Finite Group Databasebeta

← #14801969

Subgroups — #14801969

Order 2816.

848 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622336C211yesmaximal, characteristic, complemented
2C2×#10622727C211yesmaximal, characteristic
3#13073078C211yesmaximal, characteristic
4#13071641C211yesmaximal, characteristic, complemented
5#13070094C211yesmaximal, characteristic, complemented
6#13070036C211yesmaximal, characteristic, complemented
7#13070003C211yesmaximal, characteristic, complemented
8#13069934C211yesmaximal, characteristic, complemented
9#13069386C211yesmaximal, characteristic, complemented
10#13069244C211yesmaximal, characteristic, complemented
11#13068970C211yesmaximal, characteristic, complemented
12#13068936C211yesmaximal, characteristic
13#13068622C211yesmaximal, characteristic, complemented
14#13068333C211yesmaximal, characteristic, complemented
15C11×#1850C211yesmaximal, characteristic, complemented
16C23×C8×C11C2211yescharacteristic
17C2×#66983C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C2×#66977C2211yescharacteristic
21C22×#4314C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C4×C11×C22⋊C4C2211yescharacteristic
27#10622727—24no—
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32C2×#66881C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37#10622574—21no—
38#10622574—21no—
39#10622558—21no—
40#10622557—21no—
41#10622552C2211yescharacteristic
42#10622552C2211yescharacteristic
43#10622549C2211yescharacteristic
44#10622548C2211yescharacteristic
45C4×C4⋊Dic11C2211yescharacteristic
46#10622542C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622336—24no—
49#10622283—21no—
50#10622283—21no—
51#10622265—21no—
52#10622262—21no—
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C22×D44C2311yescharacteristic
64C22×Dic22C2311yescharacteristic
65C22×C8×C11—22no—
66C22×C8×C11—22no—
67C22×C8×C11—41no—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C2×C11×C22⋊C4D411yescharacteristic
73C2×C11×C22⋊C4D411yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79#66983—22no—
80#66983—22no—
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—
86#66979—22no—
87#66979—22no—
88#66979—22no—
89#66979—41no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98#66977—22no—
99#66977D414yes—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11—21no—
107C2×#4314—22no—
108C2×#4314—22no—
109C2×#4314—41no—
110C4×Dic22—22no—
111C4×Dic22—41no—
112C11×C4⋊C8—22no—
113C11×C4⋊C8—41no—
114C11×C22⋊C8—22no—
115C11×#95D411yescharacteristic
116C11×#95D411yescharacteristic
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123#66885—22no—
124#66885—22no—
125#66885—41no—
126#66882—22no—
127#66881—22no—
128#66881—22no—
129#66880—22no—
130#66880—22no—
131#66880—22no—
132#25203—111nomaximal, Sylow
133C24×C11C2×D411yescharacteristic
134C23×D11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11#4112yes—
146C22×C4×C11C2411yescharacteristic
147C2×C22⋊D11—42no—
148C2×C22⋊D11—81no—
149C2×C22⋊D11—81no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22C2×D412yes—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—44no—
181C2×C8×C11#4112yes—
182C11×C22⋊C4—22no—
183C11×C22⋊C4—41no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C22⋊Dic11—24no—
189C22⋊Dic11—42no—
190C22⋊Dic11—42no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—81no—
195(C2×D11)⋊C4—81no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—81no—
207C4⋊Dic11—81no—
208C4⋊Dic11C2×D412yes—
209C4⋊Dic11#4112yes—
210Dic11⋊C4—24no—
211Dic11⋊C4—42no—
212Dic11⋊C4—42no—
213C4×Dic11—42no—
214C4×Dic11—42no—
215C4×Dic11—42no—
216C4×Dic11—42no—
217#4314—44no—
218C2×#485—111no—
219C2×#465—111no—
220#2500—111no—
221#2362—111no—
222#2084—111no—
223#2074—111no—
224#2067—111no—
225#2055—111no—
226#1949—111no—
227#1926—111no—
228#1880—111no—
