Finite Group Databasebeta

← #14769539

Subgroups — #14769539

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×#67002C211yesmaximal, characteristic
2C2×#10622627C211yesmaximal, characteristic, complemented
3C2×C4×#4323C211yesmaximal, characteristic, complemented
4C22⋊C4×D44C211yesmaximal, characteristic, complemented
5#13069500C211yesmaximal, characteristic, complemented
6#13069473C211yesmaximal, characteristic, complemented
7#13068964C211yesmaximal, characteristic, complemented
8#13068964C211yesmaximal, characteristic, complemented
9#13068953C211yesmaximal, characteristic, complemented
10#13068953C211yesmaximal, characteristic, complemented
11#13068647C211yesmaximal, characteristic, complemented
12#13068556C211yesmaximal, characteristic, complemented
13#13068546C211yesmaximal, characteristic, complemented
14#13068400C211yesmaximal, characteristic, complemented
15C11×#2339C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C23×D44C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic, complemented
19C2×C4×D4×C11C2211yescharacteristic, complemented
20C2×#67002—24no—
21C2×#67002—24no—
22C2×#67002C418yescomplemented
23C22×#4325C2211yescharacteristic
24C22×#4325C2211yescharacteristic
25C22×#4323C2211yescharacteristic
26C22×#4323C2211yescharacteristic
27C22×#4318C2211yescharacteristic
28C2×C22⋊C4×D11—21no—
29C2×C4×D44C2211yescharacteristic
30C2×C4×D44C2211yescharacteristic
31C11×#391C2211yescharacteristic, complemented
32C11×#391C2211yescharacteristic, complemented
33C11×#386—21no—
34C11×#386—21no—
35C11×#381—21no—
36C11×#380C2211yescharacteristic
37C4×C11×C22⋊C4C2211yescharacteristic
38C2×C11×#95—21no—
39C2×#66899C2211yescharacteristic, complemented
40C2×#66899C2211yescharacteristic, complemented
41C2×#66896C2211yescharacteristic, complemented
42C2×#66896C2211yescharacteristic, complemented
43#10622825C2211yescharacteristic
44C2×C22⋊(C11⋊C8)C2211yescharacteristic
45#10622627—24no—
46C4×#4323—24no—
47C2×#66873C2211yescharacteristic
48C2×#66873C2211yescharacteristic
49C2×#66873C2211yescharacteristic
50C2×#66873C2211yescharacteristic
51C2×#66872C2211yescharacteristic, complemented
52C2×#66871C2211yescharacteristic, complemented
53#10622568—21no—
54#10622552C2211yescharacteristic
55#10622552C2211yescharacteristic
56C2×#66867C2211yescharacteristic, complemented
57C2×C4×C11⋊C8C2211yescharacteristic, complemented
58#10622278—21no—
59#10622278—21no—
60#10622167C2211yescharacteristic, complemented
61#10622167C2211yescharacteristic, complemented
62#10622162C2211yescharacteristic, complemented
63#10622162C2211yescharacteristic, complemented
64C24×D11—21no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—41no—
69C2×C11×#41—41no—
70C2×C11×#41C2×C414yescomplemented
71C22×Q8×C11C2311yescharacteristic
72C22×D4×C11—21no—
73C22×D4×C11C2311yescharacteristic
74C23×C4×C11—21no—
75C23×C4×C11—21no—
76C23×C4×C11—21no—
77C23×C4×C11C2311yescharacteristic
78C22×D44—22no—
79C22×D44—22no—
80C22×D44—21no—
81C22×D44—22no—
82C22×D44—41no—
83C22×D44—41no—
84C22×D44C2×C414yescomplemented
85C22×D44C2311yescharacteristic
86C22×D44C2311yescharacteristic
87C22×C4×D11—21no—
88C22×C4×D11—21no—
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⋊C4D411yescharacteristic
99C2×C11×C22⋊C4D411yescharacteristic
100C2×C42×C11C2311yescharacteristic
101C2×C42×C11C2311yescharacteristic
102C2×C22⋊Dic11—21no—
103#67002—232no—
104C2×#4325—22no—
105C2×#4325—22no—
106C2×#4325—22no—
107C2×#4325—22no—
108C2×#4325C2×C414yescomplemented
