Finite Group Databasebeta

← #14769548

Subgroups — #14769548

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×#66967C211yesmaximal, characteristic
2C2×#10622430C211yesmaximal, characteristic, complemented
3C2×C4×#4325C211yesmaximal, characteristic, complemented
4#13071454C211yesmaximal, characteristic, complemented
5#13071437C211yesmaximal, characteristic, complemented
6#13069489C211yesmaximal, characteristic, complemented
7#13069481C211yesmaximal, characteristic, complemented
8#13068973C211yesmaximal, characteristic, complemented
9#13068965C211yesmaximal, characteristic, complemented
10#13068963C211yesmaximal, characteristic, complemented
11#13068648C211yesmaximal, characteristic, complemented
12#13068555C211yesmaximal, characteristic, complemented
13#13068545C211yesmaximal, characteristic, complemented
14#13068396C211yesmaximal, characteristic, complemented
15C11×#1880C211yesmaximal, characteristic, complemented
16C22×#4343C2211yescharacteristic
17C22×D4×D11C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic, complemented
20C2×Q8×Dic11C2211yescharacteristic, complemented
21C22×#4325C2211yescharacteristic
22C22×#4323C2211yescharacteristic
23C2×#66967—24no—
24C2×#66967—24no—
25C2×#66967C418yescomplemented
26C22×D88C2211yescharacteristic
27C22×#4313C2211yescharacteristic
28C2×#66946C2211yescharacteristic
29C2×C22⋊C4×D11—21no—
30C2×C4×D44C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic, complemented
32C2×C11×#102C2211yescharacteristic
33C11×#390C2211yescharacteristic
34C2×#66899C2211yescharacteristic, complemented
35#10622834C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37C2×#66885C2211yescharacteristic
38C2×#66885C2211yescharacteristic, complemented
39C2×(C2×D11)⋊C8C2211yescharacteristic
40C2×#66879C2211yescharacteristic, complemented
41C4×#4325—24no—
42#10622601—21no—
43#10622601C2211yescharacteristic, complemented
44#10622600—21no—
45#10622600C2211yescharacteristic
46#10622600C2211yescharacteristic
47C2×#66873C2211yescharacteristic
48C2×#66873C2211yescharacteristic, complemented
49C2×#66872C2211yescharacteristic, complemented
50C2×#66871C2211yescharacteristic, complemented
51#10622569—21no—
52#10622569—21no—
53#10622568—21no—
54#10622552—21no—
55#10622552C2211yescharacteristic, complemented
56C4×(C2×D11)⋊C4—21no—
57C4×(C2×D11)⋊C4C2211yescharacteristic
58C2×C4×C11⋊C8C2211yescharacteristic, complemented
59#10622430—24no—
60C11×#340C2211yescharacteristic, complemented
61C11×#336C2211yescharacteristic, complemented
62#10622189C2211yescharacteristic, complemented
63#10622188C2211yescharacteristic, complemented
64C24×D11—21no—
65C22×Q8×C11C2311yescharacteristic
66C22×D4×C11C2311yescharacteristic
67C22×C22⋊D11—21no—
68C2×#4343—22no—
69C2×#4343—22no—
70C2×#4343—22no—
71C2×#4343—41no—
72C2×#4343—41no—
73C2×#4343C2×C414yescomplemented
74C2×D4×D11—22no—
75C2×D4×D11—22no—
76C2×D4×D11—22no—
77C2×D4×D11—41no—
78C2×D4×D11—41no—
79C2×D4×D11C2×C414yes—
80C22×D44—21no—
81C22×D44C2311yescharacteristic
82C22×D44C2311yescharacteristic
83C22×C4×D11—21no—
84C22×C4×D11—21no—
85C22×C4×D11—21no—
