Finite Group Databasebeta

← #14803887

Subgroups — #14803887

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×#10622700C211yesmaximal, characteristic, complemented
2C2×D4×C11⋊C8C211yesmaximal, characteristic, complemented
3#13073529C211yesmaximal, characteristic
4#13070042C212yesmaximal, complemented
5#13069798C212yesmaximal, complemented
6#13069578C211yesmaximal, characteristic, complemented
7#13069374C211yesmaximal, characteristic, complemented
8#13069042C212yesmaximal, complemented
9#13068643C212yesmaximal, complemented
10C4×#66873C211yesmaximal, characteristic, complemented
11C11×#2547C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×#124—21no—
14C2×C4×D4×C11C2211yescharacteristic
15C2×#66991—21no—
16C2×#66983C2212yes—
17C23×C11⋊C8C2212yes—
18C2×C4×D44C2211yescharacteristic
19C11×#397—22no—
20C11×#391—21no—
21C11×#380C2212yes—
22C11×#380C2212yes—
23C4×C11×C4⋊C4C2211yescharacteristic
24#10622825C2212yes—
25C2×C22⋊(C11⋊C8)C2212yes—
26#10622700—24no—
27D4×C11⋊C8—24no—
28#10622600—21no—
29C2×#66873C2212yes—
30C2×#66873C2211yescharacteristic
31C2×#66873C2211yescharacteristic
32C2×#66871C2212yes—
33C2×#66871C2212yes—
34#10622574—22no—
35#10622548C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43C22×Q8×C11—21no—
44C22×D4×C11D411yescharacteristic
45C23×C4×C11C2312yes—
46C22×C22⋊D11—22no—
47C22×D44C2311yescharacteristic
48C22×C4×D11—21no—
49C11×C4⋊Q8—22no—
50C11×C4⋊Q8—22no—
51C11×#124—44no—
52C4×D4×C11—22no—
53C4×D4×C11—22no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4D411yescharacteristic
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4D412yes—
62C2×C42×C11—21no—
63C2×C42×C11C2311yescharacteristic
64C2×C22⋊Dic11—22no—
65#66991—44no—
66#66983—24no—
67#66983—42no—
68C2×(C2×D11)⋊C4—21no—
69C2×(C2×D11)⋊C4—22no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11C2311yescharacteristic
73C2×C4⋊Dic11C2312yes—
74C22×C11⋊C8—24no—
75C22×C11⋊C8—24no—
76C22×C11⋊C8—42no—
77C22×C11⋊C8C2311yescharacteristic
78C22×C11⋊C8C2312yes—
79C22×C11⋊C8C2311yescharacteristic
80C4×D44—22no—
81C4×D44—22no—
82C11×#95—21no—
83C11×#95—22no—
84C11×#95—22no—
85C11⋊#95—22no—
86C22⋊(C11⋊C8)—24no—
87#66873—22no—
88#66873—24no—
89#66873—22no—
90#66871—24no—
91#66871—42no—
92C4⋊(C11⋊C8)D414yescomplemented
93C4×C11⋊C8—22no—
94#25338—111nomaximal, Sylow
95C24×C11C2×D412yes—
96C23×D11—21no—
97C2×Q8×C11—42no—
98C2×Q8×C11—42no—
99C2×Q8×C11—42no—
100C2×D4×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11D814yes—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2411yescharacteristic
116C2×C22⋊D11—44no—
117C2×C22⋊D11—44no—
118C2×C22⋊D11—82no—
119C22×Dic11—21no—
120C22×Dic11—22no—
121C2×D44—21no—
122C2×D44—21no—
123C2×D44—21no—
124C2×D44—21no—
125C2×D44—21no—
126C2×D44#4112yes—
127C2×C4×D11—42no—
128C2×C4×D11—42no—
129C2×C4×D11—42no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—42no—
138C11×C22⋊C4—24no—
139C11×C22⋊C4—44no—
140C11×C22⋊C4—44no—
141C42×C11—42no—
142C42×C11C2×D412yes—
143C42×C11#4112yes—
144C22⋊Dic11—44no—
145(C2×D11)⋊C4—44no—
146(C2×D11)⋊C4—42no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—22no—
150C4⋊Dic11—22no—
151C4⋊Dic11—42no—
152C4⋊Dic11—81no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—21no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—48no—
161C2×C11⋊C8C2×D414yes—
162C2×C11⋊C8#4112yes—
163C2×#474—111no—
164C2×C8×D4—111no—
165#2547D1111yescharacteristic, complemented
