Finite Group Databasebeta

← #14769549

Subgroups — #14769549

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×#66985C211yesmaximal, characteristic
2C2×#10622631C211yesmaximal, characteristic, complemented
3C2×C4×#4324C211yesmaximal, characteristic, complemented
4#13071456C211yesmaximal, characteristic, complemented
5#13069491C211yesmaximal, characteristic, complemented
6#13069481C211yesmaximal, characteristic, complemented
7#13068974C211yesmaximal, characteristic, complemented
8#13068974C211yesmaximal, characteristic, complemented
9#13068964C211yesmaximal, characteristic, complemented
10#13068964C211yesmaximal, 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×Dic22C2211yescharacteristic, complemented
30C2×C4×Dic22C2211yescharacteristic, 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#10622631—24no—
45C4×#4324—24no—
46C2×#66874C2211yescharacteristic, complemented
47C2×#66874C2211yescharacteristic, complemented
48C2×#66873C2211yescharacteristic, complemented
49C2×#66873C2211yescharacteristic, complemented
50C2×#66872C2211yescharacteristic, complemented
51C2×#66871C2211yescharacteristic, complemented
52#10622570—21no—
53#10622570—21no—
54#10622552C2211yescharacteristic, complemented
55#10622552C2211yescharacteristic, complemented
56C2×#66867C2211yescharacteristic, complemented
57C2×C4×C11⋊C8C2211yescharacteristic, complemented
58#10622280—21no—
59#10622279—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×C414yes—
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×Dic22C2311yescharacteristic
87C4×D4×C11—22no—
88C4×D4×C11—22no—
89C4×D4×C11—41no—
90C4×D4×C11—41no—
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4—21no—
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—44no—
101C2×C11×C22⋊C4D411yescharacteristic
102C2×C11×C22⋊C4D411yescharacteristic
103C2×C42×C11C2311yescharacteristic
104C2×C42×C11C2311yescharacteristic
105C2×C22⋊Dic11—21no—
106C2×#4324—22no—
107C2×#4324—22no—
108C2×#4324C2×C414yes—
109C2×#4324C2×C414yescomplemented
110C2×#4324D414yes—
111C2×#4324D414yes—
112#66985—232no—
113C2×#4323—22no—
114C2×#4323—22no—
115C2×#4323—22no—
116C2×#4323—22no—
117C2×#4323C2×C414yes—
118C2×#4323C2×C414yescomplemented
119C2×(C2×D11)⋊C4—21no—
120C2×(C2×D11)⋊C4—21no—
121C2×(C2×D11)⋊C4—21no—
122C2×(C2×D11)⋊C4—21no—
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×Dic11⋊C4—21no—
126C2×Dic11⋊C4—21no—
127C2×C4×Dic11—21no—
128C2×C4×Dic11—21no—
129C2×#4318—22no—
130C2×#4318—22no—
131C2×#4318C2×C414yescomplemented
132C22×C11⋊C8C2311yescharacteristic
133C22×C11⋊C8C2311yescharacteristic
134C22×C11⋊C8C2311yescharacteristic
135C22×C11⋊C8C2311yescharacteristic
136C4×Dic22—22no—
137C4×Dic22—22no—
138C4×Dic22—41no—
139C4×Dic22—41no—
140C11×#95—21no—
141C11×#95D411yescharacteristic
142C11×#95D411yescharacteristic
143#66896—22no—
144#66896—22no—
145#66896—41no—
146#66896—41no—
147C11⋊#95—21no—
148C22⋊(C11⋊C8)—22no—
149#66874—22no—
150#66874—22no—
151#66873—41no—
152#66873—41no—
153#66872—22no—
154#66871—22no—
155#66867—22no—
156C4×C11⋊C8—22no—
157#22443—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×D44—21no—
222C2×D44—21no—
223C2×D44C22×C412yes—
224C2×C4×D11—24no—
225C2×C4×D11—42no—
226C2×C4×D11—42no—
227C2×Dic22—21no—
228C2×Dic22—21no—
229C2×Dic22—21no—
230C2×Dic22C22×C412yes—
231C2×Dic22C2×D412yes—
232C2×Dic22C2×D412yes—
233C11×C4⋊C4—21no—
234C11×C4⋊C4—21no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4—21no—
237C11×C22⋊C4—22no—
