Finite Group Databasebeta

← #14769531

Subgroups — #14769531

Order 2816.

1650 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67002C211yesmaximal, characteristic
2C2×#10622398C211yesmaximal, characteristic, complemented
3C2×#10622369C211yesmaximal, characteristic, complemented
4#13071446C211yesmaximal, characteristic, complemented
5#13071436C211yesmaximal, characteristic, complemented
6#13069494C211yesmaximal, characteristic, complemented
7#13069467C211yesmaximal, characteristic, complemented
8#13068962C211yesmaximal, characteristic, complemented
9#13068962C211yesmaximal, characteristic, complemented
10#13068947C211yesmaximal, characteristic, complemented
11#13068947C211yesmaximal, characteristic, complemented
12#13068647C211yesmaximal, characteristic, complemented
13#13068548C211yesmaximal, characteristic, complemented
14#13068402C211yesmaximal, characteristic, complemented
15C11×#1788C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C23×D44C2211yescharacteristic
18C2×#67002—24no—
19C2×#67002—24no—
20C2×#67002C418yescomplemented
21C22×#4325C2211yescharacteristic
22C22×#4325C2211yescharacteristic
23C2×D4×Dic11C2211yescharacteristic, complemented
24C2×D4×Dic11C2211yescharacteristic, complemented
25C22×#4323C2211yescharacteristic
26C22×#4323C2211yescharacteristic
27C22×#4318C2211yescharacteristic
28C2×#66946C2211yescharacteristic
29C2×#66946C2211yescharacteristic
30C2×C22⋊C4×D11—21no—
31C2×C11×#103C2211yescharacteristic, complemented
32C2×C11×#103C2211yescharacteristic, complemented
33C2×C11×#102C2211yescharacteristic, complemented
34C2×C11×#102C2211yescharacteristic, complemented
35C2×C11×C22⋊C8C2211yescharacteristic
36C11×#380C2211yescharacteristic
37#10622843C2211yescharacteristic, complemented
38#10622843C2211yescharacteristic, complemented
39#10622833—21no—
40#10622833—21no—
41#10622825C2211yescharacteristic
42#10622824—21no—
43C4×C22⋊Dic11C2211yescharacteristic
44C2×C11⋊#95—21no—
45C2×#66885C2211yescharacteristic
46C2×#66885C2211yescharacteristic
47C2×#66885C2211yescharacteristic
48C2×#66885C2211yescharacteristic
49C2×#66879C2211yescharacteristic, complemented
50C2×C8×Dic11C2211yescharacteristic, complemented
51#10622601C2211yescharacteristic
52#10622601C2211yescharacteristic
53C2×#66872C2211yescharacteristic, complemented
54C2×#66871C2211yescharacteristic, complemented
55#10622568—21no—
56#10622398—24no—
57#10622369—24no—
58#10622278—21no—
59#10622278—21no—
60#10622188C2211yescharacteristic, complemented
61#10622188C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63#10622167C2211yescharacteristic, complemented
64C24×D11—21no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—41no—
69C2×C11×#41—41no—
70C2×C11×#41C2×C414yescomplemented
71C22×Q8×C11C2311yescharacteristic
72C22×D4×C11—21no—
73C22×D4×C11C2311yescharacteristic
74C23×C4×C11—21no—
75C23×C4×C11C2311yescharacteristic
76C23×Dic11—21no—
77C23×Dic11—21no—
78C22×D44—22no—
79C22×D44—22no—
80C22×D44—21no—
81C22×D44—22no—
82C22×D44—41no—
83C22×D44—41no—
84C22×D44C2×C414yescomplemented
85C22×D44C2311yescharacteristic
86C22×D44C2311yescharacteristic
