Finite Group Databasebeta

← #14807132

Subgroups — #14807132

Order 2816.

1126 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622682C211yesmaximal, characteristic, complemented
2C2×#10622644C211yesmaximal, characteristic, complemented
3#13073569C211yesmaximal, characteristic
4#13069624C212yesmaximal, complemented
5#13069624C212yesmaximal, complemented
6#13069574C211yesmaximal, characteristic, complemented
7#13069415C211yesmaximal, characteristic
8#13068928C212yesmaximal, complemented
9#13068923C212yesmaximal, complemented
10#13068446C211yesmaximal, characteristic, complemented
11C2×C11×#552C211yesmaximal, characteristic
12C11×#552—24no—
13C11×#552—24no—
14C2×C11×#126—21no—
15C2×C11×#125—21no—
16C2×C11×#125C2211yescharacteristic
17C2×C11×#123—21no—
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C11×#117—21no—
23C2×C11×#117C2211yescharacteristic
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×#4326C2212yes—
26C2×#66977C2212yes—
27C2×#66977C2212yes—
28C2×#66922C2211yescharacteristic
29C2×#66899C2212yes—
30#10622834—21no—
31C2×C22⋊(C11⋊C8)C2212yes—
32C2×C22⋊(C11⋊C8)C2212yes—
33#10622682—24no—
34#10622644—24no—
35#10622589—21no—
36C2×#66874C2212yes—
37C2×#66874C2212yes—
38C2×#66874C2212yes—
39#10622562—21no—
40#10622562—21no—
41C4×C4⋊Dic11C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43C2×#66867C2211yescharacteristic
44#10622167C2212yes—
45#10622167C2212yes—
46#10622167C2212yes—
47C22×Q8×C11C2311yescharacteristic
48C22×D4×C11D411yescharacteristic
49C23×C4×C11—21no—
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C22×Dic22C2312yes—
53C11×#126—28no—
54C11×#125—28no—
55C11×#125—22no—
56C11×#125D414yes—
57C11×#123—28no—
58C11×C22⋊Q8—22no—
59C11×C22⋊Q8—22no—
60C11×C22⋊Q8—22no—
61C11×C22⋊Q8—22no—
62C4×Q8×C11—22no—
63C4×Q8×C11D414yes—
64C4×D4×C11—22no—
65C4×D4×C11—22no—
66C11×#117—28no—
67C11×#117—22no—
68C11×#117—22no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4D411yescharacteristic
85C2×C11×C22⋊C4D411yescharacteristic
86C2×C42×C11—21no—
87C2×C42×C11—21no—
88C2×C42×C11C2311yescharacteristic
89C2×C22⋊Dic11—22no—
90C2×C22⋊Dic11—22no—
91C2×#4326—24no—
92C2×#4326—42no—
93C2×#4326—42no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11C2312yes—
97#66977—24no—
98#66977—24no—
99#66977—42no—
100#66977—42no—
101C2×Dic11⋊C4—22no—
102C2×Dic11⋊C4—22no—
103C2×C4×Dic11—21no—
104C22×C11⋊C8C2312yes—
105C22×C11⋊C8C2312yes—
106#66922—22no—
107#66922—22no—
108#66899—24no—
109C11⋊#95—21no—
110C22⋊(C11⋊C8)—42no—
111C22⋊(C11⋊C8)—42no—
112#66874—24no—
113#66874—24no—
114#66874—24no—
115C4⋊(C11⋊C8)—22no—
116#66867—22no—
117#25584—111nomaximal, Sylow
118C24×C11C2×D411yescharacteristic
119C24×C11C2×D411yescharacteristic
120C2×Q8×C11—21no—
121C2×Q8×C11—22no—
122C2×Q8×C11—22no—
123C2×Q8×C11C2×D412yes—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—41no—
127C22×C4×C11—24no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—42no—
141C22×C4×C11—42no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C22×Dic11—22no—
148C22×Dic11—22no—
149C2×Dic22—22no—
150C2×Dic22—22no—
151C2×Dic22—22no—
152C2×Dic22—22no—
153C2×Dic22—22no—
154C2×Dic22—22no—
155C11×C4⋊C4—24no—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4C2×D412yes—
166C11×C4⋊C4C2×D412yes—
167C11×C4⋊C4C2×D412yes—
168C11×C22⋊C4—24no—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—24no—
171C11×C22⋊C4—22no—
172C11×C22⋊C4—22no—
173C42×C11—24no—
174C42×C11—24no—
175C42×C11C2×D412yes—
176C42×C11C2×D412yes—
177C22⋊Dic11—44no—
178C22⋊Dic11—44no—
179#4326—48no—
180C4⋊Dic11—22no—
181C4⋊Dic11—42no—
182C4⋊Dic11—42no—
183C4⋊Dic11#4114yes—
184Dic11⋊C4—44no—
185Dic11⋊C4—44no—
