Finite Group Databasebeta

← #14813724

Subgroups — #14813724

Order 2816.

896 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×#10622479C211yesmaximal, characteristic, complemented
2C2×#10622608C211yesmaximal, characteristic, complemented
3#13072028C211yesmaximal, characteristic
4#13071547C211yesmaximal, characteristic, complemented
5#13070134C211yesmaximal, characteristic, complemented
6#13070101C211yesmaximal, characteristic, complemented
7#13070054C211yesmaximal, characteristic, complemented
8#13069801C211yesmaximal, characteristic, complemented
9#13069241C211yesmaximal, characteristic, complemented
10#13069190C211yesmaximal, characteristic, complemented
11#13069052C211yesmaximal, characteristic, complemented
12#13068931C211yesmaximal, characteristic, complemented
13#13068911C211yesmaximal, characteristic, complemented
14#13068812C211yesmaximal, characteristic, complemented
15C11×#1854C211yesmaximal, characteristic, complemented
16C2×C11×#117C2211yescharacteristic
17C2×#66983C2211yescharacteristic
18C2×C4×C22⋊D11C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C2×#66948C2211yescharacteristic
22C2×#66945C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C11×#380C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31#10622608—24no—
32#10622601C2211yescharacteristic
33#10622600C2211yescharacteristic
34#10622600C2211yescharacteristic
35#10622598C2211yescharacteristic
36#10622590C2211yescharacteristic
37C4⋊C4×Dic11C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44#10622574—21no—
45#10622573—21no—
46#10622571—21no—
47C22⋊C4×Dic11—21no—
48#10622553—21no—
49#10622552—21no—
50#10622479—24no—
51#10622283—21no—
52#10622268—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C22×C22⋊D11D411yescharacteristic
64C23×Dic11—21no—
65C22×D44—21no—
66C22×D44C2311yescharacteristic
67C22×C4×D11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C11×#117—22no—
71C11×#117—41no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C42×C11—21no—
79C2×C22⋊Dic11D411yescharacteristic
80#66983—22no—
81#66983—22no—
82C4×C22⋊D11—22no—
83C4×C22⋊D11—22no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4D411yescharacteristic
92C2×C4⋊Dic11—22no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11—41no—
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×Dic11⋊C4D411yescharacteristic
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11C2311yescharacteristic
103C2×#4318—22no—
104C2×#4318—22no—
105C2×#4318—22no—
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108#66948—22no—
109#66948—41no—
110#66945—22no—
111#66945—41no—
112C11×#107—41no—
113C11×#106—22no—
114C11×C22⋊C8—22no—
115C11×#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122#66885—22no—
123#66885—41no—
124(C2×D11)⋊C8—22no—
125(C2×D11)⋊C8—22no—
126#66873—22no—
127#66873—22no—
128#66872—22no—
129#66872—22no—
130#66871—22no—
131#66871D414yescomplemented
132#26156—111nomaximal, Sylow
133C24×C11C2×D411yescharacteristic
134C23×D11—21no—
135C23×D11C2×D411yescharacteristic
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×C11—21no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11#4112yes—
146C22×C4×C11#4112yes—
147C22×C4×C11C2411yescharacteristic
148C2×C22⋊D11—22no—
149C2×C22⋊D11—41no—
150C2×C22⋊D11—41no—
151C2×C22⋊D11—42no—
152C2×C22⋊D11—81no—
153C2×C22⋊D11—81no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—42no—
