Finite Group Databasebeta

← #14775196

Subgroups — #14775196

Order 2816.

930 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
1C2×#10622581C211yesmaximal, characteristic
2#13071632C211yesmaximal, characteristic
3#13071493C211yesmaximal, characteristic, complemented
4#13069358C211yesmaximal, characteristic, complemented
5#13069314C211yesmaximal, characteristic, complemented
6#13069234C211yesmaximal, characteristic, complemented
7#13069199C211yesmaximal, characteristic, complemented
8#13069197C211yesmaximal, characteristic, complemented
9#13069044C211yesmaximal, characteristic
10#13068864C211yesmaximal, characteristic, complemented
11#13068804C211yesmaximal, characteristic, complemented
12#13068512C211yesmaximal, characteristic, complemented
13#13068440C211yesmaximal, characteristic, complemented
14#13068392C211yesmaximal, characteristic, complemented
15C2×C11×#340C211yesmaximal, characteristic, complemented
16C23×C8×C11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C2×#66983C2211yescharacteristic
20C2×C4×C22⋊D11—21no—
21C2×#66946C2211yescharacteristic
22#10622826—21no—
23#10622825—21no—
24#10622825C2211yescharacteristic
25C4×C22⋊Dic11—21no—
26C4×C22⋊Dic11C2211yescharacteristic
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66879C2211yescharacteristic
31C2×#66879C2211yescharacteristic
32#10622603—21no—
33#10622602—21no—
34#10622601C2211yescharacteristic
35#10622598C2211yescharacteristic
36#10622598C2211yescharacteristic
37#10622594—21no—
38#10622594—21no—
39C4⋊C4×Dic11C2211yescharacteristic
40C4⋊C4×Dic11C2211yescharacteristic
41C4⋊C4×Dic11C2211yescharacteristic
42#10622586C2211yescharacteristic
43#10622581C418yescomplemented
44C2×#66873C2211yescharacteristic
45C2×#66873C2211yescharacteristic
46C2×#66872C2211yescharacteristic
47C2×#66872C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49C2×#66871C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11—21no—
64C22×D44C2311yescharacteristic
65C22×C4×D11—21no—
66C22×C8×C11—22no—
67C22×C8×C11—22no—
68C22×C8×C11—41no—
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—41no—
76C2×C11×C4⋊C4C2×C414yescomplemented
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11D411yescharacteristic
83C2×C22⋊Dic11D411yescharacteristic
84#66983—22no—
85#66983C2×C414yes—
86C4×C22⋊D11—44no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×Dic11⋊C4—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11C2311yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104#66946—22no—
105#66946—41no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95D411yescharacteristic
114C11⋊#95D411yescharacteristic
115C22⋊(C11⋊C8)C2×C414yescomplemented
116#66885—22no—
117#66885—41no—
118#66879—22no—
119#66879—41no—
120#66873C2×C414yescomplemented
121#66873C2×C414yescomplemented
122#66872C2×C414yescomplemented
123#66872C2×C414yescomplemented
124#66871—22no—
125#66871—41no—
126#22936—111nomaximal, Sylow
127C24×C11C2×D411yescharacteristic
128C23×D11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—24no—
137C22×C4×C11—21no—
138C22×C4×C11—42no—
139C22×C4×C11—42no—
140C22×C4×C11—81no—
141C22×C4×C11—81no—
142C22×C4×C11—81no—
143C22×C4×C11C22×C412yes—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11#4112yes—
146C22×C4×C11C2411yescharacteristic
147C2×C22⋊D11—24no—
148C2×C22⋊D11—42no—
149C2×C22⋊D11—42no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44C22×C412yes—
163C2×C4×D11—42no—
164C2×C4×D11—42no—
165C2×C4×D11—81no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—44no—
172C2×C8×C11#4112yes—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—42no—
180C11×C4⋊C4C22×C412yes—
181C11×C4⋊C4C22×C412yes—
182C11×C4⋊C4#4112yes—
183C22⋊Dic11—22no—
184C22⋊Dic11—22no—
185C22⋊Dic11—42no—
186(C2×D11)⋊C4—24no—
187(C2×D11)⋊C4—42no—
188(C2×D11)⋊C4—42no—
189(C2×D11)⋊C4—81no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—81no—
196C4⋊Dic11—81no—
197C4⋊Dic11C22×C412yes—
198Dic11⋊C4—42no—
199C4×Dic11—21no—
200C4×Dic11—21no—
201C4×Dic11—21no—
202C4×Dic11—21no—
203C4×Dic11—42no—
204C4×Dic11—81no—
205C4×Dic11—81no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8C22×C412yes—
211C2×C11⋊C8C22×C412yes—
212C2×#481—111no—
213#2361—111no—
214#2345—111no—
