Finite Group Databasebeta

← #14769537

Subgroups — #14769537

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×#66967C211yesmaximal, characteristic
2C2×#10622482C211yesmaximal, characteristic, complemented
3C2×C4×D88C211yesmaximal, characteristic, complemented
4#13071445C211yesmaximal, characteristic, complemented
5#13071437C211yesmaximal, characteristic, complemented
6#13069499C211yesmaximal, characteristic, complemented
7#13068967C211yesmaximal, characteristic, complemented
8#13068961C211yesmaximal, characteristic, complemented
9#13068953C211yesmaximal, characteristic, complemented
10#13068947C211yesmaximal, characteristic, complemented
11#13068646C211yesmaximal, characteristic, complemented
12#13068555C211yesmaximal, characteristic, complemented
13#13068545C211yesmaximal, characteristic, complemented
14#13068399C211yesmaximal, characteristic, complemented
15C11×#1968C211yesmaximal, characteristic, complemented
16C22×#4343C2211yescharacteristic
17C22×D4×D11C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C22×#4325C2211yescharacteristic
20C22×#4323C2211yescharacteristic
21C2×#66967—24no—
22C2×#66967—24no—
23C2×#66967C418yescomplemented
24C22×D88C2211yescharacteristic
25C22×#4313C2211yescharacteristic
26C2×#66946C2211yescharacteristic
27C2×#66946C2211yescharacteristic, complemented
28C2×C22⋊C4×D11—21no—
29C2×C4×D44C2211yescharacteristic
30C2×C4×D44C2211yescharacteristic, complemented
31C2×C11×#106C2211yescharacteristic, complemented
32C2×C11×#103C2211yescharacteristic, complemented
33C2×C11×#102C2211yescharacteristic
34C2×C4×C8×C11C2211yescharacteristic, complemented
35C11×#391C2211yescharacteristic, complemented
36C11×#390C2211yescharacteristic
37#10622843C2211yescharacteristic, complemented
38C2×#66899C2211yescharacteristic, complemented
39#10622834C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41C2×#66885C2211yescharacteristic
42C2×#66885C2211yescharacteristic, complemented
43C2×(C2×D11)⋊C8C2211yescharacteristic
44C2×#66882C2211yescharacteristic, complemented
45C2×#66879C2211yescharacteristic, complemented
46#10622600C2211yescharacteristic
47#10622600C2211yescharacteristic
48C2×#66873C2211yescharacteristic
49C2×#66873C2211yescharacteristic, complemented
50#10622569—21no—
51#10622569—21no—
52#10622568—21no—
53C4×(C2×D11)⋊C4C2211yescharacteristic
54#10622482—24no—
55C4×D88—24no—
56#10622278—21no—
57#10622278—21no—
58#10622277—21no—
59D11×#95—21no—
60#10622188C2211yescharacteristic, complemented
61#10622167C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63#10622162C2211yescharacteristic, 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×C414yescomplemented
80C22×D44—21no—
81C22×D44C2311yescharacteristic
82C22×D44C2311yescharacteristic
83C22×C4×D11—21no—
84C22×C4×D11—21no—
85C22×C4×D11—21no—
86C22×C4×D11—21no—
87C22×C4×D11—21no—
88C22×C4×D11C2311yescharacteristic
89C2×C11×SD16—22no—
90C2×C11×SD16—22no—
91C2×C11×SD16C2×C414yescomplemented
92C22×C8×C11C2311yescharacteristic
93C22×C8×C11C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C42×C11C2311yescharacteristic
99C2×C22⋊Dic11—21no—
100C2×C22⋊Dic11—21no—
101C2×#4325—22no—
102C2×#4325—22no—
103C2×#4325C2×C414yescomplemented
104C2×#4323—22no—
105C2×#4323—22no—
106C2×#4323C2×C414yescomplemented
107C2×(C2×D11)⋊C4—21no—
108C2×(C2×D11)⋊C4—21no—
109C2×(C2×D11)⋊C4—21no—
110C2×(C2×D11)⋊C4—21no—
111C2×(C2×D11)⋊C4—21no—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4D411yescharacteristic
