Finite Group Databasebeta

← #14769533

Subgroups — #14769533

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×#66964C211yesmaximal, characteristic
2C2×#10622398C211yesmaximal, characteristic, complemented
3C2×C4×#4323C211yesmaximal, characteristic, complemented
4#13071441C211yesmaximal, characteristic, complemented
5#13071437C211yesmaximal, characteristic, complemented
6#13069498C211yesmaximal, characteristic, complemented
7#13069469C211yesmaximal, characteristic, complemented
8#13068966C211yesmaximal, characteristic, complemented
9#13068951C211yesmaximal, characteristic, complemented
10#13068949C211yesmaximal, characteristic, complemented
11#13068648C211yesmaximal, characteristic, complemented
12#13068553C211yesmaximal, characteristic, complemented
13#13068545C211yesmaximal, characteristic, complemented
14#13068396C211yesmaximal, characteristic, complemented
15C11×#1879C211yesmaximal, characteristic, complemented
16C22×#4341C2211yescharacteristic
17C22×D4×D11C2211yescharacteristic
18C22×C11×D8C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic, complemented
20C2×D4×Dic11C2211yescharacteristic, complemented
21C22×#4324C2211yescharacteristic
22C22×#4323C2211yescharacteristic
23C2×#66964—24no—
24C2×#66964—24no—
25C2×#66964C418yescomplemented
26C22×#4314C2211yescharacteristic
27C22×#4313C2211yescharacteristic
28C2×#66946C2211yescharacteristic
29C2×C22⋊C4×D11—21no—
30C2×C4×D44C2211yescharacteristic
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic, complemented
33C11×#390C2211yescharacteristic
34#10622834C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic, complemented
37#10622826—21no—
38C2×C11⋊#95—21no—
39C2×#66885C2211yescharacteristic
40C2×(C2×D11)⋊C8C2211yescharacteristic
41C2×#66880C2211yescharacteristic, complemented
42C2×#66879C2211yescharacteristic, complemented
43C4×#4323—24no—
44#10622600C2211yescharacteristic
45#10622600C2211yescharacteristic
46#10622587C2211yescharacteristic, complemented
47C2×#66874C2211yescharacteristic, complemented
48C2×#66873C2211yescharacteristic
49C2×#66872C2211yescharacteristic, complemented
50C2×#66871C2211yescharacteristic, complemented
51#10622571—21no—
52#10622569—21no—
53#10622569—21no—
54#10622568—21no—
55#10622556—21no—
56C4×(C2×D11)⋊C4C2211yescharacteristic
57#10622542C2211yescharacteristic, complemented
58C2×C4×C11⋊C8C2211yescharacteristic, complemented
59#10622398—24no—
60C11×#340C2211yescharacteristic, complemented
61C11×#336C2211yescharacteristic, complemented
62#10622189C2211yescharacteristic, complemented
63#10622188C2211yescharacteristic, complemented
64C24×D11—21no—
65C22×D4×C11C2311yescharacteristic
66C22×D4×C11C2311yescharacteristic
67C23×C4×C11—21no—
68C22×C22⋊D11—21no—
69C22×C22⋊D11—21no—
70C23×Dic11—21no—
71C23×Dic11—21no—
72C2×#4341—22no—
73C2×#4341—22no—
74C2×#4341—22no—
75C2×#4341—41no—
76C2×#4341—41no—
77C2×#4341C2×C414yescomplemented
78C2×D4×D11—22no—
79C2×D4×D11—22no—
80C2×D4×D11—22no—
81C2×D4×D11—41no—
82C2×D4×D11—41no—
83C2×D4×D11C2×C414yescomplemented
84C22×D44C2311yescharacteristic
85C22×C4×D11—21no—
