Finite Group Databasebeta

← #14774166

Subgroups — #14774166

Order 2816.

1190 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622650C211yesmaximal, characteristic
2C2×#10622631C211yesmaximal, characteristic, complemented
3C2×#10622579C211yesmaximal, characteristic, complemented
4#13071456C211yesmaximal, characteristic, complemented
5#13069481C211yesmaximal, characteristic, complemented
6#13069312C211yesmaximal, characteristic, complemented
7#13069236C211yesmaximal, characteristic, complemented
8#13069055C211yesmaximal, characteristic, complemented
9#13068974C211yesmaximal, characteristic, complemented
10#13068964C211yesmaximal, characteristic, complemented
11#13068869C211yesmaximal, characteristic, complemented
12#13068804C211yesmaximal, characteristic, complemented
13C4×#66874C211yesmaximal, characteristic, complemented
14#13068400C211yesmaximal, characteristic, complemented
15C11×#2361C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C2×C11×#121C2211yescharacteristic
18C2×C4×D4×C11—21no—
19C2×C4×D4×C11C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×#4324C2211yescharacteristic
22C22×#4323C2211yescharacteristic
23C22×#4318C2211yescharacteristic
24C2×C4×Dic22C2211yescharacteristic
25C2×C4×Dic22C2211yescharacteristic
26C11×#390C2211yescharacteristic
27C11×#389C2211yescharacteristic
28C11×#388—21no—
29C11×#386—21no—
30C11×#385—21no—
31C4×C11×C4⋊C4C2211yescharacteristic
32C4×C11×C22⋊C4C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35#10622825C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2211yescharacteristic
37#10622650C418yescomplemented
38#10622631—24no—
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42#10622579—24no—
43C2×#66873C2211yescharacteristic
44C2×#66873C2211yescharacteristic
45C2×#66873C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47C2×#66871C2211yescharacteristic
48#10622570—21no—
49#10622570—21no—
50#10622552C2211yescharacteristic
51#10622552C2211yescharacteristic
52C2×#66867C2211yescharacteristic
53C2×C4×C11⋊C8C2211yescharacteristic
54#10622280—21no—
55#10622279—21no—
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61#10622162C2211yescharacteristic
62C22×D4×C11—21no—
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11—21no—
65C23×C4×C11—21no—
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11—21no—
68C2×#4339—22no—
69C2×#4339—22no—
70C2×#4339—22no—
71C2×#4339—41no—
72C2×#4339—41no—
73C2×#4339C2×C414yescomplemented
74C22×D44C2311yescharacteristic
75C22×C4×D11—21no—
76C22×Dic22C2311yescharacteristic
77C11×#121—22no—
78C11×#121C2×C414yes—
79C4×D4×C11—22no—
80C4×D4×C11—41no—
81C4×D4×C11—44no—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—41no—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4D411yescharacteristic
94C2×C11×C22⋊C4D411yescharacteristic
95C2×C42×C11—21no—
96C2×C42×C11C2311yescharacteristic
97C2×C42×C11C2311yescharacteristic
98C2×C22⋊Dic11—21no—
99C2×#4324—22no—
100C2×#4324—22no—
101C2×#4324C2×C414yescomplemented
102C2×#4323—41no—
103C2×#4323—41no—
104C2×#4323C2×C414yescomplemented
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107C2×(C2×D11)⋊C4—21no—
108C2×(C2×D11)⋊C4—21no—
