Finite Group Databasebeta

← #14647839

Subgroups — #14647839

Order 2816.

658 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071316C211yesmaximal, characteristic
2#13068933C211yesmaximal, characteristic
3C2×#10622108C211yesmaximal, characteristic
4#13066875C211yesmaximal, characteristic, complemented
5#13066494C211yesmaximal, characteristic, complemented
6#13066458C211yesmaximal, characteristic, complemented
7C11×#1852C211yesmaximal, characteristic, complemented
8C22×C11×C4⋊C4C2211yescharacteristic
9C2×#66983C2211yescharacteristic
10C2×(C22⋊D11)⋊C4—21no—
11C2×C11×#107—21no—
12C2×C11×C22⋊C8C2211yescharacteristic
13C11×#380C2211yescharacteristic
14C2×C11⋊#95—21no—
15C2×C11⋊#95—21no—
16C2×C11⋊#95C2211yescharacteristic
17C2×C11⋊#95C2211yescharacteristic
18C2×C22⋊(C11⋊C8)C2211yescharacteristic
19#10622603—21no—
20#10622602—21no—
21C2×#66873—21no—
22#10622571—21no—
23#10622278—21no—
24#10622267—21no—
25C11×#340—21no—
26#10622167—21no—
27#10622108C414yescomplemented
28C23×C4×C11—21no—
29C23×C4×C11C2311yescharacteristic
30C22×C22⋊D11—21no—
31C23×Dic11—21no—
32C23×Dic11D411yescharacteristic
33C23×Dic11D411yescharacteristic
34C22×D44D411yescharacteristic
35C22×C4×D11—21no—
36C22×C8×C11—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—42no—
40C2×C11×C4⋊C4D411yescharacteristic
41C2×C11×C4⋊C4D411yescharacteristic
42C2×C11×C22⋊C4—21no—
43#66983—21no—
44#66983—21no—
45#66983C2×C412yes—
46#66983Q812yes—
47C2×(C2×D11)⋊C4—21no—
48C2×(C2×D11)⋊C4—21no—
49C2×(C2×D11)⋊C4—21no—
50C2×(C2×D11)⋊C4—21no—
51C2×C4⋊Dic11D411yescharacteristic
52C2×Dic11⋊C4—21no—
53C2×C4×Dic11—21no—
54C22×C11⋊C8—21no—
55(C22⋊D11)⋊C4—42no—
56(C22⋊D11)⋊C4—42no—
57C11×#107—42no—
58C11×C22⋊C8—21no—
59C11×C22⋊C8C2×C412yescomplemented
60C11×#95—21no—
61C11⋊#95—21no—
62C11⋊#95—21no—
63C11⋊#95—21no—
64C11⋊#95—21no—
65C11⋊#95—21no—
66C11⋊#95—42no—
67C11⋊#95—42no—
68C11⋊#95C2×C412yescomplemented
69C22⋊(C11⋊C8)—21no—
70C22⋊(C11⋊C8)—21no—
71#66873—42no—
72#8869—111nomaximal, Sylow
73C24×C11C2×D411yescharacteristic
74C23×D11—21no—
75C22×C4×C11—22no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—41no—
79C22×C4×C11—41no—
80C22×C4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11C22×C411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×Q811yescharacteristic
90C22×C4×C11#4111yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C2×C22⋊D11—22no—
93C2×C22⋊D11—22no—
94C2×C22⋊D11—41no—
95C2×C22⋊D11—41no—
96C2×C22⋊D11—41no—
97C2×C22⋊D11—41no—
98C22×Dic11—22no—
99C22×Dic11—21no—
100C22×Dic11—21no—
101C22×Dic11—21no—
102C22×Dic11—21no—
103C22×Dic11—21no—
104C22×Dic11—21no—
105C22×Dic11—41no—
106C22×Dic11—41no—
107C22×Dic11—41no—
108C22×Dic11—41no—
109C22×Dic11—41no—
110C22×Dic11—41no—
111C22×Dic11—41no—
112C22×Dic11—41no—
113C22×Dic11—41no—
