Finite Group Databasebeta

← #14775269

Subgroups — #14775269

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622646C211yesmaximal, characteristic
2#13071491C211yesmaximal, characteristic, complemented
3#13069351C211yesmaximal, characteristic, complemented
4#13069302C211yesmaximal, characteristic, complemented
5#13069240C211yesmaximal, characteristic, complemented
6#13069208C211yesmaximal, characteristic, complemented
7#13069184C211yesmaximal, characteristic, complemented
8#13069055C211yesmaximal, characteristic
9#13068863C211yesmaximal, characteristic, complemented
10#13068815C211yesmaximal, characteristic, complemented
11C4×#66871C211yesmaximal, characteristic, complemented
12#13068441C211yesmaximal, characteristic, complemented
13#13068400C211yesmaximal, characteristic, complemented
14#13068337C211yesmaximal, characteristic, complemented
15C11×#2363C211yesmaximal, characteristic
16C2×C11×#121C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C11×#390—21no—
22C11×#390C2211yescharacteristic
23C11×#389C2211yescharacteristic
24C11×#388—21no—
25C11×#386—21no—
26C4×C11×C4⋊C4C2211yescharacteristic
27C4×C11×C22⋊C4—21no—
28C4×C11×C22⋊C4C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33#10622825C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35#10622646C418yescomplemented
36C2×#66872C2211yescharacteristic
37C2×#66871C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40#10622555—21no—
41C22⋊C4×Dic11—21no—
42C4×C4⋊Dic11C2211yescharacteristic
43C4×C4⋊Dic11C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622541C2211yescharacteristic
46C2×#66867C2211yescharacteristic
47C2×C4×C11⋊C8C2211yescharacteristic
48#10622267—21no—
49#10622267—21no—
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×D4×C11—21no—
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C23×Dic11—21no—
65C11×#121—22no—
66C11×#121C2×C414yes—
67C4×D4×C11—22no—
68C4×D4×C11—41no—
69C11×#117—22no—
70C11×#117—41no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4D411yescharacteristic
81C2×C11×C22⋊C4D411yescharacteristic
82C2×C42×C11—21no—
83C2×C42×C11—21no—
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C22⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11C2×C414yescomplemented
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×#4318—22no—
99C2×#4318—22no—
100C2×#4318—41no—
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C11×#95—21no—
106C11×#95—21no—
107C11×#95D411yescharacteristic
108C11×#95D411yescharacteristic
109#66896—22no—
110#66896—41no—
111#66896C2×C414yes—
112#66896C2×C414yes—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C22⋊(C11⋊C8)C2×C414yescomplemented
119#66872—41no—
120#66871—22no—
121#66871C2×C414yescomplemented
122#66871C2×C414yescomplemented
123#66867—41no—
124C4×C11⋊C8—22no—
125#22941—111nomaximal, Sylow
126C24×C11—21no—
127C24×C11C2×D411yescharacteristic
128C2×D4×C11—24no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—81no—
135C2×D4×C11—81no—
136C2×D4×C11C22×C412yes—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—42no—
145C22×C4×C11—42no—
146C22×C4×C11—81no—
147C22×C4×C11C22×C412yes—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11#4112yes—
154C22×C4×C11C2411yescharacteristic
155C22×Dic11—24no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—81no—
161C22×Dic11—81no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—81no—
167C11×C4⋊C4C22×C412yes—
168C11×C4⋊C4#4112yes—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—41no—
172C11×C22⋊C4—42no—
173C11×C22⋊C4—42no—
174C11×C22⋊C4—42no—
175C11×C22⋊C4—81no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—42no—
181C42×C11—81no—
182C22⋊Dic11—42no—
183C4⋊Dic11—24no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11C22×C412yes—
191C4⋊Dic11C22×C412yes—
192Dic11⋊C4—81no—
193Dic11⋊C4—81no—
194C4×Dic11—81no—
195C4×Dic11—81no—
196#4318—44no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8C22×C412yes—
207C2×C11⋊C8C22×C412yes—
208C2×C11⋊C8#4112yes—
209C2×#480—111no—
