Finite Group Databasebeta

← #14660450

Subgroups — #14660450

Order 2816.

1430 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623041C211yesmaximal, characteristic
2C22×#66869C212yesmaximal, complemented
3C2×#10622579C212yesmaximal, complemented
4C2×#10622168C211yesmaximal, characteristic, complemented
5C11×C4⋊#95C211yesmaximal, characteristic, complemented
6C22×#4339C2212yes—
7C22×C11×C4⋊C4C2211yescharacteristic
8C22×C11×C4⋊C4C2211yescharacteristic
9C22×C42×C11C2211yescharacteristic
10C2×#66983—22no—
11C22×#4318C2212yes—
12#10623041—24no—
13#10623041—22no—
14#10623041C414yescomplemented
15C2×#66950—22no—
16C2×#66948—22no—
17C2×C11×#95—22no—
18C2×#66874—22no—
19#10622579—24no—
20#10622579—24no—
21C2×#66873—22no—
22C2×#66869—24no—
23C2×#66869—24no—
24C2×#66869—24no—
25#10622168—22no—
26C23×C4×C11—21no—
27C23×C4×C11—21no—
28C23×C4×C11D412yes—
29C23×C4×C11C2311yescharacteristic
30C22×C22⋊D11—22no—
31C2×#4339—22no—
32C2×#4339—22no—
33C2×#4339—22no—
34C2×#4339—22no—
35C2×#4339—22no—
36C2×#4339—22no—
37C2×#4339—22no—
38C2×#4339—22no—
39C2×#4339—22no—
40C2×#4339—22no—
41C2×#4339C2×C414yes—
42C2×#4339D414yes—
43C22×D44—22no—
44C22×D44D412yes—
45C22×C4×D11—22no—
46C22×Dic22D412yes—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4C2×C412yes—
53C2×C11×C4⋊C4D412yes—
54C2×C11×C4⋊C4D412yescomplemented
55C2×C42×C11—22no—
56C2×C42×C11—22no—
57C2×C42×C11—21no—
58C2×C42×C11D412yescomplemented
59#66983—28no—
60#66983—28no—
61C2×(C2×D11)⋊C4—24no—
62C2×C4⋊Dic11—22no—
63C2×#4318—22no—
64C2×#4318—22no—
65C2×#4318—22no—
66C2×#4318—22no—
67C2×#4318—22no—
68C2×#4318D414yescomplemented
69C22×C11⋊C8—22no—
70#66950—28no—
71#66950—28no—
72#66948—28no—
73#66948—28no—
74C11×#95—44no—
75#66874—28no—
76#66873—28no—
77#66869—216no—
78#11002—111nomaximal, Sylow
79C24×C11C2×D411yescharacteristic
80C23×D11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11—42no—
92C22×C4×C11—42no—
93C22×C4×C11—42no—
94C22×C4×C11—42no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11C22⋊C414yes—
98C22×C4×C11C22×C411yescharacteristic
99C22×C4×C11C2×D412yes—
100C22×C4×C11C2×D412yes—
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11#4112yes—
106C22×C4×C11#4111yescharacteristic
107C22×C4×C11#4111yescharacteristic
108C2×C22⋊D11—24no—
109C2×C22⋊D11—24no—
110C2×C22⋊D11—42no—
111C2×C22⋊D11—42no—
112C2×C22⋊D11—42no—
113C2×C22⋊D11—42no—
114C22×Dic11—22no—
115#4339—24no—
116#4339—24no—
117#4339—24no—
118#4339—24no—
119#4339—24no—
120#4339—24no—
121#4339—24no—
122#4339—24no—
123#4339—42no—
124#4339—42no—
125#4339—42no—
126#4339—42no—
127#4339—42no—
128#4339—42no—
129#4339—42no—
130#4339—42no—
131C2×D44—28no—
132C2×D44—22no—
133C2×D44—22no—
134C2×D44—22no—
135C2×D44—22no—
136C2×D44—22no—
137C2×D44—82no—
138C2×D44—82no—
139C2×D44C22⋊C414yes—
140C2×C4×D11—24no—
141C2×C4×D11—24no—
142C2×C4×D11—42no—
143C2×C4×D11—42no—
144C2×C4×D11—42no—
145C2×C4×D11—42no—
146C2×Dic22—22no—
