Finite Group Databasebeta

← #14827045

Subgroups — #14827045

Order 2816.

802 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073196C211yesmaximal, characteristic, complemented
2#13071689C211yesmaximal, characteristic, complemented
3#13070147C211yesmaximal, characteristic, complemented
4#13069925C211yesmaximal, characteristic
5#13069855C211yesmaximal, characteristic, complemented
6#13069695C211yesmaximal, characteristic
7#13069470C211yesmaximal, characteristic, complemented
8#13069250C211yesmaximal, characteristic, complemented
9#13069241C211yesmaximal, characteristic, complemented
10#13069200C211yesmaximal, characteristic, complemented
11#13069173C211yesmaximal, characteristic, complemented
12#13068972C211yesmaximal, characteristic, complemented
13#13068964C211yesmaximal, characteristic
14#13068620C211yesmaximal, characteristic, complemented
15C4×C11×#102C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66989C2211yescharacteristic
18C22×#4323C2211yescharacteristic
19C22×#4314C2211yescharacteristic
20C2×#66940C2211yescharacteristic
21C2×#66929—21no—
22C2×C11×#102C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26#10622834C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28#10622823—21no—
29C4×C22⋊Dic11—21no—
30C2×#66885C2211yescharacteristic
31C2×#66881C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34#10622601C2211yescharacteristic
35#10622601C2211yescharacteristic
36#10622589C2211yescharacteristic
37C4⋊C4×Dic11C2211yescharacteristic
38#10622586C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43#10622558—21no—
44#10622557—21no—
45#10622553—21no—
46#10622552C2211yescharacteristic
47C4×Dic11⋊C4C2211yescharacteristic
48#10622542C2211yescharacteristic
49#10622289—21no—
50#10622288—21no—
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C22×D44C2311yescharacteristic
62C22×Dic22C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C4×D4×C11—22no—
66C4×D4×C11—41no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C22⋊C4—21no—
71C2×C42×C11—21no—
72C2×C42×C11C2311yescharacteristic
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77#66989—22no—
78#66989—22no—
79C2×#4323—22no—
80C2×#4323—41no—
81C2×#4323—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⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4D411yescharacteristic
95C2×Dic11⋊C4D411yescharacteristic
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11C2311yescharacteristic
99C2×C4×Dic11C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C2×#4314—22no—
103C2×#4314—22no—
104C2×#4314—41no—
105#66940—22no—
106#66940—41no—
107#66929—44no—
108C11×#102—22no—
109C11×#102—22no—
110C4×C8×C11—41no—
111C11×#95—21no—
112#66896—41no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95D411yescharacteristic
118C11⋊#95D411yescharacteristic
119#66885—41no—
120#66881—22no—
121#66880—41no—
122Dic11⋊C8—41no—
123#66874—22no—
124#66874—41no—
125#66873—22no—
126#66872—41no—
127#27071—111nomaximal, Sylow
128C24×C11—21no—
129C23×D11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11#4112yes—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—42no—
140C22×C4×C11—42no—
141C22×C4×C11—81no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C22×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22#4112yes—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11#4112yes—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4#4112yes—
176C11×C22⋊C4—42no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—42no—
180C22⋊Dic11—24no—
181C22⋊Dic11—24no—
182C22⋊Dic11—42no—
183C22⋊Dic11—81no—
184#4323—44no—
185(C2×D11)⋊C4—42no—
186(C2×D11)⋊C4—42no—
187(C2×D11)⋊C4—42no—
188(C2×D11)⋊C4—42no—
189(C2×D11)⋊C4—81no—
190(C2×D11)⋊C4—81no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195Dic11⋊C4—22no—
196Dic11⋊C4—22no—
197Dic11⋊C4—42no—
198Dic11⋊C4—42no—
199Dic11⋊C4—42no—
200Dic11⋊C4—81no—
201C4×Dic11—21no—
202C4×Dic11—21no—
203C4×Dic11—21no—
204C4×Dic11—21no—
205C4×Dic11—42no—
206C4×Dic11—81no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213#4314—44no—
