Finite Group Databasebeta

← #14775726

Subgroups — #14775726

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
1#13071716C211yesmaximal, characteristic, complemented
2D4×C4⋊Dic11C211yesmaximal, characteristic
3#13069586C211yesmaximal, characteristic, complemented
4#13069375C211yesmaximal, characteristic, complemented
5#13069360C211yesmaximal, characteristic, complemented
6#13069350C211yesmaximal, characteristic, complemented
7#13069210C211yesmaximal, characteristic, complemented
8#13069196C211yesmaximal, characteristic, complemented
9#13068865C211yesmaximal, characteristic
10#13068865C211yesmaximal, characteristic
11#13068493C211yesmaximal, characteristic, complemented
12#13068443C211yesmaximal, characteristic
13#13068441C211yesmaximal, characteristic
14#102×Dic11C211yesmaximal, characteristic
15C2×C11×#478C211yesmaximal, characteristic
16C2×C11×#125C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C2×D4×Dic11C2211yescharacteristic
20C22×C4⋊Dic11—21no—
21C11×#478C418yescomplemented
22C2×C11×#107C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29#10622825—21no—
30C2×#66882C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32C2×#66879C2211yescharacteristic
33C2×C8×Dic11C2211yescharacteristic
34#10622598—21no—
35#10622598C2211yescharacteristic
36#10622598C2211yescharacteristic
37#10622598C2211yescharacteristic
38#10622598C2211yescharacteristic
39#10622594—21no—
40#10622594—21no—
41C4⋊C4×Dic11—21no—
42C4⋊C4×Dic11C2211yescharacteristic
43C4⋊C4×Dic11C2211yescharacteristic
44#10622563—21no—
45#10622563—21no—
46#10622548C2211yescharacteristic
47C4×C4⋊Dic11C2211yescharacteristic
48C4×C4⋊Dic11C2211yescharacteristic
49C2×#66867C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C23×Dic11—21no—
63C23×Dic11—21no—
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C11×#125—22no—
67C11×#125C2×C414yescomplemented
68C4×D4×C11—22no—
69C4×D4×C11C2×C414yes—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C42×C11C2311yescharacteristic
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79D4×Dic11—22no—
80D4×Dic11—22no—
81D4×Dic11—41no—
82D4×Dic11—41no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—44no—
90C2×C4⋊Dic11D411yescharacteristic
91C2×C4⋊Dic11D411yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11C2311yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C11×#107C2×C414yescomplemented
104C11×#106C2×C414yescomplemented
105C11×C4⋊C8C2×C414yescomplemented
106C11×#102C2×C414yes—
107C11×#102C2×C414yes—
108#66896—22no—
109#66896Q814yes—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95D411yescharacteristic
118C11⋊#95D411yescharacteristic
119#66882—41no—
120#66882—41no—
121#66879—41no—
122C8×Dic11—41no—
123#66867—22no—
124#22974—111nomaximal, Sylow
125C24×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11C22×C412yes—
130C2×D4×C11C2×Q812yes—
131C2×D4×C11#4112yes—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—24no—
136C22×C4×C11—42no—
137C22×C4×C11—42no—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2411yescharacteristic
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—42no—
146C22×Dic11—42no—
147C22×Dic11—42no—
148C22×Dic11—42no—
149C22×Dic11—81no—
150C22×Dic11—81no—
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11C22×C412yes—
160C2×C8×C11C22×C412yes—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—24no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4C22×C412yes—
167C11×C4⋊C4C22×C412yes—
168C11×C4⋊C4C22×C412yes—
169C11×C22⋊C4—24no—
170C42×C11C22×C412yes—
171C42×C11#4112yes—
172C22⋊Dic11—42no—
173C22⋊Dic11—42no—
174C4⋊Dic11—22no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—41no—
183C4⋊Dic11—42no—
184C4⋊Dic11—42no—
185C4⋊Dic11—42no—
186C4⋊Dic11—42no—
187C4⋊Dic11—81no—
188C4⋊Dic11—81no—
