Finite Group Databasebeta

← #14812876

Subgroups — #14812876

Order 2816.

708 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073850C211yesmaximal, characteristic, complemented
2#13070144C211yesmaximal, characteristic
3#13070137C211yesmaximal, characteristic
4#13070004C211yesmaximal, characteristic
5#13069990C211yesmaximal, characteristic
6#13069384C211yesmaximal, characteristic, complemented
7#13069374C211yesmaximal, characteristic, complemented
8#13069372C211yesmaximal, characteristic, complemented
9#13069340C211yesmaximal, characteristic, complemented
10#13069208C211yesmaximal, characteristic, complemented
11#13069201C211yesmaximal, characteristic, complemented
12#13068782C211yesmaximal, characteristic, complemented
13#13068626C211yesmaximal, characteristic
14#13068441C211yesmaximal, characteristic
15C11×#2354C211yesmaximal, characteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×C11×#117—21no—
18C11×#390C2211yescharacteristic
19C11×#390C2211yescharacteristic
20C11×#388—21no—
21C11×#388—21no—
22C11×#384C2211yescharacteristic
23C11×#380—21no—
24C4×C11×C4⋊C4C2211yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26C4×C11×C4⋊C4C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31#10622599—21no—
32#10622597—21no—
33C2×#66872C2211yescharacteristic
34C2×#66872C2211yescharacteristic
35C2×#66871C2211yescharacteristic
36C2×#66871C2211yescharacteristic
37C2×#66871C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39#10622549C2211yescharacteristic
40#10622549C2211yescharacteristic
41#10622548C2211yescharacteristic
42C4×C4⋊Dic11C2211yescharacteristic
43#10622541C2211yescharacteristic
44#10622541C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×C4⋊(C11⋊C8)C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C2×#66867C2211yescharacteristic
49#10622268—21no—
50#10622267—21no—
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C4×D4×C11—22no—
62C4×D4×C11Q814yes—
63C11×#117—44no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4D411yescharacteristic
67C2×C11×C4⋊C4D411yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C42×C11—21no—
77C2×C42×C11—21no—
78C2×C42×C11C2311yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×C4×Dic11—21no—
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C11×#95—21no—
95C11×#95—21no—
96C11×#95D411yescharacteristic
97C11×#95D411yescharacteristic
98#66896—22no—
99#66896—22no—
100#66896—41no—
101#66896—41no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109#66872—22no—
110#66872—41no—
111#66871—22no—
112#66871—41no—
113#66871—41no—
114#66871—41no—
115C4⋊(C11⋊C8)—22no—
116C4⋊(C11⋊C8)—22no—
117C4⋊(C11⋊C8)—22no—
118#66867—22no—
119#26098—111nomaximal, Sylow
120C24×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11C2×Q812yes—
127C22×C4×C11—21no—
128C22×C4×C11—24no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—42no—
132C22×C4×C11—42no—
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—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—41no—
151C11×C4⋊C4—42no—
152C11×C4⋊C4—81no—
153C11×C4⋊C4C2×Q812yes—
154C11×C22⋊C4—24no—
155C11×C22⋊C4—42no—
156C11×C22⋊C4—42no—
157C11×C22⋊C4—81no—
158C11×C22⋊C4—81no—
159C42×C11—21no—
160C42×C11—21no—
161C42×C11—21no—
162C42×C11—21no—
163C42×C11—42no—
164C42×C11—42no—
165C42×C11C2×Q812yes—
166C42×C11#4112yes—
167C4⋊Dic11—21no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—42no—
176C4⋊Dic11—81no—
177Dic11⋊C4—42no—
178Dic11⋊C4—81no—
179C4×Dic11—81no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—21no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8#4112yes—
191C2×C11⋊C8#4112yes—
192#2570—111no—
193#2354D1111yescharacteristic
194#2093—111no—
195#2092—111no—
196#2067—111no—
197#2065—111no—
198#1949—111no—
