Finite Group Databasebeta

← #14816841

Subgroups — #14816841

Order 2816.

900 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622697C211yesmaximal, characteristic
2C2×C4×#4325C211yesmaximal, characteristic
3C4⋊C4×D44C211yesmaximal, characteristic
4#13070159C211yesmaximal, characteristic, complemented
5#13070092C211yesmaximal, characteristic, complemented
6#13069997C211yesmaximal, characteristic, complemented
7#13069946C211yesmaximal, characteristic, complemented
8#13069341C211yesmaximal, characteristic, complemented
9#13069175C211yesmaximal, characteristic, complemented
10#13068953C211yesmaximal, characteristic
11#13068953C211yesmaximal, characteristic
12#13068884C211yesmaximal, characteristic, complemented
13#13068876C211yesmaximal, characteristic
14#13068876C211yesmaximal, characteristic
15C11×#2451C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C22×#4325C2211yescharacteristic
19C2×C4⋊C4×D11—21no—
20C2×C4×D44C2211yescharacteristic
21C2×C4×D44C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C11×#398—21no—
24C11×#395—21no—
25C11×#391—21no—
26C11×#391C2211yescharacteristic
27C11×#391C2211yescharacteristic
28C11×#389C2211yescharacteristic
29C11×#389C2211yescharacteristic
30C11×#387—21no—
31C4×C11×C4⋊C4C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35#10622697—24no—
36C4×#4325—24no—
37#10622600—21no—
38C2×#66873C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46#10622548C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622281—21no—
52#10622281—21no—
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11—21no—
62C22×Q8×C11C2311yescharacteristic
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×C4×D11—21no—
66C22×C4×D11—21no—
67C11×C4⋊Q8—22no—
68C11×C4⋊Q8—41no—
69C4×Q8×C11—22no—
70C4×Q8×C11—41no—
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×#4325Q814yescomplemented
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—22no—
126#66872—22no—
127#66872—22no—
128#66872—41no—
129C4⋊(C11⋊C8)—22no—
130C4×C11⋊C8—22no—
131#26376—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×C11—42no—
139C2×Q8×C11—42no—
140C2×Q8×C11—81no—
141C2×Q8×C11C2×Q812yes—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44C2×D412yes—
160C2×D44C2×Q812yes—
161C2×D44#4112yes—
162C2×C4×D11—24no—
163C2×C4×D11—42no—
164C2×C4×D11—42no—
165C2×C4×D11—42no—
166C2×C4×D11—42no—
167C2×C4×D11—42no—
168C2×C4×D11—42no—
169C2×C4×D11—81no—
170C2×C4×D11—81no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—41no—
177C11×C4⋊C4—42no—
178C11×C4⋊C4—42no—
179C11×C4⋊C4—81no—
180C11×C4⋊C4—81no—
181C11×C4⋊C4SD1614yescomplemented
182C11×C4⋊C4C2×D412yes—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—42no—
190#4325—28no—
191(C2×D11)⋊C4—24no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—42no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—42no—
200C4⋊Dic11—81no—
201C4⋊Dic11#4112yes—
202Dic11⋊C4—42no—
203Dic11⋊C4—42no—
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⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8C2×D412yes—
215C2×C11⋊C8C2×Q812yes—
216C2×#476—111no—
217C2×C4×SD16—111no—
218#2451D1111yescharacteristic, complemented
219D4×C4⋊C4—111no—
220#2096—111no—
221#2084—111no—
222#2066—111no—
223#2058—111no—
224#1941—111no—
225#1916—111no—
226#1877—111no—
227#1877—111no—
228#1865—111no—
229#1864—111no—
230#1864—111no—
231C23×C11C22×D411yescharacteristic
232C22×D11—22no—
233C22×D11—22no—
234C22×D11—22no—
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—41no—
238C22×D11—41no—
239Q8×C11—22no—
240Q8×C11—22no—
241Q8×C11—41no—
242Q8×C11—41no—
243Q8×C11—84no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
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×C11—41no—
