Finite Group Databasebeta

← #14772182

Subgroups — #14772182

Order 2816.

1062 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4323C211yesmaximal, characteristic
2C2×#10622369C211yesmaximal, characteristic
3C2×#10622369C211yesmaximal, characteristic
4#13071525C211yesmaximal, characteristic, complemented
5#13071521C211yesmaximal, characteristic, complemented
6#13069348C211yesmaximal, characteristic, complemented
7#13069346C211yesmaximal, characteristic, complemented
8#13068880C211yesmaximal, characteristic, complemented
9#13068879C211yesmaximal, characteristic, complemented
10#13068874C211yesmaximal, characteristic, complemented
11#13068777C211yesmaximal, characteristic, complemented
12#13068625C211yesmaximal, characteristic, complemented
13#13068624C211yesmaximal, characteristic, complemented
14#13068477C211yesmaximal, characteristic, complemented
15C11×#1864C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C2×D4×Dic11C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C22×#4323C2211yescharacteristic
20C2×#66946C2211yescharacteristic
21C2×#66946C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28#10622823—21no—
29C2×C11⋊#95—21no—
30C2×#66885C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66881C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34C2×C8×Dic11C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36C4×#4323—24no—
37#10622602—21no—
38#10622600—21no—
39#10622598C2211yescharacteristic
40#10622590C2211yescharacteristic
41#10622590C2211yescharacteristic
42#10622586C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47#10622559—21no—
48#10622555—21no—
49C4×Dic11⋊C4C2211yescharacteristic
50#10622541C2211yescharacteristic
51C2×C4×C11⋊C8C2211yescharacteristic
52#10622369—24no—
53#10622369C418yescomplemented
54#10622281—21no—
55D11×#95—21no—
56C11×#340C2211yescharacteristic
57C11×#336C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×Dic11—21no—
65C23×Dic11—21no—
66C22×D44C2311yescharacteristic
67C22×C4×D11—21no—
68C22×C4×D11—21no—
69C22×C4×D11—21no—
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C4×D4×C11—22no—
73C4×D4×C11—41no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C42×C11C2311yescharacteristic
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82D4×Dic11—22no—
83D4×Dic11—22no—
84D4×Dic11—41no—
85D4×Dic11C2×C414yescomplemented
86C2×#4323C2×C414yes—
87C2×#4323D414yes—
88C2×#4323Q814yes—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4D411yescharacteristic
99C2×Dic11⋊C4D411yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104#66946—22no—
105#66946—22no—
106#66946—41no—
107#66946C2×C414yescomplemented
108C4×D44—22no—
109C4×D44—41no—
110C11×#106—41no—
111C11×#102—22no—
112C11×#102C2×C414yescomplemented
113C11×#95—21no—
114#66896—22no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95D411yescharacteristic
123C11⋊#95D411yescharacteristic
124#66885—22no—
125#66885C2×C414yescomplemented
126#66881—41no—
127Dic11⋊C8—22no—
128C8×Dic11—22no—
129C8×Dic11C2×C414yescomplemented
130#66873—22no—
131#66871—22no—
132#66871—22no—
133#66871C2×C414yescomplemented
134C4×C11⋊C8—22no—
135#22682—111nomaximal, Sylow
136C24×C11—21no—
137C23×D11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11C22×C412yes—
142C2×D4×C11C2×D412yes—
143C2×D4×C11C2×Q812yes—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—42no—
148C22×C4×C11—42no—
149C22×C4×C11—81no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C22×Dic11—24no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—42no—
