Finite Group Databasebeta

← #14813718

Subgroups — #14813718

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×#10622350C211yesmaximal, characteristic, complemented
2C2×#10622734C211yesmaximal, characteristic, complemented
3#13072034C211yesmaximal, characteristic
4#13071545C211yesmaximal, characteristic, complemented
5#13070136C211yesmaximal, characteristic, complemented
6#13070099C211yesmaximal, characteristic, complemented
7#13070049C211yesmaximal, characteristic, complemented
8#13069799C211yesmaximal, characteristic, complemented
9#13069244C211yesmaximal, characteristic, complemented
10#13069188C211yesmaximal, characteristic, complemented
11#13069054C211yesmaximal, characteristic, complemented
12#13068931C211yesmaximal, characteristic, complemented
13#13068817C211yesmaximal, characteristic, complemented
14#13068817C211yesmaximal, characteristic, complemented
15C11×#1870C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×#66983C2211yescharacteristic
19C2×#66983C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26#10622836—21no—
27#10622833—21no—
28#10622825C2211yescharacteristic
29#10622825C2211yescharacteristic
30#10622825C2211yescharacteristic
31#10622734—24no—
32C2×#66885C2211yescharacteristic
33C2×#66885C2211yescharacteristic
34C2×#66885C2211yescharacteristic
35C2×#66885C2211yescharacteristic
36C2×#66882C2211yescharacteristic
37C2×#66882C2211yescharacteristic
38C2×#66882C2211yescharacteristic
39C2×#66881C2211yescharacteristic
40C2×#66881C2211yescharacteristic
41C2×#66881C2211yescharacteristic
42#10622603—21no—
43#10622594—21no—
44#10622572—21no—
45#10622570—21no—
46#10622564—21no—
47C22⋊C4×Dic11—21no—
48#10622552C2211yescharacteristic
49#10622549C2211yescharacteristic
50C4×C4⋊Dic11C2211yescharacteristic
51#10622541C2211yescharacteristic
52#10622350—24no—
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61C22×D4×C11D411yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11—21no—
65C22×C22⋊D11—21no—
66C23×Dic11—21no—
67C22×D44C2311yescharacteristic
68C2×C11×M16—22no—
69C2×C11×M16—22no—
70C2×C11×M16—22no—
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C4×D4×C11—22no—
76C4×D4×C11—22no—
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C22⋊C4D411yescharacteristic
79C2×C11×C22⋊C4D411yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86#66983—22no—
87#66983—22no—
88#66983—22no—
89#66983—41no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94#66979—22no—
95#66979—22no—
96#66979—41no—
97#66979—41no—
98C2×C4⋊Dic11—22no—
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11—41no—
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4⋊Dic11C2311yescharacteristic
105C2×C4⋊Dic11C2311yescharacteristic
106C2×C4⋊Dic11C2311yescharacteristic
107C2×C4⋊Dic11C2311yescharacteristic
108C2×Dic11⋊C4—21no—
109C2×C4×Dic11—21no—
110C2×C4×Dic11—21no—
111C2×C4×Dic11—21no—
112C11×C22⋊C8—22no—
113C11×C22⋊C8—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—22no—
124#66885—22no—
125#66885—41no—
126#66882—22no—
127#66882—41no—
128#66882D414yescomplemented
129#66881—22no—
130#66881—22no—
131#66881—22no—
132#26156—111nomaximal, Sylow
133C24×C11C2×D411yescharacteristic
134C24×C11C2×D411yescharacteristic
135C23×D11—21no—
136C2×D4×C11—22no—
