Finite Group Databasebeta

← C2×#13078126 #15620666

Subgroups — C2×#13078126 #15620666

Order 2816.

2882 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66964C211yesmaximal, characteristic
2C22×SD16×D11C211yesmaximal, characteristic, complemented
3C2×#10623206C211yesmaximal, characteristic, complemented
4C2×#10623076C211yesmaximal, characteristic, complemented
5#13078126C2116yesmaximal, direct product factor
6C2×#10622400C211yesmaximal, characteristic, complemented
7C2×#10622766C211yesmaximal, characteristic, complemented
8C2×#10622670C211yesmaximal, characteristic, complemented
9C2×#10622454C211yesmaximal, characteristic, complemented
10C2×#10622632C211yesmaximal, characteristic, complemented
11C2×#10622431C211yesmaximal, characteristic, complemented
12C2×#10622775C211yesmaximal, characteristic, complemented
13C2×#10622452C211yesmaximal, characteristic, complemented
14C2×#10622415C211yesmaximal, characteristic, complemented
15C2×#10622385C211yesmaximal, characteristic, complemented
16C2×C11×#463C211yesmaximal, characteristic, complemented
17C22×Q8×D11C2211yescharacteristic
18C22×#4341C2211yescharacteristic
19C22×D4×D11C2211yescharacteristic
20C22×C11×SD16C2211yescharacteristic
21C22×C11×D8C2211yescharacteristic
22C2×C11×#124C2211yescharacteristic, complemented
23C2×C4×D4×C11C2211yescharacteristic
24C2×#66997C2211yescharacteristic, complemented
25C22×#4325C2211yescharacteristic
26C2×#66989C2211yescharacteristic, complemented
27C2×D4×Dic11C2211yescharacteristic
28C22×#4324C2211yescharacteristic
29C22×#4324C2211yescharacteristic
30C22×#4323C2211yescharacteristic
31C2×C4×C22⋊D11—21no—
32C22×(C2×D11)⋊C4—21no—
33C2×SD16×D11—28no—
34C2×SD16×D11C2218yescomplemented
35C2×#66964—28no—
36C2×#66964C2218yes—
37C22×#4314C2211yescharacteristic
38C22×#4314C2211yescharacteristic
39C22×#4313C2211yescharacteristic
40C22×C8×D11C2211yescharacteristic
41#10623206—24no—
42#10623206C2218yescomplemented
43#10623076—24no—
44#10623076C2218yescomplemented
45C2×#66946C2211yescharacteristic
46C2×#66945C2211yescharacteristic
47C2×#66936—21no—
48C2×#66936—21no—
49C2×(C22⋊D11)⋊C4—21no—
50C2×C22⋊C4×D11—21no—
51C2×#66931—21no—
52C2×#66931—21no—
53C2×C4×D44C2211yescharacteristic
54C2×#66925C2211yescharacteristic
55C2×#66922C2211yescharacteristic, complemented
56C11×#463C2218yescomplemented
57C2×C11×C4⋊C8C2211yescharacteristic, complemented
58C2×C11×#103C2211yescharacteristic, complemented
59C2×C11×#102C2211yescharacteristic, complemented
60C2×#66899C2211yescharacteristic, complemented
61C2×#66896C2211yescharacteristic, complemented
