Finite Group Databasebeta

← #14775724

Subgroups — #14775724

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×#10622460C211yesmaximal, characteristic
2#13071710C211yesmaximal, characteristic, complemented
3C4⋊C4×D44C211yesmaximal, characteristic
4#13069585C211yesmaximal, characteristic, complemented
5#13069375C211yesmaximal, characteristic, complemented
6#13069359C211yesmaximal, characteristic, complemented
7#13069349C211yesmaximal, characteristic, complemented
8#13069209C211yesmaximal, characteristic, complemented
9#13069195C211yesmaximal, characteristic, complemented
10#13068866C211yesmaximal, characteristic
11#13068866C211yesmaximal, characteristic
12#13068442C211yesmaximal, characteristic
13#13068442C211yesmaximal, characteristic
14C4×#66885C211yesmaximal, characteristic
15C11×#1771C211yesmaximal, characteristic, complemented
16C2×C4⋊C4×D11—21no—
17C2×C4×D44C2211yescharacteristic
18C2×C4×D44C2211yescharacteristic
19C2×C4×D44C2211yescharacteristic
20C2×#66923C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#97C2211yescharacteristic
23C2×C11×#97C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34#10622600—21no—
35#10622591—21no—
36#10622585—21no—
37#10622548C2211yescharacteristic
38C4×C4⋊Dic11C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40C4×C4⋊Dic11C2211yescharacteristic
41#10622541C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622541C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622460C418yescomplemented
46#10622281—21no—
47#10622281—21no—
48#10622265—21no—
49#10622262—21no—
50C11×#336C2211yescharacteristic
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60C22×D44C2311yescharacteristic
61C22×C4×D11—21no—
62C22×C4×D11—21no—
63C22×C4×D11—21no—
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×C42×C11C2311yescharacteristic
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×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C4⋊C4×D11—44no—
95C4×D44—22no—
96C4×D44—22no—
97C4×D44—22no—
98C4×D44—41no—
99C4×D44—41no—
100C4×D44C2×C414yes—
101#66923—22no—
102#66923C2×C414yescomplemented
103C11×C4⋊C8C2×C414yescomplemented
104C11×#97—22no—
105C11×#97—41no—
106C4×C8×C11—41no—
107C11×#95D411yescharacteristic
108C11×#95D411yescharacteristic
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116#66885—22no—
117#66885C2×C414yes—
118#66885C2×C414yes—
119#66885Q814yes—
120#66882—41no—
121#66882—41no—
122#66882C2×C414yescomplemented
123#66881C2×C414yescomplemented
124#22974—111nomaximal, Sylow
125C23×D11—21no—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2411yescharacteristic
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
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×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11C22×C412yes—
165C2×C8×C11C22×C412yes—
166C2×C8×C11C2×Q812yes—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—41no—
169C42×C11—21no—
170C42×C11—21no—
171C42×C11—21no—
172C42×C11—21no—
173C42×C11C22×C412yes—
174C42×C11#4112yes—
175(C2×D11)⋊C4—24no—
176(C2×D11)⋊C4—42no—
177(C2×D11)⋊C4—42no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—42no—
189C4⋊Dic11—81no—
190C4⋊Dic11C22×C412yes—
191C4⋊Dic11C22×C412yes—
192C4⋊Dic11C22×C412yes—
193C4⋊Dic11C2×Q812yes—
194Dic11⋊C4—24no—
195Dic11⋊C4—24no—
196Dic11⋊C4—42no—
197Dic11⋊C4—42no—
198Dic11⋊C4—42no—
199Dic11⋊C4—81no—
200C4×Dic11—42no—
201C4×Dic11—81no—
202C4×Dic11—81no—
203C2×#478—111no—
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#1771D1111yescharacteristic, complemented
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—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11C4×D412yes—
242C2×C4×C11C4×D412yes—
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—22no—
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271D44—22no—
272D44—22no—
273D44—22no—
274D44C4×Q814yes—
275C4×D11—48no—
276C4×D11—84no—
277C4×D11—84no—
278C8×C11—22no—
279C8×C11—22no—
280C8×C11—22no—
281C8×C11—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×#107—111no—
290C2×#107—111no—
291C2×#106—111no—
292C2×C4⋊C8C2×D1111yescharacteristic
293C2×#102—111no—
294C2×#102—111no—
295C2×#102—111no—
296C2×#102—111no—
297C2×#97C2×D1111yescharacteristic
298C2×#97C2×D1111yescharacteristic
299C2×C4×C8C2×D1111yescharacteristic
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—221no—
315C4×C4⋊C4C2×D1111yescharacteristic
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#336C2×D1111yescharacteristic
325#336C2×D1111yescharacteristic
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—22no—
342C4×C11—22no—
343C4×C11—41no—
344C4×C11—41no—
345C4×C11—41no—
346C4×C11C2×C4×Q811yescharacteristic
347C4×C11#52011yescharacteristic
348C4×C11#55211yescharacteristic
349C4×C11#55411yescharacteristic
350Dic11—42no—
351Dic11—42no—
352Dic11—42no—
