Finite Group Databasebeta

← #14803880

Subgroups — #14803880

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×#10622447C211yesmaximal, characteristic, complemented
2#13073612C211yesmaximal, characteristic, complemented
3#13073529C211yesmaximal, characteristic
4#13070040C212yesmaximal, complemented
5#13069797C212yesmaximal, complemented
6#13069578C211yesmaximal, characteristic, complemented
7#13069375C211yesmaximal, characteristic, complemented
8#13069041C212yesmaximal, complemented
9#13068642C212yesmaximal, complemented
10C4×#66896C211yesmaximal, characteristic, complemented
11C2×C11×#474C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C2×#67000—21no—
15C2×#66991C2212yes—
16C2×#66983—21no—
17C22×C8×D11C2212yes—
18C2×C4×D44C2211yescharacteristic
19C11×#474—24no—
20C2×C11×#107C2212yes—
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#102C2212yes—
23#10622843—21no—
24C2×#66896C2211yescharacteristic
25C2×#66896C2211yescharacteristic
26#10622825—21no—
27C2×(C2×D11)⋊C8C2212yes—
28C2×#66882C2212yes—
29#10622606—22no—
30#10622600C2212yes—
31#10622600C2212yes—
32#10622600C2212yes—
33#10622574—22no—
34#10622548C2211yescharacteristic
35C4×C4⋊Dic11C2211yescharacteristic
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622447—24no—
38#10622189C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43C22×Q8×C11—21no—
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C22×C22⋊D11—22no—
47C22×D44D411yescharacteristic
48C22×C4×D11C2312yes—
49C22×C8×C11C2312yes—
50C11×C4⋊Q8—22no—
51C11×C4⋊Q8—22no—
52C4×D4×C11—22no—
53C4×D4×C11—22no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C22⋊C4—21no—
58C2×C42×C11C2311yescharacteristic
59C2×C22⋊Dic11—22no—
60#67000—44no—
61#66991—24no—
62#66991—42no—
63#66983—44no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4—22no—
67C2×(C2×D11)⋊C4D412yes—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11D411yescharacteristic
71C2×C4⋊Dic11C2311yescharacteristic
72C2×C4⋊Dic11C2311yescharacteristic
73C2×C4⋊Dic11C2312yes—
74C2×C4×Dic11—21no—
75C22×C11⋊C8C2311yescharacteristic
76C22×C11⋊C8C2311yescharacteristic
77C2×C8×D11—24no—
78C2×C8×D11—24no—
79C2×C8×D11—42no—
80C4×D44—22no—
81C4×D44—22no—
82C11×#107—24no—
83C11×C4⋊C8D414yescomplemented
84C11×#102—24no—
85#66896—22no—
86#66896—22no—
87C11⋊#95—21no—
88C11⋊#95—22no—
89C11⋊#95—22no—
90C11⋊#95—22no—
91(C2×D11)⋊C8—24no—
92#66882—42no—
93C4×C11⋊C8—22no—
94#25338—111nomaximal, Sylow
95C24×C11—21no—
96C23×D11C2×D412yes—
97C2×Q8×C11—42no—
98C2×Q8×C11—42no—
99C2×Q8×C11—42no—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11—21no—
103C2×D4×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11#4112yes—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11—42no—
109C22×C4×C11—42no—
110C22×C4×C11—42no—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2411yescharacteristic
114C2×C22⋊D11—44no—
115C2×C22⋊D11—44no—
116C2×C22⋊D11—82no—
117C22×Dic11—21no—
118C22×Dic11—21no—
119C22×Dic11—22no—
120C22×Dic11C2×D412yes—
121C2×D44—22no—
122C2×D44—22no—
123C2×D44D814yes—
124C2×C4×D11—22no—
125C2×C4×D11—22no—
126C2×C4×D11—22no—
127C2×C4×D11—22no—
128C2×C4×D11—22no—
129C2×C4×D11—22no—
130C2×C8×C11—22no—
131C2×C8×C11—22no—
132C2×C8×C11C2×D414yes—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—42no—
138C11×C22⋊C4—42no—
139C42×C11C2×D412yes—
140C42×C11#4112yes—
141C22⋊Dic11—44no—
142(C2×D11)⋊C4—24no—
143(C2×D11)⋊C4—44no—
144(C2×D11)⋊C4—44no—
145(C2×D11)⋊C4—44no—
146C4⋊Dic11—22no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—22no—
150C4⋊Dic11—21no—
151C4⋊Dic11—22no—
152C4⋊Dic11—21no—
153C4⋊Dic11—42no—
154C4⋊Dic11—81no—
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×#474D1111yescharacteristic, complemented
164C2×C8×D4—111no—
165#2547—111no—
166#2537—111no—
167#2075—112no—
