Finite Group Databasebeta

← #14645556

Subgroups — #14645556

Order 2816.

868 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068919C212yesmaximal, complemented
2#13068914C211yesmaximal, characteristic, complemented
3C4×#66898C211yesmaximal, characteristic, complemented
4#13067107C212yesmaximal, complemented
5C11×#3459C211yesmaximal, characteristic
6C11×#543C411yescharacteristic, complemented
7C11×#539—22no—
8C11×#539C412yescomplemented
9C11×#538—22no—
10C11×#538—21no—
11C11×#534—21no—
12C11×#534C411yescharacteristic, complemented
13C11×#529—22no—
14C11×#529—21no—
15C11×#525—22no—
16C11×#525C2212yes—
17C2×C4×D4×C11—21no—
18C2×C4×D4×C11C2211yescharacteristic
19C22×#4318C2211yescharacteristic, complemented
20C2×#66901—22no—
21C2×#66898—21no—
22C4×C22⋊Dic11C2212yescomplemented
23C2×C22⋊(C11⋊C8)—21no—
24C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
25#10622176—22no—
26#10622175—22no—
27#10622170—22no—
28#10622164—21no—
29#10622162—21no—
30C2×C11×#41D412yes—
31C22×D4×C11—21no—
32C22×D4×C11D411yescharacteristic
33C23×C4×C11—21no—
34C23×C4×C11D411yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C11×#126—22no—
37C11×#126—22no—
38C11×#126—22no—
39C11×#125—21no—
40C11×#125—22no—
41C11×#124—22no—
42C11×#124—21no—
43C11×#123—22no—
44C11×#123—22no—
45C11×#123—22no—
46C11×#123—22no—
47C11×#123—22no—
48C11×#123—22no—
49C11×C22⋊Q8—22no—
50C11×C22⋊Q8—22no—
51C11×C22⋊Q8—21no—
52C11×C22⋊Q8—22no—
53C11×C22⋊Q8C2×C412yes—
54C11×C22⋊Q8D412yes—
55C11×#121—22no—
56C11×#121—22no—
57C11×#121—22no—
58C11×#121—21no—
59C11×#121C2×C412yes—
60C11×#121D412yes—
61C11×#120—22no—
62C11×#120—22no—
63C11×#120—22no—
64C4×Q8×C11—21no—
65C4×D4×C11—22no—
66C4×D4×C11—22no—
67C4×D4×C11—21no—
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C4×D4×C11—22no—
71C4×D4×C11—22no—
72C4×D4×C11—22no—
73C11×#117—22no—
74C11×#117D412yes—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4C2×C411yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4C2×C411yescharacteristic
80C2×C11×C22⋊C4D411yescharacteristic
81C2×C42×C11—21no—
82C2×C42×C11D411yescharacteristic
83C2×C22⋊Dic11—22no—
84C2×C4×Dic11—22no—
85C2×#4318—22no—
86C2×#4318—42no—
87C22×C11⋊C8—21no—
88C22×C11⋊C8—21no—
89#66901—44no—
90#66898—24no—
91C11⋊#95—22no—
92C22⋊(C11⋊C8)—22no—
93C22⋊(C11⋊C8)—42no—
94#8399—111nomaximal, Sylow
95C24×C11—21no—
96C24×C11C22⋊C411yescharacteristic
97C24×C11C2×D411yescharacteristic
98C11×#41—42no—
99C11×#41—42no—
100C2×Q8×C11—21no—
101C2×Q8×C11C22⋊C412yes—
102C2×D4×C11—22no—
103C2×D4×C11—22no—
104C2×D4×C11—22no—
105C2×D4×C11—22no—
106C2×D4×C11—21no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—41no—
110C2×D4×C11—42no—
111C2×D4×C11—42no—
112C2×D4×C11C22⋊C412yes—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—22no—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11—21no—
