Finite Group Databasebeta

← #14817156

Subgroups — #14817156

Order 2816.

858 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×#10622704C211yesmaximal, characteristic, complemented
2C2×#10622631C211yesmaximal, characteristic
3C4⋊C4×Dic22C211yesmaximal, characteristic, complemented
4#13070144C211yesmaximal, characteristic
5#13070087C211yesmaximal, characteristic, complemented
6#13069990C211yesmaximal, characteristic
7#13069941C211yesmaximal, characteristic, complemented
8#13069356C211yesmaximal, characteristic, complemented
9#13069182C211yesmaximal, characteristic, complemented
10#13068974C211yesmaximal, characteristic
11#13068974C211yesmaximal, characteristic
12#13068883C211yesmaximal, characteristic, complemented
13#13068869C211yesmaximal, characteristic, complemented
14#13068863C211yesmaximal, characteristic
15C11×#2452C211yesmaximal, characteristic
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×C22⋊Q8—21no—
18C2×C4×D4×C11C2211yescharacteristic
19C22×#4324C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C11×#396—21no—
24C11×#393—21no—
25C11×#390C2211yescharacteristic
26C11×#390C2211yescharacteristic
27C11×#389C2211yescharacteristic
28C11×#389C2211yescharacteristic
29C11×#385—21no—
30C4×C11×C4⋊C4C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34#10622704—24no—
35#10622631—24no—
36#10622589—21no—
37C4⋊C4×Dic11—21no—
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622548C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×#66867C2211yescharacteristic
51#10622260—21no—
52#10622260—21no—
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11—21no—
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C22×Dic22C2311yescharacteristic
65C11×C4⋊Q8—22no—
66C11×C4⋊Q8—41no—
67C11×C22⋊Q8—44no—
68C4×D4×C11—22no—
69C4×D4×C11—41no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×#4324—22no—
87C2×#4324—22no—
88C2×#4324Q814yescomplemented
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C4×Dic22—22no—
107C4×Dic22—22no—
108C4×Dic22—22no—
109C4×Dic22—22no—
110C4×Dic22—41no—
111C4×Dic22—41no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95D411yescharacteristic
115C11×#95D411yescharacteristic
116#66896—22no—
117#66896—22no—
118#66896—41no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121#66874—22no—
122#66874—22no—
123#66874D414yes—
124#66872—22no—
125#66871—22no—
126#66871—22no—
127#66871—22no—
128#66871—41no—
129C4⋊(C11⋊C8)—22no—
130#66867—22no—
131#26397—111nomaximal, Sylow
132C24×C11—21no—
133C2×Q8×C11—42no—
134C2×Q8×C11—42no—
135C2×Q8×C11—81no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11C2×Q812yes—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—42no—
146C22×C4×C11—42no—
147C22×C4×C11—81no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2411yescharacteristic
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22C2×D412yes—
163C2×Dic22C2×Q812yes—
164C2×Dic22#4112yes—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—42no—
173C11×C4⋊C4—42no—
174C11×C4⋊C4—42no—
175C11×C4⋊C4C2×D412yes—
176C11×C22⋊C4—42no—
177C11×C22⋊C4—42no—
178C11×C22⋊C4—42no—
179C11×C22⋊C4—42no—
180C11×C22⋊C4—81no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—21no—
187#4324—28no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—42no—
194C4⋊Dic11—81no—
195C4⋊Dic11#4112yes—
196Dic11⋊C4—24no—
197Dic11⋊C4—42no—
198Dic11⋊C4—42no—
199Dic11⋊C4—81no—
200Dic11⋊C4—81no—
201C4×Dic11—24no—
202C4×Dic11—42no—
203C4×Dic11—42no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8C2×D412yes—
215C2×C11⋊C8C2×Q812yes—
216C2×#477—111no—
217C2×#440—111no—
218#2452D1111yescharacteristic
219Q8×C4⋊C4—111no—
220#2093—111no—
221#2083—111no—
222#2065—111no—
223#2057—111no—
224#1944—111no—
225#1917—111no—
226#1880—111no—
227#1880—111no—
228#1865—111no—