86C22×C4×D11—21no—
87C22×C4×D11C2311yescharacteristic
88C22×Dic22C2311yescharacteristic
89C2×C11×D8—22no—
90C2×C11×D8—22no—
91C2×C11×D8C2×C414yescomplemented
92C22×C8×C11C2311yescharacteristic
93C22×C8×C11C2311yescharacteristic
94C4×D4×C11—22no—
95C4×D4×C11—41no—
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C42×C11C2311yescharacteristic
102C2×C22⋊Dic11—21no—
103C2×C22⋊Dic11—21no—
104C2×C22⋊Dic11—21no—
105D4×Dic11—22no—
106D4×Dic11—41no—
107C2×#4324—22no—
108C2×#4324—22no—
109C2×#4324C2×C414yescomplemented
110C2×#4323C2×C414yes—
111C2×#4323D414yes—
112C2×#4323D414yes—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4D411yescharacteristic
118C2×(C2×D11)⋊C4D411yescharacteristic
119C2×C4⋊Dic11C2311yescharacteristic
120C2×C4⋊Dic11C2311yescharacteristic
121C2×C4×Dic11C2311yescharacteristic
122C22×C11⋊C8C2311yescharacteristic
123C22×C11⋊C8C2311yescharacteristic
124#66964—232no—
125C2×#4314—22no—
126C2×#4314—22no—
127C2×#4314C2×C414yescomplemented
128C2×#4313—22no—
129C2×#4313—22no—
130C2×#4313C2×C414yescomplemented
131#66946—22no—
132#66946—41no—
133C22⋊C4×D11—44no—
134C4×D44—22no—
135C4×D44—41no—
136C11×#102—22no—
137C11×#102—41no—
138#66896—22no—
139#66896—41no—
140C11⋊#95—21no—
141C11⋊#95—21no—
142C11⋊#95—21no—
143C11⋊#95—21no—
144C11⋊#95—21no—
145C11⋊#95—21no—
146C11⋊#95D411yescharacteristic
147C11⋊#95D411yescharacteristic
148#66885—22no—
149(C2×D11)⋊C8—22no—
150#66880—41no—
151#66879—22no—
152#66874—41no—
153#66873—22no—
154#66872—22no—
155#66871—22no—
156C4×C11⋊C8—22no—
157#22442—111nomaximal, Sylow
158C24×C11—21no—
159C24×C11—21no—
160C23×D11—21no—
161C23×D11—24no—
162C23×D11—42no—
163C23×D11—42no—
164C23×D11—42no—
165C23×D11—42no—
166C23×D11—81no—
167C23×D11—81no—
168C23×D11C2×D411yescharacteristic
169C2×D4×C11—21no—
170C2×D4×C11—21no—
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×C11C22×C412yes—
178C2×D4×C11C22×C412yes—
179C2×D4×C11C2×D412yes—
180C2×D4×C11C2×D412yes—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—42no—
184C22×C4×C11—42no—
185C22×C4×C11—81no—
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2411yescharacteristic
189C2×C22⋊D11—24no—
190C2×C22⋊D11—24no—
191C2×C22⋊D11—42no—
192C2×C22⋊D11—42no—
193C2×C22⋊D11—42no—
194C2×C22⋊D11—42no—
195C22×Dic11—24no—
196C22×Dic11—21no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—42no—
200C22×Dic11—42no—
201C22×Dic11—42no—
202C22×Dic11—42no—
203C22×Dic11—81no—
204C22×Dic11C2×D411yescharacteristic
205C22×Dic11C2×D411yescharacteristic
206C22×Dic11C2×D411yescharacteristic
207#4341—28no—
208#4341—44no—
209#4341—44no—
210#4341—44no—
211D4×D11—28no—
212D4×D11—44no—
213D4×D11—44no—
214D4×D11—44no—
215C2×D44—21no—
216C2×D44—21no—
217C2×D44—21no—
218C2×D44C22×C412yes—
219C2×D44C2×D412yes—
220C2×D44C2×D412yes—
221C2×C4×D11—21no—
222C2×C4×D11—21no—
223C2×C4×D11—21no—
224C2×C4×D11—21no—
225C2×C4×D11—42no—
226C2×C4×D11—42no—
227C2×C4×D11—42no—
228C2×C4×D11—42no—
229C2×C4×D11—81no—
230C2×C4×D11—81no—
231C2×C4×D11C22×C412yes—
232C2×C4×D11#4112yes—
233C2×Dic22—21no—
234C2×Dic22—21no—
235C2×Dic22—21no—
236C2×Dic22—21no—