86C22×C4×D11C2311yescharacteristic
87C2×C11×SD16—22no—
88C2×C11×SD16—22no—
89C2×C11×SD16C2×C414yescomplemented
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C4×Q8×C11—22no—
93C4×Q8×C11—41no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C42×C11—21no—
100C2×C42×C11C2311yescharacteristic
101C2×C22⋊Dic11—21no—
102C2×C22⋊Dic11—21no—
103Q8×Dic11—22no—
104Q8×Dic11—41no—
105C2×#4325C2×C414yes—
106C2×#4325D414yes—
107C2×#4325D414yes—
108C2×#4323—22no—
109C2×#4323—22no—
110C2×#4323C2×C414yescomplemented
111C2×(C2×D11)⋊C4—21no—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4D411yescharacteristic
120C2×(C2×D11)⋊C4D411yescharacteristic
121C2×C4⋊Dic11—21no—
122C2×C4⋊Dic11C2311yescharacteristic
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4×Dic11—21no—
125C2×C4×Dic11C2311yescharacteristic
126C22×C11⋊C8C2311yescharacteristic
127C22×C11⋊C8C2311yescharacteristic
128#66967—232no—
129C2×D88—22no—
130C2×D88—22no—
131C2×D88C2×C414yes—
132C2×#4313—22no—
133C2×#4313—22no—
134C2×#4313C2×C414yescomplemented
135#66946—22no—
136#66946—41no—
137C22⋊C4×D11—44no—
138C4×D44—22no—
139C4×D44—41no—
140C11×#103—22no—
141C11×#102—41no—
142#66899—22no—
143#66896—41no—
144C11⋊#95—21no—
145C11⋊#95—21no—
146C11⋊#95D411yescharacteristic
147C11⋊#95D411yescharacteristic
148#66885—22no—
149#66885—41no—
150(C2×D11)⋊C8—22no—
151#66879—22no—
152#66873—22no—
153#66873—41no—
154#66872—22no—
155#66871—22no—
156C4×C11⋊C8—22no—
157#22443—111nomaximal, Sylow
158C24×C11—21no—
159C23×D11—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×Q8×C11—21no—
170C2×Q8×C11—21no—
171C2×Q8×C11—21no—
172C2×Q8×C11C22×C412yes—
173C2×Q8×C11C2×D412yes—
174C2×Q8×C11C2×D412yes—
175C2×D4×C11—21no—
176C2×D4×C11—21no—
177C2×D4×C11—21no—
178C2×D4×C11—21no—
179C2×D4×C11—21no—
180C2×D4×C11C22×C412yes—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2411yescharacteristic
187C2×C22⋊D11—24no—
188C2×C22⋊D11—42no—
189C2×C22⋊D11—42no—
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11C2×D411yescharacteristic
193C22×Dic11C2×D411yescharacteristic
194C22×Dic11C2×D411yescharacteristic
195#4343—28no—
196#4343—44no—
197#4343—44no—
198#4343—44no—
199D4×D11—28no—
200D4×D11—44no—
201D4×D11—44no—
202D4×D11—44no—
203C2×D44—24no—
204C2×D44—21no—
205C2×D44—21no—
206C2×D44—21no—
207C2×D44—21no—
208C2×D44—21no—
209C2×D44—21no—
210C2×D44—21no—
211C2×D44—21no—
212C2×D44—42no—
213C2×D44—42no—
214C2×D44C22×C412yes—
215C2×D44C22×C412yes—
216C2×D44C2×D412yes—
217C2×D44C2×D412yes—
218C2×C4×D11—24no—
219C2×C4×D11—21no—
220C2×C4×D11—21no—
221C2×C4×D11—21no—
222C2×C4×D11—21no—
223C2×C4×D11—42no—
224C2×C4×D11—42no—
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—
233C11×SD16—28no—
234C2×C8×C11—21no—
235C2×C8×C11—21no—
236C2×C8×C11—21no—
237C2×C8×C11—21no—
238C2×C8×C11—21no—
239C2×C8×C11C22×C412yes—
240C11×C4⋊C4—21no—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—21no—
243C11×C4⋊C4—21no—
244C11×C4⋊C4—42no—
245C11×C22⋊C4—42no—
246C11×C22⋊C4—81no—
247C42×C11—21no—
248C42×C11—21no—
249C42×C11—42no—
250C22⋊Dic11—42no—
251C22⋊Dic11—81no—
252#4325C22⋊C4116yescomplemented
