Finite Group Databasebeta

← #14780842

Subgroups — #14780842

Order 2816.

2094 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67003C212yesmaximal, complemented
2C2×#10623008C211yesmaximal, characteristic, complemented
3C2×#10622615C212yesmaximal, complemented
4#13069715C211yesmaximal, characteristic, complemented
5#13069709C212yesmaximal, complemented
6#13069703C211yesmaximal, characteristic, complemented
7#13069698C211yesmaximal, characteristic, complemented
8#13069692C212yesmaximal, complemented
9#13069686C211yesmaximal, characteristic, complemented
10C2×#10622162C211yesmaximal, characteristic, complemented
11C11×#2297C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C22×#4339C2212yes—
14C2×C11×#117C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C2×#67003—28no—
17C2×#67003—28no—
18C2×#67003—28no—
19C22×#4326C2212yes—
20C22×#4325C2212yes—
21C22×#4324C2212yes—
22C22×#4323C2212yes—
23C2×#66983—22no—
24C23×C11⋊C8C2212yes—
25#10623008—28no—
26C2×#66928C2212yes—
27C2×#66927C2211yescharacteristic
28C2×C4×D44—22no—
29C2×#66922C2211yescharacteristic
30C11×#391C2211yescharacteristic
31C11×#391C2211yescharacteristic
32C11×#390C2211yescharacteristic
33C11×#390C2211yescharacteristic
34C11×#386—22no—
35C4×C11×C22⋊C4—22no—
36#10622615—28no—
37C2×#66874C2212yes—
38C2×#66874C2212yes—
39C2×#66873C2212yes—
40C2×#66873C2212yes—
41#10622162C2211yescharacteristic
42#10622162C2212yes—
43#10622162C2211yescharacteristic
44C2×C11×#41—22no—
45C2×C11×#41—24no—
46C2×C11×#41—24no—
47C2×C11×#41D414yescomplemented
48C22×Q8×C11C2311yescharacteristic
49C22×D4×C11—21no—
50C22×D4×C11C2311yescharacteristic
51C23×C4×C11—21no—
52C23×C4×C11D412yes—
53C23×C4×C11C2311yescharacteristic
54C22×C22⋊D11—22no—
55C2×#4339—24no—
56C2×#4339—24no—
57C2×#4339—24no—
58C2×#4339—24no—
59C2×#4339—24no—
60C2×#4339D418yes—
61C22×D44—22no—
62C22×D44C2312yes—
63C22×C4×D11—22no—
64C22×Dic22C2312yes—
65C11×#117—24no—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—22no—
70C2×C11×C22⋊C4—22no—
71C2×C42×C11—24no—
72C2×C42×C11—21no—
73C2×C42×C11D412yes—
74C2×C42×C11C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76#67003—264no—
77C2×#4326—24no—
78C2×#4326—24no—
79C2×#4326—24no—
80C2×#4325—24no—
81C2×#4325—24no—
82C2×#4325—24no—
83C2×#4324—24no—
84C2×#4324—24no—
85C2×#4324—24no—
86C2×#4323—24no—
87C2×#4323—24no—
88C2×#4323—24no—
89#66983—216no—
90C2×(C2×D11)⋊C4—24no—
91C2×C4⋊Dic11—22no—
92C22×C11⋊C8—24no—
93C22×C11⋊C8—24no—
94C22×C11⋊C8D418yescomplemented
95C22×C11⋊C8C2312yes—
96C22×C11⋊C8C2312yes—
97#66928—24no—
98#66928—24no—
99#66927—24no—
100C4×D44—216no—
101#66922—24no—
102C11×#95—22no—
103C11×#95—22no—
104#66874—24no—
105#66874—24no—
106#66873—24no—
107#66873—24no—
108#23421—111nomaximal, Sylow
109C24×C11—21no—
110C24×C11C2×D411yescharacteristic
111C23×D11—22no—
112C11×#41—216no—
113C11×#41—48no—
114C2×Q8×C11—21no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11C2×D412yes—
118C2×D4×C11—24no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—21no—
122C2×D4×C11—42no—
123C2×D4×C11—42no—
124C2×D4×C11C2×D412yes—
