Finite Group Databasebeta

← #14816792

Subgroups — #14816792

Order 2816.

864 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622707C211yesmaximal, characteristic, complemented
2C2×#10622465C211yesmaximal, characteristic
3#13072462C211yesmaximal, characteristic
4#13071530C211yesmaximal, characteristic, complemented
5#13070146C211yesmaximal, characteristic
6#13070095C211yesmaximal, characteristic, complemented
7#13069987C211yesmaximal, characteristic
8#13069343C211yesmaximal, characteristic, complemented
9#13069176C211yesmaximal, characteristic, complemented
10#13068972C211yesmaximal, characteristic
11#13068970C211yesmaximal, characteristic
12#13068885C211yesmaximal, characteristic, complemented
13#13068881C211yesmaximal, characteristic, complemented
14#13068878C211yesmaximal, characteristic
15C11×#2058C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×#66999—21no—
18C22×#4314C2211yescharacteristic
19C2×#66946C2211yescharacteristic
20C2×#66940C2211yescharacteristic
21C2×#66940C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C11×#389C2211yescharacteristic
26#10622844—21no—
27C2×#66885C2211yescharacteristic
28C2×#66880C2211yescharacteristic
29C2×C8×Dic11C2211yescharacteristic
30#10622707—24no—
31#10622607—21no—
32#10622602—21no—
33#10622601C2211yescharacteristic
34#10622598C2211yescharacteristic
35#10622598C2211yescharacteristic
36#10622589—21no—
37#10622589C2211yescharacteristic
38#10622586C2211yescharacteristic
39#10622585—21no—
40C2×#66874C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46C2×#66872C2211yescharacteristic
47#10622552C2211yescharacteristic
48C4×Dic11⋊C4C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50#10622465—24no—
51#10622262—21no—
52#10622260—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55C11×#336C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622188C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11—21no—
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×Dic22C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×C4⋊Q8—22no—
68C11×C4⋊Q8—41no—
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
76#66999—44no—
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×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4D411yescharacteristic
93C2×Dic11⋊C4D411yescharacteristic
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11C2311yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C2×#4314—22no—
102C2×#4314—22no—
103C2×#4314Q814yescomplemented
104#66946—22no—
105#66946—41no—
106#66940—22no—
107#66940—22no—
108#66940—22no—
109#66940—41no—
110C4×Dic22—22no—
111C4×Dic22—41no—
112C11×#106—22no—
113C11×#106—41no—
114C11×#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95D411yescharacteristic
119C11⋊#95D411yescharacteristic
120#66885—41no—
121#66880—22no—
122C8×Dic11—22no—
123#66874—22no—
124#66874D414yes—
125#66873—22no—
126#66873—22no—
127#66872—22no—
128#66872—22no—
129#66872—22no—
130C4⋊(C11⋊C8)—22no—
131#26373—111nomaximal, Sylow
132C23×D11—21no—
133C2×Q8×C11—42no—
134C2×Q8×C11—42no—
135C2×Q8×C11—81no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2411yescharacteristic
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11C2×D411yescharacteristic
147C22×Dic11C2×D411yescharacteristic
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44C2×Q812yes—
156C2×C4×D11—42no—
157C2×C4×D11—42no—
158C2×C4×D11—81no—
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22C2×D412yes—
163C2×Dic22C2×Q812yes—
164C2×Dic22#4112yes—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11C2×Q812yes—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—42no—
178C11×C4⋊C4—81no—
179C11×C4⋊C4C2×D412yes—
180C11×C4⋊C4#4112yes—
181C42×C11—21no—
182C42×C11—21no—
183(C2×D11)⋊C4—42no—
184(C2×D11)⋊C4—42no—
185(C2×D11)⋊C4—42no—
186(C2×D11)⋊C4—42no—
187(C2×D11)⋊C4—81no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—42no—
193C4⋊Dic11—81no—
194Dic11⋊C4—24no—
195Dic11⋊C4—41no—
196Dic11⋊C4—42no—
197Dic11⋊C4—42no—
198Dic11⋊C4—42no—
199Dic11⋊C4—42no—
200Dic11⋊C4—81no—
201Dic11⋊C4SD1614yescomplemented
202C4×Dic11—24no—
203C4×Dic11—21no—
