Finite Group Databasebeta

← #14769532

Subgroups — #14769532

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×#66964C211yesmaximal, characteristic
2C2×D8×Dic11C211yesmaximal, characteristic, complemented
3#13071441C211yesmaximal, characteristic, complemented
4D4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
5#13069497C211yesmaximal, characteristic, complemented
6#13069468C211yesmaximal, characteristic, complemented
7#13068964C211yesmaximal, characteristic, complemented
8#13068962C211yesmaximal, characteristic, complemented
9#13068950C211yesmaximal, characteristic, complemented
10#13068948C211yesmaximal, characteristic, complemented
11#13068646C211yesmaximal, characteristic, complemented
12#13068553C211yesmaximal, characteristic, complemented
13#13068545C211yesmaximal, characteristic, complemented
14#13068401C211yesmaximal, characteristic, complemented
15C2×C11×#442C211yesmaximal, characteristic, complemented
16C22×#4341C2211yescharacteristic
17C22×D4×D11C2211yescharacteristic
18C22×C11×D8C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic, complemented
21C2×D4×Dic11C2211yescharacteristic
22C2×D4×Dic11C2211yescharacteristic, complemented
23C22×#4324C2211yescharacteristic
24C22×#4323C2211yescharacteristic
25C22×(C2×D11)⋊C4—21no—
26C2×#66964—24no—
27C2×#66964—24no—
28C2×#66964C418yescomplemented
29C22×#4314C2211yescharacteristic
30C22×#4313C2211yescharacteristic
31C11×#442—24no—
32C2×C11×#106C2211yescharacteristic, complemented
33C2×C11×#102C2211yescharacteristic
34C2×C11×#102C2211yescharacteristic, complemented
35C2×C11×#97C2211yescharacteristic, complemented
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic, complemented
38#10622826—21no—
39#10622826—21no—
40C2×C11⋊#95—21no—
41D8×Dic11—24no—
42C2×#66885C2211yescharacteristic
43C2×(C2×D11)⋊C8C2211yescharacteristic
44C2×#66882C2211yescharacteristic, complemented
45C2×#66880C2211yescharacteristic, complemented
46C2×C8×Dic11C2211yescharacteristic, complemented
47#10622601C2211yescharacteristic
48#10622600C2211yescharacteristic
49#10622600C2211yescharacteristic
50#10622587C2211yescharacteristic, complemented
51C2×#66874C2211yescharacteristic, complemented
52C2×#66873C2211yescharacteristic
53#10622571—21no—
54#10622571—21no—
55#10622568—21no—
56#10622556—21no—
57#10622552C2211yescharacteristic
58C4×(C2×D11)⋊C4C2211yescharacteristic
59#10622542C2211yescharacteristic, complemented
60#10622188C2211yescharacteristic, complemented
61#10622167C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63#10622162C2211yescharacteristic, complemented
64C24×D11—21no—
65C22×D4×C11C2311yescharacteristic
66C22×D4×C11C2311yescharacteristic
67C23×C4×C11—21no—
68C23×C4×C11—21no—
69C22×C22⋊D11—21no—
70C22×C22⋊D11—21no—
71C23×Dic11—21no—
72C23×Dic11—21no—
73C23×Dic11—21no—
74C2×#4341—22no—
75C2×#4341—22no—
76C2×#4341—22no—
77C2×#4341—41no—
78C2×#4341—41no—
79C2×#4341C2×C414yescomplemented
80C2×D4×D11—22no—
81C2×D4×D11—22no—
82C2×D4×D11—22no—
83C2×D4×D11—41no—
84C2×D4×D11—41no—
85C2×D4×D11C2×C414yescomplemented
86C22×D44C2311yescharacteristic
