Finite Group Databasebeta

← #14772118

Subgroups — #14772118

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622430C211yesmaximal, characteristic
2C2×#10622430C211yesmaximal, characteristic
3C2×C4×#4325C211yesmaximal, characteristic
4#13071534C211yesmaximal, characteristic, complemented
5#13071517C211yesmaximal, characteristic
6#13069353C211yesmaximal, characteristic, complemented
7#13069346C211yesmaximal, characteristic, complemented
8#13068874C211yesmaximal, characteristic
9#13068872C211yesmaximal, characteristic, complemented
10#13068866C211yesmaximal, characteristic
11#13068781C211yesmaximal, characteristic, complemented
12#13068625C211yesmaximal, characteristic
13#13068619C211yesmaximal, characteristic, complemented
14#13068487C211yesmaximal, characteristic, complemented
15C11×#1865C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C22×#4325C2211yescharacteristic
20C2×#66946C2211yescharacteristic
21C2×#66946C2211yescharacteristic
22C2×C4⋊C4×D11—21no—
23C2×C4×D44C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C11×#389C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32C2×#66879C2211yescharacteristic
33C2×#66879C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35C4×#4325—24no—
36#10622602—21no—
37#10622598C2211yescharacteristic
38#10622590—21no—
39#10622590C2211yescharacteristic
40#10622589C2211yescharacteristic
41#10622586—21no—
42#10622586C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47C4×Dic11⋊C4—21no—
48C4×Dic11⋊C4C2211yescharacteristic
49#10622541—21no—
50#10622541C2211yescharacteristic
51C2×C4×C11⋊C8C2211yescharacteristic
52#10622430—24no—
53#10622430C418yescomplemented
54#10622281—21no—
55#10622280—21no—
56C11×#340C2211yescharacteristic
57C11×#336C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×C4×D11—21no—
66C22×C4×D11—21no—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C4×Q8×C11—22no—
70C4×Q8×C11—41no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C42×C11—21no—
77C2×C42×C11C2311yescharacteristic
78Q8×Dic11—22no—
79Q8×Dic11—22no—
80Q8×Dic11—41no—
81Q8×Dic11C2×C414yescomplemented
82C2×#4325C2×C414yes—
83C2×#4325D414yes—
84C2×#4325Q814yes—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4D411yescharacteristic
99C2×Dic11⋊C4D411yescharacteristic
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11C2311yescharacteristic
103C2×C4×Dic11C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106#66946—22no—
107#66946—22no—
108#66946—41no—
109#66946C2×C414yes—
110C4⋊C4×D11—44no—
111C4×D44—22no—
112C4×D44—41no—
113C11×#106—41no—
114C11×#103—22no—
115C11×#103C2×C414yescomplemented
116C11×#95—21no—
117#66899—22no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95D411yescharacteristic
124C11⋊#95D411yescharacteristic
125#66885—22no—
126#66885C2×C414yes—
127#66882—41no—
128#66879—22no—
129#66879C2×C414yescomplemented
130Dic11⋊C8—22no—
131#66873—22no—
132#66872—22no—
133#66871—22no—
134#66871C2×C414yescomplemented
135C4×C11⋊C8—22no—
136#22677—111nomaximal, Sylow
137C23×D11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11C22×C412yes—
142C2×Q8×C11C2×D412yes—
143C2×Q8×C11C2×Q812yes—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44C22×C412yes—
162C2×D44C2×D412yes—
163C2×D44C2×Q812yes—
164C2×C4×D11—24no—
