Finite Group Databasebeta

← #14803203

Subgroups — #14803203

Order 2816.

794 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
1C2×#10622702C211yesmaximal, characteristic
2#13073592C211yesmaximal, characteristic
3#13071706C211yesmaximal, characteristic, complemented
4#13069992C211yesmaximal, characteristic, complemented
5#13069985C211yesmaximal, characteristic
6#13069861C211yesmaximal, characteristic, complemented
7#13069854C211yesmaximal, characteristic
8#13069546C211yesmaximal, characteristic
9#13069545C211yesmaximal, characteristic
10#13069537C211yesmaximal, characteristic, complemented
11#13069337C211yesmaximal, characteristic, complemented
12#13069249C211yesmaximal, characteristic, complemented
13#13069242C211yesmaximal, characteristic
14#13068446C211yesmaximal, characteristic, complemented
15C2×C11×#475C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×#67000C2211yescharacteristic
19C2×#66997C2211yescharacteristic
20C2×#66928C2211yescharacteristic
21C11×#475—24no—
22C2×C11×#106C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27#10622843—21no—
28#10622843—21no—
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66885C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37#10622702—24no—
38#10622607—21no—
39#10622607—21no—
40#10622601C2211yescharacteristic
41#10622598—21no—
42#10622598C2211yescharacteristic
43#10622598C2211yescharacteristic
44C4⋊C4×Dic11—21no—
45C4⋊C4×Dic11C2211yescharacteristic
46C4⋊C4×Dic11C2211yescharacteristic
47#10622587C2211yescharacteristic
48C2×#66874C2211yescharacteristic
49C2×#66874C2211yescharacteristic
50C2×#66873C2211yescharacteristic
51C2×#66873C2211yescharacteristic
52#10622553—21no—
53#10622553—21no—
54C4×C4⋊Dic11C2211yescharacteristic
55C4×C4⋊Dic11C2211yescharacteristic
56C2×#66867C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11—21no—
62C22×Q8×C11C2311yescharacteristic
63C22×D44C2311yescharacteristic
64C22×Dic22C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×C4⋊Q8—22no—
68C11×C4⋊Q8D414yes—
69C4×Q8×C11—22no—
70C4×Q8×C11—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C42×C11—21no—
77C2×C42×C11C2311yescharacteristic
78#67000—22no—
79#67000—41no—
80#66997—22no—
81#66997—41no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11D411yescharacteristic
91C2×C4⋊Dic11D411yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11C2311yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103#66928—22no—
104#66928—22no—
105C11×#106—22no—
106C11×#106—22no—
107C11×C4⋊C8—22no—
108C11×#103—22no—
109C11×#103—22no—
110#66899—22no—
111#66899—22no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95D411yescharacteristic
120C11⋊#95D411yescharacteristic
121#66885—22no—
122#66885—41no—
123#66880—22no—
124#66880—41no—
125Dic11⋊C8—41no—
126Dic11⋊C8—41no—
127#66874—22no—
128#66874—22no—
129#66873—22no—
130#66873—22no—
131#66867—22no—
132#25287—111nomaximal, Sylow
133C23×D11—21no—
134C2×Q8×C11—24no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—81no—
141C2×Q8×C11—81no—
142C2×Q8×C11#4112yes—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C11×C4⋊C4—24no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—42no—
181C11×C4⋊C4C2×D412yes—
182C11×C4⋊C4C2×D412yes—
183C42×C11—42no—
184C42×C11C2×D412yes—
185C42×C11#4112yes—
186(C2×D11)⋊C4—42no—
187(C2×D11)⋊C4—42no—
188(C2×D11)⋊C4—42no—
189(C2×D11)⋊C4—42no—
190(C2×D11)⋊C4—42no—
191(C2×D11)⋊C4—42no—
192C4⋊Dic11—22no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—41no—
197C4⋊Dic11—81no—
198C4⋊Dic11—81no—
199C4⋊Dic11#4112yes—
200Dic11⋊C4—42no—
201Dic11⋊C4—42no—
202C4×Dic11—21no—
203C4×Dic11—21no—
204C4×Dic11—21no—
205C4×Dic11—21no—
206C4×Dic11—42no—
207C4×Dic11—81no—
208C4×Dic11—81no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×#489—111no—
216C2×#475D1111yescharacteristic, complemented
217#2545—111no—
218#2369—111no—
219#2066—111no—
220#2065—111no—
221#2043—111no—
