Finite Group Databasebeta

← #14816804

Subgroups — #14816804

Order 2816.

864 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622464C211yesmaximal, characteristic, complemented
2C2×C4×#4314C211yesmaximal, characteristic
3#13072466C211yesmaximal, characteristic
4C4⋊C4×Dic22C211yesmaximal, characteristic, complemented
5#13070148C211yesmaximal, characteristic
6#13070094C211yesmaximal, characteristic, complemented
7#13069989C211yesmaximal, characteristic
8#13069950C211yesmaximal, characteristic, complemented
9#13069344C211yesmaximal, characteristic, complemented
10#13068970C211yesmaximal, characteristic
11#13068970C211yesmaximal, characteristic
12#13068887C211yesmaximal, characteristic, complemented
13#13068887C211yesmaximal, characteristic, complemented
14#13068880C211yesmaximal, characteristic
15C11×#1916C211yesmaximal, characteristic, complemented
16C22×#4314C2211yescharacteristic
17C2×#66949—21no—
18C2×C4×D44C2211yescharacteristic
19C2×#66922C2211yescharacteristic
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×#66881C2211yescharacteristic
32C2×#66881C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37#10622607—21no—
38#10622589—21no—
39C4⋊C4×Dic11—21no—
40#10622552C2211yescharacteristic
41#10622552C2211yescharacteristic
42#10622548C2211yescharacteristic
43#10622541C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622541C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622464—24no—
48C4×#4314—24no—
49#10622286—21no—
50#10622281—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×Dic22—21no—
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⋊Dic11—21no—
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×#4314—22no—
99C2×#4314—22no—
100C2×#4314Q814yescomplemented
101#66949—44no—
102C4×D44—22no—
103C4×D44—41no—
104#66922—22no—
105#66922—41no—
106C4×Dic22—22no—
107C4×Dic22—22no—
108C4×Dic22—22no—
109C4×Dic22—22no—
110C4×Dic22—41no—
111C4×Dic22—41no—
112C11×C4⋊C8—22no—
113C4×C8×C11—22no—
114C11×#95D411yescharacteristic
115C11×#95D411yescharacteristic
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120#66885—22no—
121#66885—22no—
122#66885—41no—
123#66881—22no—
124#66881—22no—
125#66881—22no—
126#66881—22no—
127#66881—41no—
128#66880—22no—
129#66880—22no—
130#66880D414yes—
131#26373—111nomaximal, Sylow
132C23×D11—21no—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44C2×Q812yes—
153C2×C4×D11—42no—
154C2×C4×D11—42no—
155C2×C4×D11—81no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—42no—
160C2×Dic22—42no—
161C2×Dic22—81no—
162C2×Dic22C2×D412yes—
163C2×Dic22C2×Q812yes—
164C2×Dic22#4112yes—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
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×C11C2×D412yes—
176C2×C8×C11C2×Q812yes—
177C11×C4⋊C4—41no—
178C11×C4⋊C4SD1614yescomplemented
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—21no—
185(C2×D11)⋊C4—42no—
186(C2×D11)⋊C4—42no—
187(C2×D11)⋊C4—42no—
188(C2×D11)⋊C4—42no—
189(C2×D11)⋊C4—81no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—42no—
201C4⋊Dic11—42no—
202C4⋊Dic11—81no—
203C4⋊Dic11C2×D412yes—
204C4⋊Dic11#4112yes—
205Dic11⋊C4—24no—
206Dic11⋊C4—42no—
207Dic11⋊C4—42no—
208Dic11⋊C4—42no—
209Dic11⋊C4—42no—
210Dic11⋊C4—81no—
211Dic11⋊C4—81no—
212C4×Dic11—24no—
213C4×Dic11—42no—
214C4×Dic11—42no—
215#4314—28no—
216C2×#475—111no—
217C2×C4×SD16—111no—
218#2452—111no—
219Q8×C4⋊C4—111no—
220#2094—111no—
221#2084—111no—
222#2065—111no—
223#2058—111no—
224#1941—111no—
225#1916D1111yescharacteristic, complemented
226#1880—111no—
227#1880—111no—
228#1865—111no—
229#1865—111no—
230#1864—111no—
231C23×C11C22×D411yescharacteristic
232C22×D11—22no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—41no—
