Finite Group Databasebeta

← #14827054

Subgroups — #14827054

Order 2816.

774 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073213C211yesmaximal, characteristic, complemented
2#13070137C211yesmaximal, characteristic, complemented
3#13069926C211yesmaximal, characteristic
4#13069852C211yesmaximal, characteristic, complemented
5#13069693C211yesmaximal, characteristic
6#13069473C211yesmaximal, characteristic, complemented
7#13069254C211yesmaximal, characteristic, complemented
8#13069236C211yesmaximal, characteristic, complemented
9#13069194C211yesmaximal, characteristic, complemented
10#13069175C211yesmaximal, characteristic, complemented
11#13068971C211yesmaximal, characteristic, complemented
12#13068964C211yesmaximal, characteristic
13#13068631C211yesmaximal, characteristic, complemented
14C4×#66896C211yesmaximal, characteristic, complemented
15C11×#2367C211yesmaximal, characteristic, complemented
16C2×C11×#124C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C22×#4325C2211yescharacteristic
20C22×#4323C2211yescharacteristic
21C11×#391C2211yescharacteristic
22C11×#390C2211yescharacteristic
23C11×#388—21no—
24C11×#388—21no—
25C11×#385—21no—
26C4×C11×C4⋊C4C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28C4×C11×C22⋊C4—21no—
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35#10622606—21no—
36#10622603—21no—
37C2×#66873C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41#10622552C2211yescharacteristic
42#10622552C2211yescharacteristic
43#10622552C2211yescharacteristic
44#10622549C2211yescharacteristic
45C4×C4⋊Dic11C2211yescharacteristic
46#10622541C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622288—21no—
50#10622282—21no—
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C22×D44C2311yescharacteristic
63C11×#124—22no—
64C11×#124—22no—
65C4×Q8×C11—22no—
66C4×Q8×C11—41no—
67C4×D4×C11—22no—
68C4×D4×C11—41no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C42×C11—21no—
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×#4325—22no—
85C2×#4325—22no—
86C2×#4325—41no—
87C2×#4323—22no—
88C2×#4323—41no—
89C2×#4323—41no—
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×(C2×D11)⋊C4—21no—
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×Dic11⋊C4—21no—
100C2×C4×Dic11—21no—
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C11×#95—21no—
106C11×#95—21no—
107C11×#95—21no—
108C11×#95D411yescharacteristic
109C11×#95D411yescharacteristic
110#66899—22no—
111#66899—41no—
112#66899—41no—
113#66896—22no—
114#66896—22no—
115#66896—41no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120#66873—22no—
121#66873—41no—
122#66872—22no—
123#66871—41no—
124C4⋊(C11⋊C8)—41no—
125C4×C11⋊C8—41no—
126#27072—111nomaximal, Sylow
127C24×C11—21no—
128C23×D11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11#4112yes—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11#4112yes—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—42no—
145C22×C4×C11—42no—
146C22×C4×C11—81no—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2411yescharacteristic
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—41no—
168C11×C4⋊C4—42no—
169C11×C4⋊C4#4112yes—
170C11×C22⋊C4—24no—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—42no—
173C11×C22⋊C4—42no—
174C11×C22⋊C4—81no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—42no—
182C42×C11—81no—
183#4325—44no—
184#4323—44no—
185(C2×D11)⋊C4—42no—
186(C2×D11)⋊C4—42no—
187(C2×D11)⋊C4—81no—
188(C2×D11)⋊C4—81no—
189(C2×D11)⋊C4—81no—
190(C2×D11)⋊C4—81no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197Dic11⋊C4—81no—
198C4×Dic11—81no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8#4112yes—
211#2513—111no—
212#2367D1111yescharacteristic, complemented
213#2092—111no—
214#2054—111no—
215#2042—111no—
216#2012—111no—
217#1968—111no—
218#1928—111no—
219#1925—111no—
220#1919—111no—
221#1916—111no—
222#1880—111no—
223#1879—111no—
224#1805—111no—
225C4×#102—111no—
