Finite Group Databasebeta

← #14752789

Subgroups — #14752789

Order 2816.

974 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622319C211yesmaximal, characteristic
2C2×#10622449C211yesmaximal, characteristic
3#13071077C211yesmaximal, characteristic
4#13068491C211yesmaximal, characteristic, complemented
5C4⋊C8×Dic11C211yesmaximal, characteristic, complemented
6#13068401C211yesmaximal, characteristic, complemented
7#13068398C211yesmaximal, characteristic, complemented
8C8×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
9#13068386C211yesmaximal, characteristic, complemented
10#13068385C211yesmaximal, characteristic, complemented
11#13068383C211yesmaximal, characteristic, complemented
12#13068364C211yesmaximal, characteristic, complemented
13#13068311C211yesmaximal, characteristic, complemented
14#13068311C211yesmaximal, characteristic, complemented
15C11×#1771C211yesmaximal, characteristic, complemented
16C22×#4313C2211yescharacteristic
17C22×#4313C2211yescharacteristic
18C22×C8×D11C2211yescharacteristic
19C22×C8×D11C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C2×#66925C2211yescharacteristic
22C2×#66925C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×#97C2211yescharacteristic
25C2×C11×#97C2211yescharacteristic
26C2×C4×C8×C11C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×C8×Dic11C2211yescharacteristic
33C2×C8×Dic11C2211yescharacteristic
34#10622601C412yes—
35#10622586C412yes—
36C4×(C2×D11)⋊C4C2211yescharacteristic
37C4×(C2×D11)⋊C4C2211yescharacteristic
38C42×Dic11C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40C2×#66867C2211yescharacteristic
41C2×#66867C2211yescharacteristic
42C2×C4×C11⋊C8C2211yescharacteristic
43#10622449C418yescomplemented
44#10622319C418yescomplemented
45#10622282C412yes—
46#10622282C412yes—
47C11×#336C2211yescharacteristic
48C11×#336C2211yescharacteristic
49#10622188C2211yescharacteristic
50#10622188C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57C22×D44C2×C411yescharacteristic
58C22×C4×D11C2311yescharacteristic
59C22×C4×D11C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C2×C11×C4⋊C4C2×C412yes—
65C2×C42×C11C2311yescharacteristic
66C2×C42×C11C2311yescharacteristic
67C2×C42×C11C2311yescharacteristic
68C2×(C2×D11)⋊C4C2×C412yes—
69C2×(C2×D11)⋊C4C2×C412yes—
70C2×(C2×D11)⋊C4C2×C412yes—
71C2×(C2×D11)⋊C4C2×C412yes—
72C2×(C2×D11)⋊C4C2×C411yescharacteristic
73C2×(C2×D11)⋊C4C2×C411yescharacteristic
74C2×C4⋊Dic11C2×C411yescharacteristic
75C2×Dic11⋊C4C2×C412yes—
76C2×Dic11⋊C4C2×C412yes—
77C2×C4×Dic11C2×C412yes—
78C2×C4×Dic11C2×C412yes—
79C2×C4×Dic11C2311yescharacteristic
80C2×C4×Dic11C2311yescharacteristic
81C22×C11⋊C8C2311yescharacteristic
82C22×C11⋊C8C2311yescharacteristic
83C22×C11⋊C8C2311yescharacteristic
84C22×C11⋊C8C2311yescharacteristic
85C2×#4313—41no—
86C2×#4313—41no—
87C2×#4313—41no—
88C2×#4313—41no—
89C2×#4313C2×C414yes—
90C2×#4313C2×C414yes—
91C2×C8×D11—41no—
92C2×C8×D11—41no—
93C2×C8×D11—41no—
94C2×C8×D11—41no—
95C2×C8×D11C2×C414yes—
96C2×C8×D11C2×C414yes—
97C4×D44C2×C414yes—
98C4×D44C2×C414yes—
99#66925—41no—
100#66925—41no—
101#66925—41no—
102#66925—41no—
103C11×C4⋊C8C2×C414yes—
104C11×#97—41no—
105C11×#97C2×C414yes—
106C4×C8×C11—41no—
107C11×#95C2×C412yes—
108C11⋊#95C2×C412yes—
