Finite Group Databasebeta

← #14774178

Subgroups — #14774178

Order 2816.

1274 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622389C211yesmaximal, characteristic
2C2×#10622631C211yesmaximal, characteristic, complemented
3C2×#10622383C211yesmaximal, characteristic
4#13071642C211yesmaximal, characteristic, complemented
5D4×(C2×D11)⋊C4C211yesmaximal, characteristic
6#13069468C211yesmaximal, characteristic, complemented
7#13069312C211yesmaximal, characteristic, complemented
8#13069234C211yesmaximal, characteristic, complemented
9#13069048C211yesmaximal, characteristic, complemented
10#13068970C211yesmaximal, characteristic, complemented
11#13068948C211yesmaximal, characteristic, complemented
12#13068814C211yesmaximal, characteristic, complemented
13#102×Dic11C211yesmaximal, characteristic, complemented
14#13068398C211yesmaximal, characteristic, complemented
15C11×#1864C211yesmaximal, characteristic, complemented
16C22×D4×D11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C22×#4324C2211yescharacteristic
20C22×(C2×D11)⋊C4—21no—
21C22×#4314C2211yescharacteristic
22C22×#4313C2211yescharacteristic
23C2×#66950C2211yescharacteristic
24C2×#66945C2211yescharacteristic
25C2×C4×Dic22C2211yescharacteristic, complemented
26C2×C11×#106C2211yescharacteristic, complemented
27C2×C11×#102C2211yescharacteristic
28C2×C11×#102C2211yescharacteristic
29C11×#389C2211yescharacteristic, complemented
30C2×#66896C2211yescharacteristic
31#10622826—21no—
32C2×#66885C2211yescharacteristic
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×#66880C2211yescharacteristic, complemented
35C2×C8×Dic11C2211yescharacteristic, complemented
36#10622631—24no—
37#10622603—21no—
38#10622601C2211yescharacteristic
39#10622600C2211yescharacteristic
40C4⋊C4×Dic11—21no—
41C4⋊C4×Dic11C2211yescharacteristic, complemented
42#10622587C2211yescharacteristic, complemented
43C2×#66874C2211yescharacteristic, complemented
44C2×#66873C2211yescharacteristic
45C2×#66873C2211yescharacteristic
46C2×#66871C2211yescharacteristic, complemented
47#10622571—21no—
48#10622568—21no—
49#10622552C2211yescharacteristic
50C4×(C2×D11)⋊C4C2211yescharacteristic
51C2×#66867C2211yescharacteristic, complemented
52#10622389C418yescomplemented
53#10622383—24no—
54#10622282—21no—
55#10622267—21no—
56C11×#340C2211yescharacteristic, complemented
57C11×#336C2211yescharacteristic, complemented
58#10622189C2211yescharacteristic, complemented
59#10622188C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61#10622167C2211yescharacteristic, complemented
62C24×D11—21no—
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11—21no—
65C22×C22⋊D11—21no—
66C23×Dic11—21no—
67C2×D4×D11—22no—
68C2×D4×D11—22no—
69C2×D4×D11—22no—
70C2×D4×D11—41no—
71C2×D4×D11—41no—
72C2×D4×D11C2×C414yes—
73C22×D44C2311yescharacteristic
74C22×C4×D11C2311yescharacteristic
75C22×Dic22C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C4×D4×C11—22no—
