Finite Group Databasebeta

← #14769547

Subgroups — #14769547

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×#66967C211yesmaximal, characteristic
2C2×SD16×Dic11C211yesmaximal, characteristic, complemented
3#13071454C211yesmaximal, characteristic, complemented
4D4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
5#13069492C211yesmaximal, characteristic, complemented
6#13069480C211yesmaximal, characteristic, complemented
7#13068971C211yesmaximal, characteristic, complemented
8#13068969C211yesmaximal, characteristic, complemented
9#13068964C211yesmaximal, characteristic, complemented
10#13068962C211yesmaximal, characteristic, complemented
11#13068650C211yesmaximal, characteristic, complemented
12#13068555C211yesmaximal, characteristic, complemented
13#13068545C211yesmaximal, characteristic, complemented
14#13068401C211yesmaximal, characteristic, complemented
15C2×C11×#440C211yesmaximal, characteristic, complemented
16C22×#4343C2211yescharacteristic
17C22×D4×D11C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic, complemented
20C2×C4×D4×C11C2211yescharacteristic
21C2×Q8×Dic11C2211yescharacteristic, complemented
22C22×#4325C2211yescharacteristic
23C2×D4×Dic11C2211yescharacteristic
24C22×#4323C2211yescharacteristic
25C22×(C2×D11)⋊C4—21no—
26C2×#66967—24no—
27C2×#66967—24no—
28C2×#66967C418yescomplemented
29C22×D88C2211yescharacteristic
30C22×#4313C2211yescharacteristic
31C11×#440—24no—
32C2×C11×#107C2211yescharacteristic, complemented
33C2×C11×#103C2211yescharacteristic, complemented
34C2×C11×#102C2211yescharacteristic
35C2×C11×#97C2211yescharacteristic, complemented
36C2×#66899C2211yescharacteristic, complemented
37C2×#66896C2211yescharacteristic
38#10622826—21no—
39SD16×Dic11—24no—
40C2×#66885C2211yescharacteristic
41C2×#66885C2211yescharacteristic, complemented
42C2×(C2×D11)⋊C8C2211yescharacteristic
43C2×#66881C2211yescharacteristic, complemented
44C2×C8×Dic11C2211yescharacteristic, complemented
45#10622601—21no—
46#10622601C2211yescharacteristic
47#10622601C2211yescharacteristic, complemented
48#10622600—21no—
49#10622600C2211yescharacteristic
50#10622600C2211yescharacteristic
51C2×#66873C2211yescharacteristic
52C2×#66873C2211yescharacteristic, complemented
53#10622571—21no—
54#10622568—21no—
55#10622552—21no—
56#10622552C2211yescharacteristic
57#10622552C2211yescharacteristic, complemented
58C4×(C2×D11)⋊C4—21no—
59C4×(C2×D11)⋊C4C2211yescharacteristic
60#10622188C2211yescharacteristic, complemented
61#10622167C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63#10622162C2211yescharacteristic, complemented
64C24×D11—21no—
65C22×Q8×C11C2311yescharacteristic
66C22×D4×C11C2311yescharacteristic
67C23×C4×C11—21no—
68C22×C22⋊D11—21no—
69C23×Dic11—21no—
70C2×#4343—22no—
71C2×#4343—22no—
72C2×#4343—22no—
73C2×#4343—41no—
74C2×#4343—41no—
75C2×#4343C2×C414yescomplemented
76C2×D4×D11—22no—
77C2×D4×D11—22no—
78C2×D4×D11—22no—
79C2×D4×D11—41no—
80C2×D4×D11—41no—
81C2×D4×D11C2×C414yes—
82C22×D44—21no—
83C22×D44C2311yescharacteristic
84C22×D44C2311yescharacteristic
85C22×C4×D11—21no—
86C22×C4×D11C2311yescharacteristic
