Finite Group Databasebeta

← #14827039

Subgroups — #14827039

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#13073202C211yesmaximal, characteristic, complemented
2#13070149C211yesmaximal, characteristic, complemented
3#13069926C211yesmaximal, characteristic
4#13069852C211yesmaximal, characteristic, complemented
5#13069693C211yesmaximal, characteristic
6#13069473C211yesmaximal, characteristic, complemented
7#13069247C211yesmaximal, characteristic, complemented
8#13069243C211yesmaximal, characteristic, complemented
9#13069201C211yesmaximal, characteristic, complemented
10#13069175C211yesmaximal, characteristic, complemented
11#13068971C211yesmaximal, characteristic, complemented
12#13068964C211yesmaximal, characteristic
13#13068621C211yesmaximal, 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
21C2×#66951—21no—
22C11×#391C2211yescharacteristic
23C11×#390C2211yescharacteristic
24C11×#388—21no—
25C11×#388—21no—
26C11×#385—21no—
27C4×C11×C4⋊C4C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C4×C11×C22⋊C4—21no—
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36#10622607—21no—
37C2×#66873C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41#10622552C2211yescharacteristic
42#10622552C2211yescharacteristic
43#10622552C2211yescharacteristic
44#10622548C2211yescharacteristic
45C4×C4⋊Dic11C2211yescharacteristic
46#10622541C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622287—21no—
50#10622283—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⋊Dic11—21no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×Dic11⋊C4—21no—
102C2×C4×Dic11—21no—
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107#66951—44no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95D411yescharacteristic
112C11×#95D411yescharacteristic
113#66899—22no—
114#66899—41no—
115#66899—41no—
116#66896—22no—
117#66896—22no—
118#66896—41no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121#66873—22no—
122#66873—41no—
123#66872—22no—
124#66872—41no—
125C4⋊(C11⋊C8)—41no—
126C4×C11⋊C8—41no—
127#27071—111nomaximal, Sylow
128C24×C11—21no—
129C23×D11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11#4112yes—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11#4112yes—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—42no—
146C22×C4×C11—42no—
147C22×C4×C11—81no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2411yescharacteristic
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—42no—
170C11×C4⋊C4#4112yes—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—42no—
174C11×C22⋊C4—42no—
175C11×C22⋊C4—81no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—42no—
183C42×C11—81no—
184#4325—44no—
185#4323—44no—
186(C2×D11)⋊C4—42no—
187(C2×D11)⋊C4—42no—
188(C2×D11)⋊C4—42no—
189(C2×D11)⋊C4—42no—
190(C2×D11)⋊C4—81no—
191(C2×D11)⋊C4—81no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—42no—
199C4⋊Dic11—81no—
200Dic11⋊C4—42no—
201C4×Dic11—42no—
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—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8#4112yes—
214#2512—111no—
215#2367D1111yescharacteristic, complemented
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×#102—111no—
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—
244Q8×C11—22no—
245Q8×C11—22no—
246Q8×C11—41no—
247Q8×C11—41no—
248D4×C11—22no—
249D4×C11—22no—
250D4×C11—41no—
251D4×C11—41no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—22no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—22no—
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—21no—
269C2×C4×C11—21no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—84no—
278C2×C4×C11#13512yes—
279C2×C4×C11AGL(1,ℤ/8)12yes—
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C11H(5,𝔽2)11yescharacteristic
285C2×C4×C11H(5,𝔽2)11yescharacteristic
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295D44—41no—
296D44—41no—
297D44—41no—
298D44—41no—
299C11⋊C8—22no—
300C11⋊C8—41no—
301C11⋊C8—41no—
302C11⋊C8—41no—
303C22×SD16—111no—
304C22×D8—111no—
305C2×#126—221no—
306C2×#124C2×D1111yescharacteristic
307C2×C4×Q8C2×D1111yescharacteristic
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×#102—111no—
319C2×#102—111no—
320C2×C4×C8—111no—
321#397—221no—
322#396—221no—
323#391C2×D1111yescharacteristic
324#390—111no—
325#390—111no—
326#390—111no—
327#390C2×D1111yescharacteristic
328#389—111no—
329#388—21no—
330#388—21no—
331#388—221no—
332#385—21no—
333#384—111no—
334C4×C4⋊C4—111no—
335C4×C4⋊C4C2×D1111yescharacteristic
336C4×C4⋊C4C2×D1111yescharacteristic
337C4×C22⋊C4—21no—
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—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—22no—
