Finite Group Databasebeta

← #14801954

Subgroups — #14801954

Order 2816.

942 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622348C211yesmaximal, characteristic
2C2×#10622727C211yesmaximal, characteristic
3#13073094C211yesmaximal, characteristic, complemented
4#13071630C211yesmaximal, characteristic
5#13070094C211yesmaximal, characteristic, complemented
6#13070021C211yesmaximal, characteristic, complemented
7#13069996C211yesmaximal, characteristic, complemented
8#13069934C211yesmaximal, characteristic, complemented
9#13069380C211yesmaximal, characteristic, complemented
10#13069251C211yesmaximal, characteristic, complemented
11#13068949C211yesmaximal, characteristic, complemented
12#13068921C211yesmaximal, characteristic, complemented
13#13068617C211yesmaximal, characteristic, complemented
14C2×#10622189C211yesmaximal, characteristic, complemented
15C11×#1850C211yesmaximal, characteristic, complemented
16C23×C8×C11C2211yescharacteristic
17C2×#66983C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C2×#66977C2211yescharacteristic
21C22×#4314C2211yescharacteristic
22C2×(C22⋊D11)⋊C4—21no—
23C2×C4×D44C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C4×C11×C22⋊C4C2211yescharacteristic
28#10622727—24no—
29C2×#66885C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66881C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34C2×#66881C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37C2×#66880C2211yescharacteristic
38#10622571—21no—
39#10622563—21no—
40#10622563—21no—
41#10622552C2211yescharacteristic
42#10622548C2211yescharacteristic
43#10622548C2211yescharacteristic
44C4×C4⋊Dic11C2211yescharacteristic
45#10622542C2211yescharacteristic
46#10622542C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622348—24no—
49#10622283—21no—
50#10622281—21no—
51#10622274—21no—
52#10622274—21no—
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C23×Dic11—21no—
64C23×Dic11—21no—
65C22×D44C2311yescharacteristic
66C22×C4×D11—21no—
67C22×Dic22C2311yescharacteristic
68C22×C8×C11—22no—
69C22×C8×C11—22no—
70C22×C8×C11—41no—
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C2×C11×C22⋊C4D411yescharacteristic
76C2×C11×C22⋊C4D411yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×C22⋊Dic11—21no—
80#66983—22no—
81#66983D414yes—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11—22no—
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11—41no—
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102#66977—22no—
103#66977—22no—
104C2×Dic11⋊C4—21no—
105C2×Dic11⋊C4—21no—
106C2×C4×Dic11—21no—
107C2×#4314—22no—
108C2×#4314—22no—
109C2×#4314—41no—
110(C22⋊D11)⋊C4—44no—
111C4×D44—22no—
112C4×D44—41no—
113C11×C4⋊C8—22no—
114C11×C4⋊C8—41no—
115C11×C22⋊C8—22no—
116C11×#95D411yescharacteristic
117C11×#95D411yescharacteristic
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124#66885—22no—
125#66885—22no—
126#66885—22no—
127#66881—22no—
128#66881—22no—
129#66881—22no—
130#66880—22no—
131#66880—22no—
132#66880—41no—
133#25202—111nomaximal, Sylow
134C24×C11C2×D411yescharacteristic
135C23×D11—21no—
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×C11C2×D411yescharacteristic
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11#4112yes—
147C22×C4×C11C2411yescharacteristic
