Finite Group Databasebeta

← #14767607

Subgroups — #14767607

Order 2816.

938 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622788C211yesmaximal, characteristic
2#13071338C211yesmaximal, characteristic
3#13071334C211yesmaximal, characteristic, complemented
4#13069438C211yesmaximal, characteristic
5#13069434C211yesmaximal, characteristic, complemented
6#13068973C211yesmaximal, characteristic, complemented
7#13068972C211yesmaximal, characteristic, complemented
8#13068969C211yesmaximal, characteristic, complemented
9#13068968C211yesmaximal, characteristic, complemented
10#13068953C211yesmaximal, characteristic, complemented
11#13068950C211yesmaximal, characteristic, complemented
12#13068949C211yesmaximal, characteristic, complemented
13#13068745C211yesmaximal, characteristic, complemented
14#13068366C211yesmaximal, characteristic, complemented
15C11×#1877C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C2×#66997C2211yescharacteristic
20C22×#4325C2211yescharacteristic
21C2×#66993C2211yescharacteristic
22C22×#4324C2211yescharacteristic
23C22×#4314C2211yescharacteristic
24C2×#66940C2211yescharacteristic
25C2×C4×D44C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C11×#391C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30#10622834C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32#10622826—21no—
33#10622826—21no—
34#10622788C418yescomplemented
35C2×#66885C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37C2×#66879C2211yescharacteristic
38C2×C8×Dic11C2211yescharacteristic
39#10622601C2211yescharacteristic
40#10622590C2211yescharacteristic
41#10622590C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44#10622569—21no—
45#10622569—21no—
46#10622545C2211yescharacteristic
47#10622542C2211yescharacteristic
48#10622268—21no—
49#10622268—21no—
50#10622265—21no—
51#10622265—21no—
52C11×#340C2211yescharacteristic
53C11×#336C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C22×C22⋊D11—21no—
64C22×C22⋊D11—21no—
65C22×D44C2311yescharacteristic
66C22×C4×D11—21no—
67C22×Dic22C2311yescharacteristic
68C2×C11×SD16—41no—
69C2×C11×SD16—41no—
70C2×C11×SD16C2×C414yescomplemented
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C4×D4×C11—41no—
74C4×D4×C11—41no—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C42×C11C2311yescharacteristic
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81Q8×Dic11—41no—
82Q8×Dic11—41no—
83#66997—22no—
84#66997C2×C414yescomplemented
85C2×#4325—41no—
86C2×#4325—41no—
87C2×#4325C2×C414yescomplemented
88#66993—22no—
89#66993C2×C414yes—
90C2×#4324—41no—
91C2×#4324—41no—
92C2×#4324C2×C414yescomplemented
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11C2311yescharacteristic
105C2×C4×Dic11C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C2×#4314—41no—
109C2×#4314—41no—
110C2×#4314C2×C414yescomplemented
111#66940—41no—
112#66940—41no—
113C4×D44—41no—
114C4×D44—41no—
115C11×#103—41no—
116C11×#102—41no—
117C11×#95—21no—
118C11×#95—21no—
119#66899—41no—
120#66896—41no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95D411yescharacteristic
128C11⋊#95D411yescharacteristic
129C11⋊#95D411yescharacteristic
130C11⋊#95D411yescharacteristic
131#66885—41no—
132#66880—41no—
133#66879—22no—
134C8×Dic11C2×C414yescomplemented
135#66874—41no—
136#66873—41no—
137#22275—111nomaximal, Sylow
138C24×C11—21no—
139C23×D11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11C22×C412yes—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11C22×C412yes—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—42no—
156C22×C4×C11—81no—
157C22×C4×C11—81no—
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2411yescharacteristic