199#1947—111no—
200#1947—111no—
201#1940—111no—
202#1921—111no—
203#1920—111no—
204#1847—111no—
205#1804—111no—
206#1762—111no—
207C23×C11—22no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11—41no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11C22×D411yescharacteristic
215D4×C11—22no—
216D4×C11—22no—
217D4×C11—41no—
218D4×C11—41no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—22no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—48no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11C22⋊Q812yes—
245C2×C4×C11C22⋊Q812yes—
246C2×C4×C11AGL(1,ℤ/8)12yes—
247C2×C4×C11C22×Q811yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11H(5,𝔽2)11yescharacteristic
252C2×C4×C112−1+411yescharacteristic
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C11⋊C8—22no—
266C11⋊C8—22no—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C2×C4×D4C2×D1111yescharacteristic
270C2×#117—21no—
271C2×#107—111no—
272C2×#107—111no—
273C2×#107—111no—
274C2×#107—111no—
275C2×#106—111no—
276C2×#106—111no—
277C2×C4⋊C8—111no—
278C2×C4⋊C8—111no—
279C2×C4⋊C8—111no—
280C2×#102—111no—
281C2×#102—111no—
282C2×#102—111no—
283C2×#102—111no—
284C2×#97—111no—
285#400—221no—
286#398—221no—
287#390C2×D1111yescharacteristic
288#390C2×D1111yescharacteristic
289#389—111no—
290#389—111no—
291#388—21no—
292#388—21no—
293#387—221no—
294#387—221no—
295#384—111no—
296#384C2×D1111yescharacteristic
297#382—111no—
298#382—111no—
299#380—21no—
300C4×C4⋊C4—111no—
301C4×C4⋊C4C2×D1111yescharacteristic
302C4×C4⋊C4C2×D1111yescharacteristic
303C4×C4⋊C4C2×D1111yescharacteristic
304#340—111no—
305#340—111no—
306#340—111no—
307#340—111no—
308#340—111no—
309#340—111no—
310#336—111no—
311#336—111no—
312C22×C11—42no—
313C22×C11—42no—
314C22×C11—42no—
315C22×C11—81no—
316C22×C11—81no—
317C22×C11—81no—
318C22×C11—81no—
319C22×C11C2×C22⋊Q811yescharacteristic
320C22×C11#54711yescharacteristic
321C22×C11#55011yescharacteristic
322C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
323C22×C11#57511yescharacteristic
324C22×C11#57611yescharacteristic
325C22×C11#57811yescharacteristic
326C4×C11—22no—
327C4×C11—22no—
328C4×C11—22no—
329C4×C11—42no—
330C4×C11—41no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11—81no—
334C4×C11—81no—
335C4×C11#53311yescharacteristic
336C4×C11#54411yescharacteristic
337C4×C11#55211yescharacteristic
338C4×C11#55311yescharacteristic
339Dic11—81no—
340Dic11—81no—
341Dic11—81no—
342Dic11—81no—
343C22×D4C22×D1111yescharacteristic
344C23×C4—21no—
345C22×C8—111no—
346C22×C8—111no—
347C22×C8—111no—
348C22×C8—111no—
349C4×D4—22no—
350C4×D4Dic2214yes—
351#117—44no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—111no—
355C2×C4⋊C4—111no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4—111no—
358C2×C4⋊C4—221no—
359C2×C4⋊C4—221no—
360C2×C4⋊C4—221no—
361C2×C4⋊C4—221no—
362C2×C4⋊C4C22⋊D1111yescharacteristic
363C2×C4⋊C4C22⋊D1111yescharacteristic
364C2×C4⋊C4C22×D1111yescharacteristic
365C2×C4⋊C4C22×D1111yescharacteristic
366C2×C4⋊C4C22×D1111yescharacteristic
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C42—21no—
373C2×C42—21no—
374C2×C42—221no—
375C2×C42C22×D1111yescharacteristic
376C2×C42C22×D1111yescharacteristic
377C2×C42C22×D1111yescharacteristic
378#107—222no—
379#107—441no—
380#107—441no—
381#107—441no—
382#106—222no—
383#106—441no—
384C4⋊C8—222no—
385C4⋊C8—222no—
386C4⋊C8—222no—
387#102—222no—
388#102—222no—
389#102—441no—
390#102—441no—
391#97—222no—
392#95—21no—
393#95—21no—
394#95—221no—
395#95—221no—
396#95—221no—
397#95—221no—
398#95—221no—
399#95—221no—
400#95—221no—
401#95C22⋊D1111yescharacteristic
402#95C22⋊D1111yescharacteristic
403C2×C11—82no—
404C2×C11#244111yescharacteristic
405C2×C11#307711yescharacteristic
