Finite Group Databasebeta

← #14810958

Subgroups — #14810958

Order 2816.

966 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622704C211yesmaximal, characteristic, complemented
2C2×#10622385C211yesmaximal, characteristic
3#13072303C211yesmaximal, characteristic, complemented
4#13071455C211yesmaximal, characteristic
5#13070139C211yesmaximal, characteristic, complemented
6#13070004C211yesmaximal, characteristic, complemented
7#13070000C211yesmaximal, characteristic, complemented
8#13068887C211yesmaximal, characteristic, complemented
9#13068871C211yesmaximal, characteristic, complemented
10#13068816C211yesmaximal, characteristic, complemented
11#13068795C211yesmaximal, characteristic, complemented
12#13068644C211yesmaximal, characteristic, complemented
13#13068630C211yesmaximal, characteristic, complemented
14#13068553C211yesmaximal, characteristic
15C11×#2023C211yesmaximal, characteristic, complemented
16C22×#4341C2211yescharacteristic
17C2×C11×C4⋊Q8C2211yescharacteristic
18C22×C8×D11C2211yescharacteristic
19C2×#66945C2211yescharacteristic
20C2×#66940C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C11×#390C2211yescharacteristic
25#10622844—21no—
26#10622843—21no—
27#10622834C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×#66881C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35#10622704—24no—
36#10622607—21no—
37#10622600C2211yescharacteristic
38#10622600C2211yescharacteristic
39#10622598C2211yescharacteristic
40#10622591—21no—
41#10622590C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43C2×#66874C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47#10622570—21no—
48#10622570—21no—
49#10622555—21no—
50C22⋊C4×Dic11—21no—
51C4×(C2×D11)⋊C4C2211yescharacteristic
52#10622541C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54#10622385—24no—
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57C11×#336C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11—21no—
62C22×D4×C11C2311yescharacteristic
63C22×C22⋊D11—21no—
64C23×Dic11—21no—
65C2×#4341—22no—
66C2×#4341—22no—
67C2×#4341—22no—
68C2×#4341—41no—
69C2×#4341—41no—
70C2×#4341Q814yescomplemented
71C22×C4×D11C2311yescharacteristic
72C22×Dic22C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C11×C4⋊Q8—22no—
76C11×C4⋊Q8—41no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C42×C11C2311yescharacteristic
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4D411yescharacteristic
90C2×(C2×D11)⋊C4D411yescharacteristic
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C2×C8×D11—22no—
105C2×C8×D11—22no—
106C2×C8×D11—41no—
107#66945—22no—
108#66945—41no—
109#66940—22no—
110#66940—41no—
111C4×Dic22—22no—
112C4×Dic22—41no—
113C11×#102—22no—
114C11×#102—41no—
115#66896—22no—
116#66896—41no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95D411yescharacteristic
124C11⋊#95D411yescharacteristic
125(C2×D11)⋊C8—22no—
126#66881—41no—
127#66880—22no—
128#66880—22no—
129Dic11⋊C8—41no—
130#66874—22no—
131#66874D414yes—
132#66871—22no—
133#66871—22no—
134#66871—41no—
135C4⋊(C11⋊C8)—22no—
136#25959—111nomaximal, Sylow
137C24×C11—21no—
138C23×D11C2×D411yescharacteristic
139C2×Q8×C11—42no—
140C2×Q8×C11—42no—
141C2×Q8×C11—81no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11C2×Q812yes—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2411yescharacteristic
