Finite Group Databasebeta

← #14769551

Subgroups — #14769551

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×#66964C211yesmaximal, characteristic
2C2×#10622631C211yesmaximal, characteristic, complemented
3C2×#10622371C211yesmaximal, characteristic, complemented
4#13071455C211yesmaximal, characteristic, complemented
5D4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
6#13069491C211yesmaximal, characteristic, complemented
7#13069479C211yesmaximal, characteristic, complemented
8#13068972C211yesmaximal, characteristic, complemented
9#13068970C211yesmaximal, characteristic, complemented
10#13068966C211yesmaximal, characteristic, complemented
11#13068648C211yesmaximal, characteristic, complemented
12#13068553C211yesmaximal, characteristic, complemented
13#13068545C211yesmaximal, characteristic, complemented
14#13068398C211yesmaximal, characteristic, complemented
15C11×#1879C211yesmaximal, characteristic, complemented
16C22×#4341C2211yescharacteristic
17C22×D4×D11C2211yescharacteristic
18C22×C11×D8C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×D4×Dic11C2211yescharacteristic
21C22×#4324C2211yescharacteristic
22C22×#4323C2211yescharacteristic
23C22×(C2×D11)⋊C4—21no—
24C2×#66964—24no—
25C2×#66964—24no—
26C2×#66964C418yescomplemented
27C22×#4314C2211yescharacteristic
28C22×#4313C2211yescharacteristic
29C2×#66940C2211yescharacteristic, complemented
30C2×C4×Dic22C2211yescharacteristic, complemented
31C2×C11×#102C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic, complemented
33C11×#390C2211yescharacteristic, complemented
34#10622834C2211yescharacteristic, complemented
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic, complemented
37#10622826—21no—
38C2×#66885C2211yescharacteristic
39C2×(C2×D11)⋊C8C2211yescharacteristic
40C2×#66880C2211yescharacteristic, complemented
41C2×C8×Dic11C2211yescharacteristic, complemented
42#10622631—24no—
43#10622601C2211yescharacteristic
44#10622600C2211yescharacteristic
45#10622600C2211yescharacteristic
46C2×#66874C2211yescharacteristic, complemented
47C2×#66873C2211yescharacteristic
48C2×#66872C2211yescharacteristic, complemented
49C2×#66871C2211yescharacteristic, complemented
50#10622571—21no—
51#10622570—21no—
52#10622570—21no—
53#10622568—21no—
54#10622555—21no—
55C22⋊C4×Dic11—21no—
56#10622552C2211yescharacteristic
57C4×(C2×D11)⋊C4C2211yescharacteristic
58C2×#66867C2211yescharacteristic, complemented
59#10622371—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×C414yes—
84C22×D44C2311yescharacteristic
85C22×C4×D11C2311yescharacteristic
86C22×Dic22C2311yescharacteristic
87C2×C11×D8—22no—
88C2×C11×D8—22no—
89C2×C11×D8C2×C414yes—
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C4×D4×C11—22no—
93C4×D4×C11—41no—
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C42×C11C2311yescharacteristic
100C2×C22⋊Dic11—21no—
101C2×C22⋊Dic11—21no—
102C2×C22⋊Dic11—21no—
103D4×Dic11—22no—
104D4×Dic11—41no—
105C2×#4324C2×C414yes—
106C2×#4324D414yes—
107C2×#4324D414yes—
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—44no—
118C2×(C2×D11)⋊C4D411yescharacteristic
119C2×(C2×D11)⋊C4D411yescharacteristic
120C2×C4⋊Dic11C2311yescharacteristic
121C2×C4⋊Dic11C2311yescharacteristic
122C2×Dic11⋊C4—21no—
123C2×Dic11⋊C4—21no—
124C2×C4×Dic11—21no—
125C2×C4×Dic11—21no—
126C2×C4×Dic11C2311yescharacteristic
127C22×C11⋊C8C2311yescharacteristic
128C22×C11⋊C8C2311yescharacteristic
129#66964—232no—
130C2×#4314—22no—