79C4×D4×C11—41no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C22⋊C4—21no—
85C2×C42×C11C2311yescharacteristic
86C2×C22⋊Dic11—21no—
87D4×Dic11—22no—
88D4×Dic11—41no—
89C2×#4324—22no—
90C2×#4324—22no—
91C2×#4324C2×C414yes—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—44no—
100C2×(C2×D11)⋊C4D411yescharacteristic
101C2×(C2×D11)⋊C4D411yescharacteristic
102C2×C4⋊Dic11—21no—
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4⋊Dic11C2311yescharacteristic
105C2×Dic11⋊C4—21no—
106C2×C4×Dic11—21no—
107C2×C4×Dic11—21no—
108C2×C4×Dic11—21no—
109C2×C4×Dic11C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C2×#4314—41no—
113C2×#4314—41no—
114C2×#4314C2×C414yescomplemented
115C2×#4313—22no—
116C2×#4313—22no—
117C2×#4313—41no—
118#66950—22no—
119#66950C2×C414yescomplemented
120#66945—22no—
121#66945—41no—
122C4×Dic22—22no—
123C4×Dic22—41no—
124C11×#106—41no—
125C11×#102—22no—
126C11×#102C2×C414yes—
127C11×#95—21no—
128#66896D414yes—
129C11⋊#95—21no—
130C11⋊#95—21no—
131C11⋊#95—21no—
132C11⋊#95—21no—
133C11⋊#95D411yescharacteristic
134C11⋊#95D411yescharacteristic
135#66885—22no—
136(C2×D11)⋊C8C2×C414yescomplemented
137#66880—41no—
138C8×Dic11—41no—
139#66874—22no—
140#66873—22no—
141#66873C2×C414yescomplemented
142#66871—22no—
143#66867—22no—
144#22864—111nomaximal, Sylow
145C24×C11—21no—
146C23×D11—21no—
147C23×D11—24no—
148C23×D11—42no—
149C23×D11—42no—
150C23×D11—42no—
151C23×D11—42no—
152C23×D11—81no—
153C23×D11—81no—
154C23×D11C2×D411yescharacteristic
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11C22×C412yes—
159C2×D4×C11C2×D412yes—
160C2×D4×C11#4112yes—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—42no—
165C22×C4×C11—42no—
166C22×C4×C11—81no—
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2411yescharacteristic
170C2×C22⋊D11—24no—
171C2×C22⋊D11—42no—
172C2×C22⋊D11—42no—
173C22×Dic11—21no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—42no—
177C22×Dic11—42no—
178C22×Dic11—81no—
179C22×Dic11C2×D411yescharacteristic
180C22×Dic11C2×D411yescharacteristic
181C22×Dic11C2×D411yescharacteristic
182D4×D11—28no—
183D4×D11—44no—
184D4×D11—44no—
185D4×D11—44no—
186C2×D44—21no—
187C2×D44—21no—
188C2×D44—21no—
189C2×D44—21no—
190C2×D44—21no—
191C2×D44C22×C412yes—
192C2×C4×D11—21no—
193C2×C4×D11—21no—
194C2×C4×D11—21no—
195C2×C4×D11—21no—
196C2×C4×D11C22×C412yes—
197C2×C4×D11#4112yes—
198C2×Dic22—21no—
199C2×Dic22—21no—
200C2×Dic22—21no—
201C2×Dic22—21no—
202C2×Dic22—21no—
203C2×Dic22C22×C412yes—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11—21no—
209C2×C8×C11C22×C412yes—
210C11×C4⋊C4—21no—
211C11×C4⋊C4—21no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4—21no—
214C11×C4⋊C4—21no—
215C11×C4⋊C4—42no—
216C11×C4⋊C4C22×C412yes—
217C11×C22⋊C4—42no—
218C42×C11—21no—
219C42×C11—21no—
220C22⋊Dic11—42no—
221#4324—28no—
222(C2×D11)⋊C4—22no—
223(C2×D11)⋊C4—24no—
224(C2×D11)⋊C4—41no—
225(C2×D11)⋊C4—42no—
