Finite Group Databasebeta

← #14775722

Subgroups — #14775722

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×#10622622C211yesmaximal, characteristic
2#13071710C211yesmaximal, characteristic, complemented
3#13069584C211yesmaximal, characteristic, complemented
4#13069372C211yesmaximal, characteristic, complemented
5#13069356C211yesmaximal, characteristic, complemented
6#13069346C211yesmaximal, characteristic, complemented
7#13069205C211yesmaximal, characteristic, complemented
8#13069191C211yesmaximal, characteristic, complemented
9#13068863C211yesmaximal, characteristic
10#13068863C211yesmaximal, characteristic
11#13068491C211yesmaximal, characteristic, complemented
12#13068441C211yesmaximal, characteristic
13#13068441C211yesmaximal, characteristic
14C4×#66896C211yesmaximal, characteristic
15D4×C11×C4⋊C4C211yesmaximal, characteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C22×C11×C4⋊C4—21no—
20C2×#66923C2211yescharacteristic
21C11×#389C2211yescharacteristic
22C11×#389C2211yescharacteristic
23C11×#385—21no—
24C11×#385—21no—
25C11×#384C2211yescharacteristic
26C11×#380—21no—
27C4×C11×C4⋊C4C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32#10622622C418yescomplemented
33#10622591—21no—
34#10622585—21no—
35C2×#66872C2211yescharacteristic
36C2×#66871C2211yescharacteristic
37C2×#66871C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40C4×C4⋊Dic11C2211yescharacteristic
41C4×C4⋊Dic11C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622541C2211yescharacteristic
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45C2×#66867C2211yescharacteristic
46C2×#66867C2211yescharacteristic
47C2×C4×C11⋊C8C2211yescharacteristic
48#10622265—21no—
49#10622262—21no—
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11—21no—
63C23×C4×C11—21no—
64C4×D4×C11—22no—
65C4×D4×C11—22no—
66C4×D4×C11—22no—
67C4×D4×C11—41no—
68C4×D4×C11—41no—
69C4×D4×C11C2×C414yes—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—44no—
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101#66923—22no—
102#66923C2×C414yescomplemented
103C11×#95—21no—
104C11×#95—21no—
105C11×#95D411yescharacteristic
106C11×#95D411yescharacteristic
107#66896—22no—
108#66896C2×C414yes—
109#66896C2×C414yes—
110#66896Q814yes—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116#66872C2×C414yescomplemented
117#66871—41no—
118#66871—41no—
119#66871C2×C414yescomplemented
120C4⋊(C11⋊C8)C2×C414yescomplemented
121#66867—22no—
122#66867—41no—
123C4×C11⋊C8—41no—
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—24no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—42no—
137C22×C4×C11—42no—
138C22×C4×C11—42no—
139C22×C4×C11—42no—
140C22×C4×C11—42no—
141C22×C4×C11—42no—
142C22×C4×C11—81no—
143C22×C4×C11—81no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—41no—
162C11×C4⋊C4—42no—
163C11×C4⋊C4—42no—
164C11×C4⋊C4—42no—
165C11×C4⋊C4—81no—
166C11×C4⋊C4C22×C412yes—
167C11×C22⋊C4—24no—
168C11×C22⋊C4—42no—
169C11×C22⋊C4—42no—
170C42×C11—21no—
171C42×C11—21no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11C22×C412yes—
175C42×C11#4112yes—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11C22×C412yes—
182C4⋊Dic11C22×C412yes—
183C4⋊Dic11C2×Q812yes—
184Dic11⋊C4—24no—
185Dic11⋊C4—24no—
186Dic11⋊C4—42no—
187Dic11⋊C4—81no—
188C4×Dic11—42no—
189C4×Dic11—81no—
190C4×Dic11—81no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8C22×C412yes—
201C2×C11⋊C8C22×C412yes—
202C2×C11⋊C8C2×Q812yes—
203C2×#478—111no—
204#2370—111no—
205D4×C4⋊C4D1111yescharacteristic
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—21no—
235C2×C4×C11—21no—
236C2×C4×C11—22no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—48no—
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—41no—
254C2×C4×C11—41no—
255C2×C4×C11—84no—
256C2×C4×C11—84no—
257C2×C4×C11C4×D412yes—
258C2×C4×C11C4×D412yes—
259C2×C4×C11AGL(1,ℤ/8)12yes—
260C2×C4×C11C23×C411yescharacteristic
261C2×C4×C11C22×Q811yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11H(5,𝔽2)11yescharacteristic
265C2×C4×C112−1+411yescharacteristic
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—22no—
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—41no—
278C11⋊C8—22no—
279C11⋊C8—22no—
280C11⋊C8—22no—
281C11⋊C8—41no—
282C2×#125—111no—
283C2×C4×D4C2×D1111yescharacteristic
284C2×C4×D4C2×D1111yescharacteristic
285C2×C4×D4C2×D1111yescharacteristic
286C22×C4⋊C4—21no—
287#478—118no—
288C2×#107—111no—
289C2×#107—111no—
290C2×#107—111no—
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×C8—111no—
300#389—111no—
301#389—111no—
302#389—221no—
303#389C2×D1111yescharacteristic
304#389C2×D1111yescharacteristic
305#387—221no—
306#387—221no—
307#385—21no—
308#385—21no—
309#384C2×D1111yescharacteristic
310#380—21no—
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#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—22no—
343C4×C11—42no—
344C4×C11—41no—
345C4×C11—41no—
