Finite Group Databasebeta

← #14771006

Subgroups — #14771006

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622845C211yesmaximal, characteristic
2#13071495C211yesmaximal, characteristic, complemented
3#13071446C211yesmaximal, characteristic
4#13069303C211yesmaximal, characteristic, complemented
5#13069289C211yesmaximal, characteristic, complemented
6#13069260C211yesmaximal, characteristic, complemented
7#13069253C211yesmaximal, characteristic, complemented
8#13068875C211yesmaximal, characteristic, complemented
9#13068861C211yesmaximal, characteristic, complemented
10#13068703C211yesmaximal, characteristic, complemented
11#13068647C211yesmaximal, characteristic, complemented
12#13068443C211yesmaximal, characteristic, complemented
13#102×Dic11C211yesmaximal, characteristic, complemented
14#13068402C211yesmaximal, characteristic, complemented
15C11×#1788C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C2×D4×Dic11C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C2×C11×#103C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C11×#380C2211yescharacteristic
27#10622845C418yescomplemented
28#10622843C2211yescharacteristic
29#10622843C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32#10622833—21no—
33#10622833—21no—
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36#10622825C2211yescharacteristic
37#10622824—21no—
38C4×C22⋊Dic11C2211yescharacteristic
39C2×C11⋊#95—21no—
40C2×#66879C2211yescharacteristic
41C2×C8×Dic11C2211yescharacteristic
42C4⋊C4×Dic11C2211yescharacteristic
43C4⋊C4×Dic11C2211yescharacteristic
44#10622586C2211yescharacteristic
45#10622586C2211yescharacteristic
46C2×#66872C2211yescharacteristic
47C2×#66871C2211yescharacteristic
48#10622555—21no—
49C22⋊C4×Dic11—21no—
50#10622266—21no—
51#10622266—21no—
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C2×C11×#41—22no—
61C2×C11×#41—22no—
62C2×C11×#41—22no—
63C2×C11×#41—41no—
64C2×C11×#41—41no—
65C2×C11×#41C2×C414yes—
66C22×Q8×C11C2311yescharacteristic
67C22×D4×C11—21no—
68C22×D4×C11C2311yescharacteristic
69C23×C4×C11—21no—
70C23×C4×C11C2311yescharacteristic
71C23×Dic11—21no—
72C23×Dic11—21no—
73C23×Dic11—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⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11D411yescharacteristic
83C2×C22⋊Dic11D411yescharacteristic
84D4×Dic11—22no—
85D4×Dic11—22no—
86D4×Dic11—41no—
87D4×Dic11—41no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—22no—
90C2×C4⋊Dic11C2×C414yescomplemented
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11C2311yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C2×#4318—41no—
102C2×#4318—41no—
103C2×#4318C2×C414yescomplemented
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C11×#103—41no—
107C11×#103—41no—
108C11×#102—22no—
109C11×#102—22no—
110C11×C22⋊C8—22no—
111C11×#95—21no—
112#66899C2×C414yescomplemented
113#66899C2×C414yescomplemented
114#66896C2×C414yes—
115#66896C2×C414yes—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95D411yescharacteristic
126C11⋊#95D411yescharacteristic
127#66879—41no—
128C8×Dic11—41no—
129#66872—41no—
130#66871—41no—
131#22578—111nomaximal, Sylow
132C24×C11—21no—
133C24×C11C2×D411yescharacteristic
134C11×#41—28no—
135C11×#41—44no—
136C11×#41—44no—
137C11×#41—44no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11C22×C412yes—