165C2×C4×D11—42no—
166C2×C4×D11—42no—
167C2×C4×D11—42no—
168C2×C4×D11—42no—
169C2×C4×D11—42no—
170C2×C4×D11—42no—
171C2×C4×D11—81no—
172C2×C4×D11—81no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11C22×C412yes—
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⋊C4C22×C412yes—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—42no—
190#4325C4⋊C4116yescomplemented
191(C2×D11)⋊C4—24no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—42no—
194C4⋊Dic11—24no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—42no—
201C4⋊Dic11—42no—
202C4⋊Dic11C22×C412yes—
203Dic11⋊C4—22no—
204Dic11⋊C4—41no—
205Dic11⋊C4—42no—
206Dic11⋊C4—42no—
207Dic11⋊C4—42no—
208Dic11⋊C4—81no—
209C4×Dic11—24no—
210C4×Dic11—21no—
211C4×Dic11—21no—
212C4×Dic11—42no—
213C4×Dic11C22×C412yes—
214C4×Dic11#4112yes—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8C22×C412yes—
219C2×C11⋊C8C2×D412yes—
220C2×C11⋊C8C2×Q812yes—
221C2×#440—111no—
222C2×#440—111no—
223C2×C4×SD16—111no—
224#2351—111no—
225D4×C4⋊C4—111no—
226#1943—111no—
227#1942—111no—
228#1865D1111yescharacteristic, complemented
229#1864—111no—
230#1863—111no—
231#1862—111no—
232#1847—111no—
233#1804—111no—
234#1803—111no—
235#1771—111no—
236C23×C11C22×D411yescharacteristic
237C22×D11—22no—
238C22×D11—22no—
239C22×D11—22no—
240C22×D11—41no—
241C22×D11—41no—
242C22×D11—41no—
243C22×D11—41no—
244Q8×C11—22no—
245Q8×C11—22no—
246Q8×C11—22no—
247Q8×C11C2×C4⋊C414yescomplemented
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—21no—
251C2×C4×C11—22no—
252C2×C4×C11—21no—
253C2×C4×C11—22no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
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×C11AGL(1,ℤ/8)12yes—
266C2×C4×C11C23×C411yescharacteristic
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C22×Q811yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11H(5,𝔽2)11yescharacteristic
271C2×C4×C112−1+411yescharacteristic
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—22no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
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×Dic11C4×D412yes—
292C2×Dic11C4×D412yes—
293D44—22no—
294D44—22no—
295D44—22no—
296D44C2×C4⋊C414yes—
297C4×D11—48no—
298C4×D11—84no—
299C4×D11—84no—
300C8×C11—22no—
301C8×C11—41no—
302C11⋊C8—41no—
303C11⋊C8C2×C4⋊C414yescomplemented
304C22×SD16—111no—
305C2×C4×Q8—111no—
306C2×C4×Q8—111no—
307C2×C4×Q8C2×D1111yescharacteristic
308C2×C4×D4—111no—
309C2×C4×D4—111no—
310C2×C4×D4—111no—
311C22×C4⋊C4—221no—
312#440—118no—
313#440—224no—
314C4×SD16—224no—
315C2×#107—111no—
316C2×#107—111no—
317C2×#107—111no—
318C2×#106—111no—
319C2×#106C2×D1111yescharacteristic
320C2×C4⋊C8—111no—
321C2×#103—111no—
322C2×#103C2×D1111yescharacteristic
323C2×#103C2×D1111yescharacteristic
324C2×#102—111no—
325C2×#102—111no—
326C2×#102—111no—
327C2×#97—111no—
328C2×#97—111no—
329C2×C4×C8—111no—
330#389—111no—
331#389—111no—
332#389—111no—
333#389—221no—
334#389—221no—
335#389C2×D1111yescharacteristic
336#385—221no—
337#385—221no—
338#384—111no—
339#382—111no—
340#382—221no—
341#380—221no—
342C4×C4⋊C4—111no—
343C4×C4⋊C4—221no—
344#340—111no—
345#340—111no—
346#340—111no—
347#340C2×D1111yescharacteristic
348#336—111no—
349#336C2×D1111yescharacteristic
350C22×C11C2×C4×D411yescharacteristic
