Finite Group Databasebeta

← #14814196

Subgroups — #14814196

Order 2816.

924 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622777C211yesmaximal, characteristic, complemented
2#13072410C211yesmaximal, characteristic, complemented
3D4×Dic11⋊C4C211yesmaximal, characteristic, complemented
4#13070142C211yesmaximal, characteristic, complemented
5#13070109C211yesmaximal, characteristic, complemented
6#13070027C211yesmaximal, characteristic, complemented
7#13069852C211yesmaximal, characteristic, complemented
8#13069310C211yesmaximal, characteristic, complemented
9#13069177C211yesmaximal, characteristic, complemented
10#13068966C211yesmaximal, characteristic
11#13068966C211yesmaximal, characteristic
12#13068952C211yesmaximal, characteristic, complemented
13#13068868C211yesmaximal, characteristic, complemented
14#13068863C211yesmaximal, characteristic, complemented
15C2×C11×#463C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C2×C11×#124C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C2×D4×Dic11C2211yescharacteristic
22C2×D4×Dic11C2211yescharacteristic
23C22×Dic11⋊C4—21no—
24C11×#463—24no—
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28#10622843C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31#10622834C2211yescharacteristic
32#10622834C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37#10622823—21no—
38#10622777—24no—
39C2×#66882C2211yescharacteristic
40C2×#66879C2211yescharacteristic
41#10622589C2211yescharacteristic
42#10622586C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44#10622566—21no—
45#10622562—21no—
46#10622559—21no—
47#10622557—21no—
48#10622557—21no—
49#10622555—21no—
50C4×Dic11⋊C4C2211yescharacteristic
51#10622541C2211yescharacteristic
52#10622541C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11—21no—
65C23×Dic11—21no—
66C23×Dic11—21no—
67C2×C11×SD16—22no—
68C2×C11×SD16—22no—
69C2×C11×SD16D414yes—
70C2×C11×D8—22no—
71C2×C11×D8—22no—
72C2×C11×D8—22no—
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C11×#124—22no—
76C11×#124—41no—
77C4×D4×C11—22no—
78C4×D4×C11—41no—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C42×C11C2311yescharacteristic
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11—21no—
89C2×C22⋊Dic11—21no—
90Q8×Dic11—22no—
91Q8×Dic11—41no—
92D4×Dic11—22no—
93D4×Dic11—22no—
94D4×Dic11—22no—
95D4×Dic11—41no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—21no—
105C2×Dic11⋊C4—21no—
106C2×Dic11⋊C4—44no—
107C2×Dic11⋊C4D411yescharacteristic
108C2×Dic11⋊C4D411yescharacteristic
109C2×C4×Dic11—21no—
110C2×C4×Dic11C2311yescharacteristic
111C2×C4×Dic11C2311yescharacteristic
112C22×C11⋊C8C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
114C11×C4⋊C8—22no—
115C11×#103—22no—
116C11×#102—22no—
117#66899—22no—
118#66899—22no—
119#66896—22no—
120#66896—22no—
121#66896—22no—
122#66896—41no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95D411yescharacteristic
129C11⋊#95D411yescharacteristic
130#66882—22no—
131#66879—22no—
132#66871—41no—
133#26188—111nomaximal, Sylow
134C24×C11—21no—
135C24×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11C2×D412yes—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11C2×D412yes—
152C2×D4×C11#4112yes—
