Finite Group Databasebeta

← #14795076

Subgroups — #14795076

Order 2816.

912 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622503C211yesmaximal, characteristic, complemented
2C2×#10622318C211yesmaximal, characteristic, complemented
3#13076967C211yesmaximal, characteristic, complemented
4#13071124C211yesmaximal, characteristic
5#13070048C211yesmaximal, characteristic, complemented
6#13070045C211yesmaximal, characteristic, complemented
7#13069808C211yesmaximal, characteristic
8#13069807C211yesmaximal, characteristic
9#13069566C211yesmaximal, characteristic, complemented
10#13069376C211yesmaximal, characteristic, complemented
11#13069356C211yesmaximal, characteristic, complemented
12#13069313C211yesmaximal, characteristic, complemented
13#13069312C211yesmaximal, characteristic, complemented
14#13068615C211yesmaximal, characteristic, complemented
15C11×#1944C211yesmaximal, characteristic, complemented
16C2×#66949—21no—
17C2×#66948C2211yescharacteristic
18C2×#66946—21no—
19C2×#66946C2211yescharacteristic
20C2×#66941C2211yescharacteristic
21C2×C42×D11C2211yescharacteristic
22C2×C11×#107C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×#97C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33#10622603—21no—
34#10622600C2211yescharacteristic
35#10622600C2211yescharacteristic
36#10622600C2211yescharacteristic
37#10622589C2211yescharacteristic
38C4⋊C4×Dic11C2211yescharacteristic
39#10622585—21no—
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44#10622552C2211yescharacteristic
45#10622541C2211yescharacteristic
46C2×#66867C2211yescharacteristic
47#10622503—24no—
48#10622318—24no—
49#10622280—21no—
50#10622279—21no—
51#10622278—21no—
52#10622259—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×D44—21no—
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×C4×D11D411yescharacteristic
65C22×C4×D11D411yescharacteristic
66C22×C4×D11C2311yescharacteristic
67C22×Dic22—21no—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
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×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11D411yescharacteristic
93C2×C4×Dic11D411yescharacteristic
94C2×C4×Dic11C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97#66949—44no—
98#66948—22no—
99#66948—22no—
100#66946—22no—
101#66946—22no—
102#66946—44no—
103#66941—22no—
104#66941—22no—
105C42×D11—22no—
106C42×D11—22no—
107C11×#107—22no—
108C11×#106—22no—
109C11×#97—22no—
110C11×#95—21no—
111C11×#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117#66885—22no—
118#66885—22no—
119(C2×D11)⋊C8—22no—
120(C2×D11)⋊C8—22no—
121Dic11⋊C8—22no—
122Dic11⋊C8D414yescomplemented
123#66873—22no—
124#66873—22no—
125#66872—22no—
126#66871—22no—
127#66867—22no—
128#24709—111nomaximal, Sylow
129C23×D11—21no—
130C23×D11C2×D411yescharacteristic
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2411yescharacteristic
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11C2×D411yescharacteristic
142C22×Dic11C2×D411yescharacteristic
143C22×Dic11C2×D411yescharacteristic
144C2×D44—24no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—42no—
151C2×D44—42no—
152C2×D44#4112yes—
153C2×C4×D11—22no—
154C2×C4×D11—22no—
155C2×C4×D11—22no—
156C2×C4×D11—22no—
157C2×C4×D11—22no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11—41no—
165C2×C4×D11—42no—
166C2×C4×D11—42no—
167C2×C4×D11—42no—
168C2×Dic22—42no—
169C2×Dic22—42no—
170C2×Dic22—42no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11C2×D412yes—
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—21no—
184C11×C4⋊C4—42no—
185C11×C4⋊C4—42no—
186C11×C4⋊C4#4112yes—
187C42×C11—21no—
188C42×C11—21no—
189(C2×D11)⋊C4—24no—
190(C2×D11)⋊C4—42no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—42no—
195(C2×D11)⋊C4—42no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202Dic11⋊C4—42no—
203Dic11⋊C4—42no—
204Dic11⋊C4—42no—
205Dic11⋊C4—42no—
206C4×Dic11—22no—
207C4×Dic11—22no—
208C4×Dic11—42no—
209C4×Dic11C2×D412yes—
210C4×Dic11#4112yes—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8C2×D412yes—
217C2×#474—111no—
218C2×#432—111no—
219#2857—111no—
220C4×#121—111no—
221#2076—111no—
222#2076—111no—
