Finite Group Databasebeta

← #14811052

Subgroups — #14811052

Order 2816.

946 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
1C2×#10622676C211yesmaximal, characteristic, complemented
2C22×#66874C211yesmaximal, characteristic
3C22⋊C4×Dic22C211yesmaximal, characteristic
4#13070167C211yesmaximal, characteristic, complemented
5#13070008C211yesmaximal, characteristic, complemented
6#13069994C211yesmaximal, characteristic, complemented
7#13069764C211yesmaximal, characteristic, complemented
8#13068883C211yesmaximal, characteristic, complemented
9#13068869C211yesmaximal, characteristic, complemented
10#13068809C211yesmaximal, characteristic
11#13068796C211yesmaximal, characteristic
12#13068643C211yesmaximal, characteristic
13#13068628C211yesmaximal, characteristic, complemented
14#13068550C211yesmaximal, characteristic
15C11×#2442C211yesmaximal, characteristic
16C23×Dic22C2211yescharacteristic
17C2×C11×#125C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C23×C11⋊C8C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C11×#400—21no—
23C11×#398—21no—
24C11×#389C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C11×#385—21no—
27C11×#382C2211yescharacteristic
28C11×#380—21no—
29C11×#380C2211yescharacteristic
30C4×C11×C22⋊C4C2211yescharacteristic
31#10622825C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33#10622676—24no—
34C2×#66874—24no—
35C2×#66874C2211yescharacteristic
36C2×#66874C2211yescharacteristic
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47#10622555—21no—
48C22⋊C4×Dic11—21no—
49#10622542C2211yescharacteristic
50#10622542C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53#10622259—21no—
54#10622259—21no—
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C23×Dic11—21no—
64C22×Dic22—22no—
65C22×Dic22—22no—
66C22×Dic22—21no—
67C22×Dic22—22no—
68C22×Dic22—41no—
69C22×Dic22—41no—
70C22×Dic22Q814yes—
71C22×Dic22C2311yescharacteristic
72C22×Dic22C2311yescharacteristic
73C11×#125—22no—
74C11×#125—41no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—41no—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4D411yescharacteristic
88C2×C11×C22⋊C4D411yescharacteristic
89C2×C42×C11C2311yescharacteristic
90C2×C42×C11C2311yescharacteristic
91C2×C22⋊Dic11—21no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C22×C11⋊C8—22no—
99C22×C11⋊C8—22no—
100C22×C11⋊C8—41no—
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C4×Dic22—22no—
106C4×Dic22—22no—
107C4×Dic22—41no—
108C4×Dic22—41no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95D411yescharacteristic
115C11×#95D411yescharacteristic
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C22⋊(C11⋊C8)—22no—
122#66874—22no—
123#66874—22no—
124#66874—22no—
125#66874—22no—
126#66874—22no—
127#66874—41no—
128#66874—41no—
129#66874D414yes—
130#66872—22no—
131#66872—41no—
132#66871—22no—
133#66871—41no—
134C4⋊(C11⋊C8)—22no—
135C4⋊(C11⋊C8)—41no—
136#25965—111nomaximal, Sylow
137C24×C11C2×D411yescharacteristic
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—42no—
147C22×C4×C11—42no—
148C22×C4×C11—81no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×Q812yes—
155C22×C4×C11#4112yes—
156C22×C4×C11C2411yescharacteristic
157C22×Dic11—24no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—42no—
163C22×Dic11—42no—
164C2×Dic22—28no—
165C2×Dic22—24no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22—21no—
173C2×Dic22—21no—
174C2×Dic22—44no—
175C2×Dic22—44no—
176C2×Dic22—44no—
177C2×Dic22—42no—
178C2×Dic22—42no—
179C2×Dic22C2×D412yes—
180C2×Dic22C2×Q812yes—
181C2×Dic22C2×Q812yes—
182C2×Dic22#4112yes—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—42no—
191C11×C4⋊C4—42no—
192C11×C4⋊C4—42no—
193C11×C4⋊C4—81no—
194C11×C4⋊C4—81no—
195C11×C4⋊C4C2×D412yes—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—22no—
198C11×C22⋊C4—42no—
199C42×C11—21no—
200C42×C11—21no—
201C42×C11—21no—
202C42×C11—21no—
203C22⋊Dic11—42no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208Dic11⋊C4—42no—
209Dic11⋊C4—42no—
210C4×Dic11—42no—
211C4×Dic11—42no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—44no—
224C2×C11⋊C8C2×D412yes—
225C2×#479—111no—