114C22×Dic11—41no—
115C22×Dic11D812yes—
116C2×D44—21no—
117C2×D44—41no—
118C2×D44—41no—
119C2×D44C4⋊C412yes—
120C2×C4×D11—42no—
121C2×C4×D11—81no—
122C2×C4×D11—81no—
123C2×C8×C11—22no—
124C2×C8×C11—41no—
125C2×C8×C11—41no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—41no—
129C11×C4⋊C4—41no—
130C11×C4⋊C4—41no—
131C11×C4⋊C4—41no—
132C11×C22⋊C4—41no—
133C11×C22⋊C4—41no—
134(C2×D11)⋊C4—22no—
135(C2×D11)⋊C4—22no—
136(C2×D11)⋊C4—42no—
137(C2×D11)⋊C4—81no—
138(C2×D11)⋊C4—81no—
139C4⋊Dic11—21no—
140C4⋊Dic11C4⋊C412yes—
141Dic11⋊C4—42no—
142C4×Dic11—42no—
143C2×C11⋊C8—41no—
144C2×C11⋊C8—41no—
145C2×C11⋊C8—41no—
146#2325—111no—
147#1874—111no—
148#1852D1111yescharacteristic, complemented
149C2×#327—111no—
150#1442—111no—
151#1294—111no—
152#1280—111no—
153C23×C11—21no—
154C23×C11—21no—
155C23×C11—21no—
156C23×C11—21no—
157C23×C11C4×D411yescharacteristic
158C23×C11#12011yescharacteristic
159C23×C11C22⋊Q811yescharacteristic
160C23×C11C2×D811yescharacteristic
161C23×C11#13511yescharacteristic
162C23×C11AGL(1,ℤ/8)11yescharacteristic
163C23×C11#13711yescharacteristic
164C22×D11—22no—
165C22×D11—41no—
166C22×D11—41no—
167C22×D11—41no—
168C22×D11—41no—
169C22×D11—41no—
170C22×D11—41no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—42no—
187C2×C4×C11—41no—
188C2×C4×C11—81no—
189C2×C4×C11—81no—
190C2×C4×C11—81no—
191C2×C4×C11—81no—
192C2×C4×C11C2×C4⋊C411yescharacteristic
193C2×C4×C11C4×D411yescharacteristic
194C2×C4×C11C22⋊Q811yescharacteristic
195C2×C4×C11#12311yescharacteristic
196C22⋊D11—42no—
197C22⋊D11—42no—
198C22⋊D11—42no—
199C22⋊D11—42no—
200C2×Dic11—22no—
201C2×Dic11—22no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—81no—
215C2×Dic11—81no—
216C2×Dic11—81no—
217C2×Dic11—81no—
218C2×Dic11—81no—
219C2×Dic11—81no—
220D44—42no—
221D44—81no—
222C4×D11—84no—
223C8×C11—42no—
224C11⋊C8—81no—
225C2×#121—111no—
226C2×C4×D4—221no—
227C22×C4⋊C4C2×D1111yescharacteristic
228C2×#107—21no—
229C2×#102—221no—
230C2×C22⋊C8—111no—
231C2×C22⋊C8C2×D1111yescharacteristic
232#388—221no—
233#387—221no—
234#386—221no—
235#386—221no—
236#385—221no—
237#380C2×D1111yescharacteristic
238C2×#95—111no—
239C2×#95—111no—
240C2×#95—221no—
241C2×#95—221no—
242#340—21no—
243#340—221no—
244#327—114no—
245C22×C11—21no—
246C22×C11—21no—
247C22×C11—21no—
248C22×C11—21no—
249C22×C11—21no—
250C22×C11—21no—
251C22×C11—21no—
252C22×C11—21no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11#38511yescharacteristic
258C22×C11C4×D811yescharacteristic
259C22×C11#44011yescharacteristic
260C22×C11#44711yescharacteristic
261C22×C11#45211yescharacteristic
262C22×C11#45411yescharacteristic
263C22×C11#45511yescharacteristic
264C22×C11B(4,𝔽2)11yescharacteristic
265C22×C11#45811yescharacteristic
266C22×C11#47411yescharacteristic