351C22×C11D4211yescharacteristic
352C22×C11D4×Q811yescharacteristic
353C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
354C22×C11#57511yescharacteristic
355C22×C11#57711yescharacteristic
356C22×C11#57811yescharacteristic
357C2×D11—24no—
358C2×D11—42no—
359C2×D11—42no—
360C2×D11—42no—
361C2×D11—42no—
362C2×D11—42no—
363C2×D11—42no—
364C4×C11—24no—
365C4×C11—22no—
366C4×C11—42no—
367C4×C11—41no—
368C4×C11—81no—
369C4×C11—81no—
370C4×C11C22×C4⋊C411yescharacteristic
371C4×C11#52011yescharacteristic
372C4×C11#54711yescharacteristic
373C4×C11#55411yescharacteristic
374Dic11—22no—
375Dic11—22no—
376Dic11—42no—
377Dic11—41no—
378Dic11—41no—
379Dic11—81no—
380Dic11—81no—
381C22×Q8C22×D1111yescharacteristic
382C22×D4—111no—
383C23×C4—221no—
384C23×C4—221no—
385C23×C4—221no—
386C2×SD16—114no—
387C2×SD16—114no—
388C2×SD16—114no—
389C22×C8—111no—
390C22×C8—111no—
391C22×C8C22×D1111yescharacteristic
392C22×C8C22×D1111yescharacteristic
393C4×Q8—22no—
394C4×Q8—41no—
395C4×Q8—114no—
396C4×Q8—222no—
397C4×Q8—222no—
398C4×Q8—441no—
399C4×D4—114no—
400C4×D4—222no—
401C4×D4—222no—
402C4×D4—222no—
403C4×D4—441no—
404C4×D4—441no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—111no—
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⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—444no—
420C2×C4⋊C4C22×D1111yescharacteristic
421C2×C4⋊C4C22×D1111yescharacteristic
422C2×C4⋊C4C22×D1111yescharacteristic
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C42—21no—
427C2×C42—111no—
428C2×C42—111no—
429C2×C42—221no—
430C2×C42—221no—
431C2×C42C22×D1111yescharacteristic
432#107—114no—
433#107—222no—
434#107—441no—
435#106—41no—
436#106—222no—
437C4⋊C8—222no—
438#103—22no—
439#103—222no—
440#103C4×D1114yescomplemented
441#102—114no—
442#102—222no—
443#102—222no—
444#97—114no—
445#97—222no—
446C4×C8—222no—
447#95—21no—
448#95—111no—
449#95—111no—
450#95—221no—
451#95—221no—
452#95—221no—
453#95—221no—
454#95—221no—
455C2×C11D4×C4⋊C411yescharacteristic
456C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
457C2×C11#294711yescharacteristic
458C2×C11#326511yescharacteristic
459C2×C11#326911yescharacteristic
460C2×C11#338611yescharacteristic
461C2×C11#338811yescharacteristic
462D11—44no—
463C24—221no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8C2×C4×D1112yes—
468C2×Q8D4×D1112yes—
469C2×Q8Q8×D1112yes—
470C2×D4—112no—
471C2×D4—112no—
472C2×D4—112no—
473C2×D4—221no—
474C2×D4—221no—
475C2×D4—221no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—111no—
481C22×C4—111no—
482C22×C4—111no—
483C22×C4—111no—
484C22×C4—224no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—442no—
489C22×C4—442no—
490C22×C4—442no—
491C22×C4—442no—
492C22×C4—442no—
493C22×C4—442no—
494C22×C4—881no—
495C22×C4—881no—
496C22×C4D4×D1111yescharacteristic
497C22×C4D4×D1111yescharacteristic
498C22×C4C23×D1111yescharacteristic
499SD16—1116no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—112no—
506C2×C8—112no—
507C2×C8—112no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8C2×C4×D1112yes—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—42no—
518C4⋊C4—42no—
519C4⋊C4—112no—
520C4⋊C4—224no—
521C4⋊C4—222no—
522C4⋊C4—221no—
523C4⋊C4—221no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—441no—