158C22×Dic11—42no—
159C22×Dic11—81no—
160C22×Dic11—81no—
161C22×Dic11—81no—
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166C2×D44—21no—
167C2×D44—21no—
168C2×D44—21no—
169C2×D44C22×C412yes—
170C2×D44C2×D412yes—
171C2×D44C2×Q812yes—
172C2×C4×D11—24no—
173C2×C4×D11—42no—
174C2×C4×D11—42no—
175C2×C4×D11—42no—
176C2×C4×D11—42no—
177C2×C4×D11—81no—
178C2×C4×D11—81no—
179C2×C4×D11—81no—
180C2×C4×D11—81no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11C22×C412yes—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—81no—
193C11×C4⋊C4C22×C412yes—
194C11×C22⋊C4—42no—
195C42×C11—21no—
196C42×C11—21no—
197C22⋊Dic11—24no—
198C22⋊Dic11—42no—
199#4323C4⋊C4116yescomplemented
200(C2×D11)⋊C4—24no—
201(C2×D11)⋊C4—42no—
202(C2×D11)⋊C4—42no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—81no—
209C4⋊Dic11C22×C412yes—
210Dic11⋊C4—22no—
211Dic11⋊C4—22no—
212Dic11⋊C4—81no—
213Dic11⋊C4—81no—
214C4×Dic11—21no—
215C4×Dic11—21no—
216C4×Dic11C22×C412yes—
217C4×Dic11#4112yes—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8C22×C412yes—
222C2×C11⋊C8C2×D412yes—
223C2×C11⋊C8C2×Q812yes—
224C2×C4×D8—111no—
225C2×C4×D8—111no—
226C2×C4×D8—111no—
227#2349—111no—
228#2349—111no—
229#1942—111no—
230#1942—111no—
231#1864—111no—
232#1864—111no—
233#1864—111no—
234#1864D1111yescharacteristic, complemented
235#1846—111no—
236#1804—111no—
237#1804—111no—
238C8×C4⋊C4—111no—
239C23×C11—22no—
240C23×C11—22no—
241C23×C11—22no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11C22×D411yescharacteristic
247C22×D11—22no—
248C22×D11—22no—
249C22×D11—22no—
250C22×D11—41no—
251C22×D11—41no—
252C22×D11—41no—
253C22×D11—41no—
254D4×C11—22no—
255D4×C11—22no—
256D4×C11—22no—
257D4×C11C2×C4⋊C414yes—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—22no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—84no—
273C2×C4×C11#13512yes—
274C2×C4×C11C23×C411yescharacteristic
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11C22×Q811yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11H(5,𝔽2)11yescharacteristic
279C2×C4×C112−1+411yescharacteristic
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—22no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
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—
299C2×Dic11—84no—
300C2×Dic11C4×D412yes—
301C2×Dic11C4×D412yes—
302C2×Dic11#13512yes—
303D44—22no—
304D44—22no—
305D44—22no—
306D44C2×C4⋊C414yes—
307C4×D11—84no—
308C4×D11—84no—
309C4×D11—84no—
310C8×C11—22no—
311C8×C11—41no—
312C11⋊C8—41no—
313C11⋊C8C2×C4⋊C414yes—
314C22×D8—111no—
315C2×C4×D4—111no—
316C2×C4×D4—111no—
317C2×C4×D4—111no—
318C2×C4×D4—111no—
319C2×C4×D4—111no—
320C2×C4×D4C2×D1111yescharacteristic
321C4×D8—118no—
322C4×D8—224no—
323C4×D8—224no—
324C2×#107—111no—
325C2×#107—111no—
326C2×#107—111no—
327C2×#106—111no—
328C2×#106C2×D1111yescharacteristic
329C2×C4⋊C8—111no—
330C2×#102—111no—
331C2×#102—111no—
332C2×#102—111no—
333C2×#102—111no—
334C2×#102C2×D1111yescharacteristic
335C2×#102C2×D1111yescharacteristic
336C2×C4×C8—111no—
337C2×C4×C8—111no—
338C2×C4×C8—111no—
339#389—111no—
340#389—111no—
341#389—111no—
342#389C2×D1111yescharacteristic
343#385—221no—
344#385—221no—
345#385—221no—
346#385—221no—
347#382—111no—
348#382—111no—
349#380—221no—
350#380—221no—
351C4×C4⋊C4—111no—
352C2×#95—221no—
353C2×#95—221no—
354#340—111no—
355#340—111no—
356#340—111no—
357#340C2×D1111yescharacteristic
358#336—111no—
359#336C2×D1111yescharacteristic
360C22×C11—24no—
361C22×C11—42no—
362C22×C11—42no—
