Finite Group Databasebeta

← #14817317

Subgroups — #14817317

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#13072314C211yesmaximal, characteristic, complemented
2#13071637C211yesmaximal, characteristic
3#13070176C211yesmaximal, characteristic, complemented
4#13070108C211yesmaximal, characteristic, complemented
5#13070004C211yesmaximal, characteristic, complemented
6#13069569C211yesmaximal, characteristic, complemented
7#13069188C211yesmaximal, characteristic, complemented
8#13069041C211yesmaximal, characteristic
9#13068930C211yesmaximal, characteristic
10#13068865C211yesmaximal, characteristic, complemented
11#13068805C211yesmaximal, characteristic, complemented
12#13068795C211yesmaximal, characteristic, complemented
13#13068614C211yesmaximal, characteristic, complemented
14D11×#340C211yesmaximal, characteristic, complemented
15C11×#2023C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×#66999—21no—
18C2×#66991C2211yescharacteristic
19C2×D4×Dic11C2211yescharacteristic
20C22×C8×D11C2211yescharacteristic
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×C4⋊C4×D11C2211yescharacteristic
23C2×(C22⋊D11)⋊C4—21no—
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C11×#390C2211yescharacteristic
27#10622842—21no—
28C2×#66896C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33#10622602—21no—
34#10622600C2211yescharacteristic
35#10622598C2211yescharacteristic
36#10622597—21no—
37#10622589C2211yescharacteristic
38#10622586C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40#10622569—21no—
41#10622559—21no—
42#10622557—21no—
43C4×(C2×D11)⋊C4C2211yescharacteristic
44C4×C4⋊Dic11C2211yescharacteristic
45#10622541C2211yescharacteristic
46C2×C4⋊(C11⋊C8)C2211yescharacteristic
47C11×#340C2211yescharacteristic
48C11×#340C2211yescharacteristic
49C11×#336C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×Q8×C11—21no—
60C22×D4×C11C2311yescharacteristic
61C22×C22⋊D11—21no—
62C23×Dic11—21no—
63C22×C4×D11—21no—
64C22×C4×D11—21no—
65C22×C4×D11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×C4⋊Q8—22no—
69C11×C4⋊Q8—41no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C42×C11C2311yescharacteristic
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79#66999—44no—
80#66991—22no—
81#66991Q814yescomplemented
82D4×Dic11—22no—
83D4×Dic11—41no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4D411yescharacteristic
86C2×(C2×D11)⋊C4D411yescharacteristic
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C2×C8×D11—22no—
103C2×C8×D11—41no—
104C2×C8×D11—41no—
105C4⋊C4×D11—22no—
106C4⋊C4×D11—22no—
107C4⋊C4×D11—41no—
108C4⋊C4×D11—41no—
109(C22⋊D11)⋊C4—44no—
110C11×#102—22no—
111C11×#102—41no—
112#66896—41no—
113#66896—41no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95D411yescharacteristic
120C11⋊#95D411yescharacteristic
121(C2×D11)⋊C8—22no—
122#66882—22no—
123Dic11⋊C8—41no—
124#66871—41no—
125C4⋊(C11⋊C8)—41no—
126#26408—111nomaximal, Sylow
127C24×C11—21no—
128C23×D11C2×D411yescharacteristic
129C2×Q8×C11—42no—
130C2×Q8×C11—42no—
131C2×Q8×C11—81no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11C2×Q812yes—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C2×C22⋊D11—24no—
145C2×C22⋊D11—42no—
146C2×C22⋊D11—42no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—42no—
152C22×Dic11—42no—
153C22×Dic11—81no—
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—42no—
162C2×C4×D11—42no—
163C2×C4×D11—42no—
164C2×C4×D11—42no—
165C2×C4×D11—81no—
166C2×C4×D11—81no—
167C2×C4×D11C2×Q812yes—
168C2×C4×D11#4112yes—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—42no—
181C11×C4⋊C4#4112yes—
182C11×C22⋊C4—42no—
183C11×C22⋊C4—81no—
184C42×C11—21no—
185C42×C11—21no—
186C22⋊Dic11—24no—
187C22⋊Dic11—42no—
188(C2×D11)⋊C4—22no—
189(C2×D11)⋊C4—42no—
190(C2×D11)⋊C4D814yes—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—42no—
198C4⋊Dic11C2×Q812yes—
199C4⋊Dic11#4112yes—
200Dic11⋊C4—42no—
201Dic11⋊C4—42no—
202Dic11⋊C4—42no—
203Dic11⋊C4—42no—
204Dic11⋊C4—42no—
205Dic11⋊C4—81no—
206C4×Dic11—21no—