62#10622775C2218yescomplemented
63#10622766C2218yescomplemented
64C2×#66880C2211yescharacteristic, complemented
65C2×#66880C2211yescharacteristic, complemented
66C2×Dic11⋊C8C2211yescharacteristic, complemented
67C2×Dic11⋊C8C2211yescharacteristic, complemented
68#10622670C2218yescomplemented
69#10622632C2218yescomplemented
70C2×#66874C2211yescharacteristic, complemented
71C2×#66874C2211yescharacteristic, complemented
72C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
73#10622454C2218yescomplemented
74#10622452C2218yescomplemented
75#10622431C2218yescomplemented
76#10622415C2218yescomplemented
77#10622400C2218yescomplemented
78#10622385C2218yescomplemented
79C24×D11—21no—
80C22×Q8×C11C2311yescharacteristic
81C22×D4×C11C2311yescharacteristic
82C22×D4×C11C2311yescharacteristic
83C23×C4×C11—21no—
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C23×Dic11—21no—
87C23×Dic11—21no—
88C2×Q8×D11—22no—
89C2×Q8×D11—24no—
90C2×Q8×D11—24no—
91C2×Q8×D11C2314yes—
92C2×#4341—24no—
93C2×#4341—22no—
94C2×#4341—24no—
95C2×#4341C2314yes—
96C2×D4×D11—22no—
97C2×D4×D11—24no—
98C2×D4×D11D418yes—
99C2×D4×D11C2314yes—
100C22×D44C2311yescharacteristic
101C22×C4×D11—21no—
102C22×C4×D11—21no—
103C22×C4×D11—21no—
104C22×C4×D11C2311yescharacteristic
105C22×Dic22—21no—
106C22×Dic22C2311yescharacteristic
107C22×Dic22C2311yescharacteristic
108C2×C11×SD16—24no—
109C2×C11×SD16C2314yes—
110C2×C11×D8—24no—
111C2×C11×D8C2314yes—
112C22×C8×C11C2311yescharacteristic
113C22×C8×C11C2311yescharacteristic
114C11×#124—22no—
115C11×#124C2314yescomplemented
116C4×D4×C11—22no—
117C4×D4×C11C2314yes—
118C2×C11×C4⋊C4C2311yescharacteristic
119C2×C11×C22⋊C4—21no—
120C2×C11×C22⋊C4—21no—
121C2×C11×C22⋊C4—21no—
122C2×C42×C11C2311yescharacteristic
123C2×C22⋊Dic11—21no—
124C2×C22⋊Dic11—21no—
125C2×C22⋊Dic11—21no—
126#66997—22no—
127#66997C2314yescomplemented
128C2×#4325—24no—
129C2×#4325C2314yes—
130#66989—22no—
131#66989C2314yescomplemented
132D4×Dic11—22no—
133D4×Dic11C2314yes—
134C2×#4324—24no—
135C2×#4324—24no—
136C2×#4324C2314yes—
137C2×#4324C2314yes—
138C2×#4323—24no—
139C2×#4323C2314yes—
140C4×C22⋊D11—28no—
141C2×(C2×D11)⋊C4—21no—
142C2×(C2×D11)⋊C4—21no—
143C2×(C2×D11)⋊C4—21no—
144C2×(C2×D11)⋊C4—28no—
145C2×(C2×D11)⋊C4D411yescharacteristic
146C2×(C2×D11)⋊C4D411yescharacteristic
147C2×C4⋊Dic11—21no—
148C2×C4⋊Dic11—21no—
149C2×C4⋊Dic11C2311yescharacteristic
150C2×Dic11⋊C4—21no—
151C2×Dic11⋊C4—21no—
152C2×Dic11⋊C4D411yescharacteristic
153C2×Dic11⋊C4D411yescharacteristic
154C2×C4×Dic11—21no—
155C2×C4×Dic11C2311yescharacteristic
156C22×C11⋊C8C2311yescharacteristic