87C2×C11×SD16C2×C414yes—
88C2×C11×SD16D414yes—
89C2×C11×SD16D414yes—
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C4×Q8×C11—22no—
93C4×Q8×C11—41no—
94C4×D4×C11—22no—
95C4×D4×C11—41no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C22⋊C4—21no—
100C2×C42×C11—21no—
101C2×C42×C11C2311yescharacteristic
102C2×C22⋊Dic11—21no—
103Q8×Dic11—22no—
104Q8×Dic11—41no—
105C2×#4325—22no—
106C2×#4325—22no—
107C2×#4325C2×C414yescomplemented
108D4×Dic11—22no—
109D4×Dic11—41no—
110C2×#4323—22no—
111C2×#4323—22no—
112C2×#4323C2×C414yes—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
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—21no—
122C2×(C2×D11)⋊C4—21no—
123C2×(C2×D11)⋊C4—44no—
124C2×(C2×D11)⋊C4D411yescharacteristic
125C2×(C2×D11)⋊C4D411yescharacteristic
126C2×C4⋊Dic11—21no—
127C2×C4⋊Dic11C2311yescharacteristic
128C2×C4⋊Dic11C2311yescharacteristic
129C2×C4×Dic11—21no—
130C2×C4×Dic11C2311yescharacteristic
131C22×C11⋊C8C2311yescharacteristic
132C22×C11⋊C8C2311yescharacteristic
133#66967—232no—
134C2×D88—22no—
135C2×D88—22no—
136C2×D88C2×C414yescomplemented
137C2×#4313—22no—
138C2×#4313—22no—
139C2×#4313C2×C414yescomplemented
140C11×#107—22no—
141C11×#103—22no—
142C11×#102—22no—
143C11×#97—22no—
144#66899—22no—
145#66896—22no—
146C11⋊#95—21no—
147C11⋊#95—21no—
148C11⋊#95D411yescharacteristic
149C11⋊#95D411yescharacteristic
150#66885—41no—
151#66885—41no—
152(C2×D11)⋊C8—22no—
153#66881—22no—
154C8×Dic11—22no—
155#66873—41no—
156#66873—41no—
157#22443—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×C11C22×C412yes—
173C2×Q8×C11C2×D412yes—
174C2×Q8×C11C2×D412yes—
175C2×D4×C11—21no—
176C2×D4×C11—21no—
177C2×D4×C11—21no—
178C2×D4×C11C22×C412yes—
179C2×D4×C11C2×D412yes—
180C2×D4×C11C2×D412yes—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—42no—
185C22×C4×C11—42no—
186C22×C4×C11—81no—
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2411yescharacteristic
190C2×C22⋊D11—24no—
191C2×C22⋊D11—42no—
192C2×C22⋊D11—42no—
193C22×Dic11—21no—
194C22×Dic11—21no—
195C22×Dic11—42no—
196C22×Dic11—42no—
197C22×Dic11—81no—
198C22×Dic11C2×D411yescharacteristic
199C22×Dic11C2×D411yescharacteristic
200C22×Dic11C2×D411yescharacteristic
201#4343—28no—
202#4343—44no—
203#4343—44no—
204#4343—44no—
205D4×D11—28no—
206D4×D11—44no—
207D4×D11—44no—
208D4×D11—44no—
209C2×D44—24no—
210C2×D44—21no—
211C2×D44—21no—
212C2×D44—21no—
213C2×D44—21no—
214C2×D44—21no—
215C2×D44—21no—
216C2×D44—21no—
217C2×D44—21no—
218C2×D44—21no—
219C2×D44—21no—
220C2×D44—42no—
221C2×D44—42no—
222C2×D44C22×C412yes—
223C2×D44C22×C412yes—
224C2×C4×D11—24no—
225C2×C4×D11—21no—
226C2×C4×D11—21no—
227C2×C4×D11—21no—
228C2×C4×D11—21no—
229C2×C4×D11—42no—
230C2×C4×D11—42no—
231C2×C4×D11C22×C412yes—
232C2×C4×D11#4112yes—
233C11×SD16C22⋊C4116yescomplemented
234C2×C8×C11—21no—
235C2×C8×C11—21no—
236C2×C8×C11—21no—
237C2×C8×C11C22×C412yes—
238C2×C8×C11C2×D412yes—
239C2×C8×C11C2×D412yes—
240C11×C4⋊C4—21no—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—21no—
243C11×C4⋊C4—21no—
244C11×C4⋊C4—42no—
245C11×C22⋊C4—42no—
246C42×C11—21no—
247C42×C11—21no—
