Finite Group Databasebeta

← #14775271

Subgroups — #14775271

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×#10622580C211yesmaximal, characteristic
2#13071654C211yesmaximal, characteristic
3#13071493C211yesmaximal, characteristic, complemented
4#13069353C211yesmaximal, characteristic, complemented
5#13069300C211yesmaximal, characteristic, complemented
6#13069241C211yesmaximal, characteristic, complemented
7#13069211C211yesmaximal, characteristic, complemented
8#13069185C211yesmaximal, characteristic, complemented
9#13069054C211yesmaximal, characteristic
10#13068864C211yesmaximal, characteristic, complemented
11#13068815C211yesmaximal, characteristic, complemented
12#13068508C211yesmaximal, characteristic, complemented
13#13068440C211yesmaximal, characteristic, complemented
14#13068397C211yesmaximal, characteristic, complemented
15C11×#1736C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C2×#66983C2211yescharacteristic
20C2×#66946C2211yescharacteristic
21#10622825—21no—
22#10622825C2211yescharacteristic
23C4×C22⋊Dic11—21no—
24C4×C22⋊Dic11C2211yescharacteristic
25C2×C22⋊(C11⋊C8)C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66879C2211yescharacteristic
29C2×C8×Dic11C2211yescharacteristic
30#10622601C2211yescharacteristic
31#10622598C2211yescharacteristic
32#10622598C2211yescharacteristic
33#10622594—21no—
34#10622594—21no—
35C4⋊C4×Dic11C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37C4⋊C4×Dic11C2211yescharacteristic
38#10622586C2211yescharacteristic
39#10622580C418yescomplemented
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622570—21no—
47#10622569—21no—
48#10622553—21no—
49C4×(C2×D11)⋊C4—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C2×C11×M16—22no—
66C2×C11×M16—22no—
67C2×C11×M16—41no—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C11×#117—22no—
71C11×#117—41no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4C2×C414yescomplemented
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C42×C11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11D411yescharacteristic
83C2×C22⋊Dic11D411yescharacteristic
84#66983—22no—
85#66983C2×C414yes—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11C2311yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103#66946—22no—
104#66946—41no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95D411yescharacteristic
113C11⋊#95D411yescharacteristic
114C22⋊(C11⋊C8)C2×C414yescomplemented
115#66885—22no—
116#66885—41no—
117#66879—41no—
118C8×Dic11—22no—
119#66873C2×C414yes—
120#66873C2×C414yes—
121#66872—41no—
122#66871—22no—
123#66871C2×C414yescomplemented
124#66871C2×C414yescomplemented
125#22941—111nomaximal, Sylow
126C24×C11C2×D411yescharacteristic
127C23×D11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—24no—
136C22×C4×C11—21no—
137C22×C4×C11—81no—
138C22×C4×C11—81no—
139C22×C4×C11C22×C412yes—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11#4112yes—
142C22×C4×C11C2411yescharacteristic
143C2×C22⋊D11—24no—
144C2×C22⋊D11—81no—
145C2×C22⋊D11—81no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11C2×D411yescharacteristic
150C22×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44C22×C412yes—
159C2×C4×D11—42no—
160C2×C4×D11—42no—
161C2×C4×D11—81no—
162C11×M16—44no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11#4112yes—
169C11×C4⋊C4—24no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4C22×C412yes—
176C11×C4⋊C4C22×C412yes—
177C11×C4⋊C4#4112yes—
178C11×C22⋊C4—42no—
179C42×C11—42no—
180C22⋊Dic11—22no—
181C22⋊Dic11—41no—
182C22⋊Dic11—42no—
183(C2×D11)⋊C4—24no—
184(C2×D11)⋊C4—42no—
185(C2×D11)⋊C4—42no—
186(C2×D11)⋊C4—81no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—81no—
193C4⋊Dic11—81no—
194C4⋊Dic11C22×C412yes—
195Dic11⋊C4—81no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C4×Dic11—81no—
201C4×Dic11—81no—
