Finite Group Databasebeta

← #14797924

Subgroups — #14797924

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×#10622423C211yesmaximal, characteristic
2C2×#10622402C211yesmaximal, characteristic, complemented
3#13072122C211yesmaximal, characteristic, complemented
4#13071454C211yesmaximal, characteristic
5#13070140C211yesmaximal, characteristic, complemented
6#13070055C211yesmaximal, characteristic, complemented
7#13069934C211yesmaximal, characteristic, complemented
8#13069822C211yesmaximal, characteristic, complemented
9#13069311C211yesmaximal, characteristic, complemented
10#13069228C211yesmaximal, characteristic, complemented
11#13068972C211yesmaximal, characteristic, complemented
12#13068957C211yesmaximal, characteristic, complemented
13#13068868C211yesmaximal, characteristic, complemented
14#13068555C211yesmaximal, characteristic
15C11×#1805C211yesmaximal, characteristic, complemented
16C22×#4343C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C22×#4314C2211yescharacteristic
21C2×#66950C2211yescharacteristic
22C2×#66940C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C11×#382C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×#66879C2211yescharacteristic
33#10622601—21no—
34#10622601C2211yescharacteristic
35#10622600—21no—
36#10622600C2211yescharacteristic
37#10622600C2211yescharacteristic
38#10622586C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44#10622552—21no—
45#10622552C2211yescharacteristic
46C4×(C2×D11)⋊C4—21no—
47C4×(C2×D11)⋊C4C2211yescharacteristic
48#10622542C2211yescharacteristic
49#10622423—24no—
50#10622402—24no—
51#10622288—21no—
52#10622282—21no—
53#10622273—21no—
54#10622268—21no—
55C11×#340C2211yescharacteristic
56C11×#340C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C2×#4343—22no—
63C2×#4343—22no—
64C2×#4343—22no—
65C2×#4343—22no—
66C2×#4343—41no—
67C2×#4343—41no—
68C22×D44—21no—
69C22×D44C2311yescharacteristic
70C22×C4×D11—21no—
71C22×C4×D11C2311yescharacteristic
72C22×Dic22C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C4×Q8×C11—22no—
76C4×Q8×C11—41no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C42×C11—21no—
82C2×C42×C11C2311yescharacteristic
83Q8×Dic11—22no—
84Q8×Dic11—41no—
85C2×#4326—22no—
86C2×#4326—22no—
87C2×#4326D414yes—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4D411yescharacteristic
96C2×(C2×D11)⋊C4D411yescharacteristic
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C2×#4314—22no—
109C2×#4314—22no—
110C2×#4314—41no—
111#66950—22no—
112#66950—41no—
113#66940—22no—
114#66940—41no—
115C11×C4⋊C8—41no—
116C11×#103—22no—
117C11×#103—22no—
118C11×#95—21no—
119C11×#95—21no—
120#66899—22no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95D411yescharacteristic
127C11⋊#95D411yescharacteristic
128#66885—22no—
129(C2×D11)⋊C8—22no—
130(C2×D11)⋊C8—41no—
131#66880—22no—
132#66879—22no—
133#66874—41no—
134#66873—22no—
135#66873—41no—
136#66872—22no—
137#66871—41no—
138#24920—111nomaximal, Sylow
139C23×D11—21no—
140C23×D11C2×D411yescharacteristic
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11C2×D412yes—
145C2×Q8×C11#4112yes—
146C2×Q8×C11#4112yes—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2411yescharacteristic
