Finite Group Databasebeta

← #14816756

Subgroups — #14816756

Order 2816.

896 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622376C211yesmaximal, characteristic, complemented
2C2×C4×#4323C211yesmaximal, characteristic
3#13072489C211yesmaximal, characteristic, complemented
4#13071521C211yesmaximal, characteristic, complemented
5#13070138C211yesmaximal, characteristic, complemented
6#13070102C211yesmaximal, characteristic, complemented
7#13070005C211yesmaximal, characteristic, complemented
8#13069956C211yesmaximal, characteristic, complemented
9#13069346C211yesmaximal, characteristic, complemented
10#13069171C211yesmaximal, characteristic, complemented
11#13068962C211yesmaximal, characteristic
12#13068962C211yesmaximal, characteristic
13#13068880C211yesmaximal, characteristic, complemented
14#13068861C211yesmaximal, characteristic, complemented
15C11×#1864C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C2×D4×Dic11C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C22×#4323C2211yescharacteristic
20C2×#66943C2211yescharacteristic
21C2×C4×D44C2211yescharacteristic
22C2×C11×#106C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C2×#66896C2211yescharacteristic
27#10622823—21no—
28C2×C11⋊#95—21no—
29C2×#66885C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66881C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33C4×#4323—24no—
34#10622607—21no—
35#10622605—21no—
36#10622601C2211yescharacteristic
37#10622601C2211yescharacteristic
38#10622590C2211yescharacteristic
39#10622586C2211yescharacteristic
40#10622586C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622559—21no—
46#10622555—21no—
47C4×Dic11⋊C4C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4×C11⋊C8C2211yescharacteristic
50#10622376—24no—
51#10622281—21no—
52#10622280—21no—
53C11×#340C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×Dic11—21no—
64C23×Dic11—21no—
65C22×D44C2311yescharacteristic
66C22×C4×D11—21no—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C4×D4×C11—22no—
70C4×D4×C11—41no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C42×C11C2311yescharacteristic
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79D4×Dic11—22no—
80D4×Dic11—22no—
81D4×Dic11—22no—
82D4×Dic11—41no—
83C2×#4323—22no—
84C2×#4323—22no—
85C2×#4323Q814yes—
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×C4⋊Dic11—21no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4D411yescharacteristic
100C2×Dic11⋊C4D411yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102C2×C4×Dic11C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105#66943—22no—
106#66943—41no—
107C4×D44—22no—
108C4×D44—41no—
109C11×#106—41no—
110C11×#102—22no—
111C11×#102—22no—
112C11×#95—21no—
113#66896D414yes—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95D411yescharacteristic
120C11⋊#95D411yescharacteristic
121#66885—22no—
122#66885—41no—
123#66881—22no—
124Dic11⋊C8—22no—
125#66873—22no—
126#66871—22no—
127#66871—22no—
128#66871—22no—
129C4×C11⋊C8—22no—
130#26370—111nomaximal, Sylow
131C24×C11—21no—
132C23×D11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11C2×D412yes—
137C2×D4×C11C2×Q812yes—
138C2×D4×C11#4112yes—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—42no—
143C22×C4×C11—42no—
144C22×C4×C11—81no—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2411yescharacteristic
148C22×Dic11—24no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—42no—
153C22×Dic11—42no—
154C22×Dic11—81no—
155C22×Dic11—81no—
156C22×Dic11—81no—
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44C2×Q812yes—
167C2×C4×D11—42no—
168C2×C4×D11—42no—
169C2×C4×D11—81no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—81no—
183C11×C22⋊C4—42no—
184C42×C11—21no—
185C42×C11—21no—
186C22⋊Dic11—24no—
187C22⋊Dic11—42no—
188#4323—28no—
189(C2×D11)⋊C4—42no—
190(C2×D11)⋊C4—42no—
191(C2×D11)⋊C4—81no—
192(C2×D11)⋊C4—81no—
193(C2×D11)⋊C4—81no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—42no—
199C4⋊Dic11C2×D412yes—
200C4⋊Dic11#4112yes—
201Dic11⋊C4—22no—
202Dic11⋊C4—41no—
203Dic11⋊C4—42no—
204Dic11⋊C4—81no—
205Dic11⋊C4—81no—
206Dic11⋊C4—81no—
207C4×Dic11—21no—
208C4×Dic11—21no—
209C4×Dic11—21no—
