Finite Group Databasebeta

← C2×#13078235 #15620919

Subgroups — C2×#13078235 #15620919

Order 2816.

3242 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66961C211yesmaximal, characteristic, complemented
2C2×#10623322C211yesmaximal, characteristic, complemented
3C22×#66983C211yesmaximal, characteristic, complemented
4#13078235C2116yesmaximal, direct product factor
5C2×#10622748C212yesmaximal, complemented
6C2×#10622747C212yesmaximal, complemented
7C2×#10622728C212yesmaximal, complemented
8C2×#10622727C212yesmaximal, complemented
9C2×#10622734C211yesmaximal, characteristic, complemented
10C2×#10622746C211yesmaximal, characteristic, complemented
11C2×#10622744C211yesmaximal, characteristic, complemented
12C23×C11×M16C211yesmaximal, characteristic, complemented
13C24×C4×C11C2211yescharacteristic
14C23×C22⋊D11—21no—
15C22×#4339C2211yescharacteristic
16C23×D44C2211yescharacteristic
17C22×C11×M16—28no—
18C22×C11×M16C2211yescharacteristic
19C22×C11×M16C2211yescharacteristic
20C22×C11×M16C2212yescomplemented
21C22×C11×M16C2218yescomplemented
22C23×C8×C11C2212yescomplemented
23C2×#67006—21no—
24#10623322—24no—
25#10623322C2218yescomplemented
26C2×#66983—21no—
27C2×#66983—21no—
28C2×#66983—24no—
29C2×#66983C2212yes—
30C2×#66983C2212yes—
31C2×#66983C2218yescomplemented
32C2×#66983C2211yescharacteristic, complemented
33C2×#66983C2211yescharacteristic, complemented
34C2×#66982—21no—
35C2×C4×C22⋊D11—21no—
36C2×C4×C22⋊D11—21no—
37C22×(C2×D11)⋊C4—21no—
38C2×#66979C2211yescharacteristic
39C22×C4⋊Dic11C2211yescharacteristic
40C2×#66977C2211yescharacteristic, complemented
41C2×#66977C2211yescharacteristic, complemented
42C2×#66961—28no—
43C2×#66961C2218yescomplemented
44C22×D88C2212yescomplemented
45C22×#4314C2212yescomplemented
46#10622748C22116yescomplemented
47#10622747C22116yescomplemented
48#10622746C2218yescomplemented
49#10622744C2218yescomplemented
50#10622734C2218yescomplemented
51#10622728C22116yescomplemented
52#10622727C22116yescomplemented
53C2×#66885C2212yescomplemented
54C2×#66885C2212yescomplemented
55C2×#66885C2212yescomplemented
56C2×#66882C2212yescomplemented
57C2×#66881C2212yescomplemented
58C2×#66880C2212yescomplemented
59C25×C11D411yescharacteristic
60C24×D11—21no—
61C23×C4×C11—24no—
62C23×C4×C11—24no—
63C23×C4×C11D411yescharacteristic
64C23×C4×C11D411yescharacteristic
65C23×C4×C11D411yescharacteristic
66C23×C4×C11D414yes—
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2314yes—
70C23×C4×C11C2311yescharacteristic
71C22×C22⋊D11—21no—
72C22×C22⋊D11—21no—
73C22×C22⋊D11—21no—
74C22×C22⋊D11—22no—
75C22×C22⋊D11—22no—
76C22×C22⋊D11—28no—
77C22×C22⋊D11—48no—
78C23×Dic11—21no—
79C2×#4339—22no—
80C2×#4339—24no—
81C2×#4339—24no—
82C2×#4339C2314yes—
83C22×D44—24no—
84C22×D44—24no—
85C22×D44—21no—
86C22×D44—22no—
87C22×D44C2312yes—
88C22×D44C2311yescharacteristic
89C22×D44C2314yes—
90C22×C4×D11—21no—
91C22×Dic22C2311yescharacteristic
92C2×C11×M16—24no—
93C2×C11×M16—232no—
94C2×C11×M16—28no—
95C2×C11×M16D418yescomplemented
96C2×C11×M16C2314yes—
97C2×C11×M16C2314yes—
