Finite Group Databasebeta

← #14656071

Subgroups — #14656071

Order 2816.

828 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622456C211yesmaximal, characteristic, complemented
2C2×#10622628C211yesmaximal, characteristic, complemented
3#13073529C211yesmaximal, characteristic, complemented
4#13069422C211yesmaximal, characteristic, complemented
5C2×#10622097C211yesmaximal, characteristic, complemented
6#13066500C211yesmaximal, characteristic, complemented
7C2×C11×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×C4×D4×C11C2211yescharacteristic
9C2×#66991—21no—
10C22×#4323—21no—
11C2×#66983—21no—
12C22×D88—21no—
13C2×#66927C2211yescharacteristic
14C2×C4×D44C2211yescharacteristic
15C2×C11×C4⋊C8C2211yescharacteristic
16C2×C4×C8×C11C2211yescharacteristic
17#10622825—21no—
18C2×#66885—21no—
19C2×#66885—22no—
20#10622628—22no—
21#10622628—22no—
22#10622600—21no—
23C2×#66873—21no—
24#10622574—22no—
25#10622548C2211yescharacteristic
26C2×C4⋊(C11⋊C8)C2211yescharacteristic
27#10622456—22no—
28#10622456—22no—
29C11×D4⋊C8—22no—
30#10622097—22no—
31C22×D4×C11D411yescharacteristic
32C23×C4×C11—21no—
33C22×C22⋊D11—22no—
34C22×D44—21no—
35C22×D44—21no—
36C22×D44—21no—
37C22×D44D411yescharacteristic
38C22×C4×D11—21no—
39C22×C8×C11—21no—
40C22×C8×C11—21no—
41C4×D4×C11—21no—
42C4×D4×C11—21no—
43C4×D4×C11—21no—
44C4×D4×C11—21no—
45C2×C11×C4⋊C4D411yescharacteristic
46C2×C11×C22⋊C4—21no—
47C2×C42×C11C2311yescharacteristic
48C2×C22⋊Dic11—22no—
49#66991—42no—
50#66991—42no—
51C2×#4323—24no—
52C2×#4323—42no—
53C2×#4323—42no—
54#66983—42no—
55#66983—42no—
56C2×(C2×D11)⋊C4—22no—
57C2×(C2×D11)⋊C4—21no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11D411yescharacteristic
61C2×C4⋊Dic11D412yes—
62C22×C11⋊C8—21no—
63C2×D88—24no—
64C2×D88—42no—
65C2×D88—42no—
66#66927—21no—
67#66927—21no—
68#66927—21no—
69#66927D412yescomplemented
70C4×D44—21no—
71C4×D44—21no—
72C4×D44—21no—
73C4×D44—21no—
74C11×C4⋊C8—21no—
75C11×C4⋊C8D412yescomplemented
76C4×C8×C11—21no—
77C4×C8×C11—21no—
78C11⋊#95—22no—
79#66885—24no—
80#66885—44no—
81#66873—24no—
82C4⋊(C11⋊C8)—21no—
83C4⋊(C11⋊C8)D412yescomplemented
84#10228—111nomaximal, Sylow
85C24×C11—21no—
86C23×D11—21no—
87C23×D11—41no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11D812yescomplemented
94C22×C4×C11—21no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C2×C22⋊D11—44no—
105C2×C22⋊D11—44no—
106C2×C22⋊D11—82no—
107C22×Dic11—21no—
108C22×Dic11—22no—
109C2×D44—21no—
110C2×D44—22no—
111C2×D44—22no—
112C2×D44—21no—
113C2×D44—22no—
114C2×D44—21no—
115C2×D44—21no—
116C2×D44—21no—
117C2×D44—42no—
118C2×D44—42no—
119C2×D44—41no—
120C2×D44—41no—
121C2×D44—41no—
122C2×D44—41no—
123C2×D44—41no—
124C2×D44—41no—
125C2×D44—41no—
126C2×D44—41no—
127C2×D44—41no—
128C2×D44—41no—
129C2×D44—41no—
130C2×D44D812yescomplemented
131C2×C4×D11—41no—
132C2×C4×D11—41no—
133C2×C4×D11—41no—
134C2×C4×D11—41no—
135C2×C4×D11—41no—
136C2×C4×D11—41no—
137C2×C8×C11—22no—
138C2×C8×C11—22no—
139C2×C8×C11—41no—
140C2×C8×C11—41no—
141C2×C8×C11—41no—
142C2×C8×C11—41no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C22⋊C4—41no—
146C11×C22⋊C4—41no—
147C42×C11C2×D411yescharacteristic