202C4×Dic11—81no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8C22×C412yes—
208C2×C11⋊C8C22×C412yes—
209C2×#480—111no—
210#2363—111no—
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#1736D1111yescharacteristic, complemented
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11C4×D412yes—
231C23×C11C22×D411yescharacteristic
232C22×D11—22no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—41no—
238C22×D11—41no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
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—41no—
256C2×C4×C11—41no—
257C2×C4×C11—84no—
258C2×C4×C11C4×D412yes—
259C2×C4×C11C23×C411yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11H(5,𝔽2)11yescharacteristic
264C2×C4×C112−1+411yescharacteristic
265C22⋊D11—84no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—22no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11#13712yes—
287D44—22no—
288D44—22no—
289D44—41no—
290D44—41no—
291C4×D11—84no—
292C8×C11—22no—
293C8×C11—41no—
294C11⋊C8—22no—
295C11⋊C8—22no—
296C22×M16C2×D1111yescharacteristic
297C2×#121—111no—
298C2×C4×D4—111no—
299C2×#117C2×D1111yescharacteristic
300C22×C4⋊C4C2×D1111yescharacteristic
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—111no—
314#390—221no—
315#389—111no—
316#389—111no—
317#389—111no—
318#388—221no—
319#387—221no—
320#387—221no—
321#386—221no—
322#380—111no—
323#380—221no—
324C4×C4⋊C4—111no—
325C4×C4⋊C4—111no—
326C4×C4⋊C4—111no—
327C4×C22⋊C4—111no—
328C4×C22⋊C4—221no—
329C4×C22⋊C4—221no—
330#340—111no—
331#340—111no—
332#340—111no—
333#340—111no—
334#340C2×D1111yescharacteristic
335#340C2×D1111yescharacteristic
336#340C2×D1111yescharacteristic
337#340C2×D1111yescharacteristic
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×C11C2×C4×D411yescharacteristic
348C22×C11#54611yescharacteristic
349C22×C11#54711yescharacteristic
350C22×C11C2×#13711yescharacteristic
351C22×C11#57511yescharacteristic
352C22×C11#57611yescharacteristic
353C22×C11#57611yescharacteristic
354C2×D11—42no—
355C2×D11—42no—
356C2×D11—42no—
357C2×D11—81no—
358C2×D11—81no—
359C2×D11—81no—
360C2×D11—81no—
361C4×C11—22no—
362C4×C11—42no—
363C4×C11—42no—
364C4×C11—42no—
365C4×C11—81no—
366C4×C11C4×#4111yescharacteristic
367C4×C11#52011yescharacteristic
368C4×C11#55111yescharacteristic
369C4×C11#55211yescharacteristic
370Dic11—22no—
371Dic11—41no—
372Dic11—41no—
373Dic11—42no—
374Dic11—41no—
375Dic11—81no—
376Dic11—81no—
377C22×D4—111no—
378C22×D4—221no—
379C23×C4—21no—
380C23×C4—221no—
381C23×C4C22×D1111yescharacteristic
382C2×M16—22no—
383C2×M16—22no—
384C2×M16—41no—
385C22×C8—111no—
386C22×C8—111no—
387C22×C8C22×D1111yescharacteristic
388C22×C8C22×D1111yescharacteristic
389#121—114no—
390#121—222no—
391C4×D4—222no—
392C4×D4—441no—
393#117—22no—
394#117—41no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4C4×D1114yescomplemented
404C2×C4⋊C4C22×D1111yescharacteristic
405C2×C4⋊C4C22×D1111yescharacteristic
406C2×C4⋊C4C22×D1111yescharacteristic
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—111no—
410C2×C22⋊C4—111no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4—221no—
416C2×C42—21no—
417C2×C42—111no—
418C2×C42—111no—
419C2×C42—221no—
420C2×C42—221no—
421C2×C42—221no—
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—111no—
434#95—111no—
435#95—221no—
436#95—221no—
437#95—221no—
438#95—221no—
439#95—221no—
440#95—221no—
441#95—221no—
442C2×C11—42no—
443C2×C11#235911yescharacteristic
444C2×C11C4×#13711yescharacteristic
445C2×C11#294811yescharacteristic
446C2×C11#332211yescharacteristic
447C2×C11#333311yescharacteristic
448C2×C11#334611yescharacteristic
449C2×C11#334711yescharacteristic
450D11—82no—
451C24—221no—
452C24D4×D1111yescharacteristic
453C2×D4—112no—
454C2×D4—224no—
455C2×D4—221no—
456C2×D4—221no—
457C2×D4—221no—
458C2×D4—221no—
459C2×D4—221no—
460C2×D4—881no—
461C2×D4—881no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—24no—