226(C2×D11)⋊C4—42no—
227(C2×D11)⋊C4—42no—
228(C2×D11)⋊C4—42no—
229(C2×D11)⋊C4—81no—
230(C2×D11)⋊C4—81no—
231C4⋊Dic11—24no—
232C4⋊Dic11—21no—
233C4⋊Dic11—21no—
234C4⋊Dic11—21no—
235C4⋊Dic11C2×D412yes—
236Dic11⋊C4—42no—
237C4×Dic11—21no—
238C4×Dic11—21no—
239C4×Dic11—42no—
240C4×Dic11—42no—
241C4×Dic11—42no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8C22×C412yes—
247C2×C11⋊C8C2×D412yes—
248#4314—44no—
249#4313—44no—
250C2×#450—111no—
251C2×#440—111no—
252C2×#418—111no—
253#2362—111no—
254D4×C22⋊C4—111no—
255#1968—111no—
256#1936—111no—
257#1925—111no—
258#1894—111no—
259#1880—111no—
260#1877—111no—
261#1864D1111yescharacteristic, complemented
262#1854—111no—
263C4×#102—111no—
264#1753—111no—
265C23×C11—22no—
266C23×C11—22no—
267C23×C11—22no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11C22×D411yescharacteristic
273C22×D11—21no—
274C22×D11—21no—
275C22×D11—21no—
276C22×D11—21no—
277C22×D11—21no—
278C22×D11—21no—
279C22×D11—22no—
280C22×D11—48no—
281C22×D11—48no—
282C22×D11—41no—
283C22×D11—41no—
284C22×D11—41no—
285C22×D11—41no—
286C22×D11—41no—
287C22×D11—41no—
288C22×D11—84no—
289C22×D11—84no—
290C22×D11—84no—
291C22×D11—84no—
292C22×D11—84no—
293C22×D11C4×D412yes—
294D4×C11—22no—
295D4×C11—22no—
296D4×C11—22no—
297D4×C11C4×D414yes—
298C2×C4×C11—22no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—84no—
314C2×C4×C11C23×C411yescharacteristic
315C2×C4×C11C22×D411yescharacteristic
316C2×C4×C11C2×#4111yescharacteristic
317C2×C4×C11C2×#4111yescharacteristic
318C2×C4×C11H(5,𝔽2)11yescharacteristic
319C2×C4×C11H(5,𝔽2)11yescharacteristic
320C22⋊D11—48no—
321C2×Dic11—21no—
322C2×Dic11—21no—
323C2×Dic11—21no—
324C2×Dic11—21no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—21no—
328C2×Dic11—21no—
329C2×Dic11—21no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—41no—
335C2×Dic11—41no—
336C2×Dic11—41no—
337C2×Dic11—84no—
338C2×Dic11C4×D412yes—
339C2×Dic11AGL(1,ℤ/8)12yes—
340D44—22no—
341D44—22no—
342D44—41no—
343D44—41no—
344C4×D11—22no—
345C4×D11—22no—
346C4×D11—22no—
347C4×D11—22no—
348Dic22—22no—
349Dic22—22no—
350Dic22—41no—
351Dic22—41no—
352C8×C11—22no—
353C8×C11—41no—
354C11⋊C8—22no—
355C11⋊C8—22no—
356C23×D4—111no—
357C22×SD16—111no—
358C22×SD16—111no—
359C22×M16—111no—
360C2×C22⋊Q8—111no—
361C2×C4×Q8—111no—
362C2×C4×D4—111no—
363C2×C4×D4C2×D1111yescharacteristic
364C2×#117—111no—
365C22×C22⋊C4—221no—
366#450—118no—
367#440—224no—
368C2×#107—111no—
369C2×#106C2×D1111yescharacteristic, complemented
370#418—224no—
371C2×#103—111no—
372C2×#103—111no—
373C2×#102—111no—
374C2×#102—111no—
375C2×#102—111no—
376C2×#102—111no—
377C2×#102C2×D1111yescharacteristic
378C2×#102C2×D1111yescharacteristic
379C2×C22⋊C8—111no—
380C2×#97—111no—
381C2×C4×C8—111no—
382#391—111no—
383#390—111no—
384#390—111no—
385#389C2×D1111yescharacteristic, complemented
386#388—221no—
387#388—221no—
388#387—221no—
389#386—221no—
390#386—221no—
