Finite Group Databasebeta

← #14797922

Subgroups — #14797922

Order 2816.

952 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×#10622852C211yesmaximal, characteristic
2C2×#10622402C211yesmaximal, characteristic, complemented
3#13072121C211yesmaximal, characteristic, complemented
4#13071457C211yesmaximal, characteristic
5#13070135C211yesmaximal, characteristic, complemented
6#13070053C211yesmaximal, characteristic, complemented
7#13069932C211yesmaximal, characteristic, complemented
8#13069820C211yesmaximal, characteristic, complemented
9#13069315C211yesmaximal, characteristic, complemented
10#13069232C211yesmaximal, characteristic, complemented
11#13068968C211yesmaximal, characteristic, complemented
12#13068955C211yesmaximal, characteristic, complemented
13#13068872C211yesmaximal, characteristic, complemented
14#13068629C211yesmaximal, characteristic, complemented
15C11×#1788C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C22×#4324C2211yescharacteristic
21C2×#66977C2211yescharacteristic
22C2×#66940C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28C11×#380C2211yescharacteristic
29#10622852—24no—
30C2×#66899C2211yescharacteristic
31#10622834—21no—
32#10622834—21no—
33#10622834C2211yescharacteristic
34#10622834C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36#10622825—21no—
37#10622825C2211yescharacteristic
38C4×C22⋊Dic11—21no—
39C4×C22⋊Dic11C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×#66882C2211yescharacteristic
42C2×#66880C2211yescharacteristic
43C2×#66880C2211yescharacteristic
44C2×#66879C2211yescharacteristic
45C2×Dic11⋊C8C2211yescharacteristic
46#10622598C2211yescharacteristic
47#10622590C2211yescharacteristic
48#10622587C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50#10622565—21no—
51#10622564—21no—
52#10622402—24no—
53#10622271—21no—
54#10622267—21no—
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C2×C11×#41—22no—
62C2×C11×#41—22no—
63C2×C11×#41—22no—
64C2×C11×#41—22no—
65C2×C11×#41—41no—
66C2×C11×#41—41no—
67C22×Q8×C11C2311yescharacteristic
68C22×D4×C11—21no—
69C22×D4×C11C2311yescharacteristic
70C23×C4×C11—21no—
71C23×C4×C11C2311yescharacteristic
72C22×Dic22C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11D411yescharacteristic
85C2×C22⋊Dic11D411yescharacteristic
86Q8×Dic11—22no—
87Q8×Dic11—22no—
88Q8×Dic11—41no—
89Q8×Dic11—41no—
90C2×#4326—22no—
91C2×#4326—22no—
92C2×#4326D414yes—
93C2×#4324—22no—
94C2×#4324—22no—
95C2×#4324—41no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102#66977—22no—
103#66977—41no—
104C2×Dic11⋊C4—21no—
105C2×Dic11⋊C4—21no—
106C2×C4×Dic11—21no—
107C2×C4×Dic11—21no—
108C2×C4×Dic11—21no—
109C2×C4×Dic11C2311yescharacteristic
110C2×C4×Dic11C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C22×C11⋊C8C2311yescharacteristic
113#66940—22no—
114#66940—41no—
115C11×#103—22no—
116C11×#103—22no—
117C11×#102—22no—
118C11×#102—41no—
119C11×C22⋊C8—41no—
120C11×#95—21no—
121#66899—22no—
122#66896—22no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95D411yescharacteristic
130C11⋊#95D411yescharacteristic
131C22⋊(C11⋊C8)—22no—
132#66882—41no—
133#66880—22no—
134#66880—41no—
135#66879—22no—
136Dic11⋊C8—41no—
137#66872—22no—
138#24920—111nomaximal, Sylow
139C24×C11—21no—
140C24×C11C2×D411yescharacteristic
141C11×#41—44no—
142C11×#41—44no—
143C11×#41—44no—
144C11×#41—44no—
