Finite Group Databasebeta

← #14810907

Subgroups — #14810907

Order 2816.

990 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622404C211yesmaximal, characteristic, complemented
2C22×#66899C211yesmaximal, characteristic
3#13072319C211yesmaximal, characteristic
4Q8×C22⋊Dic11C211yesmaximal, characteristic
5#13070157C211yesmaximal, characteristic, complemented
6#13069995C211yesmaximal, characteristic, complemented
7#13069993C211yesmaximal, characteristic, complemented
8#13069755C211yesmaximal, characteristic, complemented
9#13068886C211yesmaximal, characteristic, complemented
10#13068882C211yesmaximal, characteristic, complemented
11#13068811C211yesmaximal, characteristic
12#13068793C211yesmaximal, characteristic
13#13068639C211yesmaximal, characteristic
14#13068619C211yesmaximal, characteristic, complemented
15C11×#1787C211yesmaximal, characteristic
16C23×Q8×C11C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C23×C11⋊C8C2211yescharacteristic
21C2×#66941C2211yescharacteristic
22C2×#66931—21no—
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28C11×#380C2211yescharacteristic
29#10622843—21no—
30#10622843—21no—
31#10622843C2211yescharacteristic
32#10622843C2211yescharacteristic
33C2×#66899—24no—
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×#66899C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38#10622825—21no—
39#10622825C2211yescharacteristic
40C4×C22⋊Dic11—21no—
41C4×C22⋊Dic11C2211yescharacteristic
42C2×#66881C2211yescharacteristic
43C2×#66881C2211yescharacteristic
44C2×Dic11⋊C8C2211yescharacteristic
45C2×Dic11⋊C8C2211yescharacteristic
46#10622598C2211yescharacteristic
47#10622589C2211yescharacteristic
48#10622586C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50C2×#66872C2211yescharacteristic
51#10622559—21no—
52#10622404—24no—
53#10622270—21no—
54#10622269—21no—
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11—21no—
62C22×Q8×C11—22no—
63C22×Q8×C11—22no—
64C22×Q8×C11—22no—
65C22×Q8×C11—41no—
66C22×Q8×C11—41no—
67C22×Q8×C11Q814yescomplemented
68C22×Q8×C11C2311yescharacteristic
69C22×Q8×C11C2311yescharacteristic
70C23×C4×C11—21no—
71C23×C4×C11C2311yescharacteristic
72C23×Dic11—21no—
73C22×Dic22—21no—
74C22×C8×C11C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11D411yescharacteristic
81C2×C22⋊Dic11D411yescharacteristic
82Q8×Dic11—22no—
83Q8×Dic11—22no—
84Q8×Dic11—41no—
85Q8×Dic11—41no—
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—41no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11C2311yescharacteristic
103C2×C4×Dic11C2311yescharacteristic
104C22×C11⋊C8—22no—
105C22×C11⋊C8—22no—
106C22×C11⋊C8—41no—
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109#66941—22no—
110#66941—41no—
111#66931—44no—
112C11×#103—22no—
113C11×#103—22no—
114C11×#103—41no—
115C11×#103—41no—
116C11×C22⋊C8—22no—
117C11×#95—21no—
118#66899—22no—
119#66899—22no—
120#66899—22no—
121#66899D414yes—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95D411yescharacteristic
130C11⋊#95D411yescharacteristic
131#66881—22no—
132#66881—41no—
133Dic11⋊C8—22no—
134Dic11⋊C8—41no—
135#66872—22no—
136#66872—41no—
137#25955—111nomaximal, Sylow
138C24×C11C2×D411yescharacteristic
139C2×Q8×C11—24no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—28no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—42no—