248C42×C11—42no—
249C22⋊Dic11—42no—
250#4325—28no—
251#4323—28no—
252(C2×D11)⋊C4—22no—
253(C2×D11)⋊C4—41no—
254(C2×D11)⋊C4—42no—
255(C2×D11)⋊C4—42no—
256(C2×D11)⋊C4—42no—
257(C2×D11)⋊C4—42no—
258(C2×D11)⋊C4—42no—
259(C2×D11)⋊C4—81no—
260(C2×D11)⋊C4—81no—
261(C2×D11)⋊C4—81no—
262(C2×D11)⋊C4—81no—
263(C2×D11)⋊C4—81no—
264C4⋊Dic11—21no—
265C4⋊Dic11—21no—
266C4⋊Dic11—21no—
267C4⋊Dic11—21no—
268C4⋊Dic11—42no—
269C4×Dic11—21no—
270C4×Dic11—21no—
271C4×Dic11—42no—
272C2×C11⋊C8—21no—
273C2×C11⋊C8—21no—
274C2×C11⋊C8—21no—
275C2×C11⋊C8—21no—
276C2×C11⋊C8—21no—
277C2×C11⋊C8C22×C412yes—
278D88—28no—
279#4313—28no—
280C22×AGL(1,ℤ/8)—111no—
281C2×#440D1111yescharacteristic, complemented
282C2×C4×SD16—111no—
283#2341—111no—
284D4×C22⋊C4—111no—
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—41no—
299C23×C11—41no—
300C23×C11—41no—
301C23×C11—41no—
302C23×C11C22×D411yescharacteristic
303C22×D11—21no—
304C22×D11—21no—
305C22×D11—21no—
306C22×D11—21no—
307C22×D11—21no—
308C22×D11—21no—
309C22×D11—22no—
310C22×D11—22no—
311C22×D11—48no—
312C22×D11—48no—
313C22×D11—41no—
314C22×D11—41no—
315C22×D11—41no—
316C22×D11—41no—
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—22no—
334Q8×C11C2×C22⋊C414yescomplemented
335D4×C11—22no—
336D4×C11—22no—
337D4×C11—22no—
338D4×C11C2×C22⋊C414yes—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—21no—
343C2×C4×C11—21no—
344C2×C4×C11—21no—
345C2×C4×C11—21no—
346C2×C4×C11—21no—
347C2×C4×C11—21no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—84no—
355C2×C4×C11C23×C411yescharacteristic
356C2×C4×C11C22×D411yescharacteristic
357C2×C4×C11C22×D411yescharacteristic
358C2×C4×C11C2×#4111yescharacteristic
359C2×C4×C11H(5,𝔽2)11yescharacteristic
360C2×C4×C11H(5,𝔽2)11yescharacteristic
361C22⋊D11—48no—
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×Dic11—84no—
376C2×Dic11C4×D412yes—
377C2×Dic11AGL(1,ℤ/8)12yescomplemented
378D44—22no—
379D44—22no—
380D44—22no—
381D44—22no—
382D44—48no—
383D44—41no—
384D44—41no—
385D44—41no—
386D44—41no—
387C4×D11—22no—
388C4×D11—22no—
389C4×D11—22no—
390C4×D11—22no—
391C4×D11—48no—
392C8×C11—41no—
393C8×C11C2×C22⋊C414yescomplemented
394C11⋊C8—22no—
395C11⋊C8—41no—
396C22×#41—111no—
397C23×D4—111no—
398C2×AGL(1,ℤ/8)—118no—
399C2×AGL(1,ℤ/8)—224no—
400C2×AGL(1,ℤ/8)—224no—
401C22×SD16—111no—
402C22×SD16C2×D1111yescharacteristic
403C22×D8—111no—
404C22×D8—111no—
405C22×M16—111no—
406C2×C4×Q8—111no—
407C2×C4×Q8C2×D1111yescharacteristic, complemented
408C2×C4×D4—111no—
409C2×C4×D4C2×D1111yescharacteristic
410C22×C22⋊C4—221no—
411#440—24no—
412C4×SD16—224no—
413C2×#107C2×D1111yescharacteristic, complemented
414C2×#106—111no—
415C2×#103—111no—
416C2×#103C2×D1111yescharacteristic, complemented
417C2×#102—111no—
418C2×#102—111no—
419C2×#102—111no—
420C2×#102—111no—
421C2×#102—111no—
422C2×#102C2×D1111yescharacteristic
423C2×C22⋊C8—111no—
424C2×#97C2×D1111yescharacteristic, complemented
425C2×C4×C8—111no—
426#390—111no—
427#390—111no—
428#390—111no—
429#390—111no—
430#390—221no—
431#390—221no—
432#386—221no—
433#386—221no—
434#380—111no—
435#380—111no—
436#380—221no—
437#379—221no—