267C22×C11#47811yescharacteristic
268C2×D11—42no—
269C2×D11—42no—
270C2×D11—42no—
271C2×D11—81no—
272C2×D11—81no—
273C2×D11—81no—
274C2×D11—81no—
275C4×C11—21no—
276C4×C11—21no—
277C4×C11—21no—
278C4×C11—21no—
279C4×C11—81no—
280C4×C11—82no—
281C4×C11—81no—
282Dic11—42no—
283Dic11—42no—
284Dic11—82no—
285Dic11—81no—
286C22×D4—111no—
287C22×D4—221no—
288C23×C4—21no—
289C23×C4—111no—
290C23×C4—111no—
291C23×C4—221no—
292C23×C4—221no—
293C23×C4C22×D1111yescharacteristic
294C22×C8—21no—
295C22×C8—221no—
296#121—112no—
297#121—112no—
298#121—221no—
299#121—221no—
300C4×D4—442no—
301C4×D4—442no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—111no—
306C2×C4⋊C4—221no—
307C2×C4⋊C4C22⋊D1111yescharacteristic
308C2×C4⋊C4C22⋊D1111yescharacteristic
309C2×C22⋊C4—21no—
310C2×C22⋊C4—221no—
311C2×C22⋊C4—221no—
312C2×C22⋊C4—221no—
313C2×C22⋊C4—221no—
314C2×C42—221no—
315#107—42no—
316#102—442no—
317C22⋊C8—21no—
318C22⋊C8—221no—
319C22⋊C8—221no—
320C22⋊C8C4×D1112yescomplemented
321#95—21no—
322#95—112no—
323#95—221no—
324#95—221no—
325#95—221no—
326#95—221no—
327#95—221no—
328#95—442no—
329#95—442no—
330C2×C11—21no—
331C2×C11—21no—
332C2×C11—21no—
333C2×C11—21no—
334C2×C11#159811yescharacteristic
335C2×C11#160611yescharacteristic
336C2×C11#160711yescharacteristic
337C2×C11#161511yescharacteristic
338C2×C11#186011yescharacteristic
339C2×C11#186211yescharacteristic
340C2×C11#186711yescharacteristic
341D11—82no—
342C24—221no—
343C24D4×D1111yescharacteristic
344C2×D4—112no—
345C2×D4—222no—
346C2×D4—222no—
347C2×D4—221no—
348C2×D4—441no—
349C2×D4—441no—
350C2×D4—441no—
351C2×D4—441no—
352C2×D4—441no—
353C2×D4—441no—
354C22×C4—22no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—112no—
366C22×C4—221no—
367C22×C4—221no—
368C22×C4—221no—
369C22×C4—222no—
370C22×C4—221no—
371C22×C4—221no—
372C22×C4—221no—
373C22×C4—442no—
374C22×C4—441no—
375C22×C4—441no—
376C22×C4—441no—
377C22×C4—441no—
378C22×C4—441no—
379C22×C4—441no—
380C22×C4—441no—
381C22×C4—441no—
382C22×C4—441no—
383C22×C4—441no—
384C22×C4—881no—
385C22×C4—881no—
386C22×C4C2×C4×D1111yescharacteristic
387C22×C4#433911yescharacteristic
388C22×C4D4×D1111yescharacteristic
389C22×C4Q8×D1111yescharacteristic
390C22×C4#434311yescharacteristic
391C22×C4C2×C22⋊D1111yescharacteristic
392C2×C8—22no—
393C2×C8—41no—
394C2×C8—41no—
395C2×C8—441no—
396C2×C8—441no—
397C2×C8—441no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—41no—
401C4⋊C4—41no—
402C4⋊C4—41no—
403C4⋊C4—41no—
404C4⋊C4—112no—
405C4⋊C4—221no—
406C4⋊C4—442no—
407C22⋊C4—41no—
408C22⋊C4—41no—
409C22⋊C4—222no—
410C22⋊C4—222no—
411C22⋊C4—442no—
412C22⋊C4—881no—
413C22⋊C4—881no—
414C42—442no—
415C11#886911yescharacteristic, complemented, Sylow
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—222no—
421C23—441no—