87C22×C4×D11—21no—
88C22×C4×D11—21no—
89C22×C8×C11C2311yescharacteristic
90C22×C8×C11C2311yescharacteristic
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C22⋊C4—21no—
94C2×C22⋊Dic11—21no—
95C2×C22⋊Dic11—21no—
96C2×C22⋊Dic11—21no—
97C2×C22⋊Dic11D411yescharacteristic
98C2×C22⋊Dic11D411yescharacteristic
99#67002—232no—
100C2×#4325—22no—
101C2×#4325—22no—
102C2×#4325—22no—
103C2×#4325—22no—
104C2×#4325C2×C414yescomplemented
105C2×#4325C2×C414yescomplemented
106D4×Dic11—22no—
107D4×Dic11—22no—
108D4×Dic11—41no—
109D4×Dic11—41no—
110C2×#4323—22no—
111C2×#4323—22no—
112C2×#4323C2×C414yes—
113C2×#4323C2×C414yescomplemented
114C2×#4323D414yes—
115C2×#4323D414yes—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×(C2×D11)⋊C4—21no—
121C2×(C2×D11)⋊C4—21no—
122C2×C4⋊Dic11C2311yescharacteristic
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4×Dic11C2311yescharacteristic
125C2×C4×Dic11C2311yescharacteristic
126C2×#4318—22no—
127C2×#4318—22no—
128C2×#4318C2×C414yescomplemented
129C22×C11⋊C8C2311yescharacteristic
130C22×C11⋊C8C2311yescharacteristic
131#66946—22no—
132#66946—22no—
133#66946—41no—
134#66946—41no—
135C22⋊C4×D11—44no—
136C11×#103—41no—
137C11×#103—41no—
138C11×#102—22no—
139C11×#102—22no—
140C11×C22⋊C8—22no—
141C11×#95—21no—
142C11⋊#95—21no—
143C11⋊#95—21no—
144C11⋊#95—21no—
145C11⋊#95—21no—
146C11⋊#95—21no—
147C11⋊#95D411yescharacteristic
148C11⋊#95D411yescharacteristic
149#66885—22no—
150#66885—22no—
151#66885—41no—
152#66885—41no—
153#66879—22no—
154C8×Dic11—22no—
155#66872—22no—
156#66871—22no—
157#22442—111nomaximal, Sylow
158C24×C11—21no—
159C24×C11C2×D411yescharacteristic
160C23×D11—21no—
161C23×D11—21no—
162C23×D11—24no—
163C23×D11—42no—
164C23×D11—42no—
165C23×D11—42no—
166C23×D11—42no—
167C23×D11—81no—
168C23×D11—81no—
169C11×#41—28no—
170C11×#41—44no—
171C11×#41—44no—
172C11×#41—44no—
173C2×Q8×C11—21no—
174C2×Q8×C11—21no—
175C2×Q8×C11—21no—
176C2×Q8×C11—21no—
177C2×Q8×C11—21no—
178C2×Q8×C11C22×C412yes—
179C2×D4×C11—24no—
180C2×D4×C11—21no—
181C2×D4×C11—21no—
182C2×D4×C11—21no—
183C2×D4×C11—42no—
184C2×D4×C11—42no—
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—24no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—42no—
197C22×C4×C11—42no—
198C22×C4×C11C22×C412yes—
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11#4112yes—
201C22×C4×C11C2411yescharacteristic
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
214C2×D44—28no—
215C2×D44—24no—
216C2×D44—21no—
217C2×D44—21no—
218C2×D44—21no—
219C2×D44—21no—
220C2×D44—21no—
221C2×D44—21no—
222C2×D44—21no—
223C2×D44—21no—
224C2×D44—42no—
225C2×D44—42no—
226C2×D44—44no—
227C2×D44—44no—
228C2×D44—44no—
229C2×D44C22×C412yes—
230C2×D44C22×C412yes—
231C2×D44C2×D412yes—
232C2×D44C2×D412yes—
233C2×C4×D11—42no—
234C2×C4×D11—42no—
235C2×C4×D11—42no—
236C2×C4×D11—42no—
237C2×C4×D11—81no—
238C2×C4×D11—81no—
239C2×C8×C11—21no—
240C2×C8×C11—21no—
241C2×C8×C11—21no—
242C2×C8×C11—21no—
243C2×C8×C11—21no—
244C2×C8×C11—21no—
245C11×C4⋊C4—21no—
246C11×C4⋊C4—21no—
247C11×C4⋊C4—21no—
248C11×C4⋊C4—21no—
249C11×C22⋊C4—42no—
250C22⋊Dic11—22no—