153C2×D4×C11#4112yes—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—42no—
157C22×C4×C11—42no—
158C22×C4×C11—81no—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2411yescharacteristic
162C22×Dic11—24no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—42no—
168C22×Dic11—42no—
169C22×Dic11—42no—
170C22×Dic11—42no—
171C22×Dic11—81no—
172C22×Dic11C2×D411yescharacteristic
173C22×Dic11C2×D411yescharacteristic
174C22×Dic11C2×D411yescharacteristic
175C22×Dic11C2×D411yescharacteristic
176C11×SD16—28no—
177C11×D8—44no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11C2×D412yes—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C22⋊C4—42no—
187C11×C22⋊C4—42no—
188C11×C22⋊C4—42no—
189C42×C11—21no—
190C42×C11—21no—
191C22⋊Dic11—24no—
192C22⋊Dic11—42no—
193C22⋊Dic11—42no—
194C22⋊Dic11—42no—
195C22⋊Dic11—81no—
196C22⋊Dic11—81no—
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#4112yes—
206Dic11⋊C4—22no—
207Dic11⋊C4—41no—
208Dic11⋊C4—42no—
209Dic11⋊C4—42no—
210Dic11⋊C4—42no—
211Dic11⋊C4—81no—
212Dic11⋊C4—81no—
213C4×Dic11—21no—
214C4×Dic11—21no—
215C4×Dic11—21no—
216C4×Dic11—21no—
217C4×Dic11—42no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×#463D1111yescharacteristic
225C2×#440—111no—
226#2448—111no—
227D4×C4⋊C4—111no—
228#2093—111no—
229#2087—111no—
230#2072—111no—
231#2042—111no—
232#1936—111no—
233#1917—111no—
234#1879—111no—
235#1879—111no—
236#1877—111no—
237#1863—111no—
238#1862—111no—
239C23×C11—22no—
240C23×C11—22no—
241C23×C11—22no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11C22×D411yescharacteristic
254Q8×C11—22no—
255Q8×C11—22no—
256Q8×C11—41no—
257Q8×C11—41no—
258D4×C11—22no—
259D4×C11—22no—
260D4×C11—22no—
261D4×C11—41no—
262D4×C11—41no—
263D4×C11—41no—
264D4×C11—41no—
265D4×C11#12314yes—
266C2×C4×C11—22no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
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×D411yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11H(5,𝔽2)11yescharacteristic
284C2×C4×C112−1+411yescharacteristic
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—22no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—21no—
294C2×Dic11—21no—
295C2×Dic11—21no—
296C2×Dic11—21no—
297C2×Dic11—48no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11—41no—
306C2×Dic11—41no—
307C2×Dic11—41no—
308C2×Dic11—41no—
309C2×Dic11—84no—
310C2×Dic11AGL(1,ℤ/8)12yes—
311C8×C11—22no—
312C8×C11—41no—
313C11⋊C8—41no—
314C11⋊C8—41no—
315C22×SD16C2×D1111yescharacteristic
316C22×D8C2×D1111yescharacteristic
317C2×#124C2×D1111yescharacteristic
318C2×C4×Q8—111no—
319C2×C4×D4—111no—
320C2×C4×D4—111no—
321C2×C4×D4C2×D1111yescharacteristic
322C22×C4⋊C4—221no—
323#463—24no—
324#440—224no—
325C2×#107—111no—
326C2×#107—111no—
327C2×C4⋊C8C2×D1111yescharacteristic
328C2×#103—111no—
329C2×#103—111no—
330C2×#103C2×D1111yescharacteristic
331C2×#102—111no—
332C2×#102—111no—
333C2×#102—111no—
334C2×#102—111no—
335C2×#102C2×D1111yescharacteristic
336C2×#97—111no—
337#399—221no—
338#397—221no—
339#391—111no—
340#390—111no—
341#390—111no—
342#389—111no—
343#389—111no—
344#389—111no—
345#388—221no—
346#388—221no—
347#385—221no—
348#385—221no—
349#384—111no—
350#380—221no—
351C4×C4⋊C4—111no—
352#340—111no—
353#340—111no—
354#340—111no—
355#340—111no—
356#336—111no—
