Finite Group Databasebeta

← #14804517

Subgroups — #14804517

Order 2816.

1018 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622426C212yesmaximal, complemented
2C2×#10622703C211yesmaximal, characteristic, complemented
3C2×C8×D44C211yesmaximal, characteristic
4#13073570C211yesmaximal, characteristic
5#13073539C211yesmaximal, characteristic
6#13069817C212yesmaximal, complemented
7#13069625C212yesmaximal, complemented
8#13069372C211yesmaximal, characteristic, complemented
9#13069036C212yesmaximal, complemented
10C4×#66880C211yesmaximal, characteristic, complemented
11C11×#1956C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×#66999C2212yes—
14C2×#66999C2212yes—
15C22×#4326C2212yes—
16C22×C8×D11C2212yes—
17C2×#66950C2212yes—
18C2×C4×D44C2211yescharacteristic
19C2×C4×Dic22C2211yescharacteristic
20C2×C11×#103C2212yes—
21C2×C11×#103C2212yes—
22C2×C4×C8×C11C2211yescharacteristic
23C11×#384C2211yescharacteristic
24C2×#66899C2212yes—
25C2×(C2×D11)⋊C8C2212yes—
26C2×#66880C2211yescharacteristic
27C2×#66880C2211yescharacteristic
28#10622703—24no—
29#10622607—22no—
30#10622605—22no—
31#10622601—21no—
32#10622601—21no—
33#10622600C2212yes—
34#10622598—21no—
35#10622589—21no—
36C2×#66871C2212yes—
37C4×C4⋊Dic11C2211yescharacteristic
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39#10622426—28no—
40C8×D44—24no—
41#10622189C2211yescharacteristic
42#10622189C2211yescharacteristic
43#10622167C2212yes—
44C22×Q8×C11C2312yes—
45C22×D44D411yescharacteristic
46C22×C4×D11C2312yes—
47C22×Dic22C2311yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C11×C4⋊Q8—22no—
51C11×C4⋊Q8—22no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4C2312yes—
57C2×C42×C11C2311yescharacteristic
58#66999—24no—
59#66999—24no—
60#66999—42no—
61#66999—42no—
62C2×#4326—24no—
63C2×#4326—24no—
64C2×#4326—42no—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4—22no—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4D412yes—
70C2×C4⋊Dic11—22no—
71C2×C4⋊Dic11D411yescharacteristic
72C2×C4⋊Dic11C2311yescharacteristic
73C2×C4⋊Dic11C2311yescharacteristic
74C2×C4⋊Dic11C2311yescharacteristic
75C2×Dic11⋊C4—21no—
76C2×Dic11⋊C4—22no—
77C2×Dic11⋊C4—22no—
78C2×C4×Dic11—21no—
79C2×C4×Dic11—21no—
80C22×C11⋊C8C2312yes—
81C2×C8×D11—24no—
82C2×C8×D11—24no—
83C2×C8×D11—42no—
84#66950—24no—
85#66950—42no—
86C4×D44—22no—
87C4×D44—22no—
88C4×Dic22—22no—
89C4×Dic22—22no—
90C11×#103—24no—
91C11×#103—42no—
92C4×C8×C11—22no—
93#66899—24no—
94C11⋊#95—21no—
95C11⋊#95—22no—
96(C2×D11)⋊C8—24no—
97#66880—22no—
98#66880D414yescomplemented
99#66871—24no—
100C4⋊(C11⋊C8)D414yes—
101#25386—111nomaximal, Sylow
102C23×D11C2×D412yes—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2411yescharacteristic
114C22×Dic11—21no—
115C22×Dic11—21no—
116C22×Dic11—21no—
117C22×Dic11—21no—
118C22×Dic11C2×D412yes—
119C2×D44—22no—
120C2×D44—22no—