346C4×C11—41no—
347C4×C11—81no—
348C4×C11—81no—
349C4×C11C2×C4×Q811yescharacteristic
350C4×C11#52011yescharacteristic
351C4×C11#55211yescharacteristic
352C4×C11#55411yescharacteristic
353Dic11—42no—
354Dic11—42no—
355Dic11—42no—
356Dic11—81no—
357C22×D4C22×D1111yescharacteristic
358C23×C4—21no—
359C23×C4—21no—
360C23×C4—21no—
361C22×C8—111no—
362C22×C8—111no—
363C22×C8—111no—
364C22×C8—111no—
365#125—114no—
366#125—222no—
367C4×D4—22no—
368C4×D4—22no—
369C4×D4—22no—
370C4×D4—41no—
371C4×D4—41no—
372C4×D4C4×D1114yes—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—44no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4C22⋊D1111yescharacteristic
387C2×C4⋊C4C22⋊D1111yescharacteristic
388C2×C4⋊C4C22×D1111yescharacteristic
389C2×C4⋊C4C22×D1111yescharacteristic
390C2×C4⋊C4C22×D1111yescharacteristic
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
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⋊C8—114no—
405#102—114no—
406#102—114no—
407#102—114no—
408#102—222no—
409#97—222no—
410#97—441no—
411C4×C8—441no—
412#95—21no—
413#95—21no—
414#95—221no—
415#95—221no—
416#95—221no—
417#95—221no—
418#95—221no—
419#95C22⋊D1111yescharacteristic
420#95C22⋊D1111yescharacteristic
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×D4C2×C4×D1112yes—
434C2×D4#434112yes—
435C2×D4Q8×D1112yes—
436C22×C4—21no—
437C22×C4—24no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—81no—
447C22×C4—81no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4C2×C22⋊D1111yescharacteristic
453C22×C4C2×C22⋊D1111yescharacteristic
454C22×C4C2×C22⋊D1111yescharacteristic
455C22×C4C2×C22⋊D1111yescharacteristic
456C22×C4C2×C22⋊D1111yescharacteristic
457C22×C4C2×C22⋊D1111yescharacteristic
458C22×C4C23×D1111yescharacteristic
459C2×C8—112no—
460C2×C8—112no—
461C2×C8—112no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C4⋊C4—22no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—41no—
478C4⋊C4—42no—
479C4⋊C4—42no—
480C4⋊C4—42no—
481C4⋊C4—81no—
482C4⋊C4—112no—
483C4⋊C4—112no—
484C4⋊C4—112no—
485C4⋊C4—224no—
486C4⋊C4—224no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—442no—
493C4⋊C4—881no—
494C4⋊C4C2×C4×D1112yes—
495C22⋊C4—24no—
496C22⋊C4—42no—
497C22⋊C4—42no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—442no—
503C42—881no—
504C42—881no—
505C42C2×C4×D1112yes—
506C42#433912yes—
507C11#2297411yescharacteristic, complemented, Sylow
508C23—22no—
509C23—22no—
510C23—22no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23C22×C22⋊D1111yescharacteristic
516D4—22no—
517D4—22no—
518D4—22no—
519D4#6694014yes—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
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—21no—
536C2×C4—48no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—84no—
546C2×C4—84no—
547C2×C4—222no—
548C2×C4—222no—
549C2×C4—222no—
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—441no—
559C2×C4C4×C22⋊D1112yes—
560C2×C4C4×C22⋊D1112yes—
561C2×C4#6698512yes—
562C2×C4C22×C4×D1111yescharacteristic
563C2×C4C2×#433911yescharacteristic
564C2×C4C2×#434111yescharacteristic
565C2×C4#6703711yescharacteristic
566C2×C4C2×Q8×D1111yescharacteristic
567C2×C4#6704011yescharacteristic
568C8—222no—
569C8—222no—
570C8—222no—
571C8—441no—
572C22—24no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22C2×C4×C22⋊D1111yescharacteristic
580C22C2×#6698511yescharacteristic
581C22#1062333711yescharacteristic
582C22Q8×C22⋊D1111yescharacteristic
583C22#1062335311yescharacteristic
584C22#1062336611yescharacteristic
585C22#1062336911yescharacteristic
586C4—22no—
587C4—22no—
588C4—22no—
589C4—41no—
590C4—41no—
591C4—42no—
592C4—41no—
593C4—81no—
594C4—81no—
595C4—442no—
596C4—442no—
597C4—442no—
598C4—881no—
599C4C2×#6694011yescharacteristic
600C4#1062303511yescharacteristic
601C4#1062304211yescharacteristic
602C4#1062304411yescharacteristic
603C2—44no—
604C2#1307162111yescharacteristic
605C2C4×#6698511yescharacteristic
606C2#1307748911yescharacteristic
607C2#1308071211yescharacteristic
608C2#1308075711yescharacteristic
609C2#1308153711yescharacteristic
610C2#1308157011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingD4×C11×C4⋊C4C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenterD4×C4⋊C4D11
hypocenterC11#22974
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #13071710C2semidirect
3. #13069584C2semidirect
4. #13069372C2semidirect
5. #13069356C2semidirect
6. #13069346C2semidirect
7. #13069205C2semidirect
8. #13069191C2semidirect
11. #13068491C2semidirect
32. #10622622C4semidirect
102. #66923C2×C4semidirect
116. #66872C2×C4semidirect
119. #66871C2×C4semidirect
120. C4⋊(C11⋊C8)C2×C4semidirect
507. C11#22974semidirect

Maximal subgroups

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

subgroupindex
C2×#106226222
#130717102
#130695842
#130693722
#130693562
#130693462
#130692052
#130691912
#130688632
#130684912
#130684412
C4×#668962
D4×C11×C4⋊C42
#2297411