87C22×C4×D11C2311yescharacteristic
88C22×Dic22C2311yescharacteristic
89C2×C11×D8C2×C414yes—
90C2×C11×D8D414yes—
91C2×C11×D8D414yes—
92C22×C8×C11C2311yescharacteristic
93C22×C8×C11C2311yescharacteristic
94C4×D4×C11—22no—
95C4×D4×C11—22no—
96C4×D4×C11—41no—
97C4×D4×C11—41no—
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C42×C11C2311yescharacteristic
103C2×C22⋊Dic11—21no—
104C2×C22⋊Dic11—21no—
105D4×Dic11—22no—
106D4×Dic11—22no—
107D4×Dic11—41no—
108D4×Dic11—41no—
109C2×#4324—22no—
110C2×#4324—22no—
111C2×#4324C2×C414yescomplemented
112C2×#4323—22no—
113C2×#4323—22no—
114C2×#4323C2×C414yescomplemented
115C2×(C2×D11)⋊C4—21no—
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—44no—
122C2×(C2×D11)⋊C4D411yescharacteristic
123C2×(C2×D11)⋊C4D411yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2311yescharacteristic
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
136C11×#106—22no—
137C11×#102—22no—
138C11×#102—22no—
139C11×#97—22no—
140#66896—22no—
141#66896—22no—
142C11⋊#95—21no—
143C11⋊#95—21no—
144C11⋊#95—21no—
145C11⋊#95—21no—
146C11⋊#95—21no—
147C11⋊#95—21no—
148C11⋊#95D411yescharacteristic
149C11⋊#95D411yescharacteristic
150#66885—41no—
151(C2×D11)⋊C8—22no—
152#66882—22no—
153#66880—41no—
154C8×Dic11—22no—
155#66874—41no—
156#66873—41no—
157#22442—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×C11C22×C412yes—
176C2×D4×C11C22×C412yes—
177C2×D4×C11C2×D412yes—
178C2×D4×C11C2×D412yes—
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—42no—
186C22×C4×C11—42no—
187C22×C4×C11—81no—
188C22×C4×C11—81no—
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2411yescharacteristic
192C2×C22⋊D11—24no—
193C2×C22⋊D11—24no—
194C2×C22⋊D11—42no—
195C2×C22⋊D11—42no—
196C2×C22⋊D11—42no—
197C2×C22⋊D11—42no—
198C22×Dic11—24no—
199C22×Dic11—21no—
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11—42no—
203C22×Dic11—42no—
204C22×Dic11—42no—
205C22×Dic11—42no—
206C22×Dic11—42no—
207C22×Dic11—42no—
208C22×Dic11—81no—
209C22×Dic11—81no—
210C22×Dic11C2×D411yescharacteristic
211C22×Dic11C2×D411yescharacteristic
212C22×Dic11C2×D411yescharacteristic
213#4341—28no—
214#4341—44no—
215#4341—44no—
216#4341—44no—
217D4×D11—28no—
218D4×D11—44no—
219D4×D11—44no—
220D4×D11—44no—
221C2×D44—21no—
222C2×D44—21no—
223C2×D44—21no—
224C2×D44—21no—
225C2×D44—21no—
226C2×D44C22×C412yes—
227C2×C4×D11—21no—
228C2×C4×D11—21no—
229C2×C4×D11—21no—
230C2×C4×D11—21no—
231C2×C4×D11C22×C412yes—
232C2×C4×D11#4112yes—
233C2×Dic22—21no—
234C2×Dic22—21no—
235C2×Dic22—21no—
236C2×Dic22—21no—
237C2×Dic22—21no—
238C2×Dic22C22×C412yes—
239C11×D8C22⋊C4116yescomplemented
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—42no—
252C42×C11—21no—
253C42×C11—21no—
254C22⋊Dic11—42no—
255C22⋊Dic11—42no—
256#4324—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—81no—
264(C2×D11)⋊C4—81no—
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—
278#4314—28no—
279#4313—28no—
280C22×AGL(1,ℤ/8)—111no—
281C2×#442D1111yescharacteristic, complemented
282C2×C4×D8—111no—
283#2339—111no—
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—22no—