98C2×C11×M16C2318yescomplemented
99C22×C8×C11—28no—
100C22×C8×C11C2312yes—
101C22×C8×C11C2312yes—
102C22×C8×C11C2318yescomplemented
103#67006—28no—
104C2×C22⋊Dic11—21no—
105C2×C22⋊Dic11—21no—
106C2×C22⋊Dic11—21no—
107#66983—24no—
108#66983—24no—
109#66983—28no—
110#66983—28no—
111#66983—22no—
112#66983—22no—
113#66983C2318yes—
114#66983C2318yes—
115#66983C2314yescomplemented
116#66983C2314yescomplemented
117#66982—28no—
118C4×C22⋊D11—28no—
119C4×C22⋊D11—28no—
120C2×(C2×D11)⋊C4—22no—
121C2×(C2×D11)⋊C4—22no—
122C2×(C2×D11)⋊C4—28no—
123C2×(C2×D11)⋊C4—21no—
124C2×(C2×D11)⋊C4—21no—
125#66979—22no—
126#66979C2314yes—
127C2×C4⋊Dic11—21no—
128C2×C4⋊Dic11—22no—
129C2×C4⋊Dic11C2311yescharacteristic
130C2×C4⋊Dic11C2311yescharacteristic
131C2×C4⋊Dic11C2312yes—
132C2×C4⋊Dic11C2314yes—
133#66977—22no—
134#66977—22no—
135#66977C2314yescomplemented
136#66977C2314yescomplemented
137C2×Dic11⋊C4—21no—
138C2×Dic11⋊C4—21no—
139C2×C4×Dic11—21no—
140#66961—232no—
141C2×D88—28no—
142C2×D88C2318yescomplemented
143C2×#4314—28no—
144C2×#4314C2318yescomplemented
145#66885C2318yescomplemented
146#66885C2318yescomplemented
147#66885C2318yescomplemented
148#66882C2318yescomplemented
149#66881C2318yescomplemented
150#66880C2318yescomplemented
151C2×#3055—111nomaximal, Sylow
152C24×C11—24no—
153C24×C11—24no—
154C24×C11—42no—
155C24×C11C2×D411yescharacteristic
156C24×C11C2×D414yes—
157C24×C11C2×D411yescharacteristic
158C24×C11C2×D411yescharacteristic
159C23×D11—21no—
160C23×D11—24no—
161C23×D11—22no—
162C23×D11—44no—
163C23×D11—44no—
164C23×D11—44no—
165C22×C4×C11—24no—
166C22×C4×C11—24no—
167C22×C4×C11—24no—
168C22×C4×C11—216no—
169C22×C4×C11—22no—
170C22×C4×C11—28no—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—28no—
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D412yes—
178C22×C4×C11C2×D412yes—
179C22×C4×C11C2×D414yes—
180C22×C4×C11C2×D414yes—
181C22×C4×C11C2×D414yes—
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D412yes—
184C22×C4×C11C2×D414yes—
185C22×C4×C11#4114yes—
186C22×C4×C11C2412yes—
187C22×C4×C11C2412yes—
188C22×C4×C11C2411yescharacteristic
189C22×C4×C11C2412yes—
190C2×C22⋊D11—24no—
191C2×C22⋊D11—24no—
192C2×C22⋊D11—24no—
193C2×C22⋊D11—28no—
194C2×C22⋊D11—28no—
195C2×C22⋊D11—44no—
196C2×C22⋊D11—432no—
197C2×C22⋊D11—48no—
198C2×C22⋊D11—44no—
199C2×C22⋊D11—44no—
200C2×C22⋊D11—48no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—24no—
205C22×Dic11—22no—
206C22×Dic11—44no—
207#4339—28no—
208#4339—28no—
209#4339—48no—
210C2×D44—24no—
211C2×D44—22no—
212C2×D44—21no—
213C2×D44—24no—
214C2×D44—22no—
215C2×D44—28no—
216C2×D44—24no—
217C2×D44—28no—
218C2×D44—22no—
219C2×D44—44no—
220C2×D44—48no—
221C2×D44C2414yes—
222C2×D44C2412yes—
223C2×C4×D11—24no—
224C2×C4×D11—44no—
225C2×Dic22—22no—
226C2×Dic22—21no—
227C2×Dic22—22no—
228C2×Dic22C2412yes—
229C11×M16—216no—
230C11×M16—28no—
231C11×M16C2×D4116yescomplemented
232C2×C8×C11—216no—
233C2×C8×C11—24no—
234C2×C8×C11C2×D418yescomplemented
235C2×C8×C11C2414yes—
236C2×C8×C11C2414yes—
237C22⋊Dic11—24no—
238C22⋊Dic11—24no—
239C22⋊Dic11—24no—
