Finite Group Databasebeta

← #15620256

Subgroups — #15620256

Order 2816.

5070 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623353C211yesmaximal, characteristic, complemented
2C22×#66985C211yesmaximal, characteristic, complemented
3#13081945C211yesmaximal, characteristic, complemented
4#13077920C218yesmaximal, complemented
5#13077893C214yesmaximal, complemented
6#13077884C214yesmaximal, complemented
7#13077858C214yesmaximal, complemented
8#13077843C214yesmaximal, complemented
9#13077135C211yesmaximal, characteristic, complemented
10C2×#10622828C211yesmaximal, characteristic, complemented
11#13077061C211yesmaximal, characteristic, complemented
12C22×C11×H(5,𝔽2)C211yesmaximal, characteristic, complemented
13C2×C11×H(5,𝔽2)—22no—
14C2×C11×H(5,𝔽2)—22no—
15C2×C11×H(5,𝔽2)—28no—
16C2×C11×H(5,𝔽2)—28no—
17C2×C11×H(5,𝔽2)C2214yes—
18C2×C11×H(5,𝔽2)C2214yescomplemented
19C22×C11×#41—21no—
20C22×C11×#41C2211yescharacteristic
21C22×C11×#41C2211yescharacteristic
22C22×C11×#41C2212yescomplemented
23C23×D4×C11—21no—
24C23×D4×C11—22no—
25C23×D4×C11C2211yescharacteristic
26C23×D4×C11C2212yescomplemented
27C22×#4339C2211yescharacteristic, complemented
28#10623364C2214yescomplemented
29#10623363—22no—
30#10623361C2212yescomplemented
31#10623359—22no—
32#10623356C2212yescomplemented
33C2×#67004C2212yescomplemented
34#10623353—28no—
35C2×#67003C2214yescomplemented
36C2×#67002C2212yescomplemented
37#10623347—21no—
38C2×#66995C2212yescomplemented
39#10623336—21no—
40#10623335—22no—
41C22×#4324C2212yescomplemented
42C2×#66985—28no—
43C2×#66985C2212yescomplemented
44C2×#66985C2214yescomplemented
45C2×#66985C2214yescomplemented
46C22×#4323C2212yescomplemented
47#10623322C2214yescomplemented
48C2×#66979C2211yescharacteristic, complemented
49C22×#4318C2211yescharacteristic, complemented
50C22×#4318C2211yescharacteristic, complemented
51#10622852C22116yescomplemented
52#10622851C22116yescomplemented
53#10622847C2214yescomplemented
54#10622847C2214yescomplemented
55#10622846C2214yescomplemented
56#10622845C2214yescomplemented
57#10622838C2212yescomplemented
58#10622831C22116yescomplemented
59#10622830C22116yescomplemented
60#10622828C2212yescomplemented
61#10622828C2214yescomplemented
62#10622828C2214yescomplemented
63C2×#66896C2214yescomplemented
64#10622820C2214yescomplemented
65C25×C11—21no—
66C25×C11—22no—
67C11×H(5,𝔽2)—232no—
68C11×H(5,𝔽2)—232no—
69C11×H(5,𝔽2)—216no—
70C11×H(5,𝔽2)—216no—
71C11×H(5,𝔽2)—216no—
72C11×H(5,𝔽2)—216no—
73C2×C11×#41—216no—
74C2×C11×#41—24no—
75C2×C11×#41—24no—
76C2×C11×#41—28no—
77C2×C11×#41—28no—
78C2×C11×#41—24no—
79C2×C11×#41—21no—
80C2×C11×#41—21no—