137C2×D4×C11—41no—
138C2×D4×C11—41no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11#4112yes—
154C22×C4×C11#4112yes—
155C22×C4×C11C2411yescharacteristic
156C2×C22⋊D11—42no—
157C2×C22⋊D11—42no—
158C2×C22⋊D11—42no—
159C2×C22⋊D11—81no—
160C2×C22⋊D11—81no—
161C2×C22⋊D11—81no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—42no—
170C22×Dic11—42no—
171C22×Dic11—81no—
172C2×D44—21no—
173C2×D44—21no—
174C2×D44—21no—
175C2×D44—21no—
176C2×D44—21no—
177C2×D44—21no—
178C11×M16—28no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11C2×D412yes—
190C2×C8×C11#4112yes—
191C11×C4⋊C4—22no—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—22no—
194C42×C11—21no—
195C42×C11—21no—
196C22⋊Dic11—42no—
197C22⋊Dic11—42no—
198C22⋊Dic11—42no—
199C22⋊Dic11—81no—
200C22⋊Dic11—81no—
201(C2×D11)⋊C4—42no—
202(C2×D11)⋊C4—42no—
203(C2×D11)⋊C4—42no—
204(C2×D11)⋊C4—81no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11—21no—
216C4⋊Dic11—21no—
217C4⋊Dic11—42no—
218C4⋊Dic11C2×D412yes—
219C4⋊Dic11C2×D412yes—
220Dic11⋊C4—81no—
221C4×Dic11—42no—
222C4×Dic11—42no—
223C4×Dic11—81no—
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#1870D1111yescharacteristic, complemented
237#1854—111no—
238#1854—111no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11—21no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11#12312yes—
253C23×C11C22×D411yescharacteristic
254C22×D11—41no—
255C22×D11—41no—
256C22×D11—41no—
257C22×D11—41no—
258C22×D11—41no—
259C22×D11—41no—
260C22×D11—41no—
261D4×C11—44no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
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—21no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11#12312yes—
282C2×C4×C11C22×D411yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C11C2×#4111yescharacteristic
285C2×C4×C11C2×#4111yescharacteristic
286C2×C4×C11H(5,𝔽2)11yescharacteristic
287C2×C4×C112−1+411yescharacteristic
288C22⋊D11—84no—
289C22⋊D11—84no—
290C2×Dic11—22no—
291C2×Dic11—22no—
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—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11—41no—
306C2×Dic11—41no—
307C2×Dic11—41no—
308C2×Dic11—41no—
309C2×Dic11—41no—
310C2×Dic11—41no—
311C2×Dic11—84no—
312D44—41no—
313D44—41no—
314D44—41no—
315D44—41no—
316C8×C11—22no—
317C8×C11—22no—
318C8×C11—41no—
319C8×C11—41no—
320C22×M16C2×D1111yescharacteristic
321C2×#121—111no—
322C2×#121—111no—
323C2×C4×D4C2×D1111yescharacteristic
324C2×#117—111no—
325C2×#117—111no—
326C22×C4⋊C4—111no—
327#482—224no—
328#428—224no—
329C2×#107—111no—
330C2×#107—111no—
331C2×#107—111no—
332C2×#106—111no—
333C2×#106—111no—
334C2×#106—111no—
335C2×#102—111no—
336C2×#102—111no—
337C2×#102—111no—
338C2×#102—111no—
339C2×C22⋊C8C2×D1111yescharacteristic
340C2×C22⋊C8C2×D1111yescharacteristic
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#380—111no—
355C4×C4⋊C4—111no—
356C4×C22⋊C4—221no—
357#340—111no—
358#340—111no—
359#340—111no—
360#340—111no—
361#340—111no—
362#340—111no—
363#336C2×D1111yescharacteristic
364#336C2×D1111yescharacteristic
365C22×C11—22no—
366C22×C11—22no—
367C22×C11—22no—
368C22×C11—41no—
369C22×C11—41no—
370C22×C11—41no—
371C22×C11—41no—
372C22×C11—41no—
373C22×C11—41no—
374C22×C11—41no—
