Finite Group Databasebeta

← #14771074

Subgroups — #14771074

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622746C211yesmaximal, characteristic
2#13071487C211yesmaximal, characteristic, complemented
3#13071453C211yesmaximal, characteristic
4#13069311C211yesmaximal, characteristic, complemented
5#13069297C211yesmaximal, characteristic, complemented
6#13069242C211yesmaximal, characteristic, complemented
7#13069235C211yesmaximal, characteristic, complemented
8#13068881C211yesmaximal, characteristic, complemented
9#13068867C211yesmaximal, characteristic, complemented
10#13068704C211yesmaximal, characteristic, complemented
11#13068554C211yesmaximal, characteristic
12#13068445C211yesmaximal, characteristic, complemented
13#13068435C211yesmaximal, characteristic, complemented
14#13068397C211yesmaximal, characteristic, complemented
15C11×#1809C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C2×#66940C2211yescharacteristic
20C2×#66940C2211yescharacteristic
21C2×#66930—21no—
22C2×C11×#107C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C11×#380C2211yescharacteristic
25C11×#380C2211yescharacteristic
26C4×C22⋊Dic11C2211yescharacteristic
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28#10622746C418yescomplemented
29C2×#66885C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66879C2211yescharacteristic
34C2×C8×Dic11C2211yescharacteristic
35#10622601C2211yescharacteristic
36#10622601C2211yescharacteristic
37C4⋊C4×Dic11C2211yescharacteristic
38C4⋊C4×Dic11C2211yescharacteristic
39#10622586C2211yescharacteristic
40#10622586C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66873C2211yescharacteristic
45#10622570—21no—
46#10622570—21no—
47#10622556—21no—
48#10622280—21no—
49#10622279—21no—
50#10622267—21no—
51#10622267—21no—
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C22×C22⋊D11—21no—
62C23×Dic11—21no—
63C2×#4339—22no—
64C2×#4339—22no—
65C2×#4339—22no—
66C2×#4339—41no—
67C2×#4339—41no—
68C2×#4339C2×C414yes—
69C22×D44C2311yescharacteristic
70C22×C4×D11—21no—
71C22×Dic22C2311yescharacteristic
72C2×C11×M16—41no—
73C2×C11×M16—41no—
74C2×C11×M16C2×C414yes—
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C22⋊Dic11D411yescharacteristic
84C2×C22⋊Dic11D411yescharacteristic
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—22no—
91C2×C4⋊Dic11C2×C414yes—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11C2311yescharacteristic
103C2×C4×Dic11C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106#66940—22no—
107#66940—22no—
108#66940—41no—
109#66940—41no—
110#66930—44no—
111C11×#107—41no—
112C11×#106—41no—
113C11×#95—21no—
114C11×#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95D411yescharacteristic
120C11⋊#95D411yescharacteristic
121C22⋊(C11⋊C8)—22no—
122#66885C2×C414yes—
123#66885C2×C414yes—
124#66880C2×C414yes—
125#66880C2×C414yes—
126#66879—41no—
127C8×Dic11—41no—
128#66874—22no—
129#66874—22no—
130#66873—41no—
131#66873—41no—
132#22583—111nomaximal, Sylow
133C24×C11C2×D411yescharacteristic
134C23×D11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
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×C11C22×C412yes—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11#4112yes—
146C22×C4×C11C2411yescharacteristic
147C2×C22⋊D11—24no—
148C2×C22⋊D11—42no—
149C2×C22⋊D11—42no—
150C22×Dic11—24no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—42no—