299C23×C11—22no—
300C23×C11—22no—
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—22no—
337D4×C11C2×C22⋊C414yes—
338D4×C11C2×C22⋊C414yescomplemented
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×C11—84no—
353C2×C4×C11C23×C411yescharacteristic
354C2×C4×C11C22×D411yescharacteristic
355C2×C4×C11C22×D411yescharacteristic
356C2×C4×C11C2×#4111yescharacteristic
357C2×C4×C11H(5,𝔽2)11yescharacteristic
358C2×C4×C11H(5,𝔽2)11yescharacteristic
359C22⋊D11—48no—
360C22⋊D11—48no—
361C2×Dic11—21no—
362C2×Dic11—21no—
363C2×Dic11—21no—
364C2×Dic11—21no—
365C2×Dic11—22no—
366C2×Dic11—21no—
367C2×Dic11—21no—
368C2×Dic11—21no—
369C2×Dic11—48no—
370C2×Dic11—41no—
371C2×Dic11—41no—
372C2×Dic11—41no—
373C2×Dic11—41no—
374C2×Dic11—41no—
375C2×Dic11—41no—
376C2×Dic11—41no—
377C2×Dic11—41no—
378C2×Dic11—84no—
379C2×Dic11—84no—
380C2×Dic11C4×D412yes—
381C2×Dic11AGL(1,ℤ/8)12yescomplemented
382D44—22no—
383D44—22no—
384D44—41no—
385D44—41no—
386C4×D11—22no—
387C4×D11—22no—
388C4×D11—22no—
389C4×D11—22no—
390Dic22—22no—
391Dic22—22no—
392Dic22—41no—
393Dic22—41no—
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×SD16—111no—
405C22×D8—111no—
406C22×D8C2×D1111yescharacteristic
407C22×M16—111no—
408C2×C4×D4—111no—
409C2×C4×D4—111no—
410C2×C4×D4C2×D1111yescharacteristic
411C2×C4×D4C2×D1111yescharacteristic, complemented
412C22×C22⋊C4—221no—
413#442—24no—
414C4×D8—224no—
415C2×#107—111no—
416C2×#106C2×D1111yescharacteristic, complemented
417C2×#103—111no—
418C2×#103—111no—
419C2×#102—111no—
420C2×#102—111no—
421C2×#102—111no—
422C2×#102—111no—
423C2×#102C2×D1111yescharacteristic
424C2×#102C2×D1111yescharacteristic, complemented
425C2×C22⋊C8—111no—
426C2×#97C2×D1111yescharacteristic, complemented
427C2×C4×C8—111no—
428#391—111no—
429#391—111no—
430#390—111no—
431#390—111no—
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—24no—
447C22×C11—24no—
448C22×C11—42no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—42no—
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—22no—
468C2×D11—22no—
469C2×D11—22no—
470C2×D11—41no—
471C2×D11—41no—
472C2×D11—41no—
473C2×D11—41no—
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—41no—
483C4×C11—41no—
484C4×C11—81no—
485C4×C11—81no—
486C4×C11C22×C22⋊C411yescharacteristic
487C4×C11#51811yescharacteristic
488C4×C11#54611yescharacteristic
489C4×C11#54611yescharacteristic
490Dic11—22no—
491Dic11—22no—
492Dic11—42no—
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×Q8—111no—
504C22×D4—114no—
505C22×D4—111no—
506C22×D4—222no—
507C22×D4—221no—
508C22×D4—222no—
509C22×D4—222no—
510C22×D4—221no—
511C22×D4—441no—
512C22×D4—441no—
513C22×D4C22×D1111yescharacteristic
514C22×D4C22×D1111yescharacteristic
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—111no—
518C23×C4—221no—
519C23×C4—221no—
520C23×C4—221no—
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—222no—
530C2×D8—222no—
531C2×D8C4×D1114yes—
532C2×D8D4414yes—
533C2×D8C22⋊D1114yes—
534C2×M16—114no—
535C2×M16—222no—
536C2×M16—222no—
537C22×C8—111no—
538C22×C8—111no—
539C22×C8C22×D1111yescharacteristic
