Finite Group Databasebeta

← #14797710

Subgroups — #14797710

Order 2816.

940 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×#10622421C211yesmaximal, characteristic
2C2×C4×#4326C211yesmaximal, characteristic, complemented
3#13072142C211yesmaximal, characteristic
4Q8×(C2×D11)⋊C4C211yesmaximal, characteristic
5#13070151C211yesmaximal, characteristic, complemented
6#13070048C211yesmaximal, characteristic
7#13069940C211yesmaximal, characteristic, complemented
8#13069821C211yesmaximal, characteristic
9#13069291C211yesmaximal, characteristic, complemented
10#13069220C211yesmaximal, characteristic
11#13068956C211yesmaximal, characteristic, complemented
12#13068955C211yesmaximal, characteristic, complemented
13#13068619C211yesmaximal, characteristic, complemented
14#13068549C211yesmaximal, characteristic
15C11×#1863C211yesmaximal, characteristic, complemented
16C22×Q8×D11C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C22×Dic44C2211yescharacteristic
21C2×#66950C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×#66880C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33C4×#4326—24no—
34#10622605—21no—
35#10622600—21no—
36#10622600C2211yescharacteristic
37#10622600C2211yescharacteristic
38#10622597—21no—
39#10622589C2211yescharacteristic
40#10622587—21no—
41#10622587C2211yescharacteristic
42#10622587C2211yescharacteristic
43C2×#66874C2211yescharacteristic
44C2×#66874C2211yescharacteristic
45C2×#66874C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47C4×(C2×D11)⋊C4—21no—
48C4×(C2×D11)⋊C4C2211yescharacteristic
49#10622542—21no—
50#10622542C2211yescharacteristic
51C2×C4×C11⋊C8C2211yescharacteristic
52#10622421—24no—
53#10622282—21no—
54#10622268—21no—
55C11×#340C2211yescharacteristic
56C11×#336C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C2×Q8×D11—22no—
63C2×Q8×D11—22no—
64C2×Q8×D11—22no—
65C2×Q8×D11—22no—
66C2×Q8×D11—41no—
67C2×Q8×D11—41no—
68C22×C4×D11—21no—
69C22×C4×D11C2311yescharacteristic
70C22×Dic22—21no—
71C22×Dic22C2311yescharacteristic
72C22×Dic22C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C4×Q8×C11—22no—
76C4×Q8×C11—41no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C42×C11—21no—
83C2×C42×C11C2311yescharacteristic
84Q8×Dic11—22no—
85Q8×Dic11—41no—
86C2×#4326—22no—
87C2×#4326—22no—
88C2×#4326D414yes—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4D411yescharacteristic
93C2×(C2×D11)⋊C4D411yescharacteristic
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C2×Dic44—22no—
107C2×Dic44—22no—
108C2×Dic44—41no—
109#66950—22no—
110#66950—41no—
111C4×Dic22—22no—
112C4×Dic22—41no—
113C11×#107—41no—
114C11×#103—22no—
115C11×#103—22no—
116C11×#95—21no—
117#66899—22no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95D411yescharacteristic
127C11⋊#95D411yescharacteristic
128(C2×D11)⋊C8—22no—
129(C2×D11)⋊C8—41no—
130#66880—41no—
131#66880—41no—
132Dic11⋊C8—41no—
133#66874—22no—
134#66874—22no—
135#66874—22no—
136#66871—22no—
137C4×C11⋊C8—22no—
138#24906—111nomaximal, Sylow
139C23×D11C2×D411yescharacteristic
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11C2×D412yes—
144C2×Q8×C11#4112yes—
145C2×Q8×C11#4112yes—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160Q8×D11—44no—
161Q8×D11—44no—
162Q8×D11—44no—