251C22⋊Dic11—41no—
252C22⋊Dic11—42no—
253C22⋊Dic11—42no—
254C22⋊Dic11—81no—
255#4325—28no—
256#4325—28no—
257#4323—28no—
258#4323C22⋊C4116yescomplemented
259(C2×D11)⋊C4—42no—
260(C2×D11)⋊C4—42no—
261(C2×D11)⋊C4—42no—
262(C2×D11)⋊C4—42no—
263(C2×D11)⋊C4—81no—
264(C2×D11)⋊C4—81no—
265C4⋊Dic11—21no—
266C4⋊Dic11—21no—
267C4⋊Dic11—21no—
268C4⋊Dic11—21no—
269C4×Dic11—21no—
270C4×Dic11—21no—
271C4×Dic11—21no—
272C4×Dic11—21no—
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×#442—111no—
282C2×C4×D8—111no—
283#2339—111no—
284D4×C22⋊C4—111no—
285#1973—111no—
286#1968—111no—
287#1879—111no—
288#1879—111no—
289#1877—111no—
290#1877—111no—
291#1809—111no—
292#1788D1111yescharacteristic, complemented
293#1786—111no—
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—41no—
305C23×C11—41no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11C4×D412yes—
309C23×C11C22×D411yescharacteristic
310C22×D11—22no—
311C22×D11—22no—
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—48no—
315C22×D11—41no—
316C22×D11—41no—
317C22×D11—41no—
318C22×D11—41no—
319C22×D11—48no—
320C22×D11—41no—
321C22×D11—41no—
322C22×D11—41no—
323C22×D11—41no—
324C22×D11—41no—
325C22×D11—41no—
326C22×D11—84no—
327C22×D11—84no—
328C22×D11—84no—
329C22×D11—84no—
330C22×D11—84no—
331Q8×C11—22no—
332Q8×C11—22no—
333Q8×C11—41no—
334Q8×C11—41no—
335D4×C11—22no—
336D4×C11—22no—
337D4×C11—22no—
338D4×C11—48no—
339D4×C11C2×C22⋊C414yescomplemented
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—22no—
347C2×C4×C11—48no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11C4×D412yes—
357C2×C4×C11C23×C411yescharacteristic
358C2×C4×C11C22×D411yescharacteristic
359C2×C4×C11C22×D411yescharacteristic
360C2×C4×C11C2×#4111yescharacteristic
361C2×C4×C11H(5,𝔽2)11yescharacteristic
362C2×C4×C11H(5,𝔽2)11yescharacteristic
363C2×Dic11—21no—
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—22no—
386D44—22no—
387D44—22no—
388D44—48no—
389D44—41no—
390D44—41no—
391D44C2×C22⋊C414yes—
392C4×D11—84no—
393C4×D11—84no—
394C8×C11—41no—
395C8×C11—41no—
396C11⋊C8—22no—
397C11⋊C8C2×C22⋊C414yescomplemented
398C22×#41C2×D1111yescharacteristic
399C23×D4—111no—
400C2×AGL(1,ℤ/8)—118no—
401C2×AGL(1,ℤ/8)—224no—
402C2×AGL(1,ℤ/8)—224no—
403C22×SD16—111no—
404C22×SD16—111no—
405C22×D8—111no—
406C22×D8—111no—
407C22×M16—111no—
408C2×C4×D4—111no—
409C2×C4×D4—111no—
410C2×C4×D4—111no—
411C2×C4×D4—111no—
412C22×C22⋊C4—221no—
413#442—224no—
414C4×D8—224no—
415C2×#107—111no—
416C2×#106—111no—
417C2×#103C2×D1111yescharacteristic, complemented
418C2×#103C2×D1111yescharacteristic, complemented
419C2×#102—111no—
420C2×#102—111no—
421C2×#102—111no—
422C2×#102—111no—
423C2×#102C2×D1111yescharacteristic, complemented
424C2×#102C2×D1111yescharacteristic, complemented
425C2×C22⋊C8C2×D1111yescharacteristic
426C2×#97—111no—
427C2×C4×C8—111no—
428#391—111no—
429#391—111no—
430#390—111no—
431#390—111no—
432#386—221no—
433#386—221no—
434#386—221no—
435#386—221no—
436#381—221no—
437#380—111no—
438#380C2×D1111yescharacteristic
439#379—221no—
440C4×C22⋊C4—111no—
441C2×#95—221no—
442#340—111no—