109C2×C4⋊Dic11C2311yescharacteristic
110C2×C4⋊Dic11C2311yescharacteristic
111C2×Dic11⋊C4—21no—
112C2×Dic11⋊C4—21no—
113C2×C4×Dic11—21no—
114C2×C4×Dic11—21no—
115C2×#4318—22no—
116C2×#4318—22no—
117C2×#4318—41no—
118C22×C11⋊C8C2311yescharacteristic
119C22×C11⋊C8C2311yescharacteristic
120C22×C11⋊C8C2311yescharacteristic
121C22×C11⋊C8C2311yescharacteristic
122C4×Dic22—22no—
123C4×Dic22—22no—
124C4×Dic22—41no—
125C4×Dic22—41no—
126C11×#95—21no—
127C11×#95—21no—
128C11×#95D411yescharacteristic
129C11×#95D411yescharacteristic
130#66896—22no—
131#66896—41no—
132C11⋊#95—21no—
133C22⋊(C11⋊C8)C2×C414yescomplemented
134#66874—22no—
135#66874C2×C414yescomplemented
136#66874D414yescomplemented
137#66873—22no—
138#66873—22no—
139#66873C2×C414yescomplemented
140#66871—22no—
141#66871—41no—
142#66867—22no—
143C4×C11⋊C8—41no—
144#22863—111nomaximal, Sylow
145C24×C11—21no—
146C24×C11C2×D411yescharacteristic
147C23×D11—21no—
148C2×D4×C11—24no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—42no—
155C2×D4×C11—42no—
156C2×D4×C11C22×C412yes—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—42no—
165C22×C4×C11—42no—
166C22×C4×C11—42no—
167C22×C4×C11—42no—
168C22×C4×C11—81no—
169C22×C4×C11—81no—
170C22×C4×C11C22×C412yes—
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11#4112yes—
177C22×C4×C11C2411yescharacteristic
178C2×C22⋊D11—24no—
179C2×C22⋊D11—42no—
180C2×C22⋊D11—42no—
181C22×Dic11—21no—
182C22×Dic11—21no—
183C22×Dic11—21no—
184#4339—28no—
185#4339—44no—
186#4339—44no—
187#4339—44no—
188C2×D44—21no—
189C2×D44—21no—
190C2×D44—21no—
191C2×D44—21no—
192C2×D44—21no—
193C2×D44C22×C412yes—
194C2×C4×D11—24no—
195C2×C4×D11—42no—
196C2×C4×D11—42no—
197C2×Dic22—21no—
198C2×Dic22—21no—
199C2×Dic22—21no—
200C2×Dic22C22×C412yes—
201C2×Dic22C2×D412yes—
202C2×Dic22#4112yes—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—42no—
208C11×C4⋊C4—42no—
209C11×C4⋊C4C22×C412yes—
210C11×C4⋊C4C2×D412yes—
211C11×C22⋊C4—24no—
212C11×C22⋊C4—22no—
213C11×C22⋊C4—41no—
214C11×C22⋊C4—42no—
215C11×C22⋊C4—42no—
216C11×C22⋊C4—81no—
217C42×C11—21no—
218C42×C11—21no—
219C42×C11—21no—
220C42×C11—21no—
221C42×C11—42no—
222C22⋊Dic11—81no—
223#4324—28no—
224#4323—44no—
225(C2×D11)⋊C4—42no—
226(C2×D11)⋊C4—42no—
227(C2×D11)⋊C4—81no—
228(C2×D11)⋊C4—81no—
229C4⋊Dic11—21no—
230C4⋊Dic11—21no—
231C4⋊Dic11—21no—
232C4⋊Dic11—21no—
233Dic11⋊C4—42no—
234Dic11⋊C4—42no—
235C4×Dic11—42no—
236C4×Dic11—42no—
237#4318—44no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8C22×C412yes—
248C2×C11⋊C8C22×C412yes—
249C2×C11⋊C8C2×D412yes—
250C2×#449—111no—
251C2×#440—111no—
252C2×#417—111no—
253#2361D1111yescharacteristic, complemented
254#2341—111no—
255#1970—111no—
256#1936—111no—
257#1925—111no—
258#1895—111no—
259#1880—111no—
260#1879—111no—
261#1863—111no—
262#1852—111no—
263C4×#103—111no—
264#1753—111no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—22no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—41no—
277C23×C11—41no—
278C23×C11C4×D412yes—
279C23×C11C22×D411yescharacteristic
280C22×D11—22no—
281C22×D11—41no—
282C22×D11—41no—
283C22×D11—41no—
284C22×D11—41no—
285C22×D11—41no—
286C22×D11—41no—
287D4×C11—22no—