120C22×C4×C11—41no—
121C22×C4×C11—41no—
122C22×C4×C11—41no—
123C22×C4×C11—41no—
124C22×C4×C11—81no—
125C22×C4×C11—81no—
126C22×C4×C11C22⋊C411yescharacteristic
127C22×C4×C11C22⋊C411yescharacteristic
128C22×C4×C11C22⋊C411yescharacteristic
129C22×C4×C11C22×C411yescharacteristic
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D412yes—
133C22×Dic11—42no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4C22⋊C412yes—
144C11×C4⋊C4C22⋊C412yes—
145C11×C22⋊C4—22no—
146C11×C22⋊C4—22no—
147C11×C22⋊C4—22no—
148C11×C22⋊C4—22no—
149C11×C22⋊C4—22no—
150C11×C22⋊C4—22no—
151C11×C22⋊C4—22no—
152C11×C22⋊C4—22no—
153C11×C22⋊C4—22no—
154C11×C22⋊C4—22no—
155C11×C22⋊C4—22no—
156C11×C22⋊C4—22no—
157C42×C11—22no—
158C42×C11—22no—
159C42×C11—21no—
160C42×C11—21no—
161C22⋊Dic11—24no—
162C22⋊Dic11—42no—
163C4×Dic11—42no—
164C4×Dic11—42no—
165#4318—24no—
166#4318—42no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—41no—
169C2×C11⋊C8—41no—
170C2×C11⋊C8—41no—
171C2×C11⋊C8—41no—
172C2×C11⋊C8—41no—
173#3459D1111yescharacteristic
174#1871—112no—
175#1870—111no—
176C4×#99—111no—
177#1501—112no—
178C23×C11—21no—
179C23×C11—21no—
180C23×C11—21no—
181C23×C11—21no—
182C23×C11—22no—
183C23×C11—41no—
184C23×C11—41no—
185C23×C11—41no—
186C23×C11—41no—
187C23×C11—42no—
188C23×C11—81no—
189C23×C11—81no—
190C23×C11#10412yescomplemented
191C23×C11C2×C22⋊C411yescharacteristic
192C23×C11#12012yes—
193Q8×C11—42no—
194Q8×C11—81no—
195D4×C11—42no—
196D4×C11—44no—
197D4×C11—44no—
198D4×C11—42no—
199D4×C11—42no—
200D4×C11—82no—
201D4×C11—82no—
202D4×C11—81no—
203C2×C4×C11—21no—
204C2×C4×C11—22no—
205C2×C4×C11—21no—
206C2×C4×C11—22no—
207C2×C4×C11—21no—
208C2×C4×C11—22no—
209C2×C4×C11—21no—
210C2×C4×C11—22no—
211C2×C4×C11—21no—
212C2×C4×C11—22no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—41no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—41no—
219C2×C4×C11—42no—
220C2×C4×C11—41no—
221C2×C4×C11—42no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—81no—
225C2×C4×C11—81no—
226C2×C4×C11—82no—
227C2×C4×C11—81no—
228C2×C4×C11C2×C22⋊C412yes—
229C2×C4×C11#12011yescharacteristic
230C2×C4×C11#12011yescharacteristic
231C2×Dic11—44no—
232C2×Dic11—82no—
233C2×Dic11—82no—
234C11⋊C8—42no—
235C11⋊C8—81no—
236C22×M16—111no—
237#543Dic1111yescharacteristic, complemented
238#539—22no—
239#539Dic1112yescomplemented
240#538—22no—
241#538—21no—
242#534—21no—
243#534Dic1111yescharacteristic, complemented
244#529—22no—
245#529—21no—
246#525—22no—
247#525C2×D1112yes—
248C2×C4×D4—21no—
249C2×C4×D4C2×D1111yescharacteristic
250C2×#104—222no—
251C2×#99—221no—
252C2×C22⋊C8—111no—
253C2×C22⋊C8—221no—
254C4×C22⋊C4—112no—
255#342—221no—
256#339—222no—
257#336—221no—
258#328—222no—
259#327—222no—
260C22×C11—21no—
261C22×C11—21no—
262C22×C11—22no—
263C22×C11—22no—
264C22×C11—22no—