357#336—111no—
358#336—111no—
359#336—111no—
360C22×C11—24no—
361C22×C11—42no—
362C22×C11—42no—
363C22×C11—42no—
364C22×C11—42no—
365C22×C11—42no—
366C22×C11—42no—
367C22×C11—81no—
368C22×C11—81no—
369C22×C11—81no—
370C22×C11—81no—
371C22×C11—81no—
372C22×C11—81no—
373C22×C11—81no—
374C22×C11#52511yescharacteristic
375C22×C11D4211yescharacteristic
376C22×C11#54811yescharacteristic
377C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
378C22×C11#57511yescharacteristic
379C22×C11#57611yescharacteristic
380C22×C11#57811yescharacteristic
381C4×C11—42no—
382C4×C11—41no—
383C4×C11—41no—
384C4×C11—81no—
385C4×C11C2×#12311yescharacteristic
386C4×C11#53911yescharacteristic
387C4×C11#54711yescharacteristic
388C4×C11#55311yescharacteristic
389Dic11—22no—
390Dic11—42no—
391Dic11—41no—
392Dic11—41no—
393Dic11—41no—
394Dic11—81no—
395Dic11—81no—
396Dic11—81no—
397C22×Q8C22×D1111yescharacteristic
398C22×D4C22×D1111yescharacteristic
399C22×D4C22×D1111yescharacteristic
400C23×C4—21no—
401C23×C4—221no—
402C23×C4—221no—
403C2×SD16—22no—
404C2×SD16—22no—
405C2×SD16C22⋊D1114yes—
406C2×D8—22no—
407C2×D8—22no—
408C2×D8—22no—
409C22×C8—111no—
410C22×C8—111no—
411C22×C8C22×D1111yescharacteristic
412C22×C8C22×D1111yescharacteristic
413#124—22no—
414#124—41no—
415C4×Q8—222no—
416C4×Q8—441no—
417C4×D4—22no—
418C4×D4—41no—
419C4×D4—222no—
420C4×D4—222no—
421C4×D4—222no—
422C4×D4—441no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—111no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4—221no—
434C2×C4⋊C4—221no—
435C2×C4⋊C4—444no—
436C2×C4⋊C4C22×D1111yescharacteristic
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—221no—
441C2×C22⋊C4—221no—
442C2×C22⋊C4—221no—
443C2×C22⋊C4—221no—
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C42—111no—
447C2×C42—111no—
448C2×C42—221no—
449C2×C42C22×D1111yescharacteristic
450#107—222no—
451#107—441no—
452C4⋊C8—22no—
453#103—22no—
454#103—222no—
455#103—222no—
456#102—22no—
457#102—222no—
458#102—222no—
459#102—222no—
460#102—441no—
461#97—222no—
462#95—111no—
463#95—111no—
464#95—221no—
465#95—221no—
466#95—221no—
467#95—221no—
468#95—221no—
469C2×C11—44no—
470C2×C11—161no—
471C2×C11#244311yescharacteristic
472C2×C11#311411yescharacteristic
473C2×C11#312411yescharacteristic
474C2×C11#326911yescharacteristic
475C2×C11#327411yescharacteristic
476C2×C11#336711yescharacteristic
477C2×C11#337011yescharacteristic
478C24—21no—
479C24—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8C2×C22⋊D1112yes—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4#434112yes—
496C2×D4#434112yes—
497C2×D4C2×C22⋊D1112yes—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—81no—
503C22×C4—111no—
504C22×C4—111no—
505C22×C4—111no—
506C22×C4—111no—
507C22×C4—224no—
508C22×C4—221no—
509C22×C4—221no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4—442no—
513C22×C4—442no—
514C22×C4—442no—
515C22×C4—442no—
516C22×C4—881no—
517C22×C4D4×D1111yescharacteristic
518C22×C4D4×D1111yescharacteristic
519C22×C4C23×D1111yescharacteristic
520SD16—28no—
521D8—44no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—221no—
528C2×C8—221no—
529C2×C8—221no—
530C2×C8—221no—
531C2×C8—221no—
532C2×C8—221no—
533C2×C8C2×C22⋊D1112yes—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—112no—