253#4323—28no—
254(C2×D11)⋊C4—22no—
255(C2×D11)⋊C4—41no—
256(C2×D11)⋊C4—42no—
257(C2×D11)⋊C4—42no—
258(C2×D11)⋊C4—42no—
259(C2×D11)⋊C4—42no—
260(C2×D11)⋊C4—42no—
261(C2×D11)⋊C4—81no—
262(C2×D11)⋊C4—81no—
263(C2×D11)⋊C4—81no—
264C4⋊Dic11—21no—
265C4⋊Dic11—21no—
266C4⋊Dic11—21no—
267C4⋊Dic11—21no—
268C4⋊Dic11—42no—
269C4×Dic11—21no—
270C4×Dic11—21no—
271C4×Dic11—42no—
272C2×C11⋊C8—21no—
273C2×C11⋊C8—21no—
274C2×C11⋊C8—21no—
275C2×C11⋊C8C22×C412yes—
276C2×C11⋊C8C2×D412yes—
277C2×C11⋊C8C2×D412yes—
278D88—28no—
279#4313—28no—
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#1880D1111yescharacteristic, complemented
289#1879—111no—
290#1879—111no—
291#1809—111no—
292#1788—111no—
293#1786—111no—
294#1753—111no—
295C23×C11—22no—
296C23×C11—41no—
297C23×C11—41no—
298C23×C11—41no—
299C23×C11—41no—
300C23×C11—41no—
301C23×C11—41no—
302C23×C11C22×D411yescharacteristic
303C22×D11—22no—
304C22×D11—22no—
305C22×D11—22no—
306C22×D11—21no—
307C22×D11—21no—
308C22×D11—21no—
309C22×D11—21no—
310C22×D11—21no—
311C22×D11—21no—
312C22×D11—22no—
313C22×D11—48no—
314C22×D11—48no—
315C22×D11—41no—
316C22×D11—41no—
317C22×D11—41no—
318C22×D11—41no—
319C22×D11—41no—
320C22×D11—41no—
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—
331Q8×C11—22no—
332Q8×C11—22no—
333Q8×C11—22no—
334Q8×C11C2×C22⋊C414yescomplemented
335D4×C11—22no—
336D4×C11—22no—
337D4×C11—41no—
338D4×C11—41no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—21no—
342C2×C4×C11—22no—
343C2×C4×C11—21no—
344C2×C4×C11—21no—
345C2×C4×C11—21no—
346C2×C4×C11—21no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11AGL(1,ℤ/8)12yescomplemented
354C2×C4×C11C23×C411yescharacteristic
355C2×C4×C11C22×D411yescharacteristic
356C2×C4×C11C22×D411yescharacteristic
357C2×C4×C11C2×#4111yescharacteristic
358C2×C4×C11H(5,𝔽2)11yescharacteristic
359C2×C4×C11H(5,𝔽2)11yescharacteristic
360C22⋊D11—48no—
361C2×Dic11—21no—
362C2×Dic11—21no—
363C2×Dic11—21no—
364C2×Dic11—21no—
365C2×Dic11—21no—
366C2×Dic11—21no—
367C2×Dic11—21no—
368C2×Dic11—21no—
369C2×Dic11—41no—
370C2×Dic11—41no—
371C2×Dic11—41no—
372C2×Dic11—41no—
373C2×Dic11—41no—
374C2×Dic11—41no—
375C2×Dic11C4×D412yes—
376D44—22no—
377D44—22no—
378D44—22no—
379D44—22no—
380D44—22no—
381D44—48no—
382D44—41no—
383D44—41no—
384D44C2×C22⋊C414yes—
385C4×D11—22no—
386C4×D11—22no—
387C4×D11—22no—
388C4×D11—22no—
389C4×D11—48no—
390C4×D11—84no—
391C4×D11—84no—
392C8×C11—22no—
393C8×C11—41no—
394C11⋊C8—41no—
395C11⋊C8C2×C22⋊C414yescomplemented
396C22×#41—111no—
397C23×D4—111no—
398C2×AGL(1,ℤ/8)—118no—
399C2×AGL(1,ℤ/8)—224no—
400C2×AGL(1,ℤ/8)—224no—
401C22×SD16—111no—
402C22×SD16C2×D1111yescharacteristic
403C22×D8—111no—
404C22×D8—111no—
405C22×M16—111no—
406C2×C4×Q8—111no—
407C2×C4×Q8C2×D1111yescharacteristic, complemented
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×#103C2×D1111yescharacteristic, complemented
417C2×#102—111no—
418C2×#102—111no—
419C2×#102—111no—
420C2×#102—111no—
421C2×#102—111no—
422C2×#102C2×D1111yescharacteristic
423C2×C22⋊C8—111no—
424C2×#97—111no—
425C2×C4×C8—111no—
426#390—111no—