121C2×D44Q1614yescomplemented
122C2×C4×D11—22no—
123C2×C4×D11—22no—
124C2×C4×D11—22no—
125C2×C4×D11—22no—
126C2×C4×D11—22no—
127C2×C4×D11—22no—
128C2×Dic22—21no—
129C2×Dic22—21no—
130C2×Dic22—21no—
131C2×Dic22—21no—
132C2×Dic22—21no—
133C2×Dic22C2×D412yes—
134C2×C8×C11—21no—
135C2×C8×C11—21no—
136C2×C8×C11—21no—
137C2×C8×C11—21no—
138C2×C8×C11—21no—
139C2×C8×C11C2×D412yes—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—42no—
143C11×C4⋊C4—42no—
144C11×C4⋊C4—42no—
145C11×C4⋊C4—81no—
146C42×C11C2×D412yes—
147C42×C11#4112yes—
148#4326—48no—
149(C2×D11)⋊C4—24no—
150(C2×D11)⋊C4—44no—
151(C2×D11)⋊C4—44no—
152(C2×D11)⋊C4—44no—
153(C2×D11)⋊C4—82no—
154C4⋊Dic11—22no—
155C4⋊Dic11—21no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158C4⋊Dic11—21no—
159C4⋊Dic11—44no—
160C4⋊Dic11C2×D412yes—
161C4⋊Dic11#4112yes—
162Dic11⋊C4—44no—
163Dic11⋊C4—44no—
164Dic11⋊C4—42no—
165C4×Dic11—42no—
166C4×Dic11—42no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8C2×D414yes—
170C8×D11—48no—
171C2×#467—112no—
172C2×#462—111no—
173C2×C8×D4—111no—
174#2542—111no—
175#2538—111no—
176#2036—112no—
177#2001—112no—
178#1956D1111yescharacteristic, complemented
179#1947—111no—
180#1892—112no—
181C4×#103—111no—
182C23×C11C22×D411yescharacteristic
183C22×D11—22no—
184C22×D11—22no—
185C22×D11—22no—
186C22×D11—22no—
187C22×D11—22no—
188C22×D11—22no—
189C22×D11C2×Q1614yes—
190Q8×C11—42no—
191Q8×C11—42no—
192Q8×C11—42no—
193Q8×C11—42no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11#12112yes—
203C2×C4×C11#12112yes—
204C2×C4×C11C2×Q1612yes—
205C2×C4×C11#13512yes—
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C22×D411yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11C2×#4111yescharacteristic
210C2×C4×C11H(5,𝔽2)11yescharacteristic
211C2×C4×C11H(5,𝔽2)11yescharacteristic
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11—22no—
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227D44—28no—
228C4×D11—42no—
229C4×D11—42no—
230C4×D11—42no—
231C4×D11—42no—
232Dic22—22no—
233Dic22—22no—
234Dic22—41no—
235Dic22—41no—
236C8×C11—22no—
237C8×C11—41no—
238C11⋊C8—24no—
239C22×Q16—112no—
240C23×C8—112no—
241C2×C4⋊Q8C2×D1111yescharacteristic
242C2×C22⋊Q8—112no—
243C2×C22⋊Q8—112no—
244C2×C22⋊Q8—112no—
245C2×C4×Q8—111no—
246C2×C4×D4—111no—
247#467—228no—
248#462—224no—
249C8×D4—224no—
250C2×#107—112no—
251C2×C4⋊C8—111no—
252C2×#103—111no—
253C2×#103—112no—
254C2×#103—111no—
255C2×#103C2×D1112yes—
256C2×#103C2×D1112yes—
257C2×C22⋊C8—112no—
258C2×C4×C8C2×D1111yescharacteristic
259#399—222no—
260#396—222no—
261#390—221no—
262#390—221no—
263#389—221no—
264#384—221no—
265#384C2×D1111yescharacteristic
266#380—112no—
267C4×C4⋊C4—111no—
268#340—111no—
269#340—111no—
270#340—112no—
271C22×C11C2×#12111yescharacteristic
272C22×C11D4211yescharacteristic
273C22×C11#54611yescharacteristic
274C22×C11C22×Q1611yescharacteristic