540C22×C8C22×D1111yescharacteristic
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—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—441no—
571#103—441no—
572#102—22no—
573#102—22no—
574#102—222no—
575#102—222no—
576#102—441no—
577#102—441no—
578C22⋊C8—222no—
579#97—22no—
580C4×C8—222no—
581#95—111no—
582#95—111no—
583#95—221no—
584#95—221no—
585#95—221no—
586#95—221no—
587#95—221no—
588#95—221no—
589C2×C11—44no—
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—42no—
599D11—82no—
600C24—21no—
601C24—21no—
602C24—111no—
603C24—224no—
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—112no—
616C2×Q8—221no—
617C2×Q8—221no—
618C2×Q8—221no—
619C2×Q8—221no—
620C2×Q8—221no—
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×D4C2×D4412yes—
646C2×D4C2×D4412yes—
647C2×D4C2×C22⋊D1112yes—
648C2×D4C2×C22⋊D1112yes—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—42no—
654C22×C4—42no—
655C22×C4—81no—
656C22×C4—81no—
657C22×C4—111no—
658C22×C4—111no—
659C22×C4—112no—
660C22×C4—112no—
661C22×C4—111no—
662C22×C4—224no—
663C22×C4—221no—
664C22×C4—221no—
665C22×C4—221no—
666C22×C4—221no—
667C22×C4—221no—
668C22×C4—221no—
669C22×C4—221no—
670C22×C4—442no—
671C22×C4—442no—
672C22×C4—442no—
673C22×C4—442no—
674C22×C4—442no—
675C22×C4—442no—
676C22×C4—881no—
677C22×C4—881no—
678C22×C4D4×D1111yescharacteristic
679C22×C4D4×D1111yescharacteristic
680C22×C4C23×D1111yescharacteristic
681SD16—228no—
682SD16—228no—
683D8—228no—
684D8(C2×D11)⋊C4116yescomplemented
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×C8C2×D4412yes—
697C2×C8C2×C22⋊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—42no—
708C22⋊C4—222no—
709C22⋊C4—441no—
710C22⋊C4—442no—
711C22⋊C4—442no—
712C22⋊C4—442no—
713C22⋊C4—442no—
714C22⋊C4—442no—
715C22⋊C4—881no—
716C22⋊C4—881no—
717C22⋊C4—881no—
718C42—21no—
719C42—21no—
720C42—221no—
721C42—221no—
722C11#2244211yescharacteristic, complemented, Sylow
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—112no—
738C23—221no—
739C23—221no—
740C23—221no—
741C23—221no—
742C23—221no—
743C23—221no—
744C23—222no—
745C23—448no—
746C23—448no—
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—222no—
760Q8—222no—
761Q8—441no—
762Q8—441no—
763D4—22no—
764D4—22no—
765D4—22no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—222no—
770D4—222no—
771D4—448no—
772D4—448no—
773D4—441no—
774D4—441no—
775D4C2×(C2×D11)⋊C414yes—
776D4C2×(C2×D11)⋊C414yescomplemented
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—84no—
790C2×C4—84no—
791C2×C4—112no—
792C2×C4—112no—
793C2×C4—221no—
794C2×C4—221no—
795C2×C4—221no—
796C2×C4—221no—
797C2×C4—222no—
798C2×C4—222no—
799C2×C4—222no—
800C2×C4—222no—
801C2×C4—221no—
802C2×C4—221no—
803C2×C4—222no—
804C2×C4—221no—
805C2×C4—448no—
806C2×C4—441no—
807C2×C4—441no—
808C2×C4—441no—
809C2×C4—441no—
810C2×C4—441no—
811C2×C4—441no—
812C2×C4—441no—
813C2×C4—441no—
814C2×C4—884no—
815C2×C4—884no—
816C2×C4C22×C4×D1111yescharacteristic
817C2×C4C22×D4411yescharacteristic
818C2×C4#6703711yescharacteristic
819C2×C4#41×D1111yescharacteristic
