Finite Group Databasebeta

← #14760300

Subgroups — #14760300

Order 2816.

1066 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622770C211yesmaximal, characteristic
2C2×#10622302C211yesmaximal, characteristic, complemented
3#13071303C212yesmaximal, complemented
4#13069483C211yesmaximal, characteristic, complemented
5#13069347C211yesmaximal, characteristic, complemented
6#13069310C212yesmaximal, complemented
7#13069051C212yesmaximal, complemented
8#13068642C211yesmaximal, characteristic, complemented
9C4×#66882C211yesmaximal, characteristic, complemented
10#13068441C212yesmaximal, complemented
11C2×C4×C11×D8C211yesmaximal, characteristic, complemented
12C22×C11×D8C2211yescharacteristic
13C2×C4×D4×C11C2212yes—
14C2×#66991C2212yes—
15C22×#4313C2211yescharacteristic
16C22×C8×D11C2211yescharacteristic
17C2×#66925C2211yescharacteristic
18C4×C11×D8—24no—
19C2×C11×#107C2211yescharacteristic
20C2×C11×#102C2212yes—
21C2×C4×C8×C11C2211yescharacteristic
22#10622834C2212yes—
23C2×#66896C2212yes—
24C2×#66896C2212yes—
25#10622826—22no—
26#10622823—22no—
27#10622770C418yescomplemented
28C2×#66882C2211yescharacteristic
29C2×#66882C2211yescharacteristic
30C2×#66879C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32#10622600C2212yes—
33#10622586C2212yes—
34#10622570—22no—
35#10622558—22no—
36C4×C4⋊Dic11C2212yes—
37C2×#66867C2211yescharacteristic
38#10622302—24no—
39#10622189C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C22×D4×C11C2312yes—
43C23×C4×C11—22no—
44C22×C22⋊D11—22no—
45C22×C4×D11C2311yescharacteristic
46C2×C11×D8—22no—
47C2×C11×D8—22no—
48C2×C11×D8C2×C414yes—
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C4×D4×C11—24no—
52C4×D4×C11—24no—
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C22⋊C4—22no—
55C2×C42×C11C2311yescharacteristic
56C2×C22⋊Dic11—22no—
57C2×C22⋊Dic11—22no—
58C2×C22⋊Dic11—22no—
59#66991—24no—
60#66991C2×C418yescomplemented
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4D411yescharacteristic
63C2×(C2×D11)⋊C4D411yescharacteristic
64C2×C4⋊Dic11C2312yes—
65C2×C4⋊Dic11C2312yes—
66C2×Dic11⋊C4—22no—
67C2×Dic11⋊C4D411yescharacteristic
68C2×Dic11⋊C4D411yescharacteristic
69C2×C4×Dic11—22no—
70C2×C4×Dic11C2311yescharacteristic
71C22×C11⋊C8C2311yescharacteristic
72C22×C11⋊C8C2311yescharacteristic
73C2×#4313—22no—
74C2×#4313—22no—
75C2×#4313—22no—
76C2×C8×D11—22no—
77C2×C8×D11—22no—
78C2×C8×D11C2×C414yescomplemented
79#66925—22no—
80#66925—22no—
81C11×#107—22no—
82C11×#102—24no—
83C4×C8×C11D414yescomplemented
84#66896—24no—
85#66896C2×C418yescomplemented
86C11⋊#95—22no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89#66882—22no—
90#66882C2×C414yescomplemented
91#66879—22no—
92C8×Dic11—22no—
93#66867—22no—
94#21524—111nomaximal, Sylow
95C24×C11—22no—
96C23×D11C2×D411yescharacteristic
97C2×D4×C11—22no—
98C2×D4×C11—22no—
99C2×D4×C11—22no—
100C2×D4×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11C22×C414yes—
103C22×C4×C11—22no—
104C22×C4×C11—44no—
105C22×C4×C11—82no—
