Finite Group Databasebeta

← #14772194

Subgroups — #14772194

Order 2816.

986 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4314C211yesmaximal, characteristic
2C2×#10622465C211yesmaximal, characteristic
3C2×#10622465C211yesmaximal, characteristic
4#13071535C211yesmaximal, characteristic, complemented
5#13071525C211yesmaximal, characteristic
6#13069345C211yesmaximal, characteristic, complemented
7#13068871C211yesmaximal, characteristic, complemented
8#13068869C211yesmaximal, characteristic, complemented
9#13068864C211yesmaximal, characteristic
10#13068862C211yesmaximal, characteristic
11#13068777C211yesmaximal, characteristic, complemented
12#13068630C211yesmaximal, characteristic, complemented
13#13068625C211yesmaximal, characteristic
14C8×Dic11⋊C4C211yesmaximal, characteristic, complemented
15C11×#1941C211yesmaximal, characteristic, complemented
16C22×#4314C2211yescharacteristic
17C2×#66946C2211yescharacteristic
18C2×#66946C2211yescharacteristic
19C2×#66940C2211yescharacteristic
20C2×#66940C2211yescharacteristic
21C2×C4×D44C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C11×#389C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66881C2211yescharacteristic
30C2×#66880C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32C2×C8×Dic11C2211yescharacteristic
33C2×C8×Dic11C2211yescharacteristic
34#10622602—21no—
35#10622600—21no—
36#10622598C2211yescharacteristic
37#10622598C2211yescharacteristic
38#10622590C2211yescharacteristic
39#10622590C2211yescharacteristic
40C4⋊C4×Dic11—21no—
41#10622585—21no—
42C2×#66874C2211yescharacteristic
43C2×#66874C2211yescharacteristic
44C2×#66873C2211yescharacteristic
45C2×#66873C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47C2×#66871C2211yescharacteristic
48C4×Dic11⋊C4C2211yescharacteristic
49#10622465—24no—
50#10622465C418yescomplemented
51C4×#4314—24no—
52#10622281—21no—
53D11×#95—21no—
54#10622263—21no—
55#10622260—21no—
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×C4×D11—21no—
65C22×C4×D11—21no—
66C22×Dic22C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4D411yescharacteristic
87C2×Dic11⋊C4D411yescharacteristic
88C2×C4×Dic11—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11C2311yescharacteristic
92C2×C4×Dic11C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C2×#4314C2×C414yes—
96C2×#4314D414yes—
97C2×#4314Q814yes—
98#66946—22no—
99#66946—22no—
100#66946—41no—
101#66946C2×C414yes—
102#66940—22no—
103#66940—22no—
104#66940—41no—
105#66940C2×C414yescomplemented
106C4×D44—22no—
107C4×D44—41no—
108C4×Dic22—22no—
109C4×Dic22—41no—
110C11×#106—22no—
111C11×#106C2×C414yescomplemented
112C4×C8×C11—22no—
113C11×#95—21no—
114C11×#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95D411yescharacteristic
122C11⋊#95D411yescharacteristic
123#66885—22no—
124#66881—22no—
125#66880—22no—
126Dic11⋊C8—22no—
127C8×Dic11—22no—
128C8×Dic11C2×C414yescomplemented
129#66874—22no—
130#66874C2×C414yescomplemented
131#66873—22no—
132#66873C2×C414yes—
133#66871—41no—
134#66871—41no—
135#22683—111nomaximal, Sylow
136C23×D11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11C2×D411yescharacteristic
