Finite Group Databasebeta

← #14810940

Subgroups — #14810940

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×#10622442C211yesmaximal, characteristic, complemented
2C22×#66880C211yesmaximal, characteristic
3#13072340C211yesmaximal, characteristic
4C22⋊C4×Dic22C211yesmaximal, characteristic
5#13070163C211yesmaximal, characteristic, complemented
6#13070010C211yesmaximal, characteristic, complemented
7#13069996C211yesmaximal, characteristic, complemented
8#13069768C211yesmaximal, characteristic, complemented
9#13068887C211yesmaximal, characteristic, complemented
10#13068873C211yesmaximal, characteristic, complemented
11#13068806C211yesmaximal, characteristic
12#13068641C211yesmaximal, characteristic
13#13068632C211yesmaximal, characteristic, complemented
14#13068552C211yesmaximal, characteristic
15C11×#1850C211yesmaximal, characteristic
16C23×Dic22C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C2×#66923C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C4×C11×C22⋊C4C2211yescharacteristic
26#10622825C2211yescharacteristic
27#10622825C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29C2×#66882C2211yescharacteristic
30C2×#66881C2211yescharacteristic
31C2×#66881C2211yescharacteristic
32C2×#66880—24no—
33C2×#66880C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37C2×#66880C2211yescharacteristic
38C2×#66880C2211yescharacteristic
39C2×#66880C2211yescharacteristic
40C2×#66880C2211yescharacteristic
41#10622559—21no—
42#10622555—21no—
43#10622555—21no—
44C22⋊C4×Dic11—21no—
45#10622549C2211yescharacteristic
46#10622542C2211yescharacteristic
47#10622542C2211yescharacteristic
48#10622541C2211yescharacteristic
49#10622541C2211yescharacteristic
50#10622442—24no—
51#10622273—21no—
52#10622270—21no—
53#10622259—21no—
54#10622259—21no—
55C11×#336C2211yescharacteristic
56C11×#336C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×Dic11—21no—
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
73C22×C8×C11—22no—
74C22×C8×C11—22no—
75C22×C8×C11—41no—
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C2×C11×C22⋊C4D411yescharacteristic
81C2×C11×C22⋊C4D411yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—41no—
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
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×Dic11—21no—
103#66923—22no—
104#66923—41no—
105C4×Dic22—22no—
106C4×Dic22—22no—
107C4×Dic22—41no—
108C4×Dic22—41no—
109C11×C4⋊C8—22no—
110C11×C4⋊C8—41no—
111C11×C22⋊C8—22no—
112C11×#95D411yescharacteristic
113C11×#95D411yescharacteristic
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124#66882—22no—
125#66882—41no—
126#66881—22no—
127#66881—41no—
128#66880—22no—
129#66880—22no—
130#66880—22no—
131#66880—22no—
132#66880—22no—
133#66880—41no—
134#66880—41no—
135#66880D414yes—
136#25957—111nomaximal, Sylow
137C24×C11C2×D411yescharacteristic
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×Q812yes—
148C22×C4×C11#4112yes—
149C22×C4×C11C2411yescharacteristic
150C22×Dic11—24no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—42no—
160C22×Dic11—42no—
161C22×Dic11—42no—
162C22×Dic11—42no—
163C22×Dic11—81no—
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—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—44no—
195C2×C8×C11C2×D412yes—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—22no—
198C42×C11—21no—
199C42×C11—21no—
200C42×C11—21no—
201C42×C11—21no—
202C22⋊Dic11—42no—
203C22⋊Dic11—42no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11—42no—
216C4⋊Dic11C2×D412yes—
217Dic11⋊C4—42no—
218Dic11⋊C4—42no—
219Dic11⋊C4—42no—
220Dic11⋊C4—42no—
221Dic11⋊C4—81no—
222Dic11⋊C4—81no—
223C4×Dic11—42no—
224C4×Dic11—42no—
225C2×#479—111no—
226C22×#103—111no—
227#2442—111no—
228Q8×C22⋊C4—111no—
229#2097—111no—
230#2068—111no—
231#2066—111no—
232#2026—111no—
233#1865—111no—
234#1863—111no—
235#1852—111no—
236#1850D1111yescharacteristic
237#1807—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—21no—
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×C11C22⋊Q812yes—
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C22×Q811yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11H(5,𝔽2)11yescharacteristic
272C2×C4×C11H(5,𝔽2)11yescharacteristic
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—48no—
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—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—84no—
299Dic22—22no—
300Dic22—22no—
301Dic22—22no—
302Dic22—22no—
303Dic22—22no—
304Dic22—48no—
305Dic22—41no—
306Dic22—41no—
307Dic22C22⋊Q814yes—
308C8×C11—22no—
309C8×C11—41no—
310C8×C11—41no—
311C8×C11—41no—
312C23×Q8—111no—
313C23×C8C2×D1111yescharacteristic
314C2×#125—111no—
315C2×C4×Q8—111no—
316C2×C4×Q8—111no—
317C22×C4⋊C4—111no—
318#479—224no—
319C2×#107—111no—
320C2×#107—111no—
321C2×#106—111no—
322C2×#106—111no—
323C2×C4⋊C8C2×D1111yescharacteristic
324C2×C4⋊C8C2×D1111yescharacteristic
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⋊C8C2×D1111yescharacteristic
335#400—221no—
336#398—221no—
337#391—111no—
338#391—111no—
339#391—221no—
340#391—221no—
341#389—111no—
342#389—111no—
343#385—221no—
344#382—111no—
345#380—111no—
346#380—111no—
347#380—221no—
348#380—221no—
349C4×C22⋊C4—221no—
350C4×C22⋊C4C2×D1111yescharacteristic