106C22×C4×C11—82no—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2411yescharacteristic
110C2×C22⋊D11—28no—
111C2×C22⋊D11—82no—
112C2×C22⋊D11—82no—
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11C2×D411yescharacteristic
116C22×Dic11C2×D411yescharacteristic
117C22×Dic11C2×D411yescharacteristic
118C2×C4×D11—21no—
119C2×C4×D11—21no—
120C2×C4×D11—21no—
121C2×C4×D11—21no—
122C2×C4×D11C22×C412yes—
123C2×C4×D11#4112yes—
124C11×D8—28no—
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11C22×C412yes—
128C2×C8×C11C2×D412yes—
129C2×C8×C11C2×D412yes—
130C2×C8×C11#4112yes—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C22⋊C4—44no—
134C42×C11C2×D412yes—
135C42×C11#4112yes—
136C22⋊Dic11—28no—
137C22⋊Dic11—82no—
138C22⋊Dic11—82no—
139(C2×D11)⋊C4—22no—
140(C2×D11)⋊C4—22no—
141(C2×D11)⋊C4—82no—
142C4⋊Dic11—22no—
143C4⋊Dic11—22no—
144C4⋊Dic11—22no—
145C4⋊Dic11C22×C414yes—
146Dic11⋊C4—22no—
147Dic11⋊C4—22no—
148Dic11⋊C4—82no—
149C4×Dic11—21no—
150C4×Dic11—21no—
151C4×Dic11—82no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8—21no—
156C2×C11⋊C8C22×C412yes—
157C2×C11⋊C8#4112yes—
158#4313—28no—
159C8×D11—28no—
160C2×#466—111no—
161C2×C4×D8D1111yescharacteristic, complemented
162C2×#405—111no—
163#2324—112no—
164#1970—111no—
165#1942—111no—
166#1936—112no—
167#1895—112no—
168#1808—111no—
169C4×#107—111no—
170#1762—112no—
171C23×C11—24no—
172C23×C11—42no—
173C23×C11—42no—
174C23×C11—42no—
175C23×C11—42no—
176C23×C11—42no—
177C23×C11—42no—
178C23×C11C22×D411yescharacteristic
179C22×D11—21no—
180C22×D11—21no—
181C22×D11—21no—
182C22×D11—21no—
183C22×D11—21no—
184C22×D11—21no—
185C22×D11C4×D412yes—
186D4×C11—24no—
187D4×C11—24no—
188D4×C11—42no—
189D4×C11—42no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—88no—
198C2×C4×C11#12112yes—
199C2×C4×C11#12112yes—
200C2×C4×C11C23×C411yescharacteristic
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C22⋊D11—88no—
207C2×Dic11—21no—
208C2×Dic11—21no—
209C2×Dic11—24no—
210C2×Dic11—21no—
211C2×Dic11—21no—
212C2×Dic11—21no—
213C2×Dic11—21no—
214C2×Dic11—21no—
215C2×Dic11—21no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11C4×D412yes—
222C4×D11—22no—
223C4×D11—22no—
224C4×D11—22no—
225C4×D11—22no—
226C8×C11—22no—
227C8×C11C4×D414yes—
228C11⋊C8—22no—
229C11⋊C8—22no—
230C22×D8C2×D1111yescharacteristic
231C22×M16—111no—
232C23×C8—111no—
233C2×#121—112no—
234C2×C4×D4C2×D1112yes—
235C2×#117—111no—
236#466—118no—
237C4×D8—24no—
238C2×#107—111no—
239C2×#107—111no—
240C2×#107C2×D1111yescharacteristic
241C2×#102—112no—
242C2×#102—112no—
243C2×#102C2×D1112yes—
244#405—224no—
245C2×#97—111no—
246C2×#97—111no—
247C2×C4×C8—111no—
248C2×C4×C8C2×D1111yescharacteristic
249#390—112no—
250#390—222no—
251#389—112no—
252#388—222no—
253#386—222no—
254#385—222no—
255#380—112no—
256C4×C4⋊C4—112no—
257#340—112no—
258#340—112no—
259#340—112no—
260C22×C11—44no—
261C22×C11—44no—
262C22×C11—44no—
263C22×C11—82no—
264C22×C11—82no—
265C22×C11—82no—
266C22×C11—82no—
