Finite Group Databasebeta

← #14769557

Subgroups — #14769557

Order 2816.

1622 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66985C211yesmaximal, characteristic
2C2×#10622370C211yesmaximal, characteristic, complemented
3C2×#10622371C211yesmaximal, characteristic, complemented
4#13071453C211yesmaximal, characteristic, complemented
5D4×C22⋊Dic11C211yesmaximal, characteristic, complemented
6#13069489C211yesmaximal, characteristic, complemented
7#13069479C211yesmaximal, characteristic, complemented
8#13068968C211yesmaximal, characteristic, complemented
9#13068968C211yesmaximal, characteristic, complemented
10#13068962C211yesmaximal, characteristic, complemented
11#13068962C211yesmaximal, characteristic, complemented
12#13068647C211yesmaximal, characteristic, complemented
13#13068557C211yesmaximal, characteristic, complemented
14#13068402C211yesmaximal, characteristic, complemented
15C11×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C22×#4339C2211yescharacteristic
18C22×C22⋊Dic11—21no—
19C2×D4×Dic11C2211yescharacteristic
20C2×D4×Dic11C2211yescharacteristic
21C22×#4324C2211yescharacteristic
22C22×#4324C2211yescharacteristic
23C2×#66985—24no—
24C2×#66985—24no—
25C2×#66985C418yescomplemented
26C22×#4323C2211yescharacteristic
27C22×#4323C2211yescharacteristic
28C22×#4318C2211yescharacteristic
29C2×#66940C2211yescharacteristic, complemented
30C2×#66940C2211yescharacteristic, complemented
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic
35C2×C11×C22⋊C8C2211yescharacteristic
36C11×#380C2211yescharacteristic
37#10622860—21no—
38#10622834C2211yescharacteristic
39#10622834C2211yescharacteristic
40#10622833—21no—
41#10622833—21no—
42#10622825C2211yescharacteristic
43C4×C22⋊Dic11C2211yescharacteristic
44C2×#66885C2211yescharacteristic, complemented
45C2×#66885C2211yescharacteristic, complemented
46C2×#66880C2211yescharacteristic, complemented
47C2×#66880C2211yescharacteristic, complemented
48C2×#66879C2211yescharacteristic, complemented
49C2×C8×Dic11C2211yescharacteristic, complemented
50#10622601C2211yescharacteristic, complemented
51#10622601C2211yescharacteristic, complemented
52C2×#66872C2211yescharacteristic, complemented
53C2×#66871C2211yescharacteristic, complemented
54#10622570—21no—
55#10622570—21no—
56#10622371—24no—
57#10622370—24no—
58#10622280—21no—
59#10622279—21no—
60#10622188C2211yescharacteristic, complemented
61#10622188C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63#10622167C2211yescharacteristic, complemented
64C25×C11—21no—
65C22×D4×C11—22no—
66C22×D4×C11—22no—
67C22×D4×C11—21no—
68C22×D4×C11—22no—
69C22×D4×C11—41no—
70C22×D4×C11—41no—
71C22×D4×C11C2×C414yes—
72C22×D4×C11C2311yescharacteristic
