Finite Group Databasebeta

← #14817324

Subgroups — #14817324

Order 2816.

902 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072312C211yesmaximal, characteristic, complemented
2#13071632C211yesmaximal, characteristic
3#13070176C211yesmaximal, characteristic, complemented
4#13070108C211yesmaximal, characteristic, complemented
5#13070005C211yesmaximal, characteristic, complemented
6#13069751C211yesmaximal, characteristic, complemented
7#13069566C211yesmaximal, characteristic, complemented
8#13069185C211yesmaximal, characteristic, complemented
9#13069044C211yesmaximal, characteristic
10#13068933C211yesmaximal, characteristic
11#13068864C211yesmaximal, characteristic, complemented
12#13068804C211yesmaximal, characteristic, complemented
13#13068794C211yesmaximal, characteristic, complemented
14#13068615C211yesmaximal, 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×#66977—21no—
22C2×#66946C2211yescharacteristic
23C2×#66941C2211yescharacteristic
24#10622826—21no—
25#10622825C2211yescharacteristic
26#10622823—21no—
27C4×C22⋊Dic11C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33#10622603—21no—
34#10622602—21no—
35#10622601C2211yescharacteristic
36#10622598C2211yescharacteristic
37#10622597—21no—
38#10622592—21no—
39#10622589C2211yescharacteristic
40C4⋊C4×Dic11C2211yescharacteristic
41#10622586C2211yescharacteristic
42#10622586C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66873C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47C11×#340C2211yescharacteristic
48C11×#340C2211yescharacteristic
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C23×C4×C11—21no—
60C23×C4×C11—21no—
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×Dic22—21no—
66C22×C8×C11—22no—
67C22×C8×C11—41no—
68C22×C8×C11—41no—
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—22no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—41no—
76C2×C11×C4⋊C4—41no—
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#66983Q814yescomplemented
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⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95#66977—44no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11C2311yescharacteristic
103C2×C4×Dic11C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106#66946—22no—
107#66946—41no—
108#66941—22no—
109#66941—41no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95D411yescharacteristic
116C11⋊#95D411yescharacteristic
117C22⋊(C11⋊C8)—22no—
118#66885—41no—
119#66885—41no—
120Dic11⋊C8—41no—
121Dic11⋊C8—41no—
122#66873—22no—
123#66873—41no—
124#66871—22no—
125#66871—41no—
126#26408—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—21no—
137C22×C4×C11—42no—
138C22×C4×C11—42no—
139C22×C4×C11—42no—
140C22×C4×C11—42no—
141C22×C4×C11—81no—
142C22×C4×C11—81no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×Q812yes—
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×D44C2×Q812yes—
163C2×C4×D11—42no—
164C2×C4×D11—42no—
165C2×C4×D11—81no—
166C2×Dic22—42no—
167C2×Dic22—42no—
168C2×Dic22—81no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—44no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—42no—
183C11×C4⋊C4—42no—
184C11×C4⋊C4#4112yes—
185C11×C4⋊C4#4112yes—
186C22⋊Dic11—22no—
187C22⋊Dic11—42no—
188C22⋊Dic11D814yes—
189(C2×D11)⋊C4—24no—
190(C2×D11)⋊C4—42no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—81no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—42no—
199C4⋊Dic11C2×Q812yes—
200Dic11⋊C4—42no—
201Dic11⋊C4—42no—
202Dic11⋊C4—42no—
203Dic11⋊C4—42no—
204Dic11⋊C4—81no—
205C4×Dic11—21no—
206C4×Dic11—21no—
207C4×Dic11—21no—
208C4×Dic11—21no—
209C4×Dic11—42no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216#2440—111no—
217#2361—111no—
218#2099—111no—
219#2086—111no—
220#2067—111no—
221#2023—111no—
222#1988—111no—
223#1918—111no—
224#1893—111no—
225#1874—111no—
226#1862—111no—
227#1852—111no—
228#1850—111no—
229#1802—111no—
230C2×#340D1111yescharacteristic, complemented