168#2033—112no—
169#1990—111no—
170#1947—111no—
171#1893—112no—
172#1808—112no—
173C4×#102—111no—
174C23×C11—22no—
175C23×C11—41no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11—41no—
181C23×C11C22×D411yescharacteristic
182C22×D11—22no—
183C22×D11—22no—
184C22×D11—22no—
185C22×D11—22no—
186C22×D11—22no—
187C22×D11—22no—
188C22×D11C2×D814yes—
189Q8×C11—84no—
190D4×C11—22no—
191D4×C11—22no—
192D4×C11—41no—
193D4×C11—41no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—41no—
197C2×C4×C11—42no—
198C2×C4×C11—41no—
199C2×C4×C11—42no—
200C2×C4×C11—41no—
201C2×C4×C11—42no—
202C2×C4×C11—84no—
203C2×C4×C11#12112yes—
204C2×C4×C11#12112yes—
205C2×C4×C11C2×D812yes—
206C2×C4×C11#13512yes—
207C2×C4×C11C22×D411yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11C2×#4111yescharacteristic
210C2×C4×C11C2×#4111yescharacteristic
211C2×C4×C11H(5,𝔽2)11yescharacteristic
212C2×C4×C112−1+411yescharacteristic
213C22⋊D11—88no—
214C2×Dic11—22no—
215C2×Dic11—22no—
216C2×Dic11—22no—
217C2×Dic11—42no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226D44—28no—
227C4×D11—42no—
228C4×D11—42no—
229C4×D11—42no—
230C4×D11—42no—
231C8×C11—24no—
232C11⋊C8—22no—
233C11⋊C8—41no—
234C23×C8—112no—
235C2×C4⋊Q8C2×D1111yescharacteristic
236C2×#124—221no—
237C2×#121—112no—
238C2×#121—221no—
239C2×C4×D4—111no—
240C2×C4×D4C2×D1111yescharacteristic
241#474—24no—
242C8×D4—224no—
243C2×#107—112no—
244C2×#107C2×D1112yes—
245C2×C4⋊C8C2×D1111yescharacteristic
246C2×#102—111no—
247C2×#102—111no—
248C2×#102C2×D1112yes—
249C2×C22⋊C8—112no—
250C2×C4×C8—111no—
251#397—222no—
252#394—222no—
253#391—221no—
254#384—111no—
255#380—112no—
256#380—112no—
257#380—112no—
258#380—221no—
259C4×C4⋊C4—111no—
260#340—112no—
261#340—111no—
262#340—112no—
263#340—111no—
264#340—112no—
265C22×C11—42no—
266C22×C11—42no—
267C22×C11—42no—
268C22×C11—81no—
269C22×C11—81no—
270C22×C11—81no—
271C22×C11—81no—
272C22×C11C2×#12111yescharacteristic
273C22×C11#54611yescharacteristic
274C22×C11#54711yescharacteristic
275C22×C11C22×D811yescharacteristic
276C22×C11C2×#13511yescharacteristic
277C22×C11#57711yescharacteristic
278C22×C11#57811yescharacteristic
279C2×D11—24no—
280C2×D11—24no—
281C2×D11—24no—
282C2×D11—42no—
283C2×D11—42no—
284C2×D11—42no—
285C2×D11—42no—
286C4×C11—22no—
287C4×C11—81no—
288C4×C11—82no—
289C4×C11#46614yes—
290C4×C11#52911yescharacteristic
291C4×C11#54211yescharacteristic
292C4×C11#54611yescharacteristic
293C4×C11#54811yescharacteristic
294Dic11—42no—
295Dic11—81no—
296Dic11—81no—
297Dic11—82no—
298C22×Q8—21no—
299C22×D4—111no—
300C22×D4—222no—
301C22×D4C22×D1111yescharacteristic
302C23×C4—21no—
303C23×C4—112no—
304C22×C8—111no—
305C22×C8—111no—
306C22×C8—224no—
307C22×C8—224no—
308C22×C8—442no—
309C22×C8C22×D1112yes—
310C4⋊Q8—22no—
311C4⋊Q8—22no—
312#124—444no—
313#121—224no—
314#121—442no—
315#121—444no—
316C4×D4—22no—
317C4×D4—22no—
318C4×D4—222no—
319C4×D4—222no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—111no—
322C2×C4⋊C4—112no—
323C2×C4⋊C4—111no—
324C2×C4⋊C4—111no—
325C2×C4⋊C4—221no—
326C2×C4⋊C4—221no—
327C2×C4⋊C4C22×D1111yescharacteristic
328C2×C4⋊C4C22×D1112yes—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—112no—
331C2×C22⋊C4—222no—
332C2×C22⋊C4—222no—
333C2×C22⋊C4—222no—
334C2×C22⋊C4—222no—
335C2×C42—221no—
336C2×C42C22×D1111yescharacteristic
337#107—24no—
338#107—442no—
339C4⋊C8C22⋊D1114yescomplemented
340#102—24no—
341#102—222no—
342#102—222no—
343C22⋊C8—224no—
344C4×C8—222no—
345#95—222no—
346#95—222no—
347#95—222no—
348#95—221no—
349C2×C11—82no—
350C2×C11#242711yescharacteristic
351C2×C11C2×#46611yescharacteristic
352C2×C11#306311yescharacteristic
353C2×C11#329411yescharacteristic
354C2×C11#330211yescharacteristic
355C2×C11#333411yescharacteristic
356C2×C11#334011yescharacteristic
