Finite Group Databasebeta

← #14813909

Subgroups — #14813909

Order 2816.

826 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622798C211yesmaximal, characteristic
2#13072408C211yesmaximal, characteristic
3Q8×Dic11⋊C4C211yesmaximal, characteristic, complemented
4#13070141C211yesmaximal, characteristic
5#13070105C211yesmaximal, characteristic, complemented
6#13070027C211yesmaximal, characteristic, complemented
7#13069853C211yesmaximal, characteristic
8#13069299C211yesmaximal, characteristic
9#13069173C211yesmaximal, characteristic, complemented
10#13068971C211yesmaximal, characteristic
11#13068969C211yesmaximal, characteristic
12#13068959C211yesmaximal, characteristic, complemented
13#13068870C211yesmaximal, characteristic, complemented
14#13068868C211yesmaximal, characteristic, complemented
15C2×C4×C11×Q16C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×#67000C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic
22C22×#4325C2211yescharacteristic
23C4×C11×Q16—24no—
24C2×C11×#107C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C4×C8×C11C2211yescharacteristic
28#10622843C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32#10622798—24no—
33C2×#66885C2211yescharacteristic
34C2×#66885C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36#10622606—21no—
37#10622605—21no—
38#10622601C2211yescharacteristic
39#10622589—21no—
40#10622589C2211yescharacteristic
41#10622586—21no—
42#10622586C2211yescharacteristic
43#10622586C2211yescharacteristic
44C2×#66873C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622553—21no—
47#10622553—21no—
48#10622552C2211yescharacteristic
49C4×Dic11⋊C4—21no—
50C4×Dic11⋊C4C2211yescharacteristic
51#10622541—21no—
52#10622541C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D44C2311yescharacteristic
64C2×C11×Q16—22no—
65C2×C11×Q16—22no—
66C2×C11×Q16D414yes—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C4×Q8×C11—22no—
70C4×Q8×C11—22no—
71C4×Q8×C11—41no—
72C4×Q8×C11—41no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C42×C11—21no—
78C2×C42×C11—21no—
79C2×C42×C11C2311yescharacteristic
80#67000—22no—
81#67000—41no—
82Q8×Dic11—22no—
83Q8×Dic11—22no—
84Q8×Dic11—22no—
85Q8×Dic11—41no—
86C2×#4325—22no—
87C2×#4325—22no—
88C2×#4325—22no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—21no—
105C2×Dic11⋊C4D411yescharacteristic
106C2×Dic11⋊C4D411yescharacteristic
107C2×C4×Dic11—21no—
108C2×C4×Dic11—21no—
109C2×C4×Dic11C2311yescharacteristic
110C2×C4×Dic11C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C22×C11⋊C8C2311yescharacteristic
113C11×#107—22no—
114C11×#103—22no—
115C11×#103—22no—
116C4×C8×C11—22no—
117#66899—22no—
118#66899—22no—
119#66899—22no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95D411yescharacteristic
126C11⋊#95D411yescharacteristic
127#66885—22no—
128#66885—22no—
129Dic11⋊C8—22no—
130#66873—41no—
131#66871—41no—
132#26169—111nomaximal, Sylow
133C23×D11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11C2×D412yes—
143C2×Q8×C11C2×D412yes—
144C2×Q8×C11#4112yes—
145C2×Q8×C11#4112yes—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C11×Q16—28no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11C2×D412yes—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—42no—
178C11×C4⋊C4—42no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—42no—
182C42×C11—42no—
183#4325—44no—
184(C2×D11)⋊C4—42no—
185(C2×D11)⋊C4—42no—
186(C2×D11)⋊C4—42no—
187(C2×D11)⋊C4—42no—
188(C2×D11)⋊C4—81no—
189(C2×D11)⋊C4—81no—
190C4⋊Dic11—24no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—42no—
197C4⋊Dic11#4112yes—
198Dic11⋊C4—22no—
199Dic11⋊C4—22no—
200Dic11⋊C4—42no—
201Dic11⋊C4—81no—
202Dic11⋊C4—81no—
203Dic11⋊C4—81no—
204Dic11⋊C4—81no—
205C4×Dic11—24no—
206C4×Dic11—21no—
207C4×Dic11—21no—
208C4×Dic11—21no—
209C4×Dic11—21no—
