Finite Group Databasebeta

← #14803882

Subgroups — #14803882

Order 2816.

978 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622459C211yesmaximal, characteristic, complemented
2C2×#10622447C211yesmaximal, characteristic, complemented
3#13073611C211yesmaximal, characteristic, complemented
4#13073532C211yesmaximal, characteristic
5#13070041C212yesmaximal, complemented
6#13069800C212yesmaximal, complemented
7#13069576C211yesmaximal, characteristic, complemented
8#13069043C212yesmaximal, complemented
9#13068642C212yesmaximal, complemented
10C4×#66873C211yesmaximal, characteristic, complemented
11C11×#1947C211yesmaximal, characteristic, complemented
12C22×C8×D11C2212yes—
13C2×#66948—21no—
14C2×#66948C2212yes—
15C2×#66928—21no—
16C2×C4×D44C2211yescharacteristic
17C2×C4×D44C2211yescharacteristic
18C2×#66922C2211yescharacteristic
19C2×C11×#107C2212yes—
20C2×C11×C4⋊C8C2211yescharacteristic
21C11×#384C2211yescharacteristic
22C4×C11×C4⋊C4C2211yescharacteristic
23C2×#66885C2212yes—
24C2×(C2×D11)⋊C8C2212yes—
25C2×#66882C2212yes—
26#10622604—22no—
27#10622600—21no—
28#10622600C2212yes—
29#10622600C2212yes—
30#10622600C2212yes—
31C2×#66873C2211yescharacteristic
32C2×#66873C2211yescharacteristic
33#10622542—21no—
34C2×C4×C11⋊C8C2211yescharacteristic
35#10622459—24no—
36#10622447—24no—
37#10622287—22no—
38C11×#340C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43C22×D44—22no—
44C22×D44D411yescharacteristic
45C22×D44C2311yescharacteristic
46C22×C4×D11—21no—
47C22×C4×D11C2312yes—
48C22×Dic22—21no—
49C22×C8×C11C2312yes—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4C2311yescharacteristic
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C42×C11—21no—
56C2×C42×C11C2311yescharacteristic
57C2×(C2×D11)⋊C4—22no—
58C2×(C2×D11)⋊C4—22no—
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—21no—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4D412yes—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11D411yescharacteristic
65C2×C4⋊Dic11C2312yes—
66C2×C4⋊Dic11C2311yescharacteristic
67C22×C11⋊C8C2311yescharacteristic
68C22×C11⋊C8C2311yescharacteristic
69C2×C8×D11—24no—
70C2×C8×D11—24no—
71C2×C8×D11—42no—
72#66948—24no—
73#66948—42no—
74#66948—44no—
75#66928—44no—
76C4×D44—22no—
77C4×D44—22no—
78C4×D44—22no—
79C4×D44—22no—
80#66922—22no—
81#66922—22no—
82C11×#107—42no—
83C11×C4⋊C8D414yescomplemented
84C11×#95—21no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88#66885—24no—
89(C2×D11)⋊C8—24no—
90#66882—24no—
91#66873—22no—
92#66873—22no—
93C4×C11⋊C8—22no—
94#25338—111nomaximal, Sylow
95C23×D11—21no—
96C23×D11C2×D412yes—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—22no—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2411yescharacteristic
103C22×Dic11—22no—
104C22×Dic11—21no—
105C22×Dic11C2×D412yes—
106C2×D44—22no—
107C2×D44—22no—
108C2×D44—21no—
109C2×D44—21no—
110C2×D44—21no—
111C2×D44—21no—