125C22×C4×C11—24no—
126C22×C4×C11—21no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—42no—
132C22×C4×C11—42no—
133C22×C4×C11—42no—
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×D414yes—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D414yes—
140C22×C4×C11#4112yes—
141C22×C4×C11C2411yescharacteristic
142C2×C22⋊D11—28no—
143C2×C22⋊D11—44no—
144C2×C22⋊D11—44no—
145C22×Dic11—22no—
146#4339—216no—
147#4339—216no—
148#4339—48no—
149#4339—48no—
150C2×D44—28no—
151C2×D44—22no—
152C2×D44—22no—
153C2×D44—22no—
154C2×D44—22no—
155C2×D44—22no—
156C2×D44—44no—
157C2×D44—44no—
158C2×D44C2×D414yes—
159C2×C4×D11—28no—
160C2×C4×D11—44no—
161C2×C4×D11—44no—
162C2×Dic22—22no—
163C2×Dic22—22no—
164C2×Dic22—22no—
165C2×Dic22—22no—
166C2×Dic22—22no—
167C2×Dic22C2×D414yes—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—22no—
170C11×C22⋊C4—44no—
171C11×C22⋊C4—42no—
172C11×C22⋊C4—44no—
173C42×C11—24no—
174C42×C11—22no—
175C42×C11—22no—
176C42×C11—42no—
177#4326—216no—
178#4325—216no—
179#4324—216no—
180#4323—216no—
181(C2×D11)⋊C4—216no—
182C4⋊Dic11—28no—
183C2×C11⋊C8—216no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8C2×D414yes—
189C2×C11⋊C8C2×D414yes—
190C22×#135—112no—
191C2×#532—111no—
192C2×#416—112no—
193#2297D1111yescharacteristic, complemented
194#2016—111no—
195#2015—112no—
196#2014—111no—
197#2013—111no—
198#2012—112no—
199#2011—111no—
200C2×#336—111no—
201C23×C11—22no—
202C23×C11—22no—
203C23×C11—22no—
204C23×C11—41no—
205C23×C11—41no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11#12012yes—
209C23×C11#12112yes—
210C23×C11#12712yes—
211C23×C11C22×D411yescharacteristic
212C22×D11—24no—
213C22×D11—42no—
214C22×D11—42no—
215C22×D11—44no—
216C22×D11—44no—
217Q8×C11—24no—
218Q8×C11—42no—
219D4×C11—24no—
220D4×C11—48no—
221D4×C11—42no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—48no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—48no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11#12018yes—
237C2×C4×C11#12012yes—
238C2×C4×C11#12118yes—
239C2×C4×C11#12112yes—
240C2×C4×C11#12712yes—
241C2×C4×C11#13514yescomplemented
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C22×D412yes—
244C2×C4×C11C22×D412yes—
245C2×C4×C11C2×#4111yescharacteristic
246C22⋊D11—416no—
247C2×Dic11—24no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250D44—24no—
251D44—24no—
252D44—416no—
253D44—42no—
254D44—42no—
255C4×D11—416no—
256Dic22—24no—
257Dic22—24no—
258Dic22—42no—
259Dic22—42no—
260C11⋊C8—24no—
261C11⋊C8—24no—
262C22×#41—112no—
263C22×#41C2×D1111yescharacteristic
264C2×#135—228no—
265C2×#135—228no—
266C2×#135—228no—
267C22×Q16—112no—
268C22×SD16—112no—
269C22×SD16—112no—
270C22×D8—112no—
271C23×C8—112no—
272#532—228no—
273C2×C4⋊Q8—111no—
274C2×#127—111no—
275C2×#124—112no—
276C2×#121—222no—
277C2×C4×D4—222no—
278C2×#117C2×D1111yescharacteristic
279C22×C42C2×D1111yescharacteristic
280#416—228no—
281C2×#103—112no—
282C2×#103—112no—
283C2×#102—112no—
284C2×#102—112no—
285#391C2×D1111yescharacteristic
286#391C2×D1111yescharacteristic
287#390C2×D1111yescharacteristic
