Finite Group Databasebeta

← #14817171

Subgroups — #14817171

Order 2816.

878 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622679C211yesmaximal, characteristic
2C2×#10622639C211yesmaximal, characteristic
3C4⋊C4×D44C211yesmaximal, characteristic
4#13070159C211yesmaximal, characteristic, complemented
5#13070087C211yesmaximal, characteristic, complemented
6#13070011C211yesmaximal, characteristic, complemented
7#13069951C211yesmaximal, characteristic, complemented
8#13069351C211yesmaximal, characteristic, complemented
9#13069182C211yesmaximal, characteristic, complemented
10#13068953C211yesmaximal, characteristic
11#13068953C211yesmaximal, characteristic
12#13068876C211yesmaximal, characteristic
13#13068870C211yesmaximal, characteristic, complemented
14#13068862C211yesmaximal, characteristic
15C11×#2453C211yesmaximal, characteristic, complemented
16C2×C11×#125C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C22×#4325C2211yescharacteristic
19C2×C4⋊C4×D11—21no—
20C2×C4×D44C2211yescharacteristic
21C2×C4×D44C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C11×#400—21no—
24C11×#398—21no—
25C11×#391C2211yescharacteristic
26C11×#391C2211yescharacteristic
27C11×#389—21no—
28C11×#389C2211yescharacteristic
29C11×#389C2211yescharacteristic
30C11×#387—21no—
31C4×C11×C4⋊C4C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35#10622679—24no—
36#10622639—24no—
37#10622600—21no—
38C2×#66873C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622548C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×#66867C2211yescharacteristic
51#10622281—21no—
52#10622281—21no—
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×C4×D11—21no—
65C22×C4×D11—21no—
66C11×#125—22no—
67C11×#125—41no—
68C4×Q8×C11—22no—
69C4×Q8×C11—41no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×#4325—22no—
85C2×#4325—22no—
86C2×#4325Q814yes—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C4⋊C4×D11—44no—
102C4×D44—22no—
103C4×D44—22no—
104C4×D44—22no—
105C4×D44—22no—
106C4×D44—41no—
107C4×D44—41no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95D411yescharacteristic
115C11×#95D411yescharacteristic
116#66899—22no—
117#66899—22no—
118#66899—41no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121#66873—22no—
122#66873—22no—
123#66873D414yes—
124#66872—22no—
125#66872—41no—
126#66871—22no—
127#66871—22no—
128#66871—22no—
129C4⋊(C11⋊C8)—22no—
130#66867—22no—
131#26398—111nomaximal, Sylow
132C23×D11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11C2×Q812yes—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44C2×D412yes—
157C2×D44C2×Q812yes—
158C2×D44#4112yes—
159C2×C4×D11—24no—
160C2×C4×D11—42no—
161C2×C4×D11—42no—
162C2×C4×D11—42no—
163C2×C4×D11—42no—
164C2×C4×D11—42no—
165C2×C4×D11—42no—
166C2×C4×D11—81no—
167C2×C4×D11—81no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—41no—
175C11×C4⋊C4—42no—
176C11×C4⋊C4—42no—
177C11×C4⋊C4—42no—
178C11×C4⋊C4—42no—
179C11×C4⋊C4—42no—
180C11×C4⋊C4C2×D412yes—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—42no—
188#4325—28no—
189(C2×D11)⋊C4—24no—
190(C2×D11)⋊C4—42no—
191(C2×D11)⋊C4—42no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—42no—
198C4⋊Dic11—81no—
199C4⋊Dic11#4112yes—
200Dic11⋊C4—42no—
201Dic11⋊C4—42no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8C2×D412yes—
213C2×C11⋊C8C2×Q812yes—
214C2×#478—111no—
215C2×#440—111no—
216#2453D1111yescharacteristic, complemented
217D4×C4⋊C4—111no—
218#2096—111no—
219#2083—111no—
220#2068—111no—
221#2059—111no—
222#1943—111no—
223#1917—111no—
224#1877—111no—
225#1877—111no—
226#1864—111no—
227#1863—111no—
228#1862—111no—
229C23×C11C22×D411yescharacteristic
230C22×D11—22no—
231C22×D11—22no—
232C22×D11—22no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—41no—