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11C22⋊Q812yes—
236C23×C11C2×D812yes—
237C23×C11#13712yes—
238C23×C11C22×D411yescharacteristic
239C22×D11—22no—
240C22×D11—41no—
241C22×D11—41no—
242C22×D11—41no—
243C22×D11—41no—
244C22×D11—41no—
245C22×D11—41no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
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—41no—
263C2×C4×C11—41no—
264C2×C4×C11—84no—
265C2×C4×C11—84no—
266C2×C4×C11C22⋊Q812yes—
267C2×C4×C11C22×Q811yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11H(5,𝔽2)11yescharacteristic
272C2×C4×C11H(5,𝔽2)11yescharacteristic
273C22⋊D11—48no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—22no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11C2×D812yes—
294C2×Dic11C2×D812yes—
295D44—22no—
296D44—22no—
297D44—41no—
298D44—41no—
299C4×D11—84no—
300Dic22—84no—
301C8×C11—41no—
302C8×C11—41no—
303C11⋊C8—41no—
304C11⋊C8—41no—
305C23×C8C2×D1111yescharacteristic
306C2×C4⋊Q8—111no—
307C2×C22⋊Q8—221no—
308C2×#121—111no—
309C2×C4×D4—111no—
310C2×C4×D4—221no—
311C22×C4⋊C4C2×D1111yescharacteristic
312C22×C4⋊C4C2×D1111yescharacteristic
313C2×#107—111no—
314C2×#107—111no—
315C2×C4⋊C8—111no—
316C2×C4⋊C8—111no—
317C2×#102—111no—
318C2×#102—111no—
319C2×#102—111no—
320C2×#102—111no—
321C2×C22⋊C8—111no—
322#398—221no—
323#395—221no—
324#390—111no—
325#389—111no—
326#389—111no—
327#389—111no—
328#388—221no—
329#386—221no—
330#385—221no—
331#385—221no—
332#384—111no—
333#380—111no—
334C4×C4⋊C4—111no—
335C4×C22⋊C4—111no—
336#340—111no—
337#340—111no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#340C2×D1111yescharacteristic
343#340C2×D1111yescharacteristic
344#340C2×D1111yescharacteristic
345#340C2×D1111yescharacteristic
346#336—111no—
347#336—111no—
348C22×C11—22no—
349C22×C11—22no—
350C22×C11—22no—
351C22×C11—22no—
352C22×C11—22no—
353C22×C11—22no—
354C22×C11#47414yes—
355C22×C11C2×C22⋊Q811yescharacteristic
356C22×C11#54611yescharacteristic
357C22×C11#54611yescharacteristic
358C22×C11C22×D811yescharacteristic
359C22×C11C2×#13711yescharacteristic
360C22×C11#57711yescharacteristic
361C22×C11#57711yescharacteristic
362C2×D11—42no—
363C2×D11—42no—
364C2×D11—42no—
365C2×D11—81no—
366C2×D11—81no—
367C2×D11—81no—
368C2×D11—81no—
369C4×C11—22no—
370C4×C11—42no—
371C4×C11—42no—
372C4×C11—81no—
373C4×C11—81no—
374C4×C11#52911yescharacteristic
375C4×C11#53811yescharacteristic
376C4×C11#55411yescharacteristic
377C4×C11#55411yescharacteristic
378Dic11—22no—
379Dic11—22no—
380Dic11—41no—
381Dic11—41no—
382Dic11—42no—
383Dic11—81no—
384Dic11—81no—
385C22×Q8—221no—
386C22×D4—111no—
387C22×D4—221no—
388C23×C4—21no—
389C23×C4—21no—
390C23×C4—221no—
391C23×C4C22×D1111yescharacteristic
392C22×C8—22no—
393C22×C8—41no—
394C22×C8—41no—
395C22×C8—111no—
396C22×C8—111no—
397C22×C8C22×D1111yescharacteristic
398C22×C8C22×D1111yescharacteristic
399C4⋊Q8—222no—
400C4⋊Q8—441no—
401C22⋊Q8—444no—
402#121—114no—
403#121—222no—
404C4×D4—222no—
405C4×D4—441no—
406C4×D4—444no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—41no—
412C2×C4⋊C4—41no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4C22×D1111yescharacteristic
423C2×C4⋊C4C22×D1111yescharacteristic
424C2×C4⋊C4C22×D1111yescharacteristic
425C2×C4⋊C4C22×D1111yescharacteristic
426C2×C22⋊C4—111no—
427C2×C22⋊C4—111no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C42—111no—
434C2×C42—111no—
435C2×C42—221no—
436#107—222no—
437#107—441no—
438C4⋊C8—441no—
439C4⋊C8—441no—
440#102—222no—
441#102—441no—
442#102—441no—
443#102—441no—
444C22⋊C8—222no—
445#95—111no—
446#95—111no—
447#95—221no—
448#95—221no—
449#95—221no—
450#95—221no—
451#95—221no—
452C2×C11—24no—
453C2×C11#245011yescharacteristic
454C2×C11C2×#47411yescharacteristic
455C2×C11#308411yescharacteristic
456C2×C11#329411yescharacteristic
457C2×C11#329411yescharacteristic
458C2×C11#331611yescharacteristic
459C2×C11#332011yescharacteristic
460D11—82no—