226C23×C11—22no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11C22×D411yescharacteristic
234C22×D11—41no—
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—41no—
240C22×D11—41no—
241Q8×C11—22no—
242Q8×C11—22no—
243Q8×C11—41no—
244Q8×C11—41no—
245D4×C11—22no—
246D4×C11—22no—
247D4×C11—41no—
248D4×C11—41no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—22no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—22no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—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×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—84no—
276C2×C4×C11#13512yes—
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11H(5,𝔽2)11yescharacteristic
282C2×C4×C11H(5,𝔽2)11yescharacteristic
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292D44—41no—
293D44—41no—
294D44—41no—
295D44—41no—
296C11⋊C8—22no—
297C11⋊C8—41no—
298C11⋊C8—41no—
299C11⋊C8—41no—
300C22×SD16—111no—
301C22×D8—111no—
302C2×#124C2×D1111yescharacteristic
303C2×C4×Q8C2×D1111yescharacteristic
304C2×C4×D4C2×D1111yescharacteristic
305C2×#107—111no—
306C2×#106—111no—
307C2×C4⋊C8—111no—
308C2×#103—111no—
309C2×#103—111no—
310C2×#103—111no—
311C2×#102—111no—
312C2×#102—111no—
313C2×#102—111no—
314C2×#102—111no—
315C2×#102—111no—
316C2×C4×C8—111no—
317#397—221no—
318#397—221no—
319#391C2×D1111yescharacteristic
320#390—111no—
321#390—111no—
322#390—111no—
323#390C2×D1111yescharacteristic
324#389—111no—
325#388—21no—
326#388—21no—
327#388—221no—
328#388—221no—
329#385—21no—
330#382—111no—
331C4×C4⋊C4—111no—
332C4×C4⋊C4C2×D1111yescharacteristic
333C4×C4⋊C4C2×D1111yescharacteristic
334C4×C22⋊C4—21no—
335#340—111no—
336#340—111no—
337#340—111no—
338#340—111no—
339#336—111no—
340#336—111no—
341#336—111no—
342#336—111no—
343C22×C11—42no—
344C22×C11—42no—
345C22×C11—42no—
346C22×C11—81no—
347C22×C11—81no—
348C22×C11—81no—
349C22×C11—81no—
350C22×C11#52511yescharacteristic
351C22×C11#54611yescharacteristic
352C22×C11#55011yescharacteristic
353C22×C11C2×#13511yescharacteristic
354C22×C11#57511yescharacteristic
355C22×C11#57611yescharacteristic
356C22×C11#57711yescharacteristic
357C2×D11—81no—
358C2×D11—81no—
359C2×D11—81no—
360C2×D11—81no—
361C2×D11—81no—
362C2×D11—81no—
363C2×D11—81no—
364C4×C11—22no—
365C4×C11—41no—
366C4×C11—41no—
367C4×C11—42no—
368C4×C11—41no—
369C4×C11—42no—
370C4×C11—41no—
371C4×C11—41no—
372C4×C11—81no—
373C4×C11#52911yescharacteristic
374C4×C11#53811yescharacteristic
375C4×C11#55111yescharacteristic
376C4×C11#55311yescharacteristic
377Dic11—81no—
378Dic11—81no—
379Dic11—81no—
380C22×Q8C22×D1111yescharacteristic
381C22×D4—111no—
382C22×D4C22×D1111yescharacteristic
383C23×C4—21no—
384C2×SD16—222no—
385C2×SD16—222no—
386C2×SD16—441no—
387C2×D8—222no—
388C2×D8—441no—
389C2×D8—441no—
390C22×C8—111no—
391C22×C8—111no—
392C22×C8—111no—
393C22×C8—111no—
394#124—22no—
395#124—22no—
396C4×Q8—22no—
397C4×Q8—41no—
398C4×D4—22no—
399C4×D4—41no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4C22⋊D1111yescharacteristic
406C2×C4⋊C4C22⋊D1111yescharacteristic
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C4⋊C4C22×D1111yescharacteristic
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4—221no—
416C2×C22⋊C4—221no—
417C2×C22⋊C4—221no—
418C2×C22⋊C4—221no—
419C2×C22⋊C4—221no—
420C2×C42—21no—
421C2×C42—21no—
422C2×C42—221no—
423C2×C42C22×D1111yescharacteristic
424C2×C42C22×D1111yescharacteristic
425C2×C42C22×D1111yescharacteristic
426#107—441no—
427#106—222no—
428C4⋊C8—441no—
429#103—222no—
430#103—441no—
431#103—441no—
432#102—222no—
433#102—222no—
434#102—222no—
435#102—441no—
436#102—441no—
437C4×C8—441no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95C22⋊D1111yescharacteristic
446#95C22⋊D1111yescharacteristic
447C2×C11—82no—
448C2×C11#246711yescharacteristic
449C2×C11#310211yescharacteristic
450C2×C11#311911yescharacteristic
451C2×C11#329711yescharacteristic
452C2×C11#332111yescharacteristic