438C4×C22⋊C4—111no—
439C4×C22⋊C4—221no—
440#340—111no—
441#340—111no—
442#336—111no—
443#336—111no—
444C22×C11—24no—
445C22×C11—42no—
446C22×C11—42no—
447C22×C11—42no—
448C22×C11—42no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11C2×C4×D411yescharacteristic
452C22×C11D4211yescharacteristic
453C22×C11D4211yescharacteristic
454C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
455C22×C11#57511yescharacteristic
456C22×C11#57611yescharacteristic
457C22×C11#57711yescharacteristic
458C2×D11—22no—
459C2×D11—22no—
460C2×D11—22no—
461C2×D11—41no—
462C2×D11—41no—
463C2×D11—41no—
464C2×D11—41no—
465C2×D11—42no—
466C2×D11—42no—
467C2×D11—42no—
468C2×D11—42no—
469C2×D11—42no—
470C2×D11—42no—
471C2×D11—816no—
472C2×D11—81no—
473C2×D11—81no—
474C2×D11—81no—
475C2×D11—81no—
476C2×D11—81no—
477C2×D11—81no—
478C2×D11—81no—
479C2×D11—81no—
480C4×C11—24no—
481C4×C11—41no—
482C4×C11—41no—
483C4×C11—81no—
484C4×C11—81no—
485C4×C11C22×C22⋊C411yescharacteristic
486C4×C11#51811yescharacteristic
487C4×C11#54611yescharacteristic
488C4×C11#54611yescharacteristic
489Dic11—22no—
490Dic11—22no—
491Dic11—41no—
492Dic11—81no—
493Dic11—81no—
494C25—221no—
495C2×#41—114no—
496C2×#41—222no—
497C2×#41—222no—
498C2×#41—222no—
499C2×#41—441no—
500C2×#41—441no—
501C22×Q8C22×D1111yescharacteristic
502C22×D4—114no—
503C22×D4—111no—
504C22×D4—111no—
505C22×D4—221no—
506C22×D4—222no—
507C22×D4—221no—
508C22×D4—222no—
509C22×D4—222no—
510C22×D4—441no—
511C22×D4—441no—
512C22×D4C22×D1111yescharacteristic
513C23×C4—21no—
514C23×C4—111no—
515C23×C4—221no—
516C23×C4—221no—
517AGL(1,ℤ/8)—2232no—
518C2×SD16—114no—
519C2×SD16—222no—
520C2×SD16—222no—
521C2×SD16C4×D1114yes—
522C2×SD16D4414yes—
523C2×SD16C22⋊D1114yes—
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×C8C22×D1111yescharacteristic
536C22×C8C22×D1111yescharacteristic
537C4×Q8—22no—
538C4×Q8—41no—
539C4×Q8—222no—
540C4×Q8—441no—
541C4×D4—22no—
542C4×D4—41no—
543C4×D4—222no—
544C4×D4—441no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—111no—
547C2×C4⋊C4—111no—
548C2×C4⋊C4—221no—
549C2×C4⋊C4C22×D1111yescharacteristic
550C2×C4⋊C4C22×D1111yescharacteristic
551C2×C22⋊C4—21no—
552C2×C22⋊C4—111no—
553C2×C22⋊C4—111no—
554C2×C22⋊C4—221no—
555C2×C22⋊C4—221no—
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—221no—
564C2×C22⋊C4—221no—
565C2×C22⋊C4—444no—
566C2×C42—21no—
567C2×C42—111no—
568C2×C42—221no—
569C2×C42C22×D1111yescharacteristic
570#107—22no—
571#106—222no—
572#103—22no—
573#103—222no—
574#102—22no—
575#102—222no—
576#102—441no—
577#102—441no—
578#102—441no—
579#102—441no—
580C22⋊C8—222no—
581#97—22no—
582C4×C8—222no—
583#95—111no—
584#95—111no—
585#95—221no—
586#95—221no—
587C2×C11—44no—
588C2×C11D4×C22⋊C411yescharacteristic
589C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
590C2×C11#294611yescharacteristic
591C2×C11#326511yescharacteristic
592C2×C11#326811yescharacteristic
593C2×C11#327411yescharacteristic
594C2×C11#327511yescharacteristic
595D11—42no—
596D11—82no—
597D11—82no—
598C24—21no—
599C24—111no—
600C24—224no—
601C24—221no—
602C24—221no—
603C24—442no—