155C22×Dic11—42no—
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160#4339—28no—
161#4339—44no—
162#4339—44no—
163#4339—44no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44—21no—
169C2×D44C22×C412yes—
170C2×C4×D11—24no—
171C2×C4×D11—42no—
172C2×C4×D11—42no—
173C2×Dic22—21no—
174C2×Dic22—21no—
175C2×Dic22—21no—
176C2×Dic22C22×C412yes—
177C2×Dic22#4112yes—
178C2×Dic22#4112yes—
179C11×M16—44no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11C22×C412yes—
185C2×C8×C11C22×C412yes—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C22⋊C4—42no—
195C11×C22⋊C4—81no—
196C22⋊Dic11—22no—
197C22⋊Dic11—41no—
198(C2×D11)⋊C4—42no—
199(C2×D11)⋊C4—42no—
200(C2×D11)⋊C4—81no—
201(C2×D11)⋊C4—81no—
202C4⋊Dic11—24no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11C22×C412yes—
206C4⋊Dic11C22×C412yes—
207Dic11⋊C4—42no—
208Dic11⋊C4—42no—
209Dic11⋊C4—42no—
210Dic11⋊C4—42no—
211C4×Dic11—21no—
212C4×Dic11—21no—
213C4×Dic11—21no—
214C4×Dic11—21no—
215C4×Dic11—42no—
216C4×Dic11—42no—
217C4×Dic11—42no—
218C4×Dic11—42no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×#417—111no—
226#2344—111no—
227#2341—111no—
228#1936—111no—
229#1934—111no—
230#1926—111no—
231#1925—111no—
232#1865—111no—
233#1863—111no—
234#1824—111no—
235#1809D1111yescharacteristic, complemented
236#1788—111no—
237#1763—111no—
238C4×#103—111no—
239#1753—111no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11C4×D412yes—
247C23×C11C22×D411yescharacteristic
248C22×D11—22no—
249C22×D11—41no—
250C22×D11—41no—
251C22×D11—41no—
252C22×D11—41no—
253C22×D11—41no—
254C22×D11—41no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
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—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11C4×D412yes—
274C2×C4×C11C23×C411yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11H(5,𝔽2)11yescharacteristic
279C2×C4×C11H(5,𝔽2)11yescharacteristic
280C22⋊D11—48no—
281C2×Dic11—22no—
282C2×Dic11—21no—
283C2×Dic11—22no—
284C2×Dic11—22no—
285C2×Dic11—21no—
286C2×Dic11—22no—
287C2×Dic11—22no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—21no—
294C2×Dic11—21no—
295C2×Dic11—21no—
296C2×Dic11—21no—
297C2×Dic11—48no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11AGL(1,ℤ/8)12yes—
303D44—22no—
304D44—22no—
305D44—41no—
306D44—41no—
307C4×D11—48no—
308Dic22—22no—
309Dic22—22no—
310Dic22—22no—
311Dic22#11714yescomplemented
312C8×C11—22no—
313C8×C11—22no—
314C11⋊C8—41no—
315C11⋊C8—41no—
316C22×#41—111no—
317C22×M16C2×D1111yescharacteristic
318C2×C4×Q8—111no—
319C2×C4×Q8—111no—
320C2×#117—221no—
321C22×C4⋊C4—111no—
322C2×#107C2×D1111yescharacteristic
323C2×#106C2×D1111yescharacteristic
324#417—118no—
325C2×#103—111no—
326C2×#103—111no—
327C2×#103—111no—
328C2×#103—111no—
329C2×#102—111no—
330C2×#102—111no—
331C2×#102—111no—
332C2×#102—111no—
333C2×C22⋊C8—111no—
334C2×#97—111no—
335C2×C4×C8—111no—
336#390—111no—
337#390—111no—
338#390—221no—
339#390—221no—
340#389—111no—
341#389—111no—
342#387—221no—
343#387—221no—
344#381—221no—
345#380—221no—
346#380C2×D1111yescharacteristic
347#380C2×D1111yescharacteristic
348C4×C4⋊C4—111no—
349C4×C4⋊C4—111no—
350C4×C22⋊C4—111no—
351C4×C22⋊C4—221no—
352#340—111no—
353#340—111no—
354#340—111no—
355#340—111no—
356#340C2×D1111yescharacteristic
357#340C2×D1111yescharacteristic
358#336—111no—
359#336—111no—