288#390C2×D1111yescharacteristic
289#386—22no—
290C4×C22⋊C4—22no—
291#336—111no—
292#336—112no—
293#336—111no—
294C22×C11—22no—
295C22×C11—22no—
296C22×C11—24no—
297C22×C11—24no—
298C22×C11—42no—
299C22×C11—44no—
300C22×C11—81no—
301C22×C11—81no—
302C22×C11—82no—
303C22×C11#39214yes—
304C22×C11C2×#12011yescharacteristic
305C22×C11C2×#12111yescharacteristic
306C22×C11C2×#12711yescharacteristic
307C22×C11C2×#13512yes—
308C22×C11#57512yes—
309C2×D11—44no—
310C2×D11—48no—
311C2×D11—82no—
312C2×D11—82no—
313C2×D11—84no—
314C4×C11—24no—
315C4×C11—42no—
316C4×C11—42no—
317C4×C11—81no—
318C4×C11—81no—
319C4×C11#39214yes—
320C4×C11C2×#12012yes—
321C4×C11C2×#12112yes—
322Dic11—44no—
323C2×#41—22no—
324C2×#41—24no—
325C2×#41—24no—
326C2×#41—118no—
327C2×#41—224no—
328C2×#41—224no—
329C2×#41—224no—
330C2×#41—224no—
331C2×#41—224no—
332C2×#41D4414yescomplemented
333C22×Q8—112no—
334C22×Q8C22×D1111yescharacteristic
335C22×D4—21no—
336C22×D4—112no—
337C22×D4—222no—
338C22×D4—222no—
339C22×D4C22×D1111yescharacteristic
340C23×C4—21no—
341C23×C4—222no—
342C23×C4C22⋊D1112yes—
343C23×C4C22×D1111yescharacteristic
344#135—2264no—
345C2×Q16—224no—
346C2×Q16—224no—
347C2×Q16—224no—
348C2×SD16—224no—
349C2×SD16—224no—
350C2×SD16—224no—
351C2×SD16—224no—
352C2×SD16—224no—
353C2×SD16—224no—
354C2×D8—224no—
355C2×D8—224no—
356C2×D8—224no—
357C22×C8—118no—
358C22×C8—112no—
359C22×C8—112no—
360C22×C8—224no—
361C22×C8—224no—
362C4⋊Q8—224no—
363#127—224no—
364#124—224no—
365#124—224no—
366#121—2216no—
367C4×D4—2216no—
368#117—24no—
369C2×C4⋊C4—222no—
370C2×C4⋊C4C22×D1111yescharacteristic
371C2×C4⋊C4C22×D1111yescharacteristic
372C2×C22⋊C4—21no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—224no—
376C2×C42—24no—
377C2×C42—21no—
378C2×C42C22⋊D1112yes—
379C2×C42C22×D1111yescharacteristic
380C2×C42C22×D1111yescharacteristic
381#103—224no—
382#103—224no—
383#102—224no—
384#102—224no—
385#95—22no—
386#95—22no—
387C2×C11—24no—
388C2×C11—82no—
389C2×C11C2×#39211yescharacteristic
390C2×C11#300212yes—
391C2×C11#303512yes—
392C2×C11#314711yescharacteristic
393C2×C11#315011yescharacteristic
394D11—84no—
395C24—21no—
396C24—222no—
397C24C2×C22⋊D1111yescharacteristic
398#41—216no—
399#41—48no—
400#41—2216no—
401#41—2216no—
402#41—448no—
403#41—448no—
404C2×Q8—21no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—114no—
408C2×Q8—222no—
409C2×Q8—222no—
410C2×Q8—222no—
411C2×Q8—222no—
412C2×Q8—222no—
413C2×Q8C2×D4412yes—
414C2×D4—24no—
415C2×D4—21no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—42no—
419C2×D4—42no—
420C2×D4—114no—
421C2×D4—228no—
422C2×D4—228no—
423C2×D4—222no—
424C2×D4—222no—
425C2×D4—222no—
426C2×D4—222no—
427C2×D4—222no—
428C2×D4—444no—
429C2×D4—444no—
430C2×D4—444no—
431C2×D4—444no—
432C2×D4C2×D4412yes—
433C22×C4—24no—
434C22×C4—21no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—222no—
443C22×C4—228no—
444C22×C4—444no—
445C22×C4—444no—
446C22×C4C2×D4412yes—
447C22×C4#433912yes—
448C22×C4D4×D1114yes—
449C22×C4D4×D1114yes—
450C22×C4C2×C22⋊D1112yes—
451C22×C4C2×C22⋊D1112yes—
