Finite Group Databasebeta

← #14775717

Subgroups — #14775717

Order 2816.

870 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622504C211yesmaximal, characteristic
2#13071711C211yesmaximal, characteristic, complemented
3#13071517C211yesmaximal, characteristic
4#13069583C211yesmaximal, characteristic, complemented
5#13069371C211yesmaximal, characteristic, complemented
6#13069358C211yesmaximal, characteristic, complemented
7#13069210C211yesmaximal, characteristic, complemented
8#13069191C211yesmaximal, characteristic, complemented
9#13068862C211yesmaximal, characteristic
10#13068860C211yesmaximal, characteristic
11#13068490C211yesmaximal, characteristic, complemented
12#13068440C211yesmaximal, characteristic
13#13068440C211yesmaximal, characteristic
14C4×#66885C211yesmaximal, characteristic
15C11×#1942C211yesmaximal, characteristic, complemented
16C2×#66946C2211yescharacteristic
17C2×#66946C2211yescharacteristic
18C2×C4⋊C4×D11—21no—
19C2×#66943C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22C2×C11×#107C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66879C2211yescharacteristic
29C2×#66879C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31#10622602—21no—
32#10622598C2211yescharacteristic
33#10622589C2211yescharacteristic
34C4⋊C4×Dic11—21no—
35C4⋊C4×Dic11C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37#10622586C2211yescharacteristic
38#10622585—21no—
39C2×#66873C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43C4×C4⋊Dic11C2211yescharacteristic
44C4×Dic11⋊C4C2211yescharacteristic
45#10622504C418yescomplemented
46#10622281—21no—
47#10622280—21no—
48#10622266—21no—
49#10622265—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×D44C2311yescharacteristic
61C22×C4×D11—21no—
62C22×C4×D11—21no—
63C22×C4×D11—21no—
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4D411yescharacteristic
86C2×Dic11⋊C4D411yescharacteristic
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11C2311yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94#66946—22no—
95#66946—22no—
96#66946—41no—
97#66946C2×C414yes—
98C4⋊C4×D11—44no—
99#66943—22no—
100#66943C2×C414yescomplemented
101C4×D44—22no—
102C4×D44—41no—
103C11×#107—41no—
104C11×#107C2×C414yescomplemented
105C4×C8×C11—41no—
106C11×#95—21no—
107C11×#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95D411yescharacteristic
114C11⋊#95D411yescharacteristic
115#66885C2×C414yes—
116#66885Q814yes—
117#66879—22no—
118#66879—41no—
119Dic11⋊C8C2×C414yescomplemented
120#66873—22no—
121#66873C2×C414yes—
122#66872C2×C414yescomplemented
123#66871—41no—
124#22974—111nomaximal, Sylow
125C23×D11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2411yescharacteristic
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11C2×D411yescharacteristic
137C22×Dic11C2×D411yescharacteristic
138C22×Dic11C2×D411yescharacteristic
139C22×Dic11C2×D411yescharacteristic
140C2×D44—21no—
141C2×D44—21no—
142C2×D44—21no—
143C2×D44C22×C412yes—
144C2×D44C2×Q812yes—
145C2×D44#4112yes—
146C2×C4×D11—24no—
147C2×C4×D11—42no—
148C2×C4×D11—42no—
149C2×C4×D11—42no—
150C2×C4×D11—42no—
151C2×C4×D11—42no—
152C2×C4×D11—42no—
153C2×C4×D11—81no—
154C2×C4×D11—81no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11C22×C412yes—
160C2×C8×C11C2×Q812yes—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—42no—
168C11×C4⋊C4—42no—
169C11×C4⋊C4C22×C412yes—
170C11×C4⋊C4C22×C412yes—
171C42×C11—21no—
172C42×C11—21no—
173(C2×D11)⋊C4—24no—
174(C2×D11)⋊C4—42no—
175(C2×D11)⋊C4—42no—
176C4⋊Dic11—24no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—42no—
182C4⋊Dic11C22×C412yes—
183C4⋊Dic11C2×Q812yes—
184Dic11⋊C4—24no—
185Dic11⋊C4—22no—
186Dic11⋊C4—41no—
187Dic11⋊C4—42no—
188Dic11⋊C4—81no—
189Dic11⋊C4—81no—
190C4×Dic11—21no—
191C4×Dic11—21no—
192C4×Dic11—42no—
193C4×Dic11—81no—
194C4×Dic11—81no—
195C4×Dic11C22×C412yes—
196C4×Dic11#4112yes—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8C22×C412yes—
203C2×#478—111no—
204#2370—111no—