453C2×C11#339411yescharacteristic
454C2×C11#340311yescharacteristic
455D11—161no—
456C24—21no—
457C24—221no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8#433912yes—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—221no—
470C2×D4—221no—
471C2×D4—221no—
472C2×D4—221no—
473C2×D4—221no—
474C2×D4—221no—
475C2×D4#433912yes—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—81no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4C2×C22⋊D1111yescharacteristic
486C22×C4C2×C22⋊D1111yescharacteristic
487C22×C4C2×C22⋊D1111yescharacteristic
488C22×C4C2×C22⋊D1111yescharacteristic
489C22×C4C2×C22⋊D1111yescharacteristic
490C22×C4C2×C22⋊D1111yescharacteristic
491C22×C4C23×D1111yescharacteristic
492SD16—444no—
493D8—444no—
494C2×C8—112no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C4⋊C4—22no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—41no—
511C4⋊C4—42no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—881no—
519C4⋊C4#434112yes—
520C22⋊C4—24no—
521C22⋊C4—24no—
522C22⋊C4—42no—
523C22⋊C4—42no—
524C22⋊C4—81no—
525C22⋊C4—442no—
526C22⋊C4—442no—
527C22⋊C4—881no—
528C22⋊C4—881no—
529C22⋊C4—881no—
530C22⋊C4—881no—
531C42—21no—
532C42—21no—
533C42—21no—
534C42—21no—
535C42—21no—
536C42—21no—
537C42—42no—
538C42—81no—
539C42—881no—
540C11#2707211yescharacteristic, complemented, Sylow
541C23—22no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—441no—
549C23—441no—
550C23—441no—
551C23—441no—
552C23—441no—
553C23—441no—
554C23—441no—
555C23C22×C22⋊D1111yescharacteristic
556Q8—22no—
557Q8—22no—
558Q8—41no—
559Q8—41no—
560D4—22no—
561D4—22no—
562D4—41no—
563D4—41no—
564D4—441no—
565D4—441no—
566D4—441no—
567D4—441no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—84no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4#6700312yes—
605C2×C4C2×#433911yescharacteristic
606C2×C4C2×#433911yescharacteristic
607C2×C4C2×#434111yescharacteristic
608C2×C4#6703711yescharacteristic
609C2×C4#41×D1111yescharacteristic
610C2×C4#6704211yescharacteristic
611C8—222no—
612C8—441no—
613C8—441no—
614C8—441no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—81no—
619C22—81no—
620C22—81no—
621C22—81no—
622C22—881no—
623C22—881no—
624C22—881no—
625C22—881no—
626C22—881no—
627C22—881no—
628C22—881no—
629C22#1062332211yescharacteristic
630C22#1062333711yescharacteristic
631C22C2×#6700311yescharacteristic
632C22#1062335311yescharacteristic
633C22#1062336511yescharacteristic
634C22#1062336611yescharacteristic
635C22#1062336811yescharacteristic
636C4—22no—
637C4—42no—
638C4—41no—
639C4—41no—
640C4—41no—
641C4—42no—
642C4—41no—
643C4—41no—
644C4—81no—
645C4—881no—
646C4—881no—
647C4—881no—
648C4#1062306911yescharacteristic
649C4#1062308711yescharacteristic
650C4#1062309111yescharacteristic
651C4#1062309611yescharacteristic
652C2—82no—
653C2—1761no—
654C2#1307266111yescharacteristic
655C2#1307863411yescharacteristic
656C2#1307881511yescharacteristic
657C2#1308046611yescharacteristic
658C2#1308080211yescharacteristic
659C2#1308161211yescharacteristic
660C2#1308170011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2367C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenter#2367D11
hypocenterC11#27072
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2367

Complements

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

NH ≅ G/Ntype
1. #13073213C2semidirect
2. #13070137C2semidirect
4. #13069852C2semidirect
6. #13069473C2semidirect
7. #13069254C2semidirect
8. #13069236C2semidirect
9. #13069194C2semidirect
10. #13069175C2semidirect
11. #13068971C2semidirect
13. #13068631C2semidirect
14. C4×#66896C2semidirect
15. C11×#2367C2semidirect
212. #2367D11semidirect
540. C11#27072semidirect

Maximal subgroups

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

subgroupindex
#130732132
#130701372
#130699262
#130698522
#130696932
#130694732
#130692542
#130692362
#130691942
#130691752
#130689712
#130689642
#130686312
C4×#668962
C11×#23672
#2707211