Finite Group Databasebeta

← #14813500

Subgroups — #14813500

Order 2816.

894 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622479C211yesmaximal, characteristic, complemented
2C2×#10622473C211yesmaximal, characteristic, complemented
3#13072032C211yesmaximal, characteristic
4#13071563C211yesmaximal, characteristic, complemented
5#13070148C211yesmaximal, characteristic, complemented
6#13070087C211yesmaximal, characteristic, complemented
7#13070051C211yesmaximal, characteristic, complemented
8#13069801C211yesmaximal, characteristic, complemented
9#13069236C211yesmaximal, characteristic, complemented
10#13069043C211yesmaximal, characteristic, complemented
11#13068937C211yesmaximal, characteristic, complemented
12#13068907C211yesmaximal, characteristic, complemented
13#13068816C211yesmaximal, characteristic, complemented
14#13068816C211yesmaximal, characteristic, complemented
15C11×#1920C211yesmaximal, characteristic, complemented
16C22×C8×D11C2211yescharacteristic
17C2×#66948C2211yescharacteristic
18C2×#66948C2211yescharacteristic
19C2×#66945C2211yescharacteristic
20C2×#66945C2211yescharacteristic
21C2×#66945C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×#66881C2211yescharacteristic
32C2×#66881C2211yescharacteristic
33#10622604—21no—
34#10622601—21no—
35#10622600C2211yescharacteristic
36#10622600C2211yescharacteristic
37#10622600C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43#10622552—21no—
44#10622552C2211yescharacteristic
45#10622548C2211yescharacteristic
46C4×C4⋊Dic11—21no—
47#10622479—24no—
48#10622473—24no—
49#10622284—21no—
50#10622283—21no—
51#10622283—21no—
52#10622283—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#336C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×D44—21no—
62C22×D44—21no—
63C22×D44D411yescharacteristic
64C22×D44C2311yescharacteristic
65C22×C4×D11C2311yescharacteristic
66C22×C4×D11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C42×C11—21no—
75C2×C42×C11C2311yescharacteristic
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4D411yescharacteristic
87C2×(C2×D11)⋊C4D411yescharacteristic
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11D411yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C2×C8×D11—22no—
100C2×C8×D11—22no—
101C2×C8×D11—22no—
102#66948—22no—
103#66948—22no—
104#66948—22no—
105#66948—41no—
106#66945—22no—
107#66945—22no—
108#66945—22no—
109#66945—41no—
110#66945—41no—
111#66945—41no—
112C4×D44—22no—
113C4×D44—22no—
114C11×#106D414yescomplemented
115C11×#95—21no—
116C11×#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120#66885—22no—
121#66885—41no—
122(C2×D11)⋊C8—22no—
123(C2×D11)⋊C8—22no—
124(C2×D11)⋊C8—22no—
125#66881—22no—
126#66881—41no—
127#66873—22no—
128#66873—22no—
129#66871—22no—
130#66871—22no—
131#66871—22no—
132#26141—111nomaximal, Sylow
133C23×D11—21no—
134C23×D11C2×D411yescharacteristic
135C23×D11C2×D411yescharacteristic
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2411yescharacteristic
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11C2×D411yescharacteristic
147C22×Dic11C2×D411yescharacteristic
148C2×D44—22no—
149C2×D44—22no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—41no—
157C2×D44—42no—
158C2×D44—42no—
159C2×D44—42no—
160C2×D44—81no—
161C2×D44—81no—
162C2×D44—81no—