604C24—442no—
605C24—442no—
606C24—442no—
607C24—881no—
608C24—881no—
609#41—228no—
610#41—444no—
611#41—444no—
612#41—444no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8C2×C4×D1112yes—
617C2×Q8C2×D4412yes—
618C2×Q8C2×C22⋊D1112yes—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—112no—
623C2×D4—112no—
624C2×D4—224no—
625C2×D4—224no—
626C2×D4—228no—
627C2×D4—221no—
628C2×D4—221no—
629C2×D4—221no—
630C2×D4—221no—
631C2×D4—221no—
632C2×D4—221no—
633C2×D4—221no—
634C2×D4—221no—
635C2×D4—221no—
636C2×D4—221no—
637C2×D4—442no—
638C2×D4—442no—
639C2×D4—444no—
640C2×D4—444no—
641C2×D4—444no—
642C2×D4—442no—
643C2×D4—442no—
644C2×D4C2×C4×D1112yes—
645C2×D4C2×D4412yes—
646C2×D4C2×C22⋊D1112yes—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—42no—
651C22×C4—42no—
652C22×C4—81no—
653C22×C4—111no—
654C22×C4—111no—
655C22×C4—112no—
656C22×C4—112no—
657C22×C4—111no—
658C22×C4—224no—
659C22×C4—221no—
660C22×C4—221no—
661C22×C4—221no—
662C22×C4—221no—
663C22×C4—221no—
664C22×C4—221no—
665C22×C4—442no—
666C22×C4—442no—
667C22×C4—442no—
668C22×C4—442no—
669C22×C4—881no—
670C22×C4D4×D1111yescharacteristic
671C22×C4D4×D1111yescharacteristic
672C22×C4C23×D1111yescharacteristic
673SD16—228no—
674SD16(C2×D11)⋊C4116yescomplemented
675D8—228no—
676D8—228no—
677M16—228no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—112no—
682C2×C8—221no—
683C2×C8—221no—
684C2×C8—221no—
685C2×C8—221no—
686C2×C8—221no—
687C2×C8C2×C4×D1112yes—
688C2×C8C2×D4412yes—
689C2×C8C2×C22⋊D1112yes—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—42no—
695C4⋊C4—221no—
696C4⋊C4—221no—
697C4⋊C4—221no—
698C4⋊C4—221no—
699C4⋊C4—442no—
700C22⋊C4—42no—
701C22⋊C4—222no—
702C22⋊C4—441no—
703C22⋊C4—442no—
704C22⋊C4—442no—
705C22⋊C4—442no—
706C22⋊C4—442no—
707C22⋊C4—442no—
708C22⋊C4—442no—
709C22⋊C4—881no—
710C22⋊C4—881no—
711C22⋊C4—881no—
712C22⋊C4—881no—
713C22⋊C4—881no—
714C42—21no—
715C42—21no—
716C42—42no—
717C42—221no—
718C42—221no—
719C42—442no—
720C11#2244311yescharacteristic, complemented, Sylow
721C23—22no—
722C23—22no—
723C23—22no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—112no—
729C23—221no—
730C23—221no—
731C23—221no—
732C23—221no—
733C23—221no—
734C23—221no—
735C23—222no—
736C23—222no—
737C23—448no—
738C23—448no—
739C23—441no—
740C23—441no—
741C23—441no—
742C23—441no—
743C23—441no—
744C23—441no—
745C23—441no—
746C23—441no—
747C23—441no—
748C23—441no—
749C23—441no—
750C23—441no—
751C23—884no—
752C23—884no—
753C23—884no—
754C23—884no—
755C23—884no—
756C23C2×D4×D1111yescharacteristic
757Q8—22no—
758Q8—22no—
759Q8—22no—
760Q8C2×(C2×D11)⋊C414yescomplemented
761D4—22no—
762D4—22no—
763D4—22no—
764D4—222no—
765D4—222no—
766D4—222no—
767D4—222no—
768D4—448no—
769D4—448no—
770D4—441no—
771D4—441no—
772D4—441no—
773D4—441no—
774D4C2×(C2×D11)⋊C414yes—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
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—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×C4C22×C4×D1111yescharacteristic
813C2×C4C22×D4411yescharacteristic
814C2×C4#6703711yescharacteristic
815C2×C4#41×D1111yescharacteristic