131C2×#4314—22no—
132C2×#4314C2×C414yescomplemented
133C2×#4313—22no—
134C2×#4313—22no—
135C2×#4313C2×C414yescomplemented
136#66940—22no—
137#66940—41no—
138C4×Dic22—22no—
139C4×Dic22—41no—
140C11×#102—22no—
141C11×#102—41no—
142#66896—22no—
143#66896—41no—
144C11⋊#95—21no—
145C11⋊#95—21no—
146C11⋊#95D411yescharacteristic
147C11⋊#95D411yescharacteristic
148#66885—41no—
149(C2×D11)⋊C8—22no—
150#66880—22no—
151C8×Dic11—22no—
152#66874—22no—
153#66873—41no—
154#66872—22no—
155#66871—22no—
156#66867—22no—
157#22443—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×D44—21no—
219C2×D44—21no—
220C2×D44C22×C412yes—
221C2×C4×D11—21no—
222C2×C4×D11—21no—
223C2×C4×D11—21no—
224C2×C4×D11—21no—
225C2×C4×D11C22×C412yes—
226C2×C4×D11#4112yes—
227C2×Dic22—21no—
228C2×Dic22—21no—
229C2×Dic22—21no—
230C2×Dic22C22×C412yes—
231C2×Dic22C2×D412yes—
232C2×Dic22C2×D412yes—
233C11×D8—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×C22⋊C4—42no—
245C11×C22⋊C4—42no—
246C11×C22⋊C4—81no—
247C42×C11—21no—
248C42×C11—21no—
249C22⋊Dic11—42no—
250C22⋊Dic11—42no—
251C22⋊Dic11—81no—
252#4324C22⋊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—81no—
260(C2×D11)⋊C4—81no—
261(C2×D11)⋊C4—81no—
262C4⋊Dic11—21no—
263C4⋊Dic11—21no—
264C4⋊Dic11—21no—
265C4⋊Dic11—21no—
266Dic11⋊C4—42no—
267Dic11⋊C4—42no—
268C4×Dic11—21no—
269C4×Dic11—21no—
270C4×Dic11—42no—
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—
278#4314—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#1880—111no—
289#1879—111no—
290#1879D1111yescharacteristic, complemented
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—21no—
311C22×D11—21no—
312C22×D11—21no—
313C22×D11—21no—
314C22×D11—21no—
315C22×D11—21no—
316C22×D11—22no—
317C22×D11—48no—
318C22×D11—48no—
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—
331D4×C11—22no—
332D4×C11—22no—
333D4×C11—22no—
334D4×C11—22no—
335D4×C11—22no—
336D4×C11—41no—
337D4×C11—41no—
338D4×C11C2×C22⋊C414yes—
339C2×C4×C11—21no—
340C2×C4×C11—21no—
341C2×C4×C11—21no—
342C2×C4×C11—21no—
343C2×C4×C11—21no—
344C2×C4×C11—21no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11—41no—
351C2×C4×C11—84no—
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—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—48no—
371C2×Dic11—41no—
372C2×Dic11—41no—
373C2×Dic11—41no—
374C2×Dic11—41no—
375C2×Dic11—41no—
376C2×Dic11—41no—
377C2×Dic11—84no—
378C2×Dic11C4×D412yes—
379C2×Dic11AGL(1,ℤ/8)12yescomplemented
380D44—22no—
381D44—22no—
382D44—41no—
383D44—41no—
384C4×D11—22no—
385C4×D11—22no—
386C4×D11—22no—
387C4×D11—22no—
388Dic22—22no—
389Dic22—22no—
390Dic22—22no—
391Dic22C2×C22⋊C414yescomplemented
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×SD16—111no—
403C22×D8—111no—
404C22×D8C2×D1111yescharacteristic
405C22×M16—111no—
406C2×C4×Q8—111no—
407C2×C4×Q8—111no—
408C2×C4×D4—111no—
409C2×C4×D4C2×D1111yescharacteristic
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×#102—111no—
420C2×#102—111no—
421C2×#102C2×D1111yescharacteristic
422C2×#102C2×D1111yescharacteristic, complemented
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, complemented
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—24no—
445C22×C11—42no—
446C22×C11—42no—
447C22×C11—42no—
448C22×C11—42no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—81no—
455C22×C11—81no—
456C22×C11—81no—
457C22×C11—81no—
458C22×C11C2×C4×D411yescharacteristic
459C22×C11D4211yescharacteristic
460C22×C11D4211yescharacteristic
