Finite Group Databasebeta

← #14797946

Subgroups — #14797946

Order 2816.

926 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622799C211yesmaximal, characteristic
2C2×#10622797C211yesmaximal, characteristic, complemented
3#13072117C211yesmaximal, characteristic
4Q8×(C2×D11)⋊C4C211yesmaximal, characteristic
5#13070163C211yesmaximal, characteristic, complemented
6#13070051C211yesmaximal, characteristic
7#13069938C211yesmaximal, characteristic, complemented
8#13069818C211yesmaximal, characteristic
9#13069307C211yesmaximal, characteristic, complemented
10#13069230C211yesmaximal, characteristic
11#13068955C211yesmaximal, characteristic, complemented
12#13068872C211yesmaximal, characteristic, complemented
13#13068631C211yesmaximal, characteristic, complemented
14#13068549C211yesmaximal, characteristic
15C11×#1878C211yesmaximal, characteristic, complemented
16C22×Q8×D11C2211yescharacteristic
17C22×C11×Q16C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×#66999C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic
22C22×#4326C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C11×#391C2211yescharacteristic
26C2×#66899C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29#10622799—24no—
30#10622797—24no—
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×#66882C2211yescharacteristic
34C2×#66881C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37C2×#66879C2211yescharacteristic
38#10622600—21no—
39#10622600C2211yescharacteristic
40#10622600C2211yescharacteristic
41#10622598C2211yescharacteristic
42#10622587—21no—
43#10622587C2211yescharacteristic
44C2×#66874C2211yescharacteristic
45C4×(C2×D11)⋊C4—21no—
46C4×(C2×D11)⋊C4C2211yescharacteristic
47#10622549C2211yescharacteristic
48#10622542—21no—
49#10622542C2211yescharacteristic
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51#10622287—21no—
52#10622283—21no—
53#10622272—21no—
54#10622266—21no—
55C11×#340C2211yescharacteristic
56C11×#336C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C2×Q8×D11—22no—
64C2×Q8×D11—22no—
65C2×Q8×D11—22no—
66C2×Q8×D11—22no—
67C2×Q8×D11—41no—
68C2×Q8×D11—41no—
69C22×C4×D11—21no—
70C22×C4×D11C2311yescharacteristic
71C22×Dic22—21no—
72C22×Dic22C2311yescharacteristic
73C2×C11×Q16—22no—
74C2×C11×Q16—22no—
75C2×C11×Q16D414yes—
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C4×Q8×C11—22no—
79C4×Q8×C11—41no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C42×C11—21no—
84C2×C42×C11C2311yescharacteristic
85#66999—22no—
86#66999—41no—
87Q8×Dic11—22no—
88Q8×Dic11—22no—
89Q8×Dic11—41no—
90Q8×Dic11—41no—
91C2×#4326—22no—
92C2×#4326—22no—
93C2×#4326—41no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4D411yescharacteristic
98C2×(C2×D11)⋊C4D411yescharacteristic
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11—21no—
102C2×C4⋊Dic11C2311yescharacteristic
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4⋊Dic11C2311yescharacteristic
105C2×Dic11⋊C4—21no—
106C2×C4×Dic11—21no—
107C2×C4×Dic11—21no—
108C2×C4×Dic11C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C11×#103—22no—
112C11×#103—41no—
113C11×#95—21no—
114C11×#95—21no—
115#66899—22no—
116#66899—22no—
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⋊#95—21no—
