Finite Group Databasebeta

← #14816859

Subgroups — #14816859

Order 2816.

856 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622634C211yesmaximal, characteristic, complemented
2C2×C4×#4325C211yesmaximal, characteristic
3#13072466C211yesmaximal, characteristic
4#13070140C211yesmaximal, characteristic
5#13070098C211yesmaximal, characteristic, complemented
6#13070001C211yesmaximal, characteristic
7#13069949C211yesmaximal, characteristic, complemented
8#13069346C211yesmaximal, characteristic, complemented
9#13069175C211yesmaximal, characteristic, complemented
10#13068971C211yesmaximal, characteristic
11#13068971C211yesmaximal, characteristic
12#13068884C211yesmaximal, characteristic, complemented
13#13068870C211yesmaximal, characteristic, complemented
14#13068862C211yesmaximal, characteristic
15C11×#2351C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C22×#4325C2211yescharacteristic
20C2×#66949—21no—
21C2×C4×D44C2211yescharacteristic
22C2×#66922C2211yescharacteristic
23C11×#389—21no—
24C11×#389—21no—
25C11×#389C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C11×#382—21no—
28C11×#382C2211yescharacteristic
29C4×C11×C4⋊C4—21no—
30C4×C11×C4⋊C4C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C4×#4325—24no—
35#10622634—24no—
36#10622607—21no—
37C2×#66873C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622552C2211yescharacteristic
46#10622552C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622286—21no—
52#10622281—21no—
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×Dic22—21no—
65C4×Q8×C11—22no—
66C4×Q8×C11—22no—
67C4×Q8×C11—22no—
68C4×Q8×C11—22no—
69C4×Q8×C11—41no—
70C4×Q8×C11—41no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C42×C11—21no—
82C2×C42×C11—21no—
83C2×C42×C11—21no—
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×#4325—22no—
88C2×#4325—22no—
89C2×#4325Q814yescomplemented
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105#66949—44no—
106C4×D44—22no—
107C4×D44—41no—
108#66922—22no—
109#66922—41no—
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95D411yescharacteristic
115C11×#95D411yescharacteristic
116#66899—22no—
117#66899—22no—
118#66899D414yes—
119C11⋊#95—21no—
120C11⋊#95—21no—
121#66873—22no—
122#66873—22no—
123#66873—41no—
124#66872—22no—
125#66872—41no—
126#66871—22no—
127#66871—22no—
128#66871—22no—
129C4⋊(C11⋊C8)—22no—
130C4×C11⋊C8—22no—
131#26377—111nomaximal, Sylow
132C23×D11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11C2×D412yes—
137C2×Q8×C11C2×Q812yes—
138C2×Q8×C11#4112yes—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44C2×Q812yes—
159C2×C4×D11—42no—
160C2×C4×D11—42no—
161C2×C4×D11—81no—
162C2×Dic22—42no—
163C2×Dic22—42no—
164C2×Dic22—81no—
165C11×C4⋊C4—24no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—42no—
174C11×C4⋊C4—42no—
175C11×C4⋊C4—42no—
176C11×C4⋊C4—42no—
177C11×C4⋊C4#4112yes—
178C42×C11—24no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—42no—
186C42×C11—42no—
187#4325—28no—
188(C2×D11)⋊C4—42no—
189(C2×D11)⋊C4—42no—
190(C2×D11)⋊C4—42no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—81no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—42no—
199C4⋊Dic11C2×D412yes—
200Dic11⋊C4—42no—
201Dic11⋊C4—42no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
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⋊C8C2×D412yes—
213C2×C11⋊C8C2×Q812yes—
214C2×#477—111no—
215C2×C4×SD16—111no—
216#2452—111no—
217#2351D1111yescharacteristic, complemented
218#2092—111no—
219#2085—111no—
220#2067—111no—
221#2058—111no—
222#1942—111no—
223#1916—111no—
224#1880—111no—
225#1880—111no—
226#1865—111no—
227#1863—111no—
228#1862—111no—
229C23×C11C22×D411yescharacteristic
230C22×D11—22no—
231C22×D11—41no—
232C22×D11—41no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—41no—
236C22×D11—41no—
237Q8×C11—22no—
238Q8×C11—22no—