150C2×Q8×C11—42no—
151C2×Q8×C11—44no—
152C2×Q8×C11—44no—
153C2×Q8×C11—44no—
154C2×Q8×C11C2×D412yes—
155C2×Q8×C11C2×Q812yes—
156C2×Q8×C11C2×Q812yes—
157C2×Q8×C11#4112yes—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—24no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—42no—
168C22×C4×C11—42no—
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×Q812yes—
171C22×C4×C11#4112yes—
172C22×C4×C11C2411yescharacteristic
173C22×Dic11—21no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—42no—
178C22×Dic11—42no—
179C22×Dic11—81no—
180C22×Dic11C2×D411yescharacteristic
181C22×Dic11C2×D411yescharacteristic
182C22×Dic11C2×D411yescharacteristic
183C22×Dic11C2×D411yescharacteristic
184C2×Dic22—42no—
185C2×Dic22—42no—
186C2×Dic22—81no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C22⋊C4—42no—
198C22⋊Dic11—22no—
199C22⋊Dic11—42no—
200C22⋊Dic11SD1614yes—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—42no—
209C4⋊Dic11—42no—
210C4⋊Dic11—42no—
211C4⋊Dic11—42no—
212C4⋊Dic11C2×D412yes—
213Dic11⋊C4—42no—
214Dic11⋊C4—42no—
215Dic11⋊C4—42no—
216Dic11⋊C4—81no—
217C4×Dic11—21no—
218C4×Dic11—21no—
219C4×Dic11—21no—
220C4×Dic11—21no—
221C4×Dic11—42no—
222C4×Dic11—42no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—44no—
229C2×C11⋊C8C2×D412yes—
230C2×#475—111no—
231C22×#103—111no—
232#2440—111no—
233Q8×C22⋊C4—111no—
234#2096—111no—
235#2066—111no—
236#2066—111no—
237#2024—111no—
238#1865—111no—
239#1865—111no—
240#1853—111no—
241#1850—111no—
242#1807—111no—
243#1803—111no—
244#1787D1111yescharacteristic
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11C22⋊Q812yes—
250C23×C11C2×SD1612yes—
251C23×C11#13712yes—
252C23×C11C22×D411yescharacteristic
253Q8×C11—22no—
254Q8×C11—22no—
255Q8×C11—22no—
256Q8×C11—22no—
257Q8×C11—22no—
258Q8×C11—48no—
259Q8×C11—41no—
260Q8×C11—41no—
261Q8×C11C22⋊Q814yescomplemented
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—21no—
265C2×C4×C11—22no—
266C2×C4×C11—21no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—48no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11C22⋊Q812yes—
282C2×C4×C11C22×D411yescharacteristic
283C2×C4×C11C22×Q811yescharacteristic
284C2×C4×C11C2×#4111yescharacteristic
285C2×C4×C11C2×#4111yescharacteristic
286C2×C4×C11H(5,𝔽2)11yescharacteristic
287C2×C4×C11H(5,𝔽2)11yescharacteristic
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—22no—
294C2×Dic11—21no—
295C2×Dic11—21no—
296C2×Dic11—21no—
297C2×Dic11—21no—
298C2×Dic11—21no—
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—41no—
310C2×Dic11—84no—
311C2×Dic11C2×SD1612yes—
312C2×Dic11C2×SD1612yes—
313Dic22—84no—
314C8×C11—41no—
315C8×C11—41no—
316C11⋊C8—22no—
317C11⋊C8—41no—
318C23×Q8C2×D1111yescharacteristic
319C23×C8—111no—
320C2×C4⋊Q8—111no—
321C2×C22⋊Q8—221no—
322C2×C4×Q8—111no—
323C2×C4×Q8—111no—
324C22×C4⋊C4—111no—
325#475—224no—
326C2×#106—111no—
327C2×#106—111no—
328C2×#106—111no—
329C2×#106—111no—
330C2×C4⋊C8—111no—
331C2×C4⋊C8—111no—
332C2×#103—111no—
333C2×#103—111no—
334C2×#103—111no—
335C2×#103—111no—
336C2×#103—224no—
337C2×#103C2×D1111yescharacteristic
338C2×#103C2×D1111yescharacteristic
339C2×#103C2×D1111yescharacteristic
340C2×#103C2×D1111yescharacteristic
341C2×C22⋊C8C2×D1111yescharacteristic
342#398—221no—
343#395—221no—
344#391—111no—
345#391—111no—
346#391—221no—
