Finite Group Databasebeta

← #14769534

Subgroups — #14769534

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×#66985C211yesmaximal, characteristic
2C2×#10622627C211yesmaximal, characteristic, complemented
3C2×C4×#4323C211yesmaximal, characteristic, complemented
4#13071447C211yesmaximal, characteristic, complemented
5#13069496C211yesmaximal, characteristic, complemented
6#13069469C211yesmaximal, characteristic, complemented
7#13068967C211yesmaximal, characteristic, complemented
8#13068967C211yesmaximal, characteristic, complemented
9#13068950C211yesmaximal, characteristic, complemented
10#13068950C211yesmaximal, characteristic, complemented
11#13068647C211yesmaximal, characteristic, complemented
12#13068554C211yesmaximal, characteristic, complemented
13#13068547C211yesmaximal, characteristic, complemented
14#13068400C211yesmaximal, characteristic, complemented
15D4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C22×#4339C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C22×C11×C22⋊C4—21no—
21C22×#4324C2211yescharacteristic
22C22×#4324C2211yescharacteristic
23C2×#66985—24no—
24C2×#66985—24no—
25C2×#66985C418yescomplemented
26C22×#4323C2211yescharacteristic
27C22×#4323C2211yescharacteristic
28C22×#4318C2211yescharacteristic
29C2×C4×D44C2211yescharacteristic, complemented
30C2×C4×D44C2211yescharacteristic, complemented
31C11×#390C2211yescharacteristic
32C11×#390C2211yescharacteristic
33C11×#386—21no—
34C11×#386—21no—
35C11×#380C2211yescharacteristic
36C11×#379—21no—
37C4×C11×C22⋊C4C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42#10622825C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44#10622627—24no—
45C4×#4323—24no—
46C2×#66874C2211yescharacteristic, complemented
47C2×#66874C2211yescharacteristic, complemented
48C2×#66873C2211yescharacteristic, complemented
49C2×#66873C2211yescharacteristic, complemented
50C2×#66872C2211yescharacteristic, complemented
51C2×#66871C2211yescharacteristic, complemented
52#10622569—21no—
53#10622569—21no—
54#10622542C2211yescharacteristic, complemented
55#10622542C2211yescharacteristic, complemented
56C2×#66867C2211yescharacteristic, complemented
57C2×C4×C11⋊C8C2211yescharacteristic, complemented
58#10622277—21no—
59D11×#95—21no—
60#10622167C2211yescharacteristic, complemented
61#10622167C2211yescharacteristic, complemented
62#10622162C2211yescharacteristic, complemented
63#10622162C2211yescharacteristic, complemented
64C25×C11—21no—
65C22×D4×C11—22no—
66C22×D4×C11—22no—
67C22×D4×C11—21no—
68C22×D4×C11—22no—
69C22×D4×C11—41no—
70C22×D4×C11—41no—
71C22×D4×C11C2×C414yescomplemented
72C22×D4×C11C2311yescharacteristic
73C22×D4×C11C2311yescharacteristic
74C23×C4×C11—21no—
75C23×C4×C11—21no—
76C23×C4×C11C2311yescharacteristic
77C22×C22⋊D11—21no—
78C2×#4339—22no—
79C2×#4339—22no—
80C2×#4339—22no—
81C2×#4339—41no—
82C2×#4339—41no—
83C2×#4339C2×C414yescomplemented
84C22×D44C2311yescharacteristic
85C22×C4×D11—21no—
86C22×C4×D11—21no—
87C22×C4×D11—21no—
88C22×Dic22C2311yescharacteristic
89C4×D4×C11—22no—
90C4×D4×C11—22no—
91C4×D4×C11—41no—
92C4×D4×C11—41no—
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—44no—
103C2×C11×C22⋊C4D411yescharacteristic
104C2×C11×C22⋊C4D411yescharacteristic
105C2×C42×C11C2311yescharacteristic
106C2×C42×C11C2311yescharacteristic
107C2×C22⋊Dic11—21no—
108C2×#4324—22no—
109C2×#4324—22no—
110C2×#4324—22no—
111C2×#4324—22no—
112C2×#4324C2×C414yescomplemented
113C2×#4324C2×C414yescomplemented