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160#4343—44no—
161#4343—44no—
162#4343—44no—
163#4343—44no—
164C2×D44—24no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44—21no—
169C2×D44—21no—
170C2×D44—42no—
171C2×D44—42no—
172C2×D44#4112yes—
173C2×C4×D11—24no—
174C2×C4×D11—21no—
175C2×C4×D11—21no—
176C2×C4×D11—21no—
177C2×C4×D11—21no—
178C2×C4×D11—21no—
179C2×C4×D11—21no—
180C2×C4×D11—42no—
181C2×C4×D11—42no—
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×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—42no—
201C42×C11—21no—
202C42×C11—21no—
203C42×C11—42no—
204#4326—28no—
205(C2×D11)⋊C4—41no—
206(C2×D11)⋊C4—41no—
207(C2×D11)⋊C4—42no—
208(C2×D11)⋊C4—42no—
209(C2×D11)⋊C4—42no—
210(C2×D11)⋊C4—42no—
211(C2×D11)⋊C4—81no—
212(C2×D11)⋊C4—81no—
213(C2×D11)⋊C4—81no—
214C4⋊Dic11—21no—
215C4⋊Dic11—21no—
216C4⋊Dic11—21no—
217C4⋊Dic11—21no—
218C4⋊Dic11—42no—
219C4⋊Dic11—42no—
220Dic11⋊C4—42no—
221Dic11⋊C4—42no—
222C4×Dic11—21no—
223C4×Dic11—21no—
224C4×Dic11—42no—
225C4×Dic11—42no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8C2×D412yes—
232#4314—44no—
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#1805D1111yescharacteristic, complemented
247#1788—111no—
248C23×C11C22×D411yescharacteristic
249C22×D11—21no—
250C22×D11—22no—
251C22×D11—21no—
252C22×D11—21no—
253C22×D11—21no—
254C22×D11—21no—
255C22×D11—21no—
256C22×D11—21no—
257C22×D11—41no—
258C22×D11—41no—
259C22×D11—41no—
260C22×D11—41no—
261C22×D11—41no—
262C22×D11—41no—
263Q8×C11—22no—
264Q8×C11—22no—
265Q8×C11—22no—
266Q8×C11#12314yes—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
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—41no—
285C2×C4×C11C22×D411yescharacteristic
286C2×C4×C11C2×#4111yescharacteristic
287C2×C4×C11C2×#4111yescharacteristic
288C2×C4×C11C2×#4111yescharacteristic
289C2×C4×C11H(5,𝔽2)11yescharacteristic
290C2×C4×C11H(5,𝔽2)11yescharacteristic
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—21no—
294C2×Dic11—22no—
295C2×Dic11—21no—
296C2×Dic11—21no—
297C2×Dic11—21no—
298C2×Dic11—21no—
299C2×Dic11—21no—
300C2×Dic11—21no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11—41no—
306C2×Dic11—41no—
307C2×Dic11—41no—
308C2×Dic11—41no—
309D44—22no—
310D44—22no—
311D44—48no—
312D44—41no—
313D44—41no—
314C4×D11—48no—
315C4×D11—41no—
316C4×D11—41no—
317C4×D11—41no—
318C4×D11—41no—
319Dic22—22no—
320Dic22—22no—
321Dic22—41no—
322Dic22—41no—
323C8×C11—41no—
324C8×C11—41no—
325C11⋊C8—22no—
326C11⋊C8—41no—
327C22×#41—111no—
328C22×Q16—111no—
329C22×SD16—111no—
330C2×C22⋊Q8—111no—
331C2×C4×Q8—111no—
332C2×C4×Q8—111no—
333C2×C4×Q8C2×D1111yescharacteristic
334#452—224no—
335#441—224no—
336C2×#107—111no—
337C2×#106—111no—
338C2×C4⋊C8C2×D1111yescharacteristic
339C2×#103—111no—
340C2×#103—111no—
341C2×#103—111no—
342C2×#103C2×D1111yescharacteristic
343C2×#103C2×D1111yescharacteristic
344C2×#102—111no—
345C2×#102—111no—
346C2×#102—111no—
347C2×C22⋊C8—111no—
348C2×C22⋊C8—111no—
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#382C2×D1111yescharacteristic
361#380—111no—
362#380—111no—
363#380—221no—
364C4×C22⋊C4—111no—