207C4×Dic11—21no—
208C4×Dic11—42no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C8×D11—44no—
216#2440—111no—
217#2361—111no—
218#2099—111no—
219#2086—111no—
220#2067—111no—
221#2023D1111yescharacteristic, complemented
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×#340—111no—
231C23×C11—22no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11C22×D411yescharacteristic
239C22×D11—21no—
240C22×D11—21no—
241C22×D11—21no—
242C22×D11—21no—
243C22×D11C22⋊Q812yes—
244C22×D11C2×D812yes—
245C22×D11#13712yes—
246Q8×C11—84no—
247D4×C11—22no—
248D4×C11—22no—
249D4×C11—41no—
250D4×C11—41no—
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—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—41no—
265C2×C4×C11C2×D812yes—
266C2×C4×C11C22×Q811yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11H(5,𝔽2)11yescharacteristic
271C2×C4×C11H(5,𝔽2)11yescharacteristic
272C22⋊D11—48no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—22no—
278C2×Dic11—21no—
279C2×Dic11—22no—
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—41no—
291C2×Dic11—41no—
292C2×Dic11—84no—
293C2×Dic11C22⋊Q812yes—
294C2×Dic11C2×D812yes—
295C4×D11—22no—
296C4×D11—22no—
297C4×D11—22no—
298C4×D11—22no—
299C4×D11—84no—
300C4×D11—84no—
301C8×C11—41no—
302C8×C11—41no—
303C11⋊C8—41no—
304C11⋊C8—41no—
305C23×C8—111no—
306C2×C4⋊Q8C2×D1111yescharacteristic
307C2×C22⋊Q8—221no—
308C2×#121—111no—
309C2×C4×D4—111no—
310C2×C4×D4—221no—
311C22×C4⋊C4—111no—
312C22×C4⋊C4—111no—
313C2×#107—111no—
314C2×#107—111no—
315C2×C4⋊C8—111no—
316C2×C4⋊C8—111no—
317C2×#102—111no—
318C2×#102—111no—
319C2×#102C2×D1111yescharacteristic
320C2×#102C2×D1111yescharacteristic
321C2×C22⋊C8—111no—
322#398—221no—
323#395—221no—
324#390C2×D1111yescharacteristic
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#340—111no—
343#340—111no—
344#340C2×D1111yescharacteristic
345#340C2×D1111yescharacteristic
346#336—111no—
347#336C2×D1111yescharacteristic
348C22×C11—42no—
349C22×C11—42no—
350C22×C11—42no—
351C22×C11—81no—
352C22×C11—81no—
353C22×C11—81no—
354C22×C11—81no—
355C22×C11C2×C22⋊Q811yescharacteristic
356C22×C11#54611yescharacteristic
357C22×C11#54611yescharacteristic
358C22×C11C22×D811yescharacteristic
359C22×C11C2×#13711yescharacteristic
360C22×C11#57711yescharacteristic
361C22×C11#57711yescharacteristic
362C2×D11—22no—
363C2×D11—22no—
364C2×D11—22no—
365C2×D11—22no—
366C2×D11—22no—
367C2×D11—22no—
368C2×D11#47414yes—
369C4×C11—22no—
370C4×C11—42no—
371C4×C11—41no—
372C4×C11—81no—
373C4×C11—81no—
374C4×C11#52911yescharacteristic
375C4×C11#53811yescharacteristic
376C4×C11#55411yescharacteristic
377C4×C11#55411yescharacteristic
378Dic11—22no—
379Dic11—22no—
380Dic11—42no—
381Dic11—41no—
382Dic11—42no—
383Dic11—81no—
384Dic11—81no—
385C22×Q8—21no—
386C22×D4—221no—
387C22×D4C22×D1111yescharacteristic
388C23×C4—111no—
389C23×C4—221no—
390C23×C4—221no—
391C23×C4—221no—
392C22×C8—111no—
393C22×C8—111no—
394C22×C8—222no—
395C22×C8—441no—
396C22×C8—441no—
397C22×C8C22×D1111yescharacteristic
398C22×C8C22×D1111yescharacteristic
399C4⋊Q8—22no—
400C4⋊Q8—41no—
401C22⋊Q8—444no—
402#121—114no—
403#121—222no—
404C4×D4—222no—
405C4×D4—441no—
406C4×D4—444no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—222no—
413C2×C4⋊C4—222no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—441no—
422C2×C4⋊C4—441no—
423C2×C4⋊C4C22×D1111yescharacteristic
424C2×C4⋊C4C22×D1111yescharacteristic
425C2×C4⋊C4C22×D1111yescharacteristic
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—111no—
429C2×C22⋊C4—111no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C42—111no—
434C2×C42—221no—
435C2×C42C22×D1111yescharacteristic
436#107—222no—
437#107—441no—
438C4⋊C8—441no—
439C4⋊C8—441no—
440#102—22no—
441#102—41no—
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—82no—
453C2×C11#245011yescharacteristic
454C2×C11C2×#47411yescharacteristic
455C2×C11#308411yescharacteristic
456C2×C11#329411yescharacteristic
457C2×C11#329411yescharacteristic
458C2×C11#331611yescharacteristic
459C2×C11#332011yescharacteristic