161C2×C22⋊D11—24no—
162C2×C22⋊D11—24no—
163C2×C22⋊D11—81no—
164C2×C22⋊D11—81no—
165C2×C22⋊D11—81no—
166C2×C22⋊D11—81no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11C2×D411yescharacteristic
171C22×Dic11C2×D411yescharacteristic
172C22×Dic11C2×D411yescharacteristic
173C22×Dic11C2×D411yescharacteristic
174C2×D44—21no—
175C2×D44—21no—
176C2×D44—21no—
177C2×D44—21no—
178C2×D44—21no—
179C2×D44C22×C412yes—
180C2×C4×D11—42no—
181C2×C4×D11—81no—
182C2×C4×D11—81no—
183C2×Dic22—21no—
184C2×Dic22—21no—
185C2×Dic22—21no—
186C2×Dic22—21no—
187C2×Dic22—21no—
188C2×Dic22C22×C412yes—
189C11×SD16—44no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11C22×C412yes—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C22⋊C4—42no—
201C42×C11—21no—
202C42×C11—21no—
203C22⋊Dic11—81no—
204C22⋊Dic11—81no—
205#4325—44no—
206#4324—44no—
207(C2×D11)⋊C4—42no—
208(C2×D11)⋊C4—81no—
209(C2×D11)⋊C4—81no—
210C4⋊Dic11—21no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11—21no—
214C4⋊Dic11—42no—
215Dic11⋊C4—24no—
216Dic11⋊C4—24no—
217Dic11⋊C4—42no—
218C4×Dic11—21no—
219C4×Dic11—21no—
220C4×Dic11—42no—
221C4×Dic11—42no—
222C4×Dic11C22×C412yes—
223C4×Dic11#4112yes—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8C22×C412yes—
230#4314—44no—
231C2×#492—111no—
232#2328—111no—
233#2327—111no—
234#1961—111no—
235#1960—111no—
236#1880—111no—
237#1880—111no—
238#1880—111no—
239#1880—111no—
240#1877—111no—
241#1877—111no—
242#1877—111no—
243#1877D1111yescharacteristic, complemented
244#1835—111no—
245#1746—111no—
246C23×C11—22no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11C22×D411yescharacteristic
254C22×D11—22no—
255C22×D11—41no—
256C22×D11—41no—
257C22×D11—41no—
258C22×D11—41no—
259C22×D11—41no—
260C22×D11—41no—
261Q8×C11—22no—
262Q8×C11—22no—
263Q8×C11—41no—
264Q8×C11—41no—
265D4×C11—22no—
266D4×C11—22no—
267D4×C11—41no—
268D4×C11—41no—
269C2×C4×C11—22no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—84no—
285C2×C4×C11C23×C411yescharacteristic
286C2×C4×C11C2×#4111yescharacteristic
287C2×C4×C11H(5,𝔽2)11yescharacteristic
288C2×C4×C11H(5,𝔽2)11yescharacteristic
289C2×C4×C11H(5,𝔽2)11yescharacteristic
290C2×C4×C11H(5,𝔽2)11yescharacteristic
291C22⋊D11—84no—
292C22⋊D11—84no—
293C2×Dic11—21no—
294C2×Dic11—21no—
295C2×Dic11—21no—
296C2×Dic11—21no—
297C2×Dic11—22no—
298C2×Dic11—21no—
299C2×Dic11—21no—
300C2×Dic11—21no—
301C2×Dic11—21no—
302C2×Dic11—21no—
303C2×Dic11—21no—
304C2×Dic11—41no—
305C2×Dic11—41no—
306C2×Dic11—41no—
307C2×Dic11—41no—
308C2×Dic11—41no—
309C2×Dic11—41no—
310C2×Dic11—41no—
311C2×Dic11—41no—
312C2×Dic11C4×D412yes—
313C2×Dic11C4×D412yes—
314D44—22no—
315D44—22no—
316D44—41no—
317D44—41no—
318C4×D11—84no—
319Dic22—22no—
320Dic22—22no—
321Dic22—41no—
322Dic22—41no—
323C8×C11—22no—
324C8×C11—41no—
325C11⋊C8—22no—
326C11⋊C8—41no—
327C22×SD16—111no—
328C22×SD16—111no—
329C22×SD16—111no—
330C22×SD16C2×D1111yescharacteristic
331C2×C4⋊Q8—111no—
332C2×#127—111no—
333C2×C4×Q8—111no—
334C2×C4×Q8—111no—
335C2×C4×D4—111no—
336C2×C4×D4C2×D1111yescharacteristic
337#492—118no—
338C2×#103—111no—
339C2×#103—111no—
340C2×#103—111no—
341C2×#103C2×D1111yescharacteristic
342C2×#102—111no—
343C2×#102—111no—
344C2×#102—111no—
345C2×#102C2×D1111yescharacteristic
346C2×#97—111no—
347C2×C4×C8—111no—
348#391—111no—
349#391C2×D1111yescharacteristic
350#390—111no—
351#390—111no—
352#387—221no—
353#387—221no—
354#387—221no—
355#387—221no—
356#386—221no—
357#386—221no—
358#386—221no—
359#386—221no—
360#382—111no—
361#382—111no—
362#376—111no—
363#340—111no—
364#340—111no—
365#340—111no—
366#340C2×D1111yescharacteristic
367#336—111no—
368#336—111no—
369#336—111no—
