Finite Group Databasebeta

← #14810871

Subgroups — #14810871

Order 2816.

958 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622417C211yesmaximal, characteristic
2#13072325C211yesmaximal, characteristic, complemented
3#13071454C211yesmaximal, characteristic
4#13070146C211yesmaximal, characteristic, complemented
5#13069999C211yesmaximal, characteristic, complemented
6#13069989C211yesmaximal, characteristic, complemented
7#13069759C211yesmaximal, characteristic, complemented
8#13068886C211yesmaximal, characteristic, complemented
9#13068884C211yesmaximal, characteristic, complemented
10#13068812C211yesmaximal, characteristic, complemented
11#13068792C211yesmaximal, characteristic, complemented
12#13068638C211yesmaximal, characteristic, complemented
13#13068619C211yesmaximal, characteristic, complemented
14#13068555C211yesmaximal, characteristic
15C2×C11×#479C211yesmaximal, characteristic, complemented
16C22×#4343C2211yescharacteristic
17C2×C11×#125C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic
20C22×C8×D11C2211yescharacteristic
21C2×#66945C2211yescharacteristic
22C11×#479—24no—
23C2×C11×#107C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#103C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35#10622607—21no—
36#10622605—21no—
37#10622601—21no—
38#10622601C2211yescharacteristic
39#10622600—21no—
40#10622600C2211yescharacteristic
41#10622600C2211yescharacteristic
42#10622598C2211yescharacteristic
43#10622591—21no—
44#10622589C2211yescharacteristic
45#10622586—21no—
46C2×#66873C2211yescharacteristic
47C2×#66873C2211yescharacteristic
48C2×#66872C2211yescharacteristic
49#10622552—21no—
50#10622552C2211yescharacteristic
51C4×(C2×D11)⋊C4—21no—
52C4×(C2×D11)⋊C4C2211yescharacteristic
53#10622541C2211yescharacteristic
54#10622417—24no—
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C2×#4343—22no—
63C2×#4343—22no—
64C2×#4343—22no—
65C2×#4343—41no—
66C2×#4343—41no—
67C2×#4343Q814yes—
68C22×D44—21no—
69C22×D44C2311yescharacteristic
70C22×C4×D11—21no—
71C22×C4×D11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C11×#125—22no—
75C11×#125—41no—
76C4×Q8×C11—22no—
77C4×Q8×C11—41no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C42×C11—21no—
85C2×C42×C11C2311yescharacteristic
86Q8×Dic11—22no—
87Q8×Dic11—41no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4D411yescharacteristic
96C2×(C2×D11)⋊C4D411yescharacteristic
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—21no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11—21no—
107C2×C4×Dic11C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C2×C8×D11—22no—
111C2×C8×D11—22no—
112C2×C8×D11—41no—
113#66945—22no—
114#66945—41no—
115C11×#107—22no—
116C11×#106—22no—
117C11×C4⋊C8—22no—
118C11×#103—22no—
119C11×#103D414yes—
120#66899—22no—
121#66899—22no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95D411yescharacteristic
127C11⋊#95D411yescharacteristic
128#66885—22no—
129#66885—41no—
130(C2×D11)⋊C8—22no—
131#66881—41no—
132Dic11⋊C8—41no—
133#66873—22no—
134#66873—41no—
135#66872—41no—
136#25953—111nomaximal, Sylow
137C23×D11—21no—
138C23×D11C2×D411yescharacteristic
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11C2×D412yes—
143C2×Q8×C11C2×Q812yes—