109C11⋊#95C2×C412yes—
110(C2×D11)⋊C8C2×C414yes—
111(C2×D11)⋊C8C2×C414yes—
112(C2×D11)⋊C8C2×C414yes—
113(C2×D11)⋊C8C2×C414yes—
114C8×Dic11—41no—
115C8×Dic11—41no—
116C4⋊(C11⋊C8)C2×C414yes—
117#66867—41no—
118#66867C2×C414yes—
119C4×C11⋊C8—41no—
120#20566—111nomaximal, Sylow
121C23×D11C22×C411yescharacteristic
122C23×D11C22×C411yescharacteristic
123C22×C4×C11C22×C412yes—
124C22×C4×C11C22×C412yes—
125C22×C4×C11C22×C411yescharacteristic
126C22×C4×C11C22×C411yescharacteristic
127C22×C4×C11C2411yescharacteristic
128C22×Dic11C22×C412yes—
129C22×Dic11C22×C411yescharacteristic
130C22×Dic11C22×C411yescharacteristic
131C22×Dic11C22×C412yes—
132C2×D44—42no—
133C2×D44C4214yes—
134C2×C4×D11—21no—
135C2×C4×D11—21no—
136C2×C4×D11—21no—
137C2×C4×D11—21no—
138C2×C4×D11—21no—
139C2×C4×D11—21no—
140C2×C4×D11—21no—
141C2×C4×D11—21no—
142C2×C4×D11C22×C412yes—
143C2×C4×D11C22×C412yes—
144C2×C4×D11C22×C412yes—
145C2×C4×D11C22×C412yes—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11C22×C412yes—
155C2×C8×C11C22×C412yes—
156C2×C8×C11C22×C412yes—
157C2×C8×C11C22×C412yes—
158C11×C4⋊C4—42no—
159C42×C11—21no—
160C42×C11—21no—
161C42×C11—21no—
162C42×C11—21no—
163C42×C11C22×C412yes—
164C42×C11C22×C412yes—
165(C2×D11)⋊C4—24no—
166(C2×D11)⋊C4—24no—
167(C2×D11)⋊C4—42no—
168(C2×D11)⋊C4—42no—
169(C2×D11)⋊C4C4214yes—
170(C2×D11)⋊C4C4214yes—
171C4⋊Dic11C4214yes—
172Dic11⋊C4—42no—
173Dic11⋊C4—42no—
174C4×Dic11—24no—
175C4×Dic11—21no—
176C4×Dic11—21no—
177C4×Dic11—21no—
178C4×Dic11—21no—
179C4×Dic11—42no—
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⋊C8C22×C412yes—
189C2×C11⋊C8C22×C412yes—
190C2×C11⋊C8C22×C412yes—
191C2×C11⋊C8C22×C412yes—
192#4313—44no—
193#4313—44no—
194C8×D11—44no—
195C8×D11—44no—
196C2×#435—111no—
197C2×#435—111no—
198#2293—111no—
199#1771—111no—
200#1771D1111yescharacteristic, complemented
201C4×C4⋊C8—111no—
202#1753—111no—
203#1753—111no—
204C8×C22⋊C4—111no—
205C8×C22⋊C4—111no—
206#1750—111no—
207#1750—111no—
208#1745—111no—
209#1729—111no—
210#1729—111no—
211C23×C11C23×C411yescharacteristic
212C22×D11—21no—
213C22×D11—21no—
214C22×D11—21no—
215C22×D11—21no—
216C22×D11—22no—
217C22×D11—22no—
218C22×D11—22no—
219C22×D11—22no—
220C22×D11C2×C4212yes—
221C22×D11C2×C4212yes—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11C2×C4212yes—
231C2×C4×C11C2×C4212yes—
232C2×C4×C11C23×C411yescharacteristic
233C2×C4×C11C23×C411yescharacteristic
234C2×C4×C11H(5,𝔽2)11yescharacteristic
235C2×C4×C11H(5,𝔽2)11yescharacteristic
236C2×C4×C11H(5,𝔽2)11yescharacteristic
237C2×C4×C112−1+411yescharacteristic
238C2×Dic11—21no—
239C2×Dic11—21no—
240C2×Dic11—22no—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11C2×C4212yes—
248C2×Dic11C2×C4212yes—
249C2×Dic11#13114yes—
250D44—44no—
251C4×D11—22no—
252C4×D11—22no—
253C4×D11—22no—
254C4×D11—22no—
255C4×D11—22no—
256C4×D11—22no—
257C4×D11—22no—
258C4×D11—22no—
259C8×C11—22no—
260C8×C11—22no—
261C8×C11—22no—
262C8×C11—22no—
263C11⋊C8—22no—
264C11⋊C8—22no—
265C11⋊C8—22no—
266C11⋊C8—22no—
267C22×M16—111no—
268C22×M16—111no—
269C23×C8—111no—
270C23×C8—111no—
271C2×C4×D4—111no—
272C2×#117—111no—
273C2×#117—111no—
274#435—118no—
275#435—118no—
276C2×C4⋊C8—111no—
277C2×C4⋊C8C2×D1111yescharacteristic
278C2×C22⋊C8—111no—