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11C2×D412yes—
149C2×Q8×C11#4112yes—
150C2×Q8×C11#4112yes—
151C2×D4×C11—24no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—42no—
158C2×D4×C11—42no—
159C2×D4×C11#4112yes—
160C22×C4×C11—21no—
161C22×C4×C11—24no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—42no—
171C22×C4×C11—42no—
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2411yescharacteristic
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11C2×D411yescharacteristic
179C22×Dic11C2×D411yescharacteristic
180C22×Dic11C2×D411yescharacteristic
181C22×Dic11C2×D411yescharacteristic
182C2×Dic22—21no—
183C2×Dic22—21no—
184C2×Dic22—21no—
185C2×Dic22—21no—
186C2×Dic22—21no—
187C2×Dic22C2×D412yes—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C22⋊C4—42no—
199C22⋊Dic11—41no—
200C22⋊Dic11—41no—
201C22⋊Dic11—42no—
202C22⋊Dic11—42no—
203C22⋊Dic11—42no—
204C22⋊Dic11—81no—
205C22⋊Dic11—81no—
206C22⋊Dic11—81no—
207#4326—28no—
208#4324—44no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11—42no—
216C4⋊Dic11—42no—
217C4⋊Dic11—42no—
218Dic11⋊C4—42no—
219Dic11⋊C4—42no—
220C4×Dic11—21no—
221C4×Dic11—21no—
222C4×Dic11—21no—
223C4×Dic11—21no—
224C4×Dic11—42no—
225C4×Dic11—42no—
226C4×Dic11—42no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8C2×D412yes—
233C2×#452—111no—
234C2×#441—111no—
235#2421—111no—
236#2341—111no—
237#2092—111no—
238#2077—111no—
239#2055—111no—
240#2036—111no—
241#1936—111no—
242#1924—111no—
243#1880—111no—
244#1878—111no—
245#1863—111no—
246#1805—111no—
247#1788D1111yescharacteristic
248C23×C11—21no—
249C23×C11—22no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—21no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—41no—
257C23×C11—41no—
258C23×C11—41no—
259C23×C11—41no—
260C23×C11—41no—
261C23×C11—41no—
262C23×C11C22×D411yescharacteristic
263Q8×C11—22no—
264Q8×C11—22no—
265Q8×C11—22no—
266Q8×C11#12314yes—
267D4×C11—22no—
268D4×C11—22no—
269D4×C11—48no—
270D4×C11—41no—
271D4×C11—41no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—48no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11C22×D411yescharacteristic
290C2×C4×C11C2×#4111yescharacteristic
291C2×C4×C11C2×#4111yescharacteristic
292C2×C4×C11C2×#4111yescharacteristic
293C2×C4×C11H(5,𝔽2)11yescharacteristic
294C2×C4×C11H(5,𝔽2)11yescharacteristic
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—21no—
305C2×Dic11—21no—
306C2×Dic11—21no—
307C2×Dic11—21no—
308C2×Dic11—41no—
309C2×Dic11—41no—
310C2×Dic11—41no—
311C2×Dic11—41no—
312C2×Dic11—41no—
313C2×Dic11—41no—
314C2×Dic11—41no—
315C2×Dic11—41no—
316C2×Dic11—41no—
317C2×Dic11—41no—
318C2×Dic11—41no—
319Dic22—22no—
320Dic22—22no—
321Dic22—41no—
322Dic22—41no—
323C8×C11—41no—
324C8×C11—41no—
325C11⋊C8—22no—
326C11⋊C8—41no—
327C22×#41C2×D1111yescharacteristic
328C22×Q16—111no—
329C22×SD16—111no—
330C2×C22⋊Q8—111no—
331C2×C4×Q8—111no—
332C2×C4×Q8—111no—
333C2×C4×Q8—111no—
334#452—224no—
335#441—224no—
336C2×#107—111no—
337C2×#106—111no—
338C2×C4⋊C8—111no—
339C2×#103—111no—
340C2×#103—111no—
341C2×#103—111no—
342C2×#103C2×D1111yescharacteristic
343C2×#103C2×D1111yescharacteristic
344C2×#102—111no—
345C2×#102C2×D1111yescharacteristic
346C2×#102C2×D1111yescharacteristic
347C2×C22⋊C8—111no—
348C2×C22⋊C8C2×D1111yescharacteristic
349C2×#97—111no—
350#400—221no—
351#397—221no—
352#391—111no—
353#390—111no—
354#390—111no—