186C4×Dic11—42no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8—22no—
190C2×C11⋊C8—22no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×#552D1111yescharacteristic
194C2×#491—111no—
195C2×#462—111no—
196#2542—111no—
197#2001—112no—
198#2001—112no—
199#1989—111no—
200#1955—111no—
201#1873—112no—
202#1872—112no—
203#1763—111no—
204C23×C11—21no—
205C23×C11—22no—
206C23×C11—21no—
207C23×C11—22no—
208C23×C11—21no—
209C23×C11—22no—
210C23×C11—21no—
211C23×C11—21no—
212C23×C11—22no—
213C23×C11#13712yes—
214C23×C11C22×D411yescharacteristic
215Q8×C11—22no—
216Q8×C11—22no—
217Q8×C11—42no—
218D4×C11—44no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—22no—
222C2×C4×C11—21no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—21no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—48no—
231C2×C4×C11—42no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—42no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11#12012yes—
244C2×C4×C11#12012yes—
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C2×#4112yes—
248C2×C4×C11H(5,𝔽2)12yes—
249C2×Dic11—24no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254C2×Dic11—42no—
255Dic22—42no—
256Dic22—42no—
257Dic22—42no—
258Dic22—42no—
259C11⋊C8—42no—
260C11⋊C8—42no—
261C22×Q16—112no—
262#552—24no—
263#552—24no—
264C2×C4⋊Q8—111no—
265C2×#126—21no—
266C2×#125—21no—
267C2×#125C2×D1111yescharacteristic
268C2×#123—21no—
269C2×C22⋊Q8—112no—
270C2×C22⋊Q8—112no—
271C2×C22⋊Q8C2×D1111yescharacteristic
272C2×C22⋊Q8C2×D1111yescharacteristic
273C2×C4×Q8C2×D1111yescharacteristic
274C2×C4×D4C2×D1111yescharacteristic
275C2×#117—21no—
276C2×#117C2×D1111yescharacteristic
277C22×C4⋊C4C2×D1111yescharacteristic
278#491—224no—
279#462—224no—
280C2×C4⋊C8—111no—
281C2×#103—112no—
282C2×#103—112no—
283C2×#103—112no—
284C2×#103—112no—
285C2×C22⋊C8—112no—
286C2×C22⋊C8—112no—
287C2×#97—111no—
288#399—221no—
289#399—221no—
290#390—221no—
291#384—221no—
292C4×C4⋊C4—111no—
293#340—112no—
294#340—112no—
295#340—112no—
296C22×C11—22no—
297C22×C11—24no—
298C22×C11—41no—
299C22×C11—41no—
300C22×C11—42no—
301C22×C11—41no—
302C22×C11—41no—
303C22×C11—41no—
304C22×C11—42no—
305C22×C11—42no—
306C22×C11C2×#12011yescharacteristic
307C22×C11#54612yes—
308C22×C11C2×#13711yescharacteristic
309C22×C11#57511yescharacteristic
310C22×C11#57812yes—
311C4×C11—22no—
312C4×C11—22no—
313C4×C11—41no—
314C4×C11—41no—
315C4×C11—42no—
316C4×C11—42no—
317C4×C11—42no—
318C4×C11—42no—
319C4×C11#53211yescharacteristic
320C4×C11#53511yescharacteristic
321C4×C11#55012yes—
322Dic11—44no—
323Dic11—82no—
324C22×Q8—112no—
325C22×Q8C22×D1111yescharacteristic
326C22×D4C22⋊D1111yescharacteristic
327C23×C4—21no—
328C23×C4C22×D1111yescharacteristic
329C23×C4C22×D1111yescharacteristic
330C2×Q16—224no—
331C2×Q16—442no—
332C2×Q16—442no—
333C22×C8—112no—
334C22×C8—112no—
335C4⋊Q8—222no—
336C4⋊Q8—222no—
337#126—28no—
338#125—28no—
339#125—22no—
340#125C22⋊D1114yes—
341#123—28no—
342C22⋊Q8—22no—
343C22⋊Q8—22no—
344C22⋊Q8—22no—
345C22⋊Q8—22no—
346C22⋊Q8—224no—
347C22⋊Q8—224no—
348C22⋊Q8—442no—
349C22⋊Q8—442no—
350C4×Q8—22no—
351C4×Q8C22⋊D1114yes—
352C4×D4—22no—
353C4×D4—22no—
354#117—28no—
355#117—22no—
356#117—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—112no—
366C2×C4⋊C4—222no—
367C2×C4⋊C4—222no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4C22⋊D1111yescharacteristic
371C2×C4⋊C4C22×D1111yescharacteristic
372C2×C4⋊C4C22×D1111yescharacteristic
373C2×C4⋊C4C22×D1111yescharacteristic
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—222no—
378C2×C22⋊C4—222no—
379C2×C22⋊C4C22⋊D1111yescharacteristic
380C2×C22⋊C4C22⋊D1111yescharacteristic
381C2×C42—21no—
382C2×C42—21no—