223#2034—111no—
224#2034—111no—
225#1988—111no—
226#1948—111no—
227#1944—111no—
228#1944D1111yescharacteristic, complemented
229#1936—111no—
230#1936—111no—
231#1802—111no—
232C23×C11C22×D411yescharacteristic
233C22×D11—21no—
234C22×D11—21no—
235C22×D11—21no—
236C22×D11—21no—
237C22×D11—21no—
238C22×D11—21no—
239C22×D11—22no—
240C22×D11—41no—
241C22×D11—41no—
242C22×D11—41no—
243C22×D11—41no—
244C22×D11—41no—
245C22×D11—41no—
246C22×D11#13712yes—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—22no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—41no—
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×C11C22×D411yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C112−1+411yescharacteristic
270C2×C4×C112−1+411yescharacteristic
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—41no—
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#12112yes—
286C2×Dic11#12112yes—
287C2×Dic11AGL(1,ℤ/8)12yes—
288C2×Dic11AGL(1,ℤ/8)12yes—
289D44—22no—
290D44—22no—
291D44—48no—
292D44—41no—
293D44—41no—
294C4×D11—44no—
295C4×D11—41no—
296C4×D11—41no—
297C4×D11—41no—
298C4×D11—41no—
299C4×D11—44no—
300C4×D11—84no—
301Dic22—84no—
302C8×C11—22no—
303C8×C11—41no—
304C11⋊C8—22no—
305C11⋊C8—41no—
306C2×C4⋊Q8—111no—
307C2×C22⋊Q8—221no—
308C2×#121—111no—
309C2×C4×D4—111no—
310C2×C4×D4—221no—
311C22×C42—111no—
312#474—224no—
313#432—224no—
314C2×#107—111no—
315C2×#107C2×D1111yescharacteristic
316C2×#106—111no—
317C2×#106C2×D1111yescharacteristic
318C2×C4⋊C8—111no—
319C2×C4⋊C8—111no—
320C2×#102—111no—
321C2×#102—111no—
322C2×#102—111no—
323C2×#102—111no—
324C2×C22⋊C8—111no—
325C2×C22⋊C8—111no—
326C2×#97—111no—
327C2×#97C2×D1111yescharacteristic
328#391—221no—
329#390—111no—
330#389—111no—
331#389—221no—
332#389C2×D1111yescharacteristic
333#389C2×D1111yescharacteristic
334#388—221no—
335#386—221no—
336#384—111no—
337#380—111no—
338#380—111no—
339#380—111no—
340#380—221no—
341C4×C4⋊C4—111no—
342C4×C22⋊C4—221no—
343#340—111no—
344#340—111no—
345#340—111no—
346#340—111no—
347#340—111no—
348#340—111no—
349#340C2×D1111yescharacteristic
350#340C2×D1111yescharacteristic
351C22×C11C2×#12111yescharacteristic
352C22×C11#52511yescharacteristic
353C22×C11#53611yescharacteristic
354C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
355C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
356C22×C11C2×#13711yescharacteristic
357C22×C11#57511yescharacteristic
358C2×D11—22no—
359C2×D11—22no—
360C2×D11—22no—
361C2×D11—41no—
362C2×D11—41no—
363C2×D11—41no—
364C2×D11—41no—
365C2×D11—42no—
366C2×D11—42no—
367C2×D11—42no—
368C2×D11—81no—
369C2×D11—81no—
370C2×D11—81no—
371C2×D11—81no—
372C4×C11—42no—
373C4×C11—41no—
374C4×C11—41no—
375C4×C11—81no—
376C4×C11—81no—
377C4×C11—81no—
378C4×C11#54711yescharacteristic
379C4×C11#54811yescharacteristic
380C4×C11#55211yescharacteristic
381C4×C11#55611yescharacteristic
382Dic11—22no—
383Dic11—41no—
384Dic11—81no—
385Dic11—81no—
386Dic11—81no—
387Dic11#46914yes—
388C22×Q8—221no—
389C22×D4—111no—
390C22×D4—221no—
391C23×C4—111no—
392C23×C4—111no—
393C23×C4—111no—
394C23×C4—221no—
395C22×C8—111no—
396C22×C8—111no—
397C22×C8C22×D1111yescharacteristic
398C22×C8C22×D1111yescharacteristic
399C4⋊Q8—222no—
400C4⋊Q8—222no—
401C22⋊Q8—444no—
402#121—222no—
403#121—222no—
404C4×D4—222no—
405C4×D4—222no—
406C4×D4—444no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4C22×D1111yescharacteristic
417C2×C4⋊C4C22×D1111yescharacteristic
418C2×C4⋊C4C22×D1111yescharacteristic
419C2×C4⋊C4C22×D1111yescharacteristic
420C2×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C22⋊C4—221no—
427C2×C42—111no—
428C2×C42—111no—
429C2×C42—111no—
430C2×C42—222no—
431C2×C42—222no—
432C2×C42—221no—
433C2×C42C22×D1111yescharacteristic
434#107—22no—
435#107—222no—
436#106—22no—
437#106—222no—
438C4⋊C8—114no—
439C4⋊C8—222no—
440#102—222no—
441#102—222no—
442#102—222no—
443#102—222no—
444C22⋊C8—222no—
445C22⋊C8—222no—
446#97—22no—
447#97—222no—
448#95—21no—
449#95—21no—
450#95—221no—
451#95—221no—
452#95—221no—
453#95—221no—
454#95—221no—
455C2×C11#241511yescharacteristic
456C2×C11C2×#46911yescharacteristic
457C2×C11#305611yescharacteristic
458C2×C11#311011yescharacteristic