351#340—111no—
352#340—111no—
353#340—111no—
354#340—111no—
355#336C2×D1111yescharacteristic
356#336C2×D1111yescharacteristic
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—41no—
374C4×C11—41no—
375C4×C11—41no—
376C4×C11C2×C22⋊Q811yescharacteristic
377C4×C11#54311yescharacteristic
378C4×C11#54611yescharacteristic
379C4×C11#55111yescharacteristic
380Dic11—24no—
381Dic11—42no—
382Dic11—42no—
383Dic11—81no—
384Dic11—81no—
385Dic11—81no—
386Dic11—81no—
387Dic11—81no—
388C22×Q8—114no—
389C22×Q8—111no—
390C22×Q8—111no—
391C22×Q8—222no—
392C22×Q8—222no—
393C22×Q8—221no—
394C22×Q8—222no—
395C22×Q8—441no—
396C22×Q8—441no—
397C23×C4—221no—
398C23×C4—221no—
399C23×C4C22×D1111yescharacteristic
400C22×C8—22no—
401C22×C8—22no—
402C22×C8—41no—
403C22×C8C22×D1111yescharacteristic
404C22×C8C22×D1111yescharacteristic
405C22×C8C22×D1111yescharacteristic
406C22×C8C22×D1111yescharacteristic
407#125—222no—
408#125—441no—
409C4×Q8—222no—
410C4×Q8—222no—
411C4×Q8—441no—
412C4×Q8—441no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—222no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—441no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4D4411yescharacteristic
431C2×C22⋊C4D4411yescharacteristic
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—22no—
441C4⋊C8—41no—
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—22no—
451#95—221no—
452#95—221no—
453#95—221no—
454#95—221no—
455#95—221no—
456#95—221no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461#95D4411yescharacteristic
462#95D4411yescharacteristic
463C2×C11—24no—
464C2×C11#243711yescharacteristic
465C2×C11C2×#47911yescharacteristic
466C2×C11#308211yescharacteristic
467C2×C11#327011yescharacteristic
468C2×C11#328211yescharacteristic
469C2×C11#330011yescharacteristic
470C2×C11#332011yescharacteristic
471C24C2×D4411yescharacteristic
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—221no—
496C22×C4—224no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—442no—
505C22×C4—442no—
506C22×C4—442no—
507C22×C4—442no—
508C22×C4—881no—
509C22×C4C2×D4411yescharacteristic
510C22×C4C2×D4411yescharacteristic
511C22×C4C2×D4411yescharacteristic
512C22×C4C2×D4411yescharacteristic
513C22×C4C2×D4411yescharacteristic
514C22×C4#434112yes—
515C22×C4Q8×D1112yes—
516C22×C4C23×D1111yescharacteristic
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—44no—
529C2×C8D4×D1112yes—
530C4⋊C4—112no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—221no—
540C4⋊C4—221no—
541C4⋊C4—221no—
542C4⋊C4—442no—
543C4⋊C4—442no—
544C4⋊C4—442no—
545C4⋊C4—442no—
546C4⋊C4—442no—
547C4⋊C4—881no—
548C4⋊C4—881no—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—442no—
552C22⋊C4—442no—
553C42—21no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—442no—
558C42—442no—
559C11#2595711yescharacteristic, complemented, Sylow
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23#6695012yes—
565C23#6695712yes—
566C23#6696212yes—
567C23C22×D4411yescharacteristic
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—21no—
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—222no—
596C2×C4—222no—
597C2×C4—222no—
598C2×C4—222no—
599C2×C4—222no—
600C2×C4—448no—
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—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—884no—
621C2×C4#6695012yes—
622C2×C4C2×D4×D1111yescharacteristic
623C2×C4C2×#434111yescharacteristic
624C2×C4#6703711yescharacteristic
625C2×C4C2×Q8×D1111yescharacteristic
626C2×C4#41×D1111yescharacteristic
627C2×C4#6704211yescharacteristic
628C8—22no—
629C8—41no—
630C8—41no—
631C8—41no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22#1062244214yescomplemented
639C22C2×#6695011yescharacteristic
640C22D4×D4411yescharacteristic
641C22#1062308511yescharacteristic
642C22C2×#6695711yescharacteristic
643C22C2×#6696211yescharacteristic
644C22#1062328211yescharacteristic
645C22#1062328411yescharacteristic
646C4—22no—
647C4—41no—
648C4—41no—
649C4—41no—
650C4—41no—
651C4—224no—
652C4—442no—
653C4—442no—
654C4—881no—
655C4—881no—
656C4—881no—
657C4—881no—
658C4—881no—
659C4#1062312211yescharacteristic
660C4D11×C22⋊Q811yescharacteristic
661C4#1062316511yescharacteristic
662C4#1062318911yescharacteristic
663C2—24no—
664C2#1307228011yescharacteristic
665C2C2×#1062244211yescharacteristic
666C2#1307845911yescharacteristic
667C2#1308019111yescharacteristic
668C2#1308032811yescharacteristic
669C2#1308050511yescharacteristic
670C2#1308078911yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1850C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1850D11
hypocenterC11#25957
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. C2×#10622442C2semidirect
5. #13070163C2semidirect
6. #13070010C2semidirect
7. #13069996C2semidirect
8. #13069768C2semidirect
9. #13068887C2semidirect
10. #13068873C2semidirect
13. #13068632C2semidirect
363. C22×C11#479semidirect
559. C11#25957semidirect
638. C22#10622442semidirect

Maximal subgroups

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

subgroupindex
C2×#106224422
C22×#668802
#130723402
C22⋊C4×Dic222
#130701632
#130700102
#130699962
#130697682
#130688872
#130688732
#130688062
#130686412
#130686322
#130685522
C11×#18502
#2595711