237C2×Dic22—21no—
238C2×Dic22C22×C412yes—
239C11×D8—28no—
240C2×C8×C11—21no—
241C2×C8×C11—21no—
242C2×C8×C11—21no—
243C2×C8×C11—21no—
244C2×C8×C11—21no—
245C2×C8×C11C22×C412yes—
246C11×C4⋊C4—21no—
247C11×C4⋊C4—21no—
248C11×C4⋊C4—21no—
249C11×C4⋊C4—21no—
250C11×C22⋊C4—42no—
251C11×C22⋊C4—42no—
252C11×C22⋊C4—81no—
253C42×C11—21no—
254C42×C11—21no—
255C22⋊Dic11—42no—
256C22⋊Dic11—42no—
257C22⋊Dic11—81no—
258#4324—28no—
259#4323C22⋊C4116yescomplemented
260(C2×D11)⋊C4—22no—
261(C2×D11)⋊C4—41no—
262(C2×D11)⋊C4—42no—
263(C2×D11)⋊C4—42no—
264(C2×D11)⋊C4—42no—
265(C2×D11)⋊C4—81no—
266C4⋊Dic11—21no—
267C4⋊Dic11—21no—
268C4⋊Dic11—21no—
269C4⋊Dic11—21no—
270C4×Dic11—21no—
271C4×Dic11—21no—
272C2×C11⋊C8—21no—
273C2×C11⋊C8—21no—
274C2×C11⋊C8—21no—
275C2×C11⋊C8C22×C412yes—
276C2×C11⋊C8C2×D412yes—
277C2×C11⋊C8C2×D412yes—
278#4314—28no—
279#4313—28no—
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#1879D1111yescharacteristic, complemented
289#1877—111no—
290#1877—111no—
291#1809—111no—
292#1788—111no—
293#1786—111no—
294#1753—111no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—41no—
300C23×C11—41no—
301C23×C11—41no—
302C23×C11—41no—
303C23×C11—41no—
304C23×C11—41no—
305C23×C11—41no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11C22×D411yescharacteristic
310C22×D11—22no—
311C22×D11—22no—
312C22×D11—22no—
313C22×D11—21no—
314C22×D11—21no—
315C22×D11—21no—
316C22×D11—21no—
317C22×D11—21no—
318C22×D11—21no—
319C22×D11—48no—
320C22×D11—48no—
321C22×D11—41no—
322C22×D11—41no—
323C22×D11—41no—
324C22×D11—41no—
325C22×D11—84no—
326C22×D11—84no—
327C22×D11—84no—
328C22×D11—84no—
329C22×D11—84no—
330C22×D11C4×D412yes—
331D4×C11—22no—
332D4×C11—22no—
333D4×C11—22no—
334D4×C11—22no—
335D4×C11—22no—
336D4×C11—41no—
337D4×C11—41no—
338D4×C11C2×C22⋊C414yescomplemented
339C2×C4×C11—21no—
340C2×C4×C11—21no—
341C2×C4×C11—21no—
342C2×C4×C11—21no—
343C2×C4×C11—21no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11—84no—
351C2×C4×C11AGL(1,ℤ/8)12yescomplemented
352C2×C4×C11C23×C411yescharacteristic
353C2×C4×C11C22×D411yescharacteristic
354C2×C4×C11C22×D411yescharacteristic
355C2×C4×C11C2×#4111yescharacteristic
356C2×C4×C11H(5,𝔽2)11yescharacteristic
357C2×C4×C11H(5,𝔽2)11yescharacteristic
358C22⋊D11—48no—
359C22⋊D11—48no—
360C2×Dic11—21no—
361C2×Dic11—21no—
362C2×Dic11—22no—
363C2×Dic11—21no—
364C2×Dic11—21no—
365C2×Dic11—21no—
366C2×Dic11—21no—
367C2×Dic11—21no—
368C2×Dic11—21no—
369C2×Dic11—48no—
370C2×Dic11—41no—
371C2×Dic11—41no—
372C2×Dic11—41no—
373C2×Dic11—41no—
374C2×Dic11—41no—
375C2×Dic11—41no—
376C2×Dic11—41no—
377C2×Dic11—41no—
378C2×Dic11—84no—
379C2×Dic11C4×D412yes—
380D44—22no—
381D44—22no—
382D44—22no—
383D44C2×C22⋊C414yes—
384C4×D11—22no—
385C4×D11—22no—
386C4×D11—22no—
387C4×D11—22no—
388C4×D11—84no—
389C4×D11—84no—
390Dic22—22no—
391Dic22—22no—
392Dic22—41no—
393Dic22—41no—
394C8×C11—22no—
395C8×C11—41no—
396C11⋊C8—41no—
397C11⋊C8C2×C22⋊C414yescomplemented
398C22×#41—111no—
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×D8C2×D1111yescharacteristic
407C22×M16—111no—
408C2×C4×D4—111no—