357D11—44no—
358C24—21no—
359C24—112no—
360C2×Q8—42no—
361C2×Q8—42no—
362C2×Q8—42no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—114no—
369C2×D4—222no—
370C2×D4—222no—
371C2×D4—444no—
372C2×D4—444no—
373C2×D4—882no—
374C2×D4#434312yes—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—42no—
378C22×C4—42no—
379C22×C4—42no—
380C22×C4—112no—
381C22×C4—222no—
382C22×C4—222no—
383C22×C4—222no—
384C22×C4—222no—
385C22×C4—222no—
386C22×C4—222no—
387C22×C4—221no—
388C22×C4—221no—
389C22×C4—222no—
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×C22⋊D1114yes—
403C4⋊C4—21no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—21no—
407C4⋊C4—42no—
408C4⋊C4—222no—
409C4⋊C4—221no—
410C4⋊C4—222no—
411C4⋊C4—221no—
412C4⋊C4—221no—
413C4⋊C4—221no—
414C4⋊C4—222no—
415C4⋊C4—442no—
416C4⋊C4—881no—
417C22⋊C4—42no—
418C22⋊C4—224no—
419C22⋊C4—444no—
420C22⋊C4—444no—
421C22⋊C4—444no—
422C22⋊C4—444no—
423C42—442no—
424C42#434112yes—
425C42C2×C22⋊D1112yes—
426C11#2533811yescharacteristic, complemented, Sylow
427C23—22no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—114no—
435C23—222no—
436C23—222no—
437C23—222no—
438C23—222no—
439C23—222no—
440C23—222no—
441C23C2×D4×D1111yescharacteristic
442Q8—84no—
443D4—22no—
444D4—22no—
445D4—41no—
446D4—41no—
447D4—228no—
448D4—888no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—41no—
452C2×C4—42no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—42no—
457C2×C4—84no—
458C2×C4—222no—
459C2×C4—222no—
460C2×C4—222no—
461C2×C4—442no—
462C2×C4—442no—
463C2×C4—442no—
464C2×C4—442no—
465C2×C4—441no—
466C2×C4—441no—
467C2×C4—442no—
468C2×C4—442no—
469C2×C4—441no—
470C2×C4—441no—
471C2×C4—442no—
472C2×C4—441no—
473C2×C4—441no—
474C2×C4D8×D1112yes—
475C2×C4#6696512yes—
476C2×C4#6699112yes—
477C2×C4#6699112yes—
478C2×C4C2×#434111yescharacteristic
479C2×C4C2×#434311yescharacteristic
480C2×C4#6704011yescharacteristic
481C2×C4#41×D1111yescharacteristic
482C2×C4#6704211yescharacteristic
483C2×C4C22×C22⋊D1111yescharacteristic
484C8—24no—
485C8—222no—
486C8—441no—
487C22—42no—
488C22—42no—
489C22—42no—
490C22—81no—
491C22—81no—
492C22—81no—
493C22—81no—
494C22—224no—
495C22—224no—
496C22—224no—
497C22—442no—
498C22—442no—
499C22—442no—
500C22—442no—
501C22#1062316111yescharacteristic
502C22#1062316211yescharacteristic
503C22C2×D8×D1111yescharacteristic
504C22C2×#6696511yescharacteristic
505C22#1062330911yescharacteristic
506C22#1062331011yescharacteristic
507C22C2×#6699111yescharacteristic
508C4—22no—
509C4—81no—
510C4—82no—
511C4—442no—
512C4—882no—
513C4—881no—
514C4—881no—
515C4#1062277014yes—
516C4#1062315511yescharacteristic
517C4#1062317411yescharacteristic
518C4#1062334811yescharacteristic
519C4#1062336011yescharacteristic
520C2—82no—
521C2—444no—
522C2#1307218911yescharacteristic
523C2C2×#1062277011yescharacteristic
524C2#1307830111yescharacteristic
525C2#1308042611yescharacteristic
526C2#1308053011yescharacteristic
527C2#1308096211yescharacteristic
528C2#1308102611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#474C2
socleC23×C11C22×D4
prime radical#13073529C2
hypercenterC2×#474D11
hypocenterC11#25338
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#10622447C2semidirect
2. #13073612C2semidirect
4. #13070040C2semidirect
5. #13069797C2semidirect
6. #13069578C2semidirect
7. #13069375C2semidirect
8. #13069041C2semidirect
9. #13068642C2semidirect
10. C4×#66896C2semidirect
11. C2×C11×#474C2semidirect
83. C11×C4⋊C8D4semidirect
163. C2×#474D11semidirect
339. C4⋊C8C22⋊D11semidirect
426. C11#25338semidirect

Maximal subgroups

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

subgroupindex
C2×#106224472
#130736122
#130735292
#130700402
#130697972
#130695782
#130693752
#130690412
#130686422
C4×#668962
C2×C11×#4742
#2533811