204C4×Dic11—21no—
205C4×Dic11—21no—
206C4×Dic11—21no—
207C4×Dic11—42no—
208C4×Dic11—42no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8C2×D412yes—
215#4314—28no—
216C2×#475—111no—
217C2×C4×SD16—111no—
218#2452—111no—
219Q8×C4⋊C4—111no—
220#2094—111no—
221#2084—111no—
222#2065—111no—
223#2058D1111yescharacteristic, complemented
224#1941—111no—
225#1916—111no—
226#1880—111no—
227#1880—111no—
228#1865—111no—
229#1865—111no—
230#1864—111no—
231C23×C11C22×D411yescharacteristic
232C22×D11—22no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—41no—
238C22×D11—41no—
239Q8×C11—84no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—22no—
243C2×C4×C11—21no—
244C2×C4×C11—22no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—41no—
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×C11C2×SD1612yes—
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C22×Q811yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11H(5,𝔽2)11yescharacteristic
263C2×C4×C112−1+411yescharacteristic
264C2×Dic11—21no—
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×Dic11C2×SD1612yes—
284C2×Dic11C2×SD1612yes—
285D44—22no—
286D44—22no—
287D44—41no—
288D44—41no—
289C4×D11—84no—
290Dic22—22no—
291Dic22—22no—
292Dic22—22no—
293Dic22C22⋊Q814yescomplemented
294C8×C11—22no—
295C8×C11—41no—
296C11⋊C8—22no—
297C11⋊C8—41no—
298C22×SD16—111no—
299C2×C4⋊Q8C2×D1111yescharacteristic
300C2×C22⋊Q8—221no—
301C2×C4×Q8—111no—
302C2×C4×Q8—111no—
303C2×C4×Q8—111no—
304C2×C4×D4—111no—
305#475—224no—
306C4×SD16—224no—
307C2×#106—111no—
308C2×#106—111no—
309C2×#106—111no—
310C2×#106C2×D1111yescharacteristic
311C2×#106C2×D1111yescharacteristic
312C2×C4⋊C8—111no—
313C2×#103—111no—
314C2×#103—111no—
315C2×#103—111no—
316C2×#102—111no—
317C2×#102—111no—
318C2×#102—111no—
319C2×C4×C8—111no—
320#396—221no—
321#393—221no—
322#390—111no—
323#390—111no—
324#389—111no—
325#389—111no—
326#389—111no—
327#389—221no—
328#389—221no—
329#389C2×D1111yescharacteristic
330#385—221no—
331#384—111no—
332#384—221no—
333C4×C4⋊C4—111no—
334C4×C4⋊C4—221no—
335#340—111no—
336#340—111no—
337#340C2×D1111yescharacteristic
338#340C2×D1111yescharacteristic
339#336—111no—
340#336—111no—
341#336—111no—
342#336C2×D1111yescharacteristic
343C22×C11#52511yescharacteristic
344C22×C11D4211yescharacteristic
345C22×C11D4×Q811yescharacteristic
346C22×C11C22×SD1611yescharacteristic
347C22×C11#57511yescharacteristic
348C22×C11#57711yescharacteristic
349C22×C11#57711yescharacteristic
350C2×D11—42no—
351C2×D11—42no—
352C2×D11—42no—
353C2×D11—81no—
354C2×D11—81no—
355C2×D11—81no—
356C2×D11—81no—
357C4×C11—22no—
358C4×C11—42no—
359C4×C11—41no—
360C4×C11—42no—
361C4×C11—81no—
362C4×C11—81no—
363C4×C11C2×C22⋊Q811yescharacteristic
364C4×C11#53911yescharacteristic
365C4×C11#54711yescharacteristic
366C4×C11#55411yescharacteristic
367Dic11—22no—
368Dic11—24no—
369Dic11—22no—
370Dic11—41no—
371Dic11—41no—
372Dic11—81no—
373Dic11—81no—
374C22×Q8—21no—
375C22×Q8—111no—
376C22×D4—111no—
377C23×C4—221no—
378C2×SD16—114no—
379C2×SD16—222no—
380C2×SD16—222no—
381C22×C8—111no—
382C22×C8—111no—
383C22×C8C22×D1111yescharacteristic
384C22×C8C22×D1111yescharacteristic
385C4⋊Q8—22no—
386C4⋊Q8—41no—
387C22⋊Q8—444no—
388C4×Q8—222no—
389C4×Q8—222no—
390C4×Q8—222no—
391C4×Q8—222no—
392C4×Q8—441no—
393C4×Q8—441no—
394C4×D4—222no—
395C4×D4—441no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4C22×D1111yescharacteristic
411C2×C4⋊C4C22×D1111yescharacteristic
412C2×C4⋊C4C22×D1111yescharacteristic
413C2×C4⋊C4C22×D1111yescharacteristic
414C2×C22⋊C4—221no—
415C2×C22⋊C4—221no—
416C2×C22⋊C4—221no—
417C2×C22⋊C4—221no—
418C2×C22⋊C4—221no—
419C2×C42—111no—
420C2×C42—111no—
421C2×C42—221no—
422C2×C42—221no—
423C2×C42—221no—
424C2×C42C22×D1111yescharacteristic
425#106—22no—
426#106—41no—
427#106—222no—
428#106—222no—
429#106—222no—
430C4⋊C8—222no—
431#103—114no—
432#103—222no—
433#103—222no—
434#102—222no—
435#102—222no—
436#102—441no—
437C4×C8—222no—
438#95—21no—
439#95—111no—
440#95—111no—
441#95—221no—
442#95—221no—
443#95—221no—
444C2×C11#244911yescharacteristic
445C2×C11#310311yescharacteristic