265C22×C11—22no—
266C22×C11—42no—
267C22×C11—41no—
268C22×C11—41no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11—81no—
273C22×C11—81no—
274C22×C11—81no—
275C22×C11—84no—
276C22×C11#37911yescharacteristic
277C22×C11C2×#10411yescharacteristic
278C22×C11#42111yescharacteristic
279C4×C11—21no—
280C4×C11—22no—
281C4×C11—41no—
282C4×C11—42no—
283C4×C11—41no—
284C4×C11—42no—
285C4×C11—41no—
286C4×C11—42no—
287C4×C11B(4,𝔽2)11yescharacteristic
288C4×C11#45811yescharacteristic
289Dic11—84no—
290C2×#41C22⋊D1112yes—
291C22×D4—21no—
292C22×D4C22⋊D1111yescharacteristic
293C23×C4—21no—
294C23×C4C22⋊D1111yescharacteristic
295C23×C4C22×D1111yescharacteristic
296C2×M16—222no—
297C2×M16—442no—
298C22×C8—221no—
299C22×C8—221no—
300#126—22no—
301#126—22no—
302#126—22no—
303#125—21no—
304#125—22no—
305#124—22no—
306#124—21no—
307#123—22no—
308#123—22no—
309#123—22no—
310#123—22no—
311#123—22no—
312#123—22no—
313C22⋊Q8—22no—
314C22⋊Q8—22no—
315C22⋊Q8—21no—
316C22⋊Q8—22no—
317C22⋊Q8C2×Dic1112yes—
318C22⋊Q8C22⋊D1112yes—
319#121—22no—
320#121—22no—
321#121—22no—
322#121—21no—
323#121C2×Dic1112yes—
324#121C22⋊D1112yes—
325#120—22no—
326#120—22no—
327#120—22no—
328C4×Q8—21no—
329C4×D4—22no—
330C4×D4—22no—
331C4×D4—21no—
332C4×D4—22no—
333C4×D4—22no—
334C4×D4—22no—
335C4×D4—22no—
336C4×D4—22no—
337#117—22no—
338#117C22⋊D1112yes—
339C2×C4⋊C4—21no—
340C2×C4⋊C4C2×Dic1111yescharacteristic
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—222no—
344C2×C22⋊C4C2×Dic1111yescharacteristic
345C2×C22⋊C4C22⋊D1111yescharacteristic
346C2×C42—21no—
347C2×C42—222no—
348C2×C42C22⋊D1111yescharacteristic
349#104—444no—
350#99—224no—
351C22⋊C8—222no—
352C22⋊C8—442no—
353#95—222no—
354C2×C11—21no—
355C2×C11—21no—
356C2×C11—42no—
357C2×C11—42no—
358C2×C11—82no—
359C2×C11#178911yescharacteristic
360C2×C11#179011yescharacteristic
361C2×C11#179411yescharacteristic
362C24—21no—
363C24C22⋊Dic1111yescharacteristic
364C24C2×C22⋊D1111yescharacteristic
365#41—42no—
366#41—42no—
367C2×Q8—21no—
368C2×Q8C22⋊Dic1112yes—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—21no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—41no—
377C2×D4—42no—
378C2×D4—42no—
379C2×D4C22⋊Dic1112yes—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—21no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—81no—
392C22×C4—81no—
393C22×C4—442no—
394C22×C4C22⋊Dic1111yescharacteristic
395C22×C4C22⋊Dic1111yescharacteristic
396C22×C4C22⋊Dic1111yescharacteristic
397C22×C4C22×Dic1111yescharacteristic
398C22×C4C2×C22⋊D1112yes—
399C22×C4C2×C22⋊D1111yescharacteristic
400C22×C4C2×C22⋊D1112yes—
401M16—224no—
402M16—442no—
403C2×C8—222no—
404C2×C8—441no—
405C2×C8—441no—
406C2×C8—441no—
407C2×C8—441no—
408C2×C8—441no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4C22⋊Dic1112yes—
419C4⋊C4C22⋊Dic1112yes—
420C22⋊C4—22no—