163Q8×D11—44no—
164C2×C4×D11—24no—
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11—21no—
168C2×C4×D11—21no—
169C2×C4×D11—21no—
170C2×C4×D11—21no—
171C2×C4×D11—42no—
172C2×C4×D11—42no—
173C2×Dic22—24no—
174C2×Dic22—21no—
175C2×Dic22—21no—
176C2×Dic22—21no—
177C2×Dic22—21no—
178C2×Dic22—21no—
179C2×Dic22—21no—
180C2×Dic22—21no—
181C2×Dic22—21no—
182C2×Dic22—21no—
183C2×Dic22—21no—
184C2×Dic22—42no—
185C2×Dic22—42no—
186C2×Dic22C2×D412yes—
187C2×Dic22#4112yes—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—42no—
201C11×C4⋊C4—81no—
202C42×C11—21no—
203C42×C11—21no—
204C42×C11—42no—
205#4326—28no—
206(C2×D11)⋊C4—41no—
207(C2×D11)⋊C4—42no—
208(C2×D11)⋊C4—42no—
209(C2×D11)⋊C4—81no—
210(C2×D11)⋊C4Q1614yescomplemented
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11—42no—
216C4⋊Dic11—42no—
217Dic11⋊C4—42no—
218Dic11⋊C4—42no—
219Dic11⋊C4—81no—
220C4×Dic11—21no—
221C4×Dic11—21no—
222C4×Dic11—42no—
223C4×Dic11—42no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8C2×D412yes—
230Dic44—44no—
231C2×#451—111no—
232C2×C4×Q16—111no—
233#2423—111no—
234Q8×C22⋊C4—111no—
235#2095—111no—
236#2076—111no—
237#2056—111no—
238#2036—111no—
239#1933—111no—
240#1923—111no—
241#1878—111no—
242#1878—111no—
243#1863D1111yescharacteristic, complemented
244#1803—111no—
245#1787—111no—
246C23×C11C22×D411yescharacteristic
247C22×D11—21no—
248C22×D11—21no—
249C22×D11—21no—
250C22×D11—21no—
251C22×D11—21no—
252C22×D11—21no—
253C22×D11C2×Q1612yes—
254Q8×C11—22no—
255Q8×C11—22no—
256Q8×C11—22no—
257Q8×C11#12314yes—
258C2×C4×C11—22no—
259C2×C4×C11—21no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
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—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11C2×Q1612yes—
276C2×C4×C11C22×D411yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11H(5,𝔽2)11yescharacteristic
281C2×C4×C11H(5,𝔽2)11yescharacteristic
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—22no—
286C2×Dic11—22no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11C2×Q1612yes—
303C4×D11—48no—
304C4×D11—41no—
305C4×D11—41no—
306C4×D11—41no—
307C4×D11—41no—
308Dic22—22no—
309Dic22—22no—
310Dic22—22no—
311Dic22—22no—
312Dic22—48no—
313Dic22—41no—
314Dic22—41no—
315Dic22—41no—
316Dic22—41no—
317C8×C11—41no—
318C8×C11—41no—
319C11⋊C8—22no—
320C11⋊C8—41no—
321C23×Q8—111no—
322C22×Q16—111no—
323C22×Q16—111no—
324C2×C22⋊Q8—111no—
325C2×C4×Q8—111no—
326C2×C4×Q8—111no—
327C2×C4×Q8C2×D1111yescharacteristic
328#451—224no—
329C4×Q16—224no—
330C2×#107—111no—
331C2×#107C2×D1111yescharacteristic
332C2×C4⋊C8—111no—
333C2×#103—111no—
334C2×#103—111no—
335C2×#103—111no—
336C2×#103—111no—
337C2×#103—111no—
338C2×#103—111no—
339C2×#103C2×D1111yescharacteristic
340C2×#103C2×D1111yescharacteristic
341C2×C22⋊C8—111no—
342C2×C22⋊C8—111no—
343C2×C4×C8—111no—
344#399—221no—
345#398—221no—
346#391—111no—
347#391—111no—
348#391—111no—
349#391—221no—
350#391—221no—
351#389C2×D1111yescharacteristic
352#388—221no—
353#387—221no—
354#384—111no—
355#380—111no—
356#380—111no—
357#380—221no—
358C4×C22⋊C4—111no—
359C4×C22⋊C4—221no—
360#340—111no—
361#340—111no—
362#340—111no—
363#340C2×D1111yescharacteristic
364#336—111no—
365#336C2×D1111yescharacteristic
366C22×C11#52511yescharacteristic