114C2×(C2×D11)⋊C4D411yescharacteristic
115C2×C4⋊Dic11C2311yescharacteristic
116C2×C4⋊Dic11C2311yescharacteristic
117C2×C4×Dic11C2311yescharacteristic
118C22×C11⋊C8C2311yescharacteristic
119C22×C11⋊C8C2311yescharacteristic
120#66967—232no—
121C2×D88C2×C414yes—
122C2×D88D414yes—
123C2×D88D414yes—
124C2×#4313—22no—
125C2×#4313—22no—
126C2×#4313C2×C414yescomplemented
127#66946—22no—
128#66946—22no—
129#66946—41no—
130#66946—41no—
131C22⋊C4×D11—44no—
132C4×D44—22no—
133C4×D44—22no—
134C4×D44—41no—
135C4×D44—41no—
136C11×#106—22no—
137C11×#103—41no—
138C11×#102—41no—
139C4×C8×C11—22no—
140C11×#95—21no—
141C11×#95—21no—
142#66899—41no—
143#66896—41no—
144C11⋊#95—21no—
145C11⋊#95—21no—
146C11⋊#95—21no—
147C11⋊#95—21no—
148C11⋊#95D411yescharacteristic
149C11⋊#95D411yescharacteristic
150#66885—22no—
151#66885—22no—
152(C2×D11)⋊C8—22no—
153#66882—22no—
154#66879—22no—
155#66873—22no—
156#66873—22no—
157#22442—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×C11—21no—
173C2×Q8×C11—21no—
174C2×Q8×C11C22×C412yes—
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—42no—
211C2×D44—42no—
212C2×D44C22×C412yes—
213C2×D44C22×C412yes—
214C2×D44C2×D412yes—
215C2×D44C2×D412yes—
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—42no—
230C2×C4×D11—42no—
231C2×C4×D11—42no—
232C2×C4×D11—42no—
233C2×C4×D11—81no—
234C2×C4×D11—81no—
235C2×C4×D11—81no—
236C2×C4×D11—81no—
237C2×C4×D11C22×C412yes—
238C2×C4×D11#4112yes—
239C11×SD16—28no—
240C2×C8×C11—21no—
241C2×C8×C11—21no—
242C2×C8×C11—21no—
243C2×C8×C11C22×C412yes—
244C2×C8×C11C2×D412yes—
245C2×C8×C11C2×D412yes—
246C11×C4⋊C4—21no—
247C11×C4⋊C4—21no—
248C11×C4⋊C4—21no—
249C11×C4⋊C4—21no—
250C11×C22⋊C4—42no—
251C11×C22⋊C4—81no—
252C42×C11—21no—
253C42×C11—21no—
254C22⋊Dic11—42no—
255C22⋊Dic11—81no—
256#4325—28no—
257#4323—28no—
258(C2×D11)⋊C4—22no—
259(C2×D11)⋊C4—41no—
260(C2×D11)⋊C4—42no—
261(C2×D11)⋊C4—42no—
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⋊C8—21no—
276C2×C11⋊C8—21no—
277C2×C11⋊C8C22×C412yes—
278D88C22⋊C4116yescomplemented
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#1968D1111yescharacteristic, complemented
287#1879—111no—
288#1879—111no—
289#1877—111no—
290#1877—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—22no—
307C22×D11—22no—
308C22×D11—22no—
309C22×D11—21no—
310C22×D11—21no—
311C22×D11—21no—
312C22×D11—21no—
313C22×D11—21no—
314C22×D11—21no—
315C22×D11—48no—
316C22×D11—48no—
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—41no—
334Q8×C11—41no—
335D4×C11—22no—
336D4×C11—22no—
337D4×C11—41no—
338D4×C11—41no—
339C2×C4×C11—21no—
340C2×C4×C11—21no—
341C2×C4×C11—22no—
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—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—22no—
382D44—48no—
383D44C2×C22⋊C414yes—
384D44C2×C22⋊C414yescomplemented
385C4×D11—22no—
386C4×D11—22no—
387C4×D11—22no—
388C4×D11—22no—
389C4×D11—48no—
390C4×D11—84no—
391C4×D11—84no—
392C4×D11—84no—
393C4×D11—84no—
394C8×C11—41no—
395C8×C11C2×C22⋊C414yescomplemented
396C11⋊C8—22no—
397C11⋊C8—41no—
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×SD16C2×D1111yescharacteristic
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×#106C2×D1111yescharacteristic, complemented
417C2×#103—111no—
418C2×#103C2×D1111yescharacteristic, complemented
419C2×#102—111no—
420C2×#102—111no—
421C2×#102—111no—
422C2×#102—111no—
423C2×#102—111no—
424C2×#102C2×D1111yescharacteristic