148C42×C11C2×D411yescharacteristic
149C42×C11C2×D411yescharacteristic
150C42×C11#4111yescharacteristic
151C22⋊Dic11—44no—
152#4323—48no—
153(C2×D11)⋊C4—44no—
154(C2×D11)⋊C4—41no—
155(C2×D11)⋊C4—41no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158C4⋊Dic11—42no—
159C4⋊Dic11—41no—
160C4⋊Dic11—41no—
161C4⋊Dic11—41no—
162C4⋊Dic11—41no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—41no—
165C2×C11⋊C8—41no—
166D88—48no—
167C2×#459—111no—
168C2×#459—111no—
169#2537—111no—
170#1957—111no—
171C2×D4⋊C8—111no—
172C2×D4⋊C8D1111yescharacteristic, complemented
173#1296—111no—
174C23×C11—22no—
175C23×C11—41no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11—41no—
181C23×C11#12011yescharacteristic
182C22×D11—22no—
183C22×D11—41no—
184C22×D11—41no—
185C22×D11—41no—
186C22×D11—41no—
187C22×D11—41no—
188C22×D11—41no—
189C22×D11—42no—
190C22×D11—81no—
191C22×D11—81no—
192C22×D11—81no—
193C22×D11—81no—
194C22×D11—81no—
195C22×D11—81no—
196D4×C11—22no—
197D4×C11—22no—
198D4×C11—41no—
199D4×C11—41no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—81no—
206C2×C4×C11—81no—
207C2×C4×C11—81no—
208C2×C4×C11—81no—
209C2×C4×C11#12011yescharacteristic
210C2×C4×C11#12011yescharacteristic
211C2×C4×C11#12111yescharacteristic
212C2×C4×C11#12111yescharacteristic
213C2×C4×C11#12111yescharacteristic
214C2×C4×C11#12711yescharacteristic
215C2×C4×C11C2×D811yescharacteristic
216C2×C4×C11C2×D811yescharacteristic
217C2×C4×C11#13511yescharacteristic
218C2×C4×C11#13511yescharacteristic
219C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
220C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
221C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
222C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
223C22⋊D11—88no—
224C2×Dic11—41no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229C2×Dic11—42no—
230D44—22no—
231D44—22no—
232D44—44no—
233D44—42no—
234D44—42no—
235D44—41no—
236D44—42no—
237D44—42no—
238D44—41no—
239D44—82no—
240D44—81no—
241D44—81no—
242D44—81no—
243D44—81no—
244C4×D11—81no—
245C4×D11—81no—
246C4×D11—81no—
247C4×D11—81no—
248C8×C11—42no—
249C8×C11—42no—
250C11⋊C8—42no—
251C22×D8—221no—
252C22×D8—221no—
253C2×#127—111no—
254C2×#121—221no—
255C2×#121—221no—
256C2×C4×D4—111no—
257C2×C4×D4C2×D1111yescharacteristic
258#459—222no—
259#459—222no—
260#459—222no—
261#459—222no—
262C2×C4⋊C8—111no—
263C2×C4⋊C8C2×D1111yescharacteristic
264C2×#102—221no—
265C2×#102—221no—
266C2×#102—222no—
267C2×C4×C8C2×D1111yescharacteristic
268#394—222no—
269#384—111no—
270#380—221no—
271#380—221no—
272D4⋊C8—22no—
273D4⋊C8—222no—
274C22×C11—42no—
275C22×C11—42no—
276C22×C11—42no—
277C22×C11—81no—
278C22×C11—81no—
279C22×C11—81no—
280C22×C11—81no—
281C22×C11#39211yescharacteristic
282C22×C11#44711yescharacteristic
283C22×C11#44711yescharacteristic
284C22×C11#44911yescharacteristic
285C22×C11#44911yescharacteristic
286C22×C11#45311yescharacteristic
287C22×C11#45411yescharacteristic
288C2×D11—42no—
289C2×D11—42no—
290C2×D11—42no—
291C2×D11—81no—
292C2×D11—81no—
293C2×D11—81no—
294C2×D11—81no—
295C2×D11—82no—
296C2×D11—82no—
297C2×D11—82no—
298C2×D11—161no—
299C2×D11—161no—
300C2×D11—161no—
301C2×D11—161no—
