Finite Group Databasebeta

← #14803327

Subgroups — #14803327

Order 2816.

800 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622458C211yesmaximal, characteristic
2#13074104C211yesmaximal, characteristic
3#13073982C211yesmaximal, characteristic, complemented
4#13070003C211yesmaximal, characteristic
5#13069996C211yesmaximal, characteristic, complemented
6#13069939C211yesmaximal, characteristic, complemented
7#13069934C211yesmaximal, characteristic
8#13069477C211yesmaximal, characteristic, complemented
9#13069470C211yesmaximal, characteristic
10#13069427C211yesmaximal, characteristic
11#13069386C211yesmaximal, characteristic, complemented
12#13069299C211yesmaximal, characteristic
13#13069292C211yesmaximal, characteristic, complemented
14C4×#66880C211yesmaximal, characteristic, complemented
15C2×C8×Q8×C11C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C22×Dic44C2211yescharacteristic
18C22×#4314C2211yescharacteristic
19C2×#66928C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C8×Q8×C11—24no—
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C2×C4×C8×C11C2211yescharacteristic
27C2×C4×C8×C11C2211yescharacteristic
28#10622844—21no—
29#10622842—21no—
30C2×#66885C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66885C2211yescharacteristic
33C2×#66882C2211yescharacteristic
34C2×#66881C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37C2×#66880C2211yescharacteristic
38C2×#66880C2211yescharacteristic
39C2×#66880C2211yescharacteristic
40#10622606—21no—
41#10622603—21no—
42#10622603—21no—
43#10622595—21no—
44#10622591—21no—
45#10622591—21no—
46#10622552C2211yescharacteristic
47#10622552C2211yescharacteristic
48#10622549C2211yescharacteristic
49C4×C4⋊Dic11C2211yescharacteristic
50#10622542C2211yescharacteristic
51#10622542C2211yescharacteristic
52#10622542C2211yescharacteristic
53#10622542C2211yescharacteristic
54#10622541C2211yescharacteristic
55#10622541C2211yescharacteristic
56#10622458—24no—
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61C22×Q8×C11D411yescharacteristic
62C22×D44C2311yescharacteristic
63C22×Dic22C2311yescharacteristic
64C22×Dic22C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C4×Q8×C11—22no—
70C4×Q8×C11—22no—
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×Dic44—22no—
94C2×Dic44—22no—
95C2×Dic44—41no—
96C2×#4314—22no—
97C2×#4314—22no—
98C2×#4314—41no—
99#66928—22no—
100#66928—22no—
101C4×Dic22—22no—
102C4×Dic22—22no—
103C11×C4⋊C8—22no—
104C11×C4⋊C8—22no—
105C11×C4⋊C8D414yes—
106C4×C8×C11—22no—
107C4×C8×C11—22no—
108C4×C8×C11—22no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122#66885—22no—
123#66885—22no—
124#66885—41no—
125#66882—41no—
126#66881—41no—
127#66880—22no—
128#66880—22no—
129#66880—22no—
130#66880—22no—
131#66880—41no—
132#25297—111nomaximal, Sylow
133C23×D11—21no—
134C2×Q8×C11—22no—
135C2×Q8×C11—22no—
136C2×Q8×C11—22no—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22#4112yes—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11C2×D412yes—
179C2×C8×C11C2×D412yes—
180C2×C8×C11#4112yes—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11C2×D412yes—
189C42×C11#4112yes—
190(C2×D11)⋊C4—42no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—81no—
195(C2×D11)⋊C4—81no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206Dic11⋊C4—42no—
207Dic11⋊C4—42no—
208Dic11⋊C4—42no—
209C4×Dic11—42no—
210C4×Dic11—81no—
211Dic44—44no—
212#4314—44no—
213C2×#464—111no—
214C2×C8×Q8D1111yescharacteristic, complemented
215#2592—111no—
216#2581—111no—
217#2067—111no—
218#2066—111no—
219#2056—111no—
220#2055—111no—
221#1969—111no—
222#1968—111no—
223#1958—111no—
224#1949—111no—
225#1934—111no—
226#1933—111no—
227C4×#103—111no—
228C23×C11C22×D411yescharacteristic
229C22×D11—41no—
230C22×D11—41no—
231C22×D11—41no—
