Finite Group Databasebeta

← #14817322

Subgroups — #14817322

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#13072318C211yesmaximal, characteristic, complemented
2#13071630C211yesmaximal, characteristic
3#13070175C211yesmaximal, characteristic, complemented
4#13070104C211yesmaximal, characteristic, complemented
5#13070003C211yesmaximal, characteristic, complemented
6#13069753C211yesmaximal, characteristic, complemented
7#13069567C211yesmaximal, characteristic, complemented
8#13069188C211yesmaximal, characteristic, complemented
9#13069044C211yesmaximal, characteristic
10#13068931C211yesmaximal, characteristic
11#13068866C211yesmaximal, characteristic, complemented
12#13068806C211yesmaximal, characteristic, complemented
13#13068617C211yesmaximal, characteristic, complemented
14C2×#10622189C211yesmaximal, characteristic, complemented
15C11×#1850C211yesmaximal, characteristic, complemented
16C23×C8×C11C2211yescharacteristic
17C2×#66983C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C2×(C22⋊D11)⋊C4—21no—
21C2×#66931—21no—
22C2×C4×D44C2211yescharacteristic
23C2×#66922C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C4×C11×C22⋊C4C2211yescharacteristic
28#10622825C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66885C2211yescharacteristic
33C2×#66882C2211yescharacteristic
34C2×#66882C2211yescharacteristic
35#10622571—21no—
36#10622563—21no—
37#10622552C2211yescharacteristic
38#10622548C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40#10622541C2211yescharacteristic
41#10622541C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622283—21no—
44#10622281—21no—
45#10622274—21no—
46#10622269—21no—
47C11×#336C2211yescharacteristic
48C11×#336C2211yescharacteristic
49#10622189C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C23×Dic11—21no—
62C23×Dic11—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
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C2×C11×C22⋊C4D411yescharacteristic
74C2×C11×C22⋊C4D411yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C2×C22⋊Dic11—21no—
78#66983—22no—
79#66983Q814yescomplemented
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11—22no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—41no—
92C2×C4⋊Dic11—41no—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×C4×Dic11—21no—
104(C22⋊D11)⋊C4—44no—
105#66931—44no—
106C4×D44—22no—
107C4×D44—41no—
108#66922—22no—
109#66922—41no—
110C11×C4⋊C8—41no—
111C11×C4⋊C8—41no—
112C11×C22⋊C8—22no—
113C11×#95D411yescharacteristic
114C11×#95D411yescharacteristic
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120#66885—22no—
121#66885—41no—
122#66885—41no—
123#66885—41no—
124#66882—22no—
125#66882—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×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×Q812yes—
139C22×C4×C11#4112yes—
140C22×C4×C11C2411yescharacteristic
141C2×C22⋊D11—24no—
142C2×C22⋊D11—42no—
143C2×C22⋊D11—42no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—42no—
152C22×Dic11—42no—
153C22×Dic11—42no—
154C22×Dic11—42no—
155C22×Dic11—81no—
156C22×Dic11—81no—
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—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—44no—
182C11×C22⋊C4—22no—
183C11×C22⋊C4D814yes—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C22⋊Dic11—42no—
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—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—42no—
205C4⋊Dic11—42no—
206C4⋊Dic11—42no—
207C4⋊Dic11—42no—
208C4⋊Dic11—81no—
209C4⋊Dic11C2×Q812yes—
210C4⋊Dic11#4112yes—
211C4⋊Dic11#4112yes—
212Dic11⋊C4—42no—
213Dic11⋊C4—42no—
214Dic11⋊C4—42no—
215C4×Dic11—42no—
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#1850D1111yescharacteristic, complemented
229#1802—111no—
230C2×#340—111no—
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—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11C22⋊Q812yes—
263C2×C4×C11C2×D812yes—
264C2×C4×C11C2×D812yes—
265C2×C4×C11C22×Q811yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11H(5,𝔽2)11yescharacteristic
270C2×C4×C11H(5,𝔽2)11yescharacteristic
271C22⋊D11—48no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
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—41no—
293C2×Dic11—84no—
294C2×Dic11—84no—
295D44—22no—
296D44—22no—
297D44—41no—
298D44—41no—
299C4×D11—84no—
300Dic22—84no—
301C8×C11—41no—
302C8×C11—41no—
303C8×C11—41no—
304C8×C11—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⋊C4—111no—
312C22×C4⋊C4—111no—
313C2×#107—111no—
314C2×#107—111no—
315C2×C4⋊C8C2×D1111yescharacteristic
316C2×C4⋊C8C2×D1111yescharacteristic
317C2×#102—111no—
318C2×#102—111no—
319C2×#102—111no—
320C2×#102—111no—
321C2×C22⋊C8C2×D1111yescharacteristic
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⋊C4C2×D1111yescharacteristic
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#340—111no—
345#340—111no—
346#336C2×D1111yescharacteristic
347#336C2×D1111yescharacteristic