267C22×C11C2×C4×D411yescharacteristic
268C22×C11C2×#12111yescharacteristic
269C22×C11#53211yescharacteristic
270C22×C11#57611yescharacteristic
271C22×C11#57611yescharacteristic
272C22×C11#57611yescharacteristic
273C22×C11#57811yescharacteristic
274C2×D11—22no—
275C2×D11—22no—
276C2×D11—22no—
277C2×D11—41no—
278C2×D11—41no—
279C2×D11—41no—
280C2×D11—41no—
281C4×C11—22no—
282C4×C11—22no—
283C4×C11—82no—
284C4×C11C2×C4×D411yescharacteristic
285C4×C11C4×#4111yescharacteristic
286C4×C11#52511yescharacteristic
287C4×C11#52911yescharacteristic
288Dic11—22no—
289Dic11—44no—
290Dic11—41no—
291Dic11—41no—
292Dic11—82no—
293C22×D4—222no—
294C22×D4C22×D1112yes—
295C23×C4—22no—
296C23×C4—111no—
297C2×D8—22no—
298C2×D8—22no—
299C2×D8C4×D1114yes—
300C2×M16—222no—
301C2×M16—222no—
302C2×M16—222no—
303C22×C8—111no—
304C22×C8—111no—
305C22×C8—114no—
306C22×C8—222no—
307C22×C8—222no—
308C22×C8C22×D1111yescharacteristic
309C22×C8C22×D1111yescharacteristic
310#121—118no—
311#121—224no—
312C4×D4—24no—
313C4×D4—24no—
314#117—222no—
315#117—222no—
316C2×C4⋊C4—112no—
317C2×C4⋊C4—111no—
318C2×C4⋊C4—111no—
319C2×C4⋊C4—112no—
320C2×C4⋊C4—222no—
321C2×C4⋊C4C22×D1112yes—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—111no—
324C2×C22⋊C4—111no—
325C2×C22⋊C4—222no—
326C2×C22⋊C4—222no—
327C2×C22⋊C4—222no—
328C2×C22⋊C4—222no—
329C2×C42—111no—
330C2×C42—222no—
331C2×C42C22×D1111yescharacteristic
332#107—22no—
333#107—114no—
334#107—222no—
335#102—24no—
336#102—118no—
337#102—224no—
338#97—222no—
339#97—222no—
340C4×C8—222no—
341C4×C8C22⋊D1114yescomplemented
342#95—222no—
343#95—222no—
344#95—222no—
345C2×C11—84no—
346C2×C11C4×#12111yescharacteristic
347C2×C11#294811yescharacteristic
348C2×C11#295111yescharacteristic
349C2×C11#305811yescharacteristic
350C2×C11#306111yescharacteristic
351C2×C11#317511yescharacteristic
352C2×C11#317611yescharacteristic
353D11—42no—
354C24—22no—
355C24—111no—
356C2×D4—22no—
357C2×D4—22no—
358C2×D4—22no—
359C2×D4—22no—
360C2×D4—22no—
361C2×D4—228no—
362C2×D4—882no—
363C2×D4—882no—
364C2×D4C2×C4×D1114yes—
365C22×C4—22no—
366C22×C4—44no—
367C22×C4—82no—
368C22×C4—82no—
369C22×C4—111no—
370C22×C4—112no—
371C22×C4—112no—
372C22×C4—111no—
373C22×C4—111no—
374C22×C4—221no—
375C22×C4—221no—
376C22×C4—221no—
377C22×C4—221no—
378C22×C4—222no—
379C22×C4—222no—
380C22×C4D4×D1111yescharacteristic
381C22×C4D4×D1111yescharacteristic
382C22×C4C23×D1111yescharacteristic
383D8—28no—
384M16—228no—
385C2×C8—21no—
386C2×C8—21no—
387C2×C8—112no—
388C2×C8—112no—
389C2×C8—221no—
390C2×C8—221no—
391C2×C8—221no—
392C2×C8—221no—
393C2×C8—228no—
394C2×C8C2×C4×D1112yes—
395C2×C8#433912yes—
396C2×C8C2×C22⋊D1112yes—
397C2×C8C2×C22⋊D1112yes—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—114no—
401C4⋊C4—222no—
402C4⋊C4—222no—
403C4⋊C4—222no—
404C4⋊C4—222no—
405C4⋊C4—222no—
406C4⋊C4—882no—
407C22⋊C4—44no—
408C22⋊C4—228no—
409C22⋊C4—222no—
410C22⋊C4—222no—
411C22⋊C4—882no—
412C22⋊C4—882no—
413C22⋊C4—882no—
414C42—221no—
415C42—221no—