528C4⋊C4—442no—
529C4⋊C4—442no—
530C4⋊C4—442no—
531C4⋊C4—442no—
532C4⋊C4—442no—
533C4⋊C4—881no—
534C4⋊C4C2×C4×D1112yes—
535C22⋊C4—224no—
536C22⋊C4—442no—
537C22⋊C4—442no—
538C42—21no—
539C42—21no—
540C42—42no—
541C42—112no—
542C42—112no—
543C42—224no—
544C42—221no—
545C42—221no—
546C42—442no—
547C11#2267711yescharacteristic, complemented, Sylow
548C23—222no—
549C23—222no—
550C23—222no—
551C23—441no—
552C23—441no—
553C23—441no—
554C23—441no—
555C23C2×D4×D1111yescharacteristic
556Q8—22no—
557Q8—22no—
558Q8—22no—
559Q8C4⋊C4×D1114yescomplemented
560D4—114no—
561D4—222no—
562D4—222no—
563D4—222no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—22no—
572C2×C4—21no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—112no—
582C2×C4—112no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—221no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—222no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—448no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—884no—
604C2×C4—884no—
605C2×C4#6696712yes—
606C2×C4C22×C4×D1111yescharacteristic
607C2×C4C2×D4×D1111yescharacteristic
608C2×C4#6703711yescharacteristic
609C2×C4C2×Q8×D1111yescharacteristic
610C2×C4#41×D1111yescharacteristic
611C2×C4#6704311yescharacteristic
612C8—22no—
613C8—41no—
614C8—114no—
615C8—441no—
616C22—224no—
617C22—442no—
618C22—442no—
619C22—442no—
620C22—442no—
621C22—442no—
622C22—442no—
623C22C4×D4×D1111yescharacteristic
624C22#1062312111yescharacteristic
625C22#1062316311yescharacteristic
626C22C2×#6696711yescharacteristic
627C22#1062329911yescharacteristic
628C22#1062330911yescharacteristic
629C22#1062331011yescharacteristic
630C4—22no—
631C4—24no—
632C4—41no—
633C4—42no—
634C4—81no—
635C4—81no—
636C4—222no—
637C4—222no—
638C4—441no—
639C4—441no—
640C4—442no—
641C4—881no—
642C4—881no—
643C4C2×C4⋊C4×D1111yescharacteristic
644C4#1062307711yescharacteristic
645C4#1062316711yescharacteristic
646C4#1062318611yescharacteristic
647C2—444no—
648C2#1307151411yescharacteristic
649C2C4×#6696711yescharacteristic
650C2#1307745811yescharacteristic
651C2#1308010411yescharacteristic
652C2#1308016411yescharacteristic
653C2#1308153611yescharacteristic
654C2#1308155911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1865C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1865D11
hypocenterC11#22677
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1865

Complements

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

NH ≅ G/Ntype
4. #13071534C2semidirect
6. #13069353C2semidirect
7. #13069346C2semidirect
9. #13068872C2semidirect
11. #13068781C2semidirect
13. #13068619C2semidirect
14. #13068487C2semidirect
15. C11×#1865C2semidirect
53. #10622430C4semidirect
81. Q8×Dic11C2×C4semidirect
115. C11×#103C2×C4semidirect
129. #66879C2×C4semidirect
134. #66871C2×C4semidirect
190. #4325C4⋊C4semidirect
228. #1865D11semidirect
247. Q8×C11C2×C4⋊C4semidirect
303. C11⋊C8C2×C4⋊C4semidirect
440. #103C4×D11semidirect
547. C11#22677semidirect
559. Q8C4⋊C4×D11semidirect

Maximal subgroups

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

subgroupindex
C2×#106224302
C2×C4×#43252
#130715342
#130715172
#130693532
#130693462
#130688742
#130688722
#130688662
#130687812
#130686252
#130686192
#130684872
C11×#18652
#2267711