109C2×#4325C2×C414yescomplemented
110C2×#4323—22no—
111C2×#4323—22no—
112C2×#4323C2×C414yes—
113C2×#4323C2×C414yescomplemented
114C2×#4323D414yes—
115C2×#4323D414yes—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—21no—
120C2×(C2×D11)⋊C4—21no—
121C2×(C2×D11)⋊C4—21no—
122C2×C4⋊Dic11C2311yescharacteristic
123C2×C4⋊Dic11C2311yescharacteristic
124C2×#4318—22no—
125C2×#4318—22no—
126C2×#4318C2×C414yescomplemented
127C22×C11⋊C8C2311yescharacteristic
128C22×C11⋊C8C2311yescharacteristic
129C22×C11⋊C8C2311yescharacteristic
130C22×C11⋊C8C2311yescharacteristic
131C22⋊C4×D11—44no—
132C4×D44—22no—
133C4×D44—22no—
134C4×D44—41no—
135C4×D44—41no—
136C11×#95—21no—
137C11×#95—21no—
138C11×#95—21no—
139C11×#95—21no—
140C11×#95—21no—
141C11×#95D411yescharacteristic
142C11×#95D411yescharacteristic
143#66899—41no—
144#66899—41no—
145#66896—22no—
146#66896—22no—
147C11⋊#95—21no—
148C22⋊(C11⋊C8)—22no—
149#66873—22no—
150#66873—22no—
151#66873—41no—
152#66873—41no—
153#66872—22no—
154#66871—22no—
155#66867—22no—
156C4×C11⋊C8—22no—
157#22442—111nomaximal, Sylow
158C24×C11—21no—
159C24×C11C2×D411yescharacteristic
160C23×D11—21no—
161C23×D11—21no—
162C23×D11—24no—
163C23×D11—42no—
164C23×D11—42no—
165C23×D11—42no—
166C23×D11—42no—
167C23×D11—81no—
168C23×D11—81no—
169C11×#41—28no—
170C11×#41—44no—
171C11×#41—44no—
172C11×#41—44no—
173C2×Q8×C11—21no—
174C2×Q8×C11—21no—
175C2×Q8×C11—21no—
176C2×Q8×C11—21no—
177C2×Q8×C11—21no—
178C2×Q8×C11C22×C412yes—
179C2×D4×C11—24no—
180C2×D4×C11—21no—
181C2×D4×C11—21no—
182C2×D4×C11—21no—
183C2×D4×C11—42no—
184C2×D4×C11—42no—
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—24no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—42no—
197C22×C4×C11—42no—
198C22×C4×C11—42no—
199C22×C4×C11—42no—
200C22×C4×C11—42no—
201C22×C4×C11—42no—
202C22×C4×C11—81no—
203C22×C4×C11—81no—
204C22×C4×C11C22×C412yes—
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11#4112yes—
211C22×C4×C11C2411yescharacteristic
212C22×Dic11—21no—
213C22×Dic11—21no—
214C2×D44—28no—
215C2×D44—24no—
216C2×D44—21no—
217C2×D44—21no—
218C2×D44—21no—
219C2×D44—21no—
220C2×D44—21no—
221C2×D44—21no—
222C2×D44—21no—
223C2×D44—21no—
224C2×D44—42no—
225C2×D44—42no—
226C2×D44—44no—
227C2×D44—44no—
228C2×D44—44no—
229C2×D44C22×C412yes—
230C2×D44C22×C412yes—
231C2×D44C2×D412yes—
232C2×D44C2×D412yes—
233C2×C4×D11—42no—
234C2×C4×D11—42no—
235C2×C4×D11—42no—
236C2×C4×D11—42no—
237C2×C4×D11—81no—
238C2×C4×D11—81no—
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—81no—
248C42×C11—21no—
249C42×C11—21no—
250C42×C11—21no—
251C42×C11—21no—
252C22⋊Dic11—42no—
253#4325—28no—
254#4325—28no—
255#4323—28no—
256#4323C22⋊C4116yescomplemented
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—
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#2339D1111yescharacteristic, complemented
284D4×C22⋊C4—111no—
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—41no—
305C23×C11—41no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11C4×D412yes—
309C23×C11C22×D411yescharacteristic
310C22×D11—22no—
311C22×D11—22no—
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—48no—
315C22×D11—41no—
316C22×D11—41no—
317C22×D11—41no—
318C22×D11—41no—
319C22×D11—48no—
320C22×D11—41no—
321C22×D11—41no—
322C22×D11—41no—
323C22×D11—41no—
324C22×D11—41no—
325C22×D11—41no—
326C22×D11—84no—
327C22×D11—84no—
328C22×D11—84no—
329C22×D11—84no—
330C22×D11—84no—
331Q8×C11—22no—
332Q8×C11—22no—
333Q8×C11—41no—
334Q8×C11—41no—
335D4×C11—22no—
