Finite Group Databasebeta

← #14813800

Subgroups — #14813800

Order 2816.

840 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622458C211yesmaximal, characteristic
2C2×C4×#4314C211yesmaximal, characteristic
3#13072403C211yesmaximal, characteristic
4C4⋊C4×Dic22C211yesmaximal, characteristic, complemented
5#13070158C211yesmaximal, characteristic, complemented
6#13070114C211yesmaximal, characteristic, complemented
7#13070021C211yesmaximal, characteristic
8#13069858C211yesmaximal, characteristic
9#13069292C211yesmaximal, characteristic, complemented
10#13068970C211yesmaximal, characteristic
11#13068956C211yesmaximal, characteristic, complemented
12#13068956C211yesmaximal, characteristic, complemented
13#13068887C211yesmaximal, characteristic, complemented
14#13068880C211yesmaximal, characteristic
15C11×#1916C211yesmaximal, characteristic, complemented
16C22×Dic44C2211yescharacteristic
17C22×#4314C2211yescharacteristic
18C2×#66928C2211yescharacteristic
19C2×C4×D44C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66881C2211yescharacteristic
30C2×#66881C2211yescharacteristic
31C2×#66880C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36#10622606—21no—
37#10622602—21no—
38#10622589—21no—
39C4⋊C4×Dic11—21no—
40#10622552C2211yescharacteristic
41#10622548C2211yescharacteristic
42#10622542C2211yescharacteristic
43#10622542C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622541C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622458—24no—
48C4×#4314—24no—
49#10622288—21no—
50#10622277—21no—
51#10622260—21no—
52#10622260—21no—
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55C11×#336C2211yescharacteristic
56C11×#336C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61C22×D44C2311yescharacteristic
62C22×C4×D11—21no—
63C22×Dic22C2311yescharacteristic
64C22×Dic22C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×Dic44—22no—
96C2×Dic44—22no—
97C2×Dic44—22no—
98C2×#4314—22no—
99C2×#4314—22no—
100C2×#4314D414yes—
101#66928—22no—
102#66928—41no—
103C4×D44—22no—
104C4×D44—41no—
105C4×Dic22—22no—
106C4×Dic22—22no—
107C4×Dic22—22no—
108C4×Dic22—22no—
109C4×Dic22—41no—
110C4×Dic22—41no—
111C11×C4⋊C8—22no—
112C4×C8×C11—22no—
113C11×#95D411yescharacteristic
114C11×#95D411yescharacteristic
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#66881—22no—
126#66881—41no—
127#66880—22no—
128#66880—22no—
129#66880—22no—
130#66880—22no—
131#66880—41no—
132#26161—111nomaximal, Sylow
133C23×D11—21no—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2411yescharacteristic
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44C2×D412yes—
154C2×C4×D11—42no—
155C2×C4×D11—42no—
156C2×C4×D11—81no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22C2×D412yes—
167C2×Dic22#4112yes—
168C2×Dic22#4112yes—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11C2×D412yes—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—22no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—21no—
189(C2×D11)⋊C4—42no—
190(C2×D11)⋊C4—42no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—81no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—42no—
204C4⋊Dic11—81no—
205C4⋊Dic11#4112yes—
206Dic11⋊C4—24no—
207Dic11⋊C4—42no—
208Dic11⋊C4—42no—
209Dic11⋊C4—81no—
210Dic11⋊C4—81no—
211Dic11⋊C4—81no—
212C4×Dic11—24no—
213C4×Dic11—42no—
214C4×Dic11—42no—
215Dic44—44no—
216#4314—28no—
217C2×#464—111no—
218C2×C4×SD16—111no—
219#2447—111no—
220Q8×C4⋊C4—111no—
221#2096—111no—
222#2088—111no—
223#2071—111no—
224#2042—111no—
225#1933—111no—
226#1916D1111yescharacteristic, complemented
227#1880—111no—
228#1878—111no—
229#1878—111no—
230#1865—111no—
231#1864—111no—
232C23×C11C22×D411yescharacteristic