288D4×C11—22no—
289D4×C11—48no—
290D4×C11—41no—
291D4×C11—41no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—22no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—84no—
319C2×C4×C11—84no—
320C2×C4×C11C4×D412yes—
321C2×C4×C11AGL(1,ℤ/8)12yes—
322C2×C4×C11C23×C411yescharacteristic
323C2×C4×C11C22×D411yescharacteristic
324C2×C4×C11C2×#4111yescharacteristic
325C2×C4×C11C2×#4111yescharacteristic
326C2×C4×C11H(5,𝔽2)11yescharacteristic
327C2×C4×C11H(5,𝔽2)11yescharacteristic
328C22⋊D11—48no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—41no—
335C2×Dic11—41no—
336C2×Dic11—41no—
337C2×Dic11—41no—
338D44—22no—
339D44—22no—
340D44—41no—
341D44—41no—
342C4×D11—48no—
343Dic22—22no—
344Dic22—22no—
345Dic22—22no—
346Dic22C4×D414yescomplemented
347C11⋊C8—22no—
348C11⋊C8—22no—
349C11⋊C8—22no—
350C11⋊C8—41no—
351C22×#41—111no—
352C22×SD16—111no—
353C22×D8—111no—
354C22×M16—111no—
355C2×#121C2×D1111yescharacteristic
356C2×C4×Q8—111no—
357C2×C4×Q8—111no—
358C2×C4×D4—21no—
359C2×C4×D4C2×D1111yescharacteristic
360C22×C4⋊C4C2×D1111yescharacteristic
361#449—118no—
362#440—224no—
363C2×#107—111no—
364C2×#107—111no—
365#417—224no—
366C2×#103—111no—
367C2×#103—111no—
368C2×#103—111no—
369C2×#102—111no—
370C2×#102—111no—
371C2×#102—111no—
372C2×#102—111no—
373C2×#102—111no—
374C2×C22⋊C8—111no—
375C2×#97—111no—
376C2×C4×C8—111no—
377#390—111no—
378#390—111no—
379#390—221no—
380#390—221no—
381#390C2×D1111yescharacteristic
382#389C2×D1111yescharacteristic
383#388—21no—
384#386—21no—
385#385—21no—
386#380—111no—
387#380—221no—
388C4×C4⋊C4C2×D1111yescharacteristic
389C4×C22⋊C4—221no—
390C4×C22⋊C4C2×D1111yescharacteristic
391#340—111no—
392#340—111no—
393#340—111no—
394#340—111no—
395#336—111no—
396#336—111no—
397C22×C11—22no—
398C22×C11—22no—
399C22×C11—22no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11—41no—
403C22×C11—41no—
404C22×C11—42no—
405C22×C11—42no—
406C22×C11—42no—
407C22×C11—81no—
408C22×C11—81no—
409C22×C11—81no—
410C22×C11—81no—
411C22×C11C2×C4×D411yescharacteristic
412C22×C11D4211yescharacteristic
413C22×C11#54611yescharacteristic
414C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
415C22×C11#57511yescharacteristic
416C22×C11#57611yescharacteristic
417C22×C11#57811yescharacteristic
418C2×D11—42no—
419C2×D11—42no—
420C2×D11—42no—
421C2×D11—81no—
422C2×D11—81no—
423C2×D11—81no—
424C2×D11—81no—
425C4×C11—22no—
426C4×C11—22no—
427C4×C11—42no—
428C4×C11—41no—
429C4×C11—42no—
430C4×C11—41no—
431C4×C11—41no—
432C4×C11—81no—
433C4×C11C2×C4×D411yescharacteristic
434C4×C11#51811yescharacteristic
435C4×C11#54611yescharacteristic
436C4×C11#55111yescharacteristic
437Dic11—24no—
438Dic11—81no—
439Dic11—81no—
440C2×#41—114no—
441C2×#41—222no—
442C2×#41—222no—
443C2×#41—222no—
444C2×#41—441no—
445C2×#41—441no—
446C22×Q8—111no—
447C22×D4—21no—
448C22×D4—111no—
449C22×D4—221no—
450C22×D4C22×D1111yescharacteristic
451C23×C4—21no—
452C23×C4—21no—
453C23×C4—221no—
454C23×C4C22×D1111yescharacteristic
455C2×SD16—114no—
456C2×SD16—222no—
457C2×SD16—222no—
458C2×D8—114no—
459C2×D8—441no—
460C2×D8—441no—
461C2×M16—222no—
462C2×M16—222no—
463C2×M16—441no—
464C22×C8—111no—
465C22×C8—111no—