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11—21no—
168C2×C4×D11—21no—
169C2×C4×D11—21no—
170C2×C4×D11—21no—
171C2×C4×D11—21no—
172C2×C4×D11—21no—
173C2×C4×D11#4112yes—
174C2×C4×D11#4112yes—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11C2×D412yes—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—81no—
188C11×C4⋊C4C2×D412yes—
189C11×C4⋊C4C2×D412yes—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—42no—
193(C2×D11)⋊C4—22no—
194(C2×D11)⋊C4—22no—
195(C2×D11)⋊C4—42no—
196(C2×D11)⋊C4—42no—
197(C2×D11)⋊C4—42no—
198(C2×D11)⋊C4—42no—
199(C2×D11)⋊C4—42no—
200(C2×D11)⋊C4—42no—
201(C2×D11)⋊C4—81no—
202(C2×D11)⋊C4—81no—
203(C2×D11)⋊C4—81no—
204(C2×D11)⋊C4—81no—
205C4⋊Dic11—22no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11—21no—
212C4⋊Dic11—42no—
213C4⋊Dic11—81no—
214C4×Dic11—42no—
215C4×Dic11—42no—
216C4×Dic11—42no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8#4112yes—
223C8×D11—28no—
224C2×#482—111no—
225C2×#427—111no—
226#2414—111no—
227#2354—111no—
228#2094—111no—
229#2083—111no—
230#2077—111no—
231#2033—111no—
232#1925—111no—
233#1920D1111yescharacteristic, complemented
234#1893—111no—
235#1875—111no—
236#1869—111no—
237#1854—111no—
238#1854—111no—
239C23×C11C22×D411yescharacteristic
240C22×D11—21no—
241C22×D11—21no—
242C22×D11—21no—
243C22×D11—21no—
244C22×D11—21no—
245C22×D11—21no—
246C22×D11—21no—
247C22×D11—21no—
248C22×D11—21no—
249C22×D11—21no—
250C22×D11—21no—
251C22×D11—21no—
252C22×D11—21no—
253C22×D11—41no—
254C22×D11—41no—
255C22×D11—41no—
256C22×D11—41no—
257C22×D11—41no—
258C22×D11—41no—
259C22×D11—41no—
260C22×D11#12312yes—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
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—41no—
278C2×C4×C11#13512yes—
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11H(5,𝔽2)11yescharacteristic
284C2×C4×C112−1+411yescharacteristic
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11#12312yes—
300D44—44no—
301D44—41no—
302D44—41no—
303D44—41no—
304D44—41no—
305D44—84no—
306D44—84no—
307C4×D11—22no—
308C4×D11—22no—
309C4×D11—22no—
310C4×D11—22no—
311C4×D11—41no—
312C4×D11—41no—
313C4×D11—41no—
314C4×D11—41no—
315C8×C11—22no—
316C8×C11—41no—
317C11⋊C8—22no—
318C11⋊C8—41no—
319C23×C8—111no—
320C2×#121—111no—
321C2×#121—111no—
322C2×C4×D4—111no—
323C2×#117—111no—
324C2×#117—111no—
325C2×#117—111no—
326#482—224no—
327#427—224no—
328C2×#107—111no—
329C2×#107—111no—
330C2×#107—111no—
331C2×#106—111no—
332C2×#106—111no—
333C2×#106C2×D1111yescharacteristic
334C2×#102—111no—
335C2×#102—111no—
336C2×#102—111no—
337C2×#102—111no—
338C2×C22⋊C8—111no—
339C2×C22⋊C8—111no—
340C2×C22⋊C8—111no—
341#394—221no—
342#392—221no—
343#390—111no—
344#390—221no—
345#390—221no—
346#389C2×D1111yescharacteristic
347#388—221no—
348#388—221no—
349#388—221no—
350#384—111no—
351#380—111no—
352#380—111no—
353#380—111no—
354C4×C4⋊C4—221no—
355C4×C4⋊C4C2×D1111yescharacteristic
356#340—111no—
357#340—111no—
358#340—111no—
359#340C2×D1111yescharacteristic
360#340C2×D1111yescharacteristic
361#340C2×D1111yescharacteristic
362#336—111no—
363#336C2×D1111yescharacteristic
364C22×C11C2×#12311yescharacteristic
365C22×C11D4211yescharacteristic
366C22×C11#54711yescharacteristic
367C22×C11C2×#13511yescharacteristic
368C22×C11#57511yescharacteristic
369C22×C11#57611yescharacteristic