127C11⋊#95D411yescharacteristic
128C11⋊#95D411yescharacteristic
129(C2×D11)⋊C8—22no—
130(C2×D11)⋊C8—41no—
131#66882—41no—
132#66881—22no—
133#66880—22no—
134#66880—41no—
135#66879—22no—
136#66874—22no—
137C4⋊(C11⋊C8)—41no—
138#24922—111nomaximal, Sylow
139C23×D11C2×D411yescharacteristic
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11C2×D412yes—
149C2×Q8×C11C2×D412yes—
150C2×Q8×C11#4112yes—
151C2×Q8×C11#4112yes—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2411yescharacteristic
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166Q8×D11—44no—
167Q8×D11—44no—
168Q8×D11—44no—
169Q8×D11—44no—
170C2×C4×D11—24no—
171C2×C4×D11—21no—
172C2×C4×D11—21no—
173C2×C4×D11—21no—
174C2×C4×D11—21no—
175C2×C4×D11—21no—
176C2×C4×D11—21no—
177C2×C4×D11—42no—
178C2×C4×D11—42no—
179C2×Dic22—24no—
180C2×Dic22—21no—
181C2×Dic22—21no—
182C2×Dic22—21no—
183C2×Dic22—21no—
184C2×Dic22—21no—
185C2×Dic22—42no—
186C2×Dic22—42no—
187C2×Dic22#4112yes—
188C11×Q16—28no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11C2×D412yes—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—42no—
200C42×C11—21no—
201C42×C11—21no—
202C42×C11—42no—
203#4326—44no—
204(C2×D11)⋊C4—22no—
205(C2×D11)⋊C4—41no—
206(C2×D11)⋊C4—42no—
207(C2×D11)⋊C4—42no—
208(C2×D11)⋊C4—42no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11—42no—
216C4⋊Dic11—42no—
217C4⋊Dic11—42no—
218Dic11⋊C4—42no—
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—21no—
229C2×#451—111no—
230C2×#441—111no—
231#2421—111no—
232Q8×C22⋊C4—111no—
233#2097—111no—
234#2077—111no—
235#2056—111no—
236#2036—111no—
237#1935—111no—
238#1924—111no—
239#1878—111no—
240#1878D1111yescharacteristic, complemented
241#1863—111no—
242#1805—111no—
243#1787—111no—
244C23×C11C22×D411yescharacteristic
245C22×D11—21no—
246C22×D11—21no—
247C22×D11—21no—
248C22×D11—21no—
249C22×D11—21no—
250C22×D11—21no—
251C22×D11#13712yes—
252Q8×C11—22no—
253Q8×C11—22no—
254Q8×C11—22no—
255Q8×C11—22no—
256Q8×C11—22no—
257Q8×C11—41no—
258Q8×C11—41no—
259Q8×C11#12314yes—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—41no—
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×C11C22×D411yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11H(5,𝔽2)11yescharacteristic
283C2×C4×C11H(5,𝔽2)11yescharacteristic
284C2×Dic11—21no—
285C2×Dic11—22no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—21no—
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×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C4×D11—48no—
306C4×D11—41no—
307C4×D11—41no—
308C4×D11—41no—
309C4×D11—41no—
310Dic22—22no—
311Dic22—22no—
312Dic22—48no—
313Dic22—41no—
314Dic22—41no—
315C8×C11—22no—
316C8×C11—41no—
317C11⋊C8—41no—
318C11⋊C8—41no—
319C23×Q8—111no—
320C22×Q16—111no—
321C22×Q16C2×D1111yescharacteristic
322C2×C22⋊Q8—111no—
323C2×C4×Q8—111no—
324C2×C4×Q8—111no—
325C2×C4×Q8C2×D1111yescharacteristic
326#451—224no—
327#441—224no—
328C2×#107—111no—
329C2×#106—111no—
330C2×C4⋊C8—111no—
331C2×#103—111no—
332C2×#103—111no—
333C2×#103—111no—
334C2×#103—111no—
335C2×#103—111no—
336C2×#103—111no—
337C2×#103C2×D1111yescharacteristic
338C2×#103C2×D1111yescharacteristic
339C2×C22⋊C8—111no—
340C2×C22⋊C8—111no—
341C2×#97—111no—