157C22×C11⋊C8C2311yescharacteristic
158SD16×D11—232no—
159#66964—232no—
160C2×#4314—24no—
161C2×#4314—24no—
162C2×#4314C2314yes—
163C2×#4314C2314yes—
164C2×#4313—24no—
165C2×#4313C2314yes—
166C2×C8×D11—24no—
167C2×C8×D11C2314yes—
168#66946—22no—
169#66946C2314yes—
170#66945—22no—
171#66945C2314yes—
172#66936—28no—
173#66936—28no—
174(C22⋊D11)⋊C4—28no—
175C22⋊C4×D11—28no—
176#66931—28no—
177#66931—28no—
178C4×D44—22no—
179C4×D44C2314yes—
180#66925D414yes—
181#66925C2314yes—
182#66922—22no—
183#66922C2314yescomplemented
184C11×C4⋊C8C2314yescomplemented
185C11×#103C2314yescomplemented
186C11×#102C2314yescomplemented
187#66899C2314yescomplemented
188#66896C2314yescomplemented
189#66880C2314yescomplemented
190#66880C2314yescomplemented
191Dic11⋊C8C2314yescomplemented
192Dic11⋊C8C2314yescomplemented
193#66874C2314yescomplemented
194#66874C2314yescomplemented
195C4⋊(C11⋊C8)C2314yescomplemented
196C2×#3042—111nomaximal, Sylow
197C24×C11—21no—
198C24×C11—21no—
199C23×D11—21no—
200C23×D11—28no—
201C23×D11—24no—
202C23×D11—82no—
203C23×D11—82no—
204C23×D11C2×D411yescharacteristic
205C2×Q8×C11—21no—
206C2×Q8×C11—22no—
207C2×Q8×C11—22no—
208C2×Q8×C11C2412yes—
209C2×D4×C11—21no—
210C2×D4×C11—22no—
211C2×D4×C11—21no—
212C2×D4×C11—22no—
213C2×D4×C11—22no—
214C2×D4×C11C2×D414yes—
215C2×D4×C11C2412yes—
216C2×D4×C11C2412yes—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—24no—
220C22×C4×C11—82no—
221C22×C4×C11C2×D411yescharacteristic
222C22×C4×C11C2×D411yescharacteristic
223C22×C4×C11C2411yescharacteristic
224C2×C22⋊D11—28no—
225C2×C22⋊D11—24no—
226C2×C22⋊D11—24no—
227C2×C22⋊D11—44no—
228C22×Dic11—24no—
229C22×Dic11—24no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—21no—
233C22×Dic11—44no—
234C22×Dic11—82no—
235C22×Dic11C2×D411yescharacteristic
236C22×Dic11C2×D411yescharacteristic
237C22×Dic11C2×D411yescharacteristic
238Q8×D11—28no—
239Q8×D11—28no—
240Q8×D11—48no—
241#4341—28no—
242#4341—28no—
243#4341—48no—
244D4×D11—216no—
245D4×D11—28no—
246D4×D11C2×D4116yes—
247C2×D44—21no—
248C2×D44—22no—
249C2×D44C2×D414yes—
250C2×D44C2412yes—
251C2×C4×D11—24no—
252C2×C4×D11—24no—
253C2×C4×D11—24no—
254C2×C4×D11—44no—
255C2×C4×D11—82no—
256C2×C4×D11—82no—
257C2×C4×D11C2×D414yes—
258C2×C4×D11C2×D412yes—
259C2×C4×D11#4114yes—
260C2×C4×D11C2412yes—
261C2×Dic22—24no—
262C2×Dic22—22no—
263C2×Dic22—22no—
264C2×Dic22—21no—
265C2×Dic22—21no—
266C2×Dic22—22no—
267C2×Dic22—22no—
268C2×Dic22—44no—
269C2×Dic22C2412yes—
270C2×Dic22C2412yes—
271C11×SD16—28no—
272C11×D8—28no—
273C2×C8×C11—22no—
274C2×C8×C11—22no—