406C2×C11#308311yescharacteristic
407C2×C11#334311yescharacteristic
408C2×C11#334711yescharacteristic
409C2×C11#339911yescharacteristic
410C2×C11#340211yescharacteristic
411C24—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4C2×Dic2212yes—
418C22×C4—21no—
419C22×C4—24no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—221no—
425C22×C4—221no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4C2×C22⋊D1111yescharacteristic
429C22×C4C2×C22⋊D1111yescharacteristic
430C22×C4C2×C22⋊D1111yescharacteristic
431C22×C4C2×C22⋊D1111yescharacteristic
432C22×C4C2×C22⋊D1111yescharacteristic
433C22×C4C2×C22⋊D1111yescharacteristic
434C22×C4C23×D1111yescharacteristic
435C2×C8—112no—
436C2×C8—112no—
437C2×C8—221no—
438C2×C8—221no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8—221no—
443C2×C8—221no—
444C2×C8—221no—
445C2×C8—221no—
446C2×C8—221no—
447C4⋊C4—22no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—41no—
454C4⋊C4—42no—
455C4⋊C4—81no—
456C4⋊C4—221no—
457C4⋊C4—221no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—442no—
465C4⋊C4—442no—
466C4⋊C4—881no—
467C4⋊C4—881no—
468C4⋊C4C2×Dic2212yes—
469C22⋊C4—24no—
470C22⋊C4—42no—
471C22⋊C4—42no—
472C22⋊C4—81no—
473C22⋊C4—81no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—42no—
479C42—42no—
480C42—881no—
481C42C2×Dic2212yes—
482C42#433912yes—
483C11#2609811yescharacteristic, complemented, Sylow
484C23—22no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23C22×C22⋊D1111yescharacteristic
492D4—22no—
493D4—22no—
494D4—41no—
495D4—41no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—48no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—441no—
522C2×C4—441no—
523C2×C4—441no—
524C2×C4—441no—
525C2×C4—441no—
526C2×C4—441no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4#6697712yes—
534C2×C4#6697712yes—
535C2×C4#6698512yes—
536C2×C4C22×Dic2211yescharacteristic
537C2×C4C2×#433911yescharacteristic
538C2×C4#41×D1111yescharacteristic
539C2×C4#41×D1111yescharacteristic
540C2×C4#6704211yescharacteristic
541C2×C4#6704311yescharacteristic
542C8—222no—
543C8—222no—
544C8—441no—
545C8—441no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22C2×#6697711yescharacteristic
554C22C2×#6698511yescharacteristic
555C22#1062335311yescharacteristic
556C22#1062335511yescharacteristic
557C22#1062336511yescharacteristic
558C22#1062336611yescharacteristic
559C22#1062336911yescharacteristic
560C4—22no—
561C4—22no—
562C4—22no—
563C4—41no—
564C4—41no—
565C4—42no—
566C4—41no—
567C4—81no—
568C4—81no—
569C4—881no—
570C4—881no—
571C4—881no—
572C4—881no—
573C4#1062304811yescharacteristic
574C4#1062305011yescharacteristic
575C4#1062306011yescharacteristic
576C4#1062306111yescharacteristic
577C2—82no—
578C2#1307232311yescharacteristic
579C2#1307841311yescharacteristic
580C2#1307846711yescharacteristic
581C2#1308105011yescharacteristic
582C2#1308111611yescharacteristic
583C2#1308165811yescharacteristic
584C2#1308169111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2354C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2354D11
hypocenterC11#26098
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2354

Complements

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

NH ≅ G/Ntype
1. #13073850C2semidirect
6. #13069384C2semidirect
7. #13069374C2semidirect
8. #13069372C2semidirect
9. #13069340C2semidirect
10. #13069208C2semidirect
11. #13069201C2semidirect
12. #13068782C2semidirect
483. C11#26098semidirect

Maximal subgroups

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

subgroupindex
#130738502
#130701442
#130701372
#130700042
#130699902
#130693842
#130693742
#130693722
#130693402
#130692082
#130692012
#130687822
#130686262
#130684412
C11×#23542
#2609811