240(C2×D11)⋊C4—28no—
241(C2×D11)⋊C4—28no—
242(C2×D11)⋊C4—24no—
243(C2×D11)⋊C4—24no—
244C4⋊Dic11—21no—
245C4⋊Dic11—21no—
246C4⋊Dic11—24no—
247C4⋊Dic11—22no—
248C4⋊Dic11C2414yes—
249C4⋊Dic11C2412yes—
250C4⋊Dic11C2412yes—
251Dic11⋊C4—24no—
252Dic11⋊C4—24no—
253C4×Dic11—24no—
254D88—216no—
255#4314—216no—
256C22×AGL(1,ℤ/8)—111no—
257C23×M16D1111yescharacteristic, complemented
258C2×#525—111no—
259C22×#121—111no—
260#3055—1116no—
261C2×#469—112no—
262C2×#468—112no—
263C2×#466—112no—
264C2×#465—112no—
265C2×#428—111no—
266C2×#417—111no—
267C2×#418—111no—
268C23×C11—22no—
269C23×C11—22no—
270C23×C11—22no—
271C23×C11—22no—
272C23×C11—28no—
273C23×C11—22no—
274C23×C11—22no—
275C23×C11—28no—
276C23×C11—22no—
277C23×C11—44no—
278C23×C11—416no—
279C23×C11#12114yes—
280C23×C11AGL(1,ℤ/8)14yescomplemented
281C23×C11C22×D412yes—
282C23×C11C22×D412yes—
283C23×C11C22×D412yes—
284C23×C11C22×D411yescharacteristic
285C22×D11—22no—
286C22×D11—24no—
287C22×D11—48no—
288C22×D11—48no—
289C22×D11—42no—
290C22×D11—48no—
291C22×D11—44no—
292C22×D11—44no—
293C22×D11—42no—
294C22×D11—42no—
295C22×D11—44no—
296C22×D11—816no—
297C2×C4×C11—28no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—24no—
301C2×C4×C11—24no—
302C2×C4×C11—28no—
303C2×C4×C11—28no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11#12114yes—
309C2×C4×C11#12118yes—
310C2×C4×C11C22×D412yes—
311C2×C4×C11C22×D412yes—
312C2×C4×C11C22×D412yes—
313C2×C4×C11C22×D411yescharacteristic
314C2×C4×C11C22×D412yes—
315C2×C4×C11C22×D414yes—
316C2×C4×C11C2×#4112yes—
317C2×C4×C11C2×#4114yes—
318C2×C4×C11C2511yescharacteristic
319C22⋊D11—48no—
320C22⋊D11—416no—
321C22⋊D11—48no—
322C22⋊D11—48no—
323C22⋊D11—416no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—22no—
327C2×Dic11—24no—
328C2×Dic11—48no—
329C2×Dic11—42no—
330C2×Dic11—44no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333D44—24no—
334D44—22no—
335D44—24no—
336D44—22no—
337D44—44no—
338D44—48no—
339D44—42no—
340C4×D11—48no—
341Dic22—22no—
342Dic22—22no—
343Dic22—42no—
344C8×C11—24no—
345C8×C11C22×D418yescomplemented
346C22×#41—111no—
347C23×D4—111no—
348C23×D4—221no—
349C24×C4C2×D1111yescharacteristic
350C2×AGL(1,ℤ/8)—118no—
351C2×AGL(1,ℤ/8)—228no—
352C22×SD16—112no—
353C22×D8—112no—
354C22×M16—28no—
355C22×M16C2×D1111yescharacteristic
356C22×M16C2×D1111yescharacteristic
357C22×M16C2×D1112yescomplemented
358C22×M16C2×D1118yescomplemented
359C23×C8C2×D1112yescomplemented
360#525—118no—
361#525—224no—
362C2×#123—221no—
363C2×C22⋊Q8—111no—
364C2×C22⋊Q8—111no—
365C2×#121—112no—
366C2×#121—112no—
367C2×#121—118no—
368C2×#121—111no—
369C2×#121—111no—
370C2×#121—221no—
371C2×#121—221no—
372C2×#121—224no—
373C2×#120—221no—
374C2×C4×D4—221no—
375C2×C4×D4—221no—
376C2×#117—111no—
377C22×C4⋊C4—111no—
378C22×C22⋊C4—221no—
379#469—1116no—
380#468—1116no—
381#466—1116no—
382#465—1116no—
383#428—118no—
384C2×#107—112no—
385C2×#106—112no—
386#418—118no—
387#417—118no—
388C2×#103—112no—
389C2×#102—112no—
390C2×#102—112no—
391C2×#102—112no—
392C22×C11—22no—
393C22×C11—28no—
394C22×C11—28no—