275C2×C8×C11C2412yes—
276C2×C8×C11C2412yes—
277C11×C4⋊C4—21no—
278C11×C4⋊C4C2412yes—
279C11×C22⋊C4—24no—
280C11×C22⋊C4—24no—
281C11×C22⋊C4—24no—
282C42×C11C2×D412yes—
283C42×C11C2412yes—
284C22⋊Dic11—24no—
285C22⋊Dic11—24no—
286C22⋊Dic11—24no—
287#4325—28no—
288#4324—28no—
289#4324—28no—
290#4323—28no—
291(C2×D11)⋊C4—24no—
292(C2×D11)⋊C4—24no—
293(C2×D11)⋊C4—24no—
294(C2×D11)⋊C4C2×D414yes—
295(C2×D11)⋊C4C2×D414yes—
296C4⋊Dic11—24no—
297C4⋊Dic11—24no—
298C4⋊Dic11—21no—
299C4⋊Dic11C2412yes—
300Dic11⋊C4—24no—
301Dic11⋊C4—24no—
302Dic11⋊C4C2×D414yes—
303Dic11⋊C4C2×D414yes—
304C4×Dic11—24no—
305C4×Dic11C2×D412yes—
306C4×Dic11C2412yes—
307C2×C11⋊C8—22no—
308C2×C11⋊C8—22no—
309C2×C11⋊C8C2412yes—
310C2×C11⋊C8C2412yes—
311#4314—28no—
312#4314—28no—
313#4313—28no—
314C8×D11—28no—
315C22×AGL(1,ℤ/8)—111no—
316C23×SD16—111no—
317C2×#536—111no—
318C2×#518—111no—
319#3042—1116no—
320C2×#463—111no—
321C2×#463—111no—
322C2×#463—111no—
323C2×#463D1111yescharacteristic, complemented
324C2×#461—111no—
325C2×#461—111no—
326C2×#461—111no—
327C2×#461—111no—
328C2×#424—111no—
329C2×#419—111no—
330C2×#416—111no—
331C23×C11—24no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11—42no—
335C23×C11—42no—
336C23×C11—42no—
337C23×C11—42no—
338C23×C11—42no—
339C23×C11C22×D411yescharacteristic
340C22×D11—22no—
341C22×D11—22no—
342C22×D11—24no—
343C22×D11—22no—
344C22×D11—216no—
345C22×D11—42no—
346C22×D11—42no—
347C22×D11—816no—
348C22×D11—84no—
349C22×D11—84no—
350C22×D11#12114yes—
351C22×D11C22×D412yes—
352Q8×C11—22no—
353Q8×C11—22no—
354Q8×C11—42no—
355D4×C11—24no—
356D4×C11—22no—
357D4×C11—22no—
358D4×C11—22no—
359D4×C11—42no—
360D4×C11C22×D414yes—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—42no—
366C2×C4×C11—42no—
367C2×C4×C11—84no—
368C2×C4×C11C22×D412yes—
369C2×C4×C11C22×D412yes—
370C2×C4×C11C22×D411yescharacteristic
371C2×C4×C11C22×D412yes—
372C2×C4×C11C2×#4112yes—
373C2×C4×C11C2511yescharacteristic
374C22⋊D11—216no—
375C22⋊D11—48no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—42no—
382C2×Dic11—42no—
383C2×Dic11—42no—
384C2×Dic11—48no—
385C2×Dic11—84no—
386C2×Dic11#12114yes—
387C2×Dic11C22×D412yes—
388C2×Dic11C22×D412yes—
389C2×Dic11C22×D412yes—
390D44—24no—
391D44—22no—
392D44C22×D414yes—
393C4×D11—48no—
394C4×D11—84no—
395C4×D11—84no—
396C4×D11#12118yes—
397C4×D11C22×D414yes—
398C4×D11C2×#4114yes—
399Dic22—22no—
400Dic22—22no—
401Dic22—22no—
402Dic22—22no—
403Dic22—42no—
404Dic22—42no—
405Dic22—48no—
406C8×C11—22no—
407C8×C11—22no—
408C11⋊C8—22no—
409C11⋊C8—22no—
410C22×#41—111no—
411C23×Q8—111no—
412C23×D4—111no—