210#2363D1111yescharacteristic
211#2345—111no—
212#1943—111no—
213#1934—111no—
214#1926—111no—
215#1921—111no—
216#1918—111no—
217#1895—111no—
218#1862—111no—
219#1854—111no—
220C4×#107—111no—
221#1762—111no—
222#1753—111no—
223#1736—111no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—22no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11C4×D412yes—
238C23×C11C22×D411yescharacteristic
239D4×C11—22no—
240D4×C11—22no—
241D4×C11—41no—
242D4×C11—41no—
243D4×C11—84no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—22no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—84no—
271C2×C4×C11C4×D412yes—
272C2×C4×C11#13712yes—
273C2×C4×C11C23×C411yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11H(5,𝔽2)11yescharacteristic
278C2×C4×C112−1+411yescharacteristic
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—84no—
292C11⋊C8—22no—
293C11⋊C8—22no—
294C11⋊C8—22no—
295C11⋊C8—41no—
296C22×M16—111no—
297C2×#121C2×D1111yescharacteristic
298C2×C4×D4C2×D1111yescharacteristic
299C2×#117C2×D1111yescharacteristic
300C22×C4⋊C4—111no—
301#480—118no—
302C2×#107—111no—
303C2×#107—111no—
304C2×#107—111no—
305C2×#106—111no—
306C2×#102—111no—
307C2×#102—111no—
308C2×#102—111no—
309C2×#102—111no—
310C2×C22⋊C8—111no—
311C2×#97—111no—
312C2×C4×C8—111no—
313#390—21no—
314#390C2×D1111yescharacteristic
315#389—111no—
316#389—111no—
317#389C2×D1111yescharacteristic
318#388—21no—
319#387—221no—
320#387—221no—
321#386—21no—
322#380—111no—
323#380—221no—
324C4×C4⋊C4—111no—
325C4×C4⋊C4—111no—
326C4×C4⋊C4C2×D1111yescharacteristic
327C4×C22⋊C4—21no—
328C4×C22⋊C4—221no—
329C4×C22⋊C4C2×D1111yescharacteristic
330#340—111no—
331#340—111no—
332#340—111no—
333#340—111no—
334#340—111no—
335#340—111no—
336#340—111no—
337#340—111no—
338#336—111no—
339#336—111no—
340C22×C11—22no—
341C22×C11—22no—
342C22×C11—22no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11—42no—
348C22×C11—42no—
349C22×C11—42no—
350C22×C11—81no—
351C22×C11—81no—
352C22×C11—81no—
353C22×C11—81no—
354C22×C11C2×C4×D411yescharacteristic
355C22×C11#54611yescharacteristic
356C22×C11#54711yescharacteristic
357C22×C11C2×#13711yescharacteristic
358C22×C11#57511yescharacteristic
359C22×C11#57611yescharacteristic
360C22×C11#57611yescharacteristic
361C4×C11—22no—
362C4×C11—22no—
363C4×C11—41no—
364C4×C11—41no—
365C4×C11—42no—
366C4×C11—41no—
367C4×C11—42no—
368C4×C11—81no—
369C4×C11C4×#4111yescharacteristic
370C4×C11#52011yescharacteristic
371C4×C11#55111yescharacteristic
372C4×C11#55211yescharacteristic
373Dic11—42no—
374Dic11—42no—
375Dic11—81no—
376Dic11—81no—
377C22×D4—21no—
378C22×D4C22×D1111yescharacteristic
379C23×C4—21no—
380C23×C4—221no—
381C23×C4C22×D1111yescharacteristic
382C2×M16—222no—
383C2×M16—222no—
384C2×M16—441no—
385C22×C8—111no—
386C22×C8—111no—
387C22×C8—111no—
388C22×C8—111no—
389#121—22no—
390#121C4×D1114yes—
391C4×D4—22no—
392C4×D4—41no—
393#117—22no—
394#117—41no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—114no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—222no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4C22×D1111yescharacteristic
406C2×C4⋊C4C22×D1111yescharacteristic
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4C22⋊D1111yescharacteristic
415C2×C22⋊C4C22⋊D1111yescharacteristic
416C2×C42—21no—
417C2×C42—21no—
418C2×C42—221no—
419C2×C42—221no—
420C2×C42C22×D1111yescharacteristic
421C2×C42C22×D1111yescharacteristic
422#107—114no—
423#107—114no—
424#107—222no—
425#106—441no—
426#102—114no—
427#102—114no—
428#102—222no—
429#102—441no—
430C22⋊C8—114no—
431#97—441no—
432C4×C8—222no—
433#95—21no—
434#95—21no—
435#95—221no—
436#95—221no—
437#95—221no—
438#95—221no—
439#95—221no—
440#95C22⋊D1111yescharacteristic
441#95C22⋊D1111yescharacteristic
442C2×C11—42no—
443C2×C11—82no—
444C2×C11#235911yescharacteristic
445C2×C11C4×#13711yescharacteristic
446C2×C11#294811yescharacteristic
447C2×C11#332211yescharacteristic
448C2×C11#333311yescharacteristic
449C2×C11#334611yescharacteristic