279C2×C22⋊C8—111no—
280C2×C22⋊C8—111no—
281C2×C22⋊C8—111no—
282C2×#97—111no—
283C2×#97—111no—
284C2×#97C2×D1111yescharacteristic
285C2×#97C2×D1111yescharacteristic
286C2×C4×C8—111no—
287C2×C4×C8—111no—
288C2×C4×C8—111no—
289C2×C4×C8C2×D1111yescharacteristic
290#390—112no—
291#389—112no—
292#388—112no—
293#388—112no—
294C4×C4⋊C4C2×D1111yescharacteristic
295C4×C22⋊C4—111no—
296C4×C22⋊C4—111no—
297C43—111no—
298#336—111no—
299#336—111no—
300#336—111no—
301#336—111no—
302#336—111no—
303#336—111no—
304#336—111no—
305#336—111no—
306#336C2×D1111yescharacteristic
307#336C2×D1111yescharacteristic
308C22×C11C22×C4211yescharacteristic
309C22×C11#51811yescharacteristic
310C22×C11#52011yescharacteristic
311C22×C11C2×#13112yes—
312C22×C11#56812yes—
313C2×D11—22no—
314C2×D11—22no—
315C2×D11—22no—
316C2×D11—22no—
317C2×D11—22no—
318C2×D11—22no—
319C2×D11—42no—
320C2×D11—42no—
321C2×D11—42no—
322C2×D11—42no—
323C4×C11—22no—
324C4×C11—22no—
325C4×C11—42no—
326C4×C11—42no—
327C4×C11#51811yescharacteristic
328C4×C11#51811yescharacteristic
329C4×C11#52011yescharacteristic
330C4×C11#52011yescharacteristic
331Dic11—24no—
332Dic11—22no—
333Dic11—22no—
334Dic11—42no—
335C22×D4—111no—
336C23×C4—111no—
337C23×C4—111no—
338C2×M16—114no—
339C2×M16—114no—
340C2×M16—441no—
341C2×M16—441no—
342C2×M16—441no—
343C2×M16—441no—
344C22×C8—111no—
345C22×C8—111no—
346C22×C8—111no—
347C22×C8—111no—
348C22×C8—114no—
349C22×C8—114no—
350C22×C8—441no—
351C22×C8—441no—
352C22×C8—441no—
353C22×C8—441no—
354C22×C8C22×D1111yescharacteristic
355C22×C8C22×D1111yescharacteristic
356C22×C8C22×D1111yescharacteristic
357C22×C8C22×D1111yescharacteristic
358C4×D4—114no—
359C4×D4—114no—
360#117—441no—
361#117—441no—
362#117—441no—
363#117—441no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—112no—
366C2×C4⋊C4—112no—
367C2×C4⋊C4C4×D1112yes—
368C2×C22⋊C4—111no—
369C2×C22⋊C4—111no—
370C2×C22⋊C4—112no—
371C2×C22⋊C4—112no—
372C2×C22⋊C4—112no—
373C2×C22⋊C4—112no—
374C2×C42—112no—
375C2×C42—111no—
376C2×C42—111no—
377C2×C42—112no—
378C2×C42C22×D1111yescharacteristic
379C2×C42C22×D1111yescharacteristic
380C2×C42C22×D1111yescharacteristic
381C4⋊C8—114no—
382C4⋊C8C4×D1114yes—
383C22⋊C8—114no—
384C22⋊C8—114no—
385C22⋊C8—114no—
386C22⋊C8—114no—
387#97—41no—
388#97—114no—
389#97—441no—
390#97C4×D1114yes—
391C4×C8—41no—
392C4×C8—441no—
393C4×C8—441no—
394C4×C8—441no—
395#95—112no—
396#95—112no—
397#95C4×D1112yes—
398C2×C11#227511yescharacteristic
399C2×C11#287311yescharacteristic
400C2×C11C4×#13111yescharacteristic
401C2×C11#298112yes—
402C2×C11#299212yes—
403D11—42no—
404D11—42no—
405C24—111no—
406C24—111no—
407C2×D4—114no—
408C2×D4—442no—
409C22×C4—112no—
410C22×C4—111no—
411C22×C4—111no—
412C22×C4—112no—
413C22×C4—112no—
414C22×C4—112no—
415C22×C4—112no—
416C22×C4—112no—
417C22×C4—221no—
418C22×C4—221no—
419C22×C4—221no—
420C22×C4—221no—
421C22×C4—221no—
422C22×C4—221no—
423C22×C4—221no—
424C22×C4—221no—
425C22×C4C2×C4×D1112yes—
426C22×C4C2×C4×D1112yes—
427C22×C4C2×C4×D1111yescharacteristic
428C22×C4C2×C4×D1111yescharacteristic
429C22×C4C23×D1111yescharacteristic
430M16—444no—
431M16—444no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—112no—
441C2×C8—112no—
442C2×C8—112no—
443C2×C8—112no—