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C22×Dic11C2×D411yescharacteristic
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44C22×C412yes—
155C2×D44C2×D412yes—
156C2×D44C2×Q812yes—
157C2×C4×D11—24no—
158C2×C4×D11—42no—
159C2×C4×D11—42no—
160C2×C4×D11—42no—
161C2×C4×D11—42no—
162C2×C4×D11—81no—
163C2×C4×D11—81no—
164C2×C4×D11—81no—
165C2×C4×D11—81no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22C22×C412yes—
170C2×Dic22C2×D412yes—
171C2×Dic22C2×Q812yes—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11C22×C412yes—
176C2×C8×C11C2×D412yes—
177C2×C8×C11C2×Q812yes—
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—81no—
186C11×C4⋊C4C22×C412yes—
187C11×C4⋊C4C22×C412yes—
188C42×C11—21no—
189C42×C11—21no—
190(C2×D11)⋊C4—24no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—42no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—42no—
198C4⋊Dic11—81no—
199Dic11⋊C4—24no—
200Dic11⋊C4—22no—
201Dic11⋊C4—22no—
202Dic11⋊C4—42no—
203Dic11⋊C4—42no—
204C4×Dic11—24no—
205C4×Dic11—21no—
206C4×Dic11—21no—
207C4×Dic11—42no—
208C4×Dic11—42no—
209C4×Dic11C22×C412yes—
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⋊C8C22×C412yes—
217#4314C4⋊C4116yescomplemented
218C2×C4×SD16—111no—
219C2×C4×SD16—111no—
220C2×C4×SD16—111no—
221#2351—111no—
222#2349—111no—
223#1941—111no—
224#1941D1111yescharacteristic, complemented
225#1863—111no—
226#1863—111no—
227#1862—111no—
228#1862—111no—
229#1846—111no—
230#1805—111no—
231#1804—111no—
232C8×C4⋊C4—111no—
233C23×C11C22×D411yescharacteristic
234C22×D11—22no—
235C22×D11—22no—
236C22×D11—22no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—41no—
240C22×D11—41no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11#13512yes—
259C2×C4×C11C23×C411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C22×Q811yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11H(5,𝔽2)11yescharacteristic
264C2×C4×C112−1+411yescharacteristic
265C2×Dic11—22no—
266C2×Dic11—21no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11C4×D412yes—
284C2×Dic11C4×D412yes—
285C2×Dic11#13512yes—
286D44—22no—
287D44—22no—
288D44—22no—
289D44C2×C4⋊C414yes—
290C4×D11—84no—
291C4×D11—84no—
292C4×D11—84no—
293Dic22—22no—
294Dic22—22no—
295Dic22—22no—
296Dic22C2×C4⋊C414yes—
297C8×C11—41no—
298C8×C11C2×C4⋊C414yes—
299C11⋊C8—22no—
300C11⋊C8—41no—
301C22×SD16—111no—
302C2×C4×Q8—111no—
303C2×C4×Q8—111no—
304C2×C4×Q8—111no—
305C2×C4×D4—111no—
306C2×C4×D4—111no—
307C2×C4×D4—111no—
308C4×SD16—118no—
309C4×SD16—224no—
310C4×SD16—224no—
311C2×#107—111no—
312C2×#107—111no—
313C2×#106—111no—
314C2×#106C2×D1111yescharacteristic
315C2×#106C2×D1111yescharacteristic
316C2×C4⋊C8—111no—
317C2×#103—111no—
318C2×#103—111no—
319C2×#103—111no—
320C2×#102—111no—
321C2×#102—111no—
322C2×#102—111no—
323C2×C4×C8—111no—
324C2×C4×C8—111no—
325C2×C4×C8C2×D1111yescharacteristic
326#389—111no—
327#389—111no—
328#389—221no—
329#389—221no—
330#389C2×D1111yescharacteristic
331#389C2×D1111yescharacteristic
332#385—221no—
333#385—221no—
334#382—111no—
335#382—111no—
336#382—221no—
337#380—221no—
338C4×C4⋊C4—111no—
339C4×C4⋊C4—221no—
340C2×#95—221no—
341#340—111no—
342#340—111no—