238C11×C22⋊C4—41no—
239C11×C22⋊C4—42no—
240C11×C22⋊C4—42no—
241C11×C22⋊C4—42no—
242C11×C22⋊C4—42no—
243C11×C22⋊C4—42no—
244C11×C22⋊C4—81no—
245C11×C22⋊C4—81no—
246C42×C11—21no—
247C42×C11—21no—
248C42×C11—21no—
249C42×C11—21no—
250C22⋊Dic11—81no—
251#4324—28no—
252#4324C22⋊C4116yescomplemented
253#4323—28no—
254#4323—28no—
255(C2×D11)⋊C4—42no—
256(C2×D11)⋊C4—42no—
257(C2×D11)⋊C4—81no—
258(C2×D11)⋊C4—81no—
259C4⋊Dic11—21no—
260C4⋊Dic11—21no—
261C4⋊Dic11—21no—
262C4⋊Dic11—21no—
263Dic11⋊C4—42no—
264Dic11⋊C4—42no—
265C4×Dic11—42no—
266C4×Dic11—42no—
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×#440—111no—
282C2×C4×SD16—111no—
283#2341—111no—
284D4×C22⋊C4D1111yescharacteristic, complemented
285#1972—111no—
286#1970—111no—
287#1880—111no—
288#1880—111no—
289#1879—111no—
290#1879—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—41no—
326C22×D11—41no—
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—22no—
376C2×Dic11—22no—
377C2×Dic11—41no—
378C2×Dic11—41no—
379C2×Dic11—41no—
380C2×Dic11—41no—
381C2×Dic11—41no—
382C2×Dic11—41no—
383D44—22no—
384D44—22no—
385D44—41no—
386D44—41no—
387C4×D11—48no—
388Dic22—22no—
389Dic22—22no—
390Dic22—22no—
391Dic22C2×C22⋊C414yescomplemented
392C11⋊C8—22no—
393C11⋊C8—41no—
394C11⋊C8—41no—
395C11⋊C8C2×C22⋊C414yescomplemented
396C22×#41—111no—
397C23×D4C2×D1111yescharacteristic
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×D8—111no—
405C22×M16—111no—
406C2×C4×Q8—111no—
407C2×C4×Q8—111no—
408C2×C4×D4C2×D1111yescharacteristic
409C2×C4×D4C2×D1111yescharacteristic
410C22×C22⋊C4—21no—
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×#102—111no—
422C2×#102—111no—
423C2×C22⋊C8—111no—
424C2×#97—111no—
425C2×C4×C8—111no—
426#390—111no—
427#390—111no—
428#390—221no—
429#390—221no—
430#390C2×D1111yescharacteristic
431#390C2×D1111yescharacteristic
432#386—21no—
433#386—21no—
434#380—111no—
435#380—221no—
436#380C2×D1111yescharacteristic
437#379—21no—
438C4×C22⋊C4—221no—
439C4×C22⋊C4C2×D1111yescharacteristic
440#340—111no—
441#340—111no—
442#336—111no—
443#336—111no—
444C22×C11—22no—
445C22×C11—24no—
446C22×C11—22no—
447C22×C11—22no—
448C22×C11—42no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—41no—
452C22×C11—41no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11—41no—
456C22×C11—41no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—42no—
461C22×C11—816no—
462C22×C11—81no—
463C22×C11—81no—
464C22×C11—81no—
465C22×C11—81no—
466C22×C11C2×C4×D411yescharacteristic
467C22×C11D4211yescharacteristic
468C22×C11D4211yescharacteristic
469C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
470C22×C11#57511yescharacteristic
471C22×C11#57611yescharacteristic
472C22×C11#57711yescharacteristic
473C2×D11—42no—
474C2×D11—42no—
475C2×D11—42no—
476C2×D11—81no—
477C2×D11—81no—
478C2×D11—81no—
479C2×D11—81no—
480C4×C11—22no—
481C4×C11—22no—
482C4×C11—41no—
483C4×C11—41no—
484C4×C11—41no—
485C4×C11—81no—
486C4×C11—81no—
487C4×C11C22×C22⋊C411yescharacteristic
488C4×C11#51811yescharacteristic
489C4×C11#54611yescharacteristic
490C4×C11#54611yescharacteristic
491Dic11—24no—
492Dic11—81no—
493Dic11—81no—
494C25—21no—
495C2×#41—114no—
496C2×#41—222no—
497C2×#41—222no—
498C2×#41—222no—
499C2×#41—441no—
500C2×#41—441no—
501C22×Q8—111no—
502C22×D4—22no—
503C22×D4—22no—
504C22×D4—22no—
505C22×D4—21no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4—111no—
509C22×D4—221no—
510C22×D4C4×D1114yes—
511C22×D4C22×D1111yescharacteristic