154C2×C22⋊D11—24no—
155C2×C22⋊D11—42no—
156C2×C22⋊D11—42no—
157C22×Dic11—24no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—42no—
163C22×Dic11—42no—
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167#4341—28no—
168#4341—44no—
169#4341—44no—
170#4341—44no—
171C2×C4×D11—21no—
172C2×C4×D11—21no—
173C2×C4×D11—21no—
174C2×C4×D11—21no—
175C2×C4×D11C2×Q812yes—
176C2×C4×D11#4112yes—
177C2×Dic22—21no—
178C2×Dic22—21no—
179C2×Dic22—21no—
180C2×Dic22C2×D412yes—
181C2×Dic22C2×Q812yes—
182C2×Dic22#4112yes—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—42no—
195C11×C4⋊C4C2×D412yes—
196C11×C22⋊C4—42no—
197C11×C22⋊C4—81no—
198C42×C11—21no—
199C42×C11—21no—
200C22⋊Dic11—42no—
201C22⋊Dic11—81no—
202(C2×D11)⋊C4—22no—
203(C2×D11)⋊C4—41no—
204(C2×D11)⋊C4—42no—
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—81no—
214Dic11⋊C4—42no—
215Dic11⋊C4—42no—
216Dic11⋊C4—42no—
217C4×Dic11—21no—
218C4×Dic11—21no—
219C4×Dic11—42no—
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⋊C8C2×D412yes—
228C8×D11—44no—
229C2×#477—111no—
230C2×#416—111no—
231#2439—111no—
232#2341—111no—
233#2092—111no—
234#2067—111no—
235#2067—111no—
236#2023D1111yescharacteristic, complemented
237#1865—111no—
238#1863—111no—
239#1854—111no—
240#1850—111no—
241#1808—111no—
242#1805—111no—
243#1788—111no—
244C23×C11—22no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11C22×D411yescharacteristic
252C22×D11—21no—
253C22×D11—21no—
254C22×D11—21no—
255C22×D11—21no—
256C22×D11—21no—
257C22×D11—21no—
258C22×D11C22⋊Q812yes—
259Q8×C11—84no—
260D4×C11—22no—
261D4×C11—22no—
262D4×C11—41no—
263D4×C11—41no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—22no—
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×C11#13512yes—
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C22×Q811yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11H(5,𝔽2)11yescharacteristic
284C2×C4×C11H(5,𝔽2)11yescharacteristic
285C22⋊D11—48no—
286C2×Dic11—22no—
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—48no—
298C2×Dic11—41no—
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×Dic11C22⋊Q812yes—
308C4×D11—22no—
309C4×D11—22no—
310C4×D11—22no—
311C4×D11—22no—
312Dic22—22no—
313Dic22—22no—
314Dic22—22no—
315Dic22C22⋊Q814yes—
316C8×C11—41no—
317C8×C11—41no—
318C11⋊C8—22no—
319C11⋊C8—41no—
320C22×#41—111no—
321C23×C8—111no—
322C2×C4⋊Q8C2×D1111yescharacteristic
323C2×C4×Q8—111no—
324C2×C4×Q8—111no—
325C2×#117—111no—
326#477—224no—
327C2×#107—111no—
328C2×#107—111no—
329C2×#107—111no—
330C2×#106—111no—
331C2×C4⋊C8—111no—
332C2×C4⋊C8—111no—
333#416—224no—
334C2×#103—111no—
335C2×#103—111no—
336C2×#103—111no—
337C2×#103—111no—
338C2×#102—111no—
339C2×#102—111no—
340C2×#102C2×D1111yescharacteristic
341C2×#102C2×D1111yescharacteristic
342C2×C22⋊C8—111no—
343#396—221no—
344#393—221no—
345#391—221no—
346#390—111no—
347#390—221no—
348#390—221no—
349#390C2×D1111yescharacteristic
350#389—111no—
351#389—111no—
352#387—221no—
353#382—111no—
354#380—111no—
355#380—111no—
356#380—221no—
357C4×C22⋊C4—111no—
358C4×C22⋊C4—221no—
359#340—111no—
360#340—111no—
361#340C2×D1111yescharacteristic
362#340C2×D1111yescharacteristic
363#336—111no—
364#336C2×D1111yescharacteristic
365C22×C11—42no—
366C22×C11—42no—
367C22×C11—42no—
368C22×C11—81no—