421C22⋊C4—22no—
422C22⋊C4—22no—
423C22⋊C4—22no—
424C22⋊C4—22no—
425C22⋊C4—22no—
426C22⋊C4—22no—
427C22⋊C4—22no—
428C22⋊C4—22no—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C22⋊C4—224no—
433C22⋊C4—442no—
434C42—22no—
435C42—21no—
436C42—22no—
437C42—21no—
438C42—442no—
439C42—442no—
440C11#839911yescharacteristic, complemented, Sylow
441C23—21no—
442C23—21no—
443C23—21no—
444C23—21no—
445C23—22no—
446C23—41no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—42no—
451C23—81no—
452C23—81no—
453C23#6690112yescomplemented
454C23C2×C22⋊Dic1111yescharacteristic
455C23#6700612yes—
456Q8—42no—
457Q8—81no—
458D4—42no—
459D4—44no—
460D4—44no—
461D4—42no—
462D4—42no—
463D4—82no—
464D4—82no—
465D4—81no—
466C2×C4—22no—
467C2×C4—21no—
468C2×C4—22no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—22no—
474C2×C4—21no—
475C2×C4—22no—
476C2×C4—21no—
477C2×C4—22no—
478C2×C4—41no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—41no—
482C2×C4—42no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—81no—
488C2×C4—81no—
489C2×C4—82no—
490C2×C4—81no—
491C2×C4—444no—
492C2×C4—882no—
493C2×C4—882no—
494C2×C4C2×C22⋊Dic1112yes—
495C2×C4#6700611yescharacteristic
496C2×C4#6700611yescharacteristic
497C8—442no—
498C8—881no—
499C22—21no—
500C22—21no—
501C22—22no—
502C22—22no—
503C22—22no—
504C22—22no—
505C22—42no—
506C22—41no—
507C22—41no—
508C22—42no—
509C22—42no—
510C22—42no—
511C22—81no—
512C22—81no—
513C22—81no—
514C22—84no—
515C22C2×#6690111yescharacteristic
516C22#1062284911yescharacteristic
517C22#1062286011yescharacteristic
518C4—21no—
519C4—22no—
520C4—41no—
521C4—42no—
522C4—41no—
523C4—42no—
524C4—41no—
525C4—42no—
526C4—884no—
527C4#1062285611yescharacteristic
528C4#1062285711yescharacteristic
529C2—21no—
530C2—21no—
531C2—42no—
532C2—42no—
533C2—82no—
534C2#1306856011yescharacteristic
535C2#1306856411yescharacteristic
536C2#1306858011yescharacteristic
subgroupG/H
centerC2×C4#67006
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
Fitting, prime radicalC11×#3459C2
socleC22×C11#379
cosocleC23×C4×C11C23
hypercenter#3459D11
hypocenterC11#8399
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3459

Complements

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

NH ≅ G/Ntype
1. #13068919C2semidirect
2. #13068914C2semidirect
3. C4×#66898C2semidirect
4. #13067107C2semidirect
6. C11×#543C4semidirect
8. C11×#539C4semidirect
12. C11×#534C4semidirect
19. C22×#4318C22semidirect
22. C4×C22⋊Dic11C22semidirect
24. C2×C22⋊(C11⋊C8)C22semidirect
190. C23×C11#104semidirect
237. #543Dic11semidirect
239. #539Dic11semidirect
243. #534Dic11semidirect
440. C11#8399semidirect
453. C23#66901semidirect

Maximal subgroups

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

subgroupindex
#130689192
#130689142
C4×#668982
#130671072
C11×#34592
#839911