222#2042—111no—
223#1983—111no—
224#1983—111no—
225#1981—111no—
226#1940—111no—
227#1927—111no—
228#1926—111no—
229#1763—111no—
230C23×C11C22×D411yescharacteristic
231C22×D11—41no—
232C22×D11—41no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—41no—
238Q8×C11—22no—
239Q8×C11—22no—
240Q8×C11—41no—
241Q8×C11—41no—
242Q8×C11—84no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
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—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11#12112yes—
260C2×C4×C11#12112yes—
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11H(5,𝔽2)11yescharacteristic
266C2×C4×C112−1+411yescharacteristic
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—22no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
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#13712yes—
288D44—41no—
289D44—41no—
290D44—41no—
291D44—41no—
292Dic22—41no—
293Dic22—41no—
294Dic22—41no—
295Dic22—41no—
296C8×C11—41no—
297C8×C11—41no—
298C11⋊C8—41no—
299C11⋊C8—41no—
300C2×C4⋊Q8—111no—
301C2×C4⋊Q8C2×D1111yescharacteristic
302C2×#124—111no—
303C2×#124—111no—
304C2×C4×Q8C2×D1111yescharacteristic
305#489—224no—
306#475—24no—
307C2×#106C2×D1111yescharacteristic
308C2×#106C2×D1111yescharacteristic
309C2×C4⋊C8—111no—
310C2×C4⋊C8—111no—
311C2×C4⋊C8C2×D1111yescharacteristic
312C2×#103—111no—
313C2×#103—111no—
314C2×#103—111no—
315C2×#103—111no—
316C2×#103—111no—
317C2×#103—111no—
318C2×#103C2×D1111yescharacteristic
319C2×#103C2×D1111yescharacteristic
320C2×#102—111no—
321C2×#102—111no—
322C2×#102—111no—
323C2×#102—111no—
324C2×#97—111no—
325#396—221no—
326#396—221no—
327#391—111no—
328#391—221no—
329#391—221no—
330#390—111no—
331#389—111no—
332#389—111no—
333#389—221no—
334#388—221no—
335#388—221no—
336C4×C4⋊C4—111no—
337C4×C4⋊C4—111no—
338C4×C4⋊C4—111no—
339C4×C4⋊C4—111no—
340C4×C4⋊C4—221no—
341#340—111no—
342#340—111no—
343#336—111no—
344#336—111no—
345C22×C11C2×#12111yescharacteristic
346C22×C11#54611yescharacteristic
347C22×C11#54811yescharacteristic
348C22×C11C2×#13711yescharacteristic
349C22×C11#57511yescharacteristic
350C22×C11#57711yescharacteristic
351C22×C11#57711yescharacteristic
352C2×D11—81no—
353C2×D11—81no—
354C2×D11—81no—
355C2×D11—81no—
356C2×D11—81no—
357C2×D11—81no—
358C2×D11—81no—
359C4×C11—22no—
360C4×C11—22no—
361C4×C11—42no—
362C4×C11—42no—
363C4×C11—42no—
364C4×C11—81no—
365C4×C11#52911yescharacteristic
366C4×C11#54211yescharacteristic
367C4×C11#54811yescharacteristic
368C4×C11#55011yescharacteristic
369Dic11—22no—
370Dic11—42no—
371Dic11—41no—
372Dic11—41no—
373Dic11—41no—
374Dic11—81no—
375Dic11—81no—
376C22×Q8—21no—
377C22×Q8—111no—
378C22×Q8C22×D1111yescharacteristic
379C22×D4—111no—
380C22×C8—111no—
381C22×C8—111no—
382C22×C8C22×D1111yescharacteristic
383C22×C8C22×D1111yescharacteristic
384C4⋊Q8—22no—
385C4⋊Q8—222no—
386C4⋊Q8—441no—
387C4⋊Q8C22⋊D1114yes—
388#124—222no—
389#124—222no—
390#124—222no—
391#124—441no—
392C4×Q8—22no—
393C4×Q8—22no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
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⋊C4C22×D1111yescharacteristic
405C2×C4⋊C4C22×D1111yescharacteristic
406C2×C4⋊C4C22×D1111yescharacteristic
407C2×C22⋊C4—221no—
408C2×C22⋊C4—221no—
409C2×C22⋊C4—221no—
410C2×C22⋊C4—221no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C42—21no—
414C2×C42—111no—
415C2×C42—111no—
416C2×C42—221no—
417C2×C42—221no—
418C2×C42—221no—
419C2×C42C22×D1111yescharacteristic
420#106—22no—
421#106—22no—
422C4⋊C8—22no—
423C4⋊C8—441no—
424C4⋊C8—441no—
425#103—22no—
426#103—22no—
427#103—222no—
428#103—222no—
429#103—222no—
430#103—222no—
431#103—222no—
432#103—441no—
433#102—222no—
434#102—222no—
435#102—222no—
436#102—441no—
437#97—222no—
438#95—111no—
439#95—111no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447C2×C11#242611yescharacteristic
448C2×C11#303711yescharacteristic
449C2×C11#304211yescharacteristic