461C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
462C22×C11#57511yescharacteristic
463C22×C11#57611yescharacteristic
464C22×C11#57711yescharacteristic
465C2×D11—22no—
466C2×D11—22no—
467C2×D11—22no—
468C2×D11—41no—
469C2×D11—41no—
470C2×D11—41no—
471C2×D11—41no—
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—41no—
481C4×C11—41no—
482C4×C11—81no—
483C4×C11—81no—
484C4×C11C22×C22⋊C411yescharacteristic
485C4×C11#51811yescharacteristic
486C4×C11#54611yescharacteristic
487C4×C11#54611yescharacteristic
488Dic11—24no—
489Dic11—22no—
490Dic11—22no—
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×Q8—111no—
502C22×D4—114no—
503C22×D4—111no—
504C22×D4—222no—
505C22×D4—221no—
506C22×D4—222no—
507C22×D4—222no—
508C22×D4—221no—
509C22×D4—441no—
510C22×D4—441no—
511C22×D4C22×D1111yescharacteristic
512C22×D4C22×D1111yescharacteristic
513C23×C4—21no—
514C23×C4—111no—
515C23×C4—221no—
516C23×C4—221no—
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—22no—
525C2×D8—22no—
526C2×D8—114no—
527C2×D8—222no—
528C2×D8—222no—
529C2×D8C4×D1114yes—
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—22no—
542C4×D4—41no—
543C4×D4—222no—
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—21no—
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—221no—
568C2×C42—221no—
569C2×C42C22×D1111yescharacteristic
570#107—222no—
571#106—222no—
572#103—222no—
573#103—222no—
574#102—22no—
575#102—41no—
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—44no—
588C2×C11—82no—
589C2×C11D4×C22⋊C411yescharacteristic
590C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
591C2×C11#294611yescharacteristic
592C2×C11#326511yescharacteristic
593C2×C11#326811yescharacteristic
594C2×C11#327411yescharacteristic
595C2×C11#327511yescharacteristic
596D11—42no—
597D11—82no—
598C24—21no—
599C24—21no—
600C24—111no—
601C24—224no—
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—112no—
614C2×Q8—112no—
615C2×Q8—112no—
616C2×Q8—221no—
617C2×Q8—221no—
618C2×Q8—221no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—112no—
628C2×D4—224no—
629C2×D4—228no—
630C2×D4—224no—
631C2×D4—221no—
632C2×D4—221no—
633C2×D4—221no—
634C2×D4—221no—
635C2×D4—221no—
636C2×D4—444no—
637C2×D4—444no—
638C2×D4—444no—
639C2×D4—442no—
640C2×D4—442no—
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—42no—
650C22×C4—42no—
651C22×C4—81no—
652C22×C4—111no—
653C22×C4—111no—
654C22×C4—112no—
655C22×C4—112no—
656C22×C4—111no—
657C22×C4—224no—
658C22×C4—221no—
659C22×C4—221no—
660C22×C4—221no—
661C22×C4—221no—
662C22×C4—221no—
663C22×C4—221no—
664C22×C4—221no—
665C22×C4—442no—
666C22×C4—442no—
667C22×C4—442no—
668C22×C4—442no—
669C22×C4—881no—
670C22×C4D4×D1111yescharacteristic
671C22×C4D4×D1111yescharacteristic
672C22×C4C23×D1111yescharacteristic
673SD16—1116no—
674SD16—228no—
675D8—28no—
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—221no—
695C4⋊C4—221no—
696C4⋊C4—221no—
697C4⋊C4—221no—
698C4⋊C4—442no—
699C4⋊C4—442no—
700C22⋊C4—42no—
701C22⋊C4—42no—
702C22⋊C4—81no—
703C22⋊C4—222no—
704C22⋊C4—441no—
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—221no—
717C42—221no—
718C42—442no—
719C42—442no—
720C11#2244311yescharacteristic, complemented, Sylow
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—112no—
736C23—221no—
737C23—221no—
738C23—221no—
739C23—221no—
740C23—221no—
741C23—221no—
742C23—222no—
743C23—448no—
744C23—448no—
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—114no—