360C22×C11—22no—
361C22×C11—22no—
362C22×C11—22no—
363C22×C11—41no—
364C22×C11—41no—
365C22×C11—41no—
366C22×C11—41no—
367C22×C11C2×C4×D411yescharacteristic
368C22×C11#54611yescharacteristic
369C22×C11#54611yescharacteristic
370C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
371C22×C11#57511yescharacteristic
372C22×C11#57711yescharacteristic
373C22×C11#57811yescharacteristic
374C2×D11—42no—
375C2×D11—42no—
376C2×D11—42no—
377C2×D11—81no—
378C2×D11—81no—
379C2×D11—81no—
380C2×D11—81no—
381C4×C11—22no—
382C4×C11—81no—
383C4×C11—81no—
384C4×C11—81no—
385C4×C11—81no—
386C4×C11C2×#11711yescharacteristic
387C4×C11#51811yescharacteristic
388C4×C11#55111yescharacteristic
389C4×C11#55111yescharacteristic
390Dic11—24no—
391Dic11—22no—
392Dic11—41no—
393Dic11—42no—
394Dic11—42no—
395Dic11—41no—
396Dic11—41no—
397C2×#41—114no—
398C2×#41—222no—
399C2×#41—222no—
400C2×#41—222no—
401C2×#41—441no—
402C2×#41—441no—
403C22×Q8—111no—
404C22×D4—111no—
405C22×D4—221no—
406C23×C4—221no—
407C23×C4—221no—
408C23×C4C22×D1111yescharacteristic
409C2×M16—41no—
410C2×M16—41no—
411C2×M16C4×D1114yes—
412C22×C8—111no—
413C22×C8—111no—
414C22×C8C22×D1111yescharacteristic
415C22×C8C22×D1111yescharacteristic
416C4×Q8—222no—
417C4×Q8—222no—
418C4×Q8—441no—
419C4×Q8—441no—
420#117—444no—
421C2×C4⋊C4—114no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4—222no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4C22×D1111yescharacteristic
431C2×C4⋊C4C22×D1111yescharacteristic
432C2×C4⋊C4C22×D1111yescharacteristic
433C2×C4⋊C4C22×D1111yescharacteristic
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—111no—
437C2×C22⋊C4—111no—
438C2×C22⋊C4—221no—
439C2×C22⋊C4—221no—
440C2×C22⋊C4—221no—
441C2×C22⋊C4—221no—
442C2×C42—111no—
443C2×C42—111no—
444C2×C42—221no—
445C2×C42—221no—
446C2×C42—221no—
447C2×C42—221no—
448#107—41no—
449#106—41no—
450#103—114no—
451#103—114no—
452#103—222no—
453#103—222no—
454#102—114no—
455#102—114no—
456#102—441no—
457#102—441no—
458C22⋊C8—222no—
459#97—441no—
460C4×C8—441no—
461#95—21no—
462#95—21no—
463#95—111no—
464#95—111no—
465#95—221no—
466#95—221no—
467#95—221no—
468#95—221no—
469C2×C11—42no—
470C2×C11#234211yescharacteristic
471C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
472C2×C11#294711yescharacteristic
473C2×C11#330811yescharacteristic
474C2×C11#331711yescharacteristic
475C2×C11#332711yescharacteristic
476C2×C11#333211yescharacteristic
477D11—82no—
478C24—221no—
479C24D4×D1111yescharacteristic
480#41—228no—
481#41—444no—
482#41—444no—
483#41—444no—
484C2×Q8—112no—
485C2×Q8—112no—
486C2×Q8—112no—
487C2×Q8—221no—
488C2×Q8—221no—
489C2×Q8—221no—
490C2×D4—112no—
491C2×D4—224no—
492C2×D4—221no—
493C2×D4—221no—
494C2×D4—221no—
495C2×D4—221no—
496C2×D4—221no—
497C2×D4—442no—
498C2×D4—442no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—111no—
508C22×C4—111no—
509C22×C4—111no—
510C22×C4—111no—
511C22×C4—221no—
512C22×C4—224no—
513C22×C4—221no—
514C22×C4—221no—
515C22×C4—224no—
516C22×C4—442no—
517C22×C4—442no—
518C22×C4—442no—
519C22×C4—442no—
520C22×C4C2×C4×D1112yes—
521C22×C4D4×D1111yescharacteristic
522C22×C4#434312yes—
523C22×C4C23×D1111yescharacteristic
524M16—44no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—221no—
530C2×C8—221no—
531C2×C8—221no—
532C2×C8—221no—
533C2×C8—221no—
534C2×C8—221no—
535C2×C8C2×C4×D1112yes—