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—41no—
379C2×D11—41no—
380C2×D11—41no—
381C2×D11—41no—
382C2×D11—41no—
383C2×D11—41no—
384C2×D11—41no—
385C2×D11—81no—
386C2×D11—81no—
387C2×D11—81no—
388C2×D11—81no—
389C2×D11—81no—
390C2×D11—81no—
391C2×D11—81no—
392C4×C11—22no—
393C4×C11—41no—
394C4×C11—42no—
395C4×C11—42no—
396C4×C11—81no—
397C4×C11—81no—
398C4×C11#52511yescharacteristic
399C4×C11#53911yescharacteristic
400C4×C11#54811yescharacteristic
401C4×C11#55311yescharacteristic
402Dic11—22no—
403Dic11—41no—
404Dic11—81no—
405Dic11—81no—
406Dic11—81no—
407C22×D4—111no—
408C22×D4—111no—
409C22×D4—221no—
410C22×D4—221no—
411C23×C4—111no—
412C23×C4—111no—
413C22×C8—111no—
414C22×C8—111no—
415C22×C8—222no—
416C22×C8—222no—
417C22×C8—222no—
418C22×C8C22×D1111yescharacteristic
419C22×C8C22×D1111yescharacteristic
420#121—222no—
421#121—222no—
422#121—222no—
423#121—441no—
424C4×D4—222no—
425C4×D4—222no—
426#117—222no—
427#117—222no—
428#117—222no—
429#117—441no—
430#117—441no—
431#117—441no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—111no—
434C2×C4⋊C4—111no—
435C2×C4⋊C4—111no—
436C2×C4⋊C4—111no—
437C2×C4⋊C4—221no—
438C2×C4⋊C4—221no—
439C2×C4⋊C4C22×D1111yescharacteristic
440C2×C4⋊C4C22×D1111yescharacteristic
441C2×C4⋊C4C22×D1111yescharacteristic
442C2×C4⋊C4C22×D1111yescharacteristic
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×C22⋊C4—221no—
451C2×C22⋊C4—221no—
452C2×C22⋊C4—221no—
453C2×C22⋊C4—221no—
454C2×C22⋊C4—221no—
455C2×C42—21no—
456C2×C42—221no—
457C2×C42—221no—
458C2×C42—221no—
459C2×C42C22×D1111yescharacteristic
460#107—222no—
461#107—222no—
462#107—222no—
463#106—222no—
464#106—441no—
465#106D4414yescomplemented
466#102—222no—
467#102—222no—
468#102—222no—
469#102—441no—
470C22⋊C8—222no—
471C22⋊C8—222no—
472C22⋊C8—222no—
473#95—21no—
474#95—21no—
475#95—221no—
476#95—221no—
477#95—221no—
478C2×C11#244311yescharacteristic
479C2×C11#309111yescharacteristic
480C2×C11#309611yescharacteristic
481C2×C11#326811yescharacteristic
482C2×C11#328411yescharacteristic
483C2×C11#334111yescharacteristic
484C2×C11#335011yescharacteristic
485D11—42no—
486D11—81no—
487D11—161no—
488C24—111no—
489C24—111no—
490C24—221no—
491C2×D4—222no—
492C2×D4—222no—
493C2×D4—221no—
494C2×D4—221no—
495C2×D4—221no—
496C2×D4—221no—
497C2×D4—221no—
498C2×D4—221no—
499C2×D4—441no—
500C2×D4—442no—
501C2×D4—442no—
502C2×D4—442no—
503C2×D4—881no—
504C2×D4—881no—
505C2×D4—881no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—111no—
511C22×C4—112no—
512C22×C4—112no—
513C22×C4—111no—
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—221no—
525C22×C4—221no—
526C22×C4—221no—
527C22×C4D4×D1111yescharacteristic
528C22×C4D4×D1111yescharacteristic
529C22×C4C23×D1111yescharacteristic
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—112no—
536C2×C8—228no—
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—21no—
548C4⋊C4—21no—
549C4⋊C4—81no—
550C4⋊C4—222no—
551C4⋊C4—221no—
552C4⋊C4—221no—
553C4⋊C4—221no—
554C4⋊C4—221no—
555C4⋊C4—221no—
556C4⋊C4—221no—
557C4⋊C4—442no—
558C4⋊C4—881no—
559C4⋊C4C2×D4412yes—
560C4⋊C4C2×D4412yes—
561C22⋊C4—222no—
562C22⋊C4—222no—
563C22⋊C4—442no—
564C22⋊C4—442no—
565C22⋊C4—442no—
566C22⋊C4—442no—
567C22⋊C4—442no—
568C22⋊C4—442no—
569C22⋊C4—881no—
570C22⋊C4—881no—
571C22⋊C4—881no—
572C22⋊C4—881no—
573C42—21no—