409C2×C4×D4—111no—
410C2×C4×D4—111no—
411C2×C4×D4C2×D1111yescharacteristic, complemented
412C22×C22⋊C4—221no—
413#442—224no—
414C4×D8—224no—
415C2×#107—111no—
416C2×#106—111no—
417C2×#103—111no—
418C2×#103—111no—
419C2×#102—111no—
420C2×#102—111no—
421C2×#102—111no—
422C2×#102—111no—
423C2×#102C2×D1111yescharacteristic
424C2×#102C2×D1111yescharacteristic, complemented
425C2×C22⋊C8—111no—
426C2×#97—111no—
427C2×C4×C8—111no—
428#391—111no—
429#391—111no—
430#390—111no—
431#390C2×D1111yescharacteristic
432#386—221no—
433#386—221no—
434#386—221no—
435#386—221no—
436#381—221no—
437#380—111no—
438#380—111no—
439#379—221no—
440C4×C22⋊C4—111no—
441C2×#95—221no—
442#340—111no—
443#340C2×D1111yescharacteristic, complemented
444#336—111no—
445#336C2×D1111yescharacteristic, complemented
446C22×C11—24no—
447C22×C11—42no—
448C22×C11—42no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11—42no—
456C22×C11—81no—
457C22×C11—81no—
458C22×C11—81no—
459C22×C11—81no—
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—22no—
469C2×D11—22no—
470C2×D11—22no—
471C2×D11—42no—
472C2×D11—42no—
473C2×D11—41no—
474C2×D11—42no—
475C2×D11—41no—
476C2×D11—42no—
477C2×D11—41no—
478C2×D11—42no—
479C2×D11—41no—
480C2×D11—42no—
481C2×D11—816no—
482C4×C11—22no—
483C4×C11—41no—
484C4×C11—81no—
485C4×C11—81no—
486C4×C11C22×C22⋊C411yescharacteristic
487C4×C11#51811yescharacteristic
488C4×C11#54611yescharacteristic
489C4×C11#54611yescharacteristic
490Dic11—22no—
491Dic11—42no—
492Dic11—41no—
493Dic11—41no—
494Dic11—81no—
495Dic11—81no—
496C25—221no—
497C2×#41—114no—
498C2×#41—222no—
499C2×#41—222no—
500C2×#41—222no—
501C2×#41—441no—
502C2×#41—441no—
503C22×Q8—111no—
504C22×D4—114no—
505C22×D4—111no—
506C22×D4—222no—
507C22×D4—221no—
508C22×D4—222no—
509C22×D4—222no—
510C22×D4—221no—
511C22×D4—441no—
512C22×D4—441no—
513C22×D4C22×D1111yescharacteristic
514C22×D4C22×D1111yescharacteristic
515C23×C4—21no—
516C23×C4—111no—
517C23×C4—221no—
518C23×C4—221no—
519C23×C4—221no—
520C23×C4—221no—
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—22no—
529C2×D8—22no—
530C2×D8—114no—
531C2×D8—114no—
532C2×D8—114no—
533C2×D8C4×D1114yescomplemented
534C2×M16—114no—
535C2×M16—222no—
536C2×M16—222no—
537C22×C8—111no—
538C22×C8—111no—
539C22×C8C22×D1111yescharacteristic
540C22×C8C22×D1111yescharacteristic
541C4×D4—22no—
542C4×D4—41no—
543C4×D4—222no—
544C4×D4—222no—
545C4×D4—222no—
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—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—111no—
557C2×C22⋊C4—111no—
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×C42C22×D1111yescharacteristic
568#107—222no—
569#106—222no—
570#103—441no—
571#103—441no—
572#102—22no—
573#102—41no—
574#102—222no—
575#102—222no—
576#102—222no—
577#102—441no—
578C22⋊C8—222no—
579#97—222no—
580C4×C8—222no—
581#95—111no—
582#95—111no—
583#95—221no—
584#95—221no—
585#95—221no—
586#95—221no—
587#95—221no—
588#95—221no—
589C2×C11—44no—
590C2×C11—82no—
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—42no—
599D11—44no—
600C24—21no—
601C24—21no—
602C24—111no—