147C2×Dic22—22no—
148C2×Dic22—22no—
149C2×Dic22—22no—
150C2×Dic22—22no—
151C2×Dic22C22⋊C414yes—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—42no—
156C42×C11—24no—
157C42×C11—42no—
158(C2×D11)⋊C4—216no—
159C4⋊Dic11—28no—
160#4318—24no—
161#4318—24no—
162#4318—42no—
163#4318—42no—
164C2×C11⋊C8—24no—
165C2×C11⋊C8—42no—
166C2×C11⋊C8—42no—
167C2×#537—111no—
168C22×#104—112no—
169C2×#417—112no—
170C2×#343—111no—
171C4⋊#95D1111yescharacteristic, complemented
172C23×C11—21no—
173C23×C11—21no—
174C23×C11—21no—
175C23×C11—21no—
176C23×C11C2×C22⋊C411yescharacteristic
177C23×C11#12011yescharacteristic
178C23×C11#12011yescharacteristic
179C23×C11#12111yescharacteristic
180C23×C11#12111yescharacteristic
181C23×C11#12411yescharacteristic
182C23×C11#12711yescharacteristic
183C22×D11—24no—
184C22×D11—42no—
185C22×D11—42no—
186C22×D11—42no—
187C22×D11—42no—
188C22×D11—42no—
189C22×D11—42no—
190C2×C4×C11—24no—
191C2×C4×C11—24no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—44no—
201C2×C4×C11—44no—
202C2×C4×C11—42no—
203C2×C4×C11—82no—
204C2×C4×C11—82no—
205C2×C4×C11—81no—
206C2×C4×C11—81no—
207C2×C4×C11C2×C22⋊C412yes—
208C2×C4×C11C4×D411yescharacteristic
209C2×C4×C11C4×D411yescharacteristic
210C2×C4×C11C4×D412yes—
211C2×C4×C11#12012yes—
212C2×C4×C11#12012yes—
213C2×C4×C11#12012yes—
214C2×C4×C11#12112yes—
215C2×C4×C11#12112yes—
216C2×C4×C11#12112yes—
217C2×C4×C11#12112yes—
218C2×C4×C11#12112yes—
219C2×C4×C11#12312yes—
220C2×C4×C11#12312yes—
221C2×C4×C11#12411yescharacteristic
222C2×C4×C11#12711yescharacteristic
223C22⋊D11—44no—
224C22⋊D11—44no—
225C22⋊D11—44no—
226C22⋊D11—44no—
227C2×Dic11—24no—
228C2×Dic11—42no—
229C2×Dic11—42no—
230D44—24no—
231D44—24no—
232D44—42no—
233D44—42no—
234D44—88no—
235C4×D11—44no—
236C4×D11—44no—
237C4×D11—44no—
238C4×D11—44no—
239Dic22—24no—
240Dic22—24no—
241Dic22—42no—
242Dic22—42no—
243C11⋊C8—44no—
244C22×#41—112no—
245C22×M16—112no—
246#537—114no—
247#537—224no—
248#537—222no—
249C2×C22⋊Q8—222no—
250C2×#121—222no—
251C2×#121—222no—
252C22×C4⋊C4C2×D1111yescharacteristic
253C22×C4⋊C4C2×D1111yescharacteristic
254C22×C42C2×D1111yescharacteristic
255C2×#104—224no—
256C2×#104—224no—
257C2×#104—224no—
258#417—224no—
259#417—224no—
260C2×#103—222no—
261C2×#102—222no—
262C2×#95—22no—
263#343—222no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11—21no—
267C22×C11—21no—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—21no—
271C22×C11—21no—
272C22×C11—21no—
273C22×C11—21no—
274C22×C11—21no—
275C22×C11—21no—
276C22×C11#37911yescharacteristic
277C22×C11#39011yescharacteristic
278C22×C11#39011yescharacteristic
279C22×C11#39211yescharacteristic
280C22×C11#39211yescharacteristic
281C22×C11#39411yescharacteristic
282C22×C11#39411yescharacteristic
283C22×C11#45311yescharacteristic
284C22×C11#45411yescharacteristic
285C22×C11#45511yescharacteristic
286C22×C11#45611yescharacteristic
287C2×D11—44no—
288C2×D11—44no—