375C22×C11—41no—
376C22×C11—41no—
377C22×C11—41no—
378C22×C11—41no—
379C22×C11C2×#12311yescharacteristic
380C22×C11D4211yescharacteristic
381C22×C11#54711yescharacteristic
382C22×C11#57511yescharacteristic
383C22×C11#57511yescharacteristic
384C22×C11#57611yescharacteristic
385C22×C11#57711yescharacteristic
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—41no—
395C4×C11—41no—
396C4×C11—41no—
397C4×C11#52511yescharacteristic
398C4×C11#53911yescharacteristic
399C4×C11#54811yescharacteristic
400C4×C11#55311yescharacteristic
401Dic11—42no—
402Dic11—42no—
403Dic11—81no—
404Dic11—81no—
405Dic11—81no—
406Dic11—81no—
407Dic11—81no—
408C22×D4—111no—
409C22×D4—221no—
410C22×D4—221no—
411C22×D4D4411yescharacteristic
412C23×C4—221no—
413C23×C4C22×D1111yescharacteristic
414C23×C4C22×D1111yescharacteristic
415C2×M16—22no—
416C2×M16—22no—
417C2×M16—22no—
418C22×C8C22×D1111yescharacteristic
419C22×C8C22×D1111yescharacteristic
420C22×C8C22×D1111yescharacteristic
421C22×C8C22×D1111yescharacteristic
422#121—222no—
423#121—222no—
424#121—222no—
425#121—441no—
426C4×D4—22no—
427C4×D4—22no—
428#117—222no—
429#117—222no—
430#117—441no—
431#117—441no—
432C2×C4⋊C4—111no—
433C2×C4⋊C4—111no—
434C2×C4⋊C4—111no—
435C2×C4⋊C4—111no—
436C2×C4⋊C4—111no—
437C2×C4⋊C4—111no—
438C2×C4⋊C4—111no—
439C2×C4⋊C4—222no—
440C2×C4⋊C4—221no—
441C2×C4⋊C4—221no—
442C2×C4⋊C4—441no—
443C2×C4⋊C4D4411yescharacteristic
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C22⋊C4—221no—
447C2×C22⋊C4—221no—
448C2×C22⋊C4—221no—
449C2×C22⋊C4—221no—
450C2×C22⋊C4—221no—
451C2×C22⋊C4—221no—
452C2×C22⋊C4—221no—
453C2×C22⋊C4D4411yescharacteristic
454C2×C22⋊C4D4411yescharacteristic
455C2×C42—221no—
456C2×C42—221no—
457C2×C42—221no—
458C2×C42C22×D1111yescharacteristic
459#107—114no—
460#107—222no—
461#107—441no—
462#106—222no—
463#106—222no—
464#106—222no—
465#102—222no—
466#102—222no—
467#102—222no—
468#102—441no—
469C22⋊C8—22no—
470C22⋊C8—22no—
471C22⋊C8—22no—
472#95—221no—
473#95—221no—
474#95—221no—
475#95—221no—
476#95—221no—
477#95—221no—
478#95—221no—
479C2×C11—42no—
480C2×C11—81no—
481C2×C11#244311yescharacteristic
482C2×C11#309311yescharacteristic
483C2×C11#309611yescharacteristic
484C2×C11#327111yescharacteristic
485C2×C11#327311yescharacteristic
486C2×C11#334711yescharacteristic
487C2×C11#335111yescharacteristic
488D11—161no—
489C24—221no—
490C24C2×D4411yescharacteristic
491C24C2×D4411yescharacteristic
492C2×D4—22no—
493C2×D4—41no—
494C2×D4—41no—
495C2×D4—221no—
496C2×D4—221no—
497C2×D4—221no—
498C2×D4—221no—
499C2×D4—221no—
500C2×D4—221no—
501C2×D4—442no—
502C2×D4—442no—
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—21no—
516C22×C4—21no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4—221no—
520C22×C4—221no—
521C22×C4—221no—
522C22×C4—221no—
523C22×C4—221no—
524C22×C4—442no—
525C22×C4—442no—
526C22×C4—881no—
527C22×C4C2×D4411yescharacteristic
528C22×C4C2×D4411yescharacteristic
529C22×C4C2×D4411yescharacteristic
530C22×C4C2×D4411yescharacteristic
531C22×C4#434112yes—
532C22×C4#434112yes—
533C22×C4C23×D1111yescharacteristic
534M16—28no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8D4×D1112yes—
546C2×C8#434112yes—
547C4⋊C4—22no—
548C4⋊C4—112no—
549C4⋊C4—112no—
550C4⋊C4—221no—