144C2×Q8×C11#4112yes—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158#4343—28no—
159#4343—44no—
160#4343—44no—
161#4343—44no—
162C2×D44—24no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44—42no—
169C2×D44—42no—
170C2×D44C2×Q812yes—
171C2×C4×D11—24no—
172C2×C4×D11—21no—
173C2×C4×D11—21no—
174C2×C4×D11—21no—
175C2×C4×D11—21no—
176C2×C4×D11—42no—
177C2×C4×D11—42no—
178C2×C4×D11C2×Q812yes—
179C2×C4×D11#4112yes—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11C2×D412yes—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—42no—
192C11×C4⋊C4—42no—
193C11×C4⋊C4—42no—
194C11×C4⋊C4C2×D412yes—
195C42×C11—21no—
196C42×C11—21no—
197C42×C11—42no—
198(C2×D11)⋊C4—22no—
199(C2×D11)⋊C4—41no—
200(C2×D11)⋊C4—42no—
201(C2×D11)⋊C4—42no—
202(C2×D11)⋊C4—42no—
203(C2×D11)⋊C4—81no—
204(C2×D11)⋊C4—81no—
205(C2×D11)⋊C4—81no—
206(C2×D11)⋊C4—81no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11—42no—
214C4⋊Dic11—42no—
215Dic11⋊C4—42no—
216Dic11⋊C4—81no—
217Dic11⋊C4—81no—
218C4×Dic11—21no—
219C4×Dic11—21no—
220C4×Dic11—42no—
221C4×Dic11—42no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C8×D11—44no—
229C2×#479D1111yescharacteristic, complemented
230C2×#416—111no—
231#2441—111no—
232#2341—111no—
233#2094—111no—
234#2067—111no—
235#2065—111no—
236#2025—111no—
237#1865—111no—
238#1865—111no—
239#1854—111no—
240#1850—111no—
241#1807—111no—
242#1803—111no—
243#1788—111no—
244C23×C11C22×D411yescharacteristic
245C22×D11—21no—
246C22×D11—21no—
247C22×D11—21no—
248C22×D11—21no—
249C22×D11—21no—
250C22×D11—21no—
251C22×D11—22no—
252C22×D11—41no—
253C22×D11—41no—
254C22×D11—41no—
255C22×D11—41no—
256C22×D11—41no—
257C22×D11—41no—
258C22×D11C22⋊Q812yes—
259Q8×C11—22no—
260Q8×C11—22no—
261Q8×C11—22no—
262Q8×C11C22⋊Q814yes—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
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×D411yescharacteristic
282C2×C4×C11C22×Q811yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C11C2×#4111yescharacteristic
285C2×C4×C11H(5,𝔽2)11yescharacteristic
286C2×C4×C11H(5,𝔽2)11yescharacteristic
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×Dic11C22⋊Q812yes—
304C2×Dic11#13512yes—
305D44—22no—
306D44—22no—
307D44—48no—
308D44—41no—
309D44—41no—
310C4×D11—22no—
311C4×D11—22no—
312C4×D11—22no—
313C4×D11—22no—
314C4×D11—48no—
315C8×C11—22no—
316C8×C11—41no—
317C11⋊C8—41no—
318C11⋊C8—41no—
319C22×#41—111no—
320C23×C8—111no—
321C2×#125C2×D1111yescharacteristic
322C2×C4×Q8—111no—
323C2×C4×Q8C2×D1111yescharacteristic
324C2×#117—111no—
325#479—24no—
326C2×#107C2×D1111yescharacteristic
327C2×#106—111no—
328C2×#106—111no—
329C2×#106C2×D1111yescharacteristic
330C2×C4⋊C8—111no—
331C2×C4⋊C8C2×D1111yescharacteristic
332#416—224no—
333C2×#103—111no—
334C2×#103—111no—
335C2×#103C2×D1111yescharacteristic
336C2×#103C2×D1111yescharacteristic
337C2×#102—111no—
338C2×#102—111no—
339C2×#102—111no—
340C2×#102—111no—
341C2×C22⋊C8—111no—
342#399—221no—
343#396—221no—
344#390—111no—
345#390—111no—
346#390—221no—
347#390—221no—
348#389—111no—
349#389—111no—
350#389—221no—
351#387—221no—
352#384—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×C11C2×C22⋊Q811yescharacteristic
365C22×C11D4211yescharacteristic
366C22×C11#54611yescharacteristic
367C22×C11C2×#13511yescharacteristic
368C22×C11#57511yescharacteristic
