Finite Group Databasebeta

← #14810878

Subgroups — #14810878

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×#10622470C211yesmaximal, characteristic, complemented
2C2×#10622385C211yesmaximal, characteristic
3#13072332C211yesmaximal, characteristic, complemented
4#13071455C211yesmaximal, characteristic
5#13070004C211yesmaximal, characteristic, complemented
6#13069988C211yesmaximal, characteristic, complemented
7#13069760C211yesmaximal, characteristic, complemented
8#13068887C211yesmaximal, characteristic, complemented
9#13068881C211yesmaximal, characteristic, complemented
10#13068814C211yesmaximal, characteristic, complemented
11#13068795C211yesmaximal, characteristic, complemented
12#13068638C211yesmaximal, characteristic, complemented
13#13068618C211yesmaximal, characteristic, complemented
14#13068553C211yesmaximal, characteristic
15C11×#2094C211yesmaximal, characteristic, complemented
16C22×#4341C2211yescharacteristic
17C22×C8×D11C2211yescharacteristic
18C2×#66945C2211yescharacteristic
19C2×#66943C2211yescharacteristic
20C2×#66940C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C2×C11×#106C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C11×#390C2211yescharacteristic
27C11×#384C2211yescharacteristic
28#10622834C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×#66881C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36#10622607—21no—
37#10622605—21no—
38#10622600C2211yescharacteristic
39#10622600C2211yescharacteristic
40#10622594—21no—
41#10622586C2211yescharacteristic
42#10622585—21no—
43C2×#66874C2211yescharacteristic
44C2×#66874C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622570—21no—
47#10622570—21no—
48#10622555—21no—
49C22⋊C4×Dic11—21no—
50C4×(C2×D11)⋊C4C2211yescharacteristic
51#10622541C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53#10622470—24no—
54#10622385—24no—
55C11×#336C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C23×Dic11—21no—
64C2×#4341—22no—
65C2×#4341—22no—
66C2×#4341—22no—
67C2×#4341—41no—
68C2×#4341—41no—
69C2×#4341Q814yes—
70C22×C4×D11C2311yescharacteristic
71C22×Dic22C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C42×C11C2311yescharacteristic
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4D411yescharacteristic
88C2×(C2×D11)⋊C4D411yescharacteristic
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
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#66943—22no—
110#66943—41no—
111#66940—22no—
112#66940—41no—
113C4×Dic22—22no—
114C4×Dic22—41no—
115C11×#106—22no—
116C11×#106—41no—
117C11×#102—22no—
118C11×#102—41no—
119#66896—22no—
120#66896—41no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95D411yescharacteristic
126C11⋊#95D411yescharacteristic
127(C2×D11)⋊C8—22no—
128#66881—41no—
129#66880—22no—
130#66880D414yes—
131Dic11⋊C8—22no—
132#66874—22no—
133#66874—22no—
134#66871—22no—
135C4⋊(C11⋊C8)—41no—
136#25953—111nomaximal, Sylow
137C24×C11—21no—
138C23×D11C2×D411yescharacteristic
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11C2×Q812yes—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C2×C22⋊D11—24no—
152C2×C22⋊D11—42no—
153C2×C22⋊D11—42no—
154C22×Dic11—24no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—42no—
160C22×Dic11—42no—
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164#4341—28no—
165#4341—44no—
166#4341—44no—
167#4341—44no—
168C2×C4×D11—21no—
169C2×C4×D11—21no—
170C2×C4×D11—21no—
171C2×C4×D11—21no—
172C2×C4×D11C2×Q812yes—
173C2×C4×D11#4112yes—
174C2×Dic22—21no—
175C2×Dic22—21no—
176C2×Dic22—21no—
177C2×Dic22C2×D412yes—
178C2×Dic22C2×Q812yes—
179C2×Dic22#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—21no—
192C11×C4⋊C4—42no—
193C11×C4⋊C4—81no—
194C11×C22⋊C4—42no—
195C11×C22⋊C4—81no—
196C42×C11—21no—
197C42×C11—21no—
198C22⋊Dic11—42no—
199C22⋊Dic11—81no—
200(C2×D11)⋊C4—22no—
201(C2×D11)⋊C4—41no—
202(C2×D11)⋊C4—42no—
203(C2×D11)⋊C4—81no—
204(C2×D11)⋊C4—81no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—42no—
211C4⋊Dic11C2×D412yes—
