Finite Group Databasebeta

← #14770846

Subgroups — #14770846

Order 2816.

994 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622385C211yesmaximal, characteristic
2#13071500C211yesmaximal, characteristic, complemented
3#13071441C211yesmaximal, characteristic
4#13069307C211yesmaximal, characteristic, complemented
5#13069305C211yesmaximal, characteristic, complemented
6#13069258C211yesmaximal, characteristic, complemented
7#13069256C211yesmaximal, characteristic, complemented
8#13068865C211yesmaximal, characteristic, complemented
9#13068710C211yesmaximal, characteristic, complemented
10#13068642C211yesmaximal, characteristic, complemented
11#13068553C211yesmaximal, characteristic
12#13068443C211yesmaximal, characteristic, complemented
13#13068441C211yesmaximal, characteristic, complemented
14#13068391C211yesmaximal, characteristic, complemented
15C11×#1862C211yesmaximal, characteristic, complemented
16C22×#4341C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C22×C8×D11C2211yescharacteristic
20C2×#66945C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C2×#66896C2211yescharacteristic
26C2×#66896C2211yescharacteristic
27#10622826—21no—
28C2×C11⋊#95—21no—
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66879C2211yescharacteristic
34#10622603—21no—
35#10622600C2211yescharacteristic
36#10622600C2211yescharacteristic
37#10622598C2211yescharacteristic
38#10622590—21no—
39C4⋊C4×Dic11C2211yescharacteristic
40#10622587C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43#10622571—21no—
44#10622556—21no—
45C4×(C2×D11)⋊C4C2211yescharacteristic
46C4×C4⋊Dic11C2211yescharacteristic
47#10622542C2211yescharacteristic
48C2×#66867C2211yescharacteristic
49#10622385C418yescomplemented
50#10622283—21no—
51#10622261—21no—
52C11×#340C2211yescharacteristic
53C11×#336C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C22×C22⋊D11—21no—
63C23×Dic11—21no—
64C23×Dic11—21no—
65C2×#4341—22no—
66C2×#4341—22no—
67C2×#4341—22no—
68C2×#4341—41no—
69C2×#4341—41no—
70C2×#4341C2×C414yes—
71C22×C4×D11C2311yescharacteristic
72C22×Dic22C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C4×D4×C11—22no—
76C4×D4×C11—41no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—21no—
82C2×C42×C11C2311yescharacteristic
83C2×C22⋊Dic11—21no—
84D4×Dic11—22no—
85D4×Dic11—41no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4D411yescharacteristic
90C2×(C2×D11)⋊C4D411yescharacteristic
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C2×C8×D11—41no—
102C2×C8×D11—41no—
103C2×C8×D11C2×C414yescomplemented
104#66945—22no—
105#66945C2×C414yescomplemented
106C11×#107—41no—
107C11×#102—22no—
108C11×#102C2×C414yes—
109C11×#95—21no—
110#66896—22no—
111#66896C2×C414yes—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95D411yescharacteristic
122C11⋊#95D411yescharacteristic
123(C2×D11)⋊C8—22no—
124#66882—41no—
125#66880—41no—
126#66880C2×C414yescomplemented
127#66879—41no—
128#66874—41no—
129#66874C2×C414yescomplemented
130#66867—41no—
131#22564—111nomaximal, Sylow
132C24×C11—21no—
133C23×D11C2×D411yescharacteristic
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11C22×C412yes—
138C2×D4×C11#4112yes—
139C2×D4×C11#4112yes—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—42no—
144C22×C4×C11—42no—
145C22×C4×C11—81no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2411yescharacteristic
149C2×C22⋊D11—24no—