443#340—111no—
444#336—111no—
445#336—111no—
446C22×C11—22no—
447C22×C11—24no—
448C22×C11—22no—
449C22×C11—22no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—41no—
453C22×C11—42no—
454C22×C11—41no—
455C22×C11—42no—
456C22×C11—41no—
457C22×C11—42no—
458C22×C11—41no—
459C22×C11—42no—
460C22×C11C2×C4×D411yescharacteristic
461C22×C11D4211yescharacteristic
462C22×C11D4211yescharacteristic
463C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
464C22×C11#57511yescharacteristic
465C22×C11#57611yescharacteristic
466C22×C11#57711yescharacteristic
467C2×D11—24no—
468C2×D11—42no—
469C2×D11—42no—
470C2×D11—42no—
471C2×D11—42no—
472C2×D11—42no—
473C2×D11—42no—
474C2×D11—42no—
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—816no—
478C2×D11—81no—
479C2×D11—81no—
480C2×D11—81no—
481C2×D11—81no—
482C4×C11—22no—
483C4×C11—42no—
484C4×C11—81no—
485C4×C11—81no—
486C4×C11C22×C22⋊C411yescharacteristic
487C4×C11#51811yescharacteristic
488C4×C11#54611yescharacteristic
489C4×C11#54611yescharacteristic
490Dic11—22no—
491Dic11—41no—
492Dic11—41no—
493Dic11—41no—
494Dic11—81no—
495Dic11—81no—
496C25—221no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41C4×D1114yescomplemented
503C22×Q8C22×D1111yescharacteristic
504C22×D4—21no—
505C22×D4—114no—
506C22×D4—111no—
507C22×D4—111no—
508C22×D4—222no—
509C22×D4—222no—
510C22×D4—221no—
511C22×D4—222no—
512C22×D4—441no—
513C22×D4—441no—
514C22×D4C22×D1111yescharacteristic
515C23×C4—21no—
516C23×C4—221no—
517C23×C4—221no—
518C23×C4—221no—
519C23×C4—221no—
520C23×C4C22×D1111yescharacteristic
521AGL(1,ℤ/8)—2232no—
522C2×SD16—114no—
523C2×SD16—114no—
524C2×SD16—222no—
525C2×SD16—222no—
526C2×SD16—222no—
527C2×SD16—222no—
528C2×D8—114no—
529C2×D8—114no—
530C2×D8—114no—
531C2×D8—114no—
532C2×D8—222no—
533C2×D8—222no—
534C2×M16—114no—
535C2×M16—222no—
536C2×M16—222no—
537C22×C8—111no—
538C22×C8—111no—
539C22×C8C22×D1111yescharacteristic
540C22×C8C22×D1111yescharacteristic
541C4×D4—222no—
542C4×D4—222no—
543C4×D4—222no—
544C4×D4—222no—
545C4×D4—441no—
546C4×D4—441no—
547C4×D4—441no—
548C4×D4—441no—
549C2×C4⋊C4—111no—
550C2×C4⋊C4—111no—
551C2×C4⋊C4C22×D1111yescharacteristic
552C2×C4⋊C4C22×D1111yescharacteristic
553C2×C22⋊C4—21no—
554C2×C22⋊C4—111no—
555C2×C22⋊C4—111no—
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—
568#107—222no—
569#106—222no—
570#103—41no—
571#103—41no—
572#102—22no—
573#102—22no—
574#102—222no—
575#102—222no—
576#102—441no—
577#102—441no—
578C22⋊C8—22no—
579#97—222no—
580C4×C8—222no—
581#95—21no—
582#95—111no—
583#95—111no—
584#95—221no—
585#95—221no—
586#95—221no—
587#95—221no—
588#95—221no—
589C2×C11—42no—
590C2×C11—44no—
591C2×C11D4×C22⋊C411yescharacteristic
592C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
593C2×C11#294611yescharacteristic
594C2×C11#326411yescharacteristic
595C2×C11#326711yescharacteristic
596C2×C11#327211yescharacteristic
597C2×C11#327311yescharacteristic
598D11—44no—
599D11—82no—
600C24—21no—
601C24—221no—
602C24—221no—
603C24—224no—
604C24—442no—
605C24—442no—
606C24—442no—
607C24—442no—
608C24—881no—
609C24—881no—
610C24D4×D1111yescharacteristic