214#2512—111no—
215#2367—111no—
216#2094—111no—
217#2054—111no—
218#2042—111no—
219#2012—111no—
220#1968—111no—
221#1927—111no—
222#1926—111no—
223#1920—111no—
224#1916—111no—
225#1880—111no—
226#1879—111no—
227#1803—111no—
228C4×#102D1111yescharacteristic, complemented
229C23×C11—22no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11C22×D411yescharacteristic
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—41no—
240C22×D11—41no—
241C22×D11—41no—
242C22×D11—41no—
243C22×D11—41no—
244D4×C11—22no—
245D4×C11—22no—
246D4×C11—41no—
247D4×C11—41no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—22no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—84no—
263C2×C4×C11AGL(1,ℤ/8)12yes—
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11H(5,𝔽2)11yescharacteristic
269C2×C4×C11H(5,𝔽2)11yescharacteristic
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—22no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11#13512yes—
291D44—41no—
292D44—41no—
293D44—41no—
294D44—41no—
295Dic22—22no—
296Dic22—22no—
297Dic22—41no—
298Dic22—41no—
299C8×C11—22no—
300C8×C11—41no—
301C11⋊C8—41no—
302C11⋊C8—41no—
303C22×SD16—111no—
304C22×D8—111no—
305C2×#126—221no—
306C2×#124—111no—
307C2×C4×Q8—111no—
308C2×C4×D4C2×D1111yescharacteristic
309C2×#106—111no—
310C2×#106—111no—
311C2×C4⋊C8—111no—
312C2×#103—111no—
313C2×#103—111no—
314C2×#103—111no—
315C2×#102—111no—
316C2×#102—111no—
317C2×#102—111no—
318C2×#102C2×D1111yescharacteristic
319C2×#102C2×D1111yescharacteristic
320C2×C4×C8C2×D1111yescharacteristic
321#397—221no—
322#396—221no—
323#391—111no—
324#390—111no—
325#390—111no—
326#390—111no—
327#390—111no—
328#389—111no—
329#388—221no—
330#388—221no—
331#388—221no—
332#385—221no—
333#384—111no—
334C4×C4⋊C4—111no—
335C4×C4⋊C4—111no—
336C4×C4⋊C4C2×D1111yescharacteristic
337C4×C22⋊C4—221no—
338#340—111no—
339#340—111no—
340#340C2×D1111yescharacteristic
341#340C2×D1111yescharacteristic
342#336—111no—
343#336—111no—
344#336—111no—
345#336—111no—
346C22×C11—42no—
347C22×C11—42no—
348C22×C11—42no—
349C22×C11—81no—
350C22×C11—81no—
351C22×C11—81no—
352C22×C11—81no—
353C22×C11#52511yescharacteristic
354C22×C11#54611yescharacteristic
355C22×C11#55011yescharacteristic
356C22×C11C2×#13511yescharacteristic
357C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
358C22×C11#57711yescharacteristic
359C22×C11#57711yescharacteristic
360C2×D11—81no—
361C2×D11—81no—
362C2×D11—81no—
363C2×D11—81no—
364C2×D11—81no—
365C2×D11—81no—
366C2×D11—81no—
367C4×C11—22no—
368C4×C11—41no—
369C4×C11—42no—
370C4×C11—81no—
371C4×C11—81no—
372C4×C11#52911yescharacteristic
373C4×C11#53811yescharacteristic
374C4×C11#55111yescharacteristic
375C4×C11#55311yescharacteristic
376Dic11—22no—
377Dic11—41no—
378Dic11—41no—
379Dic11—42no—
380Dic11—41no—
381Dic11—81no—
382Dic11—81no—
383C22×Q8—111no—
384C22×D4—111no—
385C22×D4C22×D1111yescharacteristic
386C23×C4—21no—
387C2×SD16—222no—
388C2×SD16—222no—
389C2×SD16—441no—
390C2×D8—222no—
391C2×D8—441no—
392C2×D8—441no—
393C22×C8—111no—
394C22×C8—111no—
395C22×C8C22×D1111yescharacteristic
396C22×C8C22×D1111yescharacteristic
397#126—444no—
398#124—222no—
399#124—222no—
400C4×Q8—222no—
401C4×Q8—441no—
402C4×D4—22no—
403C4×D4—41no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4C22×D1111yescharacteristic
413C2×C4⋊C4C22×D1111yescharacteristic
414C2×C4⋊C4C22×D1111yescharacteristic
415C2×C22⋊C4—21no—
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×C22⋊C4—221no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C42—21no—
427C2×C42—111no—
428C2×C42—111no—
429C2×C42—221no—
430C2×C42—221no—
431C2×C42C22×D1111yescharacteristic
432#106—222no—
433#106—441no—
434C4⋊C8—441no—
435#103—222no—
436#103—441no—
437#103—441no—
438#102—22no—
439#102—22no—
440#102—222no—
441#102—441no—
442#102—441no—
443C4×C8—41no—
444#95—21no—
445#95—111no—
446#95—111no—
447#95—221no—
448#95—221no—
449#95—221no—
450#95—221no—
451C2×C11—82no—
452C2×C11#246711yescharacteristic
453C2×C11#310611yescharacteristic