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—22no—
176C23×C11—22no—
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—22no—
180C23×C11C2×D814yes—
181C23×C11C22×D411yescharacteristic
182C22×D11—22no—
183C22×D11—41no—
184C22×D11—41no—
185C22×D11—41no—
186C22×D11—41no—
187C22×D11—41no—
188C22×D11—41no—
189Q8×C11—84no—
190D4×C11—28no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11#12112yes—
210C2×C4×C11#12112yes—
211C2×C4×C11C2×D812yes—
212C2×C4×C11#13512yes—
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×C4×C11H(5,𝔽2)11yescharacteristic
218C2×C4×C112−1+411yescharacteristic
219C22⋊D11—88no—
220C2×Dic11—41no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—42no—
226D44—22no—
227D44—22no—
228D44—41no—
229D44—41no—
230C4×D11—84no—
231C11⋊C8—22no—
232C11⋊C8—24no—
233C11⋊C8—41no—
234C23×C8—112no—
235C2×C4⋊Q8C2×D1111yescharacteristic
236C2×#124—21no—
237C2×#121—112no—
238C2×#121—221no—
239C2×C4×D4—111no—
240C2×C4×D4C2×D1111yescharacteristic
241#474—224no—
242C8×D4—224no—
243C2×#107—112no—
244C2×#107—112no—
245C2×C4⋊C8—111no—
246C2×#102—111no—
247C2×#102—112no—
248C2×#102—111no—
249C2×C22⋊C8—112no—
250C2×C4×C8—111no—
251#397—22no—
252#394—222no—
253#391—21no—
254#384—111no—
255#380—112no—
256#380—221no—
257#380C2×D1112yes—
258#380C2×D1112yes—
259C4×C4⋊C4C2×D1111yescharacteristic
260#340—111no—
261#340—112no—
262#340—111no—
263#340—112no—
264#340—112no—
265C22×C11—24no—
266C22×C11—24no—
267C22×C11—24no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11C2×#12111yescharacteristic
273C22×C11#54611yescharacteristic
274C22×C11#54711yescharacteristic
275C22×C11C22×D811yescharacteristic
276C22×C11C2×#13511yescharacteristic
277C22×C11#57711yescharacteristic
278C22×C11#57811yescharacteristic
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—42no—
288C4×C11—81no—
289C4×C11—81no—
290C4×C11—82no—
291C4×C11#46614yes—
292C4×C11#52911yescharacteristic
293C4×C11#54211yescharacteristic
294C4×C11#54611yescharacteristic
295C4×C11#54811yescharacteristic
296Dic11—82no—
297Dic11—81no—
298C22×Q8—21no—
299C22×D4—111no—
300C22×D4—222no—
301C22×D4C22⋊D1111yescharacteristic
302C23×C4—221no—
303C23×C4C22×D1112yes—
304C22×C8—111no—
305C22×C8—112no—
306C22×C8—111no—
307C22×C8—224no—
308C22×C8—224no—
309C22×C8—442no—
310C4⋊Q8—22no—
311C4⋊Q8—22no—
312#124—44no—
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—221no—
324C2×C4⋊C4—221no—
325C2×C4⋊C4C22⋊D1111yescharacteristic
326C2×C4⋊C4C22×D1112yes—
327C2×C4⋊C4C22×D1111yescharacteristic
328C2×C4⋊C4C22×D1111yescharacteristic
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—222no—
332C2×C22⋊C4—221no—
333C2×C22⋊C4—222no—
334C2×C22⋊C4C22⋊D1112yes—
335C2×C42—21no—
336C2×C42C22×D1111yescharacteristic
337#107—224no—
338#107—442no—
339C4⋊C8—114no—
340#102—222no—
341#102—224no—
342#102—222no—
343C22⋊C8—224no—
344C4×C8—222no—
345#95—21no—
346#95—22no—
347#95—22no—
348#95—222no—
349C2×C11—44no—
350C2×C11#242711yescharacteristic
351C2×C11C2×#46611yescharacteristic
352C2×C11#306311yescharacteristic
353C2×C11#329411yescharacteristic
354C2×C11#330211yescharacteristic
355C2×C11#333411yescharacteristic
356C2×C11#334011yescharacteristic
357D11—82no—
358C24—221no—
359C24C2×C22⋊D1112yes—
360C2×Q8—42no—
361C2×Q8—42no—
362C2×Q8—42no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—112no—
366C2×D4—221no—
367C2×D4—221no—
368C2×D4—221no—
369C2×D4—221no—
370C2×D4—221no—
371C2×D4—444no—
372C2×D4—444no—
373C2×D4—882no—