395C22×C11—22no—
396C22×C11—22no—
397C22×C11—22no—
398C22×C11—22no—
399C22×C11—22no—
400C22×C11—22no—
401C22×C11—416no—
402C22×C11—44no—
403C22×C11C2×#12114yes—
404C22×C11C2×#12112yes—
405C22×C11C2×AGL(1,ℤ/8)12yes—
406C22×C11C2×AGL(1,ℤ/8)14yescomplemented
407C22×C11#57512yes—
408C22×C11C23×D411yescharacteristic
409C2×D11—44no—
410C2×D11—42no—
411C2×D11—44no—
412C2×D11—42no—
413C2×D11—44no—
414C2×D11—42no—
415C2×D11—816no—
416C2×D11—84no—
417C2×D11—88no—
418C4×C11—22no—
419C4×C11—22no—
420C4×C11C2×#12112yes—
421C4×C11C2×#12114yes—
422C4×C11C23×D411yescharacteristic
423C4×C11C22×#4111yescharacteristic
424Dic11—42no—
425Dic11—44no—
426Dic11—42no—
427Dic11—42no—
428C25—221no—
429C25D4411yescharacteristic
430C2×#41—114no—
431C2×#41—222no—
432C2×#41—224no—
433C2×#41—224no—
434C22×Q8—111no—
435C22×D4—111no—
436C22×D4—112no—
437C22×D4—114no—
438C22×D4—221no—
439C22×D4—221no—
440C22×D4—221no—
441C22×D4—228no—
442C22×D4—222no—
443C22×D4—222no—
444C22×D4—222no—
445C22×D4—221no—
446C22×D4—224no—
447C22×D4—224no—
448C22×D4—448no—
449C23×C4—24no—
450C23×C4—24no—
451C23×C4—221no—
452C23×C4—221no—
453C23×C4D4411yescharacteristic
454C23×C4D4411yescharacteristic
455C23×C4D4411yescharacteristic
456C23×C4D4414yes—
457C23×C4C22×D1111yescharacteristic
458C23×C4C22×D1111yescharacteristic
459C23×C4C22×D1114yes—
460C23×C4C22×D1111yescharacteristic
461AGL(1,ℤ/8)—2232no—
462C2×SD16—118no—
463C2×SD16—228no—
464C2×D8—118no—
465C2×D8—228no—
466C2×M16—24no—
467C2×M16—232no—
468C2×M16—28no—
469C2×M16C22⋊D1118yescomplemented
470C2×M16C22×D1114yes—
471C2×M16C22×D1114yes—
472C2×M16C22×D1118yescomplemented
473C22×C8—28no—
474C22×C8C22×D1112yes—
475C22×C8C22×D1112yes—
476C22×C8C22×D1118yescomplemented
477#123—228no—
478C22⋊Q8—114no—
479C22⋊Q8—114no—
480C22⋊Q8—222no—
481C22⋊Q8—222no—
482#121—118no—
483#121—118no—
484#121—114no—
485#121—114no—
486#121—228no—
487#121—228no—
488#121—224no—
489#121—224no—
490#121—222no—
491#121—222no—
492#120—228no—
493C4×D4—228no—
494C4×D4—228no—
495#117—114no—
496#117—222no—
497C2×C4⋊C4—112no—
498C2×C4⋊C4—114no—
499C2×C4⋊C4—111no—
500C2×C4⋊C4—111no—
501C2×C4⋊C4—222no—
502C2×C4⋊C4—221no—
503C2×C4⋊C4—221no—
504C2×C4⋊C4—221no—
505C2×C22⋊C4—221no—
506C2×C22⋊C4—221no—
507C2×C22⋊C4—221no—
508C2×C22⋊C4—228no—
509C2×C22⋊C4—222no—
510C2×C22⋊C4—222no—
511C2×C22⋊C4—221no—
512C2×C22⋊C4—221no—
513C2×C42—221no—
514#107—118no—
515#106—118no—
516#103—118no—
517#102—118no—
518#102—118no—
519#102—118no—
520C2×C11—24no—
521C2×C11—24no—
522C2×C11—42no—
523C2×C11#305514yescomplemented
524C2×C11C22×#12111yescharacteristic
525C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
526C2×C11C2×#57511yescharacteristic
527D11—82no—
528D11—84no—
529C24—24no—
530C24—24no—
531C24—42no—
532C24—224no—
533C24—221no—
534C24—222no—
535C24—444no—
536C24—444no—
537C24—444no—
538C24C2×D4411yescharacteristic
539C24C2×D4414yes—
540C24C2×D4411yescharacteristic
541C24C2×D4411yescharacteristic
542#41—228no—
543#41—228no—
544#41—448no—
545C2×Q8—112no—
546C2×Q8—221no—
547C2×Q8—222no—
548C2×Q8—222no—
549C2×D4—112no—
550C2×D4—114no—