158C22×Dic11—42no—
159C22×Dic11—81no—
160C22×Dic11C2×D411yescharacteristic
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44—21no—
169C2×D44—42no—
170C2×D44—42no—
171C2×D44—81no—
172C2×C4×D11—21no—
173C2×C4×D11—21no—
174C2×C4×D11—21no—
175C2×C4×D11—21no—
176C2×C4×D11—21no—
177C2×C4×D11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4C2×D412yes—
192C11×C22⋊C4—42no—
193C11×C22⋊C4—42no—
194C42×C11—42no—
195C22⋊Dic11—22no—
196(C2×D11)⋊C4—22no—
197(C2×D11)⋊C4—42no—
198(C2×D11)⋊C4—42no—
199(C2×D11)⋊C4—42no—
200(C2×D11)⋊C4—42no—
201(C2×D11)⋊C4—81no—
202(C2×D11)⋊C4—81no—
203(C2×D11)⋊C4—81no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—42no—
210C4⋊Dic11—81no—
211C4⋊Dic11C2×D412yes—
212Dic11⋊C4—22no—
213C4×Dic11—21no—
214C4×Dic11—21no—
215C4×Dic11—42no—
216C4×Dic11—81no—
217#4318—28no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8C2×D412yes—
223C2×C11⋊C8#4112yes—
224C2×#482—111no—
225C2×#428—111no—
226#2414—111no—
227#2352—111no—
228#2092—111no—
229#2085—111no—
230#2077—111no—
231#2033—111no—
232#1926—111no—
233#1918—111no—
234#1895—111no—
235#1874—111no—
236#1870—111no—
237#1854—111no—
238#1854D1111yescharacteristic, complemented
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11#12312yes—
246C23×C11C22×D411yescharacteristic
247C22×D11—21no—
248C22×D11—21no—
249C22×D11—21no—
250C22×D11—21no—
251C22×D11—21no—
252C22×D11—21no—
253C22×D11—21no—
254C22×D11—41no—
255C22×D11—41no—
256C22×D11—41no—
257C22×D11—41no—
258C22×D11—41no—
259C22×D11—41no—
260C22×D11—41no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11#12312yes—
280C2×C4×C11C22×D411yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C11H(5,𝔽2)11yescharacteristic
285C2×C4×C112−1+411yescharacteristic
286C22⋊D11—44no—
287C22⋊D11—84no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—22no—
293C2×Dic11—21no—
294C2×Dic11—21no—
295C2×Dic11—21no—
296C2×Dic11—21no—
297C2×Dic11—21no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11—41no—
306C2×Dic11—84no—
307D44—41no—
308D44—41no—
309D44—41no—
310D44—41no—
311D44—84no—
312C4×D11—41no—
313C4×D11—41no—
314C4×D11—41no—
315C4×D11—41no—
316C8×C11—41no—
317C8×C11—41no—
318C11⋊C8—22no—
319C11⋊C8—22no—
320C22×M16—111no—
321C2×#121—111no—
322C2×#121—111no—
323C2×C4×D4—111no—
324C2×#117—111no—
325C2×#117C2×D1111yescharacteristic
326C22×C4⋊C4—111no—
327#482—224no—
328#428—224no—
329C2×#107—111no—
330C2×#107—111no—
331C2×#107C2×D1111yescharacteristic
332C2×#106—111no—
333C2×#106—111no—
334C2×#106C2×D1111yescharacteristic
335C2×#102—111no—
336C2×#102—111no—
337C2×#102—111no—
338C2×#102—111no—
339C2×C22⋊C8—111no—
340C2×C22⋊C8—111no—
341C2×C22⋊C8C2×D1111yescharacteristic
342#394—221no—
343#392—221no—
344#390—111no—
345#390—221no—
346#389—111no—
347#388—221no—
348#388—221no—
349#387—221no—
350#386—221no—
351#382—111no—
352#380—111no—
353#380—111no—
354#380C2×D1111yescharacteristic
355C4×C4⋊C4—111no—
356C4×C22⋊C4—221no—
357#340—111no—
358#340—111no—
359#340—111no—
360#340—111no—
361#340C2×D1111yescharacteristic
362#340C2×D1111yescharacteristic
363#336—111no—
364#336—111no—
365C22×C11—22no—
366C22×C11—22no—
367C22×C11—22no—
368C22×C11—41no—
369C22×C11—41no—
370C22×C11—41no—
371C22×C11—41no—
372C22×C11C2×#12311yescharacteristic
373C22×C11D4211yescharacteristic
374C22×C11#54711yescharacteristic
375C22×C11#57511yescharacteristic