189C4⋊Dic11C2×Q812yes—
190C4×Dic11—21no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—42no—
195C4×Dic11—81no—
196C4×Dic11—81no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8C2×Q812yes—
203C2×#478D1111yescharacteristic
204#2370—111no—
205D4×C4⋊C4—111no—
206#1992—111no—
207#1947—111no—
208#1944—111no—
209#1942—111no—
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×C11—22no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11—41no—
222C23×C11—41no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11C22×D411yescharacteristic
226D4×C11—22no—
227D4×C11—22no—
228D4×C11—22no—
229D4×C11C4×Q814yes—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—48no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11C4×D412yes—
245C2×C4×C11C4×D412yes—
246C2×C4×C11C23×C411yescharacteristic
247C2×C4×C11C22×Q811yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11H(5,𝔽2)11yescharacteristic
251C2×C4×C112−1+411yescharacteristic
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—22no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
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—84no—
276C2×Dic11—84no—
277C2×Dic11AGL(1,ℤ/8)12yes—
278C8×C11—22no—
279C8×C11—22no—
280C11⋊C8—22no—
281C11⋊C8—41no—
282C2×#125C2×D1111yescharacteristic
283C2×C4×D4—111no—
284C2×C4×D4—111no—
285C2×C4×D4C2×D1111yescharacteristic
286C22×C4⋊C4—221no—
287#478Dic1118yescomplemented
288C2×#107—111no—
289C2×#107—111no—
290C2×#107C2×D1111yescharacteristic
291C2×#106C2×D1111yescharacteristic
292C2×C4⋊C8C2×D1111yescharacteristic
293C2×#102—111no—
294C2×#102—111no—
295C2×#102C2×D1111yescharacteristic
296C2×#102C2×D1111yescharacteristic
297C2×#97—111no—
298C2×#97—111no—
299C2×C4×C8—111no—
300#389—111no—
301#389—111no—
302#389—111no—
303#389—111no—
304#389—221no—
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#340—111no—
323#340—111no—
324#336—111no—
325#336—111no—
326C22×C11—24no—
327C22×C11—42no—
328C22×C11—42no—
329C22×C11—42no—
330C22×C11—42no—
331C22×C11—42no—
332C22×C11—42no—
333C22×C11C2×C4×D411yescharacteristic
334C22×C11#54611yescharacteristic
335C22×C11D4×Q811yescharacteristic
336C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
337C22×C11#57511yescharacteristic
338C22×C11#57611yescharacteristic
339C22×C11#57811yescharacteristic
340C4×C11—22no—
341C4×C11—22no—
342C4×C11—42no—
343C4×C11—42no—
344C4×C11—42no—
345C4×C11C2×C4×Q811yescharacteristic
346C4×C11#52011yescharacteristic
347C4×C11#55211yescharacteristic
348C4×C11#55411yescharacteristic
349Dic11—22no—
350Dic11—42no—
351Dic11—41no—
352Dic11—41no—
353Dic11—41no—
354Dic11—81no—
355Dic11—81no—
356Dic11—81no—
357C22×D4C22×D1111yescharacteristic
358C23×C4—21no—
359C23×C4—221no—
360C23×C4—221no—
361C22×C8—111no—
362C22×C8—111no—
363C22×C8C22×D1111yescharacteristic
364C22×C8C22×D1111yescharacteristic
365#125—22no—
366#125C2×Dic1114yescomplemented
367C4×D4—22no—
368C4×D4—222no—
369C4×D4—222no—
370C4×D4—441no—
371C4×D4—441no—
372C4×D4C2×Dic1114yes—
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—111no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—444no—
388C2×C4⋊C4C22×D1111yescharacteristic
389C2×C4⋊C4C22×D1111yescharacteristic
390C2×C4⋊C4C22×D1111yescharacteristic
391C2×C22⋊C4—21no—
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—441no—
401#107—441no—
402#107C2×Dic1114yescomplemented
403#106C2×Dic1114yescomplemented
404C4⋊C8C2×Dic1114yescomplemented
405#102—114no—
406#102—222no—
407#102C2×Dic1114yes—
408#102C2×Dic1114yes—
409#97—222no—
410#97—441no—
411C4×C8—441no—
412#95—111no—
413#95—111no—
414#95—221no—
415#95—221no—
416#95—221no—
417#95—221no—
418#95—221no—
419#95—221no—
420#95—221no—
421C2×C11—44no—
422C2×C11#236011yescharacteristic
423C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