422C23—441no—
423C23—441no—
424C23—441no—
425C23—441no—
426C23—441no—
427C23#6694611yescharacteristic
428C23#6694911yescharacteristic
429C23D8×D1111yescharacteristic
430C23#6696411yescharacteristic
431C23#6697111yescharacteristic
432C23#6697211yescharacteristic
433C23#6699011yescharacteristic
434D4—442no—
435D4—442no—
436D4—442no—
437D4—442no—
438D4—442no—
439D4—881no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—41no—
457C2×C4—81no—
458C2×C4—81no—
459C2×C4—81no—
460C2×C4—81no—
461C2×C4—222no—
462C2×C4—222no—
463C2×C4—441no—
464C2×C4—441no—
465C2×C4—441no—
466C2×C4—441no—
467C2×C4—442no—
468C2×C4—442no—
469C2×C4—442no—
470C2×C4—442no—
471C2×C4—442no—
472C2×C4—441no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4—884no—
476C2×C4—881no—
477C2×C4—881no—
478C2×C4—881no—
479C2×C4—881no—
480C2×C4—881no—
481C2×C4—881no—
482C2×C4C4⋊C4×D1111yescharacteristic
483C2×C4#6694711yescharacteristic
484C2×C4C4×C22⋊D1111yescharacteristic
485C2×C4#6699911yescharacteristic
486C8—42no—
487C8—881no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—442no—
501C22—442no—
502C22—442no—
503C22—881no—
504C22—881no—
505C22—881no—
506C22—881no—
507C22#1062248511yescharacteristic
508C22#1062250211yescharacteristic
509C22#1062250311yescharacteristic
510C22#1062250411yescharacteristic
511C22#1062260211yescharacteristic
512C22#1062264511yescharacteristic
513C22#1062266611yescharacteristic
514C22#1062276911yescharacteristic
515C22#1062280011yescharacteristic
516C22#1062281411yescharacteristic
517C22#1062281511yescharacteristic
518C4—21no—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—82no—
523C4—81no—
524C4—81no—
525C4—442no—
526C4—442no—
527C4—882no—
528C4—881no—
529C2—21no—
530C2—21no—
531C2—21no—
532C2—21no—
533C2—882no—
534C2#1306754911yescharacteristic
535C2#1306759511yescharacteristic
536C2#1306760011yescharacteristic
537C2#1306764611yescharacteristic
538C2#1306884611yescharacteristic
539C2#1306886011yescharacteristic
540C2#1306889511yescharacteristic
subgroupG/H
centerC23#66990
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1852C2
socleC23×C11#120
prime radicalC2×#66983C22
cosocleC23×C4×C11C23
hypercenter#1852D11
hypocenterC11#8869
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1852

Complements

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

NH ≅ G/Ntype
4. #13066875C2semidirect
5. #13066494C2semidirect
6. #13066458C2semidirect
7. C11×#1852C2semidirect
27. #10622108C4semidirect
59. C11×C22⋊C8C2×C4semidirect
68. C11⋊#95C2×C4semidirect
148. #1852D11semidirect
320. C22⋊C8C4×D11semidirect
415. C11#8869semidirect

Maximal subgroups

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

subgroupindex
#130713162
#130689332
C2×#106221082
#130668752
#130664942
#130664582
C11×#18522
#886911