611#41—28no—
612#41—44no—
613#41—44no—
614#41—44no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8C2×C4×D1112yes—
621C2×D4—24no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—112no—
628C2×D4—112no—
629C2×D4—112no—
630C2×D4—112no—
631C2×D4—228no—
632C2×D4—224no—
633C2×D4—221no—
634C2×D4—221no—
635C2×D4—221no—
636C2×D4—221no—
637C2×D4—221no—
638C2×D4—221no—
639C2×D4—221no—
640C2×D4—221no—
641C2×D4—444no—
642C2×D4—444no—
643C2×D4—444no—
644C2×D4—442no—
645C2×D4—442no—
646C2×D4C2×C4×D1112yes—
647C2×D4D4×D1112yes—
648C2×D4D4×D1112yes—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—24no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—111no—
660C22×C4—111no—
661C22×C4—111no—
662C22×C4—111no—
663C22×C4—221no—
664C22×C4—221no—
665C22×C4—442no—
666C22×C4—442no—
667C22×C4—442no—
668C22×C4—442no—
669C22×C4—442no—
670C22×C4—442no—
671C22×C4—442no—
672C22×C4—442no—
673C22×C4—881no—
674C22×C4—881no—
675C22×C4—881no—
676C22×C4—881no—
677C22×C4C2×C4×D1112yes—
678C22×C4D4×D1111yescharacteristic
679C22×C4#434112yes—
680C22×C4C23×D1111yescharacteristic
681SD16—228no—
682SD16—228no—
683D8—1116no—
684D8—228no—
685M16—228no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—112no—
693C2×C8—112no—
694C2×C8—112no—
695C2×C8—112no—
696C2×C8—221no—
697C2×C8—221no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—221no—
703C4⋊C4—221no—
704C4⋊C4—221no—
705C4⋊C4—221no—
706C22⋊C4—42no—
707C22⋊C4—222no—
708C22⋊C4—442no—
709C22⋊C4—442no—
710C22⋊C4—442no—
711C22⋊C4—442no—
712C22⋊C4—441no—
713C22⋊C4—442no—
714C22⋊C4—442no—
715C22⋊C4—881no—
716C22⋊C4—881no—
717C22⋊C4—881no—
718C42—221no—
719C42—221no—
720C42—221no—
721C42—221no—
722C11#2244211yescharacteristic, complemented, Sylow
723C23—22no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—22no—
729C23—22no—
730C23—21no—
731C23—21no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—222no—
737C23—222no—
738C23—222no—
739C23—222no—
740C23—448no—
741C23—448no—
742C23—441no—
743C23—441no—
744C23—441no—
745C23—441no—
746C23—441no—
747C23—441no—
748C23—441no—
749C23—441no—
750C23—441no—
751C23—441no—
752C23—884no—
753C23—884no—
754C23—884no—
755C23—884no—
756C23—884no—
757C23(C22⋊D11)⋊C412yes—
758C23C2×D4×D1111yescharacteristic
759Q8—22no—
760Q8—22no—
761Q8—41no—
762Q8—41no—
763D4—22no—
764D4—22no—
765D4—22no—
766D4—48no—
767D4—114no—
768D4—222no—
769D4—222no—
770D4—222no—
771D4—222no—
772D4—222no—
773D4—448no—
774D4—441no—
775D4—441no—
776D4C22⋊C4×D1114yescomplemented
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—48no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—112no—
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—221no—
803C2×C4—221no—
804C2×C4—221no—
805C2×C4—441no—
806C2×C4—441no—
807C2×C4—441no—
808C2×C4—441no—
809C2×C4—441no—
810C2×C4—441no—
811C2×C4—884no—
812C2×C4—884no—
813C2×C4—884no—
814C2×C4—884no—
815C2×C4(C22⋊D11)⋊C412yes—
816C2×C4C22×C4×D1111yescharacteristic
817C2×C4C2×D4×D1111yescharacteristic
818C2×C4C2×D4×D1111yescharacteristic
819C2×C4C2×#434111yescharacteristic
820C2×C4#6703711yescharacteristic