512C22×D4C22×D1111yescharacteristic
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—221no—
516C23×C4C22×D1111yescharacteristic
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—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×C8—111no—
536C22×C8—111no—
537C4×Q8—222no—
538C4×Q8—222no—
539C4×Q8—441no—
540C4×Q8—441no—
541C4×D4—22no—
542C4×D4—22no—
543C4×D4—41no—
544C4×D4—41no—
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—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—44no—
559C2×C22⋊C4—221no—
560C2×C22⋊C4—221no—
561C2×C22⋊C4—221no—
562C2×C22⋊C4—221no—
563C2×C22⋊C4—221no—
564C2×C22⋊C4C22⋊D1111yescharacteristic
565C2×C22⋊C4C22⋊D1111yescharacteristic
566C2×C42—221no—
567C2×C42—221no—
568C2×C42C22×D1111yescharacteristic
569C2×C42C22×D1111yescharacteristic
570#107—222no—
571#106—222no—
572#103—222no—
573#103—222no—
574#102—222no—
575#102—222no—
576#102—441no—
577#102—441no—
578#102—441no—
579#102—441no—
580C22⋊C8—222no—
581#97—222no—
582C4×C8—222no—
583#95—21no—
584#95—221no—
585#95C22⋊D1111yescharacteristic
586#95C22⋊D1111yescharacteristic
587C2×C11—42no—
588C2×C11—44no—
589C2×C11—82no—
590C2×C11D4×C22⋊C411yescharacteristic
591C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
592C2×C11#294611yescharacteristic
593C2×C11#326511yescharacteristic
594C2×C11#326811yescharacteristic
595C2×C11#327411yescharacteristic
596C2×C11#327511yescharacteristic
597D11—82no—
598C24—21no—
599C24—21no—
600C24—24no—
601C24—42no—
602C24—42no—
603C24—42no—
604C24—42no—
605C24—81no—
606C24—81no—
607C24—221no—
608C24C2×C22⋊D1111yescharacteristic
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—28no—
620C2×D4—24no—
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—44no—
630C2×D4—44no—
631C2×D4—44no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—112no—
635C2×D4—224no—
636C2×D4—221no—
637C2×D4—221no—
638C2×D4—221no—
639C2×D4—221no—
640C2×D4—221no—
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—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—42no—
654C22×C4—42no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—81no—
658C22×C4—81no—
659C22×C4—221no—
660C22×C4—224no—
661C22×C4—221no—
662C22×C4—221no—
663C22×C4—442no—
664C22×C4—442no—
665C22×C4C2×C4×D1112yes—
666C22×C4#433912yes—
667C22×C4C2×C22⋊D1111yescharacteristic
668C22×C4C2×C22⋊D1111yescharacteristic
669C22×C4C2×C22⋊D1111yescharacteristic
670C22×C4C2×C22⋊D1111yescharacteristic
671C22×C4C2×C22⋊D1111yescharacteristic
672C22×C4C23×D1111yescharacteristic
673SD16—1116no—
674SD16—228no—
675D8—228no—
676D8—228no—
677M16—228no—
678C2×C8—112no—
679C2×C8—112no—
680C2×C8—112no—
681C2×C8—112no—
682C2×C8—221no—
683C2×C8—221no—
684C2×C8—221no—
685C2×C8—221no—
686C2×C8—221no—
687C2×C8—221no—
688C2×C8—221no—
689C2×C8—221no—
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—22no—
701C22⋊C4—41no—
702C22⋊C4—42no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—81no—
708C22⋊C4—81no—
709C22⋊C4—442no—
710C22⋊C4—442no—
711C22⋊C4—881no—
712C22⋊C4—881no—
713C22⋊C4—881no—
714C42—21no—
715C42—21no—
716C42—21no—
717C42—21no—
718C42—442no—
719C42—442no—
720C11#2244311yescharacteristic, complemented, Sylow
721C23—22no—
722C23—21no—
723C23—22no—
724C23—22no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—22no—
731C23—48no—
732C23—48no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—84no—
744C23—84no—
745C23—84no—
746C23—84no—
747C23—84no—
748C23—222no—
749C23—441no—
750C23—441no—
751C23—441no—