450C2×C11#331611yescharacteristic
451C2×C11#332111yescharacteristic
452C2×C11#336911yescharacteristic
453C2×C11#337611yescharacteristic
454D11—161no—
455C24—221no—
456C2×Q8—24no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—81no—
463C2×Q8—81no—
464C2×Q8—221no—
465C2×Q8—221no—
466C2×Q8—221no—
467C2×Q8—221no—
468C2×Q8—221no—
469C2×Q8—221no—
470C2×Q8#434312yes—
471C2×D4—221no—
472C2×D4—221no—
473C2×D4—221no—
474C2×D4—221no—
475C2×D4—221no—
476C2×D4—221no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—111no—
482C22×C4—111no—
483C22×C4—111no—
484C22×C4—111no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4D4×D1111yescharacteristic
489C22×C4D4×D1111yescharacteristic
490C22×C4C23×D1111yescharacteristic
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C4⋊C4—24no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—42no—
509C4⋊C4—112no—
510C4⋊C4—222no—
511C4⋊C4—221no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—441no—
515C4⋊C4—442no—
516C4⋊C4—442no—
517C4⋊C4—881no—
518C4⋊C4—881no—
519C4⋊C4C2×C22⋊D1112yes—
520C4⋊C4C2×C22⋊D1112yes—
521C22⋊C4—442no—
522C22⋊C4—442no—
523C22⋊C4—442no—
524C22⋊C4—442no—
525C22⋊C4—442no—
526C22⋊C4—442no—
527C42—42no—
528C42—221no—
529C42—221no—
530C42—221no—
531C42—221no—
532C42—442no—
533C42—881no—
534C42—881no—
535C42#434112yes—
536C42C2×C22⋊D1112yes—
537C11#2528711yescharacteristic, complemented, Sylow
538C23—441no—
539C23—441no—
540C23—441no—
541C23—441no—
542C23—441no—
543C23—441no—
544C23—441no—
545C23C2×D4×D1111yescharacteristic
546Q8—22no—
547Q8—22no—
548Q8—41no—
549Q8—41no—
550Q8—84no—
551Q8—441no—
552Q8—441no—
553Q8—441no—
554Q8—441no—
555D4—441no—
556D4—441no—
557D4—441no—
558D4—441no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—22no—
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—41no—
574C2×C4—41no—
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—221no—
587C2×C4—222no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4#6699212yes—
597C2×C4#6699212yes—
598C2×C4C2×#434111yescharacteristic
599C2×C4C2×#434311yescharacteristic
600C2×C4#6704011yescharacteristic
601C2×C4#41×D1111yescharacteristic
602C2×C4#6704211yescharacteristic
603C2×C4C22×C22⋊D1111yescharacteristic
604C8—41no—
605C8—41no—
606C8—441no—
607C8—441no—
608C22—881no—
609C22—881no—
610C22—881no—
611C22—881no—
612C22—881no—
613C22—881no—
614C22—881no—
615C22#1062316111yescharacteristic
616C22#1062316411yescharacteristic
617C22#1062329311yescharacteristic
618C22#1062329311yescharacteristic
619C22D11×#13711yescharacteristic
620C22#1062330811yescharacteristic
621C22C2×#6699211yescharacteristic
622C4—22no—
623C4—22no—
624C4—42no—
625C4—42no—
626C4—42no—
627C4—81no—
628C4—222no—
629C4—442no—
630C4—441no—
631C4—441no—
632C4—441no—
633C4—881no—
634C4—881no—
635C4#1062315511yescharacteristic
636C4#1062317411yescharacteristic
637C4#1062334811yescharacteristic
638C4#1062336511yescharacteristic
639C2—1761no—
640C2#1307218411yescharacteristic
641C2#1307808511yescharacteristic
642C2#1307812511yescharacteristic
643C2#1308072411yescharacteristic
644C2#1308079911yescharacteristic
645C2#1308135911yescharacteristic
646C2#1308145011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#475C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenterC2×#475D11
hypocenterC11#25287
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
3. #13071706C2semidirect
4. #13069992C2semidirect
6. #13069861C2semidirect
10. #13069537C2semidirect
11. #13069337C2semidirect
12. #13069249C2semidirect
14. #13068446C2semidirect
15. C2×C11×#475C2semidirect
216. C2×#475D11semidirect
537. C11#25287semidirect

Maximal subgroups

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

subgroupindex
C2×#106227022
#130735922
#130717062
#130699922
#130699852
#130698612
#130698542
#130695462
#130695452
#130695372
#130693372
#130692492
#130692422
#130684462
C2×C11×#4752
#2528711