367C22×C11D4211yescharacteristic
368C22×C11#54611yescharacteristic
369C22×C11C22×Q1611yescharacteristic
370C22×C11#57511yescharacteristic
371C22×C11#57711yescharacteristic
372C22×C11#57811yescharacteristic
373C2×D11—22no—
374C2×D11—22no—
375C2×D11—22no—
376C2×D11—41no—
377C2×D11—41no—
378C2×D11—41no—
379C2×D11—41no—
380C4×C11—24no—
381C4×C11—22no—
382C4×C11—41no—
383C4×C11—81no—
384C4×C11—81no—
385C4×C11—81no—
386C4×C11C2×#12311yescharacteristic
387C4×C11#53811yescharacteristic
388C4×C11#54611yescharacteristic
389C4×C11#55111yescharacteristic
390Dic11—22no—
391Dic11—42no—
392Dic11—42no—
393Dic11—41no—
394Dic11—41no—
395Dic11—81no—
396Dic11—81no—
397C22×Q8—111no—
398C22×Q8—111no—
399C22×Q8—221no—
400C22×Q8—222no—
401C22×Q8—222no—
402C22×Q8—222no—
403C22×Q8—222no—
404C22×Q8—441no—
405C22×Q8—441no—
406C22×Q8C22×D1111yescharacteristic
407C23×C4—111no—
408C23×C4—221no—
409C2×Q16—114no—
410C2×Q16—222no—
411C2×Q16—222no—
412C2×Q16—222no—
413C2×Q16—222no—
414C2×Q16—441no—
415C22×C8—111no—
416C22×C8—111no—
417C22×C8C22×D1111yescharacteristic
418C22×C8C22×D1111yescharacteristic
419C22⋊Q8—222no—
420C22⋊Q8—441no—
421C4×Q8—22no—
422C4×Q8—41no—
423C4×Q8—222no—
424C4×Q8—222no—
425C4×Q8—441no—
426C4×Q8—441no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—111no—
430C2×C4⋊C4—111no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4—221no—
434C2×C4⋊C4—221no—
435C2×C4⋊C4—221no—
436C2×C4⋊C4C22×D1111yescharacteristic
437C2×C4⋊C4C22×D1111yescharacteristic
438C2×C4⋊C4C22×D1111yescharacteristic
439C2×C22⋊C4—111no—
440C2×C22⋊C4—111no—
441C2×C22⋊C4—221no—
442C2×C22⋊C4—221no—
443C2×C22⋊C4—221no—
444C2×C42—21no—
445C2×C42—111no—
446C2×C42—221no—
447C2×C42—221no—
448C2×C42C22×D1111yescharacteristic
449#107—41no—
450#107—222no—
451C4⋊C8—441no—
452#103—22no—
453#103—22no—
454#103—222no—
455#103—222no—
456#103—222no—
457#103—222no—
458#103—441no—
459#103—441no—
460C22⋊C8—222no—
461C22⋊C8—441no—
462C4×C8—222no—
463#95—21no—
464#95—111no—
465#95—111no—
466#95—221no—
467#95—221no—
468#95—221no—
469#95—221no—
470#95—221no—
471#95—221no—
472#95—221no—
473#95—221no—
474C2×C11#241811yescharacteristic
475C2×C11#310411yescharacteristic
476C2×C11#312111yescharacteristic
477C2×C11#327111yescharacteristic
478C2×C11D4×Q1611yescharacteristic
479C2×C11#329911yescharacteristic
480C2×C11#332711yescharacteristic
481D11—42no—
482C24—111no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—112no—
487C2×Q8—112no—
488C2×Q8—224no—
489C2×Q8—221no—
490C2×Q8—221no—
491C2×Q8—221no—
492C2×Q8—221no—
493C2×Q8—221no—
494C2×Q8—221no—
495C2×Q8—221no—
496C2×Q8—221no—
497C2×Q8—221no—
498C2×Q8—221no—
499C2×Q8—442no—
500C2×Q8—442no—
501C2×Q8—444no—
502C2×Q8—444no—
503C2×Q8—444no—
504C2×Q8—444no—
505C2×Q8#433912yes—
506C2×Q8D4×D1112yes—
507C2×Q8#434312yes—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—111no—
513C22×C4—111no—
514C22×C4—111no—
515C22×C4—224no—
516C22×C4—221no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4—221no—
520C22×C4—221no—
521C22×C4—221no—
522C22×C4—221no—
523C22×C4—221no—
524C22×C4—221no—
525C22×C4—221no—
526C22×C4—442no—
527C22×C4—442no—
528C22×C4D4×D1111yescharacteristic
529C22×C4D4×D1111yescharacteristic
530C22×C4C23×D1111yescharacteristic
531Q16—228no—