551C4⋊C4—221no—
552C4⋊C4—221no—
553C4⋊C4—221no—
554C4⋊C4—221no—
555C4⋊C4—221no—
556C4⋊C4—221no—
557C4⋊C4—221no—
558C4⋊C4—221no—
559C4⋊C4—221no—
560C4⋊C4—221no—
561C4⋊C4—221no—
562C4⋊C4—442no—
563C4⋊C4—881no—
564C22⋊C4—22no—
565C22⋊C4—22no—
566C22⋊C4—442no—
567C22⋊C4—442no—
568C22⋊C4—442no—
569C22⋊C4—442no—
570C22⋊C4—442no—
571C22⋊C4—442no—
572C22⋊C4—881no—
573C22⋊C4—881no—
574C22⋊C4—881no—
575C42—21no—
576C42—21no—
577C42—442no—
578C42—442no—
579C42—881no—
580C11#2615611yescharacteristic, complemented, Sylow
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—441no—
595C23—441no—
596C23—441no—
597C23—441no—
598C23—441no—
599C23—441no—
600C23—441no—
601C23#6693912yes—
602C23C22×D4411yescharacteristic
603D4—44no—
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—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—222no—
630C2×C4—222no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—441no—
634C2×C4—441no—
635C2×C4—441no—
636C2×C4—441no—
637C2×C4—441no—
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#6693912yes—
652C2×C4C2×D4×D1111yescharacteristic
653C2×C4C2×#434111yescharacteristic
654C2×C4C2×#434111yescharacteristic
655C2×C4C2×#434111yescharacteristic
656C2×C4#6704211yescharacteristic
657C2×C4#6704311yescharacteristic
658C8—22no—
659C8—22no—
660C8—41no—
661C8—41no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—881no—
677C22—881no—
678C22—881no—
679C22—881no—
680C22—881no—
681C22—881no—
682C22—881no—
683C22C2×#6693911yescharacteristic
684C22D4×D4411yescharacteristic
685C22#1062308611yescharacteristic
686C22#1062327911yescharacteristic
687C22#1062327911yescharacteristic
688C22#1062328211yescharacteristic
689C22#1062328311yescharacteristic
690C4—22no—
691C4—41no—
692C4—41no—
693C4—41no—
694C4—442no—
695C4—442no—
696C4—881no—
697C4—881no—
698C4—881no—
699C4—881no—
700C4—881no—
701C4#1062311711yescharacteristic
702C4#1062312911yescharacteristic
703C4#1062314911yescharacteristic
704C4#1062319611yescharacteristic
705C2—42no—
706C2—81no—
707C2—1761no—
708C2#1307234911yescharacteristic
709C2#1307854911yescharacteristic
710C2#1307857511yescharacteristic
711C2#1308020611yescharacteristic
712C2#1308022811yescharacteristic
713C2#1308111811yescharacteristic
714C2#1308117811yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1870C2
socleC23×C11C22×D4
prime radical#13072034C2
hypercenter#1870D11
hypocenterC11#26156
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #1870

Complements

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

NH ≅ G/Ntype
1. C2×#10622350C2semidirect
2. C2×#10622734C2semidirect
4. #13071545C2semidirect
5. #13070136C2semidirect
6. #13070099C2semidirect
7. #13070049C2semidirect
8. #13069799C2semidirect
9. #13069244C2semidirect
10. #13069188C2semidirect
11. #13069054C2semidirect
12. #13068931C2semidirect
13. #13068817C2semidirect
14. #13068817C2semidirect
15. C11×#1870C2semidirect
128. #66882D4semidirect
236. #1870D11semidirect
580. C11#26156semidirect

Maximal subgroups

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

subgroupindex
C2×#106223502
C2×#106227342
#130720342
#130715452
#130701362
#130700992
#130700492
#130697992
#130692442
#130691882
#130690542
#130689312
#130688172
C11×#18702
#2615611