236C22×D11—41no—
237Q8×C11—22no—
238Q8×C11—22no—
239Q8×C11—41no—
240Q8×C11—41no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
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—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11AGL(1,ℤ/8)12yes—
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C22×Q811yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11H(5,𝔽2)11yescharacteristic
276C2×C4×C112−1+411yescharacteristic
277C2×Dic11—22no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286D44—22no—
287D44—22no—
288D44—22no—
289D44C22⋊Q814yes—
290C4×D11—48no—
291C4×D11—84no—
292C4×D11—84no—
293C11⋊C8—22no—
294C11⋊C8—22no—
295C11⋊C8—41no—
296C11⋊C8—41no—
297C22×SD16—111no—
298C2×#125C2×D1111yescharacteristic
299C2×C4×Q8C2×D1111yescharacteristic
300C2×C4×D4—111no—
301C2×C4×D4—111no—
302C2×C4×D4—111no—
303C22×C4⋊C4—221no—
304#478—224no—
305#440—224no—
306C2×#107—111no—
307C2×#107—111no—
308C2×#107—111no—
309C2×#106—111no—
310C2×#106—111no—
311C2×C4⋊C8—111no—
312C2×#103—111no—
313C2×#103—111no—
314C2×#103—111no—
315C2×#102—111no—
316C2×#102—111no—
317C2×#102—111no—
318C2×#97—111no—
319#400—21no—
320#398—21no—
321#391C2×D1111yescharacteristic
322#391C2×D1111yescharacteristic
323#389—21no—
324#389—111no—
325#389—111no—
326#389C2×D1111yescharacteristic
327#389C2×D1111yescharacteristic
328#387—21no—
329#385—221no—
330#385—221no—
331#384—111no—
332#380—221no—
333C4×C4⋊C4C2×D1111yescharacteristic
334#340—111no—
335#340—111no—
336#340—111no—
337#340—111no—
338#336—111no—
339#336—111no—
340#336—111no—
341#336—111no—
342C22×C11#52511yescharacteristic
343C22×C11D4211yescharacteristic
344C22×C11D4×Q811yescharacteristic
345C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
346C22×C11#57511yescharacteristic
347C22×C11#57711yescharacteristic
348C22×C11#57811yescharacteristic
349C2×D11—24no—
350C2×D11—42no—
351C2×D11—42no—
352C2×D11—42no—
353C2×D11—42no—
354C2×D11—42no—
355C2×D11—42no—
356C4×C11—22no—
357C4×C11—41no—
358C4×C11—42no—
359C4×C11—41no—
360C4×C11—41no—
361C4×C11—41no—
362C4×C11—41no—
363C4×C11—42no—
364C4×C11—81no—
365C4×C11—81no—
366C4×C11C2×C22⋊Q811yescharacteristic
367C4×C11#53911yescharacteristic
368C4×C11#54711yescharacteristic
369C4×C11#55411yescharacteristic
370Dic11—42no—
371Dic11—81no—
372Dic11—81no—
373C22×Q8C22×D1111yescharacteristic
374C22×D4—111no—
375C23×C4—221no—
376C23×C4—221no—
377C23×C4—221no—
378C2×SD16—114no—
379C2×SD16—222no—
380C2×SD16—222no—
381C22×C8—111no—
382C22×C8—111no—
383C22×C8—111no—
384C22×C8—111no—
385#125—22no—
386#125—41no—
387C4×Q8—22no—
388C4×Q8—41no—
389C4×D4—222no—
390C4×D4—222no—
391C4×D4—222no—
392C4×D4—222no—
393C4×D4—441no—
394C4×D4—441no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—444no—
408C2×C4⋊C4C22⋊D1111yescharacteristic
409C2×C4⋊C4C22⋊D1111yescharacteristic
410C2×C4⋊C4C22×D1111yescharacteristic
411C2×C4⋊C4C22×D1111yescharacteristic
412C2×C4⋊C4C22×D1111yescharacteristic
413C2×C22⋊C4—221no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4—221no—
416C2×C42—21no—
417C2×C42C22×D1111yescharacteristic
418C2×C42C22×D1111yescharacteristic
419C2×C42C22×D1111yescharacteristic
420#107—222no—
421#107—222no—
422#107—222no—
423#106—222no—
424#106—441no—
425C4⋊C8—222no—
426#103—222no—
427#103—222no—
428#103—441no—
429#102—114no—
430#102—222no—
431#102—222no—
432#97—222no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—221no—
440#95—221no—
441#95C22⋊D1111yescharacteristic
442#95C22⋊D1111yescharacteristic
443C2×C11#244911yescharacteristic
444C2×C11#311411yescharacteristic
445C2×C11#312011yescharacteristic
446C2×C11#326911yescharacteristic
447C2×C11#327211yescharacteristic
448C2×C11#338611yescharacteristic
449C2×C11#338811yescharacteristic