532Q16—444no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—112no—
540C2×C8—221no—
541C2×C8—221no—
542C2×C8—221no—
543C2×C8—221no—
544C2×C8—221no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—42no—
552C4⋊C4—81no—
553C4⋊C4—221no—
554C4⋊C4—221no—
555C4⋊C4—221no—
556C4⋊C4—221no—
557C4⋊C4—442no—
558C4⋊C4—442no—
559C4⋊C4—442no—
560C4⋊C4—442no—
561C4⋊C4—881no—
562C22⋊C4—114no—
563C22⋊C4—441no—
564C22⋊C4—442no—
565C22⋊C4—442no—
566C22⋊C4—881no—
567C42—21no—
568C42—21no—
569C42—42no—
570C42—221no—
571C42—221no—
572C42—442no—
573C42—442no—
574C11#2490611yescharacteristic, complemented, Sylow
575C23—112no—
576C23—221no—
577C23—221no—
578C23—221no—
579C23—221no—
580C23—221no—
581C23—221no—
582C23C2×D4×D1111yescharacteristic
583Q8—22no—
584Q8—22no—
585Q8—22no—
586Q8—222no—
587Q8—222no—
588Q8—222no—
589Q8—222no—
590Q8—448no—
591Q8—441no—
592Q8—441no—
593Q8—441no—
594Q8—441no—
595Q8#6694714yes—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—112no—
614C2×C4—221no—
615C2×C4—221no—
616C2×C4—221no—
617C2×C4—221no—
618C2×C4—221no—
619C2×C4—222no—
620C2×C4—222no—
621C2×C4—221no—
622C2×C4—221no—
623C2×C4—221no—
624C2×C4—448no—
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—441no—
636C2×C4—441no—
637C2×C4—441no—
638C2×C4—441no—
639C2×C4Q16×D1112yes—
640C2×C4C2×#433911yescharacteristic
641C2×C4C2×D4×D1111yescharacteristic
642C2×C4#6703711yescharacteristic
643C2×C4C2×#434311yescharacteristic
644C2×C4#41×D1111yescharacteristic
645C2×C4#6704211yescharacteristic
646C8—41no—
647C8—41no—
648C8—222no—
649C8—441no—
650C22—222no—
651C22—222no—
652C22—222no—
653C22—441no—
654C22—441no—
655C22—441no—
656C22—441no—
657C22#1062307811yescharacteristic
658C22#1062312111yescharacteristic
659C22#1062316111yescharacteristic
660C22C2×Q16×D1111yescharacteristic
661C22#1062329911yescharacteristic
662C22#1062330611yescharacteristic
663C22#1062331011yescharacteristic
664C4—22no—
665C4—24no—
666C4—41no—
667C4—81no—
668C4—81no—
669C4—81no—
670C4—222no—
671C4—441no—
672C4—441no—
673C4—442no—
674C4—442no—
675C4—881no—
676C4—881no—
677C4C2×#6694711yescharacteristic
678C4#1062309111yescharacteristic
679C4#1062316811yescharacteristic
680C4#1062318511yescharacteristic
681C2—442no—
682C2#1307208011yescharacteristic
683C2#1307865311yescharacteristic
684C2#1307884311yescharacteristic
685C2#1308019411yescharacteristic
686C2#1308036111yescharacteristic
687C2#1308048911yescharacteristic
688C2#1308088111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1863C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#1863D11
hypocenterC11#24906
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1863

Complements

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

NH ≅ G/Ntype
2. C2×C4×#4326C2semidirect
5. #13070151C2semidirect
7. #13069940C2semidirect
9. #13069291C2semidirect
11. #13068956C2semidirect
12. #13068955C2semidirect
13. #13068619C2semidirect
15. C11×#1863C2semidirect
210. (C2×D11)⋊C4Q16semidirect
243. #1863D11semidirect
574. C11#24906semidirect

Maximal subgroups

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

subgroupindex
C2×#106224212
C2×C4×#43262
#130721422
Q8×(C2×D11)⋊C42
#130701512
#130700482
#130699402
#130698212
#130692912
#130692202
#130689562
#130689552
#130686192
#130685492
C11×#18632
#2490611