376C22×C11#57511yescharacteristic
377C22×C11#57611yescharacteristic
378C22×C11#57711yescharacteristic
379C2×D11—41no—
380C2×D11—41no—
381C2×D11—41no—
382C2×D11—41no—
383C2×D11—41no—
384C2×D11—41no—
385C2×D11—41no—
386C2×D11—81no—
387C2×D11—81no—
388C2×D11—81no—
389C2×D11—81no—
390C2×D11—81no—
391C2×D11—81no—
392C2×D11—81no—
393C4×C11—22no—
394C4×C11—42no—
395C4×C11—81no—
396C4×C11—81no—
397C4×C11—81no—
398C4×C11#52511yescharacteristic
399C4×C11#53911yescharacteristic
400C4×C11#54811yescharacteristic
401C4×C11#55311yescharacteristic
402Dic11—41no—
403Dic11—41no—
404Dic11—41no—
405Dic11—42no—
406Dic11—81no—
407Dic11—81no—
408C22×D4—111no—
409C22×D4—111no—
410C22×D4—221no—
411C22×D4—221no—
412C23×C4—111no—
413C23×C4—221no—
414C23×C4C22×D1111yescharacteristic
415C2×M16—222no—
416C2×M16—222no—
417C2×M16—222no—
418C22×C8—111no—
419C22×C8—111no—
420C22×C8C22×D1111yescharacteristic
421C22×C8C22×D1111yescharacteristic
422#121—222no—
423#121—222no—
424#121—222no—
425#121—441no—
426C4×D4—222no—
427C4×D4—222no—
428#117—22no—
429#117—41no—
430#117—222no—
431#117—441no—
432C2×C4⋊C4—111no—
433C2×C4⋊C4—111no—
434C2×C4⋊C4—111no—
435C2×C4⋊C4—111no—
436C2×C4⋊C4—222no—
437C2×C4⋊C4—221no—
438C2×C4⋊C4—221no—
439C2×C4⋊C4—441no—
440C2×C4⋊C4C22×D1111yescharacteristic
441C2×C4⋊C4C22×D1111yescharacteristic
442C2×C4⋊C4C22×D1111yescharacteristic
443C2×C4⋊C4C22×D1111yescharacteristic
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—111no—
447C2×C22⋊C4—111no—
448C2×C22⋊C4—221no—
449C2×C22⋊C4—221no—
450C2×C22⋊C4—221no—
451C2×C22⋊C4—221no—
452C2×C22⋊C4—221no—
453C2×C22⋊C4—221no—
454C2×C22⋊C4—221no—
455C2×C42—21no—
456C2×C42—111no—
457C2×C42—221no—
458C2×C42—221no—
459#107—41no—
460#107—114no—
461#107—222no—
462#106—22no—
463#106—222no—
464#106—222no—
465#102—222no—
466#102—222no—
467#102—222no—
468#102—441no—
469C22⋊C8—22no—
470C22⋊C8—222no—
471C22⋊C8—222no—
472#95—21no—
473#95—221no—
474#95—221no—
475#95—221no—
476#95—221no—
477#95—221no—
478#95—221no—
479C2×C11—42no—
480C2×C11#244311yescharacteristic
481C2×C11#309311yescharacteristic
482C2×C11#309611yescharacteristic
483C2×C11#327111yescharacteristic
484C2×C11#327311yescharacteristic
485C2×C11#334711yescharacteristic
486C2×C11#335111yescharacteristic
487D11—81no—
488D11—161no—
489C24—111no—
490C24—221no—
491C24D4×D1111yescharacteristic
492C2×D4—222no—
493C2×D4—221no—
494C2×D4—221no—
495C2×D4—221no—
496C2×D4—221no—
497C2×D4—221no—
498C2×D4—221no—
499C2×D4—442no—
500C2×D4—442no—
501C2×D4—441no—
502C2×D4—441no—
503C2×D4—442no—
504C2×D4—881no—
505C2×D4—881no—
506C2×D4—881no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—111no—
516C22×C4—111no—
517C22×C4—111no—
518C22×C4—221no—
519C22×C4—221no—
520C22×C4—221no—
521C22×C4—221no—
522C22×C4—221no—
523C22×C4—221no—
524C22×C4—221no—
525C22×C4—221no—
526C22×C4—221no—
527C22×C4—442no—
528C22×C4—442no—
529C22×C4—881no—
530C22×C4#433912yes—
531C22×C4D4×D1111yescharacteristic
532C22×C4#434312yes—
533C22×C4C23×D1111yescharacteristic
534M16—228no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—112no—
542C2×C8—112no—
543C2×C8—221no—
544C2×C8—221no—
545C2×C8—221no—
546C2×C8—221no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—112no—
555C4⋊C4—222no—
556C4⋊C4—221no—
557C4⋊C4—221no—
558C4⋊C4—221no—
559C4⋊C4—221no—
560C4⋊C4—221no—
561C4⋊C4—442no—
562C4⋊C4—881no—