81C2×C11×#41—24no—
82C2×C11×#41—24no—
83C2×C11×#41—24no—
84C2×C11×#41D412yes—
85C2×C11×#41D412yes—
86C2×C11×#41D418yescomplemented
87C2×C11×#41C2318yes—
88C2×C11×#41C2312yes—
89C2×C11×#41C2312yes—
90C2×C11×#41C2312yes—
91C2×C11×#41C2312yes—
92C22×Q8×C11D411yescharacteristic
93C22×Q8×C11C2311yescharacteristic
94C22×D4×C11—232no—
95C22×D4×C11—216no—
96C22×D4×C11—21no—
97C22×D4×C11—22no—
98C22×D4×C11—28no—
99C22×D4×C11—24no—
100C22×D4×C11—24no—
101C22×D4×C11—28no—
102C22×D4×C11—28no—
103C22×D4×C11—28no—
104C22×D4×C11—21no—
105C22×D4×C11—22no—
106C22×D4×C11—21no—
107C22×D4×C11—21no—
108C22×D4×C11—24no—
109C22×D4×C11—24no—
110C22×D4×C11D412yes—
111C22×D4×C11D411yescharacteristic
112C22×D4×C11D418yescomplemented
113C22×D4×C11C2318yes—
114C22×D4×C11C2312yes—
115C22×D4×C11C2312yes—
116C22×D4×C11C2312yes—
117C22×D4×C11C2311yescharacteristic
118C23×C4×C11—21no—
119C23×C4×C11—22no—
120C23×C4×C11C2312yes—
121C23×C4×C11C2311yescharacteristic
122C22×C22⋊D11—21no—
123C2×#4339—21no—
124C2×#4339—21no—
125C2×#4339—24no—
126C2×#4339—24no—
127C2×#4339C2312yes—
128C2×#4339C2312yescomplemented
129C22×D44C2311yescharacteristic, complemented
130C22×C4×D11—21no—
131C22×Dic22C2311yescharacteristic, complemented
132#67006—24no—
133C2×C22⋊Dic11—21no—
134#67004—28no—
135#67003—216no—
136#67002—28no—
137#67000—22no—
138#66999—24no—
139#66997—22no—
140C2×#4326C2314yescomplemented
141#66995—28no—
142C2×#4325C2314yescomplemented
143#66993—22no—
144#66992—28no—
145#66991—24no—
146#66990—24no—
147#66989—22no—
148#66988—24no—
149C2×#4324—28no—
150C2×#4324C2318yescomplemented
151C2×#4324C2314yescomplemented
152#66985—216no—
153#66985—216no—
154#66985—28no—
155C2×#4323—28no—
156C2×#4323C2318yescomplemented
157C2×#4323C2314yescomplemented
158#66983C2318yescomplemented
159#66982—24no—
160C4×C22⋊D11—28no—
161#66979—21no—
162#66979—21no—
163#66979C2312yes—
164#66979C2312yescomplemented
165C2×C4⋊Dic11C2312yescomplemented
166#66977C2318yescomplemented
167C2×C4×Dic11—21no—
168C2×#4318—24no—
169C2×#4318—24no—
170C2×#4318C2312yes—
171C2×#4318C2312yes—
172C2×#4318C2312yescomplemented
173C2×#4318C2312yescomplemented
174C22×C11⋊C8C2312yescomplemented
175C22×C11⋊C8C2312yescomplemented
176#66899C2318yescomplemented
177#66896C23116yescomplemented
178#66896C2318yescomplemented
179C22⋊(C11⋊C8)C23116yescomplemented
180#60367—111nomaximal, Sylow
181C24×C11—216no—
182C24×C11—21no—
183C24×C11—22no—
184C24×C11—28no—
185C24×C11—28no—
186C24×C11—22no—
187C24×C11—22no—
188C24×C11—84no—
189C24×C11—88no—
190C24×C11C2×D412yes—
191C24×C11C2×D411yescharacteristic
192C23×D11—21no—
193C11×#41—232no—
194C11×#41—232no—