212Dic11⋊C4—42no—
213Dic11⋊C4—42no—
214Dic11⋊C4—42no—
215Dic11⋊C4—42no—
216Dic11⋊C4—81no—
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⋊C8—21no—
228C8×D11—44no—
229C2×#479—111no—
230C2×#416—111no—
231#2441—111no—
232#2341—111no—
233#2094D1111yescharacteristic, complemented
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×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—
259D4×C11—22no—
260D4×C11—22no—
261D4×C11—41no—
262D4×C11—41no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
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×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11#13512yes—
278C2×C4×C11C22×D411yescharacteristic
279C2×C4×C11C22×Q811yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11H(5,𝔽2)11yescharacteristic
283C2×C4×C11H(5,𝔽2)11yescharacteristic
284C22⋊D11—48no—
285C2×Dic11—22no—
286C2×Dic11—21no—
287C2×Dic11—22no—
288C2×Dic11—22no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—22no—
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×Dic11C22⋊Q812yes—
307C4×D11—22no—
308C4×D11—22no—
309C4×D11—22no—
310C4×D11—22no—
311Dic22—22no—
312Dic22—22no—
313Dic22—22no—
314Dic22C22⋊Q814yes—
315C8×C11—22no—
316C8×C11—41no—
317C11⋊C8—41no—
318C11⋊C8—41no—
319C22×#41—111no—
320C23×C8—111no—
321C2×#125—111no—
322C2×C4×Q8—111no—
323C2×C4×Q8—111no—
324C2×#117—111no—
325#479—224no—
326C2×#107—111no—
327C2×#106—111no—
328C2×#106C2×D1111yescharacteristic
329C2×#106C2×D1111yescharacteristic
330C2×C4⋊C8—111no—
331C2×C4⋊C8—111no—
332#416—224no—
333C2×#103—111no—
334C2×#103—111no—
335C2×#103—111no—
336C2×#103—111no—
337C2×#102—111no—
338C2×#102—111no—
339C2×#102C2×D1111yescharacteristic
340C2×#102C2×D1111yescharacteristic
341C2×C22⋊C8—111no—
342#399—221no—
343#396—221no—
344#390—111no—
345#390—221no—
346#390—221no—
347#390C2×D1111yescharacteristic
348#389—111no—
349#389—111no—
350#389—221no—
351#387—221no—
352#384C2×D1111yescharacteristic
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#336C2×D1111yescharacteristic
364C22×C11—42no—
365C22×C11—42no—
366C22×C11—42no—
367C22×C11—81no—
368C22×C11—81no—
369C22×C11—81no—
370C22×C11—81no—
371C22×C11C2×C22⋊Q811yescharacteristic
372C22×C11D4211yescharacteristic
373C22×C11#54611yescharacteristic
374C22×C11C2×#13511yescharacteristic
375C22×C11#57511yescharacteristic
376C22×C11#57711yescharacteristic
377C22×C11#57711yescharacteristic
378C2×D11—22no—
379C2×D11—22no—
380C2×D11—22no—
381C2×D11—41no—
382C2×D11—41no—
383C2×D11—41no—
384C2×D11—41no—
385C4×C11—22no—
386C4×C11—41no—
387C4×C11—81no—
388C4×C11—81no—
389C4×C11—81no—
390C4×C11C2×C22⋊Q811yescharacteristic
391C4×C11#54311yescharacteristic
392C4×C11#54611yescharacteristic
393C4×C11#55111yescharacteristic
394Dic11—24no—
395Dic11—22no—
396Dic11—41no—
397Dic11—41no—
398Dic11—42no—
399Dic11—81no—
400Dic11—81no—
401C2×#41—114no—
402C2×#41—222no—
403C2×#41—222no—
404C2×#41—222no—
405C2×#41—441no—
406C2×#41—441no—
407C22×Q8—111no—
408C22×D4—221no—
409C22×D4C22×D1111yescharacteristic
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—222no—
420#125—441no—
421C4×Q8—222no—
422C4×Q8—222no—
423C4×Q8—441no—
424C4×Q8—441no—
425#117—222no—
426#117—441no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—111no—
430C2×C4⋊C4—111no—
431C2×C4⋊C4—111no—
432C2×C4⋊C4—221no—
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—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—111no—
444C2×C22⋊C4—111no—
445C2×C22⋊C4—221no—
446C2×C22⋊C4—221no—
447C2×C22⋊C4—221no—
448C2×C22⋊C4—221no—
449C2×C22⋊C4—221no—
450C2×C42—111no—
451C2×C42—221no—
452C2×C42—221no—
453C2×C42—221no—
454C2×C42C22×D1111yescharacteristic
455#107—222no—
456#106—22no—
457#106—41no—
458#106—441no—
459C4⋊C8—222no—
460C4⋊C8—441no—
461#103—114no—
462#103—222no—
463#103—222no—
464#103—222no—
465#102—22no—
466#102—41no—
467#102—222no—
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—82no—
477C2×C11#243711yescharacteristic
478C2×C11#307611yescharacteristic
479C2×C11#308411yescharacteristic
480C2×C11#327111yescharacteristic