73C22×D4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C22×C22⋊D11—21no—
76C23×Dic11—21no—
77C23×Dic11—21no—
78C2×#4339—22no—
79C2×#4339—22no—
80C2×#4339—22no—
81C2×#4339—41no—
82C2×#4339—41no—
83C2×#4339C2×C414yescomplemented
84C22×D44C2311yescharacteristic
85C22×C4×D11—21no—
86C22×Dic22C2311yescharacteristic
87C22×C8×C11C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C22⋊C4—21no—
92C2×C22⋊Dic11—21no—
93C2×C22⋊Dic11—21no—
94C2×C22⋊Dic11—21no—
95C2×C22⋊Dic11—21no—
96C2×C22⋊Dic11—21no—
97C2×C22⋊Dic11—21no—
98C2×C22⋊Dic11—21no—
99C2×C22⋊Dic11—44no—
100C2×C22⋊Dic11D411yescharacteristic
101C2×C22⋊Dic11D411yescharacteristic
102D4×Dic11—22no—
103D4×Dic11—22no—
104D4×Dic11—41no—
105D4×Dic11—41no—
106C2×#4324—22no—
107C2×#4324—22no—
108C2×#4324C2×C414yes—
109C2×#4324C2×C414yescomplemented
110C2×#4324D414yes—
111C2×#4324D414yes—
112#66985—232no—
113C2×#4323—22no—
114C2×#4323—22no—
115C2×#4323—22no—
116C2×#4323—22no—
117C2×#4323C2×C414yes—
118C2×#4323C2×C414yescomplemented
119C2×(C2×D11)⋊C4—21no—
120C2×(C2×D11)⋊C4—21no—
121C2×(C2×D11)⋊C4—21no—
122C2×(C2×D11)⋊C4—21no—
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×Dic11⋊C4—21no—
126C2×Dic11⋊C4—21no—
127C2×C4×Dic11—21no—
128C2×C4×Dic11—21no—
129C2×C4×Dic11C2311yescharacteristic
130C2×C4×Dic11C2311yescharacteristic
131C2×#4318—22no—
132C2×#4318—22no—
133C2×#4318C2×C414yescomplemented
134C22×C11⋊C8C2311yescharacteristic
135C22×C11⋊C8C2311yescharacteristic
136#66940—22no—
137#66940—22no—
138#66940—41no—
139#66940—41no—
140C11×#102—22no—
141C11×#102—22no—
142C11×#102—41no—
143C11×#102—41no—
144C11×C22⋊C8—22no—
145C11×#95—21no—
146C11⋊#95—21no—
147C11⋊#95D411yescharacteristic
148C11⋊#95D411yescharacteristic
149#66885—41no—
150#66885—41no—
151#66880—22no—
152#66880—22no—
153#66879—22no—
154C8×Dic11—22no—
155#66872—22no—
156#66871—22no—
157#22443—111nomaximal, Sylow
158C24×C11—21no—
159C24×C11—21no—
160C24×C11—24no—
161C24×C11—42no—
162C24×C11—42no—
163C24×C11—42no—
164C24×C11—42no—
165C24×C11—81no—
166C24×C11—81no—
167C24×C11C2×D411yescharacteristic
168C23×D11—21no—
169C2×D4×C11—28no—
170C2×D4×C11—24no—
171C2×D4×C11—21no—
172C2×D4×C11—21no—
173C2×D4×C11—21no—
174C2×D4×C11—21no—
175C2×D4×C11—21no—
176C2×D4×C11—21no—
177C2×D4×C11—21no—
178C2×D4×C11—21no—
179C2×D4×C11—44no—
180C2×D4×C11—44no—
181C2×D4×C11—44no—
182C2×D4×C11—42no—
183C2×D4×C11—42no—
184C2×D4×C11C22×C412yes—
185C2×D4×C11C22×C412yes—
186C2×D4×C11C2×D412yes—
187C2×D4×C11C2×D412yes—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11C22×C412yes—
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11#4112yes—
197C22×C4×C11C2411yescharacteristic
198C2×C22⋊D11—24no—
199C2×C22⋊D11—42no—
200C2×C22⋊D11—42no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—42no—
205C22×Dic11—42no—
206C22×Dic11—42no—