229#1863—111no—
230#1862—111no—
231C23×C11—22no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11C22×D411yescharacteristic
239Q8×C11—84no—
240D4×C11—22no—
241D4×C11—22no—
242D4×C11—41no—
243D4×C11—41no—
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—22no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—84no—
270C2×C4×C11AGL(1,ℤ/8)12yes—
271C2×C4×C11#13712yes—
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11C22×Q811yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11H(5,𝔽2)11yescharacteristic
277C2×C4×C112−1+411yescharacteristic
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—22no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290Dic22—22no—
291Dic22—22no—
292Dic22—22no—
293Dic22C22⋊Q814yescomplemented
294C11⋊C8—22no—
295C11⋊C8—22no—
296C11⋊C8—41no—
297C11⋊C8—41no—
298C22×SD16—111no—
299C2×C4⋊Q8C2×D1111yescharacteristic
300C2×C22⋊Q8—21no—
301C2×C4×Q8—111no—
302C2×C4×Q8—111no—
303C2×C4×Q8—111no—
304C2×C4×D4C2×D1111yescharacteristic
305#477—224no—
306#440—224no—
307C2×#107—111no—
308C2×#107—111no—
309C2×#107—111no—
310C2×#107—111no—
311C2×#106—111no—
312C2×C4⋊C8—111no—
313C2×#103—111no—
314C2×#103—111no—
315C2×#103—111no—
316C2×#102—111no—
317C2×#102—111no—
318C2×#102—111no—
319C2×#97—111no—
320#396—21no—
321#393—21no—
322#390C2×D1111yescharacteristic
323#390C2×D1111yescharacteristic
324#389—111no—
325#389—111no—
326#389—221no—
327#389—221no—
328#389C2×D1111yescharacteristic
329#389C2×D1111yescharacteristic
330#385—21no—
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#336—111no—
340#336—111no—
341#336—111no—
342#336—111no—
343C22×C11—42no—
344C22×C11—42no—
345C22×C11—42no—
346C22×C11—81no—
347C22×C11—81no—
348C22×C11—81no—
349C22×C11—81no—
350C22×C11#52511yescharacteristic
351C22×C11D4211yescharacteristic
352C22×C11D4×Q811yescharacteristic
353C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
354C22×C11C2×#13711yescharacteristic
355C22×C11#57611yescharacteristic
356C22×C11#57811yescharacteristic
357C4×C11—22no—
358C4×C11—22no—
359C4×C11—41no—
360C4×C11—41no—
361C4×C11—41no—
362C4×C11—41no—
363C4×C11—42no—
364C4×C11—81no—
365C4×C11—81no—
366C4×C11C2×C22⋊Q811yescharacteristic
367C4×C11#53911yescharacteristic
368C4×C11#54711yescharacteristic
369C4×C11#55411yescharacteristic
370Dic11—24no—
371Dic11—42no—
372Dic11—81no—
373Dic11—81no—
374C22×Q8—21no—
375C22×Q8—111no—
376C22×D4C22×D1111yescharacteristic
377C23×C4—21no—
378C2×SD16—114no—
379C2×SD16—222no—
380C2×SD16—222no—
381C22×C8—111no—
382C22×C8—111no—
383C22×C8—111no—
384C22×C8—111no—
385C4⋊Q8—22no—
386C4⋊Q8—41no—
387C22⋊Q8—44no—
388C4×Q8—222no—
389C4×Q8—222no—
390C4×Q8—222no—
391C4×Q8—222no—
392C4×Q8—441no—
393C4×Q8—441no—
394C4×D4—22no—
395C4×D4—41no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
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⋊C4C22⋊D1111yescharacteristic
410C2×C4⋊C4C22⋊D1111yescharacteristic
411C2×C4⋊C4C22×D1111yescharacteristic
412C2×C4⋊C4C22×D1111yescharacteristic
413C2×C4⋊C4C22×D1111yescharacteristic
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C42—221no—
420C2×C42—221no—
421C2×C42—221no—
422C2×C42C22×D1111yescharacteristic
423C2×C42C22×D1111yescharacteristic
424C2×C42C22×D1111yescharacteristic
425#107—222no—
426#107—222no—
427#107—222no—
428#107—441no—
429#106—222no—
430C4⋊C8—222no—
431#103—114no—
432#103—222no—
433#103—222no—
434#102—222no—
435#102—222no—
436#102—441no—
437#97—222no—
438#95—21no—
439#95—21no—
440#95—221no—
441#95—221no—
442#95C22⋊D1111yescharacteristic
443#95C22⋊D1111yescharacteristic
444C2×C11—82no—
445C2×C11#244911yescharacteristic
446C2×C11#311211yescharacteristic
447C2×C11#312411yescharacteristic
448C2×C11#327011yescharacteristic
449C2×C11#327411yescharacteristic
450C2×C11#338511yescharacteristic