195C11×#41—232no—
196C11×#41—216no—
197C11×#41—216no—
198C11×#41—28no—
199C11×#41—28no—
200C11×#41—28no—
201C11×#41—28no—
202C11×#41—24no—
203C11×#41—24no—
204C11×#41—24no—
205C11×#41—24no—
206C11×#41—24no—
207C11×#41—24no—
208C11×#41C2×D418yes—
209C11×#41C2×D418yes—
210C2×Q8×C11—24no—
211C2×Q8×C11—22no—
212C2×Q8×C11—21no—
213C2×Q8×C11C2×D414yes—
214C2×Q8×C11C2×D412yes—
215C2×Q8×C11C2×D412yes—
216C2×Q8×C11C2412yes—
217C2×D4×C11—216no—
218C2×D4×C11—216no—
219C2×D4×C11—264no—
220C2×D4×C11—264no—
221C2×D4×C11—232no—
222C2×D4×C11—232no—
223C2×D4×C11—232no—
224C2×D4×C11—28no—
225C2×D4×C11—28no—
226C2×D4×C11—28no—
227C2×D4×C11—22no—
228C2×D4×C11—22no—
229C2×D4×C11—216no—
230C2×D4×C11—216no—
231C2×D4×C11—24no—
232C2×D4×C11—28no—
233C2×D4×C11—28no—
234C2×D4×C11—28no—
235C2×D4×C11—28no—
236C2×D4×C11—22no—
237C2×D4×C11—22no—
238C2×D4×C11—21no—
239C2×D4×C11—22no—
240C2×D4×C11—24no—
241C2×D4×C11—22no—
242C2×D4×C11—24no—
243C2×D4×C11—24no—
244C2×D4×C11C2×D414yes—
245C2×D4×C11C2×D412yes—
246C2×D4×C11C2×D412yes—
247C2×D4×C11C2×D414yes—
248C2×D4×C11C2×D418yes—
249C2×D4×C11C2×D414yes—
250C2×D4×C11C2×D418yes—
251C2×D4×C11C2×D418yes—
252C2×D4×C11C2412yes—
253C2×D4×C11C2414yes—
254C22×C4×C11—216no—
255C22×C4×C11—21no—
256C22×C4×C11—28no—
257C22×C4×C11—28no—
258C22×C4×C11—22no—
259C22×C4×C11—22no—
260C22×C4×C11—24no—
261C22×C4×C11—24no—
262C22×C4×C11C2×D414yes—
263C22×C4×C11C2×D412yes—
264C22×C4×C11C2×D411yescharacteristic
265C22×C4×C11C2×D411yescharacteristic
266C22×C4×C11C2×D411yescharacteristic
267C22×C4×C11C2×D414yes—
268C22×C4×C11C2×D414yes—
269C22×C4×C11C2414yes—
270C22×C4×C11C2411yescharacteristic
271C22×C4×C11C2411yescharacteristic
272C22×C4×C11C2411yescharacteristic
273C2×C22⋊D11—22no—
274C2×C22⋊D11—22no—
275C2×C22⋊D11—28no—
276C2×C22⋊D11—44no—
277C22×Dic11—21no—
278C22×Dic11—22no—
279#4339—24no—
280#4339—24no—
281#4339—24no—
282#4339—24no—
283#4339—44no—
284#4339—44no—
285C2×D44—21no—
286C2×D44—22no—
287C2×D44—22no—
288C2×D44C2412yes—
289C2×C4×D11—22no—
290C2×C4×D11—22no—
291C2×C4×D11—44no—
292C2×Dic22—22no—
293C2×Dic22—22no—
294C2×Dic22—21no—
295C2×Dic22C2412yes—
296C22⋊Dic11—28no—
297C22⋊Dic11—22no—
298C22⋊Dic11—22no—
299#4326—28no—
300#4325—28no—
301#4324—216no—
302#4324—28no—
303#4323—216no—
304#4323—28no—
305(C2×D11)⋊C4—28no—
306C4⋊Dic11—22no—
307C4⋊Dic11C2414yes—
308Dic11⋊C4—28no—
309C4×Dic11—22no—
310C4×Dic11—22no—
311#4318—24no—
312#4318—24no—
313#4318—24no—
314#4318—24no—
315C2×C11⋊C8—24no—
316C2×C11⋊C8—24no—
317C2×C11⋊C8C2414yes—
318C2×C11⋊C8C2414yes—
319C22×H(5,𝔽2)D1111yescharacteristic, complemented
320C2×#575—111no—
321C22×AGL(1,ℤ/8)—111no—
322#3449—111no—