207C22×Dic11—42no—
208C22×Dic11—81no—
209C22×Dic11—81no—
210C22×Dic11C2×D411yescharacteristic
211C22×Dic11C2×D411yescharacteristic
212C22×Dic11C2×D411yescharacteristic
213C22×Dic11C2×D411yescharacteristic
214#4339—28no—
215#4339—44no—
216#4339—44no—
217#4339—44no—
218C2×D44—21no—
219C2×D44—21no—
220C2×D44—21no—
221C2×D44—21no—
222C2×D44—21no—
223C2×D44C22×C412yes—
224C2×C4×D11—24no—
225C2×C4×D11—42no—
226C2×C4×D11—42no—
227C2×Dic22—21no—
228C2×Dic22—21no—
229C2×Dic22—21no—
230C2×Dic22C22×C412yes—
231C2×Dic22C2×D412yes—
232C2×Dic22C2×D412yes—
233C2×C8×C11—21no—
234C2×C8×C11—21no—
235C2×C8×C11—21no—
236C2×C8×C11—21no—
237C2×C8×C11—21no—
238C2×C8×C11—21no—
239C11×C4⋊C4—21no—
240C11×C4⋊C4—21no—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—21no—
243C11×C22⋊C4—81no—
244C22⋊Dic11—22no—
245C22⋊Dic11—41no—
246C22⋊Dic11—42no—
247C22⋊Dic11—42no—
248C22⋊Dic11—42no—
249C22⋊Dic11—42no—
250C22⋊Dic11—42no—
251C22⋊Dic11—81no—
252C22⋊Dic11—81no—
253#4324—28no—
254#4324C22⋊C4116yescomplemented
255#4323—28no—
256#4323—28no—
257(C2×D11)⋊C4—42no—
258(C2×D11)⋊C4—42no—
259(C2×D11)⋊C4—81no—
260(C2×D11)⋊C4—81no—
261C4⋊Dic11—21no—
262C4⋊Dic11—21no—
263C4⋊Dic11—21no—
264C4⋊Dic11—21no—
265Dic11⋊C4—42no—
266Dic11⋊C4—42no—
267C4×Dic11—21no—
268C4×Dic11—21no—
269C4×Dic11—21no—
270C4×Dic11—21no—
271C4×Dic11—42no—
272C4×Dic11—42no—
273#4318—28no—
274C2×C11⋊C8—21no—
275C2×C11⋊C8—21no—
276C2×C11⋊C8C22×C412yes—
277C2×C11⋊C8C22×C412yes—
278C2×C11⋊C8C2×D412yes—
279C2×C11⋊C8C2×D412yes—
280C22×AGL(1,ℤ/8)—111no—
281C2×#440—111no—
282C2×C4×SD16—111no—
283#2341—111no—
284D4×C22⋊C4—111no—
285#1972—111no—
286#1970—111no—
287#1880—111no—
288#1880—111no—
289#1879—111no—
290#1879—111no—
291#1809—111no—
292#1788—111no—
293#1786D1111yescharacteristic, complemented
294#1753—111no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—21no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—22no—
305C23×C11—48no—
306C23×C11—48no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—41no—
315C23×C11—41no—
316C23×C11—41no—
317C23×C11—84no—
318C23×C11—84no—
319C23×C11—84no—
320C23×C11—84no—
321C23×C11—84no—
322C23×C11C4×D412yes—
323C23×C11C22×D411yescharacteristic
324C22×D11—22no—
325C22×D11—41no—
326C22×D11—41no—
327C22×D11—41no—
328C22×D11—41no—
329C22×D11—41no—
330C22×D11—41no—
331D4×C11—22no—
332D4×C11—22no—
333D4×C11—22no—
334D4×C11—22no—
335D4×C11—22no—
336D4×C11—48no—
337D4×C11—41no—
338D4×C11—41no—
339D4×C11C2×C22⋊C414yes—
340C2×C4×C11—21no—
341C2×C4×C11—21no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11C4×D412yes—
353C2×C4×C11C23×C411yescharacteristic
354C2×C4×C11C22×D411yescharacteristic
355C2×C4×C11C22×D411yescharacteristic
356C2×C4×C11C2×#4111yescharacteristic
357C2×C4×C11H(5,𝔽2)11yescharacteristic