336D4×C11—22no—
337D4×C11—22no—
338D4×C11—48no—
339D4×C11C2×C22⋊C414yescomplemented
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—22no—
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—21no—
358C2×C4×C11—48no—
359C2×C4×C11—41no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11—84no—
368C2×C4×C11—84no—
369C2×C4×C11C4×D412yes—
370C2×C4×C11AGL(1,ℤ/8)12yescomplemented
371C2×C4×C11C23×C411yescharacteristic
372C2×C4×C11C22×D411yescharacteristic
373C2×C4×C11C22×D411yescharacteristic
374C2×C4×C11C2×#4111yescharacteristic
375C2×C4×C11H(5,𝔽2)11yescharacteristic
376C2×C4×C11H(5,𝔽2)11yescharacteristic
377C2×Dic11—41no—
378C2×Dic11—41no—
379C2×Dic11—41no—
380C2×Dic11—41no—
381C2×Dic11—41no—
382C2×Dic11—41no—
383D44—22no—
384D44—22no—
385D44—22no—
386D44—22no—
387D44—22no—
388D44—48no—
389D44—41no—
390D44—41no—
391D44C2×C22⋊C414yes—
392C4×D11—84no—
393C4×D11—84no—
394C11⋊C8—22no—
395C11⋊C8—41no—
396C11⋊C8—41no—
397C11⋊C8C2×C22⋊C414yescomplemented
398C22×#41C2×D1111yescharacteristic
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×SD16—111no—
405C22×D8—111no—
406C22×D8—111no—
407C22×M16—111no—
408C2×C4×D4—111no—
409C2×C4×D4—111no—
410C2×C4×D4C2×D1111yescharacteristic, complemented
411C2×C4×D4C2×D1111yescharacteristic, complemented
412C22×C22⋊C4—221no—
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#391C2×D1111yescharacteristic, complemented
429#391C2×D1111yescharacteristic, complemented
430#390—111no—
431#390—111no—
432#386—21no—
433#386—21no—
434#386—221no—
435#386—221no—
436#381—21no—
437#380—111no—
438#380C2×D1111yescharacteristic
439#379—221no—
440C4×C22⋊C4C2×D1111yescharacteristic
441C2×#95—21no—
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—41no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—41no—
460C22×C11C2×C4×D411yescharacteristic
461C22×C11D4211yescharacteristic
462C22×C11D4211yescharacteristic
463C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
464C22×C11#57511yescharacteristic
465C22×C11#57611yescharacteristic
466C22×C11#57711yescharacteristic
467C2×D11—24no—
468C2×D11—42no—
469C2×D11—42no—
470C2×D11—42no—
471C2×D11—42no—
472C2×D11—42no—
473C2×D11—42no—
474C2×D11—42no—
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—816no—
478C2×D11—81no—
479C2×D11—81no—
480C2×D11—81no—
481C2×D11—81no—
482C4×C11—22no—
483C4×C11—22no—
484C4×C11—42no—
485C4×C11—41no—
486C4×C11—41no—
487C4×C11—41no—
488C4×C11—81no—
489C4×C11—81no—
490C4×C11C22×C22⋊C411yescharacteristic
491C4×C11#51811yescharacteristic
492C4×C11#54611yescharacteristic
493C4×C11#54611yescharacteristic
494Dic11—81no—
495Dic11—81no—
496C25—221no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41C4×D1114yescomplemented
503C22×Q8C22×D1111yescharacteristic
504C22×D4—21no—
505C22×D4—114no—
506C22×D4—111no—
507C22×D4—111no—
508C22×D4—222no—
509C22×D4—222no—
510C22×D4—222no—
511C22×D4—221no—
512C22×D4—441no—
513C22×D4—441no—
514C22×D4C22×D1111yescharacteristic
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
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—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—444no—
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—21no—
583#95—21no—
584#95—21no—
585#95—21no—
586#95—221no—
587#95C22⋊D1111yescharacteristic
588#95C22⋊D1111yescharacteristic
589C2×C11—42no—
590C2×C11—44no—
591C2×C11D4×C22⋊C411yescharacteristic
592C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
593C2×C11#294611yescharacteristic
594C2×C11#326411yescharacteristic