365C4×C22⋊C4—221no—
366#340—111no—
367#340—111no—
368#340C2×D1111yescharacteristic
369#340C2×D1111yescharacteristic
370#336—111no—
371#336—111no—
372C22×C11#52511yescharacteristic
373C22×C11D4211yescharacteristic
374C22×C11#54611yescharacteristic
375C22×C11#57511yescharacteristic
376C22×C11#57511yescharacteristic
377C22×C11#57711yescharacteristic
378C22×C11#57811yescharacteristic
379C2×D11—41no—
380C2×D11—42no—
381C2×D11—41no—
382C2×D11—42no—
383C2×D11—41no—
384C2×D11—42no—
385C2×D11—41no—
386C2×D11—41no—
387C2×D11—41no—
388C2×D11—41no—
389C2×D11—81no—
390C2×D11—81no—
391C2×D11—81no—
392C2×D11—81no—
393C4×C11—24no—
394C4×C11—41no—
395C4×C11—41no—
396C4×C11—81no—
397C4×C11—81no—
398C4×C11—81no—
399C4×C11C2×#12311yescharacteristic
400C4×C11#53811yescharacteristic
401C4×C11#54611yescharacteristic
402C4×C11#55111yescharacteristic
403Dic11—42no—
404Dic11—41no—
405Dic11—41no—
406Dic11—41no—
407Dic11—81no—
408Dic11—81no—
409C2×#41—222no—
410C2×#41—222no—
411C2×#41—222no—
412C2×#41—222no—
413C2×#41—441no—
414C2×#41—441no—
415C22×Q8—111no—
416C22×Q8C22×D1111yescharacteristic
417C22×D4—111no—
418C22×D4—221no—
419C23×C4—111no—
420C23×C4—221no—
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—22no—
434C4×Q8—41no—
435C4×Q8—222no—
436C4×Q8—222no—
437C4×Q8—441no—
438C4×Q8—441no—
439C2×C4⋊C4—21no—
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⋊C4C22×D1111yescharacteristic
447C2×C4⋊C4C22×D1111yescharacteristic
448C2×C4⋊C4C22×D1111yescharacteristic
449C2×C22⋊C4—111no—
450C2×C22⋊C4—111no—
451C2×C22⋊C4—221no—
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—21no—
459C2×C42—111no—
460C2×C42—221no—
461C2×C42—221no—
462C2×C42C22×D1111yescharacteristic
463#107—441no—
464#106—222no—
465C4⋊C8—41no—
466#103—22no—
467#103—22no—
468#103—222no—
469#103—222no—
470#103—441no—
471#102—222no—
472#102—222no—
473#102—441no—
474C22⋊C8—222no—
475C22⋊C8—441no—
476#97—222no—
477#95—21no—
478#95—21no—
479#95—111no—
480#95—111no—
481#95—221no—
482#95—221no—
483#95—221no—
484#95—221no—
485#95—221no—
486C2×C11#241811yescharacteristic
487C2×C11#311111yescharacteristic
488C2×C11#312011yescharacteristic
489C2×C11#327111yescharacteristic
490C2×C11#327711yescharacteristic
491C2×C11#331311yescharacteristic
492C2×C11#331711yescharacteristic
493D11—81no—
494D11—82no—
495C24—111no—
496C24—221no—
497#41—444no—
498#41—444no—
499#41—444no—
500#41—444no—
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#434312yes—
513C2×D4—112no—
514C2×D4—224no—
515C2×D4—221no—
516C2×D4—221no—
517C2×D4—221no—
518C2×D4—221no—
519C2×D4—221no—
520C2×D4—442no—
521C2×D4—442no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—111no—
527C22×C4—111no—
528C22×C4—111no—
529C22×C4—224no—
530C22×C4—221no—
531C22×C4—221no—
532C22×C4—221no—
533C22×C4—221no—
534C22×C4—221no—
535C22×C4—221no—
536C22×C4—221no—
537C22×C4—221no—
538C22×C4—221no—
539C22×C4—442no—
540C22×C4—442no—
541C22×C4D4×D1111yescharacteristic
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—21no—
563C4⋊C4—21no—
564C4⋊C4—42no—
565C4⋊C4—221no—
566C4⋊C4—221no—
567C4⋊C4—221no—
568C4⋊C4—221no—
569C4⋊C4—442no—
570C4⋊C4—442no—
571C4⋊C4—442no—
572C4⋊C4—442no—