215#1944—111no—
216#1936—111no—
217#1925—111no—
218#1920—111no—
219#1919—111no—
220#1893—111no—
221#1862—111no—
222#1852—111no—
223#1776—111no—
224#1762—111no—
225#1752—111no—
226C2×#340D1111yescharacteristic, complemented
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11C4×D412yes—
232C23×C11AGL(1,ℤ/8)12yes—
233C23×C11#13712yes—
234C23×C11C22×D411yescharacteristic
235C22×D11—22no—
236C22×D11—41no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—41no—
240C22×D11—41no—
241C22×D11—41no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
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—84no—
261C2×C4×C11—84no—
262C2×C4×C11C4×D412yes—
263C2×C4×C11C23×C411yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11H(5,𝔽2)11yescharacteristic
268C2×C4×C112−1+411yescharacteristic
269C22⋊D11—48no—
270C2×Dic11—22no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291D44—22no—
292D44—22no—
293D44—41no—
294D44—41no—
295C4×D11—84no—
296C8×C11—22no—
297C8×C11—41no—
298C11⋊C8—22no—
299C11⋊C8—22no—
300C23×C8C2×D1111yescharacteristic
301C2×#121—111no—
302C2×C4×D4—111no—
303C2×C4×D4—221no—
304C22×C4⋊C4C2×D1111yescharacteristic
305C22×C4⋊C4C2×D1111yescharacteristic
306#481—118no—
307C2×#107—111no—
308C2×#107—111no—
309C2×#106—111no—
310C2×#106—111no—
311C2×#102—111no—
312C2×#102—111no—
313C2×#102—111no—
314C2×#102—111no—
315C2×C22⋊C8—111no—
316C2×#97—111no—
317C2×#97—111no—
318#390—111no—
319#389—111no—
320#389—111no—
321#389—111no—
322#388—221no—
323#387—221no—
324#387—221no—
325#386—221no—
326#385—221no—
327#380—111no—
328#380—221no—
329C4×C4⋊C4—111no—
330C4×C4⋊C4—111no—
331C4×C4⋊C4—111no—
332C4×C22⋊C4—111no—
333C4×C22⋊C4—221no—
334#340—111no—
335#340—111no—
336#340—111no—
337#340—111no—
338#340C2×D1111yescharacteristic
339#340C2×D1111yescharacteristic
340#340C2×D1111yescharacteristic
341#340C2×D1111yescharacteristic
342#336—111no—
343#336—111no—
344C22×C11—22no—
345C22×C11—22no—
346C22×C11—22no—
347C22×C11—22no—
348C22×C11—22no—
349C22×C11—22no—
350C22×C11#44014yes—
351C22×C11C2×C4×D411yescharacteristic
352C22×C11#54611yescharacteristic
353C22×C11#54711yescharacteristic
354C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
355C22×C11C2×#13711yescharacteristic
356C22×C11#57611yescharacteristic
357C22×C11#57711yescharacteristic
358C2×D11—42no—
359C2×D11—42no—
360C2×D11—42no—
361C2×D11—81no—
362C2×D11—81no—
363C2×D11—81no—
364C2×D11—81no—
365C4×C11—22no—
366C4×C11—42no—
367C4×C11—42no—
368C4×C11—42no—
369C4×C11—81no—
370C4×C11C4×#4111yescharacteristic
371C4×C11#52011yescharacteristic
372C4×C11#55111yescharacteristic
373C4×C11#55211yescharacteristic
374Dic11—41no—
375Dic11—41no—
376Dic11—42no—
377Dic11—41no—
378Dic11—41no—
379Dic11—81no—
380Dic11—81no—
381C22×D4—111no—
382C22×D4—221no—
383C23×C4—21no—
384C23×C4—21no—
385C23×C4—221no—
386C23×C4C22×D1111yescharacteristic
387C22×C8—22no—
388C22×C8—22no—
389C22×C8—41no—
390C22×C8—111no—
391C22×C8—111no—
392C22×C8C22×D1111yescharacteristic
393C22×C8C22×D1111yescharacteristic
394#121—114no—
395#121—222no—
396C4×D4—222no—
397C4×D4—441no—
398C4×D4—444no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—41no—
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⋊C4C4×D1114yescomplemented
411C2×C4⋊C4C22×D1111yescharacteristic
412C2×C4⋊C4C22×D1111yescharacteristic
413C2×C4⋊C4C22×D1111yescharacteristic
414C2×C4⋊C4C22×D1111yescharacteristic
415C2×C22⋊C4—111no—
416C2×C22⋊C4—111no—
417C2×C22⋊C4—221no—
418C2×C22⋊C4—221no—
419C2×C22⋊C4—221no—
420C2×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C42—111no—
423C2×C42—111no—
424C2×C42—221no—
425C2×C42—221no—
426C2×C42—221no—
427#107—222no—
428#107—441no—
429#106—114no—
430#106—114no—
431#102—114no—
432#102—114no—
433#102—222no—
434#102—441no—
435C22⋊C8—114no—
436#97—222no—
437#97—441no—
438#95—111no—
439#95—111no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447C2×C11—24no—
448C2×C11#235911yescharacteristic
449C2×C11C2×#44011yescharacteristic
450C2×C11#294611yescharacteristic
451C2×C11#331611yescharacteristic
452C2×C11#331811yescharacteristic
453C2×C11#334511yescharacteristic
454C2×C11#334611yescharacteristic
455D11—82no—
456C24—221no—
457C24D4×D1111yescharacteristic
458C2×D4—112no—