232C22×D11—41no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—41no—
236Q8×C11—28no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11#12112yes—
252C2×C4×C11#12112yes—
253C2×C4×C11#13512yes—
254C2×C4×C11#13512yes—
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11H(5,𝔽2)11yescharacteristic
260C2×C4×C112−1+411yescharacteristic
261C2×Dic11—22no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
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—
281C2×Dic11—41no—
282D44—41no—
283D44—41no—
284D44—41no—
285D44—41no—
286Dic22—22no—
287Dic22—22no—
288Dic22—41no—
289Dic22—41no—
290Dic22—41no—
291Dic22—41no—
292Dic22—41no—
293Dic22—41no—
294C8×C11—22no—
295C8×C11—22no—
296C8×C11—22no—
297C8×C11—41no—
298C22×Q16—111no—
299C22×SD16—111no—
300C2×#124—111no—
301C2×C4×Q8—111no—
302C2×C4×Q8C2×D1111yescharacteristic
303#464—224no—
304C8×Q8—24no—
305C2×#107—111no—
306C2×#106—111no—
307C2×C4⋊C8C2×D1111yescharacteristic
308C2×C4⋊C8C2×D1111yescharacteristic
309C2×C4⋊C8C2×D1111yescharacteristic
310C2×#103—111no—
311C2×#103—111no—
312C2×#103—111no—
313C2×#103—111no—
314C2×#103—111no—
315C2×#102—111no—
316C2×#102—111no—
317C2×#102—111no—
318C2×C4×C8C2×D1111yescharacteristic
319C2×C4×C8C2×D1111yescharacteristic
320C2×C4×C8C2×D1111yescharacteristic
321#400—221no—
322#397—221no—
323#395—221no—
324#393—221no—
325#391—111no—
326#391—111no—
327#391—111no—
328#391—111no—
329#390—111no—
330#390—111no—
331#389—111no—
332#389—111no—
333#388—221no—
334#388—221no—
335#387—221no—
336#387—221no—
337#382—111no—
338C4×C4⋊C4—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#340—111no—
343C22×C11C2×#12111yescharacteristic
344C22×C11#54811yescharacteristic
345C22×C11#55011yescharacteristic
346C22×C11C2×#13511yescharacteristic
347C22×C11C2×#13511yescharacteristic
348C22×C11#57711yescharacteristic
349C22×C11#57811yescharacteristic
350C2×D11—81no—
351C2×D11—81no—
352C2×D11—81no—
353C2×D11—81no—
354C2×D11—81no—
355C2×D11—81no—
356C2×D11—81no—
357C4×C11—22no—
358C4×C11—22no—
359C4×C11—22no—
360C4×C11—22no—
361C4×C11—41no—
362C4×C11—41no—
363C4×C11#52911yescharacteristic
364C4×C11#54211yescharacteristic
365C4×C11#54611yescharacteristic
366C4×C11#54811yescharacteristic
367Dic11—42no—
368Dic11—81no—
369Dic11—81no—
370Dic11—81no—
371Dic11—81no—
372Dic11—81no—
373Dic11—81no—
374C22×Q8—111no—
375C22×Q8—111no—
376C22×Q8D4411yescharacteristic
377C22×D4—111no—
378C2×Q16—222no—
379C2×Q16—222no—
380C2×Q16—441no—
381C2×SD16—222no—
382C2×SD16—222no—
383C2×SD16—441no—
384C22×C8C22×D1111yescharacteristic
385C22×C8C22×D1111yescharacteristic
386C22×C8C22×D1111yescharacteristic
387C22×C8C22×D1111yescharacteristic
388#124—222no—
389#124—222no—
390C4×Q8—22no—
391C4×Q8—22no—
392C4×Q8—222no—
393C4×Q8—222no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4D4411yescharacteristic
403C2×C4⋊C4D4411yescharacteristic
404C2×C4⋊C4D4411yescharacteristic
405C2×C22⋊C4—221no—
406C2×C22⋊C4—221no—
407C2×C22⋊C4—221no—
408C2×C22⋊C4—221no—
409C2×C22⋊C4—221no—
410C2×C22⋊C4—221no—
411C2×C42—221no—
412C2×C42—221no—
413C2×C42C22×D1111yescharacteristic
414C2×C42C22×D1111yescharacteristic
415C2×C42C22×D1111yescharacteristic
416#107—441no—
417#106—441no—
418C4⋊C8—22no—
419C4⋊C8—22no—
420C4⋊C8C22⋊D1114yes—
421#103—222no—
422#103—222no—
423#103—222no—
424#103—222no—
425#103—441no—
426#102—222no—
427#102—222no—
428#102—441no—
429C4×C8—22no—
430C4×C8—22no—
431C4×C8—22no—
432#95—221no—
433#95—221no—
434#95—221no—
435#95—221no—
436#95—221no—
437#95—221no—
438#95—221no—
439#95—221no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445C2×C11#242611yescharacteristic
446C2×C11#305011yescharacteristic
447C2×C11#306311yescharacteristic
448C2×C11#336411yescharacteristic
449C2×C11#336511yescharacteristic
450C2×C11#339311yescharacteristic