466C22×C8—111no—
467C22×C8—111no—
468#121—22no—
469#121C4×D1114yes—
470C4×Q8—222no—
471C4×Q8—222no—
472C4×Q8—441no—
473C4×Q8—441no—
474C4×D4—22no—
475C4×D4—41no—
476C4×D4—44no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—41no—
481C2×C4⋊C4—111no—
482C2×C4⋊C4—111no—
483C2×C4⋊C4—221no—
484C2×C4⋊C4—221no—
485C2×C4⋊C4C22×D1111yescharacteristic
486C2×C4⋊C4C22×D1111yescharacteristic
487C2×C4⋊C4C22×D1111yescharacteristic
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—221no—
493C2×C22⋊C4—221no—
494C2×C22⋊C4—221no—
495C2×C22⋊C4—221no—
496C2×C22⋊C4—221no—
497C2×C22⋊C4C22⋊D1111yescharacteristic
498C2×C22⋊C4C22⋊D1111yescharacteristic
499C2×C42—21no—
500C2×C42—221no—
501C2×C42—221no—
502C2×C42C22×D1111yescharacteristic
503C2×C42C22×D1111yescharacteristic
504#107—222no—
505#107—441no—
506#103—114no—
507#103—114no—
508#103—222no—
509#102—114no—
510#102—222no—
511#102—222no—
512#102—222no—
513#102—441no—
514C22⋊C8—114no—
515#97—222no—
516C4×C8—441no—
517#95—21no—
518#95—21no—
519#95—221no—
520#95C22⋊D1111yescharacteristic
521#95C22⋊D1111yescharacteristic
522C2×C11—42no—
523C2×C11—82no—
524C2×C11#235811yescharacteristic
525C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
526C2×C11#295111yescharacteristic
527C2×C11#327411yescharacteristic
528C2×C11#327711yescharacteristic
529C2×C11#330811yescharacteristic
530C2×C11#330911yescharacteristic
531D11—82no—
532C24—21no—
533C24—221no—
534C24C2×C22⋊D1111yescharacteristic
535#41—228no—
536#41—444no—
537#41—444no—
538#41—444no—
539C2×Q8—112no—
540C2×Q8—112no—
541C2×Q8—112no—
542C2×Q8—221no—
543C2×Q8—221no—
544C2×Q8—221no—
545C2×D4—24no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—42no—
552C2×D4—42no—
553C2×D4—112no—
554C2×D4—224no—
555C2×D4—221no—
556C2×D4—221no—
557C2×D4—221no—
558C2×D4—221no—
559C2×D4—221no—
560C2×D4—442no—
561C2×D4—442no—
562C2×D4C2×C4×D1112yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—81no—
575C22×C4—81no—
576C22×C4—221no—
577C22×C4—224no—
578C22×C4—221no—
579C22×C4—221no—
580C22×C4—442no—
581C22×C4—442no—
582C22×C4C2×C4×D1112yes—
583C22×C4#433912yes—
584C22×C4C2×C22⋊D1111yescharacteristic
585C22×C4C2×C22⋊D1111yescharacteristic
586C22×C4C2×C22⋊D1111yescharacteristic
587C22×C4C2×C22⋊D1111yescharacteristic
588C22×C4C2×C22⋊D1111yescharacteristic
589C22×C4C23×D1111yescharacteristic
590SD16—228no—
591D8—444no—
592M16—444no—
593C2×C8—112no—
594C2×C8—112no—
595C2×C8—112no—
596C2×C8—221no—
597C2×C8—221no—
598C2×C8—221no—
599C2×C8—221no—
600C2×C8—221no—
601C2×C8—221no—
602C2×C8—221no—
603C2×C8—221no—
604C2×C8—221no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—42no—
610C4⋊C4—42no—
611C4⋊C4—221no—
612C4⋊C4—221no—
613C4⋊C4—221no—
614C4⋊C4—221no—
615C4⋊C4—442no—
616C4⋊C4—442no—
617C4⋊C4C2×C4×D1112yes—
618C4⋊C4D4×D1112yes—
619C22⋊C4—24no—
620C22⋊C4—22no—
621C22⋊C4—41no—
622C22⋊C4—42no—
623C22⋊C4—42no—
624C22⋊C4—81no—
625C22⋊C4—442no—
626C22⋊C4—442no—
627C22⋊C4—881no—
628C22⋊C4—881no—
629C22⋊C4—881no—
630C42—21no—
631C42—21no—
632C42—21no—
633C42—21no—
634C42—42no—
635C42—442no—
636C42—442no—
637C11#2286311yescharacteristic, complemented, Sylow
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—22no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—222no—