574C42—21no—
575C42—42no—
576C42—442no—
577C42—442no—
578C42—442no—
579C11#2614111yescharacteristic, complemented, Sylow
580C23—112no—
581C23—221no—
582C23—221no—
583C23—221no—
584C23—221no—
585C23—221no—
586C23—221no—
587C23—221no—
588C23—221no—
589C23—221no—
590C23—221no—
591C23—221no—
592C23—221no—
593C23—221no—
594C23—441no—
595C23—441no—
596C23—441no—
597C23—441no—
598C23—441no—
599C23—441no—
600C23—441no—
601C23C2×D4×D1111yescharacteristic
602D4—444no—
603D4—441no—
604D4—441no—
605D4—441no—
606D4—441no—
607D4—884no—
608D4—884no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—21no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—112no—
627C2×C4—221no—
628C2×C4—221no—
629C2×C4—222no—
630C2×C4—222no—
631C2×C4—222no—
632C2×C4—222no—
633C2×C4—221no—
634C2×C4—221no—
635C2×C4—221no—
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—441no—
645C2×C4—441no—
646C2×C4—441no—
647C2×C4—441no—
648C2×C4—441no—
649C2×C4#6696912yes—
650C2×C4C22×D4411yescharacteristic
651C2×C4#6704011yescharacteristic
652C2×C4#41×D1111yescharacteristic
653C2×C4#41×D1111yescharacteristic
654C2×C4#41×D1111yescharacteristic
655C2×C4#6704211yescharacteristic
656C8—22no—
657C8—41no—
658C8—222no—
659C8—441no—
660C22—222no—
661C22—222no—
662C22—222no—
663C22—441no—
664C22—441no—
665C22—441no—
666C22—441no—
667C22—441no—
668C22—441no—
669C22—441no—
670C22—441no—
671C22—441no—
672C22—441no—
673C22—441no—
674C22—881no—
675C22—881no—
676C22—881no—
677C22—881no—
678C22—881no—
679C22—881no—
680C22—881no—
681C22D4×D4411yescharacteristic
682C22#1062316211yescharacteristic
683C22D11×#12311yescharacteristic
684C22C2×#6696911yescharacteristic
685C22#1062330111yescharacteristic
686C22#1062330511yescharacteristic
687C22#1062330811yescharacteristic
688C4—22no—
689C4—42no—
690C4—41no—
691C4—42no—
692C4—81no—
693C4—81no—
694C4—222no—
695C4—441no—
696C4—881no—
697C4—881no—
698C4—881no—
699C4#1062305511yescharacteristic
700C4#1062310711yescharacteristic
701C4#1062322311yescharacteristic
702C4#1062324011yescharacteristic
703C2—442no—
704C2—881no—
705C2—1761no—
706C2#1307235611yescharacteristic
707C2#1307853011yescharacteristic
708C2#1307856911yescharacteristic
709C2#1308015811yescharacteristic
710C2#1308034711yescharacteristic
711C2#1308103711yescharacteristic
712C2#1308115811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1920C2
socleC23×C11C22×D4
prime radical#13072032C2
hypercenter#1920D11
hypocenterC11#26141
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1920

Complements

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

NH ≅ G/Ntype
1. C2×#10622479C2semidirect
2. C2×#10622473C2semidirect
4. #13071563C2semidirect
5. #13070148C2semidirect
6. #13070087C2semidirect
7. #13070051C2semidirect
8. #13069801C2semidirect
9. #13069236C2semidirect
10. #13069043C2semidirect
11. #13068937C2semidirect
12. #13068907C2semidirect
13. #13068816C2semidirect
14. #13068816C2semidirect
15. C11×#1920C2semidirect
114. C11×#106D4semidirect
233. #1920D11semidirect
465. #106D44semidirect
579. C11#26141semidirect

Maximal subgroups

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

subgroupindex
C2×#106224792
C2×#106224732
#130720322
#130715632
#130701482
#130700872
#130700512
#130698012
#130692362
#130690432
#130689372
#130689072
#130688162
C11×#19202
#2614111