Finite Group Databasebeta

← #14801971

Subgroups — #14801971

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×#10622609C211yesmaximal, characteristic, complemented
2C2×#10622727C211yesmaximal, characteristic
3#13073074C211yesmaximal, characteristic
4#13071643C211yesmaximal, characteristic, complemented
5#13070096C211yesmaximal, characteristic, complemented
6#13070038C211yesmaximal, characteristic, complemented
7#13070005C211yesmaximal, characteristic, complemented
8#13069935C211yesmaximal, characteristic, complemented
9#13069383C211yesmaximal, characteristic, complemented
10#13069241C211yesmaximal, characteristic, complemented
11#13068972C211yesmaximal, characteristic, complemented
12#13068938C211yesmaximal, characteristic
13#13068794C211yesmaximal, characteristic, complemented
14#13068620C211yesmaximal, characteristic, complemented
15C11×#1735C211yesmaximal, characteristic, complemented
16C23×C8×C11C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C2×#66983C2211yescharacteristic
20C2×#66977C2211yescharacteristic
21C22×#4314C2211yescharacteristic
22C2×#66940C2211yescharacteristic
23C4×C22⋊Dic11C2211yescharacteristic
24C2×C22⋊(C11⋊C8)C2211yescharacteristic
25#10622727—24no—
26C2×#66885C2211yescharacteristic
27C2×#66881C2211yescharacteristic
28C2×#66880C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31#10622609—24no—
32#10622601C2211yescharacteristic
33#10622601C2211yescharacteristic
34#10622590C2211yescharacteristic
35#10622589C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37#10622587C2211yescharacteristic
38#10622586C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622572—21no—
46#10622572—21no—
47#10622558—21no—
48#10622557—21no—
49#10622553—21no—
50#10622553—21no—
51#10622546—21no—
52C4×Dic11⋊C4—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
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
70C11×#117—22no—
71C11×#117—22no—
72C11×#117—22no—
73C11×#117—41no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C42×C11—21no—
81C2×C42×C11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11D411yescharacteristic
84C2×C22⋊Dic11D411yescharacteristic
85#66983—22no—
86#66983—22no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94#66977—22no—
95#66977D414yes—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11C2311yescharacteristic
104C2×C4×Dic11C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C2×#4314—22no—
108C2×#4314—22no—
109C2×#4314—41no—
110#66940—22no—
111#66940—41no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95D411yescharacteristic
119C11⋊#95D411yescharacteristic
120C22⋊(C11⋊C8)—22no—
121#66885—22no—
122#66881—22no—
123#66880—22no—
124Dic11⋊C8—22no—
125Dic11⋊C8—41no—
126#66874—22no—
127#66874—22no—
128#66873—22no—
129#66873—41no—
130#66872—22no—
131#66871—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×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D412yes—
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×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
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—44no—
175C2×C8×C11#4112yes—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4#4112yes—
184C11×C22⋊C4—42no—
185C11×C22⋊C4—42no—
186C42×C11—42no—
187C42×C11—42no—
188C22⋊Dic11—22no—
189C22⋊Dic11—24no—
190C22⋊Dic11—41no—
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⋊Dic11C2×D412yes—
200Dic11⋊C4—24no—
201Dic11⋊C4—42no—
202Dic11⋊C4—42no—
203Dic11⋊C4—81no—
204Dic11⋊C4—81no—
205C4×Dic11—21no—
206C4×Dic11—21no—
207C4×Dic11—21no—
208C4×Dic11—21no—
209C4×Dic11—42no—
210C4×Dic11—42no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
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#1850—111no—
231#1803—111no—
232#1735D1111yescharacteristic, complemented
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—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11#12112yes—
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—21no—
275C2×Dic11—21no—
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11#13512yes—
295D44—41no—
296D44—41no—
297D44—41no—
298D44—41no—
299Dic22—22no—
300Dic22—22no—
301Dic22—41no—
302Dic22—41no—
303C8×C11—22no—
304C8×C11—41no—
305C11⋊C8—41no—
306C11⋊C8—41no—
307C22×SD16—111no—
308C23×C8C2×D1111yescharacteristic
309C2×C22⋊Q8—111no—
310C2×#121—111no—
311C2×C4×Q8—111no—
312C2×#117C2×D1111yescharacteristic
313C2×#117C2×D1111yescharacteristic
314#485—224no—
315#465—224no—
316C2×#107—111no—
317C2×#106—111no—
318C2×#106—111no—
319C2×C4⋊C8—111no—
320C2×C4⋊C8—111no—
321C2×#103—111no—
322C2×#103—111no—
323C2×#103—111no—
324C2×#102—111no—
325C2×#102—111no—
326C2×#102—111no—
327C2×C22⋊C8—111no—
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⋊C4—111no—
344#340—111no—
345#340—111no—
346#340C2×D1111yescharacteristic
347#340C2×D1111yescharacteristic
348#340C2×D1111yescharacteristic