210C4×Dic11—42no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×#464—111no—
218C2×C4×Q16D1111yescharacteristic, complemented
219#2448—111no—
220Q8×C4⋊C4—111no—
221#2093—111no—
222#2086—111no—
223#2072—111no—
224#2042—111no—
225#1934—111no—
226#1916—111no—
227#1880—111no—
228#1880—111no—
229#1878—111no—
230#1863—111no—
231#1863—111no—
232C23×C11C22×D411yescharacteristic
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—41no—
240Q8×C11—22no—
241Q8×C11—22no—
242Q8×C11—22no—
243Q8×C11—22no—
244Q8×C11—22no—
245Q8×C11—41no—
246Q8×C11—41no—
247Q8×C11#12314yes—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—21no—
251C2×C4×C11—22no—
252C2×C4×C11—21no—
253C2×C4×C11—22no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11#13712yes—
266C2×C4×C11C22×D411yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11H(5,𝔽2)11yescharacteristic
271C2×C4×C112−1+411yescharacteristic
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—22no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11#13512yes—
293D44—41no—
294D44—41no—
295D44—41no—
296D44—41no—
297C8×C11—22no—
298C8×C11—41no—
299C11⋊C8—41no—
300C11⋊C8—41no—
301C22×Q16C2×D1111yescharacteristic
302C22×SD16—111no—
303C2×#124—111no—
304C2×C4×Q8—111no—
305C2×C4×Q8—111no—
306C2×C4×Q8C2×D1111yescharacteristic
307C2×C4×Q8C2×D1111yescharacteristic
308#464—224no—
309C4×Q16—24no—
310C2×#107—111no—
311C2×#107C2×D1111yescharacteristic
312C2×C4⋊C8—111no—
313C2×#103—111no—
314C2×#103—111no—
315C2×#103—111no—
316C2×#103C2×D1111yescharacteristic
317C2×#103C2×D1111yescharacteristic
318C2×#102—111no—
319C2×#102—111no—
320C2×#102—111no—
321C2×C4×C8C2×D1111yescharacteristic
322#399—221no—
323#397—221no—
324#391—111no—
325#390—111no—
326#390—111no—
327#389—111no—
328#389—111no—
329#389—111no—
330#389—221no—
331#389—221no—
332#388—221no—
333#388—221no—
334#384—111no—
335#384—221no—
336C4×C4⋊C4—111no—
337C4×C4⋊C4—221no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#336—111no—
343#336—111no—
344#336—111no—
345#336—111no—
346C22×C11#52511yescharacteristic
347C22×C11D4211yescharacteristic
348C22×C11#54811yescharacteristic
349C22×C11C2×#13511yescharacteristic
350C22×C11C2×#13711yescharacteristic
351C22×C11#57611yescharacteristic
352C22×C11#57811yescharacteristic
353C2×D11—81no—
354C2×D11—81no—
355C2×D11—81no—
356C2×D11—81no—
357C2×D11—81no—
358C2×D11—81no—
359C2×D11—81no—
360C4×C11—24no—
361C4×C11—22no—
362C4×C11—42no—
363C4×C11—41no—
364C4×C11—81no—
365C4×C11—81no—
366C4×C11C2×#12311yescharacteristic
367C4×C11#53911yescharacteristic
368C4×C11#54711yescharacteristic
369C4×C11#55311yescharacteristic
370Dic11—22no—
371Dic11—41no—
372Dic11—42no—
373Dic11—41no—
374Dic11—41no—
375Dic11—81no—
376Dic11—81no—
377C22×Q8C22×D1111yescharacteristic
378C22×Q8C22×D1111yescharacteristic
379C22×D4—111no—
380C2×Q16—22no—
381C2×Q16—22no—
382C2×Q16C22⋊D1114yes—
383C2×SD16—222no—
384C2×SD16—222no—
385C2×SD16—222no—
386C22×C8—111no—
387C22×C8—111no—
388C22×C8C22×D1111yescharacteristic
389C22×C8C22×D1111yescharacteristic
390#124—222no—
391#124—441no—
392C4×Q8—22no—
393C4×Q8—22no—
394C4×Q8—41no—
395C4×Q8—41no—
396C4×Q8—222no—
397C4×Q8—222no—
398C4×Q8—222no—
399C4×Q8—441no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4C22×D1111yescharacteristic
415C2×C4⋊C4C22×D1111yescharacteristic
416C2×C22⋊C4—221no—
417C2×C22⋊C4—221no—
418C2×C22⋊C4—221no—
419C2×C22⋊C4—221no—
420C2×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C42—21no—
423C2×C42—21no—
424C2×C42—111no—
425C2×C42—111no—
426C2×C42—221no—
427C2×C42—221no—
428C2×C42C22×D1111yescharacteristic
429#107—22no—
430#107—441no—
431C4⋊C8—222no—
432#103—22no—
433#103—22no—
434#103—222no—
435#103—222no—
436#103—222no—
437#102—222no—
438#102—222no—
439#102—441no—
440C4×C8—22no—
441#95—111no—
442#95—111no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447#95—221no—
448C2×C11#244311yescharacteristic