238C22×D11—41no—
239C2×C4×C11—21no—
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×C11C2×SD1612yes—
255C2×C4×C11C2×SD1612yes—
256C2×C4×C11C2×SD1612yes—
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C22×Q811yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11H(5,𝔽2)11yescharacteristic
262C2×C4×C112−1+411yescharacteristic
263C2×Dic11—22no—
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—
284D44—22no—
285D44—22no—
286D44—41no—
287D44—41no—
288C4×D11—84no—
289Dic22—22no—
290Dic22—22no—
291Dic22—22no—
292Dic22—84no—
293Dic22C22⋊Q814yescomplemented
294C8×C11—22no—
295C8×C11—22no—
296C8×C11—41no—
297C8×C11—41no—
298C22×SD16—111no—
299C2×C4⋊Q8—111no—
300C2×C22⋊Q8—221no—
301C2×C4×Q8—111no—
302C2×C4×Q8—111no—
303C2×C4×Q8—111no—
304C2×C4×D4—111no—
305#475—224no—
306C4×SD16—224no—
307C2×#106—111no—
308C2×#106—111no—
309C2×#106—111no—
310C2×#106—111no—
311C2×#106—111no—
312C2×C4⋊C8C2×D1111yescharacteristic
313C2×#103—111no—
314C2×#103—111no—
315C2×#103—111no—
316C2×#102—111no—
317C2×#102—111no—
318C2×#102—111no—
319C2×C4×C8C2×D1111yescharacteristic
320#396—221no—
321#393—221no—
322#390—111no—
323#390—111no—
324#389—111no—
325#389—111no—
326#389—111no—
327#389—111no—
328#389—221no—
329#389—221no—
330#385—221no—
331#384—111no—
332#384—221no—
333C4×C4⋊C4—221no—
334C4×C4⋊C4C2×D1111yescharacteristic
335#340—111no—
336#340—111no—
337#340—111no—
338#340—111no—
339#336C2×D1111yescharacteristic
340#336C2×D1111yescharacteristic
341#336C2×D1111yescharacteristic
342#336C2×D1111yescharacteristic
343C22×C11#52511yescharacteristic
344C22×C11D4211yescharacteristic
345C22×C11D4×Q811yescharacteristic
346C22×C11C22×SD1611yescharacteristic
347C22×C11#57511yescharacteristic
348C22×C11#57711yescharacteristic
349C22×C11#57711yescharacteristic
350C2×D11—42no—
351C2×D11—42no—
352C2×D11—42no—
353C2×D11—81no—
354C2×D11—81no—
355C2×D11—81no—
356C2×D11—81no—
357C4×C11—22no—
358C4×C11—22no—
359C4×C11—22no—
360C4×C11—41no—
361C4×C11—41no—
362C4×C11—41no—
363C4×C11C2×C22⋊Q811yescharacteristic
364C4×C11#53911yescharacteristic
365C4×C11#54711yescharacteristic
366C4×C11#55411yescharacteristic
367Dic11—24no—
368Dic11—42no—
369Dic11—42no—
370Dic11—81no—
371Dic11—81no—
372Dic11—81no—
373Dic11—81no—
374C22×Q8—111no—
375C22×Q8—221no—
376C22×D4—111no—
377C23×C4—221no—
378C2×SD16—114no—
379C2×SD16—222no—
380C2×SD16—222no—
381C22×C8C22×D1111yescharacteristic
382C22×C8C22×D1111yescharacteristic
383C22×C8C22×D1111yescharacteristic
384C22×C8C22×D1111yescharacteristic
385C4⋊Q8—222no—
386C4⋊Q8—441no—
387C22⋊Q8—444no—
388C4×Q8—222no—
389C4×Q8—222no—
390C4×Q8—222no—
391C4×Q8—222no—
392C4×Q8—441no—
393C4×Q8—441no—
394C4×D4—222no—
395C4×D4—441no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4D4411yescharacteristic
413C2×C4⋊C4D4411yescharacteristic
414C2×C22⋊C4—221no—
415C2×C22⋊C4—221no—
416C2×C22⋊C4—221no—
417C2×C22⋊C4—221no—
418C2×C22⋊C4—221no—
419C2×C42—221no—
420C2×C42—221no—
421C2×C42—221no—
422C2×C42C22×D1111yescharacteristic
423C2×C42C22×D1111yescharacteristic
424C2×C42C22×D1111yescharacteristic
425#106—222no—
426#106—222no—
427#106—222no—
428#106—222no—
429#106—441no—
430C4⋊C8—22no—
431#103—114no—
432#103—222no—
433#103—222no—
434#102—222no—
435#102—222no—
436#102—441no—
437C4×C8—22no—
438#95—221no—
439#95—221no—
440#95—221no—
441#95—221no—
442#95D4411yescharacteristic
443#95D4411yescharacteristic
444C2×C11#244911yescharacteristic
445C2×C11#310311yescharacteristic
446C2×C11#312511yescharacteristic
447C2×C11#327111yescharacteristic
448C2×C11D4×SD1611yescharacteristic
449C2×C11Q8×SD1611yescharacteristic
450C2×C11#338811yescharacteristic
451D11—82no—
452C24—221no—
453C2×Q8—112no—
454C2×Q8—112no—