347#391—221no—
348#389—111no—
349#389—111no—
350#385—221no—
351#384—111no—
352#380—111no—
353#380—221no—
354#380C2×D1111yescharacteristic
355C4×C22⋊C4—111no—
356C4×C22⋊C4—221no—
357#340—111no—
358#340—111no—
359#340—111no—
360#340—111no—
361#336—111no—
362#336—111no—
363C22×C11—22no—
364C22×C11—22no—
365C22×C11—22no—
366C22×C11—22no—
367C22×C11—22no—
368C22×C11—22no—
369C22×C11#47514yescomplemented
370C22×C11C2×C22⋊Q811yescharacteristic
371C22×C11D4211yescharacteristic
372C22×C11#54611yescharacteristic
373C22×C11C22×SD1611yescharacteristic
374C22×C11C2×#13711yescharacteristic
375C22×C11#57711yescharacteristic
376C22×C11#57811yescharacteristic
377C4×C11—22no—
378C4×C11—24no—
379C4×C11—42no—
380C4×C11—81no—
381C4×C11—81no—
382C4×C11C2×C22⋊Q811yescharacteristic
383C4×C11#54311yescharacteristic
384C4×C11#54611yescharacteristic
385C4×C11#55111yescharacteristic
386Dic11—22no—
387Dic11—22no—
388Dic11—41no—
389Dic11—42no—
390Dic11—41no—
391Dic11—81no—
392Dic11—81no—
393Dic11—81no—
394C22×Q8—21no—
395C22×Q8—22no—
396C22×Q8—22no—
397C22×Q8—22no—
398C22×Q8—41no—
399C22×Q8—41no—
400C22×Q8—221no—
401C22×Q8Dic2214yescomplemented
402C22×Q8C22×D1111yescharacteristic
403C22×Q8C22×D1111yescharacteristic
404C23×C4—21no—
405C23×C4—221no—
406C23×C4C22×D1111yescharacteristic
407C22×C8—111no—
408C22×C8—111no—
409C22×C8—222no—
410C22×C8—222no—
411C22×C8—441no—
412C22×C8C22×D1111yescharacteristic
413C22×C8C22×D1111yescharacteristic
414C4⋊Q8—222no—
415C4⋊Q8—441no—
416C22⋊Q8—444no—
417C4×Q8—222no—
418C4×Q8—222no—
419C4×Q8—441no—
420C4×Q8—441no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—222no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4—221no—
434C2×C4⋊C4—441no—
435C2×C4⋊C4C22×D1111yescharacteristic
436C2×C4⋊C4C22×D1111yescharacteristic
437C2×C22⋊C4—21no—
438C2×C22⋊C4—111no—
439C2×C22⋊C4—111no—
440C2×C22⋊C4—221no—
441C2×C42—111no—
442C2×C42—111no—
443C2×C42—221no—
444C2×C42—221no—
445#106—222no—
446#106—222no—
447#106—441no—
448#106—441no—
449C4⋊C8—222no—
450C4⋊C8—441no—
451#103—22no—
452#103—22no—
453#103—41no—
454#103—41no—
455#103—114no—
456#103—222no—
457#103—222no—
458#103—222no—
459C22⋊C8—22no—
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—24no—
471C2×C11#243711yescharacteristic
472C2×C11C2×#47511yescharacteristic
473C2×C11#308211yescharacteristic
474C2×C11#327011yescharacteristic
475C2×C11D4×SD1611yescharacteristic
476C2×C11#329811yescharacteristic
477C2×C11#331611yescharacteristic
478C24D4×D1111yescharacteristic
479C2×Q8—24no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—28no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—42no—
490C2×Q8—42no—
491C2×Q8—44no—
492C2×Q8—44no—
493C2×Q8—44no—
494C2×Q8—442no—
495C2×Q8—442no—
496C2×Q8—881no—
497C2×Q8C2×Dic2212yes—
498C2×Q8C2×Dic2212yes—
499C2×Q8D4×D1112yes—
500C2×Q8#434112yes—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—24no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—111no—
513C22×C4—111no—
514C22×C4—111no—
515C22×C4—111no—
516C22×C4—221no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4—221no—
520C22×C4—442no—
521C22×C4—442no—
522C22×C4—881no—
523C22×C4C2×Dic2212yes—
524C22×C4D4×D1111yescharacteristic
525C22×C4#434112yes—
526C22×C4C23×D1111yescharacteristic
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—112no—
534C2×C8—221no—
535C2×C8—221no—