229#1875—111no—
230#1850D1111yescharacteristic, complemented
231#1803—111no—
232#1735—111no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11#12112yes—
240C23×C11C22×D411yescharacteristic
241C22×D11—41no—
242C22×D11—41no—
243C22×D11—41no—
244C22×D11—41no—
245C22×D11—41no—
246C22×D11—41no—
247C22×D11—41no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11#12112yes—
266C2×C4×C11#13512yes—
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11H(5,𝔽2)11yescharacteristic
272C2×C4×C112−1+411yescharacteristic
273C22⋊D11—84no—
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
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—
295D44—41no—
296D44—41no—
297D44—41no—
298D44—41no—
299Dic22—22no—
300Dic22—22no—
301Dic22—41no—
302Dic22—41no—
303C8×C11—22no—
304C8×C11—41no—
305C8×C11—41no—
306C8×C11—41no—
307C22×SD16—111no—
308C23×C8C2×D1111yescharacteristic
309C2×C22⋊Q8—111no—
310C2×#121—111no—
311C2×C4×Q8—111no—
312C2×#117—111no—
313C2×#117—111no—
314#485—224no—
315#465—224no—
316C2×#107—111no—
317C2×#106—111no—
318C2×#106—111no—
319C2×C4⋊C8C2×D1111yescharacteristic
320C2×C4⋊C8C2×D1111yescharacteristic
321C2×#103—111no—
322C2×#103—111no—
323C2×#103—111no—
324C2×#102—111no—
325C2×#102—111no—
326C2×#102—111no—
327C2×C22⋊C8C2×D1111yescharacteristic
328#394—221no—
329#394—221no—
330#391—111no—
331#390—111no—
332#390—111no—
333#389—111no—
334#388—221no—
335#388—221no—
336#388—221no—
337#388—221no—
338#387—221no—
339#384—111no—
340#382—111no—
341C4×C4⋊C4—111no—
342C4×C4⋊C4—221no—
343C4×C22⋊C4C2×D1111yescharacteristic
344#340—111no—
345#340—111no—
346#340—111no—
347#340—111no—
348#340—111no—
349#340—111no—
350#336C2×D1111yescharacteristic
351#336C2×D1111yescharacteristic
352C22×C11—22no—
353C22×C11—22no—
354C22×C11—22no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11C2×#12111yescharacteristic
360C22×C11#54611yescharacteristic
361C22×C11#54711yescharacteristic
362C22×C11C2×#13511yescharacteristic
363C22×C11#57511yescharacteristic
364C22×C11#57711yescharacteristic
365C22×C11#57711yescharacteristic
366C2×D11—81no—
367C2×D11—81no—
368C2×D11—81no—
369C2×D11—81no—
370C2×D11—81no—
371C2×D11—81no—
372C2×D11—81no—
373C4×C11—22no—
374C4×C11—22no—
375C4×C11—41no—
376C4×C11—41no—
377C4×C11—41no—
378C4×C11#52911yescharacteristic
379C4×C11#53911yescharacteristic
380C4×C11#54611yescharacteristic
381C4×C11#54711yescharacteristic
382Dic11—42no—
383Dic11—42no—
384Dic11—42no—
385Dic11—81no—
386Dic11—81no—
387Dic11—81no—
388Dic11—81no—
389C22×Q8—111no—
390C22×D4—111no—
391C22×D4—221no—
392C23×C4C22×D1111yescharacteristic
393C2×SD16—222no—
394C2×SD16—222no—
395C2×SD16—441no—
396C22×C8—22no—
397C22×C8—22no—
398C22×C8—41no—
399C22×C8C22×D1111yescharacteristic
400C22×C8C22×D1111yescharacteristic
401C22×C8C22×D1111yescharacteristic
402C22×C8C22×D1111yescharacteristic
403C22⋊Q8—114no—
404C22⋊Q8—222no—
405#121—222no—
406#121—222no—
407C4×Q8—222no—
408C4×Q8—441no—
409#117—222no—
410#117—222no—
411#117—222no—
412#117—441no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C22⋊C4—221no—
427C2×C22⋊C4—221no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4D4411yescharacteristic
433C2×C22⋊C4D4411yescharacteristic
434C2×C42—221no—
435C2×C42—221no—
436C2×C42—221no—
437C2×C42—221no—
438C2×C42C22×D1111yescharacteristic
439C2×C42C22×D1111yescharacteristic
440#107—222no—
441#106—222no—
442#106—222no—
443C4⋊C8—22no—
444C4⋊C8—41no—
445#103—222no—
446#103—222no—
447#103—222no—
448#102—222no—
449#102—222no—
450#102—441no—
451C22⋊C8—22no—
452#95—221no—
453#95—221no—
454#95—221no—
455#95—221no—
456#95—221no—
457#95—221no—
458#95D4411yescharacteristic
459#95D4411yescharacteristic
460C2×C11—42no—
461C2×C11#242511yescharacteristic
462C2×C11#303511yescharacteristic
463C2×C11#304311yescharacteristic
464C2×C11#330111yescharacteristic