150C2×C22⋊D11—42no—
151C2×C22⋊D11—42no—
152C22×Dic11—24no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—42no—
158C22×Dic11—42no—
159C22×Dic11—42no—
160C22×Dic11—42no—
161C22×Dic11—81no—
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165#4341—28no—
166#4341—44no—
167#4341—44no—
168#4341—44no—
169C2×C4×D11—21no—
170C2×C4×D11—21no—
171C2×C4×D11—21no—
172C2×C4×D11—21no—
173C2×C4×D11C22×C412yes—
174C2×C4×D11#4112yes—
175C2×Dic22—21no—
176C2×Dic22—21no—
177C2×Dic22—21no—
178C2×Dic22—21no—
179C2×Dic22—21no—
180C2×Dic22C22×C412yes—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11C22×C412yes—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—81no—
193C11×C4⋊C4C22×C412yes—
194C11×C22⋊C4—42no—
195C42×C11—21no—
196C42×C11—21no—
197C22⋊Dic11—42no—
198(C2×D11)⋊C4—24no—
199(C2×D11)⋊C4—41no—
200(C2×D11)⋊C4—41no—
201(C2×D11)⋊C4—81no—
202(C2×D11)⋊C4—81no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—81no—
209C4⋊Dic11C22×C412yes—
210C4×Dic11—24no—
211C4×Dic11—21no—
212C4×Dic11—21no—
213C4×Dic11—42no—
214C4×Dic11—42no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8C22×C412yes—
221C8×D11—44no—
222C2×#416—111no—
223#2346—111no—
224#2339—111no—
225#1935—111no—
226#1935—111no—
227#1928—111no—
228#1928—111no—
229#1862—111no—
230#1862D1111yescharacteristic, complemented
231#1825—111no—
232#1808—111no—
233#1788—111no—
234#1762—111no—
235#1762—111no—
236#1752—111no—
237C23×C11—22no—
238C23×C11—22no—
239C23×C11—22no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11C22×D411yescharacteristic
245C22×D11—21no—
246C22×D11—21no—
247C22×D11—21no—
248C22×D11—21no—
249C22×D11—21no—
250C22×D11—21no—
251C22×D11C4×D412yes—
252D4×C11—22no—
253D4×C11—22no—
254D4×C11—22no—
255D4×C11#11714yes—
256C2×C4×C11—22no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
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—84no—
272C2×C4×C11C23×C411yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11H(5,𝔽2)11yescharacteristic
277C2×C4×C11H(5,𝔽2)11yescharacteristic
278C22⋊D11—48no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—22no—
282C2×Dic11—22no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—48no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—84no—
301C2×Dic11C4×D412yes—
302C4×D11—22no—
303C4×D11—22no—
304C4×D11—22no—
305C4×D11—22no—
306Dic22—22no—
307Dic22—22no—
308Dic22—41no—
309Dic22—41no—
310C8×C11—22no—
311C8×C11—41no—
312C11⋊C8—22no—
313C11⋊C8—41no—
314C22×#41—111no—
315C23×C8—111no—
316C2×C4×D4—111no—
317C2×C4×D4C2×D1111yescharacteristic
318C2×#117—111no—
319C2×#107—111no—
320C2×#107C2×D1111yescharacteristic
321#416—118no—
322C2×#103—111no—
323C2×#103—111no—
324C2×#103—111no—
325C2×#103—111no—
326C2×#102—111no—
327C2×#102—111no—
328C2×#102C2×D1111yescharacteristic
329C2×#102C2×D1111yescharacteristic
330C2×C22⋊C8—111no—
331C2×#97—111no—
332C2×#97—111no—
333#391—111no—
334#391—111no—
335#389—111no—
336#389C2×D1111yescharacteristic
337#388—221no—
338#388—221no—
339#386—221no—
340#386—221no—
341#382—221no—
342#381—221no—
343#380—111no—
344#380—111no—
345C4×C4⋊C4—111no—
346C4×C4⋊C4—111no—
347C4×C22⋊C4—111no—
348#376—221no—
349C2×#95—221no—
350#340—111no—
351#340—111no—
352#340—111no—
353#340—111no—
354#340—111no—
355#340C2×D1111yescharacteristic
356#336—111no—
357#336C2×D1111yescharacteristic
358C22×C11—24no—
359C22×C11—42no—
360C22×C11—42no—
361C22×C11—42no—
362C22×C11—42no—