551C2×D4—224no—
552C2×D4—224no—
553C2×D4—224no—
554C2×D4—228no—
555C2×D4—228no—
556C2×D4—224no—
557C2×D4—222no—
558C2×D4—221no—
559C2×D4—224no—
560C2×D4—228no—
561C2×D4—222no—
562C2×D4—222no—
563C2×D4—224no—
564C2×D4—228no—
565C2×D4—4432no—
566C2×D4—448no—
567C2×D4—444no—
568C2×D4—448no—
569C2×D4—444no—
570C2×D4—444no—
571C2×D4—444no—
572C2×D4—448no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—216no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—28no—
580C22×C4—22no—
581C22×C4—28no—
582C22×C4—22no—
583C22×C4—224no—
584C22×C4—221no—
585C22×C4—221no—
586C22×C4—222no—
587C22×C4—221no—
588C22×C4—224no—
589C22×C4—444no—
590C22×C4—444no—
591C22×C4C2×D4414yes—
592C22×C4C2×D4414yes—
593C22×C4C2×D4414yes—
594C22×C4C2×D4412yes—
595C22×C4C2×D4412yes—
596C22×C4C2×D4411yescharacteristic
597C22×C4C2×D4411yescharacteristic
598C22×C4C2×D4412yes—
599C22×C4C2×D4411yescharacteristic
600C22×C4#433914yes—
601C22×C4C2×C22⋊D1114yes—
602C22×C4C23×D1112yes—
603C22×C4C23×D1112yes—
604C22×C4C23×D1112yes—
605C22×C4C23×D1111yescharacteristic
606SD16—2216no—
607D8—2216no—
608M16—28no—
609M16—216no—
610M16C2×C22⋊D11116yescomplemented
611C2×C8—24no—
612C2×C8—216no—
613C2×C8C2×C22⋊D1118yescomplemented
614C2×C8C23×D1114yes—
615C2×C8C23×D1114yes—
616C4⋊C4—112no—
617C4⋊C4—112no—
618C4⋊C4—114no—
619C4⋊C4—224no—
620C4⋊C4—222no—
621C4⋊C4—221no—
622C4⋊C4—221no—
623C4⋊C4—224no—
624C4⋊C4—224no—
625C22⋊C4—224no—
626C22⋊C4—224no—
627C22⋊C4—224no—
628C22⋊C4—228no—
629C22⋊C4—228no—
630C22⋊C4—224no—
631C22⋊C4—224no—
632C42—224no—
633C11C2×#305511yescharacteristic, complemented, Sylow
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—28no—
640C23—22no—
641C23—28no—
642C23—22no—
643C23—44no—
644C23—416no—
645C23—222no—
646C23—224no—
647C23—448no—
648C23—448no—
649C23—444no—
650C23—442no—
651C23—442no—
652C23—444no—
653C23—442no—
654C23—448no—
655C23—444no—
656C23—8816no—
657C23#6696114yescomplemented
658C23#6698314yes—
659C23C22×D4412yes—
660C23C22×D4412yes—
661C23C22×D4412yes—
662C23C22×D4411yescharacteristic
663Q8—222no—
664Q8—222no—
665Q8—442no—
666D4—224no—
667D4—222no—
668D4—222no—
669D4—224no—
670D4—4416no—
671D4—448no—
672D4—4416no—
673D4—448no—
674D4—448no—
675D4—448no—
676D4—444no—
677D4—442no—
678C2×C4—28no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—28no—
682C2×C4—28no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—222no—
690C2×C4—222no—
691C2×C4—224no—
692C2×C4—222no—
693C2×C4—448no—
694C2×C4—444no—
695C2×C4—442no—
696C2×C4—442no—
697C2×C4—442no—
698C2×C4—448no—
699C2×C4#6698314yes—
700C2×C4#6698318yes—
701C2×C4C22×D4412yes—
702C2×C4C22×D4412yes—
703C2×C4C22×D4412yes—
704C2×C4C22×D4411yescharacteristic
705C2×C4C2×#433912yes—
706C2×C4C2×#433914yes—
707C2×C4C22×C22⋊D1112yes—
708C2×C4C22×C22⋊D1114yes—
709C2×C4C24×D1111yescharacteristic
710C8—24no—
711C8C22×C22⋊D1118yescomplemented
712C22—22no—
713C22—28no—
714C22—28no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—416no—
722C22—44no—
723C22—444no—
724C22—442no—
725C22—442no—
726C22—444no—
727C22—442no—
728C22—444no—
729C22—8816no—