450C2×C11#334711yescharacteristic
451C24—21no—
452C24C2×C22⋊D1111yescharacteristic
453C2×D4—24no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—81no—
460C2×D4—81no—
461C2×D4C2×C4×D1112yes—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—81no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—224no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—881no—
478C22×C4—881no—
479C22×C4C2×C4×D1112yes—
480C22×C4#433912yes—
481C22×C4C2×C22⋊D1111yescharacteristic
482C22×C4C2×C22⋊D1111yescharacteristic
483C22×C4C2×C22⋊D1111yescharacteristic
484C22×C4C2×C22⋊D1111yescharacteristic
485C22×C4C2×C22⋊D1111yescharacteristic
486C22×C4C23×D1111yescharacteristic
487M16—444no—
488C2×C8—112no—
489C2×C8—112no—
490C2×C8—112no—
491C2×C8—221no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—221no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—81no—
505C4⋊C4—112no—
506C4⋊C4—112no—
507C4⋊C4—224no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—881no—
515C4⋊C4—881no—
516C4⋊C4C2×C4×D1112yes—
517C4⋊C4#434112yes—
518C22⋊C4—24no—
519C22⋊C4—22no—
520C22⋊C4—41no—
521C22⋊C4—42no—
522C22⋊C4—42no—
523C22⋊C4—42no—
524C22⋊C4—81no—
525C22⋊C4—442no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—42no—
531C42—81no—
532C42—881no—
533C42—881no—
534C11#2294111yescharacteristic, complemented, Sylow
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—22no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23C4×C22⋊D1112yes—
549C23C22×C22⋊D1111yescharacteristic
550D4—22no—
551D4—22no—
552D4—41no—
553D4—41no—
554D4—84no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—84no—
582C2×C4—222no—
583C2×C4—222no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—884no—
595C2×C4C4×C22⋊D1112yes—
596C2×C4#6700412yes—
597C2×C4C22×C4×D1111yescharacteristic
598C2×C4C2×#433911yescharacteristic
599C2×C4C2×#434111yescharacteristic
600C2×C4#6703711yescharacteristic
601C2×C4#41×D1111yescharacteristic
602C2×C4#6704311yescharacteristic
603C8—222no—
604C8—222no—
605C8—222no—
606C8—441no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—42no—
615C22—42no—
616C22—42no—
617C22—81no—
618C22—81no—
619C22—81no—
620C22—81no—
621C22C2×C4×C22⋊D1111yescharacteristic
622C22#1062333711yescharacteristic
623C22#1062335311yescharacteristic
624C22C2×#6700411yescharacteristic
625C22#1062335511yescharacteristic
626C22#1062336611yescharacteristic
627C22#1062336611yescharacteristic
628C4—22no—
629C4—22no—
630C4—41no—
631C4—41no—
632C4—42no—
633C4—41no—
634C4—42no—
635C4—81no—
636C4—442no—
637C4—442no—
638C4—881no—
639C4—881no—
640C4C4×#434111yescharacteristic
641C4#1062307211yescharacteristic
642C4#1062307711yescharacteristic
643C4#1062308711yescharacteristic
644C2—42no—
645C2—82no—
646C2#1307160211yescharacteristic
647C2C4×#6700411yescharacteristic
648C2#1307746611yescharacteristic
649C2#1308081711yescharacteristic
650C2#1308095411yescharacteristic
651C2#1308110111yescharacteristic
652C2#1308111611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2363C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
cosocleC22×C4×C11C24
hypercenter#2363D11
hypocenterC11#22941
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2363

Complements

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

NH ≅ G/Ntype
2. #13071491C2semidirect
3. #13069351C2semidirect
4. #13069302C2semidirect
5. #13069240C2semidirect
6. #13069208C2semidirect
7. #13069184C2semidirect
9. #13068863C2semidirect
10. #13068815C2semidirect
11. C4×#66871C2semidirect
12. #13068441C2semidirect
13. #13068400C2semidirect
14. #13068337C2semidirect
35. #10622646C4semidirect
89. C2×C4⋊Dic11C2×C4semidirect
118. C22⋊(C11⋊C8)C2×C4semidirect
121. #66871C2×C4semidirect
122. #66871C2×C4semidirect
534. C11#22941semidirect

Maximal subgroups

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

subgroupindex
C2×#106226462
#130714912
#130693512
#130693022
#130692402
#130692082
#130691842
#130690552
#130688632
#130688152
C4×#668712
#130684412
#130684002
#130683372
C11×#23632
#2294111