481C2×C11#328411yescharacteristic
482C2×C11#330111yescharacteristic
483C2×C11#331711yescharacteristic
484D11—42no—
485C24—21no—
486C24—111no—
487#41—228no—
488#41—444no—
489#41—444no—
490#41—444no—
491C2×Q8—112no—
492C2×Q8—112no—
493C2×Q8—112no—
494C2×Q8—221no—
495C2×Q8—221no—
496C2×Q8—221no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—224no—
503C2×D4—442no—
504C2×D4—442no—
505C2×D4Q8×D1112yes—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—111no—
510C22×C4—112no—
511C22×C4—112no—
512C22×C4—111no—
513C22×C4—111no—
514C22×C4—224no—
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—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×C8D4×D1112yes—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—42no—
548C4⋊C4—81no—
549C4⋊C4—112no—
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—442no—
559C4⋊C4—442no—
560C4⋊C4—881no—
561C22⋊C4—42no—
562C22⋊C4—81no—
563C22⋊C4—222no—
564C22⋊C4—441no—
565C22⋊C4—442no—
566C22⋊C4—442no—
567C22⋊C4—881no—
568C22⋊C4—881no—
569C22⋊C4—881no—
570C42—21no—
571C42—21no—
572C42—221no—
573C42—221no—
574C42—442no—
575C42—442no—
576C42—442no—
577C11#2595311yescharacteristic, complemented, Sylow
578C23—22no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—112no—
586C23—221no—
587C23—221no—
588C23—221no—
589C23—221no—
590C23—221no—
591C23—221no—
592C23C2×D4×D1111yescharacteristic
593Q8—114no—
594Q8—222no—
595Q8—222no—
596Q8—222no—
597D4—22no—
598D4—22no—
599D4—41no—
600D4—41no—
601D4—448no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—112no—
617C2×C4—221no—
618C2×C4—222no—
619C2×C4—222no—
620C2×C4—222no—
621C2×C4—221no—
622C2×C4—222no—
623C2×C4—222no—
624C2×C4—222no—
625C2×C4—222no—
626C2×C4—221no—
627C2×C4—221no—
628C2×C4—222no—
629C2×C4—221no—
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#6696912yes—
643C2×C4C2×D4×D1111yescharacteristic
644C2×C4#6703711yescharacteristic
645C2×C4C2×Q8×D1111yescharacteristic
646C2×C4#41×D1111yescharacteristic
647C2×C4#41×D1111yescharacteristic
648C2×C4#6704211yescharacteristic
649C8—22no—
650C8—41no—
651C8—441no—
652C8—441no—
653C22—42no—
654C22—42no—
655C22—42no—
656C22—81no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22—222no—
661C22—222no—
662C22—222no—
663C22—441no—
664C22—441no—
665C22—441no—
666C22—441no—
667C22D11×C22⋊Q811yescharacteristic
668C22#1062318511yescharacteristic
669C22#1062324811yescharacteristic
670C22C2×#6696911yescharacteristic
671C22#1062329311yescharacteristic
672C22#1062330411yescharacteristic
673C22#1062330611yescharacteristic
674C4—22no—
675C4—41no—
676C4—81no—
677C4—81no—
678C4—81no—
679C4—222no—
680C4—224no—
681C4—441no—
682C4—442no—
683C4—441no—
684C4—881no—
685C4—881no—
686C4D11×C22⋊Q811yescharacteristic
687C4#1062316511yescharacteristic
688C4#1062318511yescharacteristic
689C4#1062319011yescharacteristic
690C2—82no—
691C2—442no—
692C2#1307228311yescharacteristic
693C2#1307840511yescharacteristic
694C2#1307847311yescharacteristic
695C2#1308020011yescharacteristic
696C2#1308034511yescharacteristic
697C2#1308051611yescharacteristic
698C2#1308074511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2094C2
socleC23×C11C22×D4
prime radicalC22×#4341C22
hypercenter#2094D11
hypocenterC11#25953
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2094

Complements

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

NH ≅ G/Ntype
1. C2×#10622470C2semidirect
3. #13072332C2semidirect
5. #13070004C2semidirect
6. #13069988C2semidirect
7. #13069760C2semidirect
8. #13068887C2semidirect
9. #13068881C2semidirect
10. #13068814C2semidirect
11. #13068795C2semidirect
12. #13068638C2semidirect
13. #13068618C2semidirect
15. C11×#2094C2semidirect
233. #2094D11semidirect
577. C11#25953semidirect

Maximal subgroups

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

subgroupindex
C2×#106224702
C2×#106223852
#130723322
#130714552
#130700042
#130699882
#130697602
#130688872
#130688812
#130688142
#130687952
#130686382
#130686182
#130685532
C11×#20942
#2595311