730C22—888no—
731C22—884no—
732C22C2×#6696112yes—
733C22C2×#6696114yescomplemented
734C22#1062327912yes—
735C22C2×#6698314yes—
736C22C2×#6698312yes—
737C22C23×D4411yescharacteristic
738C4—22no—
739C4—22no—
740C4—444no—
741C4—442no—
742C4—442no—
743C4—442no—
744C4C2×#6698314yes—
745C4C2×#6698312yes—
746C4C22×#433911yescharacteristic
747C4C23×C22⋊D1111yescharacteristic
748C2—24no—
749C2—24no—
750C2—42no—
751C2—884no—
752C2—882no—
753C2#1307823514yesdirect product factor
754C2C22×#6698311yescharacteristic
755C2C22×#6696111yescharacteristic
756C2C2×#1062327911yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC23×C11×M16C2
socleC23×C11C22×D4
hypercenterC23×M16D11
hypocenterC11C2×#3055
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C23×M16

Complements

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

NH ≅ G/Ntype
1. C22×#66961C2semidirect
2. C2×#10623322C2semidirect
3. C22×#66983C2semidirect
4. #13078235C2direct (N × H)
5. C2×#10622748C2semidirect
6. C2×#10622747C2semidirect
7. C2×#10622728C2semidirect
8. C2×#10622727C2semidirect
9. C2×#10622734C2semidirect
10. C2×#10622746C2semidirect
11. C2×#10622744C2semidirect
12. C23×C11×M16C2semidirect
20. C22×C11×M16C22semidirect
21. C22×C11×M16C22semidirect
22. C23×C8×C11C22semidirect
25. #10623322C22semidirect
31. C2×#66983C22semidirect
32. C2×#66983C22semidirect
33. C2×#66983C22semidirect
40. C2×#66977C22semidirect
41. C2×#66977C22semidirect
43. C2×#66961C22semidirect
44. C22×D88C22semidirect
45. C22×#4314C22semidirect
46. #10622748C22semidirect
47. #10622747C22semidirect
48. #10622746C22semidirect
49. #10622744C22semidirect
50. #10622734C22semidirect
51. #10622728C22semidirect
52. #10622727C22semidirect
53. C2×#66885C22semidirect
54. C2×#66885C22semidirect
55. C2×#66885C22semidirect
56. C2×#66882C22semidirect
57. C2×#66881C22semidirect
58. C2×#66880C22semidirect
95. C2×C11×M16D4semidirect
98. C2×C11×M16C23semidirect
102. C22×C8×C11C23semidirect
115. #66983C23semidirect
116. #66983C23semidirect
135. #66977C23semidirect
136. #66977C23semidirect
142. C2×D88C23semidirect
144. C2×#4314C23semidirect
145. #66885C23semidirect
146. #66885C23semidirect
147. #66885C23semidirect
148. #66882C23semidirect
149. #66881C23semidirect
150. #66880C23semidirect
231. C11×M16C2×D4semidirect
234. C2×C8×C11C2×D4semidirect
257. C23×M16D11semidirect
280. C23×C11AGL(1,ℤ/8)semidirect
345. C8×C11C22×D4semidirect
357. C22×M16C2×D11semidirect
358. C22×M16C2×D11semidirect
359. C23×C8C2×D11semidirect
406. C22×C11C2×AGL(1,ℤ/8)semidirect
469. C2×M16C22⋊D11semidirect
472. C2×M16C22×D11semidirect
476. C22×C8C22×D11semidirect
523. C2×C11#3055semidirect
610. M16C2×C22⋊D11semidirect
613. C2×C8C2×C22⋊D11semidirect
633. C11C2×#3055semidirect
657. C23#66961semidirect
711. C8C22×C22⋊D11semidirect
733. C22C2×#66961semidirect
753. C2#13078235direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669612
C2×#106233222
C22×#669832
#130782352
C2×#106227482
C2×#106227472
C2×#106227282
C2×#106227272
C2×#106227342
C2×#106227462
C2×#106227442
C23×C11×M162
C2×#305511