323#3012—118no—
324#3009—114no—
325#3008—114no—
326#3005—114no—
327#3003—114no—
328#2896—111no—
329C2×#418—111no—
330#2879—111no—
331C23×C11—232no—
332C23×C11—24no—
333C23×C11—28no—
334C23×C11—24no—
335C23×C11—24no—
336C23×C11—22no—
337C23×C11—28no—
338C23×C11—28no—
339C23×C11—42no—
340C23×C11—44no—
341C23×C11—44no—
342C23×C11—48no—
343C23×C11—84no—
344C23×C11—84no—
345C23×C11—816no—
346C23×C11—816no—
347C23×C11—832no—
348C23×C11#12014yes—
349C23×C11C22×D414yes—
350C23×C11C22×D411yescharacteristic
351C23×C11C22×D411yescharacteristic
352C23×C11C22×D411yescharacteristic
353C22×D11—22no—
354C22×D11—42no—
355C22×D11—82no—
356Q8×C11—24no—
357Q8×C11—24no—
358Q8×C11—24no—
359Q8×C11—22no—
360Q8×C11C22×D414yes—
361D4×C11—232no—
362D4×C11—232no—
363D4×C11—28no—
364D4×C11—28no—
365D4×C11—28no—
366D4×C11—28no—
367D4×C11—24no—
368D4×C11—28no—
369D4×C11—24no—
370D4×C11—24no—
371D4×C11—28no—
372D4×C11—28no—
373D4×C11—24no—
374D4×C11—22no—
375D4×C11C22×D414yes—
376D4×C11C22×D418yes—
377C2×C4×C11—232no—
378C2×C4×C11—24no—
379C2×C4×C11—24no—
380C2×C4×C11—22no—
381C2×C4×C11—28no—
382C2×C4×C11—28no—
383C2×C4×C11—28no—
384C2×C4×C11—24no—
385C2×C4×C11—24no—
386C2×C4×C11#12014yes—
387C2×C4×C11#12014yes—
388C2×C4×C11#12014yes—
389C2×C4×C11C22×D414yes—
390C2×C4×C11C22×D411yescharacteristic
391C2×C4×C11C22×D411yescharacteristic
392C2×C4×C11C22×D411yescharacteristic
393C2×C4×C11C22×D412yes—
394C2×C4×C11C22×D412yes—
395C2×C4×C11C22×D412yes—
396C2×C4×C11C22×D412yes—
397C2×C4×C11C22×D412yes—
398C2×C4×C11C22×D412yes—
399C2×C4×C11C2511yescharacteristic
400C22⋊D11—44no—
401C22⋊D11—44no—
402C22⋊D11—88no—
403C2×Dic11—24no—
404C2×Dic11—22no—
405C2×Dic11—42no—
406C2×Dic11—82no—
407D44—22no—
408D44—22no—
409D44—42no—
410C4×D11—44no—
411C4×D11—44no—
412Dic22—22no—
413Dic22—22no—
414Dic22—42no—
415C11⋊C8—24no—
416C11⋊C8—24no—
417C2×H(5,𝔽2)—22no—
418C2×H(5,𝔽2)—22no—
419C2×H(5,𝔽2)—28no—
420C2×H(5,𝔽2)—28no—
421C2×H(5,𝔽2)C2×D1114yes—
422C2×H(5,𝔽2)C2×D1114yescomplemented
423C22×#41—21no—
424C22×#41—111no—
425C22×#41C2×D1111yescharacteristic
426C22×#41C2×D1111yescharacteristic
427C22×#41C2×D1112yescomplemented
428C23×D4—21no—
429C23×D4—22no—
430C23×D4C2×D1111yescharacteristic
431C23×D4C2×D1112yescomplemented
432#575—228no—
433C2×#137—112no—
434C2×#137—112no—
435C2×AGL(1,ℤ/8)—112no—
436C2×AGL(1,ℤ/8)—112no—
437C2×AGL(1,ℤ/8)—114no—
438C2×AGL(1,ℤ/8)—114no—
439C2×AGL(1,ℤ/8)—228no—
440C2×#135—114no—
441C22×SD16—112no—
442C22×D8—112no—
443C22×M16—111no—
444C22×M16—111no—
445#537—114no—
446#536—112no—
447#536—221no—
448#535—112no—
449#535—221no—
450#534—222no—
451#532—222no—
452#525—114no—
453#525—222no—