358C2×C4×C11H(5,𝔽2)11yescharacteristic
359C22⋊D11—48no—
360C2×Dic11—22no—
361C2×Dic11—21no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—21no—
365C2×Dic11—21no—
366C2×Dic11—21no—
367C2×Dic11—21no—
368C2×Dic11—21no—
369C2×Dic11—21no—
370C2×Dic11—21no—
371C2×Dic11—21no—
372C2×Dic11—21no—
373C2×Dic11—21no—
374C2×Dic11—41no—
375C2×Dic11—41no—
376C2×Dic11—41no—
377C2×Dic11—41no—
378C2×Dic11—41no—
379C2×Dic11—41no—
380C2×Dic11—84no—
381C2×Dic11—84no—
382C2×Dic11AGL(1,ℤ/8)12yescomplemented
383D44—22no—
384D44—22no—
385D44—41no—
386D44—41no—
387C4×D11—48no—
388Dic22—22no—
389Dic22—22no—
390Dic22—22no—
391Dic22C2×C22⋊C414yescomplemented
392C8×C11—41no—
393C8×C11—41no—
394C11⋊C8—22no—
395C11⋊C8C2×C22⋊C414yescomplemented
396C22×#41—111no—
397C23×D4C2×D1111yescharacteristic
398C2×AGL(1,ℤ/8)—118no—
399C2×AGL(1,ℤ/8)—224no—
400C2×AGL(1,ℤ/8)—224no—
401C22×SD16—111no—
402C22×SD16—111no—
403C22×D8—111no—
404C22×D8—111no—
405C22×M16—111no—
406C2×C4×Q8—111no—
407C2×C4×Q8—111no—
408C2×C4×D4—111no—
409C2×C4×D4—111no—
410C22×C22⋊C4—221no—
411#440—224no—
412C4×SD16—224no—
413C2×#107—111no—
414C2×#106—111no—
415C2×#103—111no—
416C2×#103—111no—
417C2×#102—111no—
418C2×#102—111no—
419C2×#102C2×D1111yescharacteristic
420C2×#102C2×D1111yescharacteristic
421C2×#102C2×D1111yescharacteristic
422C2×#102C2×D1111yescharacteristic
423C2×C22⋊C8C2×D1111yescharacteristic
424C2×#97—111no—
425C2×C4×C8—111no—
426#390—111no—
427#390—111no—
428#390—111no—
429#390—111no—
430#390—221no—
431#390—221no—
432#386—221no—
433#386—221no—
434#380—111no—
435#380—221no—
436#380C2×D1111yescharacteristic
437#379—221no—
438C4×C22⋊C4—111no—
439C4×C22⋊C4—221no—
440#340—111no—
441#340—111no—
442#336—111no—
443#336—111no—
444C22×C11—22no—
445C22×C11—24no—
446C22×C11—22no—
447C22×C11—22no—
448C22×C11—42no—
449C22×C11—42no—
450C22×C11—41no—
451C22×C11—42no—
452C22×C11—41no—
453C22×C11—42no—
454C22×C11—41no—
455C22×C11—42no—
456C22×C11—41no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—42no—
461C22×C11—816no—
462C22×C11—81no—
463C22×C11—81no—
464C22×C11—81no—
465C22×C11—81no—
466C22×C11C2×C4×D411yescharacteristic
467C22×C11D4211yescharacteristic
468C22×C11D4211yescharacteristic
469C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
470C22×C11#57511yescharacteristic
471C22×C11#57611yescharacteristic
472C22×C11#57711yescharacteristic
473C2×D11—42no—
474C2×D11—42no—
475C2×D11—42no—
476C2×D11—81no—
477C2×D11—81no—
478C2×D11—81no—
479C2×D11—81no—
480C4×C11—22no—
481C4×C11—81no—
482C4×C11—81no—
483C4×C11C22×C22⋊C411yescharacteristic
484C4×C11#51811yescharacteristic
485C4×C11#54611yescharacteristic
486C4×C11#54611yescharacteristic
487Dic11—24no—
488Dic11—22no—
489Dic11—41no—
490Dic11—41no—
491Dic11—41no—