114#66985—232no—
115C2×#4323—22no—
116C2×#4323—22no—
117C2×#4323C2×C414yes—
118C2×#4323C2×C414yescomplemented
119C2×#4323D414yes—
120C2×#4323D414yes—
121C2×(C2×D11)⋊C4—21no—
122C2×(C2×D11)⋊C4—21no—
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×#4318—22no—
126C2×#4318—22no—
127C2×#4318C2×C414yescomplemented
128C22×C11⋊C8C2311yescharacteristic
129C22×C11⋊C8C2311yescharacteristic
130C22×C11⋊C8C2311yescharacteristic
131C22×C11⋊C8C2311yescharacteristic
132C4×D44—22no—
133C4×D44—22no—
134C4×D44—41no—
135C4×D44—41no—
136C11×#95—21no—
137C11×#95D411yescharacteristic
138C11×#95D411yescharacteristic
139#66896—22no—
140#66896—22no—
141#66896—41no—
142#66896—41no—
143C11⋊#95—21no—
144C11⋊#95—21no—
145C11⋊#95—21no—
146C11⋊#95—21no—
147C11⋊#95—21no—
148C22⋊(C11⋊C8)—22no—
149#66874—41no—
150#66874—41no—
151#66873—22no—
152#66873—22no—
153#66872—22no—
154#66871—22no—
155#66867—22no—
156C4×C11⋊C8—22no—
157#22442—111nomaximal, Sylow
158C24×C11—21no—
159C24×C11—21no—
160C24×C11—24no—
161C24×C11—42no—
162C24×C11—42no—
163C24×C11—42no—
164C24×C11—42no—
165C24×C11—81no—
166C24×C11—81no—
167C24×C11C2×D411yescharacteristic
168C23×D11—21no—
169C2×D4×C11—28no—
170C2×D4×C11—24no—
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×C11—21no—
178C2×D4×C11—21no—
179C2×D4×C11—44no—
180C2×D4×C11—44no—
181C2×D4×C11—44no—
182C2×D4×C11—42no—
183C2×D4×C11—42no—
184C2×D4×C11C22×C412yes—
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—21no—
194C22×C4×C11—42no—
195C22×C4×C11—42no—
196C22×C4×C11—42no—
197C22×C4×C11—42no—
198C22×C4×C11—81no—
199C22×C4×C11—81no—
200C22×C4×C11C22×C412yes—
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2×D411yescharacteristic
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11#4112yes—
207C22×C4×C11C2411yescharacteristic
208C2×C22⋊D11—24no—
209C2×C22⋊D11—42no—
210C2×C22⋊D11—42no—
211C22×Dic11—21no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214#4339—28no—
215#4339—44no—
216#4339—44no—
217#4339—44no—
218C2×D44—21no—
219C2×D44—21no—
220C2×D44—21no—
221C2×D44C22×C412yes—
222C2×D44C2×D412yes—
223C2×D44C2×D412yes—
224C2×C4×D11—24no—
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—81no—
232C2×C4×D11—81no—
233C2×Dic22—21no—
234C2×Dic22—21no—
235C2×Dic22—21no—
236C2×Dic22—21no—
237C2×Dic22—21no—
238C2×Dic22C22×C412yes—
239C11×C4⋊C4—21no—
240C11×C4⋊C4—21no—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—21no—
243C11×C22⋊C4—22no—
244C11×C22⋊C4—41no—
245C11×C22⋊C4—42no—
246C11×C22⋊C4—42no—
247C11×C22⋊C4—42no—
248C11×C22⋊C4—42no—
249C11×C22⋊C4—42no—
250C11×C22⋊C4—81no—
251C11×C22⋊C4—81no—
252C42×C11—21no—
253C42×C11—21no—
254C42×C11—21no—
255C42×C11—21no—
256C22⋊Dic11—81no—
257#4324—28no—
258#4324—28no—
259#4323—28no—
260#4323C22⋊C4116yescomplemented
261(C2×D11)⋊C4—42no—
262(C2×D11)⋊C4—42no—
263C4⋊Dic11—21no—
264C4⋊Dic11—21no—
265C4⋊Dic11—21no—
266C4⋊Dic11—21no—
267#4318—28no—
268C2×C11⋊C8—21no—
269C2×C11⋊C8—21no—
270C2×C11⋊C8—21no—
271C2×C11⋊C8—21no—
272C2×C11⋊C8—21no—
273C2×C11⋊C8—21no—
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⋊C4D1111yescharacteristic, complemented
285#1973—111no—
286#1968—111no—
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—22no—
297C23×C11—22no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—21no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—22no—
305C23×C11—48no—
306C23×C11—48no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—41no—
315C23×C11—41no—
316C23×C11—41no—
317C23×C11—84no—