275C22×C11C2×#13511yescharacteristic
276C22×C11#57711yescharacteristic
277C22×C11#57811yescharacteristic
278C2×D11—24no—
279C2×D11—24no—
280C2×D11—24no—
281C2×D11—42no—
282C2×D11—42no—
283C2×D11—42no—
284C2×D11—42no—
285C4×C11—22no—
286C4×C11—82no—
287C4×C11—82no—
288C4×C11#46714yescomplemented
289C4×C11#53211yescharacteristic
290C4×C11#54011yescharacteristic
291C4×C11D4211yescharacteristic
292C4×C11#55011yescharacteristic
293Dic11—42no—
294Dic11—42no—
295Dic11—42no—
296Dic11—42no—
297Dic11—81no—
298C22×Q8—111no—
299C22×Q8C22×D1112yes—
300C22×D4—111no—
301C23×C4—112no—
302C2×Q16—224no—
303C2×Q16—224no—
304C2×Q16—442no—
305C22×C8—112no—
306C22×C8—224no—
307C22×C8—224no—
308C22×C8—442no—
309C22×C8C22×D1111yescharacteristic
310C22×C8C22×D1111yescharacteristic
311C4⋊Q8—22no—
312C4⋊Q8—22no—
313C22⋊Q8—224no—
314C22⋊Q8—224no—
315C22⋊Q8—224no—
316C22⋊Q8—442no—
317C22⋊Q8—442no—
318C22⋊Q8—442no—
319C4×Q8—222no—
320C4×Q8—222no—
321C4×D4—222no—
322C4×D4—222no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—111no—
328C2×C4⋊C4—111no—
329C2×C4⋊C4—111no—
330C2×C4⋊C4—111no—
331C2×C4⋊C4—222no—
332C2×C4⋊C4—222no—
333C2×C4⋊C4—222no—
334C2×C4⋊C4—221no—
335C2×C4⋊C4C22×D1112yes—
336C2×C22⋊C4—112no—
337C2×C22⋊C4—222no—
338C2×C22⋊C4—222no—
339C2×C22⋊C4—222no—
340C2×C22⋊C4—222no—
341C2×C42—221no—
342C2×C42—221no—
343C2×C42C22×D1111yescharacteristic
344#107—224no—
345C4⋊C8—114no—
346#103—24no—
347#103—42no—
348#103—114no—
349#103—222no—
350#103—224no—
351C22⋊C8—224no—
352C4×C8—22no—
353#95—222no—
354#95—221no—
355C2×C11#242811yescharacteristic
356C2×C11C2×#46711yescharacteristic
357C2×C11#306311yescharacteristic
358C2×C11#328411yescharacteristic
359C2×C11D4×Q1611yescharacteristic
360C2×C11#329911yescharacteristic
361C2×C11#330211yescharacteristic
362D11—44no—
363C24—112no—
364C2×Q8—22no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—22no—
368C2×Q8—22no—
369C2×Q8—22no—
370C2×Q8—112no—
371C2×Q8—221no—
372C2×Q8—221no—
373C2×Q8—221no—
374C2×Q8—221no—
375C2×Q8—221no—
376C2×D4—114no—
377C2×D4—222no—
378C2×D4—222no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—112no—
382C22×C4—221no—
383C22×C4—221no—
384C22×C4—221no—
385C22×C4—222no—
386C22×C4—222no—
387C22×C4—222no—
388C22×C4—222no—
389C22×C4—222no—
390C22×C4—222no—
391C22×C4—221no—
392C22×C4D4×D1111yescharacteristic
393C22×C4D4×D1111yescharacteristic
394C22×C4C23×D1111yescharacteristic
395Q16—448no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8—21no—
400C2×C8—21no—
401C2×C8—114no—
402C2×C8—222no—
403C2×C8—222no—
404C2×C8—448no—
405C2×C8D4×D1112yes—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—42no—
409C4⋊C4—42no—
410C4⋊C4—42no—
411C4⋊C4—81no—
412C4⋊C4—112no—
413C4⋊C4—112no—
414C4⋊C4—222no—
415C4⋊C4—221no—
416C4⋊C4—221no—
417C4⋊C4—221no—
418C4⋊C4—221no—
419C4⋊C4—444no—
420C4⋊C4—444no—
421C4⋊C4—444no—
422C4⋊C4—442no—
423C22⋊C4—224no—