425C2×C22⋊C8—111no—
426C2×#97—111no—
427C2×C4×C8C2×D1111yescharacteristic, complemented
428#391—111no—
429#391C2×D1111yescharacteristic, complemented
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#340—111no—
444#336—111no—
445#336—111no—
446C22×C11—42no—
447C22×C11—42no—
448C22×C11—42no—
449C22×C11—81no—
450C22×C11—81no—
451C22×C11—81no—
452C22×C11—81no—
453C22×C11C2×C4×D411yescharacteristic
454C22×C11D4211yescharacteristic
455C22×C11D4211yescharacteristic
456C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
457C22×C11#57511yescharacteristic
458C22×C11#57611yescharacteristic
459C22×C11#57711yescharacteristic
460C2×D11—24no—
461C2×D11—24no—
462C2×D11—22no—
463C2×D11—22no—
464C2×D11—22no—
465C2×D11—42no—
466C2×D11—42no—
467C2×D11—42no—
468C2×D11—42no—
469C2×D11—41no—
470C2×D11—42no—
471C2×D11—42no—
472C2×D11—41no—
473C2×D11—42no—
474C2×D11—42no—
475C2×D11—41no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—41no—
479C2×D11—42no—
480C2×D11—42no—
481C2×D11—816no—
482C4×C11—22no—
483C4×C11—42no—
484C4×C11—41no—
485C4×C11—81no—
486C4×C11—81no—
487C4×C11C22×C22⋊C411yescharacteristic
488C4×C11#51811yescharacteristic
489C4×C11#54611yescharacteristic
490C4×C11#54611yescharacteristic
491Dic11—22no—
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×Q8C22×D1111yescharacteristic
504C22×D4—114no—
505C22×D4—111no—
506C22×D4—111no—
507C22×D4—221no—
508C22×D4—222no—
509C22×D4—221no—
510C22×D4—222no—
511C22×D4—222no—
512C22×D4—441no—
513C22×D4—441no—
514C22×D4C22×D1111yescharacteristic
515C23×C4—111no—
516C23×C4—221no—
517C23×C4—221no—
518C23×C4—221no—
519C23×C4—221no—
520C23×C4—221no—
521AGL(1,ℤ/8)—2232no—
522C2×SD16—22no—
523C2×SD16—22no—
524C2×SD16—114no—
525C2×SD16—222no—
526C2×SD16—222no—
527C2×SD16C4×D1114yescomplemented
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—21no—
555C2×C22⋊C4—111no—
556C2×C22⋊C4—111no—
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×C42C22×D1111yescharacteristic
568#107—222no—
569#106—22no—
570#103—41no—
571#103—441no—
572#102—41no—
573#102—222no—
574#102—222no—
575#102—222no—
576#102—222no—
577#102—441no—
578C22⋊C8—222no—
579#97—222no—
580C4×C8—22no—
581#95—21no—
582#95—21no—
583#95—111no—
584#95—111no—
585#95—221no—
586#95—221no—
587#95—221no—
588#95—221no—
589C2×C11—82no—
590C2×C11D4×C22⋊C411yescharacteristic
591C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
592C2×C11#294611yescharacteristic
593C2×C11#326411yescharacteristic
594C2×C11#326711yescharacteristic
595C2×C11#327211yescharacteristic
596C2×C11#327311yescharacteristic
597D11—42no—
598D11—44no—
599D11—44no—
600C24—21no—
601C24—111no—
602C24—224no—
603C24—221no—
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—21no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8C2×C4×D1112yes—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—112no—
627C2×D4—112no—
628C2×D4—112no—
629C2×D4—112no—
630C2×D4—112no—
631C2×D4—112no—
632C2×D4—224no—
633C2×D4—224no—
634C2×D4—228no—
635C2×D4—221no—
636C2×D4—221no—
637C2×D4—221no—
638C2×D4—221no—
639C2×D4—221no—
640C2×D4—221no—
641C2×D4—442no—
642C2×D4—442no—
643C2×D4—444no—
644C2×D4—444no—
645C2×D4—444no—
646C2×D4—442no—
647C2×D4—442no—
648C2×D4C2×C4×D1112yes—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—111no—
653C22×C4—112no—
654C22×C4—112no—
655C22×C4—111no—
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—442no—
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—442no—