758Q8—222no—
759Q8—222no—
760Q8—222no—
761D4—22no—
762D4—22no—
763D4—22no—
764D4—22no—
765D4—22no—
766D4—41no—
767D4—41no—
768D4—222no—
769D4—222no—
770D4—448no—
771D4—448no—
772D4—441no—
773D4—441no—
774D4C22⋊C4×D1114yes—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—84no—
788C2×C4—112no—
789C2×C4—112no—
790C2×C4—221no—
791C2×C4—222no—
792C2×C4—222no—
793C2×C4—221no—
794C2×C4—221no—
795C2×C4—222no—
796C2×C4—221no—
797C2×C4—222no—
798C2×C4—222no—
799C2×C4—222no—
800C2×C4—222no—
801C2×C4—221no—
802C2×C4—221no—
803C2×C4—221no—
804C2×C4—448no—
805C2×C4—441no—
806C2×C4—441no—
807C2×C4—441no—
808C2×C4—441no—
809C2×C4—441no—
810C2×C4—441no—
811C2×C4—884no—
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—24no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—222no—
837C22—222no—
838C22—222no—
839C22—441no—
840C22—441no—
841C22—441no—
842C22—441no—
843C22—442no—
844C22—442no—
845C22—442no—
846C22—8816no—
847C22—881no—
848C22—881no—
849C22—881no—
850C22—881no—
851C22C4×D4×D1111yescharacteristic
852C22#1062312111yescharacteristic
853C22#1062314011yescharacteristic
854C22#1062328811yescharacteristic
855C22#1062330111yescharacteristic
856C22D11×AGL(1,ℤ/8)11yescharacteristic
857C22#1062330411yescharacteristic
858C4—41no—
859C4—41no—
860C4—81no—
861C4—81no—
862C4—222no—
863C4—222no—
864C4—224no—
865C4—441no—
866C4—881no—
867C4—881no—
868C4C2×C22⋊C4×D1111yescharacteristic
869C4#1062307611yescharacteristic
870C4#1062314111yescharacteristic
871C4#1062318511yescharacteristic
872C2—44no—
873C2—82no—
874C2—442no—
875C2—882no—
876C2#1307143411yescharacteristic
877C2#1307742711yescharacteristic
878C2#1307744111yescharacteristic
879C2#1308011711yescharacteristic
880C2#1308016211yescharacteristic
881C2#1308023411yescharacteristic
882C2#1308024511yescharacteristic
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#22443
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×#10622631C2semidirect
3. C2×#10622371C2semidirect
4. #13071455C2semidirect
5. D4×(C2×D11)⋊C4C2semidirect
6. #13069491C2semidirect
7. #13069479C2semidirect
8. #13068972C2semidirect
9. #13068970C2semidirect
10. #13068966C2semidirect
11. #13068648C2semidirect
12. #13068553C2semidirect
13. #13068545C2semidirect
14. #13068398C2semidirect
15. C11×#1879C2semidirect
26. C2×#66964C4semidirect
29. C2×#66940C22semidirect
30. C2×C4×Dic22C22semidirect
32. C2×C11×#102C22semidirect
33. C11×#390C22semidirect
34. #10622834C22semidirect
36. C2×#66896C22semidirect
40. C2×#66880C22semidirect
41. C2×C8×Dic11C22semidirect
46. C2×#66874C22semidirect
48. C2×#66872C22semidirect
49. C2×#66871C22semidirect
58. C2×#66867C22semidirect
60. C11×#340C22semidirect
61. C11×#336C22semidirect
62. #10622189C22semidirect
63. #10622188C22semidirect
77. C2×#4341C2×C4semidirect
110. C2×#4323C2×C4semidirect
132. C2×#4314C2×C4semidirect
135. C2×#4313C2×C4semidirect
252. #4324C22⋊C4semidirect
290. #1879D11semidirect
379. C2×Dic11AGL(1,ℤ/8)semidirect
391. Dic22C2×C22⋊C4semidirect
395. C11⋊C8C2×C22⋊C4semidirect
422. C2×#102C2×D11semidirect
431. #390C2×D11semidirect
441. #340C2×D11semidirect
443. #336C2×D11semidirect
720. C11#22443semidirect

Maximal subgroups

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

subgroupindex
C22×#669642
C2×#106226312
C2×#106223712
#130714552
D4×(C2×D11)⋊C42
#130694912
#130694792
#130689722
#130689702
#130689662
#130686482
#130685532
#130685452
#130683982
C11×#18792
#2244311