536C2×C8C2×C4×D1112yes—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—112no—
546C4⋊C4—112no—
547C4⋊C4—224no—
548C4⋊C4—221no—
549C4⋊C4—221no—
550C4⋊C4—442no—
551C4⋊C4—442no—
552C4⋊C4—442no—
553C4⋊C4—442no—
554C22⋊C4—42no—
555C22⋊C4—81no—
556C22⋊C4—222no—
557C22⋊C4—442no—
558C22⋊C4—442no—
559C22⋊C4—441no—
560C22⋊C4—881no—
561C22⋊C4—881no—
562C42—221no—
563C42—221no—
564C42—221no—
565C42—221no—
566C42—442no—
567C42—442no—
568C42—442no—
569C42—442no—
570C11#2258311yescharacteristic, complemented, Sylow
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—222no—
578C23—441no—
579C23—441no—
580C23—441no—
581C23—441no—
582C23—441no—
583C23—441no—
584C23#6694612yes—
585C23C2×D4×D1111yescharacteristic
586Q8—114no—
587Q8—222no—
588Q8—222no—
589Q8—222no—
590D4—222no—
591D4—222no—
592D4—448no—
593D4—441no—
594D4—441no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—112no—
614C2×C4—222no—
615C2×C4—221no—
616C2×C4—221no—
617C2×C4—222no—
618C2×C4—222no—
619C2×C4—222no—
620C2×C4—222no—
621C2×C4—221no—
622C2×C4—221no—
623C2×C4—221no—
624C2×C4—221no—
625C2×C4—221no—
626C2×C4—221no—
627C2×C4—221no—
628C2×C4—221no—
629C2×C4—221no—
630C2×C4—448no—
631C2×C4—448no—
632C2×C4—441no—
633C2×C4—441no—
634C2×C4—441no—
635C2×C4—441no—
636C2×C4#6694612yes—
637C2×C4C22×C4×D1111yescharacteristic
638C2×C4#6703711yescharacteristic
639C2×C4#6703711yescharacteristic
640C2×C4C2×#434311yescharacteristic
641C2×C4#41×D1111yescharacteristic
642C2×C4#41×D1111yescharacteristic
643C8—22no—
644C8—22no—
645C8—441no—
646C8—441no—
647C22—22no—
648C22—22no—
649C22—22no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22—442no—
655C22—442no—
656C22—442no—
657C22—881no—
658C22—881no—
659C22—881no—
660C22—881no—
661C22C2×#6694611yescharacteristic
662C22#1062314111yescharacteristic
663C22#1062314111yescharacteristic
664C22D11×AGL(1,ℤ/8)11yescharacteristic
665C22#1062330611yescharacteristic
666C22#1062330811yescharacteristic
667C22#1062331011yescharacteristic
668C4—22no—
669C4—81no—
670C4—81no—
671C4—81no—
672C4—81no—
673C4—222no—
674C4—224no—
675C4—441no—
676C4—441no—
677C4—441no—
678C4—442no—
679C4—442no—
680C4#1062301711yescharacteristic
681C4D11×#11711yescharacteristic
682C4#1062316811yescharacteristic
683C4#1062316811yescharacteristic
684C2—42no—
685C2—882no—
686C2#1307146211yescharacteristic
687C2#1307742311yescharacteristic
688C2#1307745711yescharacteristic
689C2#1308060211yescharacteristic
690C2#1308073711yescharacteristic
691C2#1308087911yescharacteristic
692C2#1308093811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1809C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenter#1809D11
hypocenterC11#22583
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
2. #13071487C2semidirect
4. #13069311C2semidirect
5. #13069297C2semidirect
6. #13069242C2semidirect
7. #13069235C2semidirect
8. #13068881C2semidirect
9. #13068867C2semidirect
10. #13068704C2semidirect
12. #13068445C2semidirect
13. #13068435C2semidirect
14. #13068397C2semidirect
15. C11×#1809C2semidirect
28. #10622746C4semidirect
235. #1809D11semidirect
311. Dic22#117semidirect
570. C11#22583semidirect

Maximal subgroups

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

subgroupindex
C2×#106227462
#130714872
#130714532
#130693112
#130692972
#130692422
#130692352
#130688812
#130688672
#130687042
#130685542
#130684452
#130684352
#130683972
C11×#18092
#2258311