454C2×#117—111no—
455#452—1116no—
456#450—1116no—
457#449—1116no—
458#447—1116no—
459#419—112no—
460#418—114no—
461#418—114no—
462#418—112no—
463#417—114no—
464#416—114no—
465C2×#102—114no—
466#408—114no—
467#408—114no—
468#407—114no—
469C22×C11—22no—
470C22×C11—22no—
471C22×C11—22no—
472C22×C11—28no—
473C22×C11—24no—
474C22×C11—28no—
475C22×C11—24no—
476C22×C11—44no—
477C22×C11—48no—
478C22×C11—416no—
479C22×C11—48no—
480C22×C11—48no—
481C22×C11—44no—
482C22×C11—88no—
483C22×C11—88no—
484C22×C11—832no—
485C22×C11C2×#12012yes—
486C22×C11C2×#12012yes—
487C22×C11C2×#12012yes—
488C22×C11C23×D411yescharacteristic
489C2×D11—44no—
490C2×D11—42no—
491C2×D11—84no—
492C4×C11—24no—
493C4×C11—24no—
494C4×C11C2×#12012yes—
495C4×C11C2×#12012yes—
496C4×C11C2×#12012yes—
497C4×C11C23×D411yescharacteristic
498C4×C11C23×D411yescharacteristic
499Dic11—44no—
500Dic11—42no—
501C25—21no—
502C25—22no—
503H(5,𝔽2)—232no—
504H(5,𝔽2)—232no—
505H(5,𝔽2)—216no—
506H(5,𝔽2)—216no—
507H(5,𝔽2)—216no—
508H(5,𝔽2)—216no—
509C2×#41—216no—
510C2×#41—24no—
511C2×#41—24no—
512C2×#41—28no—
513C2×#41—28no—
514C2×#41—24no—
515C2×#41—21no—
516C2×#41—21no—
517C2×#41—24no—
518C2×#41—24no—
519C2×#41—24no—
520C2×#41—112no—
521C2×#41—112no—
522C2×#41—221no—
523C2×#41—221no—
524C2×#41—224no—
525C2×#41—224no—
526C2×#41C22⋊D1112yes—
527C2×#41C22⋊D1112yes—
528C2×#41C22⋊D1118yescomplemented
529C2×#41C22×D1118yes—
530C2×#41C22×D1112yes—
531C2×#41C22×D1112yes—
532C2×#41C22×D1112yes—
533C2×#41C22×D1112yes—
534C22×Q8—111no—
535C22×Q8C22⋊D1111yescharacteristic
536C22×Q8C22×D1111yescharacteristic
537C22×D4—232no—
538C22×D4—216no—
539C22×D4—21no—
540C22×D4—22no—
541C22×D4—28no—
542C22×D4—24no—
543C22×D4—28no—
544C22×D4—24no—
545C22×D4—28no—
546C22×D4—28no—
547C22×D4—21no—
548C22×D4—22no—
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—24no—
552C22×D4—24no—
553C22×D4—111no—
554C22×D4—221no—
555C22×D4C22⋊D1112yes—
556C22×D4C22⋊D1111yescharacteristic
557C22×D4C22⋊D1118yescomplemented
558C22×D4C22×D1118yes—
559C22×D4C22×D1112yes—
560C22×D4C22×D1112yes—
561C22×D4C22×D1112yes—
562C22×D4C22×D1111yescharacteristic
563C23×C4—21no—
564C23×C4—22no—
565C23×C4—221no—
566C23×C4C22×D1112yes—
567C23×C4C22×D1111yescharacteristic
568#137—228no—
569#137—228no—
570AGL(1,ℤ/8)—228no—
571AGL(1,ℤ/8)—2216no—
572AGL(1,ℤ/8)—2216no—
573AGL(1,ℤ/8)—228no—
574#135—2216no—
575C2×Q16—114no—
576C2×SD16—114no—
577C2×SD16—118no—
578C2×SD16—114no—
579C2×SD16—228no—
580C2×D8—118no—
581C2×D8—114no—
582C2×D8—228no—
583C2×M16—112no—
584C2×M16—112no—
585C2×M16—112no—
586C2×M16—112no—
587C2×M16—224no—
588C2×M16—224no—
589C22×C8—112no—
590C22×C8—112no—