363C22×C11—42no—
364C22×C11—42no—
365C22×C11—42no—
366C22×C11—42no—
367C22×C11C2×C4×D411yescharacteristic
368C22×C11D4211yescharacteristic
369C22×C11D4×Q811yescharacteristic
370C22×C11C2×#13511yescharacteristic
371C22×C11C2×#13511yescharacteristic
372C22×C11#57611yescharacteristic
373C22×C11#57611yescharacteristic
374C2×D11—24no—
375C2×D11—42no—
376C2×D11—42no—
377C2×D11—42no—
378C2×D11—42no—
379C2×D11—42no—
380C2×D11—42no—
381C4×C11—22no—
382C4×C11—42no—
383C4×C11—41no—
384C4×C11—81no—
385C4×C11—81no—
386C4×C11C22×C4⋊C411yescharacteristic
387C4×C11#52011yescharacteristic
388C4×C11#54711yescharacteristic
389C4×C11#55411yescharacteristic
390Dic11—22no—
391Dic11—22no—
392Dic11—22no—
393Dic11—42no—
394Dic11—41no—
395Dic11—81no—
396Dic11—81no—
397C22×D4—111no—
398C22×D4C22×D1111yescharacteristic
399C23×C4—21no—
400C23×C4—221no—
401C23×C4—221no—
402C23×C4—221no—
403C23×C4—221no—
404C23×C4—221no—
405C2×D8—114no—
406C2×D8—114no—
407C2×D8—114no—
408C22×C8—111no—
409C22×C8—111no—
410C22×C8C22×D1111yescharacteristic
411C22×C8C22×D1111yescharacteristic
412C4×D4—22no—
413C4×D4—41no—
414C4×D4—114no—
415C4×D4—114no—
416C4×D4—222no—
417C4×D4—222no—
418C4×D4—222no—
419C4×D4—222no—
420C4×D4—222no—
421C4×D4—441no—
422C4×D4—441no—
423C4×D4—441no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—111no—
429C2×C4⋊C4—111no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4C22×D1111yescharacteristic
434C2×C4⋊C4C22×D1111yescharacteristic
435C2×C4⋊C4C22×D1111yescharacteristic
436C2×C22⋊C4—21no—
437C2×C22⋊C4—221no—
438C2×C22⋊C4—221no—
439C2×C22⋊C4—221no—
440C2×C22⋊C4—221no—
441C2×C22⋊C4—221no—
442C2×C42—111no—
443C2×C42—111no—
444C2×C42C22×D1111yescharacteristic
445#107—114no—
446#107—222no—
447#107—222no—
448#106—41no—
449#106—441no—
450C4⋊C8—222no—
451#102—22no—
452#102—114no—
453#102—222no—
454#102—222no—
455#102—222no—
456#102C4×D1114yescomplemented
457C4×C8—114no—
458C4×C8—222no—
459C4×C8—222no—
460#95—21no—
461#95—111no—
462#95—111no—
463#95—221no—
464#95—221no—
465#95—221no—
466#95—221no—
467#95—221no—
468#95—221no—
469#95—221no—
470C2×C11—44no—
471C2×C11D4×C4⋊C411yescharacteristic
472C2×C11C4×#13511yescharacteristic
473C2×C11#294811yescharacteristic
474C2×C11#328011yescharacteristic
475C2×C11#328011yescharacteristic
476C2×C11#338011yescharacteristic
477C2×C11#338011yescharacteristic
478D11—44no—
479C24—21no—
480C24—221no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—112no—
485C2×D4—112no—
486C2×D4—112no—
487C2×D4—221no—
488C2×D4—221no—
489C2×D4—221no—
490C2×D4C2×C4×D1112yes—
491C2×D4D4×D1112yes—
492C2×D4Q8×D1112yes—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—81no—
499C22×C4—111no—
500C22×C4—111no—
501C22×C4—111no—
502C22×C4—111no—
503C22×C4—224no—
504C22×C4—224no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—221no—
508C22×C4—442no—
509C22×C4—442no—
510C22×C4—442no—
511C22×C4—442no—
512C22×C4—442no—
513C22×C4—442no—
514C22×C4—881no—
515C22×C4—881no—
516C22×C4—881no—
517C22×C4—881no—
518C22×C4—881no—
519C22×C4—881no—
520C22×C4—881no—
521C22×C4D4×D1111yescharacteristic
522C22×C4D4×D1111yescharacteristic
523C22×C4C23×D1111yescharacteristic
524D8—1116no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—112no—
531C2×C8—112no—
532C2×C8—112no—
533C2×C8—221no—
534C2×C8—221no—
535C2×C8—221no—
536C2×C8C2×C4×D1112yes—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—81no—
543C4⋊C4—112no—
544C4⋊C4—222no—
545C4⋊C4—222no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C4⋊C4—221no—
549C4⋊C4—221no—