302C4×C11—21no—
303C4×C11—21no—
304C4×C11—81no—
305C4×C11#44711yescharacteristic
306C4×C11#44711yescharacteristic
307C4×C11#44911yescharacteristic
308C4×C11#44911yescharacteristic
309C4×C11#46611yescharacteristic
310C4×C11#46611yescharacteristic
311C4×C11#46911yescharacteristic
312C4×C11#46911yescharacteristic
313Dic11—82no—
314Dic11—81no—
315C22×D4—111no—
316C22×D4—222no—
317C22×D4—221no—
318C22×D4—221no—
319C22×D4—221no—
320C22×D4D4411yescharacteristic
321C23×C4—21no—
322C23×C4—221no—
323C2×D8—224no—
324C2×D8—224no—
325C2×D8—442no—
326C2×D8—442no—
327C2×D8—442no—
328C2×D8—442no—
329C22×C8—21no—
330C22×C8—21no—
331C22×C8—221no—
332#127—112no—
333#127—221no—
334#127—221no—
335#127—221no—
336#121—442no—
337#121—442no—
338#121—442no—
339#121—442no—
340C4×D4—21no—
341C4×D4—21no—
342C4×D4—21no—
343C4×D4—21no—
344C4×D4—221no—
345C4×D4—221no—
346C4×D4—221no—
347C4×D4—221no—
348C2×C4⋊C4—111no—
349C2×C4⋊C4—112no—
350C2×C4⋊C4—221no—
351C2×C4⋊C4—221no—
352C2×C4⋊C4D4411yescharacteristic
353C2×C22⋊C4—21no—
354C2×C22⋊C4—222no—
355C2×C22⋊C4—222no—
356C2×C22⋊C4—221no—
357C2×C42C22×D1111yescharacteristic
358C4⋊C8—21no—
359C4⋊C8—112no—
360C4⋊C8—221no—
361C4⋊C8C22⋊D1112yescomplemented
362#102—224no—
363#102—224no—
364#102—444no—
365C4×C8—21no—
366C4×C8—21no—
367#95—222no—
368C2×C11—82no—
369C2×C11#161911yescharacteristic
370C2×C11#162411yescharacteristic
371C2×C11#162511yescharacteristic
372C2×C11#162511yescharacteristic
373C2×C11#199911yescharacteristic
374C2×C11#199911yescharacteristic
375C2×C11#200611yescharacteristic
376D11—82no—
377D11—162no—
378C24—21no—
379C24—221no—
380C24—441no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—112no—
387C2×D4—222no—
388C2×D4—221no—
389C2×D4—222no—
390C2×D4—221no—
391C2×D4—221no—
392C2×D4—221no—
393C2×D4—221no—
394C2×D4—222no—
395C2×D4—442no—
396C2×D4—442no—
397C2×D4—444no—
398C2×D4—444no—
399C2×D4—441no—
400C2×D4—441no—
401C2×D4—441no—
402C2×D4—441no—
403C2×D4—441no—
404C2×D4—441no—
405C2×D4—441no—
406C2×D4—441no—
407C2×D4—441no—
408C2×D4—441no—
409C2×D4—441no—
410C2×D4—882no—
411C2×D4D8812yescomplemented
412C22×C4—21no—
413C22×C4—41no—
414C22×C4—41no—
415C22×C4—41no—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4—41no—
419C22×C4—221no—
420C22×C4—222no—
421C22×C4—441no—
422C22×C4—441no—
423C22×C4—441no—
424C22×C4—441no—
425C22×C4—441no—
426C22×C4—441no—
427C22×C4C2×D4411yescharacteristic
428C22×C4D4×D1111yescharacteristic
429C22×C4D4×D1111yescharacteristic
430D8—448no—
431D8—448no—
432C2×C8—22no—
433C2×C8—22no—
434C2×C8—41no—
435C2×C8—41no—
436C2×C8—41no—
437C2×C8—41no—
438C2×C8—222no—
439C2×C8—441no—
440C2×C8—441no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—221no—
444C4⋊C4—221no—
445C4⋊C4—442no—
446C4⋊C4—441no—
447C4⋊C4—441no—
448C4⋊C4—441no—
449C4⋊C4—441no—
450C22⋊C4—41no—
451C22⋊C4—41no—
452C22⋊C4—444no—
453C22⋊C4—444no—
454C22⋊C4—441no—
455C22⋊C4—441no—
456C42#433911yescharacteristic
457C42D4×D1111yescharacteristic
458C42D4×D1111yescharacteristic
459C42C2×C22⋊D1111yescharacteristic
460C11#1022811yescharacteristic, complemented, Sylow
461C23—22no—
462C23—41no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—222no—
469C23—441no—