821C2×C4#6703711yescharacteristic
822C8—41no—
823C8—41no—
824C8—114no—
825C8—222no—
826C22—22no—
827C22—24no—
828C22—22no—
829C22—22no—
830C22—42no—
831C22—41no—
832C22—41no—
833C22—42no—
834C22—41no—
835C22—42no—
836C22—42no—
837C22—41no—
838C22—42no—
839C22—42no—
840C22—224no—
841C22—442no—
842C22—442no—
843C22—442no—
844C22—442no—
845C22—442no—
846C22—442no—
847C22—442no—
848C22—442no—
849C22—442no—
850C22—8816no—
851C22—881no—
852C22—881no—
853C22—881no—
854C22—881no—
855C22C2×(C22⋊D11)⋊C411yescharacteristic
856C22#1062312111yescharacteristic
857C22#1062312111yescharacteristic
858C22#1062330011yescharacteristic
859C22#1062330111yescharacteristic
860C22D11×AGL(1,ℤ/8)11yescharacteristic
861C22#1062330811yescharacteristic
862C4—22no—
863C4—42no—
864C4—81no—
865C4—81no—
866C4—222no—
867C4—441no—
868C4—441no—
869C4—441no—
870C4—881no—
871C4—881no—
872C4C2×C22⋊C4×D1111yescharacteristic
873C4#1062301711yescharacteristic
874C4#1062312211yescharacteristic
875C4#1062312211yescharacteristic
876C2—42no—
877C2—44no—
878C2—444no—
879C2—882no—
880C2#1307143211yescharacteristic
881C2#1307742911yescharacteristic
882C2#1307745111yescharacteristic
883C2#1308009911yescharacteristic
884C2#1308014411yescharacteristic
885C2#1308020911yescharacteristic
886C2#1308022011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1788C2
socleC23×C11C22×D4
prime radicalC22×#67002C2
cosocleC22×C4×C11C24
hypercenter#1788D11
hypocenterC11#22442
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×#10622398C2semidirect
3. C2×#10622369C2semidirect
4. #13071446C2semidirect
5. #13071436C2semidirect
6. #13069494C2semidirect
7. #13069467C2semidirect
8. #13068962C2semidirect
9. #13068962C2semidirect
10. #13068947C2semidirect
11. #13068947C2semidirect
12. #13068647C2semidirect
13. #13068548C2semidirect
14. #13068402C2semidirect
15. C11×#1788C2semidirect
20. C2×#67002C4semidirect
23. C2×D4×Dic11C22semidirect
24. C2×D4×Dic11C22semidirect
31. C2×C11×#103C22semidirect
32. C2×C11×#103C22semidirect
33. C2×C11×#102C22semidirect
34. C2×C11×#102C22semidirect
37. #10622843C22semidirect
38. #10622843C22semidirect
49. C2×#66879C22semidirect
50. C2×C8×Dic11C22semidirect
53. C2×#66872C22semidirect
54. C2×#66871C22semidirect
60. #10622188C22semidirect
61. #10622188C22semidirect
62. #10622167C22semidirect
63. #10622167C22semidirect
70. C2×C11×#41C2×C4semidirect
84. C22×D44C2×C4semidirect
104. C2×#4325C2×C4semidirect
105. C2×#4325C2×C4semidirect
113. C2×#4323C2×C4semidirect
128. C2×#4318C2×C4semidirect
258. #4323C22⋊C4semidirect
292. #1788D11semidirect
339. D4×C11C2×C22⋊C4semidirect
382. C2×Dic11AGL(1,ℤ/8)semidirect
397. C11⋊C8C2×C22⋊C4semidirect
417. C2×#103C2×D11semidirect
418. C2×#103C2×D11semidirect
423. C2×#102C2×D11semidirect
424. C2×#102C2×D11semidirect
502. C2×#41C4×D11semidirect
722. C11#22442semidirect
776. D4C22⋊C4×D11semidirect

Maximal subgroups

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

subgroupindex
C22×#670022
C2×#106223982
C2×#106223692
#130714462
#130714362
#130694942
#130694672
#130689622
#130689472
#130686472
#130685482
#130684022
C11×#17882
#2244211