342#400—221no—
343#397—221no—
344#391—111no—
345#391—111no—
346#391—221no—
347#391—221no—
348#391C2×D1111yescharacteristic
349#389—111no—
350#388—221no—
351#387—221no—
352#382—111no—
353#380—111no—
354#380—111no—
355#380—221no—
356C4×C22⋊C4—111no—
357C4×C22⋊C4—221no—
358#340—111no—
359#340—111no—
360#340—111no—
361#340C2×D1111yescharacteristic
362#336—111no—
363#336C2×D1111yescharacteristic
364C22×C11#52511yescharacteristic
365C22×C11D4211yescharacteristic
366C22×C11#54611yescharacteristic
367C22×C11C2×#13711yescharacteristic
368C22×C11#57511yescharacteristic
369C22×C11#57811yescharacteristic
370C22×C11#57811yescharacteristic
371C2×D11—22no—
372C2×D11—22no—
373C2×D11—22no—
374C2×D11—41no—
375C2×D11—41no—
376C2×D11—41no—
377C2×D11—41no—
378C4×C11—24no—
379C4×C11—42no—
380C4×C11—41no—
381C4×C11—41no—
382C4×C11—81no—
383C4×C11—81no—
384C4×C11C2×#12311yescharacteristic
385C4×C11#53811yescharacteristic
386C4×C11#54611yescharacteristic
387C4×C11#55111yescharacteristic
388Dic11—42no—
389Dic11—41no—
390Dic11—41no—
391Dic11—41no—
392Dic11—81no—
393Dic11—81no—
394Dic11—81no—
395C22×Q8—111no—
396C22×Q8—221no—
397C22×Q8—222no—
398C22×Q8—222no—
399C22×Q8—222no—
400C22×Q8—222no—
401C22×Q8—441no—
402C22×Q8—441no—
403C22×Q8C22×D1111yescharacteristic
404C22×Q8C22×D1111yescharacteristic
405C23×C4—111no—
406C23×C4—221no—
407C2×Q16—22no—
408C2×Q16—22no—
409C2×Q16—222no—
410C2×Q16—222no—
411C2×Q16—441no—
412C2×Q16D4414yes—
413C22×C8—111no—
414C22×C8—111no—
415C22×C8C22×D1111yescharacteristic
416C22×C8C22×D1111yescharacteristic
417C22⋊Q8—222no—
418C22⋊Q8—441no—
419C4×Q8—22no—
420C4×Q8—41no—
421C4×Q8—222no—
422C4×Q8—222no—
423C4×Q8—441no—
424C4×Q8—441no—
425C2×C4⋊C4—21no—
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⋊C4C22×D1111yescharacteristic
434C2×C4⋊C4C22×D1111yescharacteristic
435C2×C22⋊C4—111no—
436C2×C22⋊C4—111no—
437C2×C22⋊C4—221no—
438C2×C22⋊C4—221no—
439C2×C22⋊C4—221no—
440C2×C42—21no—
441C2×C42—111no—
442C2×C42—221no—
443C2×C42—221no—
444C2×C42C22×D1111yescharacteristic
445#107—441no—
446#106—222no—
447C4⋊C8—441no—
448#103—22no—
449#103—41no—
450#103—222no—
451#103—222no—
452#103—222no—
453#103—222no—
454#103—222no—
455#103—441no—
456C22⋊C8—222no—
457C22⋊C8—441no—
458#97—222no—
459#95—21no—
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—
470#95—221no—
471#95—221no—
472C2×C11#241811yescharacteristic
473C2×C11#311711yescharacteristic
474C2×C11#312711yescharacteristic
475C2×C11#327011yescharacteristic
476C2×C11#327711yescharacteristic
477C2×C11#331211yescharacteristic
478C2×C11#331311yescharacteristic
479D11—42no—
480C24—111no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—112no—
490C2×Q8—224no—
491C2×Q8—221no—
492C2×Q8—221no—
493C2×Q8—221no—
494C2×Q8—221no—
495C2×Q8—221no—
496C2×Q8—442no—
497C2×Q8—442no—
498C2×Q8—444no—
499C2×Q8—444no—
500C2×Q8—444no—
501C2×Q8—444no—
502C2×Q8C2×D4412yes—
503C2×Q8C2×D4412yes—
504C2×Q8#434112yes—
505C2×Q8#434112yes—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—111no—
511C22×C4—111no—
512C22×C4—111no—
513C22×C4—224no—
514C22×C4—221no—
515C22×C4—221no—
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—442no—
525C22×C4—442no—
526C22×C4D4×D1111yescharacteristic