536C2×C8—221no—
537C2×C8—221no—
538C2×C8—221no—
539C2×C8—444no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—112no—
545C4⋊C4—221no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C4⋊C4—221no—
549C4⋊C4—221no—
550C4⋊C4—221no—
551C4⋊C4—221no—
552C4⋊C4—442no—
553C4⋊C4—442no—
554C4⋊C4—442no—
555C4⋊C4—442no—
556C4⋊C4—442no—
557C4⋊C4—442no—
558C4⋊C4—442no—
559C4⋊C4—881no—
560C22⋊C4—42no—
561C22⋊C4—114no—
562C22⋊C4—222no—
563C22⋊C4—442no—
564C42—221no—
565C42—221no—
566C42—221no—
567C42—221no—
568C42—442no—
569C42—442no—
570C11#2595511yescharacteristic, complemented, Sylow
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23#6693112yes—
576C23SD16×D1112yes—
577C23#6697112yes—
578C23C2×D4×D1111yescharacteristic
579Q8—22no—
580Q8—22no—
581Q8—22no—
582Q8—22no—
583Q8—22no—
584Q8—48no—
585Q8—41no—
586Q8—41no—
587Q8—884no—
588Q8#6693114yescomplemented
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—48no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—112no—
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—222no—
620C2×C4—221no—
621C2×C4—441no—
622C2×C4—441no—
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—884no—
633C2×C4#6693112yes—
634C2×C4C22×Dic2211yescharacteristic
635C2×C4C2×D4×D1111yescharacteristic
636C2×C4C2×#434111yescharacteristic
637C2×C4C2×#434111yescharacteristic
638C2×C4#6703711yescharacteristic
639C2×C4#6703711yescharacteristic
640C8—41no—
641C8—41no—
642C8—222no—
643C8—441no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—22no—
648C22—22no—
649C22—22no—
650C22#1062240414yescomplemented
651C22C2×#6693111yescharacteristic
652C22#1062312111yescharacteristic
653C22#1062312211yescharacteristic
654C22C2×SD16×D1111yescharacteristic
655C22C2×#6697111yescharacteristic
656C22#1062330911yescharacteristic
657C22#1062331011yescharacteristic
658C4—22no—
659C4—24no—
660C4—42no—
661C4—81no—
662C4—81no—
663C4—222no—
664C4—222no—
665C4—441no—
666C4—441no—
667C4—442no—
668C4—881no—
669C4—881no—
670C4—881no—
671C4C2×#6693111yescharacteristic
672C4#1062301411yescharacteristic
673C4#1062311811yescharacteristic
674C4#1062312211yescharacteristic
675C2—24no—
676C2#1307228211yescharacteristic
677C2C2×#1062240411yescharacteristic
678C2#1307846011yescharacteristic
679C2#1308019011yescharacteristic
680C2#1308030511yescharacteristic
681C2#1308047411yescharacteristic
682C2#1308073111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1787C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1787D11
hypocenterC11#25955
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1787

Complements

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

NH ≅ G/Ntype
1. C2×#10622404C2semidirect
5. #13070157C2semidirect
6. #13069995C2semidirect
7. #13069993C2semidirect
8. #13069755C2semidirect
9. #13068886C2semidirect
10. #13068882C2semidirect
14. #13068619C2semidirect
67. C22×Q8×C11Q8semidirect
261. Q8×C11C22⋊Q8semidirect
369. C22×C11#475semidirect
401. C22×Q8Dic22semidirect
570. C11#25955semidirect
588. Q8#66931semidirect
650. C22#10622404semidirect

Maximal subgroups

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

subgroupindex
C2×#106224042
C22×#668992
#130723192
Q8×C22⋊Dic112
#130701572
#130699952
#130699932
#130697552
#130688862
#130688822
#130688112
#130687932
#130686392
#130686192
C11×#17872
#2595511