148C2×C22⋊D11—24no—
149C2×C22⋊D11—42no—
150C2×C22⋊D11—42no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—42no—
159C22×Dic11—42no—
160C22×Dic11—42no—
161C22×Dic11—81no—
162C22×Dic11—81no—
163C22×Dic11—81no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44—21no—
169C2×D44C2×D412yes—
170C2×C4×D11—42no—
171C2×C4×D11—42no—
172C2×C4×D11—81no—
173C2×Dic22—21no—
174C2×Dic22—21no—
175C2×Dic22—21no—
176C2×Dic22—21no—
177C2×Dic22—21no—
178C2×Dic22—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—44no—
191C2×C8×C11#4112yes—
192C11×C22⋊C4—22no—
193C11×C22⋊C4SD1614yescomplemented
194C42×C11—21no—
195C42×C11—21no—
196C42×C11—21no—
197C42×C11—21no—
198C22⋊Dic11—42no—
199(C2×D11)⋊C4—24no—
200(C2×D11)⋊C4—42no—
201(C2×D11)⋊C4—42no—
202(C2×D11)⋊C4—81no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11—42no—
214C4⋊Dic11—42no—
215C4⋊Dic11—81no—
216C4⋊Dic11—81no—
217C4⋊Dic11—81no—
218C4⋊Dic11—81no—
219C4⋊Dic11C2×D412yes—
220C4⋊Dic11#4112yes—
221Dic11⋊C4—42no—
222Dic11⋊C4—42no—
223C4×Dic11—42no—
224#4314—44no—
225C2×#481—111no—
226C2×#465—111no—
227#2502—111no—
228#2361—111no—
229#2084—111no—
230#2071—111no—
231#2066—111no—
232#2055—111no—
233#1948—111no—
234#1927—111no—
235#1877—111no—
236#1872—111no—
237#1850D1111yescharacteristic, complemented
238#1802—111no—
239C2×#340—111no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11#12112yes—
245C23×C11C2×SD1612yes—
246C23×C11#13712yes—
247C23×C11C22×D411yescharacteristic
248C22×D11—22no—
249C22×D11—41no—
250C22×D11—41no—
251C22×D11—41no—
252C22×D11—41no—
253C22×D11—41no—
254C22×D11—41no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11#12112yes—
272C2×C4×C11C2×SD1612yes—
273C2×C4×C11C2×SD1612yes—
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11H(5,𝔽2)11yescharacteristic
279C2×C4×C112−1+411yescharacteristic
280C22⋊D11—48no—
281C2×Dic11—22no—
282C2×Dic11—22no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
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—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—84no—
303C2×Dic11—84no—
304D44—22no—
305D44—22no—
306D44—41no—
307D44—41no—
308C4×D11—84no—
309Dic22—41no—
310Dic22—41no—
311Dic22—41no—
312Dic22—41no—
313C8×C11—22no—
314C8×C11—41no—
315C8×C11—41no—
316C8×C11—41no—
317C22×SD16—111no—
318C23×C8C2×D1111yescharacteristic
319C2×C22⋊Q8—111no—
320C2×#121—111no—
321C2×C4×D4—111no—
322C2×C4×D4—221no—
323C22×C4⋊C4—111no—
324C22×C4⋊C4—111no—
325#481—224no—
326#465—224no—
327C2×#106—111no—
328C2×#106—111no—
329C2×#106—111no—
330C2×C4⋊C8C2×D1111yescharacteristic
331C2×C4⋊C8C2×D1111yescharacteristic
332C2×#103—111no—
333C2×#103—111no—
334C2×#103—111no—
335C2×#102—111no—
336C2×#102—111no—
337C2×#102—111no—
338C2×C22⋊C8C2×D1111yescharacteristic
339#398—221no—
340#398—221no—
341#391—111no—
342#391—111no—
343#390—111no—
344#389—111no—
345#388—221no—
346#386—221no—
347#385—221no—
348#385—221no—
349#385—221no—
350#384—111no—
351#384—111no—
352C4×C4⋊C4—111no—
353C4×C22⋊C4C2×D1111yescharacteristic
354#340—111no—
355#340—111no—
356#340—111no—
357#340—111no—
358#340—111no—
359#340—111no—
360#336C2×D1111yescharacteristic
361#336C2×D1111yescharacteristic
362C22×C11—22no—
363C22×C11—22no—
364C22×C11—22no—
365C22×C11—22no—
366C22×C11—22no—
367C22×C11—22no—