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—22no—
371C4×C11—22no—
372C4×C11—41no—
373C4×C11—41no—
374C4×C11#52911yescharacteristic
375C4×C11#53811yescharacteristic
376C4×C11#55411yescharacteristic
377C4×C11#55411yescharacteristic
378Dic11—42no—
379Dic11—42no—
380Dic11—42no—
381Dic11—81no—
382Dic11—81no—
383Dic11—81no—
384Dic11—81no—
385C22×Q8—221no—
386C22×D4—111no—
387C22×D4—221no—
388C23×C4—221no—
389C23×C4—221no—
390C23×C4—221no—
391C23×C4C22×D1111yescharacteristic
392C22×C8—22no—
393C22×C8—41no—
394C22×C8—41no—
395C22×C8C22×D1111yescharacteristic
396C22×C8C22×D1111yescharacteristic
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—111no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—222no—
415C2×C4⋊C4—222no—
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⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4—441no—
425C2×C4⋊C4—441no—
426C2×C22⋊C4—221no—
427C2×C22⋊C4—221no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4D4411yescharacteristic
432C2×C22⋊C4D4411yescharacteristic
433C2×C42—221no—
434C2×C42C22×D1111yescharacteristic
435C2×C42C22×D1111yescharacteristic
436#107—222no—
437#107—441no—
438C4⋊C8—41no—
439C4⋊C8—41no—
440#102—222no—
441#102—441no—
442#102—441no—
443#102—441no—
444C22⋊C8—22no—
445#95—221no—
446#95—221no—
447#95—221no—
448#95—221no—
449#95—221no—
450#95D4411yescharacteristic
451#95D4411yescharacteristic
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—
462C24C2×D4411yescharacteristic
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—221no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—442no—
487C22×C4—442no—
488C22×C4—442no—
489C22×C4—442no—
490C22×C4—442no—
491C22×C4—442no—
492C22×C4—881no—
493C22×C4—881no—
494C22×C4—881no—
495C22×C4C2×D4411yescharacteristic
496C22×C4C2×D4411yescharacteristic
497C22×C4C2×D4411yescharacteristic
498C22×C4C2×D4411yescharacteristic
499C22×C4C2×D4411yescharacteristic
500C22×C4#434112yes—
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—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—44no—
516C4⋊C4—112no—
517C4⋊C4—112no—
518C4⋊C4—112no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—221no—
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—442no—
537C4⋊C4—881no—
538C22⋊C4—22no—
539C22⋊C4—224no—
540C22⋊C4—442no—
541C22⋊C4—442no—
542C22⋊C4—442no—
543C22⋊C4—881no—
544C22⋊C4D8814yes—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—21no—
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#6695012yes—
563C23C2×D8812yes—
564C23#6696212yes—
565C23C22×D4411yescharacteristic
566Q8—884no—
567D4—222no—
568D4—222no—
569D4—448no—
570D4—441no—
571D4—441no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—222no—
589C2×C4—222no—
590C2×C4—222no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
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—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—884no—
610C2×C4—884no—
611C2×C4—884no—
612C2×C4#6695012yes—
613C2×C4C2×D8812yes—
614C2×C4C2×D8812yes—
615C2×C4C2×#434111yescharacteristic
616C2×C4#6703711yescharacteristic
617C2×C4#6703711yescharacteristic
618C2×C4C2×Q8×D1111yescharacteristic
619C2×C4#41×D1111yescharacteristic
620C2×C4#41×D1111yescharacteristic
621C8—41no—
622C8—41no—
623C8—41no—
624C8—41no—
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#1062245914yes—
639C22C2×#6695011yescharacteristic
640C22#1062308511yescharacteristic
641C22#1062308511yescharacteristic
642C22C22×D8811yescharacteristic
643C22C2×#6696211yescharacteristic
644C22#1062328211yescharacteristic
645C22#1062328211yescharacteristic
646C4—22no—
647C4—22no—
648C4—22no—
649C4—41no—
650C4—41no—
651C4—442no—
652C4—442no—
653C4—442no—
654C4—881no—
655C4—881no—
656C4—881no—
657C4—881no—
658C4#1062312411yescharacteristic
659C4#1062316711yescharacteristic
660C4#1062316711yescharacteristic
661C4#1062318011yescharacteristic
662C2—24no—
663C2—882no—
664C2#1307243811yescharacteristic
665C2C2×#1062245911yescharacteristic
666C2#1307848011yescharacteristic
667C2#1308043011yescharacteristic
668C2#1308043011yescharacteristic
669C2#1308072911yescharacteristic
670C2#1308078911yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1850C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#1850D11
hypocenterC11#26408
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
1. #13072318C2semidirect
3. #13070175C2semidirect
4. #13070104C2semidirect
5. #13070003C2semidirect
6. #13069753C2semidirect
7. #13069567C2semidirect
8. #13069188C2semidirect
11. #13068866C2semidirect
12. #13068806C2semidirect
13. #13068617C2semidirect
14. C2×#10622189C2semidirect
15. C11×#1850C2semidirect
79. #66983Q8semidirect
228. #1850D11semidirect
550. C11#26408semidirect

Maximal subgroups

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

subgroupindex
#130723182
#130716302
#130701752
#130701042
#130700032
#130697532
#130695672
#130691882
#130690442
#130689312
#130688662
#130688062
#130686172
C2×#106221892
C11×#18502
#2640811