233C22×D11—22no—
234C22×D11—41no—
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—41no—
238C22×D11—41no—
239C22×D11—41no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11#13512yes—
257C2×C4×C11#13712yes—
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11H(5,𝔽2)11yescharacteristic
263C2×C4×C112−1+411yescharacteristic
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285D44—22no—
286D44—22no—
287D44—41no—
288D44—41no—
289C4×D11—84no—
290Dic22—22no—
291Dic22—22no—
292Dic22—22no—
293Dic22—41no—
294Dic22—41no—
295Dic22—41no—
296Dic22—41no—
297Dic22#12314yes—
298C8×C11—22no—
299C8×C11—41no—
300C8×C11—41no—
301C8×C11—41no—
302C22×Q16—111no—
303C22×SD16—111no—
304C2×#124—111no—
305C2×C4×Q8—111no—
306C2×C4×Q8—111no—
307C2×C4×Q8—111no—
308C2×C4×D4—111no—
309#464—224no—
310C4×SD16—224no—
311C2×#106—111no—
312C2×#106—111no—
313C2×C4⋊C8C2×D1111yescharacteristic
314C2×#103—111no—
315C2×#103—111no—
316C2×#103—111no—
317C2×#103—111no—
318C2×#103—111no—
319C2×#102—111no—
320C2×#102—111no—
321C2×#102—111no—
322C2×C4×C8C2×D1111yescharacteristic
323#397—221no—
324#397—221no—
325#391—111no—
326#391—111no—
327#390—111no—
328#389—111no—
329#389—111no—
330#389—111no—
331#389—221no—
332#389—221no—
333#385—221no—
334#384—111no—
335#384—221no—
336#381—221no—
337C4×C4⋊C4—221no—
338C4×C4⋊C4C2×D1111yescharacteristic
339#340—111no—
340#340—111no—
341#340—111no—
342#340—111no—
343#336C2×D1111yescharacteristic
344#336C2×D1111yescharacteristic
345#336C2×D1111yescharacteristic
346#336C2×D1111yescharacteristic
347C22×C11#52511yescharacteristic
348C22×C11D4211yescharacteristic
349C22×C11#54811yescharacteristic
350C22×C11C2×#13511yescharacteristic
351C22×C11C2×#13711yescharacteristic
352C22×C11#57711yescharacteristic
353C22×C11#57711yescharacteristic
354C2×D11—42no—
355C2×D11—42no—
356C2×D11—42no—
357C2×D11—81no—
358C2×D11—81no—
359C2×D11—81no—
360C2×D11—81no—
361C4×C11—22no—
362C4×C11—22no—
363C4×C11—41no—
364C4×C11—41no—
365C4×C11—41no—
366C4×C11—41no—
367C4×C11C2×#12311yescharacteristic
368C4×C11#53911yescharacteristic
369C4×C11#54711yescharacteristic
370C4×C11#55311yescharacteristic
371Dic11—24no—
372Dic11—42no—
373Dic11—81no—
374Dic11—81no—
375Dic11—81no—
376Dic11—81no—
377Dic11—81no—
378C22×Q8—111no—
379C22×Q8—111no—
380C22×D4—111no—
381C23×C4—221no—
382C2×Q16—222no—
383C2×Q16—222no—
384C2×Q16—222no—
385C2×SD16—114no—
386C2×SD16—222no—
387C2×SD16—222no—
388C22×C8C22×D1111yescharacteristic
389C22×C8C22×D1111yescharacteristic
390C22×C8C22×D1111yescharacteristic
391C22×C8C22×D1111yescharacteristic
392#124—222no—
393#124—441no—
394C4×Q8—222no—
395C4×Q8—222no—
396C4×Q8—222no—
397C4×Q8—222no—
398C4×Q8—441no—
399C4×Q8—441no—
400C4×D4—222no—
401C4×D4—441no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4D4411yescharacteristic
416C2×C4⋊C4D4411yescharacteristic
417C2×C22⋊C4—221no—
418C2×C22⋊C4—221no—
419C2×C22⋊C4—221no—
420C2×C22⋊C4—221no—
421C2×C22⋊C4—221no—
422C2×C42—221no—
423C2×C42—221no—
424C2×C42—221no—
425C2×C42C22×D1111yescharacteristic
426C2×C42C22×D1111yescharacteristic
427C2×C42C22×D1111yescharacteristic
428#106—222no—
429#106—441no—
430C4⋊C8—22no—
431#103—222no—
432#103—222no—
433#103—222no—
434#103—222no—
435#103—441no—
436#102—222no—
437#102—222no—
438#102—222no—
439C4×C8—22no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447#95D4411yescharacteristic
448#95D4411yescharacteristic
449C2×C11#244311yescharacteristic
450C2×C11#310811yescharacteristic
451C2×C11#312511yescharacteristic
452C2×C11#326611yescharacteristic
453C2×C11#328411yescharacteristic
454C2×C11#336511yescharacteristic
455C2×C11#336911yescharacteristic
456D11—82no—
457C24—221no—
458C2×Q8—112no—