591C4⋊Q8—222no—
592#127—222no—
593#124—222no—
594#124—222no—
595#123—224no—
596#123—224no—
597C22⋊Q8—118no—
598C22⋊Q8—224no—
599#121—118no—
600#121—224no—
601#121—228no—
602#120—224no—
603#120—224no—
604C4×D4—228no—
605#117—112no—
606#117—112no—
607#117—221no—
608#117—221no—
609C2×C4⋊C4—112no—
610C2×C22⋊C4—221no—
611C2×C42—221no—
612#103—118no—
613#102—1116no—
614#102—118no—
615C22⋊C8—1116no—
616C2×C11—22no—
617C2×C11—22no—
618C2×C11—22no—
619C2×C11—44no—
620C2×C11—48no—
621C2×C11—44no—
622C2×C11C22×#12011yescharacteristic
623C2×C11#358512yes—
624D11—82no—
625C24—216no—
626C24—21no—
627C24—22no—
628C24—28no—
629C24—28no—
630C24—22no—
631C24—22no—
632C24—84no—
633C24—88no—
634C24—221no—
635C24C2×C22⋊D1112yes—
636C24C2×C22⋊D1111yescharacteristic
637#41—232no—
638#41—232no—
639#41—232no—
640#41—216no—
641#41—216no—
642#41—28no—
643#41—28no—
644#41—28no—
645#41—28no—
646#41—24no—
647#41—24no—
648#41—24no—
649#41—24no—
650#41—24no—
651#41—24no—
652#41—224no—
653#41—224no—
654#41—224no—
655#41—224no—
656#41—444no—
657#41—444no—
658#41C2×C22⋊D1118yes—
659#41C2×C22⋊D1118yes—
660C2×Q8—24no—
661C2×Q8—22no—
662C2×Q8—21no—
663C2×Q8—112no—
664C2×Q8—221no—
665C2×Q8—222no—
666C2×Q8—222no—
667C2×Q8C2×C22⋊D1114yes—
668C2×Q8C2×C22⋊D1112yes—
669C2×Q8C2×C22⋊D1112yes—
670C2×Q8C23×D1112yes—
671C2×D4—216no—
672C2×D4—216no—
673C2×D4—264no—
674C2×D4—264no—
675C2×D4—232no—
676C2×D4—232no—
677C2×D4—232no—
678C2×D4—28no—
679C2×D4—28no—
680C2×D4—28no—
681C2×D4—22no—
682C2×D4—22no—
683C2×D4—216no—
684C2×D4—216no—
685C2×D4—24no—
686C2×D4—28no—
687C2×D4—28no—
688C2×D4—28no—
689C2×D4—28no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—21no—
693C2×D4—22no—
694C2×D4—24no—
695C2×D4—22no—
696C2×D4—24no—
697C2×D4—24no—
698C2×D4—112no—
699C2×D4—222no—
700C2×D4—222no—
701C2×D4—228no—
702C2×D4—222no—
703C2×D4—222no—
704C2×D4—221no—
705C2×D4—444no—
706C2×D4C2×C22⋊D1114yes—
707C2×D4C2×C22⋊D1114yes—
708C2×D4C2×C22⋊D1112yes—
709C2×D4C2×C22⋊D1112yes—
710C2×D4C2×C22⋊D1118yes—
711C2×D4C2×C22⋊D1114yes—
712C2×D4C2×C22⋊D1118yes—
713C2×D4C2×C22⋊D1118yes—
714C2×D4C23×D1112yes—
715C2×D4C23×D1114yes—
716C22×C4—216no—
717C22×C4—21no—
718C22×C4—28no—
719C22×C4—28no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—24no—
723C22×C4—24no—
724C22×C4—221no—
725C22×C4—222no—
726C22×C4—222no—
727C22×C4—222no—
728C22×C4—444no—
729C22×C4C2×C22⋊D1114yes—
730C22×C4C2×C22⋊D1112yes—
731C22×C4C2×C22⋊D1111yescharacteristic
732C22×C4C2×C22⋊D1111yescharacteristic
733C22×C4C2×C22⋊D1111yescharacteristic
734C22×C4C2×C22⋊D1114yes—
735C22×C4C2×C22⋊D1114yes—
736C22×C4C23×D1114yes—
737C22×C4C23×D1111yescharacteristic