603C24—224no—
604C24—221no—
605C24—442no—
606C24—442no—
607C24—442no—
608C24—442no—
609C24—881no—
610C24—881no—
611#41—228no—
612#41—444no—
613#41—444no—
614#41—444no—
615C2×Q8—112no—
616C2×Q8—221no—
617C2×Q8—221no—
618C2×Q8—221no—
619C2×Q8—221no—
620C2×Q8—221no—
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—112no—
630C2×D4—112no—
631C2×D4—112no—
632C2×D4—224no—
633C2×D4—228no—
634C2×D4—224no—
635C2×D4—221no—
636C2×D4—221no—
637C2×D4—221no—
638C2×D4—444no—
639C2×D4—444no—
640C2×D4—444no—
641C2×D4—442no—
642C2×D4—442no—
643C2×D4—442no—
644C2×D4—442no—
645C2×D4C2×C4×D1112yes—
646C2×D4C2×C4×D1112yes—
647C2×D4D4×D1112yes—
648C2×D4D4×D1112yes—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—81no—
654C22×C4—111no—
655C22×C4—112no—
656C22×C4—112no—
657C22×C4—111no—
658C22×C4—111no—
659C22×C4—224no—
660C22×C4—221no—
661C22×C4—221no—
662C22×C4—221no—
663C22×C4—221no—
664C22×C4—221no—
665C22×C4—221no—
666C22×C4—221no—
667C22×C4—442no—
668C22×C4—442no—
669C22×C4—442no—
670C22×C4—442no—
671C22×C4—442no—
672C22×C4—442no—
673C22×C4—442no—
674C22×C4—442no—
675C22×C4—881no—
676C22×C4—881no—
677C22×C4—881no—
678C22×C4D4×D1111yescharacteristic
679C22×C4D4×D1111yescharacteristic
680C22×C4C23×D1111yescharacteristic
681SD16—228no—
682SD16—228no—
683D8—28no—
684D8—1116no—
685M16—228no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—112no—
692C2×C8—112no—
693C2×C8—112no—
694C2×C8—221no—
695C2×C8—221no—
696C2×C8—221no—
697C2×C8C2×C4×D1112yes—
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—42no—
708C22⋊C4—81no—
709C22⋊C4—222no—
710C22⋊C4—441no—
711C22⋊C4—442no—
712C22⋊C4—442no—
713C22⋊C4—442no—
714C22⋊C4—442no—
715C22⋊C4—442no—
716C22⋊C4—881no—
717C22⋊C4—881no—
718C42—21no—
719C42—21no—
720C42—221no—
721C42—221no—
722C11#2244211yescharacteristic, complemented, Sylow
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—112no—
738C23—221no—
739C23—221no—
740C23—221no—
741C23—221no—
742C23—222no—
743C23—222no—
744C23—221no—
745C23—222no—
746C23—221no—
747C23—448no—
748C23—448no—
749C23—441no—
750C23—441no—
751C23—441no—
752C23—441no—
753C23—884no—
754C23—884no—
755C23—884no—
756C23—884no—
757C23—884no—
758C23C2×D4×D1111yescharacteristic
759Q8—222no—
760Q8—222no—
761Q8—441no—
762Q8—441no—
763D4—22no—
764D4—22no—
765D4—22no—
766D4—22no—
767D4—22no—
768D4—41no—
769D4—41no—
770D4—114no—
771D4—222no—
772D4—222no—
773D4—222no—
774D4—448no—
775D4—448no—
776D4C22⋊C4×D1114yescomplemented
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—84no—
789C2×C4—112no—
790C2×C4—221no—
791C2×C4—221no—
792C2×C4—222no—
793C2×C4—222no—
794C2×C4—222no—
795C2×C4—222no—
796C2×C4—221no—
797C2×C4—221no—
798C2×C4—221no—
799C2×C4—221no—
800C2×C4—222no—
801C2×C4—221no—
802C2×C4—221no—
803C2×C4—448no—
804C2×C4—441no—
805C2×C4—441no—
806C2×C4—441no—
807C2×C4—441no—
808C2×C4—441no—
809C2×C4—441no—
810C2×C4—441no—
811C2×C4—441no—
812C2×C4—884no—
813C2×C4—884no—
814C2×C4—884no—
815C2×C4#6696412yescomplemented
816C2×C4C22×C4×D1111yescharacteristic
817C2×C4C2×D4×D1111yescharacteristic
818C2×C4C2×D4×D1111yescharacteristic