752C23—441no—
753C23—441no—
754C23—441no—
755C23C4×C22⋊D1112yes—
756C23C22×C22⋊D1111yescharacteristic
757Q8—114no—
758Q8—222no—
759Q8—222no—
760Q8—222no—
761D4—22no—
762D4—22no—
763D4—22no—
764D4—22no—
765D4—22no—
766D4—48no—
767D4—41no—
768D4—41no—
769D4—222no—
770D4—222no—
771D4—448no—
772D4—441no—
773D4—441no—
774D4C22⋊C4×D1114yes—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—84no—
799C2×C4—84no—
800C2×C4—222no—
801C2×C4—222no—
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×C4C4×C22⋊D1112yes—
811C2×C4#6698512yescomplemented
812C2×C4C22×C4×D1111yescharacteristic
813C2×C4C2×#433911yescharacteristic
814C2×C4C2×D4×D1111yescharacteristic
815C2×C4C2×D4×D1111yescharacteristic
816C2×C4#6703711yescharacteristic
817C2×C4#6703711yescharacteristic
818C8—114no—
819C8—222no—
820C8—441no—
821C8—441no—
822C22—22no—
823C22—24no—
824C22—22no—
825C22—22no—
826C22—42no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—42no—
831C22—41no—
832C22—42no—
833C22—41no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—816no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—442no—
845C22—442no—
846C22—442no—
847C22—881no—
848C22—881no—
849C22—881no—
850C22—881no—
851C22C2×C4×C22⋊D1111yescharacteristic
852C22C2×#6698511yescharacteristic
853C22D4×C22⋊D1111yescharacteristic
854C22D4×C22⋊D1111yescharacteristic
855C22#1062335311yescharacteristic
856C22#1062336611yescharacteristic
857C22#1062336711yescharacteristic
858C4—22no—
859C4—22no—
860C4—41no—
861C4—41no—
862C4—41no—
863C4—81no—
864C4—81no—
865C4—224no—
866C4—881no—
867C4—881no—
868C4C2×C22⋊C4×D1111yescharacteristic
869C4#1062301711yescharacteristic
870C4#1062302111yescharacteristic
871C4#1062302111yescharacteristic
872C2—42no—
873C2—44no—
874C2—82no—
875C2—882no—
876C2C22⋊C4×C22⋊D1111yescharacteristic
877C2C4×#6698511yescharacteristic
878C2#1307744811yescharacteristic
879C2#1308010711yescharacteristic
880C2#1308015211yescharacteristic
881C2#1308023211yescharacteristic
882C2#1308024311yescharacteristic
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#22443
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×#10622631C2semidirect
3. C2×C4×#4324C2semidirect
4. #13071456C2semidirect
5. #13069491C2semidirect
6. #13069481C2semidirect
7. #13068974C2semidirect
8. #13068974C2semidirect
9. #13068964C2semidirect
10. #13068964C2semidirect
11. #13068647C2semidirect
12. #13068554C2semidirect
13. #13068547C2semidirect
14. #13068400C2semidirect
15. D4×C11×C22⋊C4C2semidirect
25. C2×#66985C4semidirect
29. C2×C4×Dic22C22semidirect
30. C2×C4×Dic22C22semidirect
46. C2×#66874C22semidirect
47. C2×#66874C22semidirect
48. C2×#66873C22semidirect
49. C2×#66873C22semidirect
50. C2×#66872C22semidirect
51. C2×#66871C22semidirect
54. #10622552C22semidirect
55. #10622552C22semidirect
56. C2×#66867C22semidirect
57. C2×C4×C11⋊C8C22semidirect
60. #10622167C22semidirect
61. #10622167C22semidirect
62. #10622162C22semidirect
63. #10622162C22semidirect
83. C2×#4339C2×C4semidirect
109. C2×#4324C2×C4semidirect
118. C2×#4323C2×C4semidirect
131. C2×#4318C2×C4semidirect
252. #4324C22⋊C4semidirect
284. D4×C22⋊C4D11semidirect
366. C2×C4×C11AGL(1,ℤ/8)semidirect
391. Dic22C2×C22⋊C4semidirect
395. C11⋊C8C2×C22⋊C4semidirect
720. C11#22443semidirect
811. 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×#106226312
C2×C4×#43242
#130714562
#130694912
#130694812
#130689742
#130689642
#130686472
#130685542
#130685472
#130684002
D4×C11×C22⋊C42
#2244311