450D11—44no—
451C24—221no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8Q8×D1112yes—
458C2×D4—112no—
459C2×D4—112no—
460C2×D4—112no—
461C2×D4—221no—
462C2×D4—221no—
463C2×D4—221no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—224no—
469C22×C4—221no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—442no—
473C22×C4—442no—
474C22×C4—442no—
475C22×C4—442no—
476C22×C4—442no—
477C22×C4—442no—
478C22×C4—881no—
479C22×C4—881no—
480C22×C4C2×C22⋊D1111yescharacteristic
481C22×C4C2×C22⋊D1111yescharacteristic
482C22×C4C2×C22⋊D1111yescharacteristic
483C22×C4C2×C22⋊D1111yescharacteristic
484C22×C4C2×C22⋊D1111yescharacteristic
485C22×C4C2×C22⋊D1111yescharacteristic
486C22×C4C23×D1111yescharacteristic
487SD16—228no—
488C2×C8—112no—
489C2×C8—112no—
490C2×C8—221no—
491C2×C8—221no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—221no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C4⋊C4—22no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—41no—
507C4⋊C4—42no—
508C4⋊C4—42no—
509C4⋊C4—42no—
510C4⋊C4—42no—
511C4⋊C4—42no—
512C4⋊C4—112no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—442no—
519C4⋊C4—442no—
520C4⋊C4—442no—
521C4⋊C4—881no—
522C4⋊C4D4×D1112yes—
523C22⋊C4—224no—
524C22⋊C4—442no—
525C22⋊C4—442no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—42no—
533C11#2639811yescharacteristic, complemented, Sylow
534C23—222no—
535C23—222no—
536C23—222no—
537C23—441no—
538C23—441no—
539C23—441no—
540C23—441no—
541C23C22×C22⋊D1111yescharacteristic
542Q8—22no—
543Q8—22no—
544Q8—41no—
545Q8—41no—
546D4—114no—
547D4—222no—
548D4—222no—
549D4—222no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—222no—
580C2×C4—448no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—884no—
590C2×C4—884no—
591C2×C4#6700212yes—
592C2×C4C2×D4×D1111yescharacteristic
593C2×C4#6703711yescharacteristic
594C2×C4C2×Q8×D1111yescharacteristic
595C2×C4#6704011yescharacteristic
596C2×C4#41×D1111yescharacteristic
597C2×C4#41×D1111yescharacteristic
598C8—222no—
599C8—222no—
600C8—441no—
601C8—441no—
602C22—224no—
603C22—442no—
604C22—442no—
605C22—442no—
606C22—442no—
607C22—442no—
608C22—442no—
609C22D4×C22⋊D1111yescharacteristic
610C22Q8×C22⋊D1111yescharacteristic
611C22C2×#6700211yescharacteristic
612C22#1062335311yescharacteristic
613C22#1062335911yescharacteristic
614C22#1062336811yescharacteristic
615C22#1062336911yescharacteristic
616C4—22no—
617C4—42no—
618C4—41no—
619C4—41no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—42no—
624C4—81no—
625C4—81no—
626C4—442no—
627C4—881no—
628C4—881no—
629C4D11×C22⋊Q811yescharacteristic
630C4#1062316211yescharacteristic
631C4#1062316711yescharacteristic
632C4#1062316911yescharacteristic
633C2—444no—
634C2#1307242211yescharacteristic
635C2#1307875011yescharacteristic
636C2#1307882411yescharacteristic
637C2#1308017211yescharacteristic
638C2#1308021611yescharacteristic
639C2#1308153311yescharacteristic
640C2#1308155511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2453C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2453D11
hypocenterC11#26398
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2453

Complements

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

NH ≅ G/Ntype
4. #13070159C2semidirect
5. #13070087C2semidirect
6. #13070011C2semidirect
7. #13069951C2semidirect
8. #13069351C2semidirect
9. #13069182C2semidirect
13. #13068870C2semidirect
15. C11×#2453C2semidirect
216. #2453D11semidirect
533. C11#26398semidirect

Maximal subgroups

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

subgroupindex
C2×#106226792
C2×#106226392
C4⋊C4×D442
#130701592
#130700872
#130700112
#130699512
#130693512
#130691822
#130689532
#130688762
#130688702
#130688622
C11×#24532
#2639811