368C22×C11#46114yes—
369C22×C11C2×#12111yescharacteristic
370C22×C11#54611yescharacteristic
371C22×C11#54711yescharacteristic
372C22×C11C22×SD1611yescharacteristic
373C22×C11C2×#13711yescharacteristic
374C22×C11#57611yescharacteristic
375C22×C11#57711yescharacteristic
376C2×D11—42no—
377C2×D11—42no—
378C2×D11—42no—
379C2×D11—81no—
380C2×D11—81no—
381C2×D11—81no—
382C2×D11—81no—
383C4×C11—22no—
384C4×C11—22no—
385C4×C11—22no—
386C4×C11—41no—
387C4×C11—41no—
388C4×C11#52911yescharacteristic
389C4×C11#53911yescharacteristic
390C4×C11#54611yescharacteristic
391C4×C11#54711yescharacteristic
392Dic11—42no—
393Dic11—42no—
394Dic11—81no—
395Dic11—81no—
396Dic11—81no—
397Dic11—81no—
398Dic11—81no—
399C22×Q8—111no—
400C22×D4—111no—
401C22×D4—221no—
402C23×C4—221no—
403C23×C4—221no—
404C23×C4—221no—
405C23×C4C22×D1111yescharacteristic
406C2×SD16—222no—
407C2×SD16—222no—
408C2×SD16—441no—
409C22×C8—22no—
410C22×C8—22no—
411C22×C8—41no—
412C22×C8C22×D1111yescharacteristic
413C22×C8C22×D1111yescharacteristic
414C22×C8C22×D1111yescharacteristic
415C22×C8C22×D1111yescharacteristic
416C22⋊Q8—222no—
417C22⋊Q8—222no—
418#121—114no—
419#121—222no—
420C4×D4—222no—
421C4×D4—441no—
422C4×D4—444no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—111no—
429C2×C4⋊C4—222no—
430C2×C4⋊C4—222no—
431C2×C4⋊C4—222no—
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⋊C4—221no—
439C2×C4⋊C4—221no—
440C2×C4⋊C4—441no—
441C2×C22⋊C4—221no—
442C2×C22⋊C4—221no—
443C2×C22⋊C4—221no—
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C22⋊C4D4411yescharacteristic
447C2×C22⋊C4D4411yescharacteristic
448C2×C42—221no—
449C2×C42C22×D1111yescharacteristic
450C2×C42C22×D1111yescharacteristic
451#106—222no—
452#106—222no—
453#106—222no—
454C4⋊C8—22no—
455C4⋊C8—41no—
456#103—222no—
457#103—222no—
458#103—441no—
459#102—222no—
460#102—222no—
461#102—222no—
462C22⋊C8—22no—
463#95—221no—
464#95—221no—
465#95—221no—
466#95—221no—
467#95—221no—
468#95—221no—
469#95D4411yescharacteristic
470#95D4411yescharacteristic
471C2×C11—24no—
472C2×C11#242511yescharacteristic
473C2×C11C2×#46111yescharacteristic
474C2×C11#304511yescharacteristic
475C2×C11#329511yescharacteristic
476C2×C11#331611yescharacteristic
477C2×C11#333511yescharacteristic
478C2×C11#334611yescharacteristic
479D11—82no—
480C24—221no—
481C24C2×D4411yescharacteristic
482C2×Q8—221no—
483C2×Q8—221no—
484C2×Q8—221no—
485C2×Q8—221no—
486C2×Q8—221no—
487C2×Q8—221no—
488C2×D4—112no—
489C2×D4—224no—
490C2×D4—221no—
491C2×D4—221no—
492C2×D4—221no—
493C2×D4—221no—
494C2×D4—221no—
495C2×D4—442no—
496C2×D4—442no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—221no—
508C22×C4—442no—
509C22×C4—442no—
510C22×C4—442no—
511C22×C4—442no—
512C22×C4—442no—
513C22×C4—881no—
514C22×C4—881no—
515C22×C4—881no—
516C22×C4—881no—
517C22×C4C2×D4411yescharacteristic
518C22×C4C2×D4411yescharacteristic
519C22×C4C2×D4411yescharacteristic
520C22×C4C2×D4411yescharacteristic
521C22×C4C2×D4411yescharacteristic
522C22×C4D4×D1112yes—
523C22×C4#434312yes—
524C22×C4C23×D1111yescharacteristic
525SD16—444no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—44no—
538C2×C8#434112yes—
539C4⋊C4—112no—
540C4⋊C4—112no—
541C4⋊C4—221no—
542C4⋊C4—221no—
543C4⋊C4—221no—
544C4⋊C4—221no—
