Finite Group Databasebeta

← #14782864

Subgroups — #14782864

Order 2816.

950 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622474C211yesmaximal, characteristic
2C2×#10622450C211yesmaximal, characteristic
3#13071097C211yesmaximal, characteristic
4D11×#389C211yesmaximal, characteristic
5#13070120C211yesmaximal, characteristic, complemented
6#13070117C211yesmaximal, characteristic, complemented
7#13070115C211yesmaximal, characteristic, complemented
8#13070112C211yesmaximal, characteristic, complemented
9#13070109C211yesmaximal, characteristic, complemented
10#13070108C211yesmaximal, characteristic, complemented
11#13070106C211yesmaximal, characteristic, complemented
12#13068334C211yesmaximal, characteristic
13#13068334C211yesmaximal, characteristic
14#13068334C211yesmaximal, characteristic
15C11×#2088C211yesmaximal, characteristic, complemented
16C22×#4313C2211yescharacteristic
17C22×#4313C2211yescharacteristic
18C2×#66945C2211yescharacteristic
19C2×#66945C2211yescharacteristic
20C2×C4⋊C4×D11—21no—
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×C4⋊C4×D11C2211yescharacteristic
23C2×C42×D11C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C11×#389C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31#10622602—21no—
32#10622598C2211yescharacteristic
33#10622598C2211yescharacteristic
34C4⋊C4×Dic11—21no—
35#10622586C2211yescharacteristic
36#10622586C2211yescharacteristic
37#10622585—21no—
38C2×#66872C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40#10622541C2211yescharacteristic
41#10622541C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43#10622474—24no—
44#10622450—24no—
45#10622281—21no—
46D11×#95—21no—
47#10622262—21no—
48#10622260—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×C4×D11—21no—
62C22×C4×D11—21no—
63C22×C4×D11D411yescharacteristic
64C22×C4×D11D411yescharacteristic
65C22×C4×D11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11D411yescharacteristic
92C2×C4×Dic11D411yescharacteristic
93C2×C4×Dic11C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C2×#4313—22no—
97C2×#4313—22no—
98C2×#4313—22no—
99C2×#4313—22no—
100C2×#4313—22no—
101C2×#4313D414yes—
102#66945—22no—
103#66945—22no—
104#66945—22no—
105#66945Q814yes—
106C4⋊C4×D11—22no—
107C4⋊C4×D11—22no—
108C4⋊C4×D11—22no—
109C4⋊C4×D11—44no—
110C4⋊C4×D11Q814yes—
111C42×D11—22no—
112C42×D11—22no—
113C11×#106—22no—
114C11×C4⋊C8—22no—
115C11×#95—21no—
116C11×#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123#66882—22no—
124Dic11⋊C8—22no—
125Dic11⋊C8—22no—
126#66872—22no—
127#66871—22no—
128C4⋊(C11⋊C8)—22no—
129#23670—111nomaximal, Sylow
130C23×D11C2×D411yescharacteristic
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2411yescharacteristic
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11C2×D411yescharacteristic
143C22×Dic11C2×D411yescharacteristic
144C22×Dic11C2×D411yescharacteristic
145C2×C4×D11—22no—
146C2×C4×D11—22no—
147C2×C4×D11—22no—
148C2×C4×D11—24no—
149C2×C4×D11—22no—
150C2×C4×D11—41no—
151C2×C4×D11—41no—
152C2×C4×D11—42no—
153C2×C4×D11—42no—
154C2×C4×D11—42no—
155C2×C4×D11—42no—
156C2×C4×D11—42no—
157C2×C4×D11C2×D412yes—
158C2×C4×D11C2×Q812yes—
159C2×C4×D11C2×Q812yes—
160C2×C4×D11#4112yes—
161C2×C4×D11#4112yes—
162C2×C4×D11#4112yes—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11C2×D412yes—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—42no—
176C11×C4⋊C4—42no—
177C11×C4⋊C4C2×Q812yes—
178C11×C4⋊C4C2×Q812yes—
179C42×C11—21no—
180C42×C11—21no—
181(C2×D11)⋊C4—24no—
182(C2×D11)⋊C4—42no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—42no—
190C4⋊Dic11—42no—
191C4⋊Dic11C2×Q812yes—
192C4⋊Dic11C2×Q812yes—
193Dic11⋊C4—24no—
194Dic11⋊C4—42no—
195Dic11⋊C4—42no—
196Dic11⋊C4—42no—
197Dic11⋊C4—42no—
198Dic11⋊C4—42no—
199C4×Dic11—22no—
200C4×Dic11—22no—
201C4×Dic11—24no—
202C4×Dic11—21no—
203C4×Dic11—21no—
204C4×Dic11—42no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8C2×D412yes—