527C22×C4D4×D1111yescharacteristic
528C22×C4C23×D1111yescharacteristic
529Q16—28no—
530Q16—444no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—221no—
537C2×C8—221no—
538C2×C8—221no—
539C2×C8—221no—
540C2×C8—221no—
541C2×C8—221no—
542C2×C8C2×D4412yes—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—42no—
548C4⋊C4—221no—
549C4⋊C4—221no—
550C4⋊C4—221no—
551C4⋊C4—221no—
552C4⋊C4—221no—
553C4⋊C4—221no—
554C4⋊C4—442no—
555C4⋊C4—442no—
556C4⋊C4—442no—
557C4⋊C4—442no—
558C22⋊C4—222no—
559C22⋊C4—441no—
560C22⋊C4—442no—
561C22⋊C4—442no—
562C22⋊C4—442no—
563C42—21no—
564C42—21no—
565C42—42no—
566C42—221no—
567C42—221no—
568C42—442no—
569C42—442no—
570C11#2492211yescharacteristic, complemented, Sylow
571C23—112no—
572C23—221no—
573C23—221no—
574C23—221no—
575C23—221no—
576C23—221no—
577C23—221no—
578C23C2×D4×D1111yescharacteristic
579Q8—22no—
580Q8—22no—
581Q8—22no—
582Q8—22no—
583Q8—22no—
584Q8—41no—
585Q8—41no—
586Q8—222no—
587Q8—222no—
588Q8—448no—
589Q8—441no—
590Q8—441no—
591Q8#6693914yes—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
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—448no—
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—441no—
633C2×C4—441no—
634C2×C4—441no—
635C2×C4—441no—
636C2×C4C22×D4411yescharacteristic
637C2×C4C2×#434111yescharacteristic
638C2×C4C2×#434111yescharacteristic
639C2×C4#6703711yescharacteristic
640C2×C4#41×D1111yescharacteristic
641C2×C4#6704211yescharacteristic
642C8—22no—
643C8—41no—
644C8—441no—
645C8—441no—
646C22—222no—
647C22—222no—
648C22—222no—
649C22—441no—
650C22—441no—
651C22—441no—
652C22—441no—
653C22D4×D4411yescharacteristic
654C22#1062312211yescharacteristic
655C22#1062313711yescharacteristic
656C22#1062329711yescharacteristic
657C22#1062329911yescharacteristic
658C22D11×#13711yescharacteristic
659C22#1062331011yescharacteristic
660C4—24no—
661C4—41no—
662C4—41no—
663C4—42no—
664C4—81no—
665C4—81no—
666C4—441no—
667C4—441no—
668C4—442no—
669C4—441no—
670C4—881no—
671C4—881no—
672C4—881no—
673C4C2×#6693911yescharacteristic
674C4#1062308511yescharacteristic
675C4#1062314811yescharacteristic
676C4#1062318911yescharacteristic
677C2—442no—
678C2#1307207611yescharacteristic
679C2#1307878611yescharacteristic
680C2#1307891411yescharacteristic
681C2#1308018811yescharacteristic
682C2#1308027211yescharacteristic
683C2#1308066011yescharacteristic
684C2#1308068611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1878C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#1878D11
hypocenterC11#24922
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1878

Complements

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

NH ≅ G/Ntype
2. C2×#10622797C2semidirect
5. #13070163C2semidirect
7. #13069938C2semidirect
9. #13069307C2semidirect
11. #13068955C2semidirect
12. #13068872C2semidirect
13. #13068631C2semidirect
15. C11×#1878C2semidirect
240. #1878D11semidirect
570. C11#24922semidirect

Maximal subgroups

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

subgroupindex
C2×#106227992
C2×#106227972
#130721172
Q8×(C2×D11)⋊C42
#130701632
#130700512
#130699382
#130698182
#130693072
#130692302
#130689552
#130688722
#130686312
#130685492
C11×#18782
#2492211