no—
660C4—221no—
661C4—221no—
662C4—221no—
663C4—222no—
664C4—441no—
665C4—881no—
666C4D11×#11711yescharacteristic
667C4C4×#434311yescharacteristic
668C4#1062315811yescharacteristic
669C4#1062318711yescharacteristic
670C2—21no—
671C2—21no—
672C2—442no—
673C2—881no—
674C2#1307105411yescharacteristic
675C2#1307752811yescharacteristic
676C2#1307753011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1922C2
socleC22×C11C2×C4×D4
prime radicalC2×#66957C22
cosocleC22×C4×C11C24
hypercenter#1922D11
hypocenterC11#21140
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1922

Complements

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

NH ≅ G/Ntype
2. #13077266C2semidirect
3. #13077043C2semidirect
4. #13069264C2semidirect
5. #13069262C2semidirect
6. #13069217C2semidirect
9. #13068892C2semidirect
10. #13068890C2semidirect
11. #13068517C2semidirect
12. #13068425C2semidirect
13. #13068425C2semidirect
14. #13068366C2semidirect
15. C11×#1922C2semidirect
41. #10622486C4semidirect
42. #10622486C4semidirect
43. #10622485C4semidirect
44. #10622485C4semidirect
45. #10622465C4semidirect
46. #10622465C4semidirect
47. #10622465C4semidirect
48. #10622465C4semidirect
252. #1922D11semidirect
583. C11#21140semidirect

Maximal subgroups

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

subgroupindex
#130773872
#130772662
#130770432
#130692642
#130692622
#130692172
#130689442
#130689422
#130688922
#130688902
#130685172
#130684252
#130683662
C11×#19222
#2114011