391#380—111no—
392#379—221no—
393C4×C4⋊C4—111no—
394C4×C4⋊C4—221no—
395C4×C22⋊C4—111no—
396#340—111no—
397#340—111no—
398#340—111no—
399#340C2×D1111yescharacteristic, complemented
400#336—111no—
401#336C2×D1111yescharacteristic, complemented
402C22×C11—24no—
403C22×C11—42no—
404C22×C11—42no—
405C22×C11—42no—
406C22×C11—42no—
407C22×C11—42no—
408C22×C11—42no—
409C22×C11C2×C4×D411yescharacteristic
410C22×C11D4211yescharacteristic
411C22×C11#54611yescharacteristic
412C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
413C22×C11#57511yescharacteristic
414C22×C11#57711yescharacteristic
415C22×C11#57711yescharacteristic
416C2×D11—22no—
417C2×D11—22no—
418C2×D11—22no—
419C2×D11—41no—
420C2×D11—41no—
421C2×D11—41no—
422C2×D11—41no—
423C2×D11—42no—
424C2×D11—42no—
425C2×D11—42no—
426C2×D11—816no—
427C2×D11—81no—
428C2×D11—81no—
429C2×D11—81no—
430C2×D11—81no—
431C4×C11—42no—
432C4×C11—41no—
433C4×C11—41no—
434C4×C11—81no—
435C4×C11—81no—
436C4×C11C2×C4×D411yescharacteristic
437C4×C11#51811yescharacteristic
438C4×C11#54611yescharacteristic
439C4×C11#55111yescharacteristic
440Dic11—22no—
441Dic11—22no—
442Dic11—42no—
443Dic11—42no—
444Dic11—41no—
445Dic11—81no—
446C25—221no—
447C22×Q8—111no—
448C22×D4—114no—
449C22×D4—111no—
450C22×D4—222no—
451C22×D4—221no—
452C22×D4—222no—
453C22×D4—222no—
454C22×D4—441no—
455C22×D4—441no—
456C22×D4C22×D1111yescharacteristic
457C23×C4—21no—
458C23×C4—111no—
459C23×C4—221no—
460C2×SD16—114no—
461C2×SD16—114no—
462C2×SD16—222no—
463C2×SD16—222no—
464C2×SD16—441no—
465C2×SD16—441no—
466C2×M16—222no—
467C2×M16—222no—
468C2×M16—441no—
469C22×C8—111no—
470C22×C8—111no—
471C22×C8C22×D1111yescharacteristic
472C22×C8C22×D1111yescharacteristic
473C22⋊Q8—114no—
474C22⋊Q8—222no—
475C4×Q8—222no—
476C4×Q8—441no—
477C4×D4—22no—
478C4×D4—41no—
479C4×D4—222no—
480C4×D4—441no—
481#117—222no—
482#117—441no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—111no—
485C2×C4⋊C4—111no—
486C2×C4⋊C4—221no—
487C2×C4⋊C4—221no—
488C2×C4⋊C4C22×D1111yescharacteristic
489C2×C4⋊C4C22×D1111yescharacteristic
490C2×C4⋊C4C22×D1111yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—111no—
493C2×C22⋊C4—111no—
494C2×C22⋊C4—221no—
495C2×C22⋊C4—221no—
496C2×C22⋊C4—221no—
497C2×C22⋊C4—221no—
498C2×C22⋊C4—221no—
499C2×C22⋊C4—221no—
500C2×C22⋊C4—221no—
501C2×C22⋊C4—221no—
502C2×C22⋊C4—444no—
503C2×C42—111no—
504C2×C42—221no—
505C2×C42—221no—
506C2×C42—221no—
507C2×C42C22×D1111yescharacteristic
508#107—222no—
509#106—41no—
510#103—222no—
511#103—441no—
512#102—22no—
513#102—114no—
514#102—114no—
515#102—222no—
516#102—222no—
517#102C4×D1114yes—
518C22⋊C8—114no—
519#97—222no—
520C4×C8—441no—
521#95—21no—
522#95—111no—
523#95—111no—
524#95—221no—
525#95—221no—
526#95—221no—
527#95—221no—
528C2×C11—44no—
529C2×C11#235811yescharacteristic
530C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
531C2×C11#294911yescharacteristic
532C2×C11#327211yescharacteristic