349#340C2×D1111yescharacteristic
350#336—111no—
351#336—111no—
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—42no—
375C4×C11—81no—
376C4×C11—81no—
377C4×C11—81no—
378C4×C11#52911yescharacteristic
379C4×C11#53911yescharacteristic
380C4×C11#54611yescharacteristic
381C4×C11#54711yescharacteristic
382Dic11—22no—
383Dic11—41no—
384Dic11—41no—
385Dic11—42no—
386Dic11—42no—
387Dic11—41no—
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×C8—111no—
400C22×C8—111no—
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—22no—
410#117—22no—
411#117—22no—
412#117—41no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4C22×D1111yescharacteristic
421C2×C4⋊C4C22×D1111yescharacteristic
422C2×C4⋊C4C22×D1111yescharacteristic
423C2×C4⋊C4C22×D1111yescharacteristic
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—111no—
427C2×C22⋊C4—111no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C42—21no—
435C2×C42—21no—
436C2×C42—111no—
437C2×C42—111no—
438C2×C42—221no—
439C2×C42—221no—
440#107—222no—
441#106—222no—
442#106—222no—
443C4⋊C8—222no—
444C4⋊C8—441no—
445#103—222no—
446#103—222no—
447#103—222no—
448#102—222no—
449#102—222no—
450#102—441no—
451C22⋊C8—222no—
452#95—111no—
453#95—111no—
454#95—221no—
455#95—221no—
456#95—221no—
457#95—221no—
458#95—221no—
459#95—221no—
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—
470C24D4×D1111yescharacteristic
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—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—111no—
495C22×C4—111no—
496C22×C4—111no—
497C22×C4—111no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4#433912yes—
502C22×C4D4×D1111yescharacteristic
503C22×C4D4×D1112yes—
504C22×C4C23×D1111yescharacteristic
505SD16—444no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—44no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8#433912yes—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—112no—
527C4⋊C4—224no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—442no—
532C4⋊C4—442no—
533C4⋊C4—881no—
534C4⋊C4—881no—
535C4⋊C4#433912yes—
536C22⋊C4—42no—
537C22⋊C4—42no—
538C22⋊C4—222no—
539C22⋊C4—224no—
540C22⋊C4—442no—
541C22⋊C4—442no—
542C22⋊C4—441no—
543C22⋊C4—442no—
544C22⋊C4—881no—
545C22⋊C4—881no—
546C42—42no—
547C42—42no—
548C42—221no—
549C42—221no—
550C42—221no—
551C42—221no—
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#6693712yes—
569C23C2×D4×D1111yescharacteristic
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—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—112no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—222no—
601C2×C4—222no—
602C2×C4—221no—
603C2×C4—221no—
604C2×C4—221no—
605C2×C4—221no—
606C2×C4—221no—
607C2×C4—221no—
608C2×C4—221no—
609C2×C4—221no—
610C2×C4—221no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4#6693712yes—
619C2×C4C2×#433911yescharacteristic
620C2×C4C2×#433911yescharacteristic
621C2×C4C2×#433911yescharacteristic
622C2×C4C2×D4×D1111yescharacteristic
623C2×C4#6703711yescharacteristic
624C2×C4#6704011yescharacteristic
625C8—22no—
626C8—41no—
627C8—441no—
628C8—441no—
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×#6693711yescharacteristic
644C22#1062302111yescharacteristic
645C22#1062303811yescharacteristic
646C22D11×#13511yescharacteristic
647C22#1062329911yescharacteristic
648C22#1062330111yescharacteristic
649C22#1062330111yescharacteristic
650C4—22no—
651C4—42no—
652C4—81no—
653C4—81no—
654C4—81no—
655C4—222no—
656C4—441no—
657C4—442no—
658C4—441no—
659C4—442no—
660C4—441no—
661C4—881no—
662C4#1062301011yescharacteristic
663C4#1062302111yescharacteristic
664C4#1062303811yescharacteristic
665C4#1062304611yescharacteristic
666C2—42no—
667C2—1761no—
668C2#1307216711yescharacteristic
669C2#1307806911yescharacteristic
670C2#1307814011yescharacteristic
671C2#1308051911yescharacteristic
672C2#1308058811yescharacteristic
673C2#1308102511yescharacteristic
674C2#1308112711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1735C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#1735D11
hypocenterC11#25203
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1735

Complements

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

NH ≅ G/Ntype
1. C2×#10622609C2semidirect
4. #13071643C2semidirect
5. #13070096C2semidirect
6. #13070038C2semidirect
7. #13070005C2semidirect
8. #13069935C2semidirect
9. #13069383C2semidirect
10. #13069241C2semidirect
11. #13068972C2semidirect
13. #13068794C2semidirect
14. #13068620C2semidirect
15. C11×#1735C2semidirect
232. #1735D11semidirect
554. C11#25203semidirect

Maximal subgroups

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

subgroupindex
C2×#106226092
C2×#106227272
#130730742
#130716432
#130700962
#130700382
#130700052
#130699352
#130693832
#130692412
#130689722
#130689382
#130687942
#130686202
C11×#17352
#2520311