449C2×C11#310811yescharacteristic
450C2×C11#312411yescharacteristic
451C2×C11#327011yescharacteristic
452C2×C11#328711yescharacteristic
453C2×C11#336411yescharacteristic
454C2×C11#337511yescharacteristic
455D11—161no—
456C24—221no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8#433912yes—
466C2×Q8#433912yes—
467C2×Q8C2×C22⋊D1112yes—
468C2×Q8C2×C22⋊D1112yes—
469C2×D4—221no—
470C2×D4—221no—
471C2×D4—221no—
472C2×D4—221no—
473C2×D4—221no—
474C2×D4—221no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—111no—
480C22×C4—111no—
481C22×C4—111no—
482C22×C4—111no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4D4×D1111yescharacteristic
487C22×C4D4×D1111yescharacteristic
488C22×C4C23×D1111yescharacteristic
489Q16—28no—
490SD16—444no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8C2×C22⋊D1112yes—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—42no—
508C4⋊C4—42no—
509C4⋊C4—112no—
510C4⋊C4—222no—
511C4⋊C4—224no—
512C4⋊C4—222no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—442no—
519C4⋊C4—442no—
520C4⋊C4—881no—
521C4⋊C4—881no—
522C4⋊C4—881no—
523C4⋊C4—881no—
524C22⋊C4—442no—
525C22⋊C4—442no—
526C22⋊C4—442no—
527C22⋊C4—442no—
528C22⋊C4—881no—
529C22⋊C4—881no—
530C42—21no—
531C42—21no—
532C42—42no—
533C42—42no—
534C42—224no—
535C42—221no—
536C42—221no—
537C42—221no—
538C42—221no—
539C42—442no—
540C11#2616911yescharacteristic, complemented, Sylow
541C23—441no—
542C23—441no—
543C23—441no—
544C23—441no—
545C23—441no—
546C23—441no—
547C23—441no—
548C23C2×D4×D1111yescharacteristic
549Q8—22no—
550Q8—22no—
551Q8—22no—
552Q8—22no—
553Q8—22no—
554Q8—41no—
555Q8—41no—
556Q8#6698214yes—
557D4—441no—
558D4—441no—
559D4—441no—
560D4—441no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—112no—
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—221no—
588C2×C4—221no—
589C2×C4—222no—
590C2×C4—221no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4#6697112yes—
600C2×C4C2×#433911yescharacteristic
601C2×C4C2×#433911yescharacteristic
602C2×C4#6703711yescharacteristic
603C2×C4#41×D1111yescharacteristic
604C2×C4#6704311yescharacteristic
605C2×C4C22×C22⋊D1111yescharacteristic
606C8—22no—
607C8—41no—
608C8—441no—
609C8—441no—
610C22—881no—
611C22—881no—
612C22—881no—
613C22—881no—
614C22—881no—
615C22—881no—
616C22—881no—
617C22#1062307811yescharacteristic
618C22#1062308311yescharacteristic
619C22C2×#6697111yescharacteristic
620C22#1062329711yescharacteristic
621C22D11×#13511yescharacteristic
622C22#1062330011yescharacteristic
623C22D4×C22⋊D1111yescharacteristic
624C4—22no—
625C4—24no—
626C4—41no—
627C4—42no—
628C4—81no—
629C4—81no—
630C4—222no—
631C4—441no—
632C4—441no—
633C4—442no—
634C4—441no—
635C4—881no—
636C4—881no—
637C4#1062307111yescharacteristic
638C4#1062309511yescharacteristic
639C4C2×#6698211yescharacteristic
640C4#1062335511yescharacteristic
641C2—1761no—
642C2#1307234511yescharacteristic
643C2#1307870011yescharacteristic
644C2#1307888411yescharacteristic
645C2#1308018611yescharacteristic
646C2#1308037011yescharacteristic
647C2#1308130211yescharacteristic
648C2#1308142811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C4×C11×Q16C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenterC2×C4×Q16D11
hypocenterC11#26169
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
3. Q8×Dic11⋊C4C2semidirect
5. #13070105C2semidirect
6. #13070027C2semidirect
9. #13069173C2semidirect
12. #13068959C2semidirect
13. #13068870C2semidirect
14. #13068868C2semidirect
15. C2×C4×C11×Q16C2semidirect
218. C2×C4×Q16D11semidirect
540. C11#26169semidirect

Maximal subgroups

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

subgroupindex
C2×#106227982
#130724082
Q8×Dic11⋊C42
#130701412
#130701052
#130700272
#130698532
#130692992
#130691732
#130689712
#130689692
#130689592
#130688702
#130688682
C2×C4×C11×Q162
#2616911