819C2×C4#6703711yescharacteristic
820C2×C4#41×D1111yescharacteristic
821C2×C4#6704211yescharacteristic
822C8—22no—
823C8—41no—
824C8—114no—
825C8—441no—
826C22—24no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—222no—
841C22—224no—
842C22—222no—
843C22—222no—
844C22—442no—
845C22—441no—
846C22—441no—
847C22—442no—
848C22—442no—
849C22—441no—
850C22—441no—
851C22—442no—
852C22—442no—
853C22—442no—
854C22—8816no—
855C22C4×D4×D1111yescharacteristic
856C22#1062312111yescharacteristic
857C22#1062314011yescharacteristic
858C22C2×#6696411yescharacteristic
859C22#1062329911yescharacteristic
860C22#1062330511yescharacteristic
861C22#1062330611yescharacteristic
862C4—22no—
863C4—41no—
864C4—81no—
865C4—81no—
866C4—222no—
867C4—442no—
868C4—441no—
869C4—441no—
870C4—881no—
871C4—881no—
872C4C2×C22⋊C4×D1111yescharacteristic
873C4#1062307611yescharacteristic
874C4#1062314111yescharacteristic
875C4#1062318511yescharacteristic
876C2—44no—
877C2—82no—
878C2—442no—
879C2—444no—
880C2#1307143411yescharacteristic
881C2C4×#6696411yescharacteristic
882C2#1307744511yescharacteristic
883C2#1308008911yescharacteristic
884C2#1308013411yescharacteristic
885C2#1308021111yescharacteristic
886C2#1308022211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1879C2
socleC23×C11C22×D4
prime radicalC22×#66964C2
cosocleC22×C4×C11C24
hypercenter#1879D11
hypocenterC11#22442
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
2. C2×#10622398C2semidirect
3. C2×C4×#4323C2semidirect
4. #13071441C2semidirect
5. #13071437C2semidirect
6. #13069498C2semidirect
7. #13069469C2semidirect
8. #13068966C2semidirect
9. #13068951C2semidirect
10. #13068949C2semidirect
11. #13068648C2semidirect
12. #13068553C2semidirect
13. #13068545C2semidirect
14. #13068396C2semidirect
15. C11×#1879C2semidirect
19. C2×C4×D4×C11C22semidirect
20. C2×D4×Dic11C22semidirect
25. C2×#66964C4semidirect
32. C2×C11×#102C22semidirect
36. C2×#66896C22semidirect
41. C2×#66880C22semidirect
42. C2×#66879C22semidirect
46. #10622587C22semidirect
47. C2×#66874C22semidirect
49. C2×#66872C22semidirect
50. C2×#66871C22semidirect
57. #10622542C22semidirect
58. C2×C4×C11⋊C8C22semidirect
60. C11×#340C22semidirect
61. C11×#336C22semidirect
62. #10622189C22semidirect
63. #10622188C22semidirect
77. C2×#4341C2×C4semidirect
83. C2×D4×D11C2×C4semidirect
91. C2×C11×D8C2×C4semidirect
109. C2×#4324C2×C4semidirect
127. C2×#4314C2×C4semidirect
130. C2×#4313C2×C4semidirect
259. #4323C22⋊C4semidirect
288. #1879D11semidirect
338. D4×C11C2×C22⋊C4semidirect
351. C2×C4×C11AGL(1,ℤ/8)semidirect
397. C11⋊C8C2×C22⋊C4semidirect
411. C2×C4×D4C2×D11semidirect
424. C2×#102C2×D11semidirect
443. #340C2×D11semidirect
445. #336C2×D11semidirect
533. C2×D8C4×D11semidirect
722. C11#22442semidirect
776. D4C22⋊C4×D11semidirect
815. C2×C4#66964semidirect

Maximal subgroups

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

subgroupindex
C22×#669642
C2×#106223982
C2×C4×#43232
#130714412
#130714372
#130694982
#130694692
#130689662
#130689512
#130689492
#130686482
#130685532
#130685452
#130683962
C11×#18792
#2244211