318C23×C11—84no—
319C23×C11—84no—
320C23×C11—84no—
321C23×C11—84no—
322C23×C11C4×D412yes—
323C23×C11C22×D411yescharacteristic
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—41no—
328C22×D11—41no—
329C22×D11—41no—
330C22×D11—41no—
331D4×C11—22no—
332D4×C11—22no—
333D4×C11—22no—
334D4×C11—22no—
335D4×C11—22no—
336D4×C11—48no—
337D4×C11—41no—
338D4×C11—41no—
339D4×C11C2×C22⋊C414yes—
340C2×C4×C11—21no—
341C2×C4×C11—21no—
342C2×C4×C11—21no—
343C2×C4×C11—21no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—21no—
349C2×C4×C11—21no—
350C2×C4×C11—21no—
351C2×C4×C11—21no—
352C2×C4×C11—21no—
353C2×C4×C11—21no—
354C2×C4×C11—21no—
355C2×C4×C11—21no—
356C2×C4×C11—21no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
359C2×C4×C11—41no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11—84no—
364C2×C4×C11—84no—
365C2×C4×C11C4×D412yes—
366C2×C4×C11AGL(1,ℤ/8)12yescomplemented
367C2×C4×C11C23×C411yescharacteristic
368C2×C4×C11C22×D411yescharacteristic
369C2×C4×C11C22×D411yescharacteristic
370C2×C4×C11C2×#4111yescharacteristic
371C2×C4×C11H(5,𝔽2)11yescharacteristic
372C2×C4×C11H(5,𝔽2)11yescharacteristic
373C22⋊D11—48no—
374C2×Dic11—22no—
375C2×Dic11—41no—
376C2×Dic11—41no—
377C2×Dic11—41no—
378C2×Dic11—41no—
379C2×Dic11—41no—
380C2×Dic11—41no—
381C2×Dic11—41no—
382C2×Dic11—41no—
383D44—22no—
384D44—22no—
385D44—22no—
386D44C2×C22⋊C414yescomplemented
387C4×D11—48no—
388C4×D11—84no—
389C4×D11—84no—
390Dic22—22no—
391Dic22—22no—
392Dic22—41no—
393Dic22—41no—
394C11⋊C8—22no—
395C11⋊C8—41no—
396C11⋊C8—41no—
397C11⋊C8C2×C22⋊C414yescomplemented
398C22×#41—111no—
399C23×D4C2×D1111yescharacteristic
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×D4C2×D1111yescharacteristic
411C2×C4×D4C2×D1111yescharacteristic
412C22×C22⋊C4—21no—
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×#102—111no—
424C2×#102—111no—
425C2×C22⋊C8—111no—
426C2×#97—111no—
427C2×C4×C8—111no—
428#391—111no—
429#391—111no—
430#390C2×D1111yescharacteristic
431#390C2×D1111yescharacteristic
432#386—21no—
433#386—21no—
434#386—221no—
435#386—221no—
436#381—221no—
437#380—111no—
438#380C2×D1111yescharacteristic
439#379—21no—
440C4×C22⋊C4C2×D1111yescharacteristic
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—42no—
453C22×C11—41no—
454C22×C11—41no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—41no—
458C22×C11—41no—
459C22×C11—42no—
460C22×C11—42no—
461C22×C11—42no—
462C22×C11—42no—
463C22×C11—816no—
464C22×C11—81no—
465C22×C11—81no—
466C22×C11—81no—
467C22×C11—81no—
468C22×C11C2×C4×D411yescharacteristic
469C22×C11D4211yescharacteristic
470C22×C11D4211yescharacteristic
471C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
472C22×C11#57511yescharacteristic
473C22×C11#57611yescharacteristic
474C22×C11#57711yescharacteristic
475C2×D11—24no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—42no—
479C2×D11—42no—
480C2×D11—42no—
481C2×D11—42no—
482C4×C11—22no—
483C4×C11—22no—
484C4×C11—41no—
485C4×C11—41no—
486C4×C11—41no—
487C4×C11—81no—
488C4×C11—81no—
489C4×C11C22×C22⋊C411yescharacteristic
490C4×C11#51811yescharacteristic
491C4×C11#54611yescharacteristic
492C4×C11#54611yescharacteristic
493Dic11—42no—
494Dic11—81no—
495Dic11—81no—
496C25—21no—
497C2×#41—114no—
498C2×#41—222no—
499C2×#41—222no—
500C2×#41—222no—
501C2×#41—441no—
502C2×#41—441no—
503C22×Q8—111no—
504C22×D4—22no—
505C22×D4—22no—
506C22×D4—22no—
507C22×D4—21no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4—111no—