492Dic11—81no—
493Dic11—81no—
494C25—21no—
495C2×#41—114no—
496C2×#41—222no—
497C2×#41—222no—
498C2×#41—222no—
499C2×#41—441no—
500C2×#41—441no—
501C22×Q8—111no—
502C22×D4—22no—
503C22×D4—22no—
504C22×D4—21no—
505C22×D4—22no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4—111no—
509C22×D4—221no—
510C22×D4C4×D1114yes—
511C22×D4C22×D1111yescharacteristic
512C22×D4C22×D1111yescharacteristic
513C23×C4—221no—
514C23×C4—221no—
515C23×C4—221no—
516C23×C4C22×D1111yescharacteristic
517AGL(1,ℤ/8)—2232no—
518C2×SD16—114no—
519C2×SD16—114no—
520C2×SD16—114no—
521C2×SD16—114no—
522C2×SD16—222no—
523C2×SD16—222no—
524C2×D8—114no—
525C2×D8—114no—
526C2×D8—222no—
527C2×D8—222no—
528C2×D8—222no—
529C2×D8—222no—
530C2×M16—114no—
531C2×M16—222no—
532C2×M16—222no—
533C22×C8—111no—
534C22×C8—111no—
535C22×C8C22×D1111yescharacteristic
536C22×C8C22×D1111yescharacteristic
537C4×Q8—222no—
538C4×Q8—222no—
539C4×Q8—441no—
540C4×Q8—441no—
541C4×D4—222no—
542C4×D4—222no—
543C4×D4—441no—
544C4×D4—441no—
545C2×C4⋊C4—111no—
546C2×C4⋊C4—111no—
547C2×C4⋊C4—221no—
548C2×C4⋊C4—221no—
549C2×C4⋊C4C22×D1111yescharacteristic
550C2×C4⋊C4C22×D1111yescharacteristic
551C2×C22⋊C4—21no—
552C2×C22⋊C4—111no—
553C2×C22⋊C4—111no—
554C2×C22⋊C4—221no—
555C2×C22⋊C4—221no—
556C2×C22⋊C4—221no—
557C2×C22⋊C4—221no—
558C2×C22⋊C4—221no—
559C2×C22⋊C4—221no—
560C2×C22⋊C4—221no—
561C2×C22⋊C4—221no—
562C2×C22⋊C4—221no—
563C2×C22⋊C4—221no—
564C2×C22⋊C4—221no—
565C2×C22⋊C4—444no—
566C2×C42—111no—
567C2×C42—111no—
568C2×C42—221no—
569C2×C42—221no—
570#107—222no—
571#106—222no—
572#103—222no—
573#103—222no—
574#102—22no—
575#102—22no—
576#102—41no—
577#102—41no—
578#102—441no—
579#102—441no—
580C22⋊C8—22no—
581#97—222no—
582C4×C8—222no—
583#95—21no—
584#95—111no—
585#95—111no—
586#95—221no—
587C2×C11—42no—
588C2×C11—44no—
589C2×C11—82no—
590C2×C11D4×C22⋊C411yescharacteristic
591C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
592C2×C11#294611yescharacteristic
593C2×C11#326511yescharacteristic
594C2×C11#326811yescharacteristic
595C2×C11#327411yescharacteristic
596C2×C11#327511yescharacteristic
597D11—82no—
598C24—21no—
599C24—21no—
600C24—24no—
601C24—42no—
602C24—42no—
603C24—42no—
604C24—42no—
605C24—81no—
606C24—81no—
607C24—221no—
608C24D4×D1111yescharacteristic
609#41—228no—
610#41—444no—
611#41—444no—
612#41—444no—
613C2×Q8—112no—
614C2×Q8—112no—
615C2×Q8—112no—
616C2×Q8—221no—
617C2×Q8—221no—
618C2×Q8—221no—
619C2×D4—28no—
620C2×D4—24no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—44no—
630C2×D4—44no—
631C2×D4—44no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—112no—
635C2×D4—224no—
636C2×D4—221no—
637C2×D4—221no—
638C2×D4—221no—
639C2×D4—221no—
640C2×D4—221no—
641C2×D4—442no—
642C2×D4—442no—