226C22×#103—111no—
227#2442D1111yescharacteristic
228Q8×C22⋊C4—111no—
229#2097—111no—
230#2068—111no—
231#2066—111no—
232#2026—111no—
233#1865—111no—
234#1863—111no—
235#1853—111no—
236#1850—111no—
237#1808—111no—
238#1805—111no—
239#1787—111no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11C22⋊Q812yes—
245C23×C11#13512yes—
246C23×C11#13712yes—
247C23×C11C22×D411yescharacteristic
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—22no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
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—41no—
278C2×C4×C11—84no—
279C2×C4×C11C22⋊Q812yes—
280C2×C4×C11C22×D411yescharacteristic
281C2×C4×C11C22×Q811yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C11H(5,𝔽2)11yescharacteristic
285C2×C4×C11H(5,𝔽2)11yescharacteristic
286C2×Dic11—22no—
287C2×Dic11—22no—
288C2×Dic11—22no—
289C2×Dic11—22no—
290C2×Dic11—48no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299Dic22—22no—
300Dic22—22no—
301Dic22—22no—
302Dic22—22no—
303Dic22—22no—
304Dic22—48no—
305Dic22—41no—
306Dic22—41no—
307Dic22C22⋊Q814yes—
308C11⋊C8—22no—
309C11⋊C8—41no—
310C11⋊C8—41no—
311C11⋊C8—41no—
312C23×Q8—111no—
313C23×C8—111no—
314C2×#125C2×D1111yescharacteristic
315C2×C4×Q8—111no—
316C2×C4×Q8—111no—
317C22×C4⋊C4C2×D1111yescharacteristic
318#479—224no—
319C2×#107—111no—
320C2×#107—111no—
321C2×#106—111no—
322C2×#106—111no—
323C2×C4⋊C8—111no—
324C2×C4⋊C8—111no—
325C2×#103—111no—
326C2×#103—111no—
327C2×#103—111no—
328C2×#103—111no—
329C2×#103—111no—
330C2×#103—111no—
331C2×#103—111no—
332C2×#103—111no—
333C2×#103—224no—
334C2×C22⋊C8—111no—
335#400—21no—
336#398—21no—
337#391—111no—
338#391—111no—
339#391—221no—
340#391—221no—
341#389C2×D1111yescharacteristic
342#389C2×D1111yescharacteristic
343#385—21no—
344#382C2×D1111yescharacteristic
345#380—21no—
346#380—111no—
347#380—221no—
348#380C2×D1111yescharacteristic
349C4×C22⋊C4—221no—
350C4×C22⋊C4C2×D1111yescharacteristic
351#340—111no—
352#340—111no—
353#340—111no—
354#340—111no—
355#336—111no—
356#336—111no—
357C22×C11—22no—
358C22×C11—22no—
359C22×C11—22no—
360C22×C11—22no—
361C22×C11—22no—
362C22×C11—22no—
363C22×C11#47914yescomplemented
364C22×C11C2×C22⋊Q811yescharacteristic
365C22×C11D4211yescharacteristic
366C22×C11#54611yescharacteristic
367C22×C11C2×#13511yescharacteristic
368C22×C11C2×#13711yescharacteristic
369C22×C11#57711yescharacteristic
370C22×C11#57811yescharacteristic
371C4×C11—22no—
372C4×C11—41no—
373C4×C11—42no—
374C4×C11—41no—
375C4×C11—41no—
376C4×C11—41no—
377C4×C11—81no—
378C4×C11—81no—
379C4×C11—81no—
380C4×C11C2×C22⋊Q811yescharacteristic
381C4×C11#54311yescharacteristic
382C4×C11#54611yescharacteristic
383C4×C11#55111yescharacteristic
384Dic11—24no—
385Dic11—42no—
386Dic11—81no—
387Dic11—81no—
388C22×Q8—114no—
389C22×Q8—111no—
390C22×Q8—111no—
391C22×Q8—222no—
392C22×Q8—222no—
393C22×Q8—222no—
394C22×Q8—221no—
395C22×Q8—441no—
396C22×Q8—441no—
397C23×C4—21no—
398C23×C4—221no—
399C23×C4C22×D1111yescharacteristic
400C22×C8—111no—
401C22×C8—111no—
402C22×C8—111no—
403C22×C8—111no—
404C22×C8—222no—
405C22×C8—222no—
406C22×C8—441no—
407#125—22no—
408#125—41no—
409C4×Q8—222no—
410C4×Q8—222no—
411C4×Q8—441no—
412C4×Q8—441no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—41no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4C22×D1111yescharacteristic
425C2×C4⋊C4C22×D1111yescharacteristic
426C2×C4⋊C4C22×D1111yescharacteristic
427C2×C4⋊C4C22×D1111yescharacteristic
428C2×C22⋊C4—21no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4C22⋊D1111yescharacteristic
431C2×C22⋊C4C22⋊D1111yescharacteristic
432C2×C42—221no—
433C2×C42—221no—
434C2×C42C22×D1111yescharacteristic
435C2×C42C22×D1111yescharacteristic
436#107—222no—
437#107—441no—
438#106—222no—
439#106—441no—
440C4⋊C8—222no—
441C4⋊C8—441no—
442#103—114no—
443#103—222no—
444#103—222no—
445#103—222no—
446#103—222no—
447#103—222no—
448#103—441no—
449#103—441no—
450C22⋊C8—222no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—21no—
456#95—221no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461#95C22⋊D1111yescharacteristic
462#95C22⋊D1111yescharacteristic