343#340C2×D1111yescharacteristic
344#340C2×D1111yescharacteristic
345#336—111no—
346#336—111no—
347C22×C11C2×C4×D411yescharacteristic
348C22×C11D4211yescharacteristic
349C22×C11D4×Q811yescharacteristic
350C22×C11C2×#13511yescharacteristic
351C22×C11C2×#13511yescharacteristic
352C22×C11#57711yescharacteristic
353C22×C11#57711yescharacteristic
354C2×D11—24no—
355C2×D11—42no—
356C2×D11—42no—
357C2×D11—42no—
358C2×D11—42no—
359C2×D11—42no—
360C2×D11—42no—
361C4×C11—22no—
362C4×C11—42no—
363C4×C11—42no—
364C4×C11—41no—
365C4×C11—81no—
366C4×C11—81no—
367C4×C11C22×C4⋊C411yescharacteristic
368C4×C11#52011yescharacteristic
369C4×C11#54711yescharacteristic
370C4×C11#55411yescharacteristic
371Dic11—24no—
372Dic11—22no—
373Dic11—22no—
374Dic11—22no—
375Dic11—41no—
376Dic11—81no—
377Dic11—81no—
378C22×Q8—111no—
379C22×D4—111no—
380C23×C4—221no—
381C23×C4—221no—
382C23×C4—221no—
383C2×SD16—114no—
384C2×SD16—114no—
385C2×SD16—114no—
386C22×C8—111no—
387C22×C8—111no—
388C22×C8C22×D1111yescharacteristic
389C22×C8C22×D1111yescharacteristic
390C4×Q8—114no—
391C4×Q8—222no—
392C4×Q8—222no—
393C4×Q8—222no—
394C4×Q8—441no—
395C4×Q8—441no—
396C4×D4—114no—
397C4×D4—222no—
398C4×D4—222no—
399C4×D4—222no—
400C4×D4—441no—
401C4×D4—441no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4C22×D1111yescharacteristic
414C2×C4⋊C4C22×D1111yescharacteristic
415C2×C4⋊C4C22×D1111yescharacteristic
416C2×C4⋊C4C22×D1111yescharacteristic
417C2×C22⋊C4—221no—
418C2×C22⋊C4—221no—
419C2×C22⋊C4—221no—
420C2×C42—111no—
421C2×C42—111no—
422C2×C42—221no—
423C2×C42—221no—
424C2×C42—221no—
425C2×C42C22×D1111yescharacteristic
426#107—441no—
427#107—441no—
428#106—22no—
429#106—222no—
430#106C4×D1114yescomplemented
431C4⋊C8—222no—
432#103—114no—
433#103—222no—
434#103—222no—
435#102—114no—
436#102—222no—
437#102—222no—
438C4×C8—22no—
439C4×C8—114no—
440C4×C8—222no—
441#95—21no—
442#95—21no—
443#95—111no—
444#95—111no—
445#95—221no—
446#95—221no—
447#95—221no—
448#95—221no—
449#95—221no—
450#95—221no—
451C2×C11D4×C4⋊C411yescharacteristic
452C2×C11C4×#13511yescharacteristic
453C2×C11#294911yescharacteristic
454C2×C11#328211yescharacteristic
455C2×C11#328211yescharacteristic
456C2×C11#338111yescharacteristic
457C2×C11#338111yescharacteristic
458D11—44no—
459C24—221no—
460C2×Q8—112no—
461C2×Q8—112no—
462C2×Q8—112no—
463C2×Q8—221no—
464C2×Q8—221no—
465C2×Q8—221no—
466C2×D4—112no—
467C2×D4—112no—
468C2×D4—112no—
469C2×D4—221no—
470C2×D4—221no—
471C2×D4—221no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—111no—
477C22×C4—111no—
478C22×C4—111no—
479C22×C4—111no—
480C22×C4—224no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—442no—
485C22×C4—442no—
486C22×C4—442no—
487C22×C4—442no—
488C22×C4—881no—
489C22×C4—881no—
490C22×C4—881no—
491C22×C4—881no—
492C22×C4D4×D1111yescharacteristic
493C22×C4D4×D1111yescharacteristic
494C22×C4C23×D1111yescharacteristic
495SD16—1116no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—112no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8C2×C4×D1112yes—
506C2×C8D4×D1112yes—
507C2×C8Q8×D1112yes—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—42no—
515C4⋊C4—81no—
516C4⋊C4—222no—