427#390—111no—
428#390—111no—
429#390—221no—
430#390—221no—
431#390C2×D1111yescharacteristic
432#386—221no—
433#386—221no—
434#380—111no—
435#380—111no—
436#380—221no—
437#379—221no—
438C4×C22⋊C4—111no—
439C4×C22⋊C4—221no—
440#340—111no—
441#340C2×D1111yescharacteristic, complemented
442#336—111no—
443#336C2×D1111yescharacteristic, complemented
444C22×C11—42no—
445C22×C11—42no—
446C22×C11—42no—
447C22×C11—81no—
448C22×C11—81no—
449C22×C11—81no—
450C22×C11—81no—
451C22×C11C2×C4×D411yescharacteristic
452C22×C11D4211yescharacteristic
453C22×C11D4211yescharacteristic
454C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
455C22×C11#57511yescharacteristic
456C22×C11#57611yescharacteristic
457C22×C11#57711yescharacteristic
458C2×D11—24no—
459C2×D11—22no—
460C2×D11—22no—
461C2×D11—22no—
462C2×D11—42no—
463C2×D11—42no—
464C2×D11—41no—
465C2×D11—42no—
466C2×D11—41no—
467C2×D11—42no—
468C2×D11—41no—
469C2×D11—42no—
470C2×D11—41no—
471C2×D11—42no—
472C2×D11—42no—
473C2×D11—42no—
474C2×D11—42no—
475C2×D11—816no—
476C2×D11—81no—
477C2×D11—81no—
478C2×D11—81no—
479C2×D11—81no—
480C4×C11—24no—
481C4×C11—22no—
482C4×C11—41no—
483C4×C11—81no—
484C4×C11—81no—
485C4×C11C22×C22⋊C411yescharacteristic
486C4×C11#51811yescharacteristic
487C4×C11#54611yescharacteristic
488C4×C11#54611yescharacteristic
489Dic11—22no—
490Dic11—41no—
491Dic11—41no—
492Dic11—81no—
493Dic11—81no—
494C25—221no—
495C2×#41—114no—
496C2×#41—222no—
497C2×#41—222no—
498C2×#41—222no—
499C2×#41—441no—
500C2×#41—441no—
501C22×Q8C22×D1111yescharacteristic
502C22×D4—114no—
503C22×D4—111no—
504C22×D4—111no—
505C22×D4—221no—
506C22×D4—222no—
507C22×D4—221no—
508C22×D4—222no—
509C22×D4—222no—
510C22×D4—441no—
511C22×D4—441no—
512C22×D4C22×D1111yescharacteristic
513C23×C4—111no—
514C23×C4—221no—
515C23×C4—221no—
516C23×C4—221no—
517AGL(1,ℤ/8)—2232no—
518C2×SD16—22no—
519C2×SD16—22no—
520C2×SD16—114no—
521C2×SD16—114no—
522C2×SD16—114no—
523C2×SD16C4×D1114yescomplemented
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—22no—
538C4×Q8—41no—
539C4×Q8—222no—
540C4×Q8—441no—
541C4×D4—222no—
542C4×D4—222no—
543C4×D4—441no—
544C4×D4—441no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—111no—
547C2×C4⋊C4—111no—
548C2×C4⋊C4—221no—
549C2×C4⋊C4C22×D1111yescharacteristic
550C2×C4⋊C4C22×D1111yescharacteristic
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—111no—
554C2×C22⋊C4—111no—
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—21no—
567C2×C42—111no—
568C2×C42—221no—
569C2×C42C22×D1111yescharacteristic
570#107—222no—
571#106—222no—
572#103—22no—
573#103—222no—
574#102—41no—
575#102—222no—
576#102—222no—
577#102—441no—
578#102—441no—
579#102—441no—
580C22⋊C8—222no—
581#97—222no—
582C4×C8—222no—
583#95—111no—
584#95—111no—
585#95—221no—
586#95—221no—
587C2×C11—82no—
588C2×C11D4×C22⋊C411yescharacteristic
589C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
590C2×C11#294611yescharacteristic
591C2×C11#326511yescharacteristic
592C2×C11#326811yescharacteristic
593C2×C11#327411yescharacteristic
594C2×C11#327511yescharacteristic
595D11—42no—