459C2×D4—224no—
460C2×D4—221no—
461C2×D4—221no—
462C2×D4—221no—
463C2×D4—221no—
464C2×D4—221no—
465C2×D4—442no—
466C2×D4—442no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—24no—
475C22×C4—21no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—81no—
479C22×C4—81no—
480C22×C4—81no—
481C22×C4—111no—
482C22×C4—111no—
483C22×C4—111no—
484C22×C4—111no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—442no—
489C22×C4—442no—
490C22×C4—881no—
491C22×C4C2×C4×D1112yes—
492C22×C4D4×D1111yescharacteristic
493C22×C4#434112yes—
494C22×C4C23×D1111yescharacteristic
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—44no—
501C2×C8—112no—
502C2×C8—112no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8#433912yes—
508C4⋊C4—24no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—42no—
515C4⋊C4—112no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—442no—
522C4⋊C4—881no—
523C4⋊C4—881no—
524C4⋊C4C2×C4×D1112yes—
525C4⋊C4C2×C4×D1112yes—
526C4⋊C4#433912yes—
527C22⋊C4—222no—
528C22⋊C4—222no—
529C22⋊C4—224no—
530C22⋊C4—442no—
531C22⋊C4—442no—
532C22⋊C4—442no—
533C22⋊C4—881no—
534C42—221no—
535C42—221no—
536C42—221no—
537C42—221no—
538C42—442no—
539C42—881no—
540C42—881no—
541C11#2293611yescharacteristic, complemented, Sylow
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—222no—
547C23—441no—
548C23—441no—
549C23—441no—
550C23—441no—
551C23—441no—
552C23—441no—
553C23(C22⋊D11)⋊C412yes—
554C23#6696712yes—
555C23#6697112yes—
556C23C2×D4×D1111yescharacteristic
557D4—222no—
558D4—222no—
559D4—448no—
560D4—441no—
561D4—441no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—84no—
581C2×C4—84no—
582C2×C4—222no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—221no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—221no—
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—884no—
604C2×C4(C22⋊D11)⋊C412yes—
605C2×C4C22×C4×D1111yescharacteristic
606C2×C4C2×#433911yescharacteristic
607C2×C4C2×#433911yescharacteristic
608C2×C4C2×#434111yescharacteristic
609C2×C4#6703711yescharacteristic
610C2×C4#6704011yescharacteristic
611C8—22no—
612C8—41no—
613C8—222no—
614C8—222no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—22no—
621C22—442no—
622C22—442no—
623C22—442no—
624C22—881no—
625C22—881no—
626C22—881no—
627C22—881no—
628C22#1062243014yes—
629C22C2×(C22⋊D11)⋊C411yescharacteristic
630C22#1062302111yescharacteristic
631C22#1062303811yescharacteristic
632C22#1062328811yescharacteristic
633C22C2×#6696711yescharacteristic
634C22#1062329311yescharacteristic
635C22C2×#6697111yescharacteristic
636C4—22no—
637C4—42no—
638C4—42no—
639C4—42no—
640C4—81no—
641C4—441no—
642C4—441no—
643C4—442no—
644C4—441no—
645C4—441no—
646C4—881no—
647C4—881no—
648C4C4×#433911yescharacteristic
649C4#1062302611yescharacteristic
650C4#1062303511yescharacteristic
651C4#1062304411yescharacteristic
652C2—24no—
653C2—882no—
654C2#1307160411yescharacteristic
655C2C2×#1062243011yescharacteristic
656C2#1307744211yescharacteristic
657C2#1308072311yescharacteristic
658C2#1308075311yescharacteristic
659C2#1308108211yescharacteristic
660C2#1308109711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#340C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
cosocleC22×C4×C11C24
hypercenterC2×#340D11
hypocenterC11#22936
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
3. #13071493C2semidirect
4. #13069358C2semidirect
5. #13069314C2semidirect
6. #13069234C2semidirect
7. #13069199C2semidirect
8. #13069197C2semidirect
10. #13068864C2semidirect
11. #13068804C2semidirect
12. #13068512C2semidirect
13. #13068440C2semidirect
14. #13068392C2semidirect
15. C2×C11×#340C2semidirect
43. #10622581C4semidirect
76. C2×C11×C4⋊C4C2×C4semidirect
115. C22⋊(C11⋊C8)C2×C4semidirect
120. #66873C2×C4semidirect
121. #66873C2×C4semidirect
122. #66872C2×C4semidirect
123. #66872C2×C4semidirect
226. C2×#340D11semidirect
410. C2×C4⋊C4C4×D11semidirect
541. C11#22936semidirect

Maximal subgroups

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

subgroupindex
C2×#106225812
#130716322
#130714932
#130693582
#130693142
#130692342
#130691992
#130691972
#130690442
#130688642
#130688042
#130685122
#130684402
#130683922
C2×C11×#3402
#2293611