595C2×C11#326711yescharacteristic
596C2×C11#327211yescharacteristic
597C2×C11#327311yescharacteristic
598D11—44no—
599D11—82no—
600C24—21no—
601C24—221no—
602C24—221no—
603C24—224no—
604C24—442no—
605C24—442no—
606C24—442no—
607C24—442no—
608C24—881no—
609C24—881no—
610C24C2×C22⋊D1111yescharacteristic
611#41—28no—
612#41—44no—
613#41—44no—
614#41—44no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8C2×C4×D1112yes—
621C2×D4—24no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—112no—
628C2×D4—112no—
629C2×D4—112no—
630C2×D4—112no—
631C2×D4—228no—
632C2×D4—224no—
633C2×D4—221no—
634C2×D4—221no—
635C2×D4—221no—
636C2×D4—221no—
637C2×D4—221no—
638C2×D4—221no—
639C2×D4—221no—
640C2×D4—221no—
641C2×D4—444no—
642C2×D4—444no—
643C2×D4—444no—
644C2×D4—442no—
645C2×D4—442no—
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—24no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—81no—
664C22×C4—81no—
665C22×C4—221no—
666C22×C4—221no—
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—81no—
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—21no—
721C42—21no—
722C11#2244211yescharacteristic, complemented, Sylow
723C23—22no—
724C23—22no—
725C23—22no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—222no—
737C23—222no—
738C23—222no—
739C23—222no—
740C23—448no—
741C23—448no—
742C23—441no—
743C23—441no—
744C23—441no—
745C23—441no—
746C23—441no—
747C23—441no—
748C23—441no—
749C23—441no—
750C23—441no—
751C23—441no—
752C23—884no—
753C23—884no—
754C23—884no—
755C23—884no—
756C23—884no—
757C23C4×C22⋊D1112yes—
758C23C22×C22⋊D1111yescharacteristic
759Q8—22no—
760Q8—22no—
761Q8—41no—
762Q8—41no—
763D4—22no—
764D4—22no—
765D4—22no—
766D4—48no—
767D4—114no—
768D4—222no—
769D4—222no—
770D4—222no—
771D4—222no—
772D4—222no—
773D4—448no—
774D4—441no—
775D4—441no—
776D4C22⋊C4×D1114yescomplemented
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—22no—
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—21no—
795C2×C4—48no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—84no—
805C2×C4—84no—
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#6700212yescomplemented
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—41no—
835C22—42no—
836C22—42no—
837C22—41no—
838C22—42no—
839C22—42no—
840C22—224no—
841C22—442no—
842C22—442no—
843C22—442no—
844C22—442no—
845C22—442no—
846C22—442no—
847C22—442no—
848C22—442no—
849C22—442no—
850C22—8816no—
851C22—881no—
852C22—881no—
853C22—881no—
854C22—881no—
855C22C2×C4×C22⋊D1111yescharacteristic
856C22D4×C22⋊D1111yescharacteristic
857C22D4×C22⋊D1111yescharacteristic
858C22C2×#6700211yescharacteristic
859C22#1062335311yescharacteristic
860C22#1062336611yescharacteristic
861C22#1062336811yescharacteristic
862C4—22no—
863C4—22no—
864C4—42no—
865C4—41no—
866C4—41no—
867C4—41no—
868C4—81no—
869C4—81no—
870C4—881no—
871C4—881no—
872C4C2×C22⋊C4×D1111yescharacteristic
873C4#1062301711yescharacteristic
874C4#1062302111yescharacteristic
875C4#1062302111yescharacteristic
876C2—42no—
877C2—44no—
878C2—444no—
879C2—882no—
880C2C22⋊C4×C22⋊D1111yescharacteristic
881C2C4×#6700211yescharacteristic
882C2#1307744411yescharacteristic
883C2#1308009711yescharacteristic
884C2#1308014211yescharacteristic
885C2#1308021611yescharacteristic
886C2#1308022311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2339C2
socleC23×C11C22×D4
prime radicalC22×#67002C2
cosocleC22×C4×C11C24
hypercenter#2339D11
hypocenterC11#22442
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2339