383C2×C42—221no—
384C2×C42C22×D1111yescharacteristic
385C4⋊C8—222no—
386#103—224no—
387#103—224no—
388#103—224no—
389#103—224no—
390C22⋊C8—442no—
391C22⋊C8—442no—
392#97—222no—
393#95—221no—
394C2×C11—42no—
395C2×C11—81no—
396C2×C11#243111yescharacteristic
397C2×C11#300711yescharacteristic
398C2×C11#301111yescharacteristic
399C2×C11#331212yes—
400C2×C11#331512yes—
401C24C2×C22⋊D1111yescharacteristic
402C24C2×C22⋊D1111yescharacteristic
403C2×Q8—21no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—222no—
407C2×Q8—222no—
408C2×Q8—222no—
409C2×Q8—222no—
410C2×Q8—222no—
411C2×Q8—222no—
412C2×Q8C2×C22⋊D1112yes—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—41no—
416C22×C4—24no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—222no—
432C22×C4—222no—
433C22×C4C2×C22⋊D1111yescharacteristic
434C22×C4C2×C22⋊D1111yescharacteristic
435C22×C4C2×C22⋊D1111yescharacteristic
436C22×C4C2×C22⋊D1111yescharacteristic
437C22×C4C23×D1111yescharacteristic
438Q16—448no—
439C2×C8—222no—
440C2×C8—222no—
441C2×C8—222no—
442C2×C8—222no—
443C2×C8—222no—
444C2×C8—222no—
445C4⋊C4—24no—
446C4⋊C4—24no—
447C4⋊C4—24no—
448C4⋊C4—24no—
449C4⋊C4—24no—
450C4⋊C4—24no—
451C4⋊C4—22no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—114no—
456C4⋊C4—222no—
457C4⋊C4—444no—
458C4⋊C4—444no—
459C4⋊C4—442no—
460C4⋊C4—442no—
461C4⋊C4C2×C22⋊D1112yes—
462C4⋊C4C2×C22⋊D1112yes—
463C4⋊C4C2×C22⋊D1112yes—
464C22⋊C4—24no—
465C22⋊C4—24no—
466C22⋊C4—24no—
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—444no—
470C22⋊C4—444no—
471C42—24no—
472C42—24no—
473C42—442no—
474C42C2×C22⋊D1112yes—
475C42C2×C22⋊D1112yes—
476C11#2558411yescharacteristic, complemented, Sylow
477C23—21no—
478C23—22no—
479C23—22no—
480C23—21no—
481C23—21no—
482C23—21no—
483C23—22no—
484C23—22no—
485C23—21no—
486C23#6700412yes—
487C23C22×C22⋊D1111yescharacteristic
488Q8—22no—
489Q8—22no—
490Q8—42no—
491Q8—442no—
492Q8—442no—
493Q8—442no—
494Q8—442no—
495D4—44no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—48no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—224no—
521C2×C4—442no—
522C2×C4—442no—
523C2×C4—442no—
524C2×C4—442no—
525C2×C4—442no—
526C2×C4#6700612yes—
527C2×C4#6700612yes—
528C2×C4#41×D1112yes—
529C2×C4#6704212yes—
530C2×C4C22×C22⋊D1111yescharacteristic
531C2×C4C22×C22⋊D1111yescharacteristic
532C8—442no—
533C8—442no—
534C22—24no—
535C22—22no—
536C22—41no—
537C22—42no—
538C22—41no—
539C22—42no—
540C22—41no—
541C22—41no—
542C22—42no—
543C22—41no—
544C22#1062335311yescharacteristic
545C22C2×#6700411yescharacteristic
546C22#1062336012yes—
547C22#1062336912yes—
548C22C2×#6700611yescharacteristic
549C4—22no—
550C4—22no—
551C4—41no—
552C4—41no—
553C4—42no—
554C4—42no—
555C4—42no—
556C4—42no—
557C4—444no—
558C4—882no—
559C4#1062336111yescharacteristic
560C4#1062336311yescharacteristic
561C4#1062336512yes—
562C2—42no—
563C2—81no—
564C2#1307223111yescharacteristic
565C2#1307787611yescharacteristic
566C2#1307791111yescharacteristic
567C2#1308066112yes—
568C2#1308070612yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#552C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenterC2×#552D11
hypocenterC11#25584
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
1. C2×#10622682C2semidirect
2. C2×#10622644C2semidirect
4. #13069624C2semidirect
5. #13069624C2semidirect
6. #13069574C2semidirect
8. #13068928C2semidirect
9. #13068923C2semidirect
10. #13068446C2semidirect
476. C11#25584semidirect

Maximal subgroups

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

subgroupindex
C2×#106226822
C2×#106226442
#130735692
#130696242
#130695742
#130694152
#130689282
#130689232
#130684462
C2×C11×#5522
#2558411