533C2×C11#327511yescharacteristic
534C2×C11#331011yescharacteristic
535C2×C11#331111yescharacteristic
536D11—42no—
537D11—82no—
538C24—21no—
539C24—111no—
540C24—224no—
541C24—221no—
542C24—442no—
543C24—442no—
544C24—442no—
545C24—442no—
546C24—881no—
547C24—881no—
548C2×Q8—112no—
549C2×Q8—221no—
550C2×Q8—221no—
551C2×Q8—221no—
552C2×Q8—221no—
553C2×Q8—221no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—112no—
558C2×D4—224no—
559C2×D4—228no—
560C2×D4—221no—
561C2×D4—221no—
562C2×D4—221no—
563C2×D4—221no—
564C2×D4—221no—
565C2×D4—444no—
566C2×D4—444no—
567C2×D4—444no—
568C2×D4—442no—
569C2×D4—442no—
570C2×D4C2×C4×D1112yes—
571C2×D4D4×D1112yes—
572C2×D4#434312yes—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—81no—
579C22×C4—111no—
580C22×C4—111no—
581C22×C4—112no—
582C22×C4—112no—
583C22×C4—111no—
584C22×C4—221no—
585C22×C4—221no—
586C22×C4—221no—
587C22×C4—221no—
588C22×C4—221no—
589C22×C4—221no—
590C22×C4—221no—
591C22×C4—442no—
592C22×C4—442no—
593C22×C4—881no—
594C22×C4D4×D1111yescharacteristic
595C22×C4D4×D1111yescharacteristic
596C22×C4C23×D1111yescharacteristic
597SD16—228no—
598SD16—444no—
599M16—444no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—112no—
606C2×C8—112no—
607C2×C8—221no—
608C2×C8—221no—
609C2×C8—221no—
610C2×C8—221no—
611C2×C8C2×C4×D1112yes—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—42no—
618C4⋊C4—112no—
619C4⋊C4—224no—
620C4⋊C4—221no—
621C4⋊C4—221no—
622C4⋊C4—221no—
623C4⋊C4—442no—
624C4⋊C4C2×C4×D1112yes—
625C22⋊C4—42no—
626C22⋊C4—222no—
627C22⋊C4—224no—
628C22⋊C4—441no—
629C22⋊C4—442no—
630C22⋊C4—442no—
631C22⋊C4—442no—
632C22⋊C4—442no—
633C22⋊C4—442no—
634C22⋊C4—881no—
635C22⋊C4—881no—
636C42—21no—
637C42—21no—
638C42—221no—
639C42—221no—
640C42—442no—
641C42—442no—
642C42—442no—
643C11#2286411yescharacteristic, complemented, Sylow
644C23—22no—
645C23—22no—
646C23—22no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—112no—
652C23—221no—
653C23—221no—
654C23—221no—
655C23—221no—
656C23—221no—
657C23—221no—
658C23—222no—
659C23—448no—
660C23—448no—
661C23—441no—
662C23—441no—
663C23—441no—
664C23—441no—
665C23—441no—
666C23—441no—
667C23—884no—
668C23—884no—
669C23—884no—
670C23—884no—
671C23—884no—
672C23C2×D4×D1111yescharacteristic
673Q8—222no—
674Q8—222no—
675Q8—441no—
676Q8—441no—
677D4—22no—
678D4—22no—
679D4—22no—
680D4—222no—
681D4—222no—
682D4—448no—
683D4—441no—
684D4—441no—
685D4#6694614yes—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—84no—
702C2×C4—112no—
703C2×C4—112no—
704C2×C4—221no—
705C2×C4—221no—
706C2×C4—221no—
707C2×C4—221no—
708C2×C4—222no—
709C2×C4—222no—
710C2×C4—222no—
711C2×C4—222no—
712C2×C4—221no—
713C2×C4—221no—
714C2×C4—222no—
715C2×C4—222no—
716C2×C4—221no—
717C2×C4—441no—
718C2×C4—441no—
719C2×C4—441no—
720C2×C4—441no—
721C2×C4—441no—
722C2×C4—441no—
723C2×C4—441no—
724C2×C4—884no—
725C2×C4C22×C4×D1111yescharacteristic