369C22×C11#57711yescharacteristic
370C22×C11#57711yescharacteristic
371C2×D11—22no—
372C2×D11—22no—
373C2×D11—22no—
374C2×D11—41no—
375C2×D11—41no—
376C2×D11—41no—
377C2×D11—41no—
378C2×D11—42no—
379C2×D11—42no—
380C2×D11—42no—
381C2×D11—81no—
382C2×D11—81no—
383C2×D11—81no—
384C2×D11—81no—
385C4×C11—24no—
386C4×C11—41no—
387C4×C11—41no—
388C4×C11—42no—
389C4×C11—81no—
390C4×C11—81no—
391C4×C11C2×C22⋊Q811yescharacteristic
392C4×C11#54311yescharacteristic
393C4×C11#54611yescharacteristic
394C4×C11#55111yescharacteristic
395Dic11—22no—
396Dic11—22no—
397Dic11—41no—
398Dic11—81no—
399Dic11—81no—
400Dic11—81no—
401C2×#41—114no—
402C2×#41—222no—
403C2×#41—222no—
404C2×#41—222no—
405C2×#41—441no—
406C2×#41—441no—
407C22×Q8C22×D1111yescharacteristic
408C22×D4—111no—
409C22×D4—221no—
410C23×C4—111no—
411C23×C4—221no—
412C22×C8—111no—
413C22×C8—111no—
414C22×C8—222no—
415C22×C8—222no—
416C22×C8—441no—
417C22×C8C22×D1111yescharacteristic
418C22×C8C22×D1111yescharacteristic
419#125—22no—
420#125—41no—
421C4×Q8—22no—
422C4×Q8—41no—
423C4×Q8—222no—
424C4×Q8—441no—
425#117—222no—
426#117—441no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—111no—
431C2×C4⋊C4—111no—
432C2×C4⋊C4—111no—
433C2×C4⋊C4—221no—
434C2×C4⋊C4—221no—
435C2×C4⋊C4—221no—
436C2×C4⋊C4—221no—
437C2×C4⋊C4—221no—
438C2×C4⋊C4C22×D1111yescharacteristic
439C2×C4⋊C4C22×D1111yescharacteristic
440C2×C4⋊C4C22×D1111yescharacteristic
441C2×C22⋊C4—111no—
442C2×C22⋊C4—111no—
443C2×C22⋊C4—221no—
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C22⋊C4—221no—
447C2×C22⋊C4—221no—
448C2×C22⋊C4—221no—
449C2×C22⋊C4—221no—
450C2×C42—21no—
451C2×C42—111no—
452C2×C42—221no—
453C2×C42—221no—
454C2×C42C22×D1111yescharacteristic
455#107—22no—
456#106—22no—
457#106—441no—
458#106—441no—
459C4⋊C8—22no—
460C4⋊C8—441no—
461#103—22no—
462#103—222no—
463#103—222no—
464#103C22⋊D1114yes—
465#102—222no—
466#102—222no—
467#102—441no—
468#102—441no—
469C22⋊C8—222no—
470#95—111no—
471#95—111no—
472#95—221no—
473#95—221no—
474#95—221no—
475#95—221no—
476C2×C11#243711yescharacteristic
477C2×C11#307611yescharacteristic
478C2×C11#308411yescharacteristic
479C2×C11#327111yescharacteristic
480C2×C11#328411yescharacteristic
481C2×C11#330111yescharacteristic
482C2×C11#331711yescharacteristic
483D11—42no—
484D11—82no—
485C24—111no—
486C24—221no—
487#41—228no—
488#41—444no—
489#41—444no—
490#41—444no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8Q8×D1112yes—
495C2×Q8#434312yes—
496C2×Q8C2×C22⋊D1112yes—
497C2×D4—112no—
498C2×D4—224no—
499C2×D4—221no—
500C2×D4—221no—
501C2×D4—221no—
502C2×D4—221no—
503C2×D4—221no—
504C2×D4—442no—
505C2×D4—442no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—111no—
511C22×C4—111no—
512C22×C4—112no—
513C22×C4—112no—
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—442no—
524C22×C4—442no—
525C22×C4D4×D1111yescharacteristic
526C22×C4D4×D1111yescharacteristic
527C22×C4C23×D1111yescharacteristic
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—221no—
534C2×C8—221no—
535C2×C8—221no—
536C2×C8—221no—
537C2×C8—221no—
538C2×C8—221no—
539C2×C8—444no—
540C2×C8C2×C22⋊D1112yes—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—42no—
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—
558C4⋊C4—881no—