674C22×C4—881no—
675C22×C4—881no—
676C22×C4—881no—
677C22×C4—881no—
678C22×C4D4×D1111yescharacteristic
679C22×C4D4×D1111yescharacteristic
680C22×C4C23×D1111yescharacteristic
681SD16—28no—
682SD16—228no—
683D8—1116no—
684D8—228no—
685M16—228no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—112no—
690C2×C8—221no—
691C2×C8—221no—
692C2×C8—221no—
693C2×C8—221no—
694C2×C8—221no—
695C2×C8C2×C4×D1112yes—
696C2×C8D4×D1112yes—
697C2×C8D4×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—81no—
708C22⋊C4—222no—
709C22⋊C4—441no—
710C22⋊C4—442no—
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—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—112no—
731C23—222no—
732C23—222no—
733C23—221no—
734C23—221no—
735C23—221no—
736C23—221no—
737C23—221no—
738C23—222no—
739C23—222no—
740C23—222no—
741C23—222no—
742C23—221no—
743C23—448no—
744C23—448no—
745C23—441no—
746C23—441no—
747C23—441no—
748C23—441no—
749C23—441no—
750C23—441no—
751C23—441no—
752C23—441no—
753C23—884no—
754C23—884no—
755C23—884no—
756C23—884no—
757C23—884no—
758C23C2×D4×D1111yescharacteristic
759Q8—22no—
760Q8—22no—
761Q8—41no—
762Q8—41no—
763D4—22no—
764D4—22no—
765D4—41no—
766D4—41no—
767D4—114no—
768D4—114no—
769D4—222no—
770D4—222no—
771D4—222no—
772D4—222no—
773D4—222no—
774D4—222no—
775D4—448no—
776D4—448no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—21no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—112no—
792C2×C4—221no—
793C2×C4—221no—
794C2×C4—222no—
795C2×C4—222no—
796C2×C4—222no—
797C2×C4—222no—
798C2×C4—221no—
799C2×C4—221no—
800C2×C4—221no—
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×C4—884no—
813C2×C4—884no—
814C2×C4—884no—
815C2×C4#6696712yescomplemented
816C2×C4C22×C4×D1111yescharacteristic
817C2×C4C2×D4×D1111yescharacteristic
818C2×C4C2×D4×D1111yescharacteristic
819C2×C4#6703711yescharacteristic
820C2×C4#41×D1111yescharacteristic
821C2×C4#6704211yescharacteristic
822C8—41no—
823C8—222no—
824C8—441no—
825C8C22⋊C4×D1114yescomplemented
826C22—42no—
827C22—42no—
828C22—42no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—222no—
834C22—224no—
835C22—224no—
836C22—222no—
837C22—222no—
838C22—442no—
839C22—442no—
840C22—441no—
841C22—441no—
842C22—442no—
843C22—442no—
844C22—442no—
845C22—441no—
846C22—442no—
847C22—442no—
848C22—441no—
849C22—442no—
850C22—442no—
851C22—442no—
852C22—442no—
853C22—442no—
854C22—8816no—
855C22C4×D4×D1111yescharacteristic
856C22#1062314011yescharacteristic
857C22#1062324811yescharacteristic
858C22C2×#6696711yescharacteristic
859C22#1062329311yescharacteristic
860C22#1062329911yescharacteristic
861C22#1062330011yescharacteristic
862C4—22no—
863C4—41no—
864C4—42no—
865C4—81no—
866C4—81no—
867C4—222no—
868C4—441no—
869C4—441no—
870C4—881no—
871C4—881no—
872C4C2×C22⋊C4×D1111yescharacteristic
873C4#1062307611yescharacteristic
874C4#1062314311yescharacteristic
875C4#1062320711yescharacteristic
876C2—82no—
877C2—442no—
878C2—444no—
879C2—444no—
880C2#1307143711yescharacteristic
881C2C4×#6696711yescharacteristic
882C2#1307744311yescharacteristic
883C2#1308009311yescharacteristic
884C2#1308013811yescharacteristic
885C2#1308021511yescharacteristic
886C2#1308022511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1968C2
socleC23×C11C22×D4
prime radicalC22×#66967C2
cosocleC22×C4×C11C24
hypercenter#1968D11
hypocenterC11#22442
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1968