550C4⋊C4—221no—
551C4⋊C4—881no—
552C4⋊C4—881no—
553C4⋊C4—881no—
554C4⋊C4C2×C4×D1112yes—
555C22⋊C4—42no—
556C22⋊C4—224no—
557C22⋊C4—224no—
558C22⋊C4—442no—
559C22⋊C4—442no—
560C22⋊C4—442no—
561C42—21no—
562C42—21no—
563C42—112no—
564C42—112no—
565C42—221no—
566C42—221no—
567C11#2268211yescharacteristic, complemented, Sylow
568C23—22no—
569C23—22no—
570C23—22no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—222no—
576C23—222no—
577C23—222no—
578C23—441no—
579C23—441no—
580C23—441no—
581C23—441no—
582C23C2×D4×D1111yescharacteristic
583D4—22no—
584D4—22no—
585D4—22no—
586D4—114no—
587D4—222no—
588D4—222no—
589D4—222no—
590D4C4⋊C4×D1114yes—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—21no—
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—84no—
606C2×C4—112no—
607C2×C4—112no—
608C2×C4—112no—
609C2×C4—221no—
610C2×C4—221no—
611C2×C4—221no—
612C2×C4—221no—
613C2×C4—221no—
614C2×C4—221no—
615C2×C4—221no—
616C2×C4—221no—
617C2×C4—222no—
618C2×C4—221no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—884no—
628C2×C4—884no—
629C2×C4—884no—
630C2×C4—884no—
631C2×C4—884no—
632C2×C4#6696912yes—
633C2×C4C22×C4×D1111yescharacteristic
634C2×C4C2×D4×D1111yescharacteristic
635C2×C4#6703711yescharacteristic
636C2×C4C2×Q8×D1111yescharacteristic
637C2×C4#41×D1111yescharacteristic
638C2×C4#6704311yescharacteristic
639C8—22no—
640C8—41no—
641C8—114no—
642C8—441no—
643C22—24no—
644C22—42no—
645C22—42no—
646C22—42no—
647C22—42no—
648C22—42no—
649C22—42no—
650C22—224no—
651C22—442no—
652C22—442no—
653C22—442no—
654C22—442no—
655C22—442no—
656C22—442no—
657C22C4×D4×D1111yescharacteristic
658C22#1062312111yescharacteristic
659C22#1062316311yescharacteristic
660C22C2×#6696911yescharacteristic
661C22D11×#13511yescharacteristic
662C22#1062330511yescharacteristic
663C22#1062330511yescharacteristic
664C4—22no—
665C4—42no—
666C4—41no—
667C4—81no—
668C4—81no—
669C4—222no—
670C4—222no—
671C4—222no—
672C4—442no—
673C4—441no—
674C4—881no—
675C4—881no—
676C4C2×C4⋊C4×D1111yescharacteristic
677C4#1062307711yescharacteristic
678C4#1062316711yescharacteristic
679C4#1062318611yescharacteristic
680C2—44no—
681C2—444no—
682C2#1307151411yescharacteristic
683C2C4×#6696911yescharacteristic
684C2#1307746511yescharacteristic
685C2#1308029411yescharacteristic
686C2#1308029911yescharacteristic
687C2#1308147811yescharacteristic
688C2#1308148211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1864C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
cosocleC22×C4×C11C24
hypercenter#1864D11
hypocenterC11#22682
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1864

Complements

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

NH ≅ G/Ntype
4. #13071525C2semidirect
5. #13071521C2semidirect
6. #13069348C2semidirect
7. #13069346C2semidirect
8. #13068880C2semidirect
9. #13068879C2semidirect
10. #13068874C2semidirect
11. #13068777C2semidirect
12. #13068625C2semidirect
13. #13068624C2semidirect
14. #13068477C2semidirect
15. C11×#1864C2semidirect
53. #10622369C4semidirect
85. D4×Dic11C2×C4semidirect
107. #66946C2×C4semidirect
112. C11×#102C2×C4semidirect
125. #66885C2×C4semidirect
129. C8×Dic11C2×C4semidirect
133. #66871C2×C4semidirect
199. #4323C4⋊C4semidirect
234. #1864D11semidirect
456. #102C4×D11semidirect
567. C11#22682semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43232
C2×#106223692
#130715252
#130715212
#130693482
#130693462
#130688802
#130688792
#130688742
#130687772
#130686252
#130686242
#130684772
C11×#18642
#2268211