643C2×D4C2×C4×D1112yes—
644C2×D4C2×C4×D1112yes—
645C2×D4D4×D1112yes—
646C2×D4D4×D1112yes—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—111no—
654C22×C4—111no—
655C22×C4—111no—
656C22×C4—111no—
657C22×C4—221no—
658C22×C4—224no—
659C22×C4—221no—
660C22×C4—221no—
661C22×C4—442no—
662C22×C4—442no—
663C22×C4—442no—
664C22×C4—442no—
665C22×C4—442no—
666C22×C4—442no—
667C22×C4—881no—
668C22×C4—881no—
669C22×C4C2×C4×D1112yes—
670C22×C4D4×D1111yescharacteristic
671C22×C4#434112yes—
672C22×C4C23×D1111yescharacteristic
673SD16—1116no—
674SD16—228no—
675D8—228no—
676D8—228no—
677M16—228no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—112no—
685C2×C8—112no—
686C2×C8—112no—
687C2×C8—112no—
688C2×C8—221no—
689C2×C8—221no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—221no—
695C4⋊C4—221no—
696C4⋊C4—221no—
697C4⋊C4—221no—
698C4⋊C4—442no—
699C4⋊C4—442no—
700C22⋊C4—81no—
701C22⋊C4—222no—
702C22⋊C4—442no—
703C22⋊C4—442no—
704C22⋊C4—442no—
705C22⋊C4—441no—
706C22⋊C4—442no—
707C22⋊C4—442no—
708C22⋊C4—442no—
709C22⋊C4—442no—
710C22⋊C4—881no—
711C22⋊C4—881no—
712C22⋊C4—881no—
713C22⋊C4—881no—
714C42—221no—
715C42—221no—
716C42—221no—
717C42—221no—
718C42—442no—
719C42—442no—
720C11#2244311yescharacteristic, complemented, Sylow
721C23—22no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—22no—
727C23—22no—
728C23—21no—
729C23—21no—
730C23—22no—
731C23—48no—
732C23—48no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—84no—
744C23—84no—
745C23—84no—
746C23—84no—
747C23—84no—
748C23—222no—
749C23—441no—
750C23—441no—
751C23—441no—
752C23—441no—
753C23—441no—
754C23—441no—
755C23(C22⋊D11)⋊C412yes—
756C23C2×D4×D1111yescharacteristic
757Q8—114no—
758Q8—222no—
759Q8—222no—
760Q8—222no—
761D4—22no—
762D4—22no—
763D4—22no—
764D4—22no—
765D4—22no—
766D4—48no—
767D4—41no—
768D4—41no—
769D4—222no—
770D4—222no—
771D4—448no—
772D4—441no—
773D4—441no—
774D4C22⋊C4×D1114yes—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—112no—
788C2×C4—222no—
789C2×C4—221no—
790C2×C4—221no—
791C2×C4—222no—
792C2×C4—222no—
793C2×C4—221no—
794C2×C4—221no—
795C2×C4—221no—
796C2×C4—221no—
797C2×C4—221no—
798C2×C4—221no—
799C2×C4—221no—
800C2×C4—221no—
801C2×C4—221no—
802C2×C4—448no—
803C2×C4—441no—
804C2×C4—441no—
805C2×C4—441no—
806C2×C4—441no—
807C2×C4—441no—
808C2×C4—441no—
809C2×C4—884no—
810C2×C4—884no—
811C2×C4(C22⋊D11)⋊C412yes—
812C2×C4C22×C4×D1111yescharacteristic
813C2×C4C2×D4×D1111yescharacteristic
814C2×C4C2×D4×D1111yescharacteristic
815C2×C4C2×#434111yescharacteristic
816C2×C4#6703711yescharacteristic
817C2×C4#6703711yescharacteristic
818C8—41no—
819C8—41no—
820C8—114no—
821C8—222no—
822C22—22no—
823C22—24no—
824C22—22no—
825C22—22no—
826C22—42no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—42no—