470C22×C4—21no—
471C22×C4—81no—
472C22×C4—81no—
473C22×C4—111no—
474C22×C4—111no—
475C22×C4—111no—
476C22×C4—111no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—442no—
481C22×C4—442no—
482C22×C4—881no—
483C22×C4C2×C4×D1112yes—
484C22×C4D4×D1111yescharacteristic
485C22×C4#434112yes—
486C22×C4C23×D1111yescharacteristic
487M16—44no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—112no—
494C2×C8—112no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8#433912yes—
500C4⋊C4—24no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—112no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4—881no—
513C4⋊C4—881no—
514C4⋊C4—881no—
515C4⋊C4C2×C4×D1112yes—
516C4⋊C4C2×C4×D1112yes—
517C4⋊C4#433912yes—
518C22⋊C4—42no—
519C22⋊C4—222no—
520C22⋊C4—224no—
521C22⋊C4—442no—
522C22⋊C4—442no—
523C22⋊C4—441no—
524C22⋊C4—442no—
525C22⋊C4—881no—
526C42—42no—
527C42—221no—
528C42—221no—
529C42—221no—
530C42—221no—
531C42—881no—
532C42—881no—
533C42—881no—
534C11#2294111yescharacteristic, complemented, Sylow
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—222no—
542C23—441no—
543C23—441no—
544C23—441no—
545C23—441no—
546C23—441no—
547C23—441no—
548C23(C22⋊D11)⋊C412yes—
549C23C2×D4×D1111yescharacteristic
550D4—222no—
551D4—222no—
552D4—441no—
553D4—441no—
554D4—884no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—84no—
574C2×C4—112no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—222no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—221no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—221no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—884no—
596C2×C4(C22⋊D11)⋊C412yes—
597C2×C4C22×C4×D1111yescharacteristic
598C2×C4C2×#433911yescharacteristic
599C2×C4C2×#433911yescharacteristic
600C2×C4C2×#434111yescharacteristic
601C2×C4#6703711yescharacteristic
602C2×C4#6704011yescharacteristic
603C8—22no—
604C8—41no—
605C8—222no—
606C8—222no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—442no—
615C22—442no—
616C22—442no—
617C22—881no—
618C22—881no—
619C22—881no—
620C22—881no—
621C22C2×(C22⋊D11)⋊C411yescharacteristic
622C22#1062302111yescharacteristic
623C22#1062303811yescharacteristic
624C22#1062330511yescharacteristic
625C22#1062330511yescharacteristic
626C22D11×#13711yescharacteristic
627C22#1062330811yescharacteristic
628C4—22no—
629C4—42no—
630C4—42no—
631C4—42no—
632C4—81no—
633C4—222no—
634C4—441no—
635C4—441no—
636C4—442no—
637C4—441no—
638C4—881no—
639C4—881no—
640C4C4×#433911yescharacteristic
641C4#1062302611yescharacteristic
642C4#1062303511yescharacteristic
643C4#1062304411yescharacteristic
644C2—42no—
645C2—882no—
646C2#1307160411yescharacteristic
647C2#1307743111yescharacteristic
648C2#1307746411yescharacteristic
649C2#1308081811yescharacteristic
650C2#1308095011yescharacteristic
651C2#1308110211yescharacteristic
652C2#1308111711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1736C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
cosocleC22×C4×C11C24
hypercenter#1736D11
hypocenterC11#22941
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
3. #13071493C2semidirect
4. #13069353C2semidirect
5. #13069300C2semidirect
6. #13069241C2semidirect
7. #13069211C2semidirect
8. #13069185C2semidirect
10. #13068864C2semidirect
11. #13068815C2semidirect
12. #13068508C2semidirect
13. #13068440C2semidirect
14. #13068397C2semidirect
15. C11×#1736C2semidirect
39. #10622580C4semidirect
74. C2×C11×C4⋊C4C2×C4semidirect
114. C22⋊(C11⋊C8)C2×C4semidirect
123. #66871C2×C4semidirect
124. #66871C2×C4semidirect
223. #1736D11semidirect
403. C2×C4⋊C4C4×D11semidirect
534. C11#22941semidirect

Maximal subgroups

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

subgroupindex
C2×#106225802
#130716542
#130714932
#130693532
#130693002
#130692412
#130692112
#130691852
#130690542
#130688642
#130688152
#130685082
#130684402
#130683972
C11×#17362
#2294111