446C2×C11#312511yescharacteristic
447C2×C11#327111yescharacteristic
448C2×C11D4×SD1611yescharacteristic
449C2×C11Q8×SD1611yescharacteristic
450C2×C11#338811yescharacteristic
451D11—82no—
452C24—221no—
453C2×Q8—42no—
454C2×Q8—42no—
455C2×Q8—81no—
456C2×Q8—112no—
457C2×Q8—112no—
458C2×Q8—112no—
459C2×Q8—221no—
460C2×Q8—221no—
461C2×Q8—221no—
462C2×D4—112no—
463C2×D4—221no—
464C2×D4—221no—
465C2×D4—221no—
466C2×D4—221no—
467C2×D4—221no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—111no—
473C22×C4—111no—
474C22×C4—111no—
475C22×C4—111no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—442no—
480C22×C4—442no—
481C22×C4—881no—
482C22×C4D4×D1111yescharacteristic
483C22×C4D4×D1111yescharacteristic
484C22×C4C23×D1111yescharacteristic
485SD16—228no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—112no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—221no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8Q8×D1112yes—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—42no—
505C4⋊C4—81no—
506C4⋊C4—114no—
507C4⋊C4—224no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4—441no—
513C4⋊C4—442no—
514C4⋊C4—442no—
515C4⋊C4—442no—
516C4⋊C4—442no—
517C4⋊C4—442no—
518C4⋊C4—881no—
519C4⋊C4—881no—
520C4⋊C4D4×D1112yes—
521C4⋊C4#434312yes—
522C22⋊C4—442no—
523C22⋊C4—442no—
524C22⋊C4—442no—
525C22⋊C4—442no—
526C22⋊C4—881no—
527C42—21no—
528C42—21no—
529C42—224no—
530C42—221no—
531C42—221no—
532C42—221no—
533C42—221no—
534C42—442no—
535C42—442no—
536C11#2637311yescharacteristic, complemented, Sylow
537C23—222no—
538C23—441no—
539C23—441no—
540C23—441no—
541C23—441no—
542C23—441no—
543C23—441no—
544C23C2×D4×D1111yescharacteristic
545Q8—84no—
546Q8—114no—
547Q8—222no—
548Q8—222no—
549Q8—222no—
550D4—222no—
551D4—222no—
552D4—441no—
553D4—441no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—112no—
572C2×C4—112no—
573C2×C4—222no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—222no—
578C2×C4—221no—
579C2×C4—222no—
580C2×C4—221no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—884no—
593C2×C4SD16×D1112yes—
594C2×C4C2×D4×D1111yescharacteristic
595C2×C4#6703711yescharacteristic
596C2×C4C2×Q8×D1111yescharacteristic
597C2×C4C2×#434311yescharacteristic
598C2×C4#6704011yescharacteristic
599C2×C4#41×D1111yescharacteristic
600C8—22no—
601C8—41no—
602C8—222no—
603C8—441no—
604C22—442no—
605C22—442no—
606C22—442no—
607C22—881no—
608C22—881no—
609C22—881no—
610C22—881no—
611C22#1062312111yescharacteristic
612C22#1062315811yescharacteristic
613C22#1062325811yescharacteristic
614C22C2×SD16×D1111yescharacteristic
615C22#1062329311yescharacteristic
616C22#1062330611yescharacteristic
617C22#1062330811yescharacteristic
618C4—22no—
619C4—42no—
620C4—41no—
621C4—42no—
622C4—81no—
623C4—81no—
624C4—224no—
625C4—222no—
626C4—222no—
627C4—441no—
628C4—441no—
629C4—881no—
630C4—881no—
631C4D11×C22⋊Q811yescharacteristic
632C4#1062316911yescharacteristic
633C4#1062325711yescharacteristic
634C4#1062326111yescharacteristic
635C2—882no—
636C2#1307241811yescharacteristic
637C2#1307864911yescharacteristic
638C2#1307889811yescharacteristic
639C2#1308020411yescharacteristic
640C2#1308031011yescharacteristic
641C2#1308147311yescharacteristic
642C2#1308156011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2058C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2058D11
hypocenterC11#26373
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2058

Complements

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

NH ≅ G/Ntype
1. C2×#10622707C2semidirect
4. #13071530C2semidirect
6. #13070095C2semidirect
8. #13069343C2semidirect
9. #13069176C2semidirect
12. #13068885C2semidirect
13. #13068881C2semidirect
15. C11×#2058C2semidirect
103. C2×#4314Q8semidirect
201. Dic11⋊C4SD16semidirect
223. #2058D11semidirect
293. Dic22C22⋊Q8semidirect
536. C11#26373semidirect

Maximal subgroups

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

subgroupindex
C2×#106227072
C2×#106224652
#130724622
#130715302
#130701462
#130700952
#130699872
#130693432
#130691762
#130689722
#130689702
#130688852
#130688812
#130688782
C11×#20582
#2637311