289C2×D11—44no—
290C2×D11—82no—
291C2×D11—82no—
292C2×D11—82no—
293C2×D11—82no—
294C4×C11—44no—
295C4×C11—44no—
296C4×C11—82no—
297C4×C11#38612yes—
298C4×C11#38612yes—
299C4×C11#39212yes—
300C4×C11#39412yes—
301Dic11—44no—
302C2×#41—114no—
303C2×#41—114no—
304C2×#41—222no—
305C2×#41—222no—
306C2×#41—222no—
307C2×#41—222no—
308C2×#41—222no—
309C2×#41—222no—
310C2×#41—222no—
311C2×#41—222no—
312C2×#41—222no—
313C2×#41—222no—
314C22×Q8—112no—
315C22×D4—112no—
316C22×D4—222no—
317C22×D4—222no—
318C23×C4—21no—
319C23×C4—21no—
320C23×C4—222no—
321C23×C4C22⋊D1112yes—
322C23×C4C22×D1111yescharacteristic
323C2×M16—114no—
324C2×M16—222no—
325C2×M16—222no—
326C2×M16—222no—
327C2×M16—222no—
328C2×M16—222no—
329C22×C8—222no—
330C22⋊Q8—228no—
331C22⋊Q8—228no—
332#121—228no—
333#121—228no—
334#121—228no—
335#121—228no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—222no—
342C2×C4⋊C4C4×D1112yes—
343C2×C4⋊C4D4412yes—
344C2×C4⋊C4D4412yescomplemented
345C2×C22⋊C4—224no—
346C2×C42—22no—
347C2×C42—22no—
348C2×C42—21no—
349C2×C42D4412yescomplemented
350#104—2216no—
351#103—228no—
352#102—228no—
353#95—44no—
354C2×C11—21no—
355C2×C11—21no—
356C2×C11—21no—
357C2×C11—21no—
358C2×C11#143811yescharacteristic
359C2×C11#179211yescharacteristic
360C2×C11#179311yescharacteristic
361C2×C11#200611yescharacteristic
362C2×C11#200711yescharacteristic
363C2×C11#203911yescharacteristic
364C2×C11#204011yescharacteristic
365D11—84no—
366C24—222no—
367C24C2×C22⋊D1111yescharacteristic
368#41—224no—
369#41—224no—
370#41—224no—
371#41—224no—
372#41—224no—
373#41—224no—
374#41—224no—
375#41—224no—
376#41—442no—
377#41—442no—
378#41—442no—
379#41—442no—
380#41—442no—
381#41—442no—
382#41—442no—
383#41—442no—
384C2×Q8—114no—
385C2×Q8—222no—
386C2×Q8—222no—
387C2×Q8—222no—
388C2×Q8—222no—
389C2×Q8—222no—
390C2×D4—114no—
391C2×D4—228no—
392C2×D4—224no—
393C2×D4—224no—
394C2×D4—222no—
395C2×D4—222no—
396C2×D4—222no—
397C2×D4—222no—
398C2×D4—222no—
399C2×D4—442no—
400C2×D4—442no—
401C2×D4—442no—
402C2×D4—442no—
403C2×D4—882no—
404C2×D4—882no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—41no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—222no—
422C22×C4—224no—
423C22×C4—224no—
424C22×C4—442no—
425C22×C4—442no—
426C22×C4—442no—
427C22×C4—442no—
428C22×C4(C2×D11)⋊C414yes—
429C22×C4C2×C4×D1111yescharacteristic
430C22×C4C2×D4411yescharacteristic
431C22×C4C2×D4411yescharacteristic
432C22×C4C2×D4411yescharacteristic
433C22×C4#433911yescharacteristic
434C22×C4#433911yescharacteristic
435C22×C4D4×D1112yes—
436C22×C4D4×D1112yes—
437C22×C4D4×D1112yes—
438C22×C4#434312yes—
439M16—224no—
440M16—224no—
441M16—442no—
442M16—442no—
443C2×C8—224no—
444C2×C8—442no—
445C2×C8—442no—
446C4⋊C4—24no—
447C4⋊C4—24no—
448C4⋊C4—24no—
449C4⋊C4—42no—
450C4⋊C4—228no—
451C22⋊C4—2216no—
452C42—24no—
453C42—42no—
454C11#1100211yescharacteristic, complemented, Sylow