511C22×D4—221no—
512C22×D4C4×D1114yescomplemented
513C22×D4C22×D1111yescharacteristic
514C22×D4C22×D1111yescharacteristic
515C23×C4—21no—
516C23×C4—21no—
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×C8—111no—
540C22×C8—111no—
541C4×D4—22no—
542C4×D4—22no—
543C4×D4—41no—
544C4×D4—41no—
545C4×D4—222no—
546C4×D4—222no—
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—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—44no—
561C2×C22⋊C4—221no—
562C2×C22⋊C4—221no—
563C2×C22⋊C4—221no—
564C2×C22⋊C4C22⋊D1111yescharacteristic
565C2×C22⋊C4C22⋊D1111yescharacteristic
566C2×C42C22×D1111yescharacteristic
567C2×C42C22×D1111yescharacteristic
568#107—222no—
569#106—222no—
570#103—441no—
571#103—441no—
572#102—222no—
573#102—222no—
574#102—222no—
575#102—222no—
576#102—441no—
577#102—441no—
578C22⋊C8—222no—
579#97—222no—
580C4×C8—222no—
581#95—21no—
582#95—221no—
583#95—221no—
584#95—221no—
585#95—221no—
586#95—221no—
587#95C22⋊D1111yescharacteristic
588#95C22⋊D1111yescharacteristic
589C2×C11—42no—
590C2×C11—44no—
591C2×C11—82no—
592C2×C11D4×C22⋊C411yescharacteristic
593C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
594C2×C11#294611yescharacteristic
595C2×C11#326411yescharacteristic
596C2×C11#326711yescharacteristic
597C2×C11#327211yescharacteristic
598C2×C11#327311yescharacteristic
599D11—44no—
600C24—21no—
601C24—21no—
602C24—24no—
603C24—42no—
604C24—42no—
605C24—42no—
606C24—42no—
607C24—81no—
608C24—81no—
609C24—221no—
610C24C2×C22⋊D1111yescharacteristic
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—28no—
622C2×D4—24no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—44no—
632C2×D4—44no—
633C2×D4—44no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4—112no—
637C2×D4—112no—
638C2×D4—112no—
639C2×D4—224no—
640C2×D4—221no—
641C2×D4—221no—
642C2×D4—221no—
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—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—81no—
660C22×C4—81no—
661C22×C4—221no—
662C22×C4—224no—
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—881no—
672C22×C4—881no—
673C22×C4C2×C4×D1112yes—
674C22×C4#433912yes—
675C22×C4C2×C22⋊D1111yescharacteristic
676C22×C4C2×C22⋊D1111yescharacteristic
677C22×C4C2×C22⋊D1111yescharacteristic
678C22×C4C2×C22⋊D1111yescharacteristic
679C22×C4C2×C22⋊D1111yescharacteristic
680C22×C4C23×D1111yescharacteristic
681SD16—228no—
682SD16—228no—
683D8—1116no—
684D8—228no—
685M16—228no—
686C2×C8—112no—
687C2×C8—112no—
688C2×C8—112no—
689C2×C8—112no—
690C2×C8—221no—
691C2×C8—221no—
692C2×C8—221no—
693C2×C8—221no—
694C2×C8—221no—
695C2×C8—221no—
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—22no—
707C22⋊C4—41no—
708C22⋊C4—42no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—42no—
713C22⋊C4—81no—
714C22⋊C4—81no—
715C22⋊C4—442no—
716C22⋊C4—442no—
717C22⋊C4—881no—
718C42—21no—
719C42—21no—
720C42—21no—
721C42—21no—
722C11#2244211yescharacteristic, complemented, Sylow
723C23—22no—
724C23—21no—
725C23—22no—
726C23—22no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—22no—
733C23—48no—
734C23—48no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—84no—
746C23—84no—
747C23—84no—
748C23—84no—
749C23—84no—
750C23—222no—
751C23—222no—
752C23—222no—
753C23—441no—
754C23—441no—
755C23—441no—
756C23—441no—
757C23C4×C22⋊D1112yes—
758C23C22×C22⋊D1111yescharacteristic
759Q8—222no—
760Q8—222no—
761Q8—441no—
762Q8—441no—
763D4—22no—
764D4—22no—
765D4—22no—
766D4—22no—
767D4—22no—