461C24—221no—
462C24D4×D1111yescharacteristic
463C2×Q8—442no—
464C2×Q8—442no—
465C2×Q8—881no—
466C2×D4—112no—
467C2×D4—224no—
468C2×D4—221no—
469C2×D4—221no—
470C2×D4—221no—
471C2×D4—221no—
472C2×D4—221no—
473C2×D4—442no—
474C2×D4—442no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—81no—
488C22×C4—81no—
489C22×C4—111no—
490C22×C4—111no—
491C22×C4—111no—
492C22×C4—111no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—442no—
497C22×C4—442no—
498C22×C4—881no—
499C22×C4#433912yes—
500C22×C4D4×D1111yescharacteristic
501C22×C4Q8×D1112yes—
502C22×C4C23×D1111yescharacteristic
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—44no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—42no—
523C4⋊C4—42no—
524C4⋊C4—112no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—442no—
531C4⋊C4—442no—
532C4⋊C4—442no—
533C4⋊C4—442no—
534C4⋊C4—442no—
535C4⋊C4—881no—
536C4⋊C4#433912yes—
537C4⋊C4#433912yes—
538C22⋊C4—114no—
539C22⋊C4—222no—
540C22⋊C4—224no—
541C22⋊C4—442no—
542C22⋊C4—442no—
543C22⋊C4—442no—
544C22⋊C4—881no—
545C42—221no—
546C42—221no—
547C42—221no—
548C42—221no—
549C42—442no—
550C11#2640811yescharacteristic, complemented, Sylow
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—222no—
556C23—441no—
557C23—441no—
558C23—441no—
559C23—441no—
560C23—441no—
561C23—441no—
562C23#6694912yes—
563C23D8×D1112yes—
564C23#6697112yes—
565C23C2×D4×D1111yescharacteristic
566Q8—884no—
567D4—222no—
568D4—222no—
569D4—448no—
570D4—441no—
571D4—441no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
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—41no—
589C2×C4—41no—
590C2×C4—84no—
591C2×C4—84no—
592C2×C4—112no—
593C2×C4—112no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—222no—
603C2×C4—221no—
604C2×C4—221no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—884no—
614C2×C4#6694912yes—
615C2×C4C2×#433911yescharacteristic
616C2×C4C2×#433911yescharacteristic
617C2×C4C2×#433911yescharacteristic
618C2×C4#6703711yescharacteristic
619C2×C4#6703711yescharacteristic
620C2×C4C2×Q8×D1111yescharacteristic
621C8—41no—
622C8—41no—
623C8—441no—
624C8—441no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—442no—
632C22—442no—
633C22—442no—
634C22—881no—
635C22—881no—
636C22—881no—
637C22—881no—
638C22#1062250314yes—
639C22#1062302111yescharacteristic
640C22#1062302111yescharacteristic
641C22C2×#6694911yescharacteristic
642C22C2×D8×D1111yescharacteristic
643C22#1062329311yescharacteristic
644C22#1062329311yescharacteristic
645C22C2×#6697111yescharacteristic
646C4—22no—
647C4—42no—
648C4—42no—
649C4—81no—
650C4—81no—
651C4—222no—
652C4—222no—
653C4—442no—
654C4—441no—
655C4—441no—
656C4—881no—
657C4—881no—
658C4#1062301011yescharacteristic
659C4#1062302511yescharacteristic
660C4#1062304211yescharacteristic
661C4#1062304211yescharacteristic
662C2—24no—
663C2—882no—
664C2#1307244011yescharacteristic
665C2C2×#1062250311yescharacteristic
666C2#1307848311yescharacteristic
667C2#1308042511yescharacteristic
668C2#1308042511yescharacteristic
669C2#1308072311yescharacteristic
670C2#1308078311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#340C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenterC2×#340D11
hypocenterC11#26408
LCSG ▷ C22×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
1. #13072312C2semidirect
3. #13070176C2semidirect
4. #13070108C2semidirect
5. #13070005C2semidirect
6. #13069751C2semidirect
7. #13069566C2semidirect
8. #13069185C2semidirect
11. #13068864C2semidirect
12. #13068804C2semidirect
13. #13068794C2semidirect
14. #13068615C2semidirect
15. C2×C11×#340C2semidirect
85. #66983Q8semidirect
230. C2×#340D11semidirect
550. C11#26408semidirect

Maximal subgroups

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

subgroupindex
#130723122
#130716322
#130701762
#130701082
#130700052
#130697512
#130695662
#130691852
#130690442
#130689332
#130688642
#130688042
#130687942
#130686152
C2×C11×#3402
#2640811