726C2×C4C2×D4×D1111yescharacteristic
727C2×C4#6703711yescharacteristic
728C2×C4C2×#434311yescharacteristic
729C2×C4#41×D1111yescharacteristic
730C2×C4#6704211yescharacteristic
731C8—22no—
732C8—41no—
733C8—222no—
734C8—222no—
735C22—24no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—222no—
743C22—222no—
744C22—222no—
745C22—441no—
746C22—441no—
747C22—441no—
748C22—441no—
749C22—442no—
750C22—442no—
751C22—442no—
752C22—8816no—
753C22—881no—
754C22—881no—
755C22—881no—
756C22—881no—
757C22C4×D4×D1111yescharacteristic
758C22#1062312111yescharacteristic
759C22#1062316111yescharacteristic
760C22#1062329311yescharacteristic
761C22#1062330111yescharacteristic
762C22D11×AGL(1,ℤ/8)11yescharacteristic
763C22#1062330411yescharacteristic
764C4—41no—
765C4—42no—
766C4—41no—
767C4—81no—
768C4—81no—
769C4—222no—
770C4—222no—
771C4—441no—
772C4—442no—
773C4—442no—
774C4—881no—
775C4C2×#6694611yescharacteristic
776C4#1062307611yescharacteristic
777C4#1062316811yescharacteristic
778C4#1062318511yescharacteristic
779C2—44no—
780C2—442no—
781C2—882no—
782C2#1307159211yescharacteristic
783C2#1307742711yescharacteristic
784C2#1307747011yescharacteristic
785C2#1308021411yescharacteristic
786C2#1308024511yescharacteristic
787C2#1308063411yescharacteristic
788C2#1308064911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1864C2
socleC23×C11C22×D4
prime radicalC22×D4×D11C22
cosocleC22×C4×C11C24
hypercenter#1864D11
hypocenterC11#22864
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1864

Complements

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

NH ≅ G/Ntype
2. C2×#10622631C2semidirect
4. #13071642C2semidirect
6. #13069468C2semidirect
7. #13069312C2semidirect
8. #13069234C2semidirect
9. #13069048C2semidirect
10. #13068970C2semidirect
11. #13068948C2semidirect
12. #13068814C2semidirect
13. #102×Dic11C2semidirect
14. #13068398C2semidirect
15. C11×#1864C2semidirect
25. C2×C4×Dic22C22semidirect
26. C2×C11×#106C22semidirect
29. C11×#389C22semidirect
34. C2×#66880C22semidirect
35. C2×C8×Dic11C22semidirect
41. C4⋊C4×Dic11C22semidirect
42. #10622587C22semidirect
43. C2×#66874C22semidirect
46. C2×#66871C22semidirect
51. C2×#66867C22semidirect
52. #10622389C4semidirect
56. C11×#340C22semidirect
57. C11×#336C22semidirect
58. #10622189C22semidirect
59. #10622188C22semidirect
60. #10622167C22semidirect
61. #10622167C22semidirect
114. C2×#4314C2×C4semidirect
119. #66950C2×C4semidirect
136. (C2×D11)⋊C8C2×C4semidirect
141. #66873C2×C4semidirect
261. #1864D11semidirect
369. C2×#106C2×D11semidirect
385. #389C2×D11semidirect
399. #340C2×D11semidirect
401. #336C2×D11semidirect
643. C11#22864semidirect

Maximal subgroups

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

subgroupindex
C2×#106223892
C2×#106226312
C2×#106223832
#130716422
D4×(C2×D11)⋊C42
#130694682
#130693122
#130692342
#130690482
#130689702
#130689482
#130688142
#102×Dic112
#130683982
C11×#18642
#2286411