768D4—48no—
769D4—41no—
770D4—41no—
771D4—114no—
772D4—222no—
773D4—222no—
774D4—222no—
775D4—448no—
776D4C22⋊C4×D1114yes—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—84no—
801C2×C4—84no—
802C2×C4—222no—
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×C4C4×C22⋊D1112yes—
815C2×C4#6698512yescomplemented
816C2×C4C22×C4×D1111yescharacteristic
817C2×C4C2×#433911yescharacteristic
818C2×C4C2×D4×D1111yescharacteristic
819C2×C4C2×D4×D1111yescharacteristic
820C2×C4#6703711yescharacteristic
821C2×C4#6703711yescharacteristic
822C8—114no—
823C8—222no—
824C8—441no—
825C8—441no—
826C22—22no—
827C22—24no—
828C22—22no—
829C22—22no—
830C22—42no—
831C22—41no—
832C22—41no—
833C22—42no—
834C22—42no—
835C22—41no—
836C22—41no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—816no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—224no—
849C22—442no—
850C22—442no—
851C22—442no—
852C22—442no—
853C22—442no—
854C22—442no—
855C22C2×C4×C22⋊D1111yescharacteristic
856C22C2×#6698511yescharacteristic
857C22D4×C22⋊D1111yescharacteristic
858C22D4×C22⋊D1111yescharacteristic
859C22#1062335311yescharacteristic
860C22#1062336611yescharacteristic
861C22#1062336711yescharacteristic
862C4—22no—
863C4—22no—
864C4—41no—
865C4—41no—
866C4—41no—
867C4—81no—
868C4—81no—
869C4—442no—
870C4—881no—
871C4—881no—
872C4C2×C22⋊C4×D1111yescharacteristic
873C4#1062301711yescharacteristic
874C4#1062302111yescharacteristic
875C4#1062302111yescharacteristic
876C2—42no—
877C2—44no—
878C2—82no—
879C2—444no—
880C2C22⋊C4×C22⋊D1111yescharacteristic
881C2C4×#6698511yescharacteristic
882C2#1307744811yescharacteristic
883C2#1308009211yescharacteristic
884C2#1308013711yescharacteristic
885C2#1308021211yescharacteristic
886C2#1308022311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingD4×C11×C22⋊C4C2
socleC23×C11C22×D4
prime radicalC22×#66985C2
cosocleC22×C4×C11C24
hypercenterD4×C22⋊C4D11
hypocenterC11#22442
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#10622627C2semidirect
3. C2×C4×#4323C2semidirect
4. #13071447C2semidirect
5. #13069496C2semidirect
6. #13069469C2semidirect
7. #13068967C2semidirect
8. #13068967C2semidirect
9. #13068950C2semidirect
10. #13068950C2semidirect
11. #13068647C2semidirect
12. #13068554C2semidirect
13. #13068547C2semidirect
14. #13068400C2semidirect
15. D4×C11×C22⋊C4C2semidirect
25. C2×#66985C4semidirect
29. C2×C4×D44C22semidirect
30. C2×C4×D44C22semidirect
46. C2×#66874C22semidirect
47. C2×#66874C22semidirect
48. C2×#66873C22semidirect
49. C2×#66873C22semidirect
50. C2×#66872C22semidirect
51. C2×#66871C22semidirect
54. #10622542C22semidirect
55. #10622542C22semidirect
56. C2×#66867C22semidirect
57. C2×C4×C11⋊C8C22semidirect
60. #10622167C22semidirect
61. #10622167C22semidirect
62. #10622162C22semidirect
63. #10622162C22semidirect
71. C22×D4×C11C2×C4semidirect
83. C2×#4339C2×C4semidirect
112. C2×#4324C2×C4semidirect
113. C2×#4324C2×C4semidirect
118. C2×#4323C2×C4semidirect
127. C2×#4318C2×C4semidirect
260. #4323C22⋊C4semidirect
284. D4×C22⋊C4D11semidirect
366. C2×C4×C11AGL(1,ℤ/8)semidirect
386. D44C2×C22⋊C4semidirect
397. C11⋊C8C2×C22⋊C4semidirect
512. C22×D4C4×D11semidirect
722. C11#22442semidirect
815. C2×C4#66985semidirect

Maximal subgroups

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

subgroupindex
C22×#669852
C2×#106226272
C2×C4×#43232
#130714472
#130694962
#130694692
#130689672
#130689502
#130686472
#130685542
#130685472
#130684002
D4×C11×C22⋊C42
#2244211