370#336C2×D1111yescharacteristic
371C22×C11—42no—
372C22×C11—42no—
373C22×C11—42no—
374C22×C11—81no—
375C22×C11—81no—
376C22×C11—81no—
377C22×C11—81no—
378C22×C11C2×C4×D411yescharacteristic
379C22×C11#53511yescharacteristic
380C22×C11#53511yescharacteristic
381C22×C11#57711yescharacteristic
382C22×C11#57711yescharacteristic
383C22×C11#57711yescharacteristic
384C22×C11#57711yescharacteristic
385C2×D11—42no—
386C2×D11—42no—
387C2×D11—42no—
388C2×D11—81no—
389C2×D11—81no—
390C2×D11—81no—
391C2×D11—81no—
392C4×C11—42no—
393C4×C11—41no—
394C4×C11—41no—
395C4×C11—81no—
396C4×C11—81no—
397C4×C11#51811yescharacteristic
398C4×C11#51811yescharacteristic
399C4×C11#54011yescharacteristic
400C4×C11#54011yescharacteristic
401Dic11—22no—
402Dic11—22no—
403Dic11—42no—
404Dic11—41no—
405Dic11—41no—
406Dic11—81no—
407Dic11—81no—
408C22×Q8—111no—
409C22×Q8C22×D1111yescharacteristic
410C22×D4—111no—
411C22×D4—221no—
412C22×D4—221no—
413C22×D4C22×D1111yescharacteristic
414C23×C4—21no—
415C23×C4—221no—
416C2×SD16—41no—
417C2×SD16—41no—
418C2×SD16—114no—
419C2×SD16—114no—
420C2×SD16—114no—
421C2×SD16—441no—
422C2×SD16—441no—
423C2×SD16—441no—
424C2×SD16—441no—
425C2×SD16—441no—
426C2×SD16—441no—
427C2×SD16C4×D1114yescomplemented
428C22×C8—111no—
429C22×C8—111no—
430C22×C8C22×D1111yescharacteristic
431C22×C8C22×D1111yescharacteristic
432C4⋊Q8—114no—
433C4⋊Q8—222no—
434#127—114no—
435#127—222no—
436C4×Q8—441no—
437C4×Q8—441no—
438C4×Q8—441no—
439C4×Q8—441no—
440C4×D4—41no—
441C4×D4—41no—
442C4×D4—441no—
443C4×D4—441no—
444C2×C4⋊C4—111no—
445C2×C4⋊C4—111no—
446C2×C4⋊C4—221no—
447C2×C4⋊C4—221no—
448C2×C4⋊C4—221no—
449C2×C4⋊C4—221no—
450C2×C4⋊C4C22×D1111yescharacteristic
451C2×C4⋊C4C22×D1111yescharacteristic
452C2×C22⋊C4—21no—
453C2×C22⋊C4—221no—
454C2×C22⋊C4—221no—
455C2×C22⋊C4—221no—
456C2×C22⋊C4—221no—
457C2×C22⋊C4—221no—
458C2×C42—111no—
459C2×C42—111no—
460C2×C42—221no—
461C2×C42—221no—
462C2×C42C22×D1111yescharacteristic
463#103—41no—
464#103—441no—
465#103—441no—
466#103—441no—
467#102—41no—
468#102—441no—
469#102—441no—
470#102—441no—
471#97—222no—
472C4×C8—114no—
473#95—21no—
474#95—21no—
475#95—111no—
476#95—111no—
477#95—111no—
478#95—111no—
479#95—221no—
480#95—221no—
481#95—221no—
482#95—221no—
483#95—221no—
484#95—221no—
485C2×C11—82no—
486C2×C11#232811yescharacteristic
487C2×C11#294911yescharacteristic
488C2×C11#294911yescharacteristic
489C2×C11#322111yescharacteristic
490C2×C11#322111yescharacteristic
491C2×C11#322211yescharacteristic
492C2×C11#322211yescharacteristic
493D11—82no—
494C24—21no—
495C24—221no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—112no—
502C2×Q8—221no—
503C2×Q8—221no—
504C2×Q8—221no—
505C2×Q8—221no—
506C2×Q8—221no—
507C2×Q8C2×C4×D1112yes—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—112no—
514C2×D4—224no—
515C2×D4—224no—
516C2×D4—221no—
517C2×D4—221no—
518C2×D4—221no—
519C2×D4—221no—
520C2×D4—221no—
521C2×D4—881no—
522C2×D4—881no—
523C2×D4—881no—
524C2×D4—881no—
525C2×D4C2×C4×D1112yes—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—42no—
530C22×C4—81no—
531C22×C4—81no—
532C22×C4—111no—
533C22×C4—111no—
534C22×C4—111no—
535C22×C4—111no—
536C22×C4—221no—
537C22×C4—221no—
538C22×C4—221no—
539C22×C4—442no—
540C22×C4—881no—
541C22×C4—881no—
542C22×C4D4×D1111yescharacteristic
543C22×C4D4×D1111yescharacteristic
544C22×C4C23×D1111yescharacteristic
545SD16—44no—
546SD16—444no—
547SD16—444no—
548SD16—444no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—112no—
555C2×C8—221no—
556C2×C8—221no—
557C2×C8—221no—
558C2×C8—221no—
559C2×C8—221no—
560C2×C8C2×C4×D1112yes—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—224no—
566C4⋊C4—224no—