353Dic11—42no—
354Dic11—81no—
355Dic11—81no—
356Dic11—81no—
357C22×D4—111no—
358C23×C4—221no—
359C23×C4—221no—
360C23×C4—221no—
361C22×C8C22×D1111yescharacteristic
362C22×C8C22×D1111yescharacteristic
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—111no—
374C2×C4⋊C4—111no—
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—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—444no—
389C2×C4⋊C4D4411yescharacteristic
390C2×C4⋊C4D4411yescharacteristic
391C2×C22⋊C4—221no—
392C2×C22⋊C4—221no—
393C2×C22⋊C4—221no—
394C2×C42—221no—
395C2×C42—221no—
396C2×C42—221no—
397C2×C42C22×D1111yescharacteristic
398C2×C42C22×D1111yescharacteristic
399C2×C42C22×D1111yescharacteristic
400#107—114no—
401#107—441no—
402#107—441no—
403#106—114no—
404C4⋊C8C4×D1114yescomplemented
405#102—114no—
406#102—114no—
407#102—114no—
408#102—222no—
409#97—22no—
410#97—41no—
411C4×C8—41no—
412#95—221no—
413#95—221no—
414#95—221no—
415#95—221no—
416#95—221no—
417#95—221no—
418#95—221no—
419#95D4411yescharacteristic
420#95D4411yescharacteristic
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—221no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4—221no—
440C22×C4—224no—
441C22×C4—221no—
442C22×C4—221no—
443C22×C4—221no—
444C22×C4—442no—
445C22×C4—442no—
446C22×C4—442no—
447C22×C4—442no—
448C22×C4—442no—
449C22×C4—442no—
450C22×C4—881no—
451C22×C4—881no—
452C22×C4C2×D4411yescharacteristic
453C22×C4C2×D4411yescharacteristic
454C22×C4C2×D4411yescharacteristic
455C22×C4C2×D4411yescharacteristic
456C22×C4C2×D4411yescharacteristic
457C22×C4C2×D4411yescharacteristic
458C22×C4C23×D1111yescharacteristic
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8C2×C4×D1112yes—
469C2×C8C2×C4×D1112yes—
470C2×C8Q8×D1112yes—
471C4⋊C4—22no—
472C4⋊C4—41no—
473C4⋊C4—112no—
474C4⋊C4—112no—
475C4⋊C4—112no—
476C4⋊C4—112no—
477C4⋊C4—224no—
478C4⋊C4—224no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—442no—
490C4⋊C4—442no—
491C4⋊C4—442no—
492C4⋊C4—442no—
493C4⋊C4—881no—
494C4⋊C4—881no—
495C22⋊C4—224no—
496C22⋊C4—442no—
497C22⋊C4—442no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—442no—
503C42—881no—
504C42—881no—
505C42C2×C4×D1112yes—
506C42#433912yes—
507C11#2297411yescharacteristic, complemented, Sylow
508C23—222no—
509C23—222no—
510C23—222no—
511C23—441no—
512C23—441no—
513C23—441no—
514C23—441no—
515C23C22×D4411yescharacteristic
516D4—114no—
517D4—222no—
518D4—222no—
519D4—222no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—222no—
536C2×C4—222no—
537C2×C4—222no—
538C2×C4—222no—
539C2×C4—448no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
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—884no—
558C2×C4—884no—
559C2×C4C4×D4412yes—
560C2×C4C4×D4412yes—
561C2×C4#6696112yes—
562C2×C4C22×C4×D1111yescharacteristic
563C2×C4C2×#433911yescharacteristic
564C2×C4#6703711yescharacteristic
565C2×C4C2×Q8×D1111yescharacteristic
566C2×C4#41×D1111yescharacteristic
567C2×C4#6704311yescharacteristic
568C8—22no—
569C8—22no—
570C8—22no—
571C8—41no—
572C22—224no—
573C22—442no—
574C22—442no—
575C22—442no—
576C22—442no—
577C22—442no—
578C22—442no—
579C22C2×C4×D4411yescharacteristic
580C22#1062308511yescharacteristic
581C22Q8×D4411yescharacteristic
582C22C2×#6696111yescharacteristic
583C22#1062327911yescharacteristic
584C22#1062328311yescharacteristic
585C22#1062328411yescharacteristic
586C4—22no—
587C4—22no—
588C4—22no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—442no—
593C4—442no—
594C4—442no—
595C4—442no—
596C4—881no—
597C4—881no—
598C4—881no—
599C4#1062304211yescharacteristic
600C4#1062306011yescharacteristic
601C4#1062307711yescharacteristic
602C4C4×Q8×D1111yescharacteristic
603C2—444no—
604C2#1307162311yescharacteristic
605C2C4×#6696111yescharacteristic
606C2#1307749311yescharacteristic
607C2#1308071411yescharacteristic
608C2#1308075911yescharacteristic
609C2#1308153911yescharacteristic
610C2#1308157611yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1771C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1771D11
hypocenterC11#22974
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1771

Complements

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

NH ≅ G/Ntype
2. #13071710C2semidirect
4. #13069585C2semidirect
5. #13069375C2semidirect
6. #13069359C2semidirect
7. #13069349C2semidirect
8. #13069209C2semidirect
9. #13069195C2semidirect
15. C11×#1771C2semidirect
45. #10622460C4semidirect
102. #66923C2×C4semidirect
103. C11×C4⋊C8C2×C4semidirect
122. #66882C2×C4semidirect
123. #66881C2×C4semidirect
214. #1771D11semidirect
404. C4⋊C8C4×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×#106224602
#130717102
C4⋊C4×D442
#130695852
#130693752
#130693592
#130693492
#130692092
#130691952
#130688662
#130684422
C4×#668852
C11×#17712
#2297411