831C22—41no—
832C22—42no—
833C22—41no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—816no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—442no—
845C22—442no—
846C22—442no—
847C22—881no—
848C22—881no—
849C22—881no—
850C22—881no—
851C22C2×(C22⋊D11)⋊C411yescharacteristic
852C22#1062312111yescharacteristic
853C22#1062312111yescharacteristic
854C22#1062328811yescharacteristic
855C22#1062329311yescharacteristic
856C22D11×AGL(1,ℤ/8)11yescharacteristic
857C22#1062330411yescharacteristic
858C4—22no—
859C4—81no—
860C4—81no—
861C4—222no—
862C4—224no—
863C4—441no—
864C4—441no—
865C4—441no—
866C4—881no—
867C4—881no—
868C4C2×C22⋊C4×D1111yescharacteristic
869C4#1062301711yescharacteristic
870C4#1062312211yescharacteristic
871C4#1062312211yescharacteristic
872C2—42no—
873C2—44no—
874C2—82no—
875C2—882no—
876C2#1307143211yescharacteristic
877C2#1307742011yescharacteristic
878C2#1307744211yescharacteristic
879C2#1308010911yescharacteristic
880C2#1308015411yescharacteristic
881C2#1308023411yescharacteristic
882C2#1308025111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1786C2
socleC23×C11C22×D4
prime radicalC22×#66985C2
cosocleC22×C4×C11C24
hypercenter#1786D11
hypocenterC11#22443
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

Complements

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

NH ≅ G/Ntype
2. C2×#10622370C2semidirect
3. C2×#10622371C2semidirect
4. #13071453C2semidirect
5. D4×C22⋊Dic11C2semidirect
6. #13069489C2semidirect
7. #13069479C2semidirect
8. #13068968C2semidirect
9. #13068968C2semidirect
10. #13068962C2semidirect
11. #13068962C2semidirect
12. #13068647C2semidirect
13. #13068557C2semidirect
14. #13068402C2semidirect
15. C11×#1786C2semidirect
25. C2×#66985C4semidirect
29. C2×#66940C22semidirect
30. C2×#66940C22semidirect
44. C2×#66885C22semidirect
45. C2×#66885C22semidirect
46. C2×#66880C22semidirect
47. C2×#66880C22semidirect
48. C2×#66879C22semidirect
49. C2×C8×Dic11C22semidirect
50. #10622601C22semidirect
51. #10622601C22semidirect
52. C2×#66872C22semidirect
53. C2×#66871C22semidirect
60. #10622188C22semidirect
61. #10622188C22semidirect
62. #10622167C22semidirect
63. #10622167C22semidirect
83. C2×#4339C2×C4semidirect
109. C2×#4324C2×C4semidirect
118. C2×#4323C2×C4semidirect
133. C2×#4318C2×C4semidirect
254. #4324C22⋊C4semidirect
293. #1786D11semidirect
382. C2×Dic11AGL(1,ℤ/8)semidirect
391. Dic22C2×C22⋊C4semidirect
395. C11⋊C8C2×C22⋊C4semidirect
720. C11#22443semidirect

Maximal subgroups

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

subgroupindex
C22×#669852
C2×#106223702
C2×#106223712
#130714532
D4×C22⋊Dic112
#130694892
#130694792
#130689682
#130689622
#130686472
#130685572
#130684022
C11×#17862
#2244311