144C2×D4×C11—24no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—42no—
149C2×D4×C11—42no—
150C2×D4×C11C22×C412yes—
151C2×D4×C11#4112yes—
152C2×D4×C11#4112yes—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—24no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—42no—
162C22×C4×C11—42no—
163C22×C4×C11C22×C412yes—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11#4112yes—
166C22×C4×C11C2411yescharacteristic
167C22×Dic11—24no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—42no—
173C22×Dic11—42no—
174C22×Dic11—42no—
175C22×Dic11—42no—
176C22×Dic11—81no—
177C22×Dic11—81no—
178C22×Dic11—81no—
179C22×Dic11—81no—
180C22×Dic11C2×D411yescharacteristic
181C22×Dic11C2×D411yescharacteristic
182C22×Dic11C2×D411yescharacteristic
183C22×Dic11C2×D411yescharacteristic
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C22⋊C4—42no—
195C22⋊Dic11—22no—
196C22⋊Dic11—41no—
197C22⋊Dic11—42no—
198C22⋊Dic11—42no—
199C22⋊Dic11—81no—
200C4⋊Dic11—24no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11C22×C412yes—
208C4⋊Dic11C22×C412yes—
209Dic11⋊C4—81no—
210Dic11⋊C4—81no—
211C4×Dic11—21no—
212C4×Dic11—21no—
213C4×Dic11—21no—
214C4×Dic11—21no—
215C4×Dic11—81no—
216C4×Dic11—81no—
217#4318—44no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8C22×C412yes—
223C2×C11⋊C8C22×C412yes—
224C2×#417—111no—
225#2345—111no—
226#2339—111no—
227#1935—111no—
228#1933—111no—
229#1928—111no—
230#1927—111no—
231#1864—111no—
232#1862—111no—
233#1823—111no—
234#1809—111no—
235#1788D1111yescharacteristic
236#1762—111no—
237C4×#102—111no—
238#1753—111no—
239C23×C11—22no—
240C23×C11—22no—
241C23×C11—22no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11C4×D412yes—
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—48no—
262D4×C11#11714yes—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—48no—
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—41no—
279C2×C4×C11C4×D412yes—
280C2×C4×C11C23×C411yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C11H(5,𝔽2)11yescharacteristic
285C2×C4×C11H(5,𝔽2)11yescharacteristic
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—22no—
289C2×Dic11—22no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—21no—
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—84no—
310C2×Dic11—84no—
311C2×Dic11—84no—
312C2×Dic11#13712yes—
313C8×C11—41no—
314C8×C11—41no—
315C11⋊C8—22no—
316C11⋊C8—22no—
317C22×#41C2×D1111yescharacteristic
318C22×M16—111no—
319C2×C4×D4—111no—
320C2×C4×D4—111no—
321C22×C4⋊C4—111no—
322C2×#107—111no—
323C2×#106—111no—
324#417—118no—
325C2×#103—111no—
326C2×#103—111no—
327C2×#103C2×D1111yescharacteristic
328C2×#103C2×D1111yescharacteristic
329C2×#102—111no—
330C2×#102—111no—
331C2×#102C2×D1111yescharacteristic
332C2×#102C2×D1111yescharacteristic
333C2×C22⋊C8C2×D1111yescharacteristic
334C2×#97—111no—
335C2×C4×C8—111no—
336#391—111no—
337#391—111no—
338#389—111no—
339#389—111no—
340#387—221no—
341#387—221no—
342#386—221no—
343#386—221no—
344#381—221no—
345#380—111no—
346#380—221no—
347#380C2×D1111yescharacteristic
348C4×C4⋊C4—111no—
349C4×C4⋊C4—111no—
350C4×C22⋊C4—111no—
351C4×C22⋊C4—221no—
352C2×#95—221no—
353#340—111no—
354#340—111no—
355#340—111no—
356#340—111no—
357#340—111no—
358#340—111no—
359#336—111no—
360#336—111no—
361C22×C11—22no—
362C22×C11—24no—
363C22×C11—22no—
364C22×C11—22no—
365C22×C11—41no—