363C22×C11—42no—
364C22×C11—42no—
365C22×C11C2×C4×D411yescharacteristic
366C22×C11#54611yescharacteristic
367C22×C11#54611yescharacteristic
368C22×C11#57511yescharacteristic
369C22×C11#57511yescharacteristic
370C22×C11#57611yescharacteristic
371C22×C11#57811yescharacteristic
372C2×D11—22no—
373C2×D11—22no—
374C2×D11—22no—
375C2×D11—41no—
376C2×D11—41no—
377C2×D11—41no—
378C2×D11—41no—
379C4×C11—42no—
380C4×C11—41no—
381C4×C11—41no—
382C4×C11—81no—
383C4×C11—81no—
384C4×C11C2×#11711yescharacteristic
385C4×C11#51811yescharacteristic
386C4×C11#55111yescharacteristic
387C4×C11#55111yescharacteristic
388Dic11—22no—
389Dic11—42no—
390Dic11—42no—
391Dic11—41no—
392Dic11—41no—
393Dic11—81no—
394Dic11—81no—
395C2×#41—114no—
396C2×#41—222no—
397C2×#41—222no—
398C2×#41—222no—
399C2×#41—441no—
400C2×#41—441no—
401C22×Q8—111no—
402C22×D4—221no—
403C22×D4C22×D1111yescharacteristic
404C23×C4—21no—
405C23×C4—111no—
406C23×C4—221no—
407C23×C4—221no—
408C22×C8—111no—
409C22×C8—114no—
410C22×C8—111no—
411C22×C8—441no—
412C22×C8—441no—
413C22×C8C22×D1111yescharacteristic
414C22×C8C22×D1111yescharacteristic
415C4×D4—22no—
416C4×D4—41no—
417C4×D4—222no—
418C4×D4—441no—
419#117—114no—
420#117—222no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4C22×D1111yescharacteristic
427C2×C4⋊C4C22×D1111yescharacteristic
428C2×C4⋊C4C22×D1111yescharacteristic
429C2×C22⋊C4—21no—
430C2×C22⋊C4—111no—
431C2×C22⋊C4—111no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C42—111no—
437C2×C42—221no—
438C2×C42—221no—
439C2×C42—221no—
440C2×C42C22×D1111yescharacteristic
441#107—41no—
442#107—441no—
443#103—114no—
444#103—114no—
445#103—441no—
446#103—441no—
447#102—22no—
448#102—114no—
449#102—222no—
450#102C4×D1114yes—
451C22⋊C8—222no—
452#97—441no—
453#97—441no—
454#95—21no—
455#95—111no—
456#95—111no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461#95—221no—
462#95—221no—
463#95—221no—
464#95—221no—
465#95—221no—
466C2×C11—44no—
467C2×C11#234211yescharacteristic
468C2×C11#294311yescharacteristic
469C2×C11#295111yescharacteristic
470C2×C11#331511yescharacteristic
471C2×C11#331511yescharacteristic
472C2×C11#331911yescharacteristic
473C2×C11#331911yescharacteristic
474D11—42no—
475C24—21no—
476C24—111no—
477#41—228no—
478#41—444no—
479#41—444no—
480#41—444no—
481C2×Q8—112no—
482C2×Q8—221no—
483C2×Q8—221no—
484C2×Q8—221no—
485C2×Q8—221no—
486C2×Q8—221no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—224no—
491C2×D4—442no—
492C2×D4—442no—
493C2×D4C2×C4×D1112yes—
494C2×D4#434112yes—
495C2×D4#434312yes—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—81no—
502C22×C4—111no—
503C22×C4—112no—
504C22×C4—112no—
505C22×C4—111no—
506C22×C4—111no—
507C22×C4—224no—
508C22×C4—221no—
509C22×C4—221no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4—221no—
513C22×C4—221no—
514C22×C4—221no—
515C22×C4—221no—
516C22×C4—442no—
517C22×C4—442no—
518C22×C4—442no—
519C22×C4—442no—
520C22×C4—881no—
521C22×C4D4×D1111yescharacteristic
522C22×C4D4×D1111yescharacteristic
523C22×C4C23×D1111yescharacteristic
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—112no—
530C2×C8—221no—
531C2×C8—221no—
532C2×C8—221no—
533C2×C8—221no—
534C2×C8—221no—
535C2×C8—444no—
536C2×C8C2×C4×D1112yes—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—81no—
543C4⋊C4—112no—
544C4⋊C4—221no—
545C4⋊C4—221no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C4⋊C4—221no—