112C2×D44—21no—
113C2×D44—44no—
114C2×D44—44no—
115C2×D44—82no—
116C2×D44D814yes—
117C2×D44#4112yes—
118C2×C4×D11—22no—
119C2×C4×D11—22no—
120C2×C4×D11—22no—
121C2×C4×D11—22no—
122C2×C4×D11—22no—
123C2×C4×D11—22no—
124C2×C4×D11—42no—
125C2×C4×D11—42no—
126C2×C4×D11—42no—
127C2×Dic22—42no—
128C2×Dic22—42no—
129C2×Dic22—42no—
130C2×C8×C11—22no—
131C2×C8×C11—22no—
132C2×C8×C11C2×D414yes—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—42no—
140C11×C4⋊C4—81no—
141C42×C11—42no—
142C42×C11C2×D412yes—
143C42×C11#4112yes—
144(C2×D11)⋊C4—24no—
145(C2×D11)⋊C4—44no—
146(C2×D11)⋊C4—44no—
147(C2×D11)⋊C4—44no—
148(C2×D11)⋊C4—44no—
149(C2×D11)⋊C4—42no—
150C4⋊Dic11—22no—
151C4⋊Dic11—21no—
152C4⋊Dic11—22no—
153C4⋊Dic11—22no—
154C4⋊Dic11—21no—
155C4⋊Dic11—42no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8—21no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—21no—
161C2×C11⋊C8#4112yes—
162C8×D11—48no—
163C2×#474—111no—
164C2×C8×D4—111no—
165#2547—111no—
166#2537—111no—
167#2075—112no—
168#2033—112no—
169#1990—111no—
170#1947D1111yescharacteristic, complemented
171#1893—112no—
172#1808—112no—
173C4×#102—111no—
174C23×C11C22×D411yescharacteristic
175C22×D11—22no—
176C22×D11—22no—
177C22×D11—22no—
178C22×D11—22no—
179C22×D11—22no—
180C22×D11—22no—
181C22×D11—22no—
182C22×D11—41no—
183C22×D11—41no—
184C22×D11—41no—
185C22×D11—41no—
186C22×D11—41no—
187C22×D11—41no—
188C22×D11C2×D814yes—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—42no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11#12112yes—
201C2×C4×C11#12112yes—
202C2×C4×C11C2×D812yes—
203C2×C4×C11#13512yes—
204C2×C4×C11C22×D411yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C2×C4×C11H(5,𝔽2)11yescharacteristic
209C2×C4×C112−1+411yescharacteristic
210C2×Dic11—22no—
211C2×Dic11—22no—
212C2×Dic11—22no—
213C2×Dic11—42no—
214C2×Dic11—41no—
215C2×Dic11—42no—
216C2×Dic11—41no—
217C2×Dic11—42no—
218C2×Dic11—41no—
219D44—22no—
220D44—22no—
221D44—28no—
222D44—41no—
223D44—41no—
224D44—88no—
225C4×D11—42no—
226C4×D11—42no—
227C4×D11—42no—
228C4×D11—42no—
229C4×D11—84no—
230Dic22—84no—
231C8×C11—24no—
232C11⋊C8—22no—
233C11⋊C8—41no—
234C23×C8—112no—
235C2×C4⋊Q8—111no—
236C2×#124—221no—
237C2×#121—112no—
238C2×#121—221no—
239C2×C4×D4—111no—
240C2×C4×D4—111no—
241#474—224no—
242C8×D4—224no—
243C2×#107—112no—
244C2×#107C2×D1112yes—
245C2×C4⋊C8C2×D1111yescharacteristic
246C2×#102—112no—
247C2×#102—111no—
248C2×#102—111no—
249C2×C22⋊C8—112no—
250C2×C4×C8—111no—
251#397—222no—
252#394—222no—
253#391—221no—
254#384C2×D1111yescharacteristic
255#380—112no—
256#380—112no—
257#380—112no—
258#380—221no—
259C4×C4⋊C4C2×D1111yescharacteristic
260#340—111no—
261#340—112no—
262#340—111no—
263#340—112no—
264#340C2×D1112yes—
265C22×C11C2×#12111yescharacteristic
266C22×C11#54611yescharacteristic
267C22×C11#54711yescharacteristic
268C22×C11C22×D811yescharacteristic