451C2×C11#338611yescharacteristic
452C24—21no—
453C2×Q8—42no—
454C2×Q8—42no—
455C2×Q8—81no—
456C2×Q8—112no—
457C2×Q8—112no—
458C2×Q8—112no—
459C2×Q8—221no—
460C2×Q8—221no—
461C2×Q8—221no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4Q8×D1112yes—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—81no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4C2×C22⋊D1111yescharacteristic
479C22×C4C2×C22⋊D1111yescharacteristic
480C22×C4C2×C22⋊D1111yescharacteristic
481C22×C4C2×C22⋊D1111yescharacteristic
482C22×C4C2×C22⋊D1111yescharacteristic
483C22×C4C2×C22⋊D1111yescharacteristic
484C22×C4C23×D1111yescharacteristic
485SD16—228no—
486C2×C8—112no—
487C2×C8—112no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8—221no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—221no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8—221no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—42no—
506C4⋊C4—42no—
507C4⋊C4—42no—
508C4⋊C4—112no—
509C4⋊C4—224no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—442no—
516C4⋊C4—442no—
517C4⋊C4—442no—
518C4⋊C4—881no—
519C4⋊C4—881no—
520C4⋊C4—881no—
521C4⋊C4D4×D1112yes—
522C22⋊C4—42no—
523C22⋊C4—42no—
524C22⋊C4—42no—
525C22⋊C4—42no—
526C22⋊C4—81no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—224no—
534C42—442no—
535C42—442no—
536C11#2639711yescharacteristic, complemented, Sylow
537C23—22no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23C22×C22⋊D1111yescharacteristic
545Q8—84no—
546Q8—114no—
547Q8—222no—
548Q8—222no—
549Q8—222no—
550D4—22no—
551D4—22no—
552D4—41no—
553D4—41no—
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—22no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—84no—
580C2×C4—222no—
581C2×C4—222no—
582C2×C4—222no—
583C2×C4—222no—
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#6698512yes—
593C2×C4#6700412yes—
594C2×C4C2×D4×D1111yescharacteristic
595C2×C4#6703711yescharacteristic
596C2×C4C2×Q8×D1111yescharacteristic
597C2×C4#6704011yescharacteristic
598C2×C4#41×D1111yescharacteristic
599C2×C4#41×D1111yescharacteristic
600C8—222no—
601C8—222no—
602C8—441no—
603C8—441no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22C2×#6698511yescharacteristic
612C22D4×C22⋊D1111yescharacteristic
613C22Q8×C22⋊D1111yescharacteristic
614C22C2×#6700411yescharacteristic
615C22#1062335911yescharacteristic
616C22#1062336611yescharacteristic
617C22#1062336911yescharacteristic
618C4—22no—
619C4—22no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—41no—
624C4—42no—
625C4—81no—
626C4—81no—
627C4—224no—
628C4—442no—
629C4—881no—
630C4—881no—
631C4D11×C22⋊Q811yescharacteristic
632C4#1062316211yescharacteristic
633C4#1062316711yescharacteristic
634C4#1062316911yescharacteristic
635C2—82no—
636C2#1307242211yescharacteristic
637C2#1307873411yescharacteristic
638C2#1307887211yescharacteristic
639C2#1308018211yescharacteristic
640C2#1308023211yescharacteristic
641C2#1308152611yescharacteristic
642C2#1308153711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2452C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2452D11
hypocenterC11#26397
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2452

Complements

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

NH ≅ G/Ntype
1. C2×#10622704C2semidirect
3. C4⋊C4×Dic22C2semidirect
5. #13070087C2semidirect
7. #13069941C2semidirect
8. #13069356C2semidirect
9. #13069182C2semidirect
12. #13068883C2semidirect
13. #13068869C2semidirect
88. C2×#4324Q8semidirect
293. Dic22C22⋊Q8semidirect
536. C11#26397semidirect

Maximal subgroups

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

subgroupindex
C2×#106227042
C2×#106226312
C4⋊C4×Dic222
#130701442
#130700872
#130699902
#130699412
#130693562
#130691822
#130689742
#130688832
#130688692
#130688632
C11×#24522
#2639711