205D4×C4⋊C4—111no—
206#1992—111no—
207#1947—111no—
208#1944—111no—
209#1942D1111yescharacteristic, complemented
210#1921—111no—
211#1919—111no—
212#1862—111no—
213#1862—111no—
214#1771—111no—
215#1762—111no—
216#1762—111no—
217C4×#102—111no—
218C23×C11C22×D411yescharacteristic
219C22×D11—22no—
220C22×D11—22no—
221C22×D11—22no—
222C22×D11—41no—
223C22×D11—41no—
224C22×D11—41no—
225C22×D11—41no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11AGL(1,ℤ/8)12yes—
244C2×C4×C11C23×C411yescharacteristic
245C2×C4×C11C22×Q811yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11H(5,𝔽2)11yescharacteristic
249C2×C4×C112−1+411yescharacteristic
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—22no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—22no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11C4×D412yes—
270C2×Dic11C4×D412yes—
271D44—22no—
272D44—22no—
273D44—22no—
274D44C4×Q814yes—
275C4×D11—48no—
276C4×D11—84no—
277C4×D11—84no—
278C8×C11—22no—
279C8×C11—22no—
280C11⋊C8—22no—
281C11⋊C8—41no—
282C2×#125—111no—
283C2×C4×D4—111no—
284C2×C4×D4—111no—
285C2×C4×D4—111no—
286C22×C4⋊C4—221no—
287#478—118no—
288C2×#107—111no—
289C2×#107C2×D1111yescharacteristic
290C2×#107C2×D1111yescharacteristic
291C2×#106—111no—
292C2×C4⋊C8—111no—
293C2×#102—111no—
294C2×#102—111no—
295C2×#102—111no—
296C2×#102—111no—
297C2×#97—111no—
298C2×#97—111no—
299C2×C4×C8C2×D1111yescharacteristic
300#389—111no—
301#389—111no—
302#389—221no—
303#389C2×D1111yescharacteristic
304#389C2×D1111yescharacteristic
305#387—221no—
306#387—221no—
307#385—221no—
308#385—221no—
309#384—111no—
310#380—221no—
311C4×C4⋊C4—111no—
312C4×C4⋊C4—111no—
313C4×C4⋊C4—111no—
314C4×C4⋊C4—111no—
315C4×C4⋊C4—221no—
316#340—111no—
317#340—111no—
318#340—111no—
319#340—111no—
320#340—111no—
321#340—111no—
322#340C2×D1111yescharacteristic
323#340C2×D1111yescharacteristic
324#336—111no—
325#336—111no—
326C22×C11C2×C4×D411yescharacteristic
327C22×C11#54611yescharacteristic
328C22×C11D4×Q811yescharacteristic
329C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
330C22×C11#57511yescharacteristic
331C22×C11#57611yescharacteristic
332C22×C11#57811yescharacteristic
333C2×D11—24no—
334C2×D11—42no—
335C2×D11—42no—
336C2×D11—42no—
337C2×D11—42no—
338C2×D11—42no—
339C2×D11—42no—
340C4×C11—22no—
341C4×C11—42no—
342C4×C11—42no—
343C4×C11—41no—
344C4×C11—81no—
345C4×C11—81no—
346C4×C11C2×C4×Q811yescharacteristic
347C4×C11#52011yescharacteristic
348C4×C11#55211yescharacteristic
349C4×C11#55411yescharacteristic
350Dic11—22no—
351Dic11—22no—
352Dic11—42no—
353Dic11—42no—
354Dic11—41no—
355Dic11—41no—
356Dic11—81no—
357C22×D4—111no—
358C23×C4—221no—
359C23×C4—221no—
360C23×C4—221no—
361C22×C8—111no—
362C22×C8—111no—
363C22×C8C22×D1111yescharacteristic
364C22×C8C22×D1111yescharacteristic
365#125—114no—
366#125—222no—
367C4×D4—114no—
368C4×D4—222no—
369C4×D4—222no—
370C4×D4—222no—
371C4×D4—441no—
372C4×D4—441no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—111no—
376C2×C4⋊C4—111no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—444no—
387C2×C4⋊C4C22×D1111yescharacteristic
388C2×C4⋊C4C22×D1111yescharacteristic
389C2×C4⋊C4C22×D1111yescharacteristic
390C2×C4⋊C4C22×D1111yescharacteristic
391C2×C22⋊C4—221no—
392C2×C22⋊C4—221no—
393C2×C22⋊C4—221no—
394C2×C42—111no—
395C2×C42—111no—
396C2×C42—221no—
397C2×C42—221no—
398C2×C42—221no—
399C2×C42C22×D1111yescharacteristic
400#107—41no—
401#107—441no—
402#107C4×D1114yescomplemented
403#106—114no—
404C4⋊C8—114no—
405#102—114no—
406#102—114no—
407#102—114no—
408#102—222no—
409#97—222no—
410#97—441no—
411C4×C8—41no—
412#95—21no—
413#95—21no—
414#95—111no—
415#95—111no—
416#95—221no—
417#95—221no—
418#95—221no—
419#95—221no—
420#95—221no—
421C2×C11#236011yescharacteristic
422C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
423C2×C11#295111yescharacteristic
424C2×C11#331511yescharacteristic
425C2×C11#331811yescharacteristic
426C2×C11#338611yescharacteristic