596D11—44no—
597D11—82no—
598C24—21no—
599C24—111no—
600C24—224no—
601C24—221no—
602C24—221no—
603C24—442no—
604C24—442no—
605C24—442no—
606C24—442no—
607C24—881no—
608C24—881no—
609#41—228no—
610#41—444no—
611#41—444no—
612#41—444no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8C2×C4×D1112yes—
617C2×Q8D4×D1112yes—
618C2×Q8D4×D1112yes—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—112no—
625C2×D4—112no—
626C2×D4—112no—
627C2×D4—112no—
628C2×D4—224no—
629C2×D4—224no—
630C2×D4—228no—
631C2×D4—221no—
632C2×D4—221no—
633C2×D4—221no—
634C2×D4—221no—
635C2×D4—221no—
636C2×D4—221no—
637C2×D4—221no—
638C2×D4—221no—
639C2×D4—442no—
640C2×D4—442no—
641C2×D4—444no—
642C2×D4—444no—
643C2×D4—444no—
644C2×D4—442no—
645C2×D4—442no—
646C2×D4C2×C4×D1112yes—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—111no—
651C22×C4—112no—
652C22×C4—112no—
653C22×C4—111no—
654C22×C4—111no—
655C22×C4—224no—
656C22×C4—221no—
657C22×C4—221no—
658C22×C4—221no—
659C22×C4—221no—
660C22×C4—221no—
661C22×C4—221no—
662C22×C4—442no—
663C22×C4—442no—
664C22×C4—442no—
665C22×C4—442no—
666C22×C4—442no—
667C22×C4—442no—
668C22×C4—881no—
669C22×C4—881no—
670C22×C4D4×D1111yescharacteristic
671C22×C4D4×D1111yescharacteristic
672C22×C4C23×D1111yescharacteristic
673SD16—28no—
674SD16—1116no—
675D8—228no—
676D8—228no—
677M16—228no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—112no—
684C2×C8—112no—
685C2×C8—112no—
686C2×C8—221no—
687C2×C8—221no—
688C2×C8—221no—
689C2×C8C2×C4×D1112yes—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—42no—
695C4⋊C4—221no—
696C4⋊C4—221no—
697C4⋊C4—221no—
698C4⋊C4—221no—
699C4⋊C4—442no—
700C22⋊C4—42no—
701C22⋊C4—81no—
702C22⋊C4—222no—
703C22⋊C4—441no—
704C22⋊C4—442no—
705C22⋊C4—442no—
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—21no—
715C42—21no—
716C42—42no—
717C42—221no—
718C42—221no—
719C42—442no—
720C11#2244311yescharacteristic, complemented, Sylow
721C23—22no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—112no—
729C23—221no—
730C23—221no—
731C23—221no—
732C23—221no—
733C23—222no—
734C23—222no—
735C23—221no—
736C23—222no—
737C23—221no—
738C23—222no—
739C23—448no—
740C23—448no—
741C23—441no—
742C23—441no—
743C23—441no—
744C23—441no—
745C23—441no—
746C23—441no—
747C23—441no—
748C23—441no—
749C23—441no—
750C23—441no—
751C23—884no—
752C23—884no—
753C23—884no—
754C23—884no—
755C23—884no—
756C23C2×D4×D1111yescharacteristic
757Q8—22no—
758Q8—22no—
759Q8—22no—
760Q8C22⋊C4×D1114yescomplemented
761D4—22no—
762D4—22no—
763D4—41no—
764D4—41no—
765D4—114no—
766D4—222no—
767D4—222no—
768D4—222no—
769D4—222no—
770D4—222no—
771D4—448no—
772D4—448no—
773D4—441no—
774D4—441no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
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—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#6696712yescomplemented
812C2×C4C22×C4×D1111yescharacteristic
813C2×C4C2×D4×D1111yescharacteristic
814C2×C4C2×D4×D1111yescharacteristic
815C2×C4#6703711yescharacteristic
816C2×C4#41×D1111yescharacteristic
817C2×C4#6704211yescharacteristic
818C8—22no—
819C8—41no—