271C2×C4×C11C2×SD1612yes—
272C2×C4×C11C2×SD1612yes—
273C2×C4×C11C2×SD1612yes—
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C22×Q811yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11H(5,𝔽2)11yescharacteristic
279C2×C4×C112−1+411yescharacteristic
280C2×Dic11—22no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289D44—22no—
290D44—22no—
291D44—22no—
292D44C22⋊Q814yes—
293C4×D11—48no—
294C4×D11—84no—
295C4×D11—84no—
296C11⋊C8—22no—
297C11⋊C8—22no—
298C11⋊C8—41no—
299C11⋊C8—41no—
300C22×SD16—111no—
301C2×C4⋊Q8C2×D1111yescharacteristic
302C2×C4×Q8C2×D1111yescharacteristic
303C2×C4×D4—111no—
304C2×C4×D4—111no—
305C2×C4×D4—111no—
306C22×C4⋊C4—221no—
307#476—224no—
308C4×SD16—224no—
309C2×#106—111no—
310C2×#106—111no—
311C2×#106—111no—
312C2×#106—111no—
313C2×#106—111no—
314C2×C4⋊C8—111no—
315C2×#103—111no—
316C2×#103—111no—
317C2×#103—111no—
318C2×#102—111no—
319C2×#102—111no—
320C2×#102—111no—
321C2×C4×C8—111no—
322#398—21no—
323#395—21no—
324#391—21no—
325#391C2×D1111yescharacteristic
326#391C2×D1111yescharacteristic
327#389—111no—
328#389—111no—
329#389C2×D1111yescharacteristic
330#389C2×D1111yescharacteristic
331#387—21no—
332#385—221no—
333#385—221no—
334#384—111no—
335#380—221no—
336C4×C4⋊C4C2×D1111yescharacteristic
337#340—111no—
338#340—111no—
339#340—111no—
340#340—111no—
341#336—111no—
342#336—111no—
343#336—111no—
344#336—111no—
345C22×C11#52511yescharacteristic
346C22×C11D4211yescharacteristic
347C22×C11D4×Q811yescharacteristic
348C22×C11C22×SD1611yescharacteristic
349C22×C11#57511yescharacteristic
350C22×C11#57711yescharacteristic
351C22×C11#57711yescharacteristic
352C2×D11—24no—
353C2×D11—42no—
354C2×D11—42no—
355C2×D11—42no—
356C2×D11—42no—
357C2×D11—42no—
358C2×D11—42no—
359C4×C11—22no—
360C4×C11—22no—
361C4×C11—22no—
362C4×C11—41no—
363C4×C11—42no—
364C4×C11—41no—
365C4×C11—41no—
366C4×C11—42no—
367C4×C11—81no—
368C4×C11—81no—
369C4×C11C2×C22⋊Q811yescharacteristic
370C4×C11#53911yescharacteristic
371C4×C11#54711yescharacteristic
372C4×C11#55411yescharacteristic
373Dic11—42no—
374Dic11—81no—
375Dic11—81no—
376C22×Q8—21no—
377C22×Q8C22×D1111yescharacteristic
378C22×D4—111no—
379C23×C4—221no—
380C23×C4—221no—
381C23×C4—221no—
382C2×SD16—114no—
383C2×SD16—222no—
384C2×SD16—222no—
385C22×C8—111no—
386C22×C8—111no—
387C22×C8—111no—
388C22×C8—111no—
389C4⋊Q8—22no—
390C4⋊Q8—41no—
391C4×Q8—22no—
392C4×Q8—41no—
393C4×D4—222no—
394C4×D4—222no—
395C4×D4—222no—
396C4×D4—222no—
397C4×D4—441no—
398C4×D4—441no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—444no—
411C2×C4⋊C4C22⋊D1111yescharacteristic
412C2×C4⋊C4C22⋊D1111yescharacteristic
413C2×C4⋊C4C22×D1111yescharacteristic
414C2×C4⋊C4C22×D1111yescharacteristic
415C2×C4⋊C4C22×D1111yescharacteristic
416C2×C22⋊C4—221no—
417C2×C22⋊C4—221no—
418C2×C22⋊C4—221no—
419C2×C42—21no—
420C2×C42C22×D1111yescharacteristic
421C2×C42C22×D1111yescharacteristic
422C2×C42C22×D1111yescharacteristic
423#106—222no—
424#106—222no—
425#106—222no—
426#106—222no—
427#106—441no—
428C4⋊C8—222no—
429#103—222no—
430#103—222no—
431#103—441no—
432#102—114no—
433#102—222no—
434#102—222no—
435C4×C8—222no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95—221no—
443#95—221no—
444#95C22⋊D1111yescharacteristic
445#95C22⋊D1111yescharacteristic
446C2×C11#244911yescharacteristic
447C2×C11#310111yescharacteristic
448C2×C11#312511yescharacteristic
449C2×C11#326711yescharacteristic
450C2×C11D4×SD1611yescharacteristic
451C2×C11Q8×SD1611yescharacteristic
452C2×C11#338811yescharacteristic
453D11—44no—
454C24—221no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—42no—
461C2×Q8—42no—
462C2×Q8—81no—
463C2×Q8Q8×D1112yes—
464C2×D4—112no—
465C2×D4—112no—