465C2×C11#330711yescharacteristic
466C2×C11#334011yescharacteristic
467C2×C11#334811yescharacteristic
468D11—161no—
469C24—221no—
470C24C2×D4411yescharacteristic
471C2×Q8—112no—
472C2×Q8—221no—
473C2×Q8—221no—
474C2×Q8—221no—
475C2×Q8—221no—
476C2×Q8—221no—
477C2×D4—221no—
478C2×D4—221no—
479C2×D4—221no—
480C2×D4—221no—
481C2×D4—221no—
482C2×D4—221no—
483C2×D4—442no—
484C2×D4—881no—
485C2×D4—881no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4C2×D4411yescharacteristic
498C22×C4C2×D4411yescharacteristic
499C22×C4C2×D4411yescharacteristic
500C22×C4C2×D4411yescharacteristic
501C22×C4C2×D4411yescharacteristic
502C22×C4D4×D1112yes—
503C22×C4#434312yes—
504C22×C4C23×D1111yescharacteristic
505SD16—444no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—44no—
518C2×C8#434112yes—
519C4⋊C4—112no—
520C4⋊C4—112no—
521C4⋊C4—224no—
522C4⋊C4—221no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—442no—
533C4⋊C4—442no—
534C4⋊C4—881no—
535C4⋊C4—881no—
536C22⋊C4—22no—
537C22⋊C4—41no—
538C22⋊C4—224no—
539C22⋊C4—442no—
540C22⋊C4—442no—
541C22⋊C4—442no—
542C22⋊C4—442no—
543C22⋊C4—442no—
544C22⋊C4—881no—
545C22⋊C4—881no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—442no—
551C42—442no—
552C42—442no—
553C42—442no—
554C11#2520311yescharacteristic, complemented, Sylow
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—441no—
562C23—441no—
563C23—441no—
564C23—441no—
565C23—441no—
566C23—441no—
567C23—441no—
568C23#6694812yes—
569C23C22×D4411yescharacteristic
570Q8—222no—
571Q8—222no—
572Q8—441no—
573Q8—441no—
574D4—441no—
575D4—441no—
576D4—441no—
577D4—441no—
578D4—884no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—222no—
597C2×C4—222no—
598C2×C4—222no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4#6694812yes—
618C2×C4#6695712yes—
619C2×C4C2×D4×D1111yescharacteristic
620C2×C4C2×#434111yescharacteristic
621C2×C4#6703711yescharacteristic
622C2×C4C2×#434311yescharacteristic
623C2×C4#41×D1111yescharacteristic
624C2×C4#6704311yescharacteristic
625C8—22no—
626C8—41no—
627C8—41no—
628C8—41no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—881no—
637C22—881no—
638C22—881no—
639C22—881no—
640C22—881no—
641C22—881no—
642C22—881no—
643C22C2×#6694811yescharacteristic
644C22#1062308511yescharacteristic
645C22#1062308611yescharacteristic
646C22C2×#6695711yescharacteristic
647C22#1062327911yescharacteristic
648C22#1062328211yescharacteristic
649C22#1062328211yescharacteristic
650C4—22no—
651C4—22no—
652C4—41no—
653C4—41no—
654C4—41no—
655C4—442no—
656C4—442no—
657C4—442no—
658C4—881no—
659C4—881no—
660C4—881no—
661C4—881no—
662C4#1062312211yescharacteristic
663C4#1062315511yescharacteristic
664C4#1062317611yescharacteristic
665C4#1062318611yescharacteristic
666C2—42no—
667C2—1761no—
668C2#1307216511yescharacteristic
669C2#1307807311yescharacteristic
670C2#1307813811yescharacteristic
671C2#1308052011yescharacteristic
672C2#1308059411yescharacteristic
673C2#1308103011yescharacteristic
674C2#1308113311yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1850C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#1850D11
hypocenterC11#25203
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
1. C2×#10622336C2semidirect
4. #13071641C2semidirect
5. #13070094C2semidirect
6. #13070036C2semidirect
7. #13070003C2semidirect
8. #13069934C2semidirect
9. #13069386C2semidirect
10. #13069244C2semidirect
11. #13068970C2semidirect
13. #13068622C2semidirect
14. #13068333C2semidirect
15. C11×#1850C2semidirect
230. #1850D11semidirect
554. C11#25203semidirect

Maximal subgroups

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

subgroupindex
C2×#106223362
C2×#106227272
#130730782
#130716412
#130700942
#130700362
#130700032
#130699342
#130693862
#130692442
#130689702
#130689362
#130686222
#130683332
C11×#18502
#2520311