239Q8×C11—22no—
240Q8×C11C22⋊Q814yescomplemented
241C2×C4×C11—22no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—22no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
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#13512yes—
270C2×C4×C11AGL(1,ℤ/8)12yes—
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C22×Q811yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11H(5,𝔽2)11yescharacteristic
276C2×C4×C112−1+411yescharacteristic
277C2×Dic11—22no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286D44—22no—
287D44—22no—
288D44—41no—
289D44—41no—
290C4×D11—84no—
291Dic22—84no—
292C11⋊C8—22no—
293C11⋊C8—22no—
294C11⋊C8—41no—
295C11⋊C8—41no—
296C22×SD16—111no—
297C2×C4⋊Q8—111no—
298C2×C22⋊Q8—221no—
299C2×C4×Q8C2×D1111yescharacteristic
300C2×C4×Q8C2×D1111yescharacteristic
301C2×C4×Q8C2×D1111yescharacteristic
302C2×C4×D4—111no—
303#477—224no—
304C4×SD16—224no—
305C2×#107—111no—
306C2×#107—111no—
307C2×#107—111no—
308C2×#106—111no—
309C2×#106—111no—
310C2×C4⋊C8—111no—
311C2×#103—111no—
312C2×#103—111no—
313C2×#103—111no—
314C2×#102—111no—
315C2×#102—111no—
316C2×#102—111no—
317C2×C4×C8—111no—
318#396—221no—
319#393—221no—
320#390—111no—
321#390—111no—
322#389—21no—
323#389—21no—
324#389—111no—
325#389—111no—
326#389C2×D1111yescharacteristic
327#389C2×D1111yescharacteristic
328#385—221no—
329#382—21no—
330#382C2×D1111yescharacteristic
331C4×C4⋊C4—21no—
332C4×C4⋊C4C2×D1111yescharacteristic
333#340—111no—
334#340—111no—
335#340—111no—
336#340—111no—
337#336—111no—
338#336—111no—
339#336—111no—
340#336—111no—
341C22×C11#52511yescharacteristic
342C22×C11D4211yescharacteristic
343C22×C11D4×Q811yescharacteristic
344C22×C11C2×#13511yescharacteristic
345C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
346C22×C11#57711yescharacteristic
347C22×C11#57811yescharacteristic
348C2×D11—42no—
349C2×D11—42no—
350C2×D11—42no—
351C2×D11—81no—
352C2×D11—81no—
353C2×D11—81no—
354C2×D11—81no—
355C4×C11—24no—
356C4×C11—22no—
357C4×C11—22no—
358C4×C11—41no—
359C4×C11—42no—
360C4×C11—41no—
361C4×C11—41no—
362C4×C11—41no—
363C4×C11—81no—
364C4×C11—81no—
365C4×C11C2×C22⋊Q811yescharacteristic
366C4×C11#53911yescharacteristic
367C4×C11#54711yescharacteristic
368C4×C11#55411yescharacteristic
369Dic11—42no—
370Dic11—81no—
371Dic11—81no—
372C22×Q8—221no—
373C22×Q8C22×D1111yescharacteristic
374C22×D4—111no—
375C23×C4—221no—
376C2×SD16—114no—
377C2×SD16—222no—
378C2×SD16—222no—
379C22×C8—111no—
380C22×C8—111no—
381C22×C8—111no—
382C22×C8—111no—
383C4⋊Q8—222no—
384C4⋊Q8—441no—
385C22⋊Q8—444no—
386C4×Q8—22no—
387C4×Q8—22no—
388C4×Q8—22no—
389C4×Q8—22no—
390C4×Q8—41no—
391C4×Q8—41no—
392C4×D4—222no—
393C4×D4—441no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
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⋊C4C22⋊D1111yescharacteristic
406C2×C4⋊C4C22⋊D1111yescharacteristic
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C4⋊C4C22×D1111yescharacteristic
409C2×C4⋊C4C22×D1111yescharacteristic
410C2×C22⋊C4—221no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—221no—
415C2×C42—21no—
416C2×C42—21no—
417C2×C42—21no—
418C2×C42C22×D1111yescharacteristic
419C2×C42C22×D1111yescharacteristic
420C2×C42C22×D1111yescharacteristic
421#107—222no—
422#107—222no—
423#107—222no—
424#106—222no—
425#106—441no—
426C4⋊C8—222no—
427#103—114no—
428#103—222no—
429#103—222no—
430#102—222no—
431#102—222no—
432#102—441no—
433C4×C8—222no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—221no—
439#95—221no—
440#95C22⋊D1111yescharacteristic
441#95C22⋊D1111yescharacteristic
442C2×C11#244911yescharacteristic
443C2×C11#310611yescharacteristic
444C2×C11#312111yescharacteristic
445C2×C11#326511yescharacteristic
446C2×C11#328511yescharacteristic
447C2×C11#338111yescharacteristic
448C2×C11#338611yescharacteristic
449D11—82no—