Complements

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

NH ≅ G/Ntype
2. C2×#10622627C2semidirect
3. C2×C4×#4323C2semidirect
4. C22⋊C4×D44C2semidirect
5. #13069500C2semidirect
6. #13069473C2semidirect
7. #13068964C2semidirect
8. #13068964C2semidirect
9. #13068953C2semidirect
10. #13068953C2semidirect
11. #13068647C2semidirect
12. #13068556C2semidirect
13. #13068546C2semidirect
14. #13068400C2semidirect
15. C11×#2339C2semidirect
18. C2×C4×D4×C11C22semidirect
19. C2×C4×D4×C11C22semidirect
22. C2×#67002C4semidirect
31. C11×#391C22semidirect
32. C11×#391C22semidirect
39. C2×#66899C22semidirect
40. C2×#66899C22semidirect
41. C2×#66896C22semidirect
42. C2×#66896C22semidirect
51. C2×#66872C22semidirect
52. C2×#66871C22semidirect
56. C2×#66867C22semidirect
57. C2×C4×C11⋊C8C22semidirect
60. #10622167C22semidirect
61. #10622167C22semidirect
62. #10622162C22semidirect
63. #10622162C22semidirect
70. C2×C11×#41C2×C4semidirect
84. C22×D44C2×C4semidirect
108. C2×#4325C2×C4semidirect
109. C2×#4325C2×C4semidirect
113. C2×#4323C2×C4semidirect
126. C2×#4318C2×C4semidirect
256. #4323C22⋊C4semidirect
283. #2339D11semidirect
339. D4×C11C2×C22⋊C4semidirect
370. C2×C4×C11AGL(1,ℤ/8)semidirect
397. C11⋊C8C2×C22⋊C4semidirect
410. C2×C4×D4C2×D11semidirect
411. C2×C4×D4C2×D11semidirect
428. #391C2×D11semidirect
429. #391C2×D11semidirect
502. C2×#41C4×D11semidirect
722. C11#22442semidirect
776. D4C22⋊C4×D11semidirect
815. C2×C4#67002semidirect

Maximal subgroups

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

subgroupindex
C22×#670022
C2×#106226272
C2×C4×#43232
C22⋊C4×D442
#130695002
#130694732
#130689642
#130689532
#130686472
#130685562
#130685462
#130684002
C11×#23392
#2244211