Finite Group Databasebeta

← #14797642

Subgroups — #14797642

Order 2816.

932 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
2#13072113C211yesmaximal, characteristic
3Q8×(C2×D11)⋊C4C211yesmaximal, characteristic
4#13070161C211yesmaximal, characteristic, complemented
5#13070040C211yesmaximal, characteristic
6#13069937C211yesmaximal, characteristic, complemented
7#13069810C211yesmaximal, characteristic
8#13069292C211yesmaximal, characteristic, complemented
9#13069222C211yesmaximal, characteristic
10#13068959C211yesmaximal, characteristic, complemented
11#13068957C211yesmaximal, characteristic, complemented
12#13068884C211yesmaximal, characteristic, complemented
13#13068629C211yesmaximal, characteristic, complemented
14#13068549C211yesmaximal, characteristic
15C2×C4×C11×Q16C211yesmaximal, characteristic, complemented
16C22×Q8×D11C2211yescharacteristic
17C22×C11×Q16C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×#66999C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic
22C22×#4326C2211yescharacteristic
23C4×C11×Q16—24no—
24C2×C11×#107C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C4×C8×C11C2211yescharacteristic
28#10622843C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32#10622799—24no—
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×(C2×D11)⋊C8C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37C2×Dic11⋊C8C2211yescharacteristic
38#10622606—21no—
39#10622600—21no—
40#10622600C2211yescharacteristic
41#10622600C2211yescharacteristic
42#10622595—21no—
43#10622590C2211yescharacteristic
44#10622587—21no—
45#10622587C2211yescharacteristic
46C2×#66874C2211yescharacteristic
47C2×#66872C2211yescharacteristic
48#10622553—21no—
49C4×(C2×D11)⋊C4—21no—
50C4×(C2×D11)⋊C4C2211yescharacteristic
51#10622546—21no—
52#10622542—21no—
53#10622542C2211yescharacteristic
54#10622541C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
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—22no—
80C4×Q8×C11—41no—
81C4×Q8×C11—41no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C42×C11—21no—
87C2×C42×C11—21no—
88C2×C42×C11C2311yescharacteristic
89#66999—22no—
90#66999—41no—
91Q8×Dic11—22no—
92Q8×Dic11—41no—
93C2×#4326—22no—
94C2×#4326—22no—
95C2×#4326—41no—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4D411yescharacteristic
100C2×(C2×D11)⋊C4D411yescharacteristic
101C2×C4⋊Dic11—21no—
102C2×C4⋊Dic11C2311yescharacteristic
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4⋊Dic11C2311yescharacteristic
105C2×Dic11⋊C4—21no—
106C2×Dic11⋊C4—21no—
107C2×C4×Dic11—21no—
108C2×C4×Dic11C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C11×#107—22no—
112C11×#103—22no—
113C11×#103—22no—
114C4×C8×C11—22no—
115#66899—22no—
116#66899—22no—
117#66899—41no—
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⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95D411yescharacteristic
130C11⋊#95D411yescharacteristic
131(C2×D11)⋊C8—22no—
132(C2×D11)⋊C8—41no—
133#66880—22no—
134#66880—22no—
135Dic11⋊C8—41no—
136#66874—41no—
137#66872—41no—
138#24902—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—
200C11×C4⋊C4—42no—
201C42×C11—21no—
202C42×C11—21no—
203C42×C11—42no—
204C42×C11—42no—
205#4326—44no—
206(C2×D11)⋊C4—22no—
207(C2×D11)⋊C4—22no—
208(C2×D11)⋊C4—42no—
209(C2×D11)⋊C4—42no—
210(C2×D11)⋊C4—42no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11—21no—
216C4⋊Dic11—21no—
217C4⋊Dic11—42no—
218Dic11⋊C4—42no—
219Dic11⋊C4—42no—
220C4×Dic11—21no—
221C4×Dic11—21no—
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×C4×Q16D1111yescharacteristic, complemented
231#2421—111no—
232Q8×C22⋊C4—111no—
233#2097—111no—
234#2075—111no—
235#2056—111no—
236#2035—111no—
237#1933—111no—
238#1923—111no—
239#1878—111no—
240#1878—111no—
241#1865—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#13512yes—
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—21no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—21no—
265C2×C4×C11—22no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
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×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11#13712yes—
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×Q8C2×D1111yescharacteristic
325C2×C4×Q8C2×D1111yescharacteristic
326#451—224no—
327C4×Q16—24no—
328C2×#107C2×D1111yescharacteristic
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×C4×C8C2×D1111yescharacteristic
342#400—221no—
343#397—221no—
344#391—111no—
345#391—111no—
346#391—111no—
347#391—221no—
348#391—221no—
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#340—111no—