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—224no—
460C23—442no—
461C23—442no—
462C23—442no—
463C23—442no—
464C23—442no—
465C23—442no—
466C23C2×(C2×D11)⋊C411yescharacteristic
467C23#6698311yescharacteristic
468C23#6698311yescharacteristic
469C23#6699011yescharacteristic
470C23#6699011yescharacteristic
471C23#6699311yescharacteristic
472C23#6700011yescharacteristic
473Q8—224no—
474Q8—224no—
475Q8—442no—
476Q8—442no—
477D4—224no—
478D4—224no—
479D4—444no—
480D4—444no—
481D4—444no—
482D4—444no—
483D4—442no—
484D4—442no—
485D4—888no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—44no—
497C2×C4—44no—
498C2×C4—42no—
499C2×C4—82no—
500C2×C4—82no—
501C2×C4—81no—
502C2×C4—81no—
503C2×C4—224no—
504C2×C4—442no—
505C2×C4—442no—
506C2×C4—444no—
507C2×C4—444no—
508C2×C4—444no—
509C2×C4—444no—
510C2×C4C4×D4411yescharacteristic
511C2×C4C4×D4411yescharacteristic
512C2×C4#6692711yescharacteristic
513C2×C4#6692811yescharacteristic
514C2×C4C22⋊C4×D1112yes—
515C2×C4#6693512yes—
516C2×C4#6693512yes—
517C2×C4#6693512yes—
518C2×C4#6693712yes—
519C2×C4#6693712yes—
520C2×C4#6694612yes—
521C2×C4#6694712yes—
522C2×C4#6694712yes—
523C2×C4#6694812yes—
524C2×C4#6694812yes—
525C2×C4#6694812yes—
526C8—444no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—444no—
540C22—444no—
541C22—444no—
542C22—882no—
543C22—882no—
544C22—882no—
545C22—882no—
546C22#1062255211yescharacteristic
547C22#1062256811yescharacteristic
548C22#1062257311yescharacteristic
549C22#1062257311yescharacteristic
550C22#1062260111yescharacteristic
551C22#1062260411yescharacteristic
552C22#1062260411yescharacteristic
553C22#1062267411yescharacteristic
554C22#1062267511yescharacteristic
555C22#1062269011yescharacteristic
556C22#1062270811yescharacteristic
557C4—44no—
558C4—44no—
559C4—82no—
560C4—444no—
561C4#1062227812yes—
562C4#1062227812yes—
563C4#1062228412yes—
564C4#1062228512yes—
565C2—21no—
566C2—21no—
567C2—21no—
568C2—21no—
569C2—884no—
570C2#1306685611yescharacteristic
571C2#1306856911yescharacteristic
572C2#1306857411yescharacteristic
573C2#1306965711yescharacteristic
574C2#1306966211yescharacteristic
575C2#1306984011yescharacteristic
576C2#1306984511yescharacteristic
subgroupG/H
centerC23#66990
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×C4⋊#95C2
socleC23×C11#120
prime radicalC2×#10623041C2
cosocleC23×C4×C11C23
hypercenterC4⋊#95D11
hypocenterC11#11002
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C22×#66869C2semidirect
3. C2×#10622579C2semidirect
4. C2×#10622168C2semidirect
5. C11×C4⋊#95C2semidirect
14. #10623041C4semidirect
54. C2×C11×C4⋊C4D4semidirect
58. C2×C42×C11D4semidirect
68. C2×#4318D4semidirect
171. C4⋊#95D11semidirect
344. C2×C4⋊C4D44semidirect
349. C2×C42D44semidirect
454. C11#11002semidirect

Maximal subgroups

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

subgroupindex
C2×#106230412
C22×#668692
C2×#106225792
C2×#106221682
C11×C4⋊#952
#1100211