424C22⋊C4—444no—
425C22⋊C4—444no—
426C22⋊C4—444no—
427C22⋊C4—882no—
428C42—442no—
429C42—442no—
430C42#433912yes—
431C42D4×D1112yes—
432C11#2538611yescharacteristic, complemented, Sylow
433C23—114no—
434C23—222no—
435C23—222no—
436C23—222no—
437C23—222no—
438C23—222no—
439C23—222no—
440C23C2×D4×D1111yescharacteristic
441Q8—42no—
442Q8—42no—
443Q8—42no—
444Q8—42no—
445Q8—222no—
446Q8—222no—
447Q8—441no—
448Q8—441no—
449D4—228no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—222no—
459C2×C4—222no—
460C2×C4—222no—
461C2×C4—222no—
462C2×C4—222no—
463C2×C4—222no—
464C2×C4—441no—
465C2×C4—441no—
466C2×C4—441no—
467C2×C4—441no—
468C2×C4—441no—
469C2×C4—441no—
470C2×C4—442no—
471C2×C4—442no—
472C2×C4—442no—
473C2×C4—442no—
474C2×C4—441no—
475C2×C4—441no—
476C2×C4—441no—
477C2×C4#6693712yes—
478C2×C4#6693712yes—
479C2×C4#6696912yes—
480C2×C4Q16×D1112yes—
481C2×C4C2×#433911yescharacteristic
482C2×C4C2×D4×D1111yescharacteristic
483C2×C4C2×D4×D1111yescharacteristic
484C2×C4#6703711yescharacteristic
485C2×C4#41×D1111yescharacteristic
486C2×C4#6704211yescharacteristic
487C8—22no—
488C8—41no—
489C8—224no—
490C22—224no—
491C22—224no—
492C22—224no—
493C22—442no—
494C22—442no—
495C22—442no—
496C22—442no—
497C22C2×#6693711yescharacteristic
498C22#1062320711yescharacteristic
499C22#1062324811yescharacteristic
500C22C2×#6696911yescharacteristic
501C22#1062329311yescharacteristic
502C22C2×Q16×D1111yescharacteristic
503C22#1062329711yescharacteristic
504C4—22no—
505C4—82no—
506C4—82no—
507C4—442no—
508C4—442no—
509C4—442no—
510C4—442no—
511C4—881no—
512C4#1062242614yescomplemented
513C4#1062307911yescharacteristic
514C4#1062309311yescharacteristic
515C4#1062313011yescharacteristic
516C4#1062314011yescharacteristic
517C2—444no—
518C2#1307220511yescharacteristic
519C2C2×#1062242611yescharacteristic
520C2#1307830511yescharacteristic
521C2#1308034511yescharacteristic
522C2#1308036611yescharacteristic
523C2#1308049111yescharacteristic
524C2#1308053211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1956C2
socleC23×C11C22×D4
prime radicalC22×D44D4
hypercenter#1956D11
hypocenterC11#25386
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

Complements

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

NH ≅ G/Ntype
1. C2×#10622426C2semidirect
2. C2×#10622703C2semidirect
6. #13069817C2semidirect
7. #13069625C2semidirect
8. #13069372C2semidirect
9. #13069036C2semidirect
10. C4×#66880C2semidirect
11. C11×#1956C2semidirect
98. #66880D4semidirect
121. C2×D44Q16semidirect
178. #1956D11semidirect
288. C4×C11#467semidirect
432. C11#25386semidirect
512. C4#10622426semidirect

Maximal subgroups

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

subgroupindex
C2×#106224262
C2×#106227032
C2×C8×D442
#130735702
#130735392
#130698172
#130696252
#130693722
#130690362
C4×#668802
C11×#19562
#2538611