427C2×C11#338911yescharacteristic
428D11—44no—
429C24—221no—
430C2×D4—112no—
431C2×D4—112no—
432C2×D4—112no—
433C2×D4—221no—
434C2×D4—221no—
435C2×D4—221no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—111no—
441C22×C4—111no—
442C22×C4—111no—
443C22×C4—111no—
444C22×C4—224no—
445C22×C4—221no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4—442no—
449C22×C4—442no—
450C22×C4—442no—
451C22×C4—442no—
452C22×C4—442no—
453C22×C4—442no—
454C22×C4—881no—
455C22×C4—881no—
456C22×C4D4×D1111yescharacteristic
457C22×C4D4×D1111yescharacteristic
458C22×C4C23×D1111yescharacteristic
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—112no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8C2×C4×D1112yes—
470C2×C8Q8×D1112yes—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—42no—
478C4⋊C4—42no—
479C4⋊C4—112no—
480C4⋊C4—112no—
481C4⋊C4—224no—
482C4⋊C4—224no—
483C4⋊C4—222no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—441no—
489C4⋊C4—442no—
490C4⋊C4—442no—
491C4⋊C4—881no—
492C4⋊C4—881no—
493C4⋊C4C2×C4×D1112yes—
494C4⋊C4C2×C4×D1112yes—
495C22⋊C4—224no—
496C22⋊C4—442no—
497C22⋊C4—442no—
498C42—21no—
499C42—21no—
500C42—112no—
501C42—112no—
502C42—221no—
503C42—221no—
504C42—442no—
505C42—881no—
506C42—881no—
507C11#2297411yescharacteristic, complemented, Sylow
508C23—222no—
509C23—222no—
510C23—222no—
511C23—441no—
512C23—441no—
513C23—441no—
514C23—441no—
515C23C2×D4×D1111yescharacteristic
516D4—114no—
517D4—222no—
518D4—222no—
519D4—222no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—112no—
538C2×C4—112no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—222no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—222no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—448no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—884no—
560C2×C4—884no—
561C2×C4#6696412yes—
562C2×C4C22×C4×D1111yescharacteristic
563C2×C4#6703711yescharacteristic
564C2×C4C2×Q8×D1111yescharacteristic
565C2×C4#6704011yescharacteristic
566C2×C4#41×D1111yescharacteristic
567C2×C4#41×D1111yescharacteristic
568C8—22no—
569C8—22no—
570C8—222no—
571C8—441no—
572C22—224no—
573C22—442no—
574C22—442no—
575C22—442no—
576C22—442no—
577C22—442no—
578C22—442no—
579C22C4×D4×D1111yescharacteristic
580C22#1062314111yescharacteristic
581C22#1062325811yescharacteristic
582C22C2×#6696411yescharacteristic
583C22#1062329711yescharacteristic
584C22#1062329911yescharacteristic
585C22#1062330011yescharacteristic
586C4—22no—
587C4—41no—
588C4—42no—
589C4—42no—
590C4—81no—
591C4—81no—
592C4—222no—
593C4—222no—
594C4—441no—
595C4—441no—
596C4—442no—
597C4—442no—
598C4—881no—
599C4#1062303511yescharacteristic
600C4C4×Q8×D1111yescharacteristic
601C4#1062316711yescharacteristic
602C4#1062322411yescharacteristic
603C2—444no—
604C2#1307161811yescharacteristic
605C2C4×#6696411yescharacteristic
606C2#1307749111yescharacteristic
607C2#1308071811yescharacteristic
608C2#1308076311yescharacteristic
609C2#1308154211yescharacteristic
610C2#1308157711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1942C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1942D11
hypocenterC11#22974
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1942

Complements

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

NH ≅ G/Ntype
2. #13071711C2semidirect
4. #13069583C2semidirect
5. #13069371C2semidirect
6. #13069358C2semidirect
7. #13069210C2semidirect
8. #13069191C2semidirect
11. #13068490C2semidirect
15. C11×#1942C2semidirect
45. #10622504C4semidirect
100. #66943C2×C4semidirect
104. C11×#107C2×C4semidirect
119. Dic11⋊C8C2×C4semidirect
122. #66872C2×C4semidirect
209. #1942D11semidirect
402. #107C4×D11semidirect
507. C11#22974semidirect

Maximal subgroups

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

subgroupindex
C2×#106225042
#130717112
#130715172
#130695832
#130693712
#130693582
#130692102
#130691912
#130688622
#130688602
#130684902
#130684402
C4×#668852
C11×#19422
#2297411