355#390—221no—
356#390—221no—
357#389—111no—
358#388—221no—
359#387—221no—
360#382—111no—
361#380—111no—
362#380—221no—
363#380C2×D1111yescharacteristic
364C4×C22⋊C4—111no—
365C4×C22⋊C4—221no—
366#340—111no—
367#340—111no—
368#340—111no—
369#340—111no—
370#336—111no—
371#336—111no—
372C22×C11—41no—
373C22×C11—42no—
374C22×C11—41no—
375C22×C11—42no—
376C22×C11—42no—
377C22×C11—41no—
378C22×C11—41no—
379C22×C11—41no—
380C22×C11—41no—
381C22×C11—41no—
382C22×C11—81no—
383C22×C11—81no—
384C22×C11—81no—
385C22×C11—81no—
386C22×C11#52511yescharacteristic
387C22×C11D4211yescharacteristic
388C22×C11#54611yescharacteristic
389C22×C11#57511yescharacteristic
390C22×C11#57511yescharacteristic
391C22×C11#57711yescharacteristic
392C22×C11#57811yescharacteristic
393C4×C11—24no—
394C4×C11—41no—
395C4×C11—81no—
396C4×C11—81no—
397C4×C11C2×#12311yescharacteristic
398C4×C11#53811yescharacteristic
399C4×C11#54611yescharacteristic
400C4×C11#55111yescharacteristic
401Dic11—42no—
402Dic11—41no—
403Dic11—41no—
404Dic11—41no—
405Dic11—41no—
406Dic11—81no—
407Dic11—81no—
408Dic11—81no—
409C2×#41—22no—
410C2×#41—22no—
411C2×#41—22no—
412C2×#41—22no—
413C2×#41—41no—
414C2×#41—41no—
415C22×Q8—111no—
416C22×Q8C22×D1111yescharacteristic
417C22×D4—21no—
418C22×D4C22×D1111yescharacteristic
419C23×C4—21no—
420C23×C4C22×D1111yescharacteristic
421C2×Q16—114no—
422C2×Q16—222no—
423C2×Q16—222no—
424C2×SD16—222no—
425C2×SD16—222no—
426C2×SD16—441no—
427C22×C8—111no—
428C22×C8—111no—
429C22×C8C22×D1111yescharacteristic
430C22×C8C22×D1111yescharacteristic
431C22⋊Q8—222no—
432C22⋊Q8—441no—
433C4×Q8—222no—
434C4×Q8—222no—
435C4×Q8—222no—
436C4×Q8—441no—
437C4×Q8—441no—
438C4×Q8—441no—
439C2×C4⋊C4—111no—
440C2×C4⋊C4—111no—
441C2×C4⋊C4—111no—
442C2×C4⋊C4—221no—
443C2×C4⋊C4—221no—
444C2×C4⋊C4—221no—
445C2×C4⋊C4—221no—
446C2×C4⋊C4—221no—
447C2×C4⋊C4C22×D1111yescharacteristic
448C2×C4⋊C4C22×D1111yescharacteristic
449C2×C22⋊C4—21no—
450C2×C22⋊C4—111no—
451C2×C22⋊C4—111no—
452C2×C22⋊C4—221no—
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×C42—221no—
463#107—441no—
464#106—222no—
465C4⋊C8—441no—
466#103—22no—
467#103—22no—
468#103—222no—
469#103—222no—
470#103—441no—
471#102—22no—
472#102—41no—
473#102—222no—
474C22⋊C8—41no—
475C22⋊C8—222no—
476#97—222no—
477#95—21no—
478#95—111no—
479#95—111no—
480#95—221no—
481#95—221no—
482#95—221no—
483#95—221no—
484#95—221no—
485#95—221no—
486C2×C11—81no—
487C2×C11—82no—
488C2×C11#241811yescharacteristic
489C2×C11#311111yescharacteristic
490C2×C11#312011yescharacteristic
491C2×C11#327111yescharacteristic
492C2×C11#327711yescharacteristic
493C2×C11#331311yescharacteristic
494C2×C11#331711yescharacteristic
495C24—21no—
496C24D4×D1111yescharacteristic
497#41—44no—
498#41—44no—
499#41—44no—
500#41—44no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—112no—
505C2×Q8—221no—
506C2×Q8—221no—
507C2×Q8—221no—
508C2×Q8—221no—
509C2×Q8—221no—
510C2×Q8#433912yes—
511C2×Q8D4×D1112yes—
512C2×Q8#434112yes—
513C2×D4—24no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—42no—
520C2×D4—42no—
521C2×D4#434112yes—
522C22×C4—21no—
523C22×C4—24no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—111no—
535C22×C4—111no—
536C22×C4—111no—
537C22×C4—111no—
538C22×C4—221no—
539C22×C4—221no—
540C22×C4—221no—
541C22×C4—221no—
542C22×C4D4×D1111yescharacteristic
543C22×C4C23×D1111yescharacteristic