820C8—114no—
821C8—441no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—222no—
830C22—224no—
831C22—222no—
832C22—222no—
833C22—442no—
834C22—441no—
835C22—441no—
836C22—442no—
837C22—442no—
838C22—441no—
839C22—442no—
840C22—441no—
841C22—442no—
842C22—442no—
843C22—442no—
844C22—442no—
845C22—442no—
846C22—8816no—
847C22—881no—
848C22—881no—
849C22—881no—
850C22—881no—
851C22C4×D4×D1111yescharacteristic
852C22#1062312111yescharacteristic
853C22#1062314011yescharacteristic
854C22C2×#6696711yescharacteristic
855C22#1062329911yescharacteristic
856C22#1062330511yescharacteristic
857C22#1062330911yescharacteristic
858C4—22no—
859C4—24no—
860C4—41no—
861C4—81no—
862C4—81no—
863C4—222no—
864C4—441no—
865C4—441no—
866C4—881no—
867C4—881no—
868C4C2×C22⋊C4×D1111yescharacteristic
869C4#1062307611yescharacteristic
870C4#1062314111yescharacteristic
871C4#1062318511yescharacteristic
872C2—82no—
873C2—442no—
874C2—444no—
875C2—882no—
876C2#1307143411yescharacteristic
877C2C4×#6696711yescharacteristic
878C2#1307744711yescharacteristic
879C2#1308010411yescharacteristic
880C2#1308014911yescharacteristic
881C2#1308023111yescharacteristic
882C2#1308024211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1880C2
socleC23×C11C22×D4
prime radicalC22×#66967C2
cosocleC22×C4×C11C24
hypercenter#1880D11
hypocenterC11#22443
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1880

Complements

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

NH ≅ G/Ntype
2. C2×#10622430C2semidirect
3. C2×C4×#4325C2semidirect
4. #13071454C2semidirect
5. #13071437C2semidirect
6. #13069489C2semidirect
7. #13069481C2semidirect
8. #13068973C2semidirect
9. #13068965C2semidirect
10. #13068963C2semidirect
11. #13068648C2semidirect
12. #13068555C2semidirect
13. #13068545C2semidirect
14. #13068396C2semidirect
15. C11×#1880C2semidirect
19. C2×C4×Q8×C11C22semidirect
20. C2×Q8×Dic11C22semidirect
25. C2×#66967C4semidirect
31. C2×C11×#103C22semidirect
34. C2×#66899C22semidirect
38. C2×#66885C22semidirect
40. C2×#66879C22semidirect
43. #10622601C22semidirect
48. C2×#66873C22semidirect
49. C2×#66872C22semidirect
50. C2×#66871C22semidirect
55. #10622552C22semidirect
58. C2×C4×C11⋊C8C22semidirect
60. C11×#340C22semidirect
61. C11×#336C22semidirect
62. #10622189C22semidirect
63. #10622188C22semidirect
73. C2×#4343C2×C4semidirect
89. C2×C11×SD16C2×C4semidirect
110. C2×#4323C2×C4semidirect
134. C2×#4313C2×C4semidirect
252. #4325C22⋊C4semidirect
288. #1880D11semidirect
334. Q8×C11C2×C22⋊C4semidirect
353. C2×C4×C11AGL(1,ℤ/8)semidirect
395. C11⋊C8C2×C22⋊C4semidirect
407. C2×C4×Q8C2×D11semidirect
416. C2×#103C2×D11semidirect
441. #340C2×D11semidirect
443. #336C2×D11semidirect
523. C2×SD16C4×D11semidirect
720. C11#22443semidirect
760. Q8C22⋊C4×D11semidirect
811. C2×C4#66967semidirect

Maximal subgroups

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

subgroupindex
C22×#669672
C2×#106224302
C2×C4×#43252
#130714542
#130714372
#130694892
#130694812
#130689732
#130689652
#130689632
#130686482
#130685552
#130685452
#130683962
C11×#18802
#2244311