459C2×C11#311511yescharacteristic
460C2×C11#323511yescharacteristic
461C2×C11#323911yescharacteristic
462D11—42no—
463D11—82no—
464C24—111no—
465C24—221no—
466C2×Q8—442no—
467C2×Q8—442no—
468C2×Q8—442no—
469C2×D4—112no—
470C2×D4—224no—
471C2×D4—221no—
472C2×D4—221no—
473C2×D4—221no—
474C2×D4—221no—
475C2×D4—221no—
476C2×D4—442no—
477C2×D4—442no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—111no—
483C22×C4—111no—
484C22×C4—111no—
485C22×C4—222no—
486C22×C4—222no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4—222no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—441no—
500C22×C4—442no—
501C22×C4—442no—
502C22×C4—442no—
503C22×C4D4×D1111yescharacteristic
504C22×C4D4×D1111yescharacteristic
505C22×C4C23×D1111yescharacteristic
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—112no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8D4×D1112yes—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—42no—
526C4⋊C4—42no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—442no—
534C4⋊C4—442no—
535C4⋊C4—442no—
536C4⋊C4—442no—
537C4⋊C4#433912yes—
538C22⋊C4—224no—
539C22⋊C4—442no—
540C22⋊C4—442no—
541C22⋊C4—442no—
542C22⋊C4—442no—
543C22⋊C4—442no—
544C22⋊C4—442no—
545C42—21no—
546C42—21no—
547C42—112no—
548C42—112no—
549C42—222no—
550C42—222no—
551C42—442no—
552C11#2470911yescharacteristic, complemented, Sylow
553C23—112no—
554C23—221no—
555C23—221no—
556C23—221no—
557C23—221no—
558C23—221no—
559C23—221no—
560C23—222no—
561C23—441no—
562C23—441no—
563C23—441no—
564C23—441no—
565C23—441no—
566C23—441no—
567C23C2×D4×D1111yescharacteristic
568Q8—884no—
569D4—222no—
570D4—222no—
571D4—448no—
572D4—441no—
573D4—441no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—112no—
593C2×C4—112no—
594C2×C4—112no—
595C2×C4—112no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—221no—
601C2×C4—444no—
602C2×C4—444no—
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—884no—
617C2×C4C2×#433911yescharacteristic
618C2×C4C2×D4×D1111yescharacteristic
619C2×C4#6704011yescharacteristic
620C2×C4#6704011yescharacteristic
621C2×C4#41×D1111yescharacteristic
622C2×C4#41×D1111yescharacteristic
623C8—22no—
624C8—41no—
625C8—222no—
626C8—441no—
627C22—222no—
628C22—222no—
629C22—222no—
630C22—441no—
631C22—441no—
632C22—441no—
633C22—441no—
634C22—442no—
635C22—442no—
636C22—442no—
637C22—881no—
638C22—881no—
639C22—881no—
640C22—881no—
641C22#1062307811yescharacteristic
642C22D11×#12111yescharacteristic
643C22#1062325511yescharacteristic
644C22D11×AGL(1,ℤ/8)11yescharacteristic
645C22D11×AGL(1,ℤ/8)11yescharacteristic
646C22D11×#13711yescharacteristic
647C22#1062330811yescharacteristic
648C4—42no—
649C4—41no—
650C4—41no—
651C4—81no—
652C4—81no—
653C4—81no—
654C4—114no—
655C4—222no—
656C4—441no—
657C4—881no—
658C4—881no—
659C4—881no—
660C4#1062303811yescharacteristic
661C4#1062309911yescharacteristic
662C4#1062316411yescharacteristic
663C4#1062322411yescharacteristic
664C2—442no—
665C2—882no—
666C2#1307204411yescharacteristic
667C2D11×#46911yescharacteristic
668C2#1307824511yescharacteristic
669C2#1307871311yescharacteristic
670C2#1307876511yescharacteristic
671C2#1307981511yescharacteristic
672C2#1307984711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1944C2
socleC23×C11C22×D4
prime radicalC2×#66948C22
hypercenter#1944D11
hypocenterC11#24709
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1944

Complements

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

NH ≅ G/Ntype
1. C2×#10622503C2semidirect
2. C2×#10622318C2semidirect
3. #13076967C2semidirect
5. #13070048C2semidirect
6. #13070045C2semidirect
9. #13069566C2semidirect
10. #13069376C2semidirect
11. #13069356C2semidirect
12. #13069313C2semidirect
13. #13069312C2semidirect
14. #13068615C2semidirect
15. C11×#1944C2semidirect
122. Dic11⋊C8D4semidirect
228. #1944D11semidirect
552. C11#24709semidirect

Maximal subgroups

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

subgroupindex
C2×#106225032
C2×#106223182
#130769672
#130711242
#130700482
#130700452
#130698082
#130698072
#130695662
#130693762
#130693562
#130693132
#130693122
#130686152
C11×#19442
#2470911