559C4⋊C4—881no—
560C4⋊C4C2×C22⋊D1112yes—
561C22⋊C4—222no—
562C22⋊C4—441no—
563C22⋊C4—442no—
564C22⋊C4—442no—
565C22⋊C4—442no—
566C22⋊C4—881no—
567C22⋊C4—881no—
568C22⋊C4—881no—
569C22⋊C4—881no—
570C42—21no—
571C42—21no—
572C42—42no—
573C42—221no—
574C42—221no—
575C42—442no—
576C42—442no—
577C11#2595311yescharacteristic, complemented, Sylow
578C23—112no—
579C23—221no—
580C23—221no—
581C23—221no—
582C23—221no—
583C23—221no—
584C23—221no—
585C23—222no—
586C23—441no—
587C23—441no—
588C23—441no—
589C23—441no—
590C23—441no—
591C23—441no—
592C23C2×D4×D1111yescharacteristic
593Q8—22no—
594Q8—22no—
595Q8—22no—
596Q8#6699914yes—
597D4—222no—
598D4—222no—
599D4—448no—
600D4—441no—
601D4—441no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—22no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—112no—
621C2×C4—112no—
622C2×C4—221no—
623C2×C4—221no—
624C2×C4—221no—
625C2×C4—221no—
626C2×C4—222no—
627C2×C4—222no—
628C2×C4—222no—
629C2×C4—222no—
630C2×C4—221no—
631C2×C4—221no—
632C2×C4—221no—
633C2×C4—448no—
634C2×C4—441no—
635C2×C4—441no—
636C2×C4—441no—
637C2×C4—441no—
638C2×C4—441no—
639C2×C4—441no—
640C2×C4—441no—
641C2×C4—441no—
642C2×C4—441no—
643C2×C4#6703711yescharacteristic
644C2×C4C2×Q8×D1111yescharacteristic
645C2×C4C2×#434311yescharacteristic
646C2×C4#41×D1111yescharacteristic
647C2×C4#6704211yescharacteristic
648C2×C4C22×C22⋊D1111yescharacteristic
649C8—22no—
650C8—41no—
651C8—441no—
652C8—441no—
653C22—222no—
654C22—222no—
655C22—222no—
656C22—441no—
657C22—441no—
658C22—441no—
659C22—441no—
660C22—442no—
661C22—442no—
662C22—442no—
663C22—881no—
664C22—881no—
665C22—881no—
666C22—881no—
667C22D11×C22⋊Q811yescharacteristic
668C22#1062316111yescharacteristic
669C22D11×#13511yescharacteristic
670C22#1062330111yescharacteristic
671C22#1062330811yescharacteristic
672C22#1062330911yescharacteristic
673C22D4×C22⋊D1111yescharacteristic
674C4—24no—
675C4—41no—
676C4—42no—
677C4—41no—
678C4—81no—
679C4—81no—
680C4—222no—
681C4—222no—
682C4—441no—
683C4—881no—
684C4—881no—
685C4—881no—
686C4#1062316511yescharacteristic
687C4#1062316811yescharacteristic
688C4C2×#6699911yescharacteristic
689C4#1062336011yescharacteristic
690C2—442no—
691C2—882no—
692C2#1307227911yescharacteristic
693C2#1307840311yescharacteristic
694C2#1307848111yescharacteristic
695C2#1308019511yescharacteristic
696C2#1308034011yescharacteristic
697C2#1308051511yescharacteristic
698C2#1308073911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#479C2
socleC23×C11C22×D4
prime radicalC22×#4343C22
hypercenterC2×#479D11
hypocenterC11#25953
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
2. #13072325C2semidirect
4. #13070146C2semidirect
5. #13069999C2semidirect
6. #13069989C2semidirect
7. #13069759C2semidirect
8. #13068886C2semidirect
9. #13068884C2semidirect
10. #13068812C2semidirect
11. #13068792C2semidirect
12. #13068638C2semidirect
13. #13068619C2semidirect
15. C2×C11×#479C2semidirect
229. C2×#479D11semidirect
577. C11#25953semidirect

Maximal subgroups

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

subgroupindex
C2×#106224172
#130723252
#130714542
#130701462
#130699992
#130699892
#130697592
#130688862
#130688842
#130688122
#130687922
#130686382
#130686192
#130685552
C2×C11×#4792
#2595311