369C22×C11—81no—
370C22×C11—81no—
371C22×C11—81no—
372C22×C11C2×C22⋊Q811yescharacteristic
373C22×C11D4211yescharacteristic
374C22×C11#54611yescharacteristic
375C22×C11C2×#13511yescharacteristic
376C22×C11#57511yescharacteristic
377C22×C11#57611yescharacteristic
378C22×C11#57811yescharacteristic
379C2×D11—22no—
380C2×D11—22no—
381C2×D11—22no—
382C2×D11—41no—
383C2×D11—41no—
384C2×D11—41no—
385C2×D11—41no—
386C4×C11—22no—
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—24no—
396Dic11—22no—
397Dic11—41no—
398Dic11—41no—
399Dic11—81no—
400Dic11—81no—
401Dic11—81no—
402C2×#41—114no—
403C2×#41—222no—
404C2×#41—222no—
405C2×#41—222no—
406C2×#41—441no—
407C2×#41—441no—
408C22×Q8—21no—
409C22×Q8—111no—
410C22×D4—221no—
411C22×D4C22×D1111yescharacteristic
412C23×C4—111no—
413C23×C4—221no—
414C22×C8—111no—
415C22×C8—111no—
416C22×C8—222no—
417C22×C8—222no—
418C22×C8—441no—
419C22×C8C22×D1111yescharacteristic
420C22×C8C22×D1111yescharacteristic
421C4⋊Q8—22no—
422C4⋊Q8—41no—
423C4×Q8—222no—
424C4×Q8—222no—
425C4×Q8—441no—
426C4×Q8—441no—
427#117—222no—
428#117—441no—
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⋊C4C22×D1111yescharacteristic
438C2×C4⋊C4C22×D1111yescharacteristic
439C2×C4⋊C4C22×D1111yescharacteristic
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—111no—
443C2×C22⋊C4—111no—
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C22⋊C4—221no—
447C2×C22⋊C4—221no—
448C2×C22⋊C4—221no—
449C2×C42—111no—
450C2×C42—221no—
451C2×C42—221no—
452C2×C42—221no—
453C2×C42C22×D1111yescharacteristic
454#107—222no—
455#107—222no—
456#107—441no—
457#106—441no—
458C4⋊C8—222no—
459C4⋊C8—441no—
460#103—114no—
461#103—222no—
462#103—222no—
463#103—222no—
464#102—22no—
465#102—41no—
466#102—222no—
467#102—441no—
468C22⋊C8—222no—
469#95—111no—
470#95—111no—
471#95—221no—
472#95—221no—
473#95—221no—
474#95—221no—
475#95—221no—
476#95—221no—
477C2×C11—82no—
478C2×C11#243711yescharacteristic
479C2×C11#307611yescharacteristic
480C2×C11#308311yescharacteristic
481C2×C11#326811yescharacteristic
482C2×C11#328511yescharacteristic
483C2×C11#330511yescharacteristic
484C2×C11#331311yescharacteristic
485D11—42no—
486C24—21no—
487C24—111no—
488#41—228no—
489#41—444no—
490#41—444no—
491#41—444no—
492C2×Q8—42no—
493C2×Q8—42no—
494C2×Q8—81no—
495C2×Q8—112no—
496C2×Q8—112no—
497C2×Q8—112no—
498C2×Q8—221no—
499C2×Q8—221no—
500C2×Q8—221no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—224no—
507C2×D4—442no—
508C2×D4—442no—
509C2×D4Q8×D1112yes—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—111no—
514C22×C4—112no—
515C22×C4—112no—
516C22×C4—111no—
517C22×C4—111no—
518C22×C4—224no—
519C22×C4—221no—
520C22×C4—221no—
521C22×C4—221no—
522C22×C4—221no—
523C22×C4—221no—
524C22×C4—221no—
525C22×C4—221no—
526C22×C4—221no—
527C22×C4—442no—
528C22×C4—442no—
529C22×C4D4×D1111yescharacteristic
530C22×C4D4×D1111yescharacteristic
531C22×C4C23×D1111yescharacteristic
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—112no—
539C2×C8—221no—
540C2×C8—221no—
541C2×C8—221no—
542C2×C8—221no—
543C2×C8—221no—
544C2×C8—444no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—42no—
551C4⋊C4—221no—
552C4⋊C4—221no—
553C4⋊C4—221no—
554C4⋊C4—221no—
555C4⋊C4—221no—
556C4⋊C4—221no—
557C4⋊C4—442no—
558C4⋊C4—442no—
559C4⋊C4—442no—
560C4⋊C4—881no—