211#4313—28no—
212#4313—44no—
213C2×#428—111no—
214C2×#423—111no—
215#2296—111no—
216C2×#389—111no—
217#2088—111no—
218#2088—111no—
219#2088—111no—
220#2088D1111yescharacteristic, complemented
221#2087—111no—
222#2087—111no—
223#2086—111no—
224#2086—111no—
225#1736—111no—
226#1736—111no—
227#1736—111no—
228C23×C11C22×D411yescharacteristic
229C22×D11—21no—
230C22×D11—21no—
231C22×D11—21no—
232C22×D11—21no—
233C22×D11#12112yes—
234C22×D11C22⋊Q812yes—
235C22×D11C22⋊Q812yes—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
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#13712yes—
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C22×Q811yescharacteristic
256C2×C4×C11C22×Q811yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11#12112yes—
278C2×Dic11C22⋊Q812yes—
279C2×Dic11C22⋊Q812yes—
280C2×Dic11AGL(1,ℤ/8)12yes—
281C4×D11—44no—
282C4×D11—44no—
283C4×D11—48no—
284C4×D11—84no—
285C4×D11#12314yes—
286C4×D11#12514yes—
287C4×D11#12514yes—
288C4×D11C4⋊Q814yes—
289C8×C11—22no—
290C8×C11—41no—
291C11⋊C8—22no—
292C11⋊C8—41no—
293C22×M16—111no—
294C22×M16—111no—
295C2×#117—111no—
296C2×#117—111no—
297C22×C4⋊C4—111no—
298C22×C4⋊C4—111no—
299C22×C4⋊C4—221no—
300C22×C42—111no—
301#428—224no—
302C2×#107—111no—
303C2×#107—111no—
304C2×#106—111no—
305C2×#106C2×D1111yescharacteristic
306#423—224no—
307C2×C4⋊C8—111no—
308C2×C4⋊C8—111no—
309C2×C4⋊C8—111no—
310C2×C4⋊C8C2×D1111yescharacteristic
311#389—111no—
312#389—111no—
313#389—111no—
314#389—111no—
315#389—111no—
316#389—111no—
317#389—221no—
318#389—221no—
319#389C2×D1111yescharacteristic
320#389C2×D1111yescharacteristic
321#385—221no—
322#385—221no—
323C4×C4⋊C4—221no—
324C4×C4⋊C4—221no—
325C2×#95—221no—
326#340—111no—
327#340—111no—
328#340—111no—
329#340—111no—
330#340—111no—
331#340—111no—
332#340—111no—
333#340—111no—
334#340—111no—
335#340C2×D1111yescharacteristic
336#340C2×D1111yescharacteristic
337#340C2×D1111yescharacteristic
338C22×C11C2×#12111yescharacteristic
339C22×C11C2×C22⋊Q811yescharacteristic
340C22×C11C2×C22⋊Q811yescharacteristic
341C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
342C22×C11C2×#13711yescharacteristic
343C22×C11#57511yescharacteristic
344C22×C11#57511yescharacteristic
345C2×D11—22no—
346C2×D11—22no—
347C2×D11—22no—
348C2×D11—22no—
349C2×D11—22no—
350C2×D11—22no—
351C2×D11#39814yes—
352C4×C11—22no—
353C4×C11—42no—
354C4×C11—42no—
355C4×C11—41no—
356C4×C11—81no—
357C4×C11—81no—
358C4×C11C2×#12311yescharacteristic
359C4×C11C2×#12511yescharacteristic
360C4×C11C2×#12511yescharacteristic
361C4×C11C2×C4⋊Q811yescharacteristic
362Dic11—22no—
363Dic11—42no—
364Dic11—42no—
365Dic11—41no—
366Dic11—81no—
367Dic11—81no—
368Dic11#39814yes—
369C23×C4—111no—
370C23×C4—111no—
371C23×C4—111no—
372C23×C4—221no—
373C23×C4—221no—
374C2×M16—114no—
375C2×M16—222no—
376C2×M16—222no—
377C2×M16—222no—
378C2×M16—222no—
379C2×M16—222no—
380C22×C8—111no—
381C22×C8—111no—
382C22×C8C22×D1111yescharacteristic
383C22×C8C22×D1111yescharacteristic
384#117—114no—
385#117—222no—
386#117—222no—
387#117—222no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—114no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—222no—
396C2×C4⋊C4—222no—
397C2×C4⋊C4—222no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—444no—
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C4⋊C4C22×D1111yescharacteristic
409C2×C4⋊C4C22×D1111yescharacteristic
410C2×C4⋊C4C22×D1111yescharacteristic
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C42—111no—
414C2×C42—111no—
415C2×C42—111no—
416C2×C42—222no—
417C2×C42—222no—
418C2×C42—221no—
419C2×C42—221no—
420C2×C42C22×D1111yescharacteristic
421#107—222no—
422#107—222no—
423#106—22no—
424#106—222no—
425C4⋊C8—22no—
426C4⋊C8—222no—
427C4⋊C8—222no—
428C4⋊C8—222no—
429#95—21no—
430#95—21no—
431#95—221no—
432#95—221no—
433#95—221no—
434#95—221no—
435#95—221no—
436#95—221no—
437C2×C11C2×#39811yescharacteristic
438C2×C11#305511yescharacteristic