459C2×Q8—112no—
460C2×Q8—112no—
461C2×Q8—221no—
462C2×Q8—221no—
463C2×Q8—221no—
464C2×Q8—221no—
465C2×Q8—221no—
466C2×Q8—221no—
467C2×Q8—221no—
468C2×Q8—221no—
469C2×Q8—221no—
470C2×D4—112no—
471C2×D4—221no—
472C2×D4—221no—
473C2×D4—221no—
474C2×D4—221no—
475C2×D4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—442no—
484C22×C4—442no—
485C22×C4—881no—
486C22×C4C2×D4411yescharacteristic
487C22×C4C2×D4411yescharacteristic
488C22×C4C2×D4411yescharacteristic
489C22×C4C2×D4411yescharacteristic
490C22×C4C2×D4411yescharacteristic
491C22×C4C2×D4411yescharacteristic
492C22×C4C23×D1111yescharacteristic
493Q16—444no—
494SD16—228no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8D4×D1112yes—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—112no—
510C4⋊C4—224no—
511C4⋊C4—221no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—442no—
521C4⋊C4—442no—
522C4⋊C4—442no—
523C4⋊C4—881no—
524C4⋊C4—881no—
525C4⋊C4—881no—
526C4⋊C4—881no—
527C22⋊C4—442no—
528C22⋊C4—442no—
529C22⋊C4—442no—
530C22⋊C4—442no—
531C22⋊C4—881no—
532C42—21no—
533C42—21no—
534C42—21no—
535C42—21no—
536C42—21no—
537C42—21no—
538C42—224no—
539C42—442no—
540C42—442no—
541C11#2616111yescharacteristic, complemented, Sylow
542C23—222no—
543C23—441no—
544C23—441no—
545C23—441no—
546C23—441no—
547C23—441no—
548C23—441no—
549C23C22×D4411yescharacteristic
550Q8—114no—
551Q8—222no—
552Q8—222no—
553Q8—222no—
554Q8—441no—
555Q8—441no—
556Q8—441no—
557Q8—441no—
558D4—222no—
559D4—222no—
560D4—441no—
561D4—441no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—222no—
579C2×C4—222no—
580C2×C4—222no—
581C2×C4—222no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—884no—
600C2×C4#6695712yes—
601C2×C4#6696212yes—
602C2×C4C2×D4×D1111yescharacteristic
603C2×C4#6704011yescharacteristic
604C2×C4#41×D1111yescharacteristic
605C2×C4#41×D1111yescharacteristic
606C2×C4#41×D1111yescharacteristic
607C2×C4#6704211yescharacteristic
608C8—22no—
609C8—41no—
610C8—41no—
611C8—41no—
612C22—442no—
613C22—442no—
614C22—442no—
615C22—881no—
616C22—881no—
617C22—881no—
618C22—881no—
619C22#1062305511yescharacteristic
620C22D4×D4411yescharacteristic
621C22#1062310711yescharacteristic
622C22C2×#6695711yescharacteristic
623C22C2×#6696211yescharacteristic
624C22#1062328211yescharacteristic
625C22#1062328211yescharacteristic
626C4—22no—
627C4—22no—
628C4—41no—
629C4—41no—
630C4—41no—
631C4—41no—
632C4—224no—
633C4—442no—
634C4—881no—
635C4—881no—
636C4—881no—
637C4—881no—
638C4—881no—
639C4#1062316211yescharacteristic
640C4D11×#12311yescharacteristic
641C4#1062322311yescharacteristic
642C4#1062324011yescharacteristic
643C2—882no—
644C2#1307235611yescharacteristic
645C2#1307869811yescharacteristic
646C2#1307889511yescharacteristic
647C2#1308013111yescharacteristic
648C2#1308034811yescharacteristic
649C2#1308131411yescharacteristic
650C2#1308135811yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1916C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1916D11
hypocenterC11#26161
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1916

Complements

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

NH ≅ G/Ntype
4. C4⋊C4×Dic22C2semidirect
5. #13070158C2semidirect
6. #13070114C2semidirect
9. #13069292C2semidirect
11. #13068956C2semidirect
12. #13068956C2semidirect
13. #13068887C2semidirect
15. C11×#1916C2semidirect
226. #1916D11semidirect
541. C11#26161semidirect

Maximal subgroups

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

subgroupindex
C2×#106224582
C2×C4×#43142
#130724032
C4⋊C4×Dic222
#130701582
#130701142
#130700212
#130698582
#130692922
#130689702
#130689562
#130688872
#130688802
C11×#19162
#2616111