563C4⋊C4D4×D1112yes—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—222no—
567C22⋊C4—222no—
568C22⋊C4—442no—
569C22⋊C4—442no—
570C22⋊C4—442no—
571C22⋊C4—442no—
572C22⋊C4—881no—
573C22⋊C4—881no—
574C22⋊C4—881no—
575C42—42no—
576C42—221no—
577C42—221no—
578C42—442no—
579C42—881no—
580C11#2615611yescharacteristic, complemented, Sylow
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—221no—
588C23—221no—
589C23—221no—
590C23—221no—
591C23—221no—
592C23—221no—
593C23—221no—
594C23—441no—
595C23—441no—
596C23—441no—
597C23—441no—
598C23—441no—
599C23—441no—
600C23—441no—
601C23#6694712yes—
602C23C2×D4×D1111yescharacteristic
603D4—444no—
604D4—441no—
605D4—441no—
606D4—441no—
607D4—441no—
608D4—884no—
609D4—884no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—221no—
629C2×C4—221no—
630C2×C4—221no—
631C2×C4—221no—
632C2×C4—221no—
633C2×C4—221no—
634C2×C4—221no—
635C2×C4—221no—
636C2×C4—222no—
637C2×C4—221no—
638C2×C4—441no—
639C2×C4—441no—
640C2×C4—441no—
641C2×C4—441no—
642C2×C4—441no—
643C2×C4—441no—
644C2×C4—441no—
645C2×C4—441no—
646C2×C4—441no—
647C2×C4—441no—
648C2×C4—441no—
649C2×C4—441no—
650C2×C4—884no—
651C2×C4#6694712yes—
652C2×C4C2×#433911yescharacteristic
653C2×C4C2×D4×D1111yescharacteristic
654C2×C4#6703711yescharacteristic
655C2×C4C2×#434311yescharacteristic
656C2×C4#41×D1111yescharacteristic
657C2×C4#6704311yescharacteristic
658C8—41no—
659C8—41no—
660C8—222no—
661C8—222no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—441no—
670C22—441no—
671C22—441no—
672C22—441no—
673C22—441no—
674C22—441no—
675C22—441no—
676C22—881no—
677C22—881no—
678C22—881no—
679C22—881no—
680C22—881no—
681C22—881no—
682C22—881no—
683C22C2×#6694711yescharacteristic
684C22#1062312111yescharacteristic
685C22#1062318611yescharacteristic
686C22#1062330011yescharacteristic
687C22#1062330111yescharacteristic
688C22#1062330411yescharacteristic
689C22#1062330811yescharacteristic
690C4—22no—
691C4—42no—
692C4—81no—
693C4—81no—
694C4—81no—
695C4—441no—
696C4—441no—
697C4—442no—
698C4—441no—
699C4—881no—
700C4—881no—
701C4#1062307111yescharacteristic
702C4#1062308311yescharacteristic
703C4#1062315811yescharacteristic
704C4#1062317611yescharacteristic
705C2—42no—
706C2—881no—
707C2—1761no—
708C2#1307235511yescharacteristic
709C2#1307855011yescharacteristic
710C2#1307857711yescharacteristic
711C2#1308019911yescharacteristic
712C2#1308022011yescharacteristic
713C2#1308110911yescharacteristic
714C2#1308117411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1854C2
socleC23×C11C22×D4
prime radical#13072028C2
hypercenter#1854D11
hypocenterC11#26156
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
1. C2×#10622479C2semidirect
2. C2×#10622608C2semidirect
4. #13071547C2semidirect
5. #13070134C2semidirect
6. #13070101C2semidirect
7. #13070054C2semidirect
8. #13069801C2semidirect
9. #13069241C2semidirect
10. #13069190C2semidirect
11. #13069052C2semidirect
12. #13068931C2semidirect
13. #13068911C2semidirect
14. #13068812C2semidirect
15. C11×#1854C2semidirect
131. #66871D4semidirect
238. #1854D11semidirect
580. C11#26156semidirect

Maximal subgroups

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

subgroupindex
C2×#106224792
C2×#106226082
#130720282
#130715472
#130701342
#130701012
#130700542
#130698012
#130692412
#130691902
#130690522
#130689312
#130689112
#130688122
C11×#18542
#2615611