455C2×Q8—112no—
456C2×Q8—221no—
457C2×Q8—221no—
458C2×Q8—221no—
459C2×Q8—442no—
460C2×Q8—442no—
461C2×Q8—881no—
462C2×D4—112no—
463C2×D4—221no—
464C2×D4—221no—
465C2×D4—221no—
466C2×D4—221no—
467C2×D4—221no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—442no—
476C22×C4—442no—
477C22×C4—881no—
478C22×C4C2×D4411yescharacteristic
479C22×C4C2×D4411yescharacteristic
480C22×C4C2×D4411yescharacteristic
481C22×C4C2×D4411yescharacteristic
482C22×C4C2×D4411yescharacteristic
483C22×C4C2×D4411yescharacteristic
484C22×C4C23×D1111yescharacteristic
485SD16—228no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8D4×D1112yes—
497C2×C8Q8×D1112yes—
498C4⋊C4—41no—
499C4⋊C4—112no—
500C4⋊C4—112no—
501C4⋊C4—224no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4—442no—
513C4⋊C4—442no—
514C4⋊C4—442no—
515C4⋊C4—442no—
516C4⋊C4—442no—
517C4⋊C4—442no—
518C4⋊C4—881no—
519C4⋊C4—881no—
520C4⋊C4—881no—
521C4⋊C4#431414yescomplemented
522C22⋊C4—442no—
523C22⋊C4—442no—
524C22⋊C4—442no—
525C22⋊C4—442no—
526C22⋊C4—881no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—224no—
534C42—442no—
535C42—442no—
536C11#2637311yescharacteristic, complemented, Sylow
537C23—222no—
538C23—441no—
539C23—441no—
540C23—441no—
541C23—441no—
542C23—441no—
543C23—441no—
544C23C22×D4411yescharacteristic
545Q8—114no—
546Q8—222no—
547Q8—222no—
548Q8—222no—
549Q8—884no—
550D4—222no—
551D4—222no—
552D4—441no—
553D4—441no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—222no—
570C2×C4—222no—
571C2×C4—222no—
572C2×C4—222no—
573C2×C4—222no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
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—884no—
591C2×C4C2×#431412yes—
592C2×C4C2×#431412yes—
593C2×C4C2×#431412yes—
594C2×C4C2×D4×D1111yescharacteristic
595C2×C4C2×Q8×D1111yescharacteristic
596C2×C4#41×D1111yescharacteristic
597C2×C4#41×D1111yescharacteristic
598C2×C4#6704211yescharacteristic
599C2×C4#6704311yescharacteristic
600C8—22no—
601C8—22no—
602C8—41no—
603C8—41no—
604C22—442no—
605C22—442no—
606C22—442no—
607C22—881no—
608C22—881no—
609C22—881no—
610C22—881no—
611C22#1062305511yescharacteristic
612C22D4×D4411yescharacteristic
613C22Q8×D4411yescharacteristic
614C22C22×#431411yescharacteristic
615C22#1062327911yescharacteristic
616C22#1062328211yescharacteristic
617C22#1062328211yescharacteristic
618C4—22no—
619C4—22no—
620C4—22no—
621C4—41no—
622C4—41no—
623C4—41no—
624C4—224no—
625C4—442no—
626C4—442no—
627C4—881no—
628C4—881no—
629C4—881no—
630C4—881no—
631C4D11×C22⋊Q811yescharacteristic
632C4#1062318611yescharacteristic
633C4#1062322111yescharacteristic
634C4#1062323811yescharacteristic
635C2—882no—
636C2#1307243011yescharacteristic
637C2#1307864811yescharacteristic
638C2#1307889511yescharacteristic
639C2#1308020611yescharacteristic
640C2D4×#431411yescharacteristic
641C2Q8×#431411yescharacteristic
642C2#1308156311yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1916C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1916D11
hypocenterC11#26373
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
1. C2×#10622464C2semidirect
4. C4⋊C4×Dic22C2semidirect
6. #13070094C2semidirect
8. #13069950C2semidirect
9. #13069344C2semidirect
12. #13068887C2semidirect
13. #13068887C2semidirect
15. C11×#1916C2semidirect
100. C2×#4314Q8semidirect
178. C11×C4⋊C4SD16semidirect
225. #1916D11semidirect
293. Dic22C22⋊Q8semidirect
521. C4⋊C4#4314semidirect
536. C11#26373semidirect

Maximal subgroups

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

subgroupindex
C2×#106224642
C2×C4×#43142
#130724662
C4⋊C4×Dic222
#130701482
#130700942
#130699892
#130699502
#130693442
#130689702
#130688872
#130688802
C11×#19162
#2637311