454C2×C11#312511yescharacteristic
455C2×C11#330111yescharacteristic
456C2×C11#330611yescharacteristic
457C2×C11#339411yescharacteristic
458C2×C11#339711yescharacteristic
459D11—161no—
460C24—21no—
461C24—221no—
462C2×Q8—112no—
463C2×Q8—221no—
464C2×Q8—221no—
465C2×Q8—221no—
466C2×Q8—221no—
467C2×Q8—221no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—221no—
474C2×D4—221no—
475C2×D4—221no—
476C2×D4—221no—
477C2×D4—221no—
478C2×D4—221no—
479C2×D4#433912yes—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—81no—
486C22×C4—111no—
487C22×C4—111no—
488C22×C4—111no—
489C22×C4—111no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4D4×D1111yescharacteristic
494C22×C4D4×D1111yescharacteristic
495C22×C4C23×D1111yescharacteristic
496SD16—444no—
497D8—444no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8#433912yes—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—222no—
516C4⋊C4—222no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—442no—
522C4⋊C4—442no—
523C4⋊C4—442no—
524C4⋊C4—881no—
525C4⋊C4#433912yes—
526C22⋊C4—42no—
527C22⋊C4—224no—
528C22⋊C4—224no—
529C22⋊C4—442no—
530C22⋊C4—442no—
531C22⋊C4—442no—
532C22⋊C4—442no—
533C22⋊C4—442no—
534C22⋊C4—881no—
535C22⋊C4—881no—
536C22⋊C4—881no—
537C42—21no—
538C42—21no—
539C42—42no—
540C42—221no—
541C42—221no—
542C42—221no—
543C42—221no—
544C42—442no—
545C42—881no—
546C11#2707111yescharacteristic, complemented, Sylow
547C23—22no—
548C23—41no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—441no—
555C23—441no—
556C23—441no—
557C23—441no—
558C23—441no—
559C23—441no—
560C23—441no—
561C23C2×D4×D1111yescharacteristic
562Q8—222no—
563Q8—222no—
564Q8—441no—
565Q8—441no—
566D4—22no—
567D4—22no—
568D4—41no—
569D4—41no—
570D4—441no—
571D4—441no—
572D4—441no—
573D4—441no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—84no—
589C2×C4—112no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—221no—
601C2×C4—222no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4#6696412yes—
611C2×C4C2×#433911yescharacteristic
612C2×C4C2×#433911yescharacteristic
613C2×C4C2×#433911yescharacteristic
614C2×C4#6703711yescharacteristic
615C2×C4#41×D1111yescharacteristic
616C2×C4#6704211yescharacteristic
617C8—22no—
618C8—41no—
619C8—441no—
620C8—441no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—81no—
628C22—881no—
629C22—881no—
630C22—881no—
631C22—881no—
632C22—881no—
633C22—881no—
634C22—881no—
635C22#1062302111yescharacteristic
636C22#1062307811yescharacteristic
637C22#1062308411yescharacteristic
638C22C2×#6696411yescharacteristic
639C22#1062329311yescharacteristic
640C22D11×#13511yescharacteristic
641C22#1062330111yescharacteristic
642C4—22no—
643C4—41no—
644C4—42no—
645C4—81no—
646C4—81no—
647C4—222no—
648C4—442no—
649C4—441no—
650C4—441no—
651C4—441no—
652C4—881no—
653C4—881no—
654C4#1062301011yescharacteristic
655C4#1062306111yescharacteristic
656C4#1062308711yescharacteristic
657C4#1062309111yescharacteristic
658C2—82no—
659C2—1761no—
660C2#1307266711yescharacteristic
661C2#1307867211yescharacteristic
662C2#1307888911yescharacteristic
663C2#1308051911yescharacteristic
664C2#1308057311yescharacteristic
665C2#1308161311yescharacteristic
666C2#1308163411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#102C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenterC4×#102D11
hypocenterC11#27071
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
1. #13073196C2semidirect
2. #13071689C2semidirect
3. #13070147C2semidirect
5. #13069855C2semidirect
7. #13069470C2semidirect
8. #13069250C2semidirect
9. #13069241C2semidirect
10. #13069200C2semidirect
11. #13069173C2semidirect
12. #13068972C2semidirect
14. #13068620C2semidirect
15. C4×C11×#102C2semidirect
228. C4×#102D11semidirect
546. C11#27071semidirect

Maximal subgroups

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

subgroupindex
#130731962
#130716892
#130701472
#130699252
#130698552
#130696952
#130694702
#130692502
#130692412
#130692002
#130691732
#130689722
#130689642
#130686202
C4×C11×#1022
#2707111