374C2×D4#432314yes—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—22no—
384C22×C4—221no—
385C22×C4—222no—
386C22×C4—442no—
387C22×C4—442no—
388C22×C4—442no—
389C22×C4C2×C22⋊D1112yes—
390C22×C4C2×C22⋊D1111yescharacteristic
391C22×C4C2×C22⋊D1111yescharacteristic
392C22×C4C23×D1111yescharacteristic
393C2×C8—114no—
394C2×C8—112no—
395C2×C8—221no—
396C2×C8—222no—
397C2×C8—222no—
398C2×C8—221no—
399C2×C8—221no—
400C2×C8—221no—
401C2×C8—221no—
402C2×C8—448no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—42no—
411C4⋊C4—221no—
412C4⋊C4—221no—
413C4⋊C4—222no—
414C4⋊C4—222no—
415C4⋊C4—442no—
416C4⋊C4—881no—
417C22⋊C4—24no—
418C22⋊C4—44no—
419C22⋊C4—44no—
420C22⋊C4—444no—
421C22⋊C4—444no—
422C22⋊C4—442no—
423C42—42no—
424C42D4×D1112yes—
425C42#434112yes—
426C11#2533811yescharacteristic, complemented, Sylow
427C23—22no—
428C23—22no—
429C23—22no—
430C23—22no—
431C23—22no—
432C23—22no—
433C23—222no—
434C23—441no—
435C23—441no—
436C23—441no—
437C23—441no—
438C23—441no—
439C23—441no—
440C23C2×#432314yes—
441C23C22×C22⋊D1111yescharacteristic
442Q8—84no—
443D4—28no—
444D4—222no—
445D4—222no—
446D4—441no—
447D4—441no—
448D4—888no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—441no—
468C2×C4—442no—
469C2×C4—441no—
470C2×C4—441no—
471C2×C4—442no—
472C2×C4—442no—
473C2×C4—884no—
474C2×C4C2×#432312yes—
475C2×C4#6699212yes—
476C2×C4#6699212yes—
477C2×C4#6700312yes—
478C2×C4C2×D4×D1111yescharacteristic
479C2×C4C2×#434111yescharacteristic
480C2×C4#41×D1111yescharacteristic
481C2×C4#41×D1111yescharacteristic
482C2×C4#6704211yescharacteristic
483C2×C4#6704311yescharacteristic
484C8—222no—
485C8—224no—
486C8—441no—
487C22—24no—
488C22—24no—
489C22—24no—
490C22—42no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—442no—
495C22—442no—
496C22—442no—
497C22—881no—
498C22—881no—
499C22—881no—
500C22—881no—
501C22C22×#432311yescharacteristic
502C22C2×#6699211yescharacteristic
503C22C2×#6700311yescharacteristic
504C22#1062335511yescharacteristic
505C22#1062336011yescharacteristic
506C22#1062336811yescharacteristic
507C22#1062336911yescharacteristic
508C4—22no—
509C4—42no—
510C4—81no—
511C4—81no—
512C4—82no—
513C4—882no—
514C4—881no—
515C4#1062265114yes—
516C4#1062320711yescharacteristic
517C4#1062320811yescharacteristic
518C4#1062321111yescharacteristic
519C4#1062321311yescharacteristic
520C2—44no—
521C2—882no—
522C2#1307219611yescharacteristic
523C2C2×#1062265111yescharacteristic
524C2#1307830311yescharacteristic
525C2#1308042311yescharacteristic
526C2#1308052711yescharacteristic
527C2#1308095911yescharacteristic
528C2#1308102311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2547C2
socleC23×C11C22×D4
prime radical#13073529C2
hypercenter#2547D11
hypocenterC11#25338
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2547

Complements

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

NH ≅ G/Ntype
1. C2×#10622700C2semidirect
2. C2×D4×C11⋊C8C2semidirect
4. #13070042C2semidirect
5. #13069798C2semidirect
6. #13069578C2semidirect
7. #13069374C2semidirect
8. #13069042C2semidirect
9. #13068643C2semidirect
10. C4×#66873C2semidirect
11. C11×#2547C2semidirect
92. C4⋊(C11⋊C8)D4semidirect
165. #2547D11semidirect
426. C11#25338semidirect

Maximal subgroups

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

subgroupindex
C2×#106227002
C2×D4×C11⋊C82
#130735292
#130700422
#130697982
#130695782
#130693742
#130690422
#130686432
C4×#668732
C11×#25472
#2533811