366C22×C11—42no—
367C22×C11—42no—
368C22×C11—42no—
369C22×C11—41no—
370C22×C11—42no—
371C22×C11—41no—
372C22×C11—42no—
373C22×C11—41no—
374C22×C11—42no—
375C22×C11C2×C4×D411yescharacteristic
376C22×C11#54611yescharacteristic
377C22×C11#54611yescharacteristic
378C22×C11C2×#13711yescharacteristic
379C22×C11#57511yescharacteristic
380C22×C11#57611yescharacteristic
381C22×C11#57711yescharacteristic
382C4×C11—22no—
383C4×C11—42no—
384C4×C11—81no—
385C4×C11—81no—
386C4×C11C2×#11711yescharacteristic
387C4×C11#51811yescharacteristic
388C4×C11#55111yescharacteristic
389C4×C11#55111yescharacteristic
390Dic11—22no—
391Dic11—41no—
392Dic11—42no—
393Dic11—42no—
394Dic11—41no—
395Dic11—41no—
396Dic11—81no—
397Dic11—81no—
398C2×#41—22no—
399C2×#41—22no—
400C2×#41—22no—
401C2×#41—41no—
402C2×#41—41no—
403C2×#41C4×D1114yes—
404C22×Q8C22×D1111yescharacteristic
405C22×D4—21no—
406C22×D4C22×D1111yescharacteristic
407C23×C4—21no—
408C23×C4—221no—
409C23×C4—221no—
410C23×C4—221no—
411C23×C4C22×D1111yescharacteristic
412C2×M16—114no—
413C2×M16—441no—
414C2×M16—441no—
415C22×C8—111no—
416C22×C8—111no—
417C22×C8C22×D1111yescharacteristic
418C22×C8C22×D1111yescharacteristic
419C4×D4—222no—
420C4×D4—222no—
421C4×D4—441no—
422C4×D4—441no—
423C2×C4⋊C4—114no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4—222no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4C22×D1111yescharacteristic
433C2×C4⋊C4C22×D1111yescharacteristic
434C2×C22⋊C4—21no—
435C2×C22⋊C4—111no—
436C2×C22⋊C4—111no—
437C2×C22⋊C4—221no—
438C2×C22⋊C4—221no—
439C2×C22⋊C4—221no—
440C2×C42—111no—
441C2×C42—111no—
442C2×C42—221no—
443C2×C42—221no—
444#107—441no—
445#106—441no—
446#103—41no—
447#103—41no—
448#103—114no—
449#103—114no—
450#102—22no—
451#102—22no—
452#102—114no—
453#102—114no—
454C22⋊C8—22no—
455#97—441no—
456C4×C8—441no—
457#95—21no—
458#95—111no—
459#95—111no—
460#95—221no—
461#95—221no—
462#95—221no—
463#95—221no—
464#95—221no—
465#95—221no—
466#95—221no—
467#95—221no—
468#95—221no—
469C2×C11—42no—
470C2×C11—44no—
471C2×C11#234211yescharacteristic
472C2×C11C4×#13711yescharacteristic
473C2×C11#294611yescharacteristic
474C2×C11#330711yescharacteristic
475C2×C11#331411yescharacteristic
476C2×C11#332211yescharacteristic
477C2×C11#333111yescharacteristic
478C24—21no—
479C24D4×D1111yescharacteristic
480#41—28no—
481#41—44no—
482#41—44no—
483#41—44no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8C2×C4×D1112yes—
490C2×D4—24no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4C2×C4×D1112yes—
497C2×D4#434112yes—
498C2×D4#434112yes—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—24no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—111no—
510C22×C4—111no—
511C22×C4—111no—
512C22×C4—111no—
513C22×C4—221no—
514C22×C4—221no—
515C22×C4—224no—
516C22×C4—221no—
517C22×C4—221no—
518C22×C4—442no—
519C22×C4—442no—
520C22×C4—442no—
521C22×C4—442no—
522C22×C4—881no—
523C22×C4—881no—
524C22×C4—881no—
525C22×C4—881no—
526C22×C4C2×C4×D1112yes—
527C22×C4D4×D1111yescharacteristic
528C22×C4#434112yes—
529C22×C4C23×D1111yescharacteristic
530M16—444no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—112no—
538C2×C8—112no—
539C2×C8—221no—
540C2×C8—221no—
541C2×C8—221no—
542C2×C8—221no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—112no—
548C4⋊C4—112no—
549C4⋊C4—224no—
550C4⋊C4—221no—