549C4⋊C4—881no—
550C4⋊C4C2×C4×D1112yes—
551C22⋊C4—42no—
552C22⋊C4—224no—
553C22⋊C4—441no—
554C22⋊C4—441no—
555C22⋊C4—442no—
556C22⋊C4—881no—
557C22⋊C4—881no—
558C42—21no—
559C42—21no—
560C42—224no—
561C42—221no—
562C42—221no—
563C42—442no—
564C42—442no—
565C11#2256411yescharacteristic, complemented, Sylow
566C23—22no—
567C23—22no—
568C23—22no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—112no—
574C23—221no—
575C23—221no—
576C23—221no—
577C23—221no—
578C23—221no—
579C23—221no—
580C23C2×D4×D1111yescharacteristic
581Q8—222no—
582Q8—222no—
583Q8—441no—
584Q8—441no—
585D4—22no—
586D4—22no—
587D4—22no—
588D4—448no—
589D4#6694514yes—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—84no—
606C2×C4—112no—
607C2×C4—221no—
608C2×C4—221no—
609C2×C4—222no—
610C2×C4—222no—
611C2×C4—222no—
612C2×C4—222no—
613C2×C4—221no—
614C2×C4—221no—
615C2×C4—221no—
616C2×C4—221no—
617C2×C4—222no—
618C2×C4—222no—
619C2×C4—221no—
620C2×C4—221no—
621C2×C4—448no—
622C2×C4—441no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—884no—
633C2×C4C22×C4×D1111yescharacteristic
634C2×C4C2×#434111yescharacteristic
635C2×C4#6703711yescharacteristic
636C2×C4C2×#434311yescharacteristic
637C2×C4#41×D1111yescharacteristic
638C2×C4#6704211yescharacteristic
639C8—22no—
640C8—41no—
641C8—222no—
642C8—441no—
643C22—24no—
644C22—42no—
645C22—42no—
646C22—42no—
647C22—42no—
648C22—42no—
649C22—42no—
650C22—222no—
651C22—222no—
652C22—222no—
653C22—441no—
654C22—441no—
655C22—441no—
656C22—441no—
657C22C4×D4×D1111yescharacteristic
658C22#1062312211yescharacteristic
659C22#1062316111yescharacteristic
660C22#1062328811yescharacteristic
661C22#1062330211yescharacteristic
662C22#1062330411yescharacteristic
663C22#1062330811yescharacteristic
664C4—41no—
665C4—41no—
666C4—42no—
667C4—81no—
668C4—81no—
669C4—222no—
670C4—442no—
671C4—441no—
672C4—442no—
673C4—441no—
674C4—881no—
675C4—881no—
676C4C2×#6694511yescharacteristic
677C4#1062307611yescharacteristic
678C4#1062316811yescharacteristic
679C4#1062318911yescharacteristic
680C2—44no—
681C2—442no—
682C2#1307146311yescharacteristic
683C2#1307741111yescharacteristic
684C2#1307748611yescharacteristic
685C2#1308070511yescharacteristic
686C2#1308070911yescharacteristic
687C2#1308076511yescharacteristic
688C2#1308076911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1862C2
socleC23×C11C22×D4
prime radicalC22×#4341C22
cosocleC22×C4×C11C24
hypercenter#1862D11
hypocenterC11#22564
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1862

Complements

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

NH ≅ G/Ntype
2. #13071500C2semidirect
4. #13069307C2semidirect
5. #13069305C2semidirect
6. #13069258C2semidirect
7. #13069256C2semidirect
8. #13068865C2semidirect
9. #13068710C2semidirect
10. #13068642C2semidirect
12. #13068443C2semidirect
13. #13068441C2semidirect
14. #13068391C2semidirect
15. C11×#1862C2semidirect
49. #10622385C4semidirect
103. C2×C8×D11C2×C4semidirect
105. #66945C2×C4semidirect
126. #66880C2×C4semidirect
129. #66874C2×C4semidirect
230. #1862D11semidirect
565. C11#22564semidirect

Maximal subgroups

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

subgroupindex
C2×#106223852
#130715002
#130714412
#130693072
#130693052
#130692582
#130692562
#130688652
#130687102
#130686422
#130685532
#130684432
#130684412
#130683912
C11×#18622
#2256411