450C24—221no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—442no—
455C2×Q8—442no—
456C2×Q8—881no—
457C2×Q8#433912yes—
458C2×Q8D4×D1112yes—
459C2×Q8Q8×D1112yes—
460C2×D4—112no—
461C2×D4—221no—
462C2×D4—221no—
463C2×D4—221no—
464C2×D4—221no—
465C2×D4—221no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—442no—
474C22×C4—442no—
475C22×C4—881no—
476C22×C4C2×C22⋊D1111yescharacteristic
477C22×C4C2×C22⋊D1111yescharacteristic
478C22×C4C2×C22⋊D1111yescharacteristic
479C22×C4C2×C22⋊D1111yescharacteristic
480C22×C4C2×C22⋊D1111yescharacteristic
481C22×C4C2×C22⋊D1111yescharacteristic
482C22×C4C23×D1111yescharacteristic
483SD16—228no—
484C2×C8—112no—
485C2×C8—112no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8—221no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—221no—
495C2×C8—221no—
496C4⋊C4—24no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—42no—
505C4⋊C4—42no—
506C4⋊C4—42no—
507C4⋊C4—42no—
508C4⋊C4—112no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—442no—
515C4⋊C4—442no—
516C4⋊C4—442no—
517C4⋊C4#433912yes—
518C22⋊C4—442no—
519C22⋊C4—442no—
520C22⋊C4—442no—
521C22⋊C4—442no—
522C22⋊C4—881no—
523C42—24no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—42no—
531C42—42no—
532C11#2637711yescharacteristic, complemented, Sylow
533C23—222no—
534C23—441no—
535C23—441no—
536C23—441no—
537C23—441no—
538C23—441no—
539C23—441no—
540C23C22×C22⋊D1111yescharacteristic
541Q8—22no—
542Q8—22no—
543Q8—22no—
544Q8—884no—
545Q8#6694914yescomplemented
546D4—222no—
547D4—222no—
548D4—441no—
549D4—441no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—22no—
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—21no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—222no—
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—884no—
588C2×C4#6700212yes—
589C2×C4#6700312yes—
590C2×C4C2×#433911yescharacteristic
591C2×C4C2×#433911yescharacteristic
592C2×C4C2×D4×D1111yescharacteristic
593C2×C4#6703711yescharacteristic
594C2×C4C2×Q8×D1111yescharacteristic
595C2×C4#6704011yescharacteristic
596C8—222no—
597C8—222no—
598C8—441no—
599C8—441no—
600C22—442no—
601C22—442no—
602C22—442no—
603C22—881no—
604C22—881no—
605C22—881no—
606C22—881no—
607C22#1062332211yescharacteristic
608C22D4×C22⋊D1111yescharacteristic
609C22Q8×C22⋊D1111yescharacteristic
610C22C2×#6700211yescharacteristic
611C22C2×#6700311yescharacteristic
612C22#1062336811yescharacteristic
613C22#1062336911yescharacteristic
614C4—22no—
615C4—24no—
616C4—22no—
617C4—41no—
618C4—41no—
619C4—41no—
620C4—41no—
621C4—42no—
622C4—81no—
623C4—81no—
624C4—442no—
625C4—881no—
626C4—881no—
627C4#1062303811yescharacteristic
628C4C2×#6694911yescharacteristic
629C4#1062304211yescharacteristic
630C4#1062304611yescharacteristic
631C2—882no—
632C2#1307242511yescharacteristic
633C2#1307867611yescharacteristic
634C2#1307884511yescharacteristic
635C2#1308011211yescharacteristic
636C2#1308035311yescharacteristic
637C2#1308148711yescharacteristic
638C2#1308153311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2351C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2351D11
hypocenterC11#26377
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2351

Complements

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

NH ≅ G/Ntype
1. C2×#10622634C2semidirect
5. #13070098C2semidirect
7. #13069949C2semidirect
8. #13069346C2semidirect
9. #13069175C2semidirect
12. #13068884C2semidirect
13. #13068870C2semidirect
15. C11×#2351C2semidirect
89. C2×#4325Q8semidirect
217. #2351D11semidirect
240. Q8×C11C22⋊Q8semidirect
532. C11#26377semidirect
545. Q8#66949semidirect

Maximal subgroups

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

subgroupindex
C2×#106226342
C2×C4×#43252
#130724662
#130701402
#130700982
#130700012
#130699492
#130693462
#130691752
#130689712
#130688842
#130688702
#130688622
C11×#23512
#2637711