210C4×Dic11—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8C2×D412yes—
216C2×C11⋊C8C2×Q812yes—
217C2×#478—111no—
218C2×C4×D8—111no—
219#2454—111no—
220#2349—111no—
221#2092—111no—
222#2085—111no—
223#2067—111no—
224#2059—111no—
225#1942—111no—
226#1916—111no—
227#1879—111no—
228#1879—111no—
229#1864—111no—
230#1864D1111yescharacteristic, complemented
231#1862—111no—
232C23×C11—22no—
233C23×C11—22no—
234C23×C11—22no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11C22×D411yescharacteristic
240C22×D11—22no—
241C22×D11—41no—
242C22×D11—41no—
243C22×D11—41no—
244C22×D11—41no—
245C22×D11—41no—
246C22×D11—41no—
247D4×C11—22no—
248D4×C11—22no—
249D4×C11—22no—
250D4×C11C22⋊Q814yes—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—84no—
266C2×C4×C11#13512yes—
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C22×Q811yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11H(5,𝔽2)11yescharacteristic
272C2×C4×C112−1+411yescharacteristic
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—22no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—22no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—84no—
295C2×Dic11—84no—
296D44—22no—
297D44—22no—
298D44—41no—
299D44—41no—
300C4×D11—84no—
301C8×C11—41no—
302C8×C11—41no—
303C11⋊C8—22no—
304C11⋊C8—22no—
305C22×D8—111no—
306C2×#125—111no—
307C2×C4×D4—111no—
308C2×C4×D4—111no—
309C2×C4×D4—111no—
310C2×C4×D4C2×D1111yescharacteristic
311#478—224no—
312C4×D8—224no—
313C2×#107—111no—
314C2×#107—111no—
315C2×#107—111no—
316C2×#106—111no—
317C2×#106C2×D1111yescharacteristic
318C2×C4⋊C8—111no—
319C2×#102—111no—
320C2×#102—111no—
321C2×#102—111no—
322C2×#102—111no—
323C2×#102C2×D1111yescharacteristic
324C2×#102C2×D1111yescharacteristic
325C2×C4×C8—111no—
326#399—221no—
327#396—221no—
328#390—111no—
329#390—111no—
330#389—111no—
331#389—111no—
332#389—111no—
333#389C2×D1111yescharacteristic
334#385—221no—
335#385—221no—
336#385—221no—
337#382—111no—
338#380—221no—
339#380—221no—
340C4×C4⋊C4—111no—
341C2×#95—221no—
342#340—111no—
343#340—111no—
344#340—111no—
345#340C2×D1111yescharacteristic
346#336—111no—
347#336—111no—
348#336—111no—
349#336C2×D1111yescharacteristic
350C22×C11—24no—
351C22×C11—42no—
352C22×C11—42no—
353C22×C11—42no—
354C22×C11—42no—
355C22×C11—42no—
356C22×C11—42no—
357C22×C11#52511yescharacteristic
358C22×C11D4211yescharacteristic
359C22×C11D4×Q811yescharacteristic
360C22×C11C2×#13511yescharacteristic
361C22×C11#57511yescharacteristic
362C22×C11#57611yescharacteristic
363C22×C11#57611yescharacteristic
364C2×D11—42no—
365C2×D11—42no—
366C2×D11—42no—
367C2×D11—81no—
368C2×D11—81no—
369C2×D11—81no—
370C2×D11—81no—
371C4×C11—22no—
372C4×C11—41no—
373C4×C11—81no—
374C4×C11—81no—
375C4×C11—81no—
376C4×C11C2×C22⋊Q811yescharacteristic
377C4×C11#53911yescharacteristic
378C4×C11#54711yescharacteristic
379C4×C11#55411yescharacteristic
380Dic11—41no—
381Dic11—41no—
382Dic11—42no—
383Dic11—41no—
384Dic11—42no—
385Dic11—41no—
386Dic11—81no—
387C22×D4—111no—
388C22×D4C22×D1111yescharacteristic
389C23×C4—21no—
390C23×C4—221no—
391C23×C4—221no—
392C23×C4—221no—
393C2×D8—114no—
394C2×D8—222no—
395C2×D8—222no—
396C22×C8—111no—
397C22×C8—111no—
398C22×C8C22×D1111yescharacteristic
399C22×C8C22×D1111yescharacteristic
400#125—222no—
401#125—441no—
402C4×D4—22no—
403C4×D4—41no—
404C4×D4—222no—
405C4×D4—222no—
406C4×D4—222no—
407C4×D4—222no—
408C4×D4—441no—
409C4×D4—441no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4C22×D1111yescharacteristic
422C2×C4⋊C4C22×D1111yescharacteristic
423C2×C4⋊C4C22×D1111yescharacteristic
424C2×C22⋊C4—21no—
425C2×C22⋊C4—221no—
426C2×C22⋊C4—221no—
427C2×C22⋊C4—221no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C42—111no—
433C2×C42—111no—
434C2×C42C22×D1111yescharacteristic
435#107—222no—
436#107—222no—
437#107—222no—
438#106—41no—
439#106—222no—
440C4⋊C8—222no—
441#102—22no—
442#102—22no—
443#102—114no—
444#102—222no—
445#102—222no—
446#102—441no—
447C4×C8—222no—
448#95—21no—
449#95—111no—
450#95—111no—
451#95—221no—
452#95—221no—
453#95—221no—
454#95—221no—
455#95—221no—
456C2×C11—44no—
457C2×C11#244911yescharacteristic
458C2×C11#310211yescharacteristic
459C2×C11#312211yescharacteristic