551C4⋊C4—221no—
552C4⋊C4—221no—
553C4⋊C4—221no—
554C4⋊C4—221no—
555C4⋊C4—221no—
556C4⋊C4—881no—
557C4⋊C4—881no—
558C22⋊C4—42no—
559C22⋊C4—222no—
560C22⋊C4—441no—
561C22⋊C4—442no—
562C22⋊C4—442no—
563C22⋊C4—881no—
564C42—221no—
565C42—221no—
566C42—221no—
567C42—221no—
568C42—881no—
569C42—881no—
570C11#2257811yescharacteristic, complemented, Sylow
571C23—22no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—22no—
577C23—22no—
578C23—21no—
579C23—21no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23(C22⋊D11)⋊C412yes—
585C23C2×D4×D1111yescharacteristic
586Q8—22no—
587Q8—22no—
588Q8—41no—
589Q8—41no—
590D4—22no—
591D4—22no—
592D4—22no—
593D4—48no—
594D4#6693014yes—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—48no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—112no—
612C2×C4—221no—
613C2×C4—221no—
614C2×C4—222no—
615C2×C4—222no—
616C2×C4—221no—
617C2×C4—221no—
618C2×C4—221no—
619C2×C4—221no—
620C2×C4—221no—
621C2×C4—221no—
622C2×C4—221no—
623C2×C4—221no—
624C2×C4—221no—
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—441no—
635C2×C4—884no—
636C2×C4—884no—
637C2×C4—884no—
638C2×C4(C22⋊D11)⋊C412yes—
639C2×C4C22×C4×D1111yescharacteristic
640C2×C4C2×#434111yescharacteristic
641C2×C4C2×#434111yescharacteristic
642C2×C4C2×#434111yescharacteristic
643C2×C4#6703711yescharacteristic
644C2×C4#6703711yescharacteristic
645C8—41no—
646C8—41no—
647C8—222no—
648C8—222no—
649C22—22no—
650C22—24no—
651C22—22no—
652C22—22no—
653C22—41no—
654C22—42no—
655C22—41no—
656C22—42no—
657C22—42no—
658C22—41no—
659C22—42no—
660C22—42no—
661C22—42no—
662C22—41no—
663C22C2×(C22⋊D11)⋊C411yescharacteristic
664C22#1062312211yescharacteristic
665C22#1062312211yescharacteristic
666C22#1062330011yescharacteristic
667C22#1062330111yescharacteristic
668C22#1062330411yescharacteristic
669C22D11×#13711yescharacteristic
670C4—22no—
671C4—42no—
672C4—81no—
673C4—81no—
674C4—222no—
675C4—441no—
676C4—441no—
677C4—442no—
678C4—442no—
679C4—441no—
680C4—881no—
681C4—881no—
682C4C2×#6693011yescharacteristic
683C4#1062301711yescharacteristic
684C4#1062311811yescharacteristic
685C4#1062311811yescharacteristic
686C2—42no—
687C2—44no—
688C2#1307146711yescharacteristic
689C2#1307744011yescharacteristic
690C2#1307745111yescharacteristic
691C2#1308058511yescharacteristic
692C2#1308069011yescharacteristic
693C2#1308081011yescharacteristic
694C2#1308092511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1788C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenter#1788D11
hypocenterC11#22578
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. #13071495C2semidirect
4. #13069303C2semidirect
5. #13069289C2semidirect
6. #13069260C2semidirect
7. #13069253C2semidirect
8. #13068875C2semidirect
9. #13068861C2semidirect
10. #13068703C2semidirect
11. #13068647C2semidirect
12. #13068443C2semidirect
13. #102×Dic11C2semidirect
14. #13068402C2semidirect
27. #10622845C4semidirect
90. C2×C4⋊Dic11C2×C4semidirect
103. C2×#4318C2×C4semidirect
112. #66899C2×C4semidirect
113. #66899C2×C4semidirect
570. C11#22578semidirect

Maximal subgroups

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

subgroupindex
C2×#106228452
#130714952
#130714462
#130693032
#130692892
#130692602
#130692532
#130688752
#130688612
#130687032
#130686472
#130684432
#102×Dic112
#130684022
C11×#17882
#2257811