820C2×C4#6704211yescharacteristic
821C2×C4C22×C22⋊D1111yescharacteristic
822C8—41no—
823C8—222no—
824C8—441no—
825C8C2×(C2×D11)⋊C414yescomplemented
826C22—24no—
827C22—24no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—222no—
841C22—222no—
842C22—222no—
843C22—441no—
844C22—441no—
845C22—441no—
846C22—441no—
847C22—442no—
848C22—442no—
849C22—442no—
850C22—8816no—
851C22—881no—
852C22—881no—
853C22—881no—
854C22—881no—
855C22C4×D4×D1111yescharacteristic
856C22D4×D4411yescharacteristic
857C22D11×AGL(1,ℤ/8)11yescharacteristic
858C22#1062330411yescharacteristic
859C22#1062330511yescharacteristic
860C22#1062330611yescharacteristic
861C22D4×C22⋊D1111yescharacteristic
862C4—41no—
863C4—41no—
864C4—81no—
865C4—81no—
866C4—222no—
867C4—222no—
868C4—442no—
869C4—441no—
870C4—881no—
871C4—881no—
872C4#1062307611yescharacteristic
873C4#1062308511yescharacteristic
874C4C22×(C2×D11)⋊C411yescharacteristic
875C4#1062336011yescharacteristic
876C2—44no—
877C2—44no—
878C2—442no—
879C2—882no—
880C2D4×(C2×D11)⋊C411yescharacteristic
881C2#1307742711yescharacteristic
882C2#1307744511yescharacteristic
883C2#1308009811yescharacteristic
884C2#1308014311yescharacteristic
885C2#1308021011yescharacteristic
886C2#1308022111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#442C2
socleC23×C11C22×D4
prime radicalC22×#66964C2
cosocleC22×C4×C11C24
hypercenterC2×#442D11
hypocenterC11#22442
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
2. C2×D8×Dic11C2semidirect
3. #13071441C2semidirect
4. D4×(C2×D11)⋊C4C2semidirect
5. #13069497C2semidirect
6. #13069468C2semidirect
7. #13068964C2semidirect
8. #13068962C2semidirect
9. #13068950C2semidirect
10. #13068948C2semidirect
11. #13068646C2semidirect
12. #13068553C2semidirect
13. #13068545C2semidirect
14. #13068401C2semidirect
15. C2×C11×#442C2semidirect
20. C2×C4×D4×C11C22semidirect
22. C2×D4×Dic11C22semidirect
28. C2×#66964C4semidirect
32. C2×C11×#106C22semidirect
34. C2×C11×#102C22semidirect
35. C2×C11×#97C22semidirect
37. C2×#66896C22semidirect
44. C2×#66882C22semidirect
45. C2×#66880C22semidirect
46. C2×C8×Dic11C22semidirect
50. #10622587C22semidirect
51. C2×#66874C22semidirect
59. #10622542C22semidirect
60. #10622188C22semidirect
61. #10622167C22semidirect
62. #10622167C22semidirect
63. #10622162C22semidirect
79. C2×#4341C2×C4semidirect
85. C2×D4×D11C2×C4semidirect
111. C2×#4324C2×C4semidirect
114. C2×#4323C2×C4semidirect
132. C2×#4314C2×C4semidirect
135. C2×#4313C2×C4semidirect
239. C11×D8C22⋊C4semidirect
281. C2×#442D11semidirect
338. D4×C11C2×C22⋊C4semidirect
381. C2×Dic11AGL(1,ℤ/8)semidirect
395. C8×C11C2×C22⋊C4semidirect
411. C2×C4×D4C2×D11semidirect
416. C2×#106C2×D11semidirect
424. C2×#102C2×D11semidirect
426. C2×#97C2×D11semidirect
684. D8(C2×D11)⋊C4semidirect
722. C11#22442semidirect
776. D4C2×(C2×D11)⋊C4semidirect
825. C8C2×(C2×D11)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#669642
C2×D8×Dic112
#130714412
D4×(C2×D11)⋊C42
#130694972
#130694682
#130689642
#130689622
#130689502
#130689482
#130686462
#130685532
#130685452
#130684012
C2×C11×#4422
#2244211