269C22×C11C2×#13511yescharacteristic
270C22×C11#57711yescharacteristic
271C22×C11#57811yescharacteristic
272C2×D11—24no—
273C2×D11—24no—
274C2×D11—24no—
275C2×D11—42no—
276C2×D11—42no—
277C2×D11—42no—
278C2×D11—42no—
279C2×D11—42no—
280C2×D11—42no—
281C2×D11—42no—
282C2×D11—81no—
283C2×D11—81no—
284C2×D11—81no—
285C2×D11—81no—
286C4×C11—22no—
287C4×C11—81no—
288C4×C11—81no—
289C4×C11—82no—
290C4×C11#46614yes—
291C4×C11#52911yescharacteristic
292C4×C11#54211yescharacteristic
293C4×C11#54611yescharacteristic
294C4×C11#54811yescharacteristic
295Dic11—42no—
296Dic11—82no—
297Dic11—81no—
298C22×Q8—221no—
299C22×D4—111no—
300C22×D4—111no—
301C22×D4—222no—
302C23×C4—112no—
303C23×C4—221no—
304C22×C8—111no—
305C22×C8—111no—
306C22×C8—224no—
307C22×C8—224no—
308C22×C8—442no—
309C22×C8C22×D1112yes—
310C4⋊Q8—222no—
311C4⋊Q8—222no—
312#124—444no—
313#121—224no—
314#121—442no—
315#121—444no—
316C4×D4—222no—
317C4×D4—222no—
318C4×D4—222no—
319C4×D4—222no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—111no—
323C2×C4⋊C4—111no—
324C2×C4⋊C4—112no—
325C2×C4⋊C4—221no—
326C2×C4⋊C4C22×D1112yes—
327C2×C4⋊C4C22×D1111yescharacteristic
328C2×C4⋊C4C22×D1111yescharacteristic
329C2×C22⋊C4—112no—
330C2×C22⋊C4—222no—
331C2×C22⋊C4—222no—
332C2×C22⋊C4—222no—
333C2×C22⋊C4—222no—
334C2×C22⋊C4—221no—
335C2×C42—21no—
336C2×C42C22×D1111yescharacteristic
337#107—42no—
338#107—224no—
339C4⋊C8D4414yescomplemented
340#102—222no—
341#102—222no—
342#102—224no—
343C22⋊C8—224no—
344C4×C8—222no—
345#95—21no—
346#95—222no—
347#95—222no—
348#95—222no—
349C2×C11#242711yescharacteristic
350C2×C11C2×#46611yescharacteristic
351C2×C11#306311yescharacteristic
352C2×C11#329411yescharacteristic
353C2×C11#330211yescharacteristic
354C2×C11#333411yescharacteristic
355C2×C11#334011yescharacteristic
356D11—44no—
357D11—82no—
358C24—112no—
359C24—221no—
360C2×Q8—442no—
361C2×Q8—442no—
362C2×Q8—442no—
363C2×D4—114no—
364C2×D4—112no—
365C2×D4—222no—
366C2×D4—222no—
367C2×D4—221no—
368C2×D4—221no—
369C2×D4—221no—
370C2×D4—221no—
371C2×D4—221no—
372C2×D4—444no—
373C2×D4—444no—
374C2×D4—882no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—112no—
379C22×C4—222no—
380C22×C4—222no—
381C22×C4—222no—
382C22×C4—222no—
383C22×C4—222no—
384C22×C4—222no—
385C22×C4—221no—
386C22×C4—222no—
387C22×C4—442no—
388C22×C4—442no—
389C22×C4—442no—
390C22×C4D4×D1111yescharacteristic
391C22×C4D4×D1111yescharacteristic
392C22×C4C23×D1111yescharacteristic
393C2×C8—22no—
394C2×C8—22no—
395C2×C8—112no—
396C2×C8—221no—
397C2×C8—221no—
398C2×C8—221no—
399C2×C8—221no—
400C2×C8—221no—
401C2×C8—448no—
402C2×C8C2×D4414yes—
403C4⋊C4—21no—
404C4⋊C4—22no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—22no—
409C4⋊C4—42no—
410C4⋊C4—81no—
411C4⋊C4—222no—
412C4⋊C4—222no—
413C4⋊C4—221no—
414C4⋊C4—221no—
415C4⋊C4—222no—
416C4⋊C4—442no—
417C22⋊C4—224no—
418C22⋊C4—444no—
419C22⋊C4—444no—
420C22⋊C4—444no—