466C2×D4—112no—
467C2×D4—221no—
468C2×D4—221no—
469C2×D4—221no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—224no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—442no—
479C22×C4—442no—
480C22×C4—442no—
481C22×C4—442no—
482C22×C4—442no—
483C22×C4—442no—
484C22×C4—881no—
485C22×C4—881no—
486C22×C4C2×C22⋊D1111yescharacteristic
487C22×C4C2×C22⋊D1111yescharacteristic
488C22×C4C2×C22⋊D1111yescharacteristic
489C22×C4C2×C22⋊D1111yescharacteristic
490C22×C4C2×C22⋊D1111yescharacteristic
491C22×C4C2×C22⋊D1111yescharacteristic
492C22×C4C23×D1111yescharacteristic
493SD16—228no—
494C2×C8—112no—
495C2×C8—112no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—41no—
512C4⋊C4—42no—
513C4⋊C4—42no—
514C4⋊C4—81no—
515C4⋊C4—81no—
516C4⋊C4—112no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—442no—
523C4⋊C4—442no—
524C4⋊C4—442no—
525C4⋊C4—881no—
526C4⋊C4#432514yescomplemented
527C4⋊C4D4×D1112yes—
528C22⋊C4—224no—
529C22⋊C4—442no—
530C22⋊C4—442no—
531C42—21no—
532C42—21no—
533C42—21no—
534C42—21no—
535C42—21no—
536C42—21no—
537C42—42no—
538C11#2637611yescharacteristic, complemented, Sylow
539C23—222no—
540C23—222no—
541C23—222no—
542C23—441no—
543C23—441no—
544C23—441no—
545C23—441no—
546C23C22×C22⋊D1111yescharacteristic
547Q8—22no—
548Q8—22no—
549Q8—41no—
550Q8—41no—
551Q8—84no—
552D4—114no—
553D4—222no—
554D4—222no—
555D4—222no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
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—41no—
582C2×C4—41no—
583C2×C4—222no—
584C2×C4—448no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—884no—
594C2×C4—884no—
595C2×C4C2×#432512yes—
596C2×C4C2×#432512yes—
597C2×C4C2×#432512yes—
598C2×C4C2×D4×D1111yescharacteristic
599C2×C4#6703711yescharacteristic
600C2×C4C2×Q8×D1111yescharacteristic
601C2×C4#6704011yescharacteristic
602C2×C4#41×D1111yescharacteristic
603C2×C4#41×D1111yescharacteristic
604C8—222no—
605C8—222no—
606C8—441no—
607C8—441no—
608C22—224no—
609C22—442no—
610C22—442no—
611C22—442no—
612C22—442no—
613C22—442no—
614C22—442no—
615C22D4×C22⋊D1111yescharacteristic
616C22C22×#432511yescharacteristic
617C22Q8×C22⋊D1111yescharacteristic
618C22#1062335311yescharacteristic
619C22#1062335911yescharacteristic
620C22#1062336711yescharacteristic
621C22#1062336811yescharacteristic
622C4—22no—
623C4—22no—
624C4—22no—
625C4—42no—
626C4—41no—
627C4—41no—
628C4—42no—
629C4—41no—
630C4—81no—
631C4—81no—
632C4—442no—
633C4—881no—
634C4—881no—
635C4D11×C22⋊Q811yescharacteristic
636C4#1062316211yescharacteristic
637C4#1062316711yescharacteristic
638C4#1062316911yescharacteristic
639C2—444no—
640C2#1307242211yescharacteristic
641C2#1307862011yescharacteristic
642C2#1307888711yescharacteristic
643C2#1308013711yescharacteristic
644C2D4×#432511yescharacteristic
645C2Q8×#432511yescharacteristic
646C2#1308155511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2451C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2451D11
hypocenterC11#26376
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2451

Complements

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

NH ≅ G/Ntype
4. #13070159C2semidirect
5. #13070092C2semidirect
6. #13069997C2semidirect
7. #13069946C2semidirect
8. #13069341C2semidirect
9. #13069175C2semidirect
12. #13068884C2semidirect
15. C11×#2451C2semidirect
86. C2×#4325Q8semidirect
181. C11×C4⋊C4SD16semidirect
218. #2451D11semidirect
526. C4⋊C4#4325semidirect
538. C11#26376semidirect

Maximal subgroups

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

subgroupindex
C2×#106226972
C2×C4×#43252
C4⋊C4×D442
#130701592
#130700922
#130699972
#130699462
#130693412
#130691752
#130689532
#130688842
#130688762
C11×#24512
#2637611