460D11—24no—
461C24—21no—
462C24—111no—
463C2×Q8—42no—
464C2×Q8—42no—
465C2×Q8—81no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—224no—
472C2×D4—442no—
473C2×D4—442no—
474C2×D4Q8×D1112yes—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—111no—
479C22×C4—111no—
480C22×C4—112no—
481C22×C4—112no—
482C22×C4—111no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—442no—
492C22×C4—442no—
493C22×C4—442no—
494C22×C4—442no—
495C22×C4—442no—
496C22×C4—442no—
497C22×C4—881no—
498C22×C4—881no—
499C22×C4—881no—
500C22×C4D4×D1111yescharacteristic
501C22×C4D4×D1111yescharacteristic
502C22×C4C23×D1111yescharacteristic
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—444no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—42no—
522C4⋊C4—112no—
523C4⋊C4—112no—
524C4⋊C4—221no—
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—442no—
536C4⋊C4—881no—
537C4⋊C4#434112yes—
538C22⋊C4—42no—
539C22⋊C4—81no—
540C22⋊C4—114no—
541C22⋊C4—222no—
542C22⋊C4—224no—
543C22⋊C4—442no—
544C22⋊C4—442no—
545C42—21no—
546C42—21no—
547C42—221no—
548C42—221no—
549C42—442no—
550C11#2640811yescharacteristic, complemented, Sylow
551C23—22no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—112no—
559C23—112no—
560C23—112no—
561C23—221no—
562C23—221no—
563C23—221no—
564C23—221no—
565C23C2×D4×D1111yescharacteristic
566Q8—84no—
567D4—22no—
568D4—22no—
569D4—41no—
570D4—41no—
571D4—448no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—112no—
587C2×C4—112no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—222no—
593C2×C4—222no—
594C2×C4—222no—
595C2×C4—222no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—222no—
599C2×C4—221no—
600C2×C4—222no—
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—441no—
610C2×C4—441no—
611C2×C4—884no—
612C2×C4—884no—
613C2×C4—884no—
614C2×C4D8×D1112yes—
615C2×C4C2×#434111yescharacteristic
616C2×C4#6703711yescharacteristic
617C2×C4C2×Q8×D1111yescharacteristic
618C2×C4#41×D1111yescharacteristic
619C2×C4#41×D1111yescharacteristic
620C2×C4#6704211yescharacteristic
621C8—41no—
622C8—41no—
623C8—441no—
624C8—441no—
625C22—42no—
626C22—42no—
627C22—42no—
628C22—81no—
629C22—81no—
630C22—81no—
631C22—81no—
632C22—114no—
633C22—222no—
634C22—222no—
635C22—222no—
636C22—222no—
637C22—222no—
638C22—222no—
639C22#1062312211yescharacteristic
640C22D11×C22⋊Q811yescharacteristic
641C22#1062320711yescharacteristic
642C22C2×D8×D1111yescharacteristic
643C22#1062329311yescharacteristic
644C22#1062330611yescharacteristic
645C22D11×#13711yescharacteristic
646C4—22no—
647C4—42no—
648C4—41no—
649C4—81no—
650C4—81no—
651C4—222no—
652C4—222no—
653C4—442no—
654C4—442no—
655C4—441no—
656C4—881no—
657C4—881no—
658C4#1062316611yescharacteristic
659C4#1062316711yescharacteristic
660C4#1062320911yescharacteristic
661C4#1062321111yescharacteristic
662C2—82no—
663C2—224no—
664C2#1307243311yescharacteristic
665C2D11×#47411yescharacteristic
666C2#1307847311yescharacteristic
667C2#1308042211yescharacteristic
668C2#1308042811yescharacteristic
669C2#1308072611yescharacteristic
670C2#1308078011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2023C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
hypercenter#2023D11
hypocenterC11#26408
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2023

Complements

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

NH ≅ G/Ntype
1. #13072314C2semidirect
3. #13070176C2semidirect
4. #13070108C2semidirect
5. #13070004C2semidirect
6. #13069569C2semidirect
7. #13069188C2semidirect
10. #13068865C2semidirect
11. #13068805C2semidirect
12. #13068795C2semidirect
13. #13068614C2semidirect
14. D11×#340C2semidirect
15. C11×#2023C2semidirect
81. #66991Q8semidirect
221. #2023D11semidirect
550. C11#26408semidirect

Maximal subgroups

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

subgroupindex
#130723142
#130716372
#130701762
#130701082
#130700042
#130695692
#130691882
#130690412
#130689302
#130688652
#130688052
#130687952
#130686142
D11×#3402
C11×#20232
#2640811