816C2×C4#6704211yescharacteristic
817C2×C4C22×C22⋊D1111yescharacteristic
818C8—41no—
819C8—222no—
820C8—441no—
821C8C2×(C2×D11)⋊C414yescomplemented
822C22—24no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—222no—
830C22—222no—
831C22—222no—
832C22—441no—
833C22—441no—
834C22—441no—
835C22—441no—
836C22—442no—
837C22—442no—
838C22—442no—
839C22—442no—
840C22—442no—
841C22—442no—
842C22—8816no—
843C22—881no—
844C22—881no—
845C22—881no—
846C22—881no—
847C22—881no—
848C22—881no—
849C22—881no—
850C22—881no—
851C22C4×D4×D1111yescharacteristic
852C22D4×D4411yescharacteristic
853C22D11×AGL(1,ℤ/8)11yescharacteristic
854C22#1062330511yescharacteristic
855C22#1062330811yescharacteristic
856C22#1062330911yescharacteristic
857C22D4×C22⋊D1111yescharacteristic
858C4—24no—
859C4—41no—
860C4—41no—
861C4—81no—
862C4—81no—
863C4—222no—
864C4—222no—
865C4—441no—
866C4—881no—
867C4—881no—
868C4#1062307611yescharacteristic
869C4#1062308511yescharacteristic
870C4C22×(C2×D11)⋊C411yescharacteristic
871C4#1062336011yescharacteristic
872C2—44no—
873C2—442no—
874C2—882no—
875C2—882no—
876C2D4×(C2×D11)⋊C411yescharacteristic
877C2#1307742111yescharacteristic
878C2#1307744711yescharacteristic
879C2#1308011311yescharacteristic
880C2#1308015811yescharacteristic
881C2#1308023011yescharacteristic
882C2#1308024111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#440C2
socleC23×C11C22×D4
prime radicalC22×#66967C2
cosocleC22×C4×C11C24
hypercenterC2×#440D11
hypocenterC11#22443
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
2. C2×SD16×Dic11C2semidirect
3. #13071454C2semidirect
4. D4×(C2×D11)⋊C4C2semidirect
5. #13069492C2semidirect
6. #13069480C2semidirect
7. #13068971C2semidirect
8. #13068969C2semidirect
9. #13068964C2semidirect
10. #13068962C2semidirect
11. #13068650C2semidirect
12. #13068555C2semidirect
13. #13068545C2semidirect
14. #13068401C2semidirect
15. C2×C11×#440C2semidirect
19. C2×C4×Q8×C11C22semidirect
21. C2×Q8×Dic11C22semidirect
28. C2×#66967C4semidirect
32. C2×C11×#107C22semidirect
33. C2×C11×#103C22semidirect
35. C2×C11×#97C22semidirect
36. C2×#66899C22semidirect
41. C2×#66885C22semidirect
43. C2×#66881C22semidirect
44. C2×C8×Dic11C22semidirect
47. #10622601C22semidirect
52. C2×#66873C22semidirect
57. #10622552C22semidirect
60. #10622188C22semidirect
61. #10622167C22semidirect
62. #10622167C22semidirect
63. #10622162C22semidirect
75. C2×#4343C2×C4semidirect
107. C2×#4325C2×C4semidirect
136. C2×D88C2×C4semidirect
139. C2×#4313C2×C4semidirect
233. C11×SD16C22⋊C4semidirect
281. C2×#440D11semidirect
334. Q8×C11C2×C22⋊C4semidirect
377. C2×Dic11AGL(1,ℤ/8)semidirect
393. C8×C11C2×C22⋊C4semidirect
407. C2×C4×Q8C2×D11semidirect
413. C2×#107C2×D11semidirect
416. C2×#103C2×D11semidirect
424. C2×#97C2×D11semidirect
674. SD16(C2×D11)⋊C4semidirect
720. C11#22443semidirect
760. Q8C2×(C2×D11)⋊C4semidirect
821. 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×#669672
C2×SD16×Dic112
#130714542
D4×(C2×D11)⋊C42
#130694922
#130694802
#130689712
#130689692
#130689642
#130689622
#130686502
#130685552
#130685452
#130684012
C2×C11×#4402
#2244311