463C2×C11—24no—
464C2×C11#243711yescharacteristic
465C2×C11C2×#47911yescharacteristic
466C2×C11#308211yescharacteristic
467C2×C11#326611yescharacteristic
468C2×C11#328511yescharacteristic
469C2×C11#330111yescharacteristic
470C2×C11#331211yescharacteristic
471C24C2×C22⋊D1111yescharacteristic
472C2×Q8—112no—
473C2×Q8—112no—
474C2×Q8—112no—
475C2×Q8—112no—
476C2×Q8—228no—
477C2×Q8—224no—
478C2×Q8—221no—
479C2×Q8—221no—
480C2×Q8—221no—
481C2×Q8—221no—
482C2×Q8—221no—
483C2×Q8—221no—
484C2×Q8—221no—
485C2×Q8—221no—
486C2×Q8—442no—
487C2×Q8—442no—
488C2×Q8—444no—
489C2×Q8—444no—
490C2×Q8—444no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—81no—
502C22×C4—221no—
503C22×C4—224no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—442no—
508C22×C4—442no—
509C22×C4Q8×D1112yes—
510C22×C4#434312yes—
511C22×C4C2×C22⋊D1111yescharacteristic
512C22×C4C2×C22⋊D1111yescharacteristic
513C22×C4C2×C22⋊D1111yescharacteristic
514C22×C4C2×C22⋊D1111yescharacteristic
515C22×C4C2×C22⋊D1111yescharacteristic
516C22×C4C23×D1111yescharacteristic
517C2×C8—112no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8—221no—
523C2×C8—221no—
524C2×C8—221no—
525C2×C8—221no—
526C2×C8—221no—
527C2×C8—221no—
528C2×C8—221no—
529C2×C8—444no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—42no—
538C4⋊C4—42no—
539C4⋊C4—42no—
540C4⋊C4—81no—
541C4⋊C4—81no—
542C4⋊C4—221no—
543C4⋊C4—221no—
544C4⋊C4—221no—
545C4⋊C4—221no—
546C4⋊C4—442no—
547C4⋊C4—442no—
548C4⋊C4D4×D1112yes—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—42no—
552C22⋊C4—442no—
553C42—21no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—442no—
558C42—442no—
559C11#2596511yescharacteristic, complemented, Sylow
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23#6699912yes—
565C23#6700312yes—
566C23#6700412yes—
567C23C22×C22⋊D1111yescharacteristic
568Q8—114no—
569Q8—222no—
570Q8—222no—
571Q8—222no—
572Q8—222no—
573Q8—222no—
574Q8—448no—
575Q8—441no—
576Q8—441no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—84no—
608C2×C4—222no—
609C2×C4—222no—
610C2×C4—222no—
611C2×C4—222no—
612C2×C4—448no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4#6699912yes—
622C2×C4C2×D4×D1111yescharacteristic
623C2×C4#6703711yescharacteristic
624C2×C4C2×Q8×D1111yescharacteristic
625C2×C4C2×#434311yescharacteristic
626C2×C4#41×D1111yescharacteristic
627C2×C4#6704211yescharacteristic
628C8—222no—
629C8—441no—
630C8—441no—
631C8—441no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22#1062267614yescomplemented
639C22D4×C22⋊D1111yescharacteristic
640C22C2×#6699911yescharacteristic
641C22C2×#6700311yescharacteristic
642C22C2×#6700411yescharacteristic
643C22#1062336011yescharacteristic
644C22#1062336711yescharacteristic
645C22#1062336911yescharacteristic
646C4—22no—
647C4—41no—
648C4—41no—
649C4—42no—
650C4—41no—
651C4—41no—
652C4—81no—
653C4—81no—
654C4—81no—
655C4—224no—
656C4—442no—
657C4—881no—
658C4—881no—
659C4D11×C22⋊Q811yescharacteristic
660C4#1062316111yescharacteristic
661C4#1062316511yescharacteristic
662C4#1062316811yescharacteristic
663C2—24no—
664C2#1307227911yescharacteristic
665C2C2×#1062267611yescharacteristic
666C2#1307845211yescharacteristic
667C2#1308012211yescharacteristic
668C2#1308035311yescharacteristic
669C2#1308051211yescharacteristic
670C2#1308066111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2442C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#2442D11
hypocenterC11#25965
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2442

Complements

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

NH ≅ G/Ntype
1. C2×#10622676C2semidirect
4. #13070167C2semidirect
5. #13070008C2semidirect
6. #13069994C2semidirect
7. #13069764C2semidirect
8. #13068883C2semidirect
9. #13068869C2semidirect
13. #13068628C2semidirect
363. C22×C11#479semidirect
559. C11#25965semidirect
638. C22#10622676semidirect

Maximal subgroups

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

subgroupindex
C2×#106226762
C22×#668742
C22⋊C4×Dic222
#130701672
#130700082
#130699942
#130697642
#130688832
#130688692
#130688092
#130687962
#130686432
#130686282
#130685502
C11×#24422
#2596511