545C4⋊C4—221no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C4⋊C4—221no—
549C4⋊C4—221no—
550C4⋊C4—221no—
551C4⋊C4—442no—
552C4⋊C4—442no—
553C4⋊C4—442no—
554C4⋊C4—442no—
555C4⋊C4—881no—
556C4⋊C4—881no—
557C4⋊C4—881no—
558C4⋊C4—881no—
559C22⋊C4—22no—
560C22⋊C4—224no—
561C22⋊C4—442no—
562C22⋊C4—442no—
563C22⋊C4—442no—
564C22⋊C4—881no—
565C22⋊C4#431414yescomplemented
566C42—21no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—442no—
571C11#2520211yescharacteristic, complemented, Sylow
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—222no—
577C23—441no—
578C23—441no—
579C23—441no—
580C23—441no—
581C23—441no—
582C23—441no—
583C23#6694812yes—
584C23C2×#431412yes—
585C23#6696212yes—
586C23C22×D4411yescharacteristic
587Q8—441no—
588Q8—441no—
589Q8—441no—
590Q8—441no—
591D4—222no—
592D4—222no—
593D4—448no—
594D4—441no—
595D4—441no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—222no—
613C2×C4—222no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
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—884no—
634C2×C4—884no—
635C2×C4—884no—
636C2×C4#6694812yes—
637C2×C4C2×#431412yes—
638C2×C4C2×#431412yes—
639C2×C4C2×D4×D1111yescharacteristic
640C2×C4C2×#434111yescharacteristic
641C2×C4#6703711yescharacteristic
642C2×C4C2×#434311yescharacteristic
643C2×C4#41×D1111yescharacteristic
644C2×C4#6704311yescharacteristic
645C8—22no—
646C8—41no—
647C8—41no—
648C8—41no—
649C22—22no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—442no—
656C22—442no—
657C22—442no—
658C22—881no—
659C22—881no—
660C22—881no—
661C22—881no—
662C22#1062245414yes—
663C22C2×#6694811yescharacteristic
664C22#1062308511yescharacteristic
665C22#1062308611yescharacteristic
666C22C22×#431411yescharacteristic
667C22C2×#6696211yescharacteristic
668C22#1062328211yescharacteristic
669C22#1062328311yescharacteristic
670C4—22no—
671C4—22no—
672C4—22no—
673C4—41no—
674C4—41no—
675C4—442no—
676C4—442no—
677C4—881no—
678C4—881no—
679C4—881no—
680C4—881no—
681C4—881no—
682C4#1062312211yescharacteristic
683C4#1062315511yescharacteristic
684C4#1062317611yescharacteristic
685C4#1062318611yescharacteristic
686C2—24no—
687C2—882no—
688C2#1307216511yescharacteristic
689C2C2×#1062245411yescharacteristic
690C2#1307815711yescharacteristic
691C2#1308044111yescharacteristic
692C2#1308072911yescharacteristic
693C2#1308097411yescharacteristic
694C2#1308110311yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1850C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#1850D11
hypocenterC11#25202
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
3. #13073094C2semidirect
5. #13070094C2semidirect
6. #13070021C2semidirect
7. #13069996C2semidirect
8. #13069934C2semidirect
9. #13069380C2semidirect
10. #13069251C2semidirect
11. #13068949C2semidirect
12. #13068921C2semidirect
13. #13068617C2semidirect
14. C2×#10622189C2semidirect
15. C11×#1850C2semidirect
193. C11×C22⋊C4SD16semidirect
237. #1850D11semidirect
565. C22⋊C4#4314semidirect
571. C11#25202semidirect

Maximal subgroups

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

subgroupindex
C2×#106223482
C2×#106227272
#130730942
#130716302
#130700942
#130700212
#130699962
#130699342
#130693802
#130692512
#130689492
#130689212
#130686172
C2×#106221892
C11×#18502
#2520211