362#336—111no—
363#336—111no—
364C22×C11#52511yescharacteristic
365C22×C11D4211yescharacteristic
366C22×C11#54611yescharacteristic
367C22×C11C2×#13511yescharacteristic
368C22×C11C2×#13711yescharacteristic
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—22no—
380C4×C11—42no—
381C4×C11—41no—
382C4×C11—81no—
383C4×C11—81no—
384C4×C11C2×#12311yescharacteristic
385C4×C11#53811yescharacteristic
386C4×C11#54611yescharacteristic
387C4×C11#55111yescharacteristic
388Dic11—41no—
389Dic11—42no—
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×Q16C22⋊D1114yes—
413C22×C8—111no—
414C22×C8—111no—
415C22×C8C22×D1111yescharacteristic
416C22×C8C22×D1111yescharacteristic
417C22⋊Q8—222no—
418C22⋊Q8—441no—
419C4×Q8—22no—
420C4×Q8—22no—
421C4×Q8—41no—
422C4×Q8—41no—
423C4×Q8—222no—
424C4×Q8—441no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—111no—
429C2×C4⋊C4—111no—
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—21no—
442C2×C42—111no—
443C2×C42—221no—
444C2×C42C22×D1111yescharacteristic
445#107—22no—
446#106—441no—
447C4⋊C8—441no—
448#103—22no—
449#103—22no—
450#103—222no—
451#103—222no—
452#103—222no—
453#103—222no—
454#103—441no—
455#103—441no—
456C22⋊C8—222no—
457C22⋊C8—441no—
458C4×C8—22no—
459#95—111no—
460#95—111no—
461#95—221no—
462#95—221no—
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#310811yescharacteristic
474C2×C11#312711yescharacteristic
475C2×C11#327011yescharacteristic
476C2×C11#328511yescharacteristic
477C2×C11#330011yescharacteristic
478C2×C11#332811yescharacteristic
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×Q8#433912yes—
503C2×Q8#433912yes—
504C2×Q8C2×C22⋊D1112yes—
505C2×Q8C2×C22⋊D1112yes—
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×C22⋊D1112yes—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—42no—
548C4⋊C4—42no—
549C4⋊C4—221no—
550C4⋊C4—221no—
551C4⋊C4—221no—
552C4⋊C4—221no—
553C4⋊C4—221no—
554C4⋊C4—221no—
555C4⋊C4—442no—
556C4⋊C4—442no—
557C4⋊C4—442no—
558C22⋊C4—222no—
559C22⋊C4—222no—
560C22⋊C4—442no—
561C22⋊C4—442no—
562C22⋊C4—442no—
563C42—21no—
564C42—21no—
565C42—42no—
566C42—42no—
567C42—221no—
568C42—221no—
569C42—442no—
570C11#2490211yescharacteristic, 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#6698214yes—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—22no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—221no—
610C2×C4—221no—
611C2×C4—221no—
612C2×C4—221no—
613C2×C4—221no—
614C2×C4—221no—
615C2×C4—222no—
616C2×C4—221no—
617C2×C4—221no—
618C2×C4—221no—
619C2×C4—448no—
620C2×C4—441no—
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#6697112yes—
636C2×C4C2×#433911yescharacteristic
637C2×C4C2×#433911yescharacteristic
638C2×C4#6703711yescharacteristic
639C2×C4#41×D1111yescharacteristic
640C2×C4#6704211yescharacteristic
641C2×C4C22×C22⋊D1111yescharacteristic
642C8—22no—
643C8—41no—
644C8—441no—
645C8—441no—
646C22—222no—
647C22—222no—
648C22—222no—
649C22—441no—
650C22—441no—
651C22—441no—
652C22—441no—
653C22#1062307811yescharacteristic
654C22#1062308111yescharacteristic
655C22C2×#6697111yescharacteristic
656C22#1062329711yescharacteristic
657C22D11×#13511yescharacteristic
658C22#1062330211yescharacteristic
659C22D4×C22⋊D1111yescharacteristic
660C4—22no—
661C4—24no—
662C4—41no—
663C4—42no—
664C4—81no—
665C4—81no—
666C4—441no—
667C4—441no—
668C4—441no—
669C4—442no—
670C4—881no—
671C4—881no—
672C4—881no—
673C4#1062308711yescharacteristic
674C4#1062309111yescharacteristic
675C4C2×#6698211yescharacteristic
676C4#1062336011yescharacteristic
677C2—442no—
678C2#1307207211yescharacteristic
679C2#1307870011yescharacteristic
680C2#1307891311yescharacteristic
681C2#1308018611yescharacteristic
682C2#1308035111yescharacteristic
683C2#1308050811yescharacteristic
684C2#1308090111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C4×C11×Q16C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenterC2×C4×Q16D11
hypocenterC11#24902
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
4. #13070161C2semidirect
6. #13069937C2semidirect
8. #13069292C2semidirect
10. #13068959C2semidirect
11. #13068957C2semidirect
12. #13068884C2semidirect
13. #13068629C2semidirect
15. C2×C4×C11×Q16C2semidirect
230. C2×C4×Q16D11semidirect
570. C11#24902semidirect

Maximal subgroups

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

subgroupindex
C2×#106227992
#130721132
Q8×(C2×D11)⋊C42
#130701612
#130700402
#130699372
#130698102
#130692922
#130692222
#130689592
#130689572
#130688842
#130686292
#130685492
C2×C4×C11×Q162
#2490211