452C22×C4C2×C22⋊D1111yescharacteristic
453C22×C4C23×D1111yescharacteristic
454Q16—2216no—
455SD16—2216no—
456SD16—2216no—
457D8—2216no—
458C2×C8—114no—
459C2×C8—114no—
460C2×C8—2216no—
461C2×C8—222no—
462C2×C8—222no—
463C2×C8—222no—
464C2×C8—222no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—228no—
468C22⋊C4—44no—
469C22⋊C4—42no—
470C22⋊C4—44no—
471C22⋊C4—2216no—
472C42—24no—
473C42—22no—
474C42—22no—
475C42—42no—
476C11#2342111yescharacteristic, complemented, Sylow
477C23—22no—
478C23—22no—
479C23—22no—
480C23—41no—
481C23—41no—
482C23—42no—
483C23—42no—
484C23—224no—
485C23—442no—
486C23—442no—
487C23—444no—
488C23—444no—
489C23#6698312yes—
490C23#6699012yes—
491C23#6699312yes—
492C23C22×C22⋊D1111yescharacteristic
493Q8—24no—
494Q8—42no—
495Q8—224no—
496Q8—224no—
497Q8—442no—
498Q8—442no—
499D4—24no—
500D4—48no—
501D4—42no—
502D4—224no—
503D4—224no—
504D4—4416no—
505D4—4416no—
506D4—442no—
507D4—442no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—48no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—48no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—224no—
523C2×C4—442no—
524C2×C4—442no—
525C2×C4—4416no—
526C2×C4#6693518yes—
527C2×C4#6693718yes—
528C2×C4#6698312yes—
529C2×C4#6699012yes—
530C2×C4#6699312yes—
531C2×C4#6700314yescomplemented
532C2×C4C22×D4411yescharacteristic
533C2×C4C2×#433911yescharacteristic
534C2×C4C2×D4×D1112yes—
535C2×C4C2×D4×D1112yes—
536C8—224no—
537C8—224no—
538C22—22no—
539C22—22no—
540C22—24no—
541C22—24no—
542C22—44no—
543C22—42no—
544C22—81no—
545C22—81no—
546C22—82no—
547C22—448no—
548C22—444no—
549C22—882no—
550C22—882no—
551C22—884no—
552C22#1062257314yes—
553C22C2×#6698311yescharacteristic
554C22C2×#6699011yescharacteristic
555C22C2×#6699311yescharacteristic
556C22C2×#6700312yes—
557C22#1062335312yes—
558C4—24no—
559C4—42no—
560C4—42no—
561C4—81no—
562C4—81no—
563C4—444no—
564C4#1062257314yes—
565C4C2×#6693512yes—
566C4C2×#6693712yes—
567C2—24no—
568C2—82no—
569C2—884no—
570C2C2×#1062257311yescharacteristic
571C2#1307783212yes—
572C2#1307807112yes—
573C2#1307904211yescharacteristic
574C2#1307906111yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2297C2
socleC23×C11C22×D4
hypercenter#2297D11
hypocenterC11#23421
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ #2297

Complements

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

NH ≅ G/Ntype
1. C22×#67003C2semidirect
2. C2×#10623008C2semidirect
3. C2×#10622615C2semidirect
4. #13069715C2semidirect
5. #13069709C2semidirect
6. #13069703C2semidirect
7. #13069698C2semidirect
8. #13069692C2semidirect
9. #13069686C2semidirect
10. C2×#10622162C2semidirect
11. C11×#2297C2semidirect
47. C2×C11×#41D4semidirect
94. C22×C11⋊C8D4semidirect
193. #2297D11semidirect
241. C2×C4×C11#135semidirect
332. C2×#41D44semidirect
476. C11#23421semidirect
531. C2×C4#67003semidirect

Maximal subgroups

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

subgroupindex
C22×#670032
C2×#106230082
C2×#106226152
#130697152
#130697092
#130697032
#130696982
#130696922
#130696862
C2×#106221622
C11×#22972
#2342111