561C4⋊C4D4×D1112yes—
562C22⋊C4—42no—
563C22⋊C4—81no—
564C22⋊C4—222no—
565C22⋊C4—441no—
566C22⋊C4—442no—
567C22⋊C4—442no—
568C22⋊C4—881no—
569C22⋊C4—881no—
570C22⋊C4—881no—
571C42—21no—
572C42—21no—
573C42—221no—
574C42—221no—
575C42—442no—
576C42—442no—
577C42—442no—
578C11#2595911yescharacteristic, complemented, Sylow
579C23—22no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—112no—
587C23—221no—
588C23—221no—
589C23—221no—
590C23—221no—
591C23—221no—
592C23—221no—
593C23C2×D4×D1111yescharacteristic
594Q8—84no—
595Q8—114no—
596Q8—222no—
597Q8—222no—
598Q8—222no—
599D4—22no—
600D4—22no—
601D4—41no—
602D4—41no—
603D4—448no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—22no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—112no—
619C2×C4—221no—
620C2×C4—222no—
621C2×C4—222no—
622C2×C4—222no—
623C2×C4—221no—
624C2×C4—222no—
625C2×C4—222no—
626C2×C4—222no—
627C2×C4—222no—
628C2×C4—221no—
629C2×C4—221no—
630C2×C4—221no—
631C2×C4—221no—
632C2×C4—221no—
633C2×C4—221no—
634C2×C4—448no—
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—441no—
644C2×C4#6696912yes—
645C2×C4C2×D4×D1111yescharacteristic
646C2×C4#6703711yescharacteristic
647C2×C4C2×Q8×D1111yescharacteristic
648C2×C4#41×D1111yescharacteristic
649C2×C4#41×D1111yescharacteristic
650C2×C4#6704211yescharacteristic
651C8—41no—
652C8—41no—
653C8—222no—
654C8—441no—
655C22—42no—
656C22—42no—
657C22—42no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22—81no—
662C22—222no—
663C22—222no—
664C22—222no—
665C22—441no—
666C22—441no—
667C22—441no—
668C22—441no—
669C22#1062312111yescharacteristic
670C22D11×C22⋊Q811yescharacteristic
671C22#1062320711yescharacteristic
672C22#1062328811yescharacteristic
673C22C2×#6696911yescharacteristic
674C22#1062330411yescharacteristic
675C22#1062331011yescharacteristic
676C4—22no—
677C4—41no—
678C4—42no—
679C4—81no—
680C4—81no—
681C4—222no—
682C4—224no—
683C4—441no—
684C4—441no—
685C4—881no—
686C4—881no—
687C4—881no—
688C4D11×C22⋊Q811yescharacteristic
689C4#1062316511yescharacteristic
690C4#1062320711yescharacteristic
691C4#1062321011yescharacteristic
692C2—82no—
693C2—442no—
694C2#1307227611yescharacteristic
695C2#1307840511yescharacteristic
696C2#1307846211yescharacteristic
697C2#1308015411yescharacteristic
698C2#1308035011yescharacteristic
699C2#1308056511yescharacteristic
700C2#1308068111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2023C2
socleC23×C11C22×D4
prime radicalC22×#4341C22
hypercenter#2023D11
hypocenterC11#25959
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2023

Complements

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

NH ≅ G/Ntype
1. C2×#10622704C2semidirect
3. #13072303C2semidirect
5. #13070139C2semidirect
6. #13070004C2semidirect
7. #13070000C2semidirect
8. #13068887C2semidirect
9. #13068871C2semidirect
10. #13068816C2semidirect
11. #13068795C2semidirect
12. #13068644C2semidirect
13. #13068630C2semidirect
15. C11×#2023C2semidirect
70. C2×#4341Q8semidirect
236. #2023D11semidirect
578. C11#25959semidirect

Maximal subgroups

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

subgroupindex
C2×#106227042
C2×#106223852
#130723032
#130714552
#130701392
#130700042
#130700002
#130688872
#130688712
#130688162
#130687952
#130686442
#130686302
#130685532
C11×#20232
#2595911