369C4×C11—41no—
370C4×C11—41no—
371C4×C11—42no—
372C4×C11—41no—
373C4×C11—41no—
374C4×C11—42no—
375C4×C11—81no—
376C4×C11#52911yescharacteristic
377C4×C11#53811yescharacteristic
378C4×C11#55111yescharacteristic
379C4×C11#55311yescharacteristic
380Dic11—81no—
381Dic11—81no—
382Dic11—81no—
383C22×Q8C22×D1111yescharacteristic
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×C8—111no—
396C22×C8—111no—
397#126—444no—
398#124—22no—
399#124—22no—
400C4×Q8—22no—
401C4×Q8—41no—
402C4×D4—22no—
403C4×D4—41no—
404C2×C4⋊C4—21no—
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⋊C4C22⋊D1111yescharacteristic
412C2×C4⋊C4C22⋊D1111yescharacteristic
413C2×C4⋊C4C22×D1111yescharacteristic
414C2×C4⋊C4C22×D1111yescharacteristic
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
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—21no—
428C2×C42—221no—
429C2×C42C22×D1111yescharacteristic
430C2×C42C22×D1111yescharacteristic
431C2×C42C22×D1111yescharacteristic
432#106—222no—
433#106—441no—
434C4⋊C8—441no—
435#103—222no—
436#103—441no—
437#103—441no—
438#102—222no—
439#102—222no—
440#102—222no—
441#102—441no—
442#102—441no—
443C4×C8—441no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95—221no—
448#95—221no—
449#95C22⋊D1111yescharacteristic
450#95C22⋊D1111yescharacteristic
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—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8#433912yes—
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—221no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4C2×C22⋊D1111yescharacteristic
490C22×C4C2×C22⋊D1111yescharacteristic
491C22×C4C2×C22⋊D1111yescharacteristic
492C22×C4C2×C22⋊D1111yescharacteristic
493C22×C4C2×C22⋊D1111yescharacteristic
494C22×C4C2×C22⋊D1111yescharacteristic
495C22×C4C23×D1111yescharacteristic
496SD16—444no—
497D8—444no—
498C2×C8—112no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—221no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—42no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—442no—
523C4⋊C4—442no—
524C4⋊C4—881no—
525C4⋊C4#434112yes—
526C22⋊C4—24no—
527C22⋊C4—24no—
528C22⋊C4—42no—
529C22⋊C4—42no—
530C22⋊C4—81no—
531C22⋊C4—442no—
532C22⋊C4—442no—
533C22⋊C4—442no—
534C22⋊C4—442no—
535C22⋊C4—881no—
536C22⋊C4—881no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—42no—
544C42—81no—
545C42—442no—
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—
561C23C22×C22⋊D1111yescharacteristic
562Q8—22no—
563Q8—22no—
564Q8—41no—
565Q8—41no—
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—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—84no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4#6700212yes—
610C2×C4#6700312yes—
611C2×C4C2×#433911yescharacteristic
612C2×C4C2×#433911yescharacteristic
613C2×C4C2×#434111yescharacteristic
614C2×C4#6703711yescharacteristic
615C2×C4#41×D1111yescharacteristic
616C2×C4#6704211yescharacteristic
617C8—222no—
618C8—441no—
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#1062332211yescharacteristic
636C22#1062333711yescharacteristic
637C22C2×#6700211yescharacteristic
638C22C2×#6700311yescharacteristic
639C22#1062336511yescharacteristic
640C22#1062336711yescharacteristic
641C22#1062336811yescharacteristic
642C4—22no—
643C4—22no—
644C4—41no—
645C4—42no—
646C4—42no—
647C4—41no—
648C4—41no—
649C4—41no—
650C4—81no—
651C4—881no—
652C4—881no—
653C4—881no—
654C4#1062306911yescharacteristic
655C4#1062308711yescharacteristic
656C4#1062309111yescharacteristic
657C4#1062309611yescharacteristic
658C2—82no—
659C2—1761no—
660C2#1307266111yescharacteristic
661C2#1307867611yescharacteristic
662C2#1307889311yescharacteristic
663C2#1308051811yescharacteristic
664C2#1308057711yescharacteristic
665C2#1308160811yescharacteristic
666C2#1308163611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2367C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenter#2367D11
hypocenterC11#27071
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. #13073202C2semidirect
2. #13070149C2semidirect
4. #13069852C2semidirect
6. #13069473C2semidirect
7. #13069247C2semidirect
8. #13069243C2semidirect
9. #13069201C2semidirect
10. #13069175C2semidirect
11. #13068971C2semidirect
13. #13068621C2semidirect
14. C4×#66896C2semidirect
15. C11×#2367C2semidirect
215. #2367D11semidirect
546. C11#27071semidirect

Maximal subgroups

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

subgroupindex
#130732022
#130701492
#130699262
#130698522
#130696932
#130694732
#130692472
#130692432
#130692012
#130691752
#130689712
#130689642
#130686212
C4×#668962
C11×#23672
#2707111