738C22×C4C23×D1111yescharacteristic
739C22×C4C23×D1111yescharacteristic
740Q16—228no—
741SD16—228no—
742SD16—2216no—
743SD16—228no—
744D8—2216no—
745D8—228no—
746M16—224no—
747M16—224no—
748M16—224no—
749M16—224no—
750C2×C8—114no—
751C2×C8—114no—
752C2×C8—224no—
753C2×C8—224no—
754C4⋊C4—114no—
755C4⋊C4—222no—
756C4⋊C4—228no—
757C22⋊C4—222no—
758C22⋊C4—222no—
759C22⋊C4—228no—
760C22⋊C4—228no—
761C42—222no—
762C42—222no—
763C11#6036711yescharacteristic, complemented, Sylow
764C23—232no—
765C23—24no—
766C23—28no—
767C23—24no—
768C23—24no—
769C23—22no—
770C23—28no—
771C23—28no—
772C23—42no—
773C23—44no—
774C23—44no—
775C23—48no—
776C23—84no—
777C23—84no—
778C23—816no—
779C23—816no—
780C23—832no—
781C23—222no—
782C23—442no—
783C23—882no—
784C23#6700614yes—
785C23C22×C22⋊D1114yes—
786C23C22×C22⋊D1111yescharacteristic
787C23C22×C22⋊D1111yescharacteristic
788C23C22×C22⋊D1111yescharacteristic
789Q8—24no—
790Q8—24no—
791Q8—24no—
792Q8—22no—
793Q8—222no—
794Q8—222no—
795Q8—442no—
796Q8C22×C22⋊D1114yes—
797D4—232no—
798D4—232no—
799D4—28no—
800D4—28no—
801D4—28no—
802D4—28no—
803D4—24no—
804D4—24no—
805D4—28no—
806D4—28no—
807D4—24no—
808D4—28no—
809D4—24no—
810D4—22no—
811D4—222no—
812D4—222no—
813D4—444no—
814D4—444no—
815D4—442no—
816D4—888no—
817D4C22×C22⋊D1114yes—
818D4C22×C22⋊D1118yes—
819C2×C4—232no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—22no—
823C2×C4—28no—
824C2×C4—28no—
825C2×C4—28no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—224no—
829C2×C4—222no—
830C2×C4—442no—
831C2×C4—444no—
832C2×C4—444no—
833C2×C4—882no—
834C2×C4#6700614yes—
835C2×C4#6700614yes—
836C2×C4#6700614yes—
837C2×C4C22×C22⋊D1114yes—
838C2×C4C22×C22⋊D1111yescharacteristic
839C2×C4C22×C22⋊D1111yescharacteristic
840C2×C4C22×C22⋊D1111yescharacteristic
841C2×C4C22×C22⋊D1112yes—
842C2×C4C22×C22⋊D1112yes—
843C2×C4C22×C22⋊D1112yes—
844C2×C4C22×C22⋊D1112yes—
845C2×C4C22×C22⋊D1112yes—
846C2×C4C22×C22⋊D1112yes—
847C2×C4C24×D1111yescharacteristic
848C8—224no—
849C8—224no—
850C22—22no—
851C22—22no—
852C22—22no—
853C22—28no—
854C22—24no—
855C22—28no—
856C22—24no—
857C22—44no—
858C22—48no—
859C22—416no—
860C22—48no—
861C22—48no—
862C22—44no—
863C22—88no—
864C22—88no—
865C22—832no—
866C22—444no—
867C22—442no—
868C22—884no—
869C22C2×#6700612yes—
870C22C2×#6700612yes—
871C22C2×#6700612yes—
872C22C23×C22⋊D1111yescharacteristic
873C4—24no—
874C4—24no—
875C4—444no—
876C4—442no—
877C4C2×#6700612yes—
878C4C2×#6700612yes—
879C4C2×#6700612yes—
880C4C23×C22⋊D1111yescharacteristic
881C4C23×C22⋊D1111yescharacteristic
882C2—22no—
883C2—22no—
884C2—22no—
885C2—44no—
886C2—48no—
887C2—44no—
888C2—882no—