544Q16—228no—
545SD16—444no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—112no—
553C2×C8—221no—
554C2×C8—221no—
555C2×C8—221no—
556C2×C8—221no—
557C2×C8—221no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—221no—
563C4⋊C4—221no—
564C4⋊C4—221no—
565C4⋊C4—221no—
566C4⋊C4—221no—
567C4⋊C4—221no—
568C4⋊C4—442no—
569C4⋊C4—442no—
570C4⋊C4—442no—
571C4⋊C4—442no—
572C4⋊C4—442no—
573C22⋊C4—42no—
574C22⋊C4—441no—
575C22⋊C4—441no—
576C22⋊C4—442no—
577C22⋊C4—442no—
578C22⋊C4—442no—
579C22⋊C4—881no—
580C22⋊C4—881no—
581C22⋊C4—881no—
582C42—221no—
583C42—221no—
584C42—221no—
585C42—221no—
586C42—442no—
587C42—442no—
588C42—442no—
589C11#2492011yescharacteristic, complemented, Sylow
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—22no—
597C23—21no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23C2×D4×D1111yescharacteristic
605Q8—22no—
606Q8—22no—
607Q8—22no—
608Q8—222no—
609Q8—222no—
610Q8—441no—
611Q8—441no—
612Q8#6693614yes—
613D4—22no—
614D4—22no—
615D4—48no—
616D4—41no—
617D4—41no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—48no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—221no—
636C2×C4—221no—
637C2×C4—221no—
638C2×C4—221no—
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—441no—
649C2×C4—441no—
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—441no—
659C2×C4C2×#433911yescharacteristic
660C2×C4C2×D4×D1111yescharacteristic
661C2×C4C2×#434111yescharacteristic
662C2×C4C2×#434111yescharacteristic
663C2×C4#6703711yescharacteristic
664C2×C4#6703711yescharacteristic
665C8—41no—
666C8—41no—
667C8—222no—
668C8—441no—
669C22—41no—
670C22—42no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—42no—
676C22—41no—
677C22—42no—
678C22—41no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22#1062302111yescharacteristic
684C22#1062311711yescharacteristic
685C22#1062312111yescharacteristic
686C22#1062329911yescharacteristic
687C22#1062330211yescharacteristic
688C22#1062330411yescharacteristic
689C22#1062330911yescharacteristic
690C4—24no—
691C4—41no—
692C4—81no—
693C4—81no—
694C4—441no—
695C4—441no—
696C4—441no—
697C4—441no—
698C4—442no—
699C4—881no—
700C4—881no—
701C4—881no—
702C4C2×#6693611yescharacteristic
703C4#1062302611yescharacteristic
704C4#1062312211yescharacteristic
705C4#1062312411yescharacteristic
706C2—81no—
707C2—82no—
708C2#1307208211yescharacteristic
709C2#1307871811yescharacteristic
710C2#1307883111yescharacteristic
711C2#1308020511yescharacteristic
712C2#1308026611yescharacteristic
713C2#1308067811yescharacteristic
714C2#1308074311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1788C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
hypercenter#1788D11
hypocenterC11#24920
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×#10622402C2semidirect
3. #13072121C2semidirect
5. #13070135C2semidirect
6. #13070053C2semidirect
7. #13069932C2semidirect
8. #13069820C2semidirect
9. #13069315C2semidirect
10. #13069232C2semidirect
11. #13068968C2semidirect
12. #13068955C2semidirect
13. #13068872C2semidirect
14. #13068629C2semidirect
589. C11#24920semidirect

Maximal subgroups

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

subgroupindex
C2×#106228522
C2×#106224022
#130721212
#130714572
#130701352
#130700532
#130699322
#130698202
#130693152
#130692322
#130689682
#130689552
#130688722
#130686292
C11×#17882
#2492011