424C2×C11#295111yescharacteristic
425C2×C11#331511yescharacteristic
426C2×C11#331811yescharacteristic
427C2×C11#338611yescharacteristic
428C2×C11#338911yescharacteristic
429C24—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4Q8×D1112yes—
434C2×D4#434312yes—
435C2×D4C22×Dic1112yes—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—24no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—111no—
443C22×C4—111no—
444C22×C4—111no—
445C22×C4—111no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4—221no—
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×C8C22×Dic1112yes—
470C2×C8C22×Dic1112yes—
471C4⋊C4—24no—
472C4⋊C4—24no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—112no—
477C4⋊C4—222no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—441no—
486C4⋊C4—442no—
487C4⋊C4—442no—
488C4⋊C4—442no—
489C4⋊C4—442no—
490C4⋊C4—881no—
491C4⋊C4—881no—
492C4⋊C4C22×Dic1112yes—
493C4⋊C4C22×Dic1112yes—
494C4⋊C4C22×Dic1112yes—
495C22⋊C4—24no—
496C22⋊C4—442no—
497C22⋊C4—442no—
498C42—221no—
499C42—221no—
500C42—221no—
501C42—221no—
502C42—442no—
503C42—881no—
504C42—881no—
505C42#434112yes—
506C42C22×Dic1112yes—
507C11#2297411yescharacteristic, complemented, Sylow
508C23—22no—
509C23—22no—
510C23—22no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23C2×D4×D1111yescharacteristic
516D4—22no—
517D4—22no—
518D4—22no—
519D4Q8×Dic1114yes—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—48no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—112no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—222no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—884no—
559C2×C4—884no—
560C2×C4D4×Dic1112yes—
561C2×C4D4×Dic1112yes—
562C2×C4C2×#434111yescharacteristic
563C2×C4C2×Q8×D1111yescharacteristic
564C2×C4C2×#434311yescharacteristic
565C2×C4#6704211yescharacteristic
566C2×C4#6704311yescharacteristic
567C2×C4C23×Dic1111yescharacteristic
568C8—22no—
569C8—22no—
570C8—222no—
571C8—441no—
572C22—24no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22#1062316111yescharacteristic
580C22#1062316311yescharacteristic
581C22#1062330011yescharacteristic
582C22#1062330211yescharacteristic
583C22D11×AGL(1,ℤ/8)11yescharacteristic
584C22#1062330411yescharacteristic
585C22C2×D4×Dic1111yescharacteristic
586C4—22no—
587C4—22no—
588C4—42no—
589C4—42no—
590C4—42no—
591C4—222no—
592C4—441no—
593C4—441no—
594C4—441no—
595C4—442no—
596C4—881no—
597C4—881no—
598C4—881no—
599C4#1062316611yescharacteristic
600C4#1062317311yescharacteristic
601C4C2×Q8×Dic1111yescharacteristic
602C4#1062335811yescharacteristic
603C2—44no—
604C2#1307162511yescharacteristic
605C2AGL(1,ℤ/8)×Dic1111yescharacteristic
606C2#1307749211yescharacteristic
607C2#1308070911yescharacteristic
608C2#1308075411yescharacteristic
609C2#1308153211yescharacteristic
610C2#1308157311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#478C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenterC2×#478D11
hypocenterC11#22974
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. #13071716C2semidirect
3. #13069586C2semidirect
4. #13069375C2semidirect
5. #13069360C2semidirect
6. #13069350C2semidirect
7. #13069210C2semidirect
8. #13069196C2semidirect
11. #13068493C2semidirect
21. C11×#478C4semidirect
67. C11×#125C2×C4semidirect
103. C11×#107C2×C4semidirect
104. C11×#106C2×C4semidirect
105. C11×C4⋊C8C2×C4semidirect
287. #478Dic11semidirect
366. #125C2×Dic11semidirect
402. #107C2×Dic11semidirect
403. #106C2×Dic11semidirect
404. C4⋊C8C2×Dic11semidirect
507. C11#22974semidirect

Maximal subgroups

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

subgroupindex
#130717162
D4×C4⋊Dic112
#130695862
#130693752
#130693602
#130693502
#130692102
#130691962
#130688652
#130684932
#130684432
#130684412
#102×Dic112
C2×C11×#4782
#2297411