517C4⋊C4—224no—
518C4⋊C4—222no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—442no—
524C4⋊C4—442no—
525C4⋊C4—442no—
526C4⋊C4—881no—
527C4⋊C4C2×C4×D1112yes—
528C4⋊C4C2×C4×D1112yes—
529C22⋊C4—224no—
530C22⋊C4—442no—
531C22⋊C4—442no—
532C42—21no—
533C42—21no—
534C42—112no—
535C42—112no—
536C42—224no—
537C42—221no—
538C42—221no—
539C42—442no—
540C42—442no—
541C11#2268311yescharacteristic, complemented, Sylow
542C23—222no—
543C23—222no—
544C23—222no—
545C23—441no—
546C23—441no—
547C23—441no—
548C23—441no—
549C23C2×D4×D1111yescharacteristic
550Q8—114no—
551Q8—222no—
552Q8—222no—
553Q8—222no—
554D4—114no—
555D4—222no—
556D4—222no—
557D4—222no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—21no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—112no—
576C2×C4—112no—
577C2×C4—112no—
578C2×C4—222no—
579C2×C4—221no—
580C2×C4—221no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—222no—
585C2×C4—221no—
586C2×C4—222no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—884no—
597C2×C4—884no—
598C2×C4—884no—
599C2×C4#6696912yes—
600C2×C4C22×C4×D1111yescharacteristic
601C2×C4C2×D4×D1111yescharacteristic
602C2×C4C2×Q8×D1111yescharacteristic
603C2×C4#6704011yescharacteristic
604C2×C4#41×D1111yescharacteristic
605C2×C4#6704211yescharacteristic
606C8—41no—
607C8—222no—
608C8—441no—
609C8C4⋊C4×D1114yes—
610C22—224no—
611C22—442no—
612C22—442no—
613C22—442no—
614C22—442no—
615C22—442no—
616C22—442no—
617C22C4×D4×D1111yescharacteristic
618C22#1062314011yescharacteristic
619C22#1062325811yescharacteristic
620C22C2×#6696911yescharacteristic
621C22#1062329311yescharacteristic
622C22D11×#13511yescharacteristic
623C22#1062330111yescharacteristic
624C4—22no—
625C4—41no—
626C4—42no—
627C4—42no—
628C4—81no—
629C4—81no—
630C4—222no—
631C4—222no—
632C4—224no—
633C4—222no—
634C4—441no—
635C4—881no—
636C4—881no—
637C4C2×C4⋊C4×D1111yescharacteristic
638C4#1062310511yescharacteristic
639C4#1062316211yescharacteristic
640C4#1062322111yescharacteristic
641C2—444no—
642C2#1307151711yescharacteristic
643C2C4×#6696911yescharacteristic
644C2#1307747011yescharacteristic
645C2#1308032011yescharacteristic
646C2#1308033011yescharacteristic
647C2#1308148811yescharacteristic
648C2#1308149611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1941C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1941D11
hypocenterC11#22683
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1941

Complements

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

NH ≅ G/Ntype
4. #13071535C2semidirect
6. #13069345C2semidirect
7. #13068871C2semidirect
8. #13068869C2semidirect
11. #13068777C2semidirect
12. #13068630C2semidirect
14. C8×Dic11⋊C4C2semidirect
15. C11×#1941C2semidirect
50. #10622465C4semidirect
105. #66940C2×C4semidirect
111. C11×#106C2×C4semidirect
128. C8×Dic11C2×C4semidirect
130. #66874C2×C4semidirect
217. #4314C4⋊C4semidirect
224. #1941D11semidirect
430. #106C4×D11semidirect
541. C11#22683semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43142
C2×#106224652
#130715352
#130715252
#130693452
#130688712
#130688692
#130688642
#130688622
#130687772
#130686302
#130686252
C8×Dic11⋊C42
C11×#19412
#2268311