439C2×C11#305611yescharacteristic
440C2×C11#307711yescharacteristic
441C2×C11#307811yescharacteristic
442C2×C11#307911yescharacteristic
443C2×C11#308011yescharacteristic
444D11—24no—
445C24—111no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—111no—
451C22×C4—112no—
452C22×C4—112no—
453C22×C4—112no—
454C22×C4—112no—
455C22×C4—112no—
456C22×C4—112no—
457C22×C4—111no—
458C22×C4—111no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4—222no—
462C22×C4—224no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—222no—
466C22×C4—221no—
467C22×C4—221no—
468C22×C4—441no—
469C22×C4—441no—
470C22×C4—442no—
471C22×C4—442no—
472C22×C4—442no—
473C22×C4—442no—
474C22×C4—442no—
475C22×C4D4×D1111yescharacteristic
476C22×C4D4×D1111yescharacteristic
477C22×C4C23×D1111yescharacteristic
478M16—228no—
479M16—444no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—112no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8D4×D1112yes—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—42no—
499C4⋊C4—42no—
500C4⋊C4—112no—
501C4⋊C4—112no—
502C4⋊C4—224no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—442no—
510C4⋊C4—442no—
511C4⋊C4—442no—
512C4⋊C4—442no—
513C4⋊C4—442no—
514C4⋊C4—442no—
515C4⋊C4—442no—
516C4⋊C4Q8×D1112yes—
517C4⋊C4Q8×D1112yes—
518C22⋊C4—224no—
519C22⋊C4—442no—
520C42—21no—
521C42—21no—
522C42—222no—
523C42—222no—
524C42—224no—
525C42—221no—
526C42—221no—
527C42—442no—
528C11#2367011yescharacteristic, complemented, Sylow
529C23—112no—
530C23—112no—
531C23—112no—
532C23—221no—
533C23—221no—
534C23—221no—
535C23—221no—
536C23C2×D4×D1111yescharacteristic
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—112no—
555C2×C4—112no—
556C2×C4—112no—
557C2×C4—114no—
558C2×C4—114no—
559C2×C4—114no—
560C2×C4—114no—
561C2×C4—112no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—221no—
567C2×C4—222no—
568C2×C4—222no—
569C2×C4—444no—
570C2×C4—444no—
571C2×C4—448no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—884no—
583C2×C4#6696812yes—
584C2×C4C2×D4×D1111yescharacteristic
585C2×C4C2×Q8×D1111yescharacteristic
586C2×C4C2×Q8×D1111yescharacteristic
587C2×C4#41×D1111yescharacteristic
588C2×C4#41×D1111yescharacteristic
589C2×C4#41×D1111yescharacteristic
590C8—22no—
591C8—41no—
592C8—222no—
593C8—441no—
594C22—114no—
595C22—222no—
596C22—222no—
597C22—222no—
598C22—222no—
599C22—222no—
600C22—222no—
601C22D11×#12111yescharacteristic
602C22D11×C22⋊Q811yescharacteristic
603C22D11×C22⋊Q811yescharacteristic
604C22C2×#6696811yescharacteristic
605C22#1062329911yescharacteristic
606C22D11×AGL(1,ℤ/8)11yescharacteristic
607C22#1062330811yescharacteristic
608C4—22no—
609C4—42no—
610C4—42no—
611C4—41no—
612C4—81no—
613C4—81no—
614C4—114no—
615C4—222no—
616C4—442no—
617C4—442no—
618C4—441no—
619C4—881no—
620C4—881no—
621C4D11×#12311yescharacteristic
622C4D11×#12511yescharacteristic
623C4D11×#12511yescharacteristic
624C4D11×C4⋊Q811yescharacteristic
625C2—224no—
626C2D11×#39811yescharacteristic
627C2#1307823011yescharacteristic
628C2#1307823911yescharacteristic
629C2#1307841111yescharacteristic
630C2#1307841611yescharacteristic
631C2#1307842811yescharacteristic
632C2#1307843511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2088C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#2088D11
hypocenterC11#23670
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2088

Complements

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

NH ≅ G/Ntype
5. #13070120C2semidirect
6. #13070117C2semidirect
7. #13070115C2semidirect
8. #13070112C2semidirect
9. #13070109C2semidirect
10. #13070108C2semidirect
11. #13070106C2semidirect
15. C11×#2088C2semidirect
220. #2088D11semidirect
528. C11#23670semidirect

Maximal subgroups

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

subgroupindex
C2×#106224742
C2×#106224502
#130710972
D11×#3892
#130701202
#130701172
#130701152
#130701122
#130701092
#130701082
#130701062
#130683342
C11×#20882
#2367011