573C22⋊C4—441no—
574C22⋊C4—441no—
575C22⋊C4—442no—
576C22⋊C4—442no—
577C22⋊C4—442no—
578C22⋊C4—442no—
579C22⋊C4—881no—
580C22⋊C4—881no—
581C22⋊C4—881no—
582C42—21no—
583C42—21no—
584C42—42no—
585C42—221no—
586C42—221no—
587C42—442no—
588C42—442no—
589C11#2492011yescharacteristic, complemented, Sylow
590C23—221no—
591C23—221no—
592C23—221no—
593C23—221no—
594C23—221no—
595C23—221no—
596C23—222no—
597C23—221no—
598C23—441no—
599C23—441no—
600C23—441no—
601C23—441no—
602C23—441no—
603C23—441no—
604C23C2×D4×D1111yescharacteristic
605Q8—22no—
606Q8—22no—
607Q8—22no—
608Q8—222no—
609Q8—222no—
610Q8—441no—
611Q8—441no—
612Q8#6694714yes—
613D4—222no—
614D4—222no—
615D4—448no—
616D4—441no—
617D4—441no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
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—41no—
636C2×C4—221no—
637C2×C4—221no—
638C2×C4—221no—
639C2×C4—221no—
640C2×C4—221no—
641C2×C4—221no—
642C2×C4—221no—
643C2×C4—222no—
644C2×C4—221no—
645C2×C4—221no—
646C2×C4—448no—
647C2×C4—441no—
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×C4#6703711yescharacteristic
662C2×C4C2×#434311yescharacteristic
663C2×C4#41×D1111yescharacteristic
664C2×C4#6704211yescharacteristic
665C8—41no—
666C8—41no—
667C8—222no—
668C8—441no—
669C22—441no—
670C22—442no—
671C22—441no—
672C22—441no—
673C22—441no—
674C22—441no—
675C22—442no—
676C22—441no—
677C22—442no—
678C22—441no—
679C22—881no—
680C22—881no—
681C22—881no—
682C22—881no—
683C22#1062302111yescharacteristic
684C22#1062314011yescharacteristic
685C22#1062315811yescharacteristic
686C22#1062329911yescharacteristic
687C22#1062330111yescharacteristic
688C22#1062330811yescharacteristic
689C22#1062331011yescharacteristic
690C4—24no—
691C4—41no—
692C4—41no—
693C4—81no—
694C4—81no—
695C4—81no—
696C4—441no—
697C4—441no—
698C4—441no—
699C4—442no—
700C4—881no—
701C4—881no—
702C4C2×#6694711yescharacteristic
703C4#1062305811yescharacteristic
704C4#1062314111yescharacteristic
705C4#1062317511yescharacteristic
706C2—881no—
707C2—882no—
708C2#1307208411yescharacteristic
709C2#1307873211yescharacteristic
710C2#1307883711yescharacteristic
711C2#1308020711yescharacteristic
712C2#1308026811yescharacteristic
713C2#1308068311yescharacteristic
714C2#1308073811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1805C2
socleC23×C11C22×D4
prime radicalC22×#4343C22
hypercenter#1805D11
hypocenterC11#24920
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1805

Complements

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

NH ≅ G/Ntype
2. C2×#10622402C2semidirect
3. #13072122C2semidirect
5. #13070140C2semidirect
6. #13070055C2semidirect
7. #13069934C2semidirect
8. #13069822C2semidirect
9. #13069311C2semidirect
10. #13069228C2semidirect
11. #13068972C2semidirect
12. #13068957C2semidirect
13. #13068868C2semidirect
15. C11×#1805C2semidirect
246. #1805D11semidirect
589. C11#24920semidirect

Maximal subgroups

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

subgroupindex
C2×#106224232
C2×#106224022
#130721222
#130714542
#130701402
#130700552
#130699342
#130698222
#130693112
#130692282
#130689722
#130689572
#130688682
#130685552
C11×#18052
#2492011