567C4⋊C4—221no—
568C4⋊C4—221no—
569C4⋊C4—221no—
570C4⋊C4—221no—
571C4⋊C4—442no—
572C4⋊C4—442no—
573C22⋊C4—42no—
574C22⋊C4—442no—
575C22⋊C4—881no—
576C22⋊C4—881no—
577C22⋊C4—881no—
578C22⋊C4—881no—
579C42—21no—
580C42—21no—
581C42—112no—
582C42—112no—
583C42—221no—
584C42—221no—
585C42—442no—
586C42—442no—
587C11#2227511yescharacteristic, complemented, Sylow
588C23—22no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—222no—
596C23—441no—
597C23—441no—
598C23—441no—
599C23—441no—
600C23—441no—
601C23—441no—
602C23C2×D4×D1111yescharacteristic
603Q8—22no—
604Q8—22no—
605Q8—41no—
606Q8—41no—
607Q8—222no—
608Q8—222no—
609Q8—441no—
610Q8—441no—
611D4—22no—
612D4—22no—
613D4—41no—
614D4—41no—
615D4—222no—
616D4—222no—
617D4—441no—
618D4—441no—
619D4—884no—
620D4—884no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—22no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—84no—
637C2×C4—112no—
638C2×C4—112no—
639C2×C4—221no—
640C2×C4—221no—
641C2×C4—221no—
642C2×C4—221no—
643C2×C4—221no—
644C2×C4—221no—
645C2×C4—221no—
646C2×C4—221no—
647C2×C4—222no—
648C2×C4—221no—
649C2×C4—221no—
650C2×C4—441no—
651C2×C4—441no—
652C2×C4—441no—
653C2×C4—441no—
654C2×C4—441no—
655C2×C4—441no—
656C2×C4—441no—
657C2×C4—441no—
658C2×C4—884no—
659C2×C4C22×C4×D1111yescharacteristic
660C2×C4#6703711yescharacteristic
661C2×C4#6703711yescharacteristic
662C2×C4#6703711yescharacteristic
663C2×C4#41×D1111yescharacteristic
664C2×C4#6704211yescharacteristic
665C8—22no—
666C8—41no—
667C8—222no—
668C8—441no—
669C22—42no—
670C22—42no—
671C22—42no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—442no—
677C22—442no—
678C22—442no—
679C22—881no—
680C22—881no—
681C22—881no—
682C22—881no—
683C22C4×D4×D1111yescharacteristic
684C22#1062312311yescharacteristic
685C22#1062313811yescharacteristic
686C22#1062329311yescharacteristic
687C22#1062330111yescharacteristic
688C22#1062330611yescharacteristic
689C22#1062330911yescharacteristic
690C4—41no—
691C4—41no—
692C4—42no—
693C4—81no—
694C4—81no—
695C4—222no—
696C4—222no—
697C4—441no—
698C4—441no—
699C4—442no—
700C4—881no—
701C4—881no—
702C4#1062301711yescharacteristic
703C4#1062307611yescharacteristic
704C4#1062314611yescharacteristic
705C4#1062319411yescharacteristic
706C2—82no—
707C2—882no—
708C2#1307133711yescharacteristic
709C2#1307747011yescharacteristic
710C2#1307747211yescharacteristic
711C2#1307967411yescharacteristic
712C2#1307967611yescharacteristic
713C2#1307968411yescharacteristic
714C2#1307968611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1877C2
socleC23×C11C22×D4
prime radicalC2×#66993C22
cosocleC22×C4×C11C24
hypercenter#1877D11
hypocenterC11#22275
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1877

Complements

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

NH ≅ G/Ntype
3. #13071334C2semidirect
5. #13069434C2semidirect
6. #13068973C2semidirect
7. #13068972C2semidirect
8. #13068969C2semidirect
9. #13068968C2semidirect
10. #13068953C2semidirect
11. #13068950C2semidirect
12. #13068949C2semidirect
13. #13068745C2semidirect
14. #13068366C2semidirect
15. C11×#1877C2semidirect
34. #10622788C4semidirect
70. C2×C11×SD16C2×C4semidirect
84. #66997C2×C4semidirect
87. C2×#4325C2×C4semidirect
92. C2×#4324C2×C4semidirect
110. C2×#4314C2×C4semidirect
134. C8×Dic11C2×C4semidirect
243. #1877D11semidirect
427. C2×SD16C4×D11semidirect
587. C11#22275semidirect

Maximal subgroups

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

subgroupindex
C2×#106227882
#130713382
#130713342
#130694382
#130694342
#130689732
#130689722
#130689692
#130689682
#130689532
#130689502
#130689492
#130687452
#130683662
C11×#18772
#2227511