537C4⋊C4—222no—
538C4⋊C4—221no—
539C4⋊C4—221no—
540C4⋊C4—221no—
541C4⋊C4—221no—
542C4⋊C4—221no—
543C4⋊C4—221no—
544C4⋊C4—221no—
545C4⋊C4—441no—
546C4⋊C4—442no—
547C4⋊C4—442no—
548C4⋊C4—442no—
549C4⋊C4—442no—
550C4⋊C4—881no—
551C4⋊C4—881no—
552C22⋊C4—42no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—224no—
556C22⋊C4—442no—
557C22⋊C4—442no—
558C22⋊C4—442no—
559C22⋊C4—881no—
560C22⋊C4—881no—
561C42—21no—
562C42—21no—
563C42—221no—
564C42—221no—
565C42—221no—
566C42—221no—
567C42—442no—
568C11#2618811yescharacteristic, complemented, Sylow
569C23—22no—
570C23—22no—
571C23—22no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23C2×D4×D1111yescharacteristic
584Q8—22no—
585Q8—22no—
586Q8—41no—
587Q8—41no—
588D4—22no—
589D4—22no—
590D4—22no—
591D4—41no—
592D4—41no—
593D4—41no—
594D4—41no—
595D4#6698814yes—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—84no—
609C2×C4—112no—
610C2×C4—221no—
611C2×C4—221no—
612C2×C4—221no—
613C2×C4—221no—
614C2×C4—221no—
615C2×C4—221no—
616C2×C4—221no—
617C2×C4—221no—
618C2×C4—221no—
619C2×C4—221no—
620C2×C4—221no—
621C2×C4—222no—
622C2×C4—448no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—441no—
634C2×C4—884no—
635C2×C4C2×#434111yescharacteristic
636C2×C4C2×#434111yescharacteristic
637C2×C4#6703711yescharacteristic
638C2×C4#41×D1111yescharacteristic
639C2×C4#6704311yescharacteristic
640C2×C4C22×C22⋊D1111yescharacteristic
641C8—22no—
642C8—41no—
643C8—441no—
644C8—441no—
645C22—24no—
646C22—42no—
647C22—42no—
648C22—42no—
649C22—42no—
650C22—42no—
651C22—42no—
652C22—81no—
653C22—81no—
654C22—81no—
655C22—81no—
656C22—81no—
657C22—81no—
658C22—81no—
659C22#1062312911yescharacteristic
660C22#1062313711yescharacteristic
661C22#1062329911yescharacteristic
662C22#1062330211yescharacteristic
663C22D11×AGL(1,ℤ/8)11yescharacteristic
664C22#1062330511yescharacteristic
665C22D4×C22⋊D1111yescharacteristic
666C4—41no—
667C4—41no—
668C4—42no—
669C4—81no—
670C4—222no—
671C4—441no—
672C4—441no—
673C4—441no—
674C4—442no—
675C4—881no—
676C4—881no—
677C4—881no—
678C4#1062313211yescharacteristic
679C4#1062313311yescharacteristic
680C4C2×#6698811yescharacteristic
681C4#1062335511yescharacteristic
682C2—44no—
683C2—161no—
684C2#1307234711yescharacteristic
685C2#1307875311yescharacteristic
686C2#1307887511yescharacteristic
687C2#1308017111yescharacteristic
688C2#1308023011yescharacteristic
689C2#1308132911yescharacteristic
690C2#1308137311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#463C2
socleC23×C11C22×D4
prime radicalC22×C11×D8C22
hypercenterC2×#463D11
hypocenterC11#26188
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#10622777C2semidirect
2. #13072410C2semidirect
3. D4×Dic11⋊C4C2semidirect
4. #13070142C2semidirect
5. #13070109C2semidirect
6. #13070027C2semidirect
7. #13069852C2semidirect
8. #13069310C2semidirect
9. #13069177C2semidirect
12. #13068952C2semidirect
13. #13068868C2semidirect
14. #13068863C2semidirect
568. C11#26188semidirect

Maximal subgroups

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

subgroupindex
C2×#106227772
#130724102
D4×Dic11⋊C42
#130701422
#130701092
#130700272
#130698522
#130693102
#130691772
#130689662
#130689522
#130688682
#130688632
C2×C11×#4632
#2618811