451C2×C11#339411yescharacteristic
452D11—161no—
453C24—221no—
454C2×Q8—22no—
455C2×Q8—22no—
456C2×Q8—22no—
457C2×Q8—112no—
458C2×Q8—221no—
459C2×Q8—221no—
460C2×Q8—221no—
461C2×Q8—221no—
462C2×Q8—221no—
463C2×Q8—221no—
464C2×Q8—221no—
465C2×Q8—221no—
466C2×Q8—221no—
467C2×Q8—221no—
468C2×Q8—221no—
469C2×D4—221no—
470C2×D4—221no—
471C2×D4—221no—
472C2×D4—221no—
473C2×D4—221no—
474C2×D4—221no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4C2×D4411yescharacteristic
483C22×C4C2×D4411yescharacteristic
484C22×C4C2×D4411yescharacteristic
485C22×C4C2×D4411yescharacteristic
486C22×C4C2×D4411yescharacteristic
487C22×C4C2×D4411yescharacteristic
488C22×C4C23×D1111yescharacteristic
489Q16—444no—
490SD16—444no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8#434312yes—
501C2×C8C2×C22⋊D1112yes—
502C2×C8C2×C22⋊D1112yes—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—442no—
517C4⋊C4—442no—
518C4⋊C4—442no—
519C22⋊C4—442no—
520C22⋊C4—442no—
521C22⋊C4—442no—
522C22⋊C4—442no—
523C22⋊C4—881no—
524C22⋊C4—881no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—442no—
530C42—881no—
531C42#433912yes—
532C42C2×C22⋊D1112yes—
533C11#2529711yescharacteristic, complemented, Sylow
534C23—441no—
535C23—441no—
536C23—441no—
537C23—441no—
538C23—441no—
539C23—441no—
540C23—441no—
541C23C22×D4411yescharacteristic
542Q8—28no—
543Q8—222no—
544Q8—222no—
545Q8—441no—
546Q8—441no—
547Q8—441no—
548Q8—441no—
549Q8—441no—
550Q8—441no—
551D4—441no—
552D4—441no—
553D4—441no—
554D4—441no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—222no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
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—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4#6695712yes—
591C2×C4#6695712yes—
592C2×C4#6698312yes—
593C2×C4#6698312yes—
594C2×C4C2×#433911yescharacteristic
595C2×C4C2×#434311yescharacteristic
596C2×C4#6704011yescharacteristic
597C2×C4#41×D1111yescharacteristic
598C2×C4#6704211yescharacteristic
599C2×C4C22×C22⋊D1111yescharacteristic
600C8—22no—
601C8—22no—
602C8—22no—
603C8—41no—
604C22—881no—
605C22—881no—
606C22—881no—
607C22—881no—
608C22—881no—
609C22—881no—
610C22—881no—
611C22#1062310711yescharacteristic
612C22#1062310811yescharacteristic
613C22C2×#6695711yescharacteristic
614C22C2×#6695711yescharacteristic
615C22#1062328211yescharacteristic
616C22#1062328411yescharacteristic
617C22C2×#6698311yescharacteristic
618C4—22no—
619C4—22no—
620C4—22no—
621C4—22no—
622C4—41no—
623C4—41no—
624C4—442no—
625C4—881no—
626C4—881no—
627C4—881no—
628C4—881no—
629C4—881no—
630C4—881no—
631C4#1062311111yescharacteristic
632C4#1062311311yescharacteristic
633C4#1062334811yescharacteristic
634C4#1062336011yescharacteristic
635C2—1761no—
636C2#1307217611yescharacteristic
637C2#1307819711yescharacteristic
638C2#1307830711yescharacteristic
639C2#1308130311yescharacteristic
640C2#1308131411yescharacteristic
641C2#1308160511yescharacteristic
642C2#1308161411yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C8×Q8×C11C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenterC2×C8×Q8D11
hypocenterC11#25297
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×C8×Q8

Complements

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

NH ≅ G/Ntype
3. #13073982C2semidirect
5. #13069996C2semidirect
6. #13069939C2semidirect
8. #13069477C2semidirect
11. #13069386C2semidirect
13. #13069292C2semidirect
14. C4×#66880C2semidirect
15. C2×C8×Q8×C11C2semidirect
214. C2×C8×Q8D11semidirect
533. C11#25297semidirect

Maximal subgroups

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

subgroupindex
C2×#106224582
#130741042
#130739822
#130700032
#130699962
#130699392
#130699342
#130694772
#130694702
#130694272
#130693862
#130692992
#130692922
C4×#668802
C2×C8×Q8×C112
#2529711