652C23—441no—
653C23—441no—
654C23—441no—
655C23—441no—
656C23—441no—
657C23—441no—
658C23C4×C22⋊D1112yes—
659C23C22×C22⋊D1111yescharacteristic
660Q8—114no—
661Q8—222no—
662Q8—222no—
663Q8—222no—
664D4—22no—
665D4—22no—
666D4—48no—
667D4—41no—
668D4—41no—
669D4—222no—
670D4—222no—
671D4—448no—
672D4—441no—
673D4—441no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
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—84no—
701C2×C4—84no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—448no—
706C2×C4—441no—
707C2×C4—441no—
708C2×C4—441no—
709C2×C4—441no—
710C2×C4—441no—
711C2×C4—441no—
712C2×C4C4×C22⋊D1112yes—
713C2×C4#6698512yes—
714C2×C4C22×C4×D1111yescharacteristic
715C2×C4C2×#433911yescharacteristic
716C2×C4C2×D4×D1111yescharacteristic
717C2×C4#6703711yescharacteristic
718C2×C4#41×D1111yescharacteristic
719C2×C4#6704211yescharacteristic
720C8—222no—
721C8—222no—
722C8—222no—
723C8—441no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22—442no—
739C22—442no—
740C22—442no—
741C22—881no—
742C22—881no—
743C22—881no—
744C22—881no—
745C22C2×C4×C22⋊D1111yescharacteristic
746C22C2×#6698511yescharacteristic
747C22D4×C22⋊D1111yescharacteristic
748C22#1062335311yescharacteristic
749C22#1062336011yescharacteristic
750C22#1062336611yescharacteristic
751C22#1062336911yescharacteristic
752C4—22no—
753C4—22no—
754C4—41no—
755C4—41no—
756C4—42no—
757C4—42no—
758C4—41no—
759C4—81no—
760C4—224no—
761C4—881no—
762C4—881no—
763C4C4×D4×D1111yescharacteristic
764C4#1062307611yescharacteristic
765C4#1062308111yescharacteristic
766C4#1062308711yescharacteristic
767C2—42no—
768C2—82no—
769C2—882no—
770C2#1307159311yescharacteristic
771C2C4×#6698511yescharacteristic
772C2#1307748911yescharacteristic
773C2#1308023211yescharacteristic
774C2#1308026911yescharacteristic
775C2#1308060111yescharacteristic
776C2#1308061611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2361C2
socleC23×C11C22×D4
prime radicalC2×#10622650C2
cosocleC22×C4×C11C24
hypercenter#2361D11
hypocenterC11#22863
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2361

Complements

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

NH ≅ G/Ntype
2. C2×#10622631C2semidirect
3. C2×#10622579C2semidirect
4. #13071456C2semidirect
5. #13069481C2semidirect
6. #13069312C2semidirect
7. #13069236C2semidirect
8. #13069055C2semidirect
9. #13068974C2semidirect
10. #13068964C2semidirect
11. #13068869C2semidirect
12. #13068804C2semidirect
13. C4×#66874C2semidirect
14. #13068400C2semidirect
15. C11×#2361C2semidirect
37. #10622650C4semidirect
73. C2×#4339C2×C4semidirect
101. C2×#4324C2×C4semidirect
104. C2×#4323C2×C4semidirect
133. C22⋊(C11⋊C8)C2×C4semidirect
135. #66874C2×C4semidirect
136. #66874D4semidirect
139. #66873C2×C4semidirect
253. #2361D11semidirect
346. Dic22C4×D4semidirect
637. C11#22863semidirect

Maximal subgroups

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

subgroupindex
C2×#106226502
C2×#106226312
C2×#106225792
#130714562
#130694812
#130693122
#130692362
#130690552
#130689742
#130689642
#130688692
#130688042
C4×#668742
#130684002
C11×#23612
#2286311