444C2×C8—221no—
445C2×C8—221no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—444no—
453C2×C8—444no—
454C2×C8C2×C4×D1112yes—
455C2×C8C2×C4×D1112yes—
456C2×C8C2×C4×D1112yes—
457C2×C8C2×C4×D1112yes—
458C4⋊C4—42no—
459C4⋊C4—114no—
460C4⋊C4—442no—
461C4⋊C4—442no—
462C22⋊C4—114no—
463C22⋊C4—114no—
464C22⋊C4—224no—
465C22⋊C4—224no—
466C22⋊C4—442no—
467C22⋊C4—442no—
468C42—21no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—224no—
473C42—221no—
474C42—221no—
475C42—221no—
476C42—221no—
477C42—442no—
478C42C2×C4×D1112yes—
479C42C2×C4×D1112yes—
480C11#2056611yescharacteristic, complemented, Sylow
481C23—112no—
482C23—112no—
483C23—222no—
484C23—222no—
485C23—222no—
486C23—222no—
487C23—221no—
488C23—221no—
489C23—221no—
490C23—221no—
491C23C22×C4×D1111yescharacteristic
492D4—444no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—112no—
502C2×C4—112no—
503C2×C4—114no—
504C2×C4—222no—
505C2×C4—221no—
506C2×C4—221no—
507C2×C4—222no—
508C2×C4—221no—
509C2×C4—221no—
510C2×C4—222no—
511C2×C4—222no—
512C2×C4—222no—
513C2×C4—222no—
514C2×C4—222no—
515C2×C4—222no—
516C2×C4—222no—
517C2×C4—222no—
518C2×C4—222no—
519C2×C4—222no—
520C2×C4—222no—
521C2×C4C42×D1112yes—
522C2×C4C42×D1112yes—
523C2×C4C22×C4×D1111yescharacteristic
524C2×C4C22×C4×D1111yescharacteristic
525C2×C4#6703711yescharacteristic
526C2×C4#6704011yescharacteristic
527C2×C4#6704211yescharacteristic
528C2×C4#6704211yescharacteristic
529C8—22no—
530C8—22no—
531C8—22no—
532C8—22no—
533C8—222no—
534C8—222no—
535C8—222no—
536C8—222no—
537C22—222no—
538C22—222no—
539C22—222no—
540C22—222no—
541C22—222no—
542C22—222no—
543C22—442no—
544C22—442no—
545C22—442no—
546C22—442no—
547C22C2×C42×D1111yescharacteristic
548C22#1062307611yescharacteristic
549C22#1062310511yescharacteristic
550C22#1062327612yes—
551C22D11×#13112yes—
552C4—22no—
553C4—22no—
554C4—42no—
555C4—42no—
556C4—222no—
557C4—222no—
558C4—224no—
559C4—442no—
560C4#1062303511yescharacteristic
561C4#1062305211yescharacteristic
562C4#1062307611yescharacteristic
563C4#1062310511yescharacteristic
564C2—442no—
565C2—442no—
566C2#1307097611yescharacteristic
567C2#1307703311yescharacteristic
568C2#1307703811yescharacteristic
569C2#1307768812yes—
570C2#1307775412yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C22×C42
FittingC11×#1771C2
socleC23×C11C23×C4
prime radicalC22×D44C2×C4
cosocleC22×C4×C11C24
hypercenter#1771D11
hypocenterC11#20566
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1771

Complements

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

NH ≅ G/Ntype
4. #13068491C2semidirect
5. C4⋊C8×Dic11C2semidirect
6. #13068401C2semidirect
7. #13068398C2semidirect
8. C8×(C2×D11)⋊C4C2semidirect
9. #13068386C2semidirect
10. #13068385C2semidirect
11. #13068383C2semidirect
12. #13068364C2semidirect
13. #13068311C2semidirect
14. #13068311C2semidirect
15. C11×#1771C2semidirect
43. #10622449C4semidirect
44. #10622319C4semidirect
200. #1771D11semidirect
480. C11#20566semidirect

Maximal subgroups

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

subgroupindex
C2×#106223192
C2×#106224492
#130710772
#130684912
C4⋊C8×Dic112
#130684012
#130683982
C8×(C2×D11)⋊C42
#130683862
#130683852
#130683832
#130683642
#130683112
C11×#17712
#2056611