889C2C22×#6700611yescharacteristic
890C2#1308339612yes—
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×H(5,𝔽2)C2
socleC22×C11C23×D4
hypercenterC22×H(5,𝔽2)D11
hypocenterC11#60367
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×#41 ◁ C22×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. C2×#10623353C2semidirect
2. C22×#66985C2semidirect
3. #13081945C2semidirect
4. #13077920C2semidirect
5. #13077893C2semidirect
6. #13077884C2semidirect
7. #13077858C2semidirect
8. #13077843C2semidirect
9. #13077135C2semidirect
10. C2×#10622828C2semidirect
11. #13077061C2semidirect
12. C22×C11×H(5,𝔽2)C2semidirect
18. C2×C11×H(5,𝔽2)C22semidirect
22. C22×C11×#41C22semidirect
26. C23×D4×C11C22semidirect
27. C22×#4339C22semidirect
28. #10623364C22semidirect
30. #10623361C22semidirect
32. #10623356C22semidirect
33. C2×#67004C22semidirect
35. C2×#67003C22semidirect
36. C2×#67002C22semidirect
38. C2×#66995C22semidirect
41. C22×#4324C22semidirect
43. C2×#66985C22semidirect
44. C2×#66985C22semidirect
45. C2×#66985C22semidirect
46. C22×#4323C22semidirect
47. #10623322C22semidirect
48. C2×#66979C22semidirect
49. C22×#4318C22semidirect
50. C22×#4318C22semidirect
51. #10622852C22semidirect
52. #10622851C22semidirect
53. #10622847C22semidirect
54. #10622847C22semidirect
55. #10622846C22semidirect
56. #10622845C22semidirect
57. #10622838C22semidirect
58. #10622831C22semidirect
59. #10622830C22semidirect
60. #10622828C22semidirect
61. #10622828C22semidirect
62. #10622828C22semidirect
63. C2×#66896C22semidirect
64. #10622820C22semidirect
86. C2×C11×#41D4semidirect
112. C22×D4×C11D4semidirect
128. C2×#4339C23semidirect
129. C22×D44C23semidirect
131. C22×Dic22C23semidirect
140. C2×#4326C23semidirect
142. C2×#4325C23semidirect
150. C2×#4324C23semidirect
151. C2×#4324C23semidirect
156. C2×#4323C23semidirect
157. C2×#4323C23semidirect
158. #66983C23semidirect
164. #66979C23semidirect
165. C2×C4⋊Dic11C23semidirect
166. #66977C23semidirect
172. C2×#4318C23semidirect
173. C2×#4318C23semidirect
174. C22×C11⋊C8C23semidirect
175. C22×C11⋊C8C23semidirect
176. #66899C23semidirect
177. #66896C23semidirect
178. #66896C23semidirect
179. C22⋊(C11⋊C8)C23semidirect
319. C22×H(5,𝔽2)D11semidirect
422. C2×H(5,𝔽2)C2×D11semidirect
427. C22×#41C2×D11semidirect
431. C23×D4C2×D11semidirect
528. C2×#41C22⋊D11semidirect
557. C22×D4C22⋊D11semidirect
763. C11#60367semidirect

Maximal subgroups

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

subgroupindex
C2×#106233532
C22×#669852
#130819452
#130779202
#130778932
#130778842
#130778582
#130778432
#130771352
C2×#106228282
#130770612
C22×C11×H(5,𝔽2)2
#6036711