Complements

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

NH ≅ G/Ntype
2. C2×#10622482C2semidirect
3. C2×C4×D88C2semidirect
4. #13071445C2semidirect
5. #13071437C2semidirect
6. #13069499C2semidirect
7. #13068967C2semidirect
8. #13068961C2semidirect
9. #13068953C2semidirect
10. #13068947C2semidirect
11. #13068646C2semidirect
12. #13068555C2semidirect
13. #13068545C2semidirect
14. #13068399C2semidirect
15. C11×#1968C2semidirect
23. C2×#66967C4semidirect
27. C2×#66946C22semidirect
30. C2×C4×D44C22semidirect
31. C2×C11×#106C22semidirect
32. C2×C11×#103C22semidirect
34. C2×C4×C8×C11C22semidirect
35. C11×#391C22semidirect
37. #10622843C22semidirect
38. C2×#66899C22semidirect
42. C2×#66885C22semidirect
44. C2×#66882C22semidirect
45. C2×#66879C22semidirect
49. C2×#66873C22semidirect
60. #10622188C22semidirect
61. #10622167C22semidirect
62. #10622167C22semidirect
63. #10622162C22semidirect
73. C2×#4343C2×C4semidirect
79. C2×D4×D11C2×C4semidirect
91. C2×C11×SD16C2×C4semidirect
103. C2×#4325C2×C4semidirect
106. C2×#4323C2×C4semidirect
126. C2×#4313C2×C4semidirect
278. D88C22⋊C4semidirect
286. #1968D11semidirect
353. C2×C4×C11AGL(1,ℤ/8)semidirect
384. D44C2×C22⋊C4semidirect
395. C8×C11C2×C22⋊C4semidirect
416. C2×#106C2×D11semidirect
418. C2×#103C2×D11semidirect
427. C2×C4×C8C2×D11semidirect
429. #391C2×D11semidirect
527. C2×SD16C4×D11semidirect
722. C11#22442semidirect
815. C2×C4#66967semidirect
825. C8C22⋊C4×D11semidirect

Maximal subgroups

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

subgroupindex
C22×#669672
C2×#106224822
C2×C4×D882
#130714452
#130714372
#130694992
#130689672
#130689612
#130689532
#130689472
#130686462
#130685552
#130685452
#130683992
C11×#19682
#2244211