460C2×C11#326811yescharacteristic
461C2×C11#328011yescharacteristic
462C2×C11#338011yescharacteristic
463C2×C11#338911yescharacteristic
464D11—82no—
465C24—21no—
466C24—221no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—112no—
471C2×D4—221no—
472C2×D4—221no—
473C2×D4—221no—
474C2×D4—221no—
475C2×D4—221no—
476C2×D4#433912yes—
477C2×D4D4×D1112yes—
478C2×D4Q8×D1112yes—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—81no—
485C22×C4—111no—
486C22×C4—111no—
487C22×C4—111no—
488C22×C4—111no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—224no—
492C22×C4—221no—
493C22×C4—442no—
494C22×C4—442no—
495C22×C4—442no—
496C22×C4—442no—
497C22×C4—881no—
498C22×C4—881no—
499C22×C4—881no—
500C22×C4—881no—
501C22×C4D4×D1111yescharacteristic
502C22×C4D4×D1111yescharacteristic
503C22×C4C23×D1111yescharacteristic
504D8—228no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—112no—
512C2×C8—112no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—81no—
524C4⋊C4—112no—
525C4⋊C4—112no—
526C4⋊C4—222no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—441no—
532C4⋊C4—442no—
533C4⋊C4—442no—
534C4⋊C4—881no—
535C4⋊C4—881no—
536C4⋊C4—881no—
537C22⋊C4—42no—
538C22⋊C4—224no—
539C22⋊C4—442no—
540C22⋊C4—442no—
541C22⋊C4—442no—
542C22⋊C4—881no—
543C22⋊C4—881no—
544C22⋊C4—881no—
545C42—21no—
546C42—21no—
547C42—221no—
548C42—221no—
549C42—221no—
550C42—221no—
551C11#2637011yescharacteristic, complemented, Sylow
552C23—22no—
553C23—22no—
554C23—22no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—222no—
560C23—441no—
561C23—441no—
562C23—441no—
563C23—441no—
564C23—441no—
565C23—441no—
566C23C2×D4×D1111yescharacteristic
567D4—22no—
568D4—22no—
569D4—22no—
570D4—222no—
571D4—222no—
572D4—441no—
573D4—441no—
574D4#6694914yes—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—84no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—222no—
601C2×C4—221no—
602C2×C4—221no—
603C2×C4—222no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—884no—
612C2×C4—884no—
613C2×C4—884no—
614C2×C4#6696912yes—
615C2×C4C2×#433911yescharacteristic
616C2×C4C2×D4×D1111yescharacteristic
617C2×C4#6703711yescharacteristic
618C2×C4C2×Q8×D1111yescharacteristic
619C2×C4#41×D1111yescharacteristic
620C2×C4#6704311yescharacteristic
621C8—41no—
622C8—41no—
623C8—222no—
624C8—222no—
625C22—24no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—442no—
633C22—442no—
634C22—442no—
635C22—881no—
636C22—881no—
637C22—881no—
638C22—881no—
639C22#1062307811yescharacteristic
640C22#1062312111yescharacteristic
641C22#1062316311yescharacteristic
642C22C2×#6696911yescharacteristic
643C22#1062329911yescharacteristic
644C22#1062330511yescharacteristic
645C22#1062330511yescharacteristic
646C4—22no—
647C4—41no—
648C4—81no—
649C4—81no—
650C4—81no—
651C4—441no—
652C4—442no—
653C4—441no—
654C4—441no—
655C4—441no—
656C4—442no—
657C4—881no—
658C4C2×#6694911yescharacteristic
659C4#1062309511yescharacteristic
660C4#1062316711yescharacteristic
661C4#1062318611yescharacteristic
662C2—44no—
663C2—882no—
664C2#1307242711yescharacteristic
665C2#1307863811yescharacteristic
666C2#1307885811yescharacteristic
667C2#1308016011yescharacteristic
668C2#1308029411yescharacteristic
669C2#1308148211yescharacteristic
670C2#1308157411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1864C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenter#1864D11
hypocenterC11#26370
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1864

Complements

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

NH ≅ G/Ntype
1. C2×#10622376C2semidirect
3. #13072489C2semidirect
4. #13071521C2semidirect
5. #13070138C2semidirect
6. #13070102C2semidirect
7. #13070005C2semidirect
8. #13069956C2semidirect
9. #13069346C2semidirect
10. #13069171C2semidirect
13. #13068880C2semidirect
14. #13068861C2semidirect
15. C11×#1864C2semidirect
230. #1864D11semidirect
551. C11#26370semidirect

Maximal subgroups

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

subgroupindex
C2×#106223762
C2×C4×#43232
#130724892
#130715212
#130701382
#130701022
#130700052
#130699562
#130693462
#130691712
#130689622
#130688802
#130688612
C11×#18642
#2637011