421C22⋊C4—444no—
422C22⋊C4—442no—
423C42—42no—
424C42C2×D4412yes—
425C42#434312yes—
426C11#2533811yescharacteristic, complemented, Sylow
427C23—114no—
428C23—222no—
429C23—222no—
430C23—222no—
431C23—222no—
432C23—222no—
433C23—222no—
434C23—222no—
435C23—441no—
436C23—441no—
437C23—441no—
438C23—441no—
439C23—441no—
440C23—441no—
441C23C2×D4×D1111yescharacteristic
442Q8—884no—
443D4—228no—
444D4—222no—
445D4—222no—
446D4—441no—
447D4—441no—
448D4—888no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—222no—
461C2×C4—222no—
462C2×C4—222no—
463C2×C4—442no—
464C2×C4—442no—
465C2×C4—442no—
466C2×C4—442no—
467C2×C4—441no—
468C2×C4—442no—
469C2×C4—441no—
470C2×C4—442no—
471C2×C4—441no—
472C2×C4—442no—
473C2×C4—884no—
474C2×C4#6694812yes—
475C2×C4#6694812yes—
476C2×C4D8×D1112yes—
477C2×C4#6697212yes—
478C2×C4C22×D4411yescharacteristic
479C2×C4#6703711yescharacteristic
480C2×C4C2×#434311yescharacteristic
481C2×C4#6704011yescharacteristic
482C2×C4#41×D1111yescharacteristic
483C2×C4#41×D1111yescharacteristic
484C8—24no—
485C8—222no—
486C8—441no—
487C22—224no—
488C22—224no—
489C22—224no—
490C22—442no—
491C22—442no—
492C22—442no—
493C22—442no—
494C22—442no—
495C22—442no—
496C22—442no—
497C22—881no—
498C22—881no—
499C22—881no—
500C22—881no—
501C22C2×#6694811yescharacteristic
502C22#1062314311yescharacteristic
503C22#1062316211yescharacteristic
504C22C2×D8×D1111yescharacteristic
505C22C2×#6697211yescharacteristic
506C22#1062330611yescharacteristic
507C22#1062331011yescharacteristic
508C4—22no—
509C4—82no—
510C4—81no—
511C4—81no—
512C4—442no—
513C4—881no—
514C4—882no—
515C4#1062249614yes—
516C4#1062308511yescharacteristic
517C4#1062310711yescharacteristic
518C4#1062322211yescharacteristic
519C4#1062326411yescharacteristic
520C2—444no—
521C2—882no—
522C2#1307219111yescharacteristic
523C2C2×#1062249611yescharacteristic
524C2#1307830811yescharacteristic
525C2#1308043211yescharacteristic
526C2#1308053611yescharacteristic
527C2#1308096211yescharacteristic
528C2#1308103211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1947C2
socleC23×C11C22×D4
prime radical#13073532C2
hypercenter#1947D11
hypocenterC11#25338
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1947

Complements

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

NH ≅ G/Ntype
1. C2×#10622459C2semidirect
2. C2×#10622447C2semidirect
3. #13073611C2semidirect
5. #13070041C2semidirect
6. #13069800C2semidirect
7. #13069576C2semidirect
8. #13069043C2semidirect
9. #13068642C2semidirect
10. C4×#66873C2semidirect
11. C11×#1947C2semidirect
83. C11×C4⋊C8D4semidirect
170. #1947D11semidirect
339. C4⋊C8D44semidirect
426. C11#25338semidirect

Maximal subgroups

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

subgroupindex
C2×#106224592
C2×#106224472
#130736112
#130735322
#130700412
#130698002
#130695762
#130690432
#130686422
C4×#668732
C11×#19472
#2533811