470C23—441no—
471C23—441no—
472C23—441no—
473C23—441no—
474C23—441no—
475C23—442no—
476C23—881no—
477C23—881no—
478C23—881no—
479C23—881no—
480C23—881no—
481C23—881no—
482C23#6693511yescharacteristic
483D4—22no—
484D4—22no—
485D4—41no—
486D4—41no—
487D4—222no—
488D4—222no—
489D4—444no—
490D4—442no—
491D4—441no—
492D4—442no—
493D4—442no—
494D4—442no—
495D4—441no—
496D4—882no—
497D4—888no—
498D4—881no—
499D4—881no—
500D4—881no—
501D4—881no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—81no—
508C2×C4—81no—
509C2×C4—81no—
510C2×C4—81no—
511C2×C4—441no—
512C2×C4—441no—
513C2×C4—442no—
514C2×C4—441no—
515C2×C4—442no—
516C2×C4—442no—
517C2×C4—881no—
518C2×C4—881no—
519C2×C4—881no—
520C2×C4—881no—
521C2×C4#6693511yescharacteristic
522C2×C4#6693711yescharacteristic
523C2×C4#6693711yescharacteristic
524C2×C4C2×D8811yescharacteristic
525C2×C4#6695711yescharacteristic
526C2×C4#6696111yescharacteristic
527C2×C4#6696111yescharacteristic
528C2×C4D8×D1111yescharacteristic
529C2×C4#6696411yescharacteristic
530C2×C4#6696711yescharacteristic
531C2×C4#6696911yescharacteristic
532C2×C4#6698311yescharacteristic
533C2×C4#6699011yescharacteristic
534C2×C4#6699311yescharacteristic
535C8—42no—
536C8—42no—
537C8—442no—
538C22—42no—
539C22—42no—
540C22—42no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22—81no—
545C22—442no—
546C22—442no—
547C22—442no—
548C22—881no—
549C22—881no—
550C22—881no—
551C22—881no—
552C22—882no—
553C22—882no—
554C22—882no—
555C22—1761no—
556C22—1761no—
557C22—1761no—
558C22—1761no—
559C22#1062234511yescharacteristic
560C22#1062234711yescharacteristic
561C22#1062238611yescharacteristic
562C22#1062239411yescharacteristic
563C22#1062243511yescharacteristic
564C22#1062244011yescharacteristic
565C22#1062257311yescharacteristic
566C4—21no—
567C4—21no—
568C4—81no—
569C4—881no—
570C4—882no—
571C4#1062234511yescharacteristic
572C4#1062234711yescharacteristic
573C4#1062238811yescharacteristic
574C4#1062239511yescharacteristic
575C4#1062272811yescharacteristic
576C4#1062274811yescharacteristic
577C4#1062276911yescharacteristic
578C4#1062278511yescharacteristic
579C2—82no—
580C2—882no—
581C2—1762no—
582C2#1306767211yescharacteristic
583C2#1306770111yescharacteristic
584C2#1306770711yescharacteristic
585C2#1306770811yescharacteristic
586C2#1306961311yescharacteristic
587C2#1306961411yescharacteristic
588C2#1306965911yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×D4⋊C8C2
socleC23×C11#120
hypercenterC2×D4⋊C8D11
hypocenterC11#10228
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#10622456C2semidirect
2. C2×#10622628C2semidirect
3. #13073529C2semidirect
4. #13069422C2semidirect
5. C2×#10622097C2semidirect
6. #13066500C2semidirect
7. C2×C11×D4⋊C8C2semidirect
69. #66927D4semidirect
75. C11×C4⋊C8D4semidirect
83. C4⋊(C11⋊C8)D4semidirect
93. C2×D4×C11D8semidirect
130. C2×D44D8semidirect
172. C2×D4⋊C8D11semidirect
361. C4⋊C8C22⋊D11semidirect
411. C2×D4D88semidirect
460. C11#10228semidirect

Maximal subgroups

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

subgroupindex
C2×#106224562
C2×#106226282
#130735292
#130694222
C2×#106220972
#130665002
C2×C11×D4⋊C82
#1022811