416C42—882no—
417C42#434112yes—
418C42C2×C22⋊D1112yes—
419C11#2152411yescharacteristic, complemented, Sylow
420C23—24no—
421C23—42no—
422C23—42no—
423C23—42no—
424C23—42no—
425C23—42no—
426C23—42no—
427C23—112no—
428C23—221no—
429C23—221no—
430C23—221no—
431C23—221no—
432C23—221no—
433C23—221no—
434C23C2×D4×D1111yescharacteristic
435D4—24no—
436D4—24no—
437D4—42no—
438D4—42no—
439D4—888no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—88no—
448C2×C4—112no—
449C2×C4—221no—
450C2×C4—221no—
451C2×C4—222no—
452C2×C4—222no—
453C2×C4—222no—
454C2×C4—222no—
455C2×C4—221no—
456C2×C4—221no—
457C2×C4—221no—
458C2×C4—221no—
459C2×C4—224no—
460C2×C4—221no—
461C2×C4—221no—
462C2×C4—442no—
463C2×C4—442no—
464C2×C4—442no—
465C2×C4—442no—
466C2×C4—442no—
467C2×C4#6699112yes—
468C2×C4#6699112yes—
469C2×C4C22×C4×D1111yescharacteristic
470C2×C4C2×#433911yescharacteristic
471C2×C4C2×#434111yescharacteristic
472C2×C4#41×D1111yescharacteristic
473C2×C4#41×D1111yescharacteristic
474C2×C4C22×C22⋊D1111yescharacteristic
475C8—22no—
476C8—222no—
477C8—222no—
478C8C4×C22⋊D1114yes—
479C22—44no—
480C22—44no—
481C22—44no—
482C22—82no—
483C22—82no—
484C22—82no—
485C22—82no—
486C22—222no—
487C22—222no—
488C22—222no—
489C22—441no—
490C22—441no—
491C22—441no—
492C22—441no—
493C22C4×D4×D1111yescharacteristic
494C22#1062307911yescharacteristic
495C22#1062328811yescharacteristic
496C22#1062328811yescharacteristic
497C22#1062330011yescharacteristic
498C22#1062330211yescharacteristic
499C22C2×#6699111yescharacteristic
500C4—22no—
501C4—22no—
502C4—82no—
503C4—222no—
504C4—441no—
505C4—444no—
506C4—441no—
507C4—882no—
508C4C4×#434111yescharacteristic
509C4#1062308811yescharacteristic
510C4C2×C4×C22⋊D1111yescharacteristic
511C4#1062335911yescharacteristic
512C2—84no—
513C2—442no—
514C2C4×#6699111yescharacteristic
515C2#1307746311yescharacteristic
516C2#1307748611yescharacteristic
517C2#1307826011yescharacteristic
518C2#1307828211yescharacteristic
519C2#1307925111yescharacteristic
520C2#1307926211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C4×C11×D8C2
socleC23×C11C22×D4
prime radicalC2×#10622770C2
cosocleC22×C4×C11C24
hypercenterC2×C4×D8D11
hypocenterC11#21524
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
2. C2×#10622302C2semidirect
3. #13071303C2semidirect
4. #13069483C2semidirect
5. #13069347C2semidirect
6. #13069310C2semidirect
7. #13069051C2semidirect
8. #13068642C2semidirect
9. C4×#66882C2semidirect
10. #13068441C2semidirect
11. C2×C4×C11×D8C2semidirect
27. #10622770C4semidirect
60. #66991C2×C4semidirect
78. C2×C8×D11C2×C4semidirect
83. C4×C8×C11D4semidirect
85. #66896C2×C4semidirect
90. #66882C2×C4semidirect
161. C2×C4×D8D11semidirect
341. C4×C8C22⋊D11semidirect
419. C11#21524semidirect

Maximal subgroups

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

subgroupindex
C2×#106227702
C2×#106223022
#130713032
#130694832
#130693472
#130693102
#130690512
#130686422
C4×#668822
#130684412
C2×C4×C11×D82
#2152411