413C2×AGL(1,ℤ/8)—118no—
414C2×AGL(1,ℤ/8)—228no—
415C22×SD16—111no—
416C22×SD16—111no—
417C22×SD16—111no—
418C22×SD16—118no—
419C22×SD16—111no—
420C22×SD16—111no—
421C22×SD16—228no—
422C22×SD16C2×D1111yescharacteristic
423C22×D8—111no—
424C22×D8C2×D1111yescharacteristic
425C22×M16—111no—
426C23×C8—111no—
427#536—118no—
428#536—224no—
429C2×C4⋊Q8—111no—
430C2×C4⋊Q8—111no—
431C2×#124—111no—
432C2×#124C2×D1111yescharacteristic, complemented
433C2×#123—221no—
434C2×#123—221no—
435C2×C22⋊Q8—221no—
436C2×C22⋊Q8—221no—
437#518—118no—
438#518—224no—
439C2×C4×D4—111no—
440C2×C4×D4—111no—
441C2×C4×D4—111no—
442C2×C4×D4—221no—
443C2×C4×D4—221no—
444C2×C4×D4C2×D1111yescharacteristic
445C2×#117—111no—
446C2×#117—111no—
447C22×C22⋊C4—221no—
448C22×C22⋊C4—221no—
449#463—118no—
450#463—118no—
451#463—118no—
452#463C2×D1118yescomplemented
453#461—118no—
454#461—118no—
455#461—118no—
456#461—118no—
457#424—118no—
458C2×C4⋊C8—111no—
459C2×C4⋊C8—111no—
460C2×C4⋊C8—111no—
461C2×C4⋊C8C2×D1111yescharacteristic, complemented
462#419—118no—
463#416—118no—
464C2×#103—111no—
465C2×#103—111no—
466C2×#103—111no—
467C2×#103—111no—
468C2×#103—111no—
469C2×#103C2×D1111yescharacteristic, complemented
470C2×#102—111no—
471C2×#102C2×D1111yescharacteristic, complemented
472C22×C11—24no—
473C22×C11—48no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11—42no—
477C22×C11—42no—
478C22×C11—42no—
479C22×C11—84no—
480C22×C11C2×#12112yes—
481C22×C11#57712yes—
482C22×C11#57712yes—
483C22×C11C23×D411yescharacteristic
484C2×D11—28no—
485C2×D11—22no—
486C2×D11—22no—
487C2×D11—24no—
488C2×D11—48no—
489C2×D11—42no—
490C2×D11—42no—
491C2×D11—816no—
492C2×D11C2×#12114yes—
493C4×C11—22no—
494C4×C11—22no—
495C4×C11—42no—
496C4×C11—42no—
497C4×C11C2×#12112yes—
498C4×C11C23×D411yescharacteristic
499C4×C11C22×#4111yescharacteristic
500Dic11—22no—
501Dic11—22no—
502Dic11—42no—
503Dic11—42no—
504Dic11—42no—
505Dic11C2×#12114yes—
506C25—221no—
507C2×#41—114no—
508C2×#41—222no—
509C2×#41—224no—
510C2×#41—224no—
511C22×Q8—114no—
512C22×Q8—111no—
513C22×Q8—111no—
514C22×Q8—221no—
515C22×Q8—222no—
516C22×Q8—224no—
517C22×Q8—224no—
518C22×Q8C22×D1111yescharacteristic
519C22×D4—118no—
520C22×D4—114no—
521C22×D4—111no—
522C22×D4—222no—
523C22×D4—224no—
524C22×D4—221no—
525C22×D4—221no—
526C22×D4C22×D1111yescharacteristic
527C22×D4C22×D1111yescharacteristic
528C23×C4—21no—
529C23×C4—111no—
530C23×C4—221no—
531C23×C4—221no—
532C23×C4—221no—
533C23×C4—221no—
534C23×C4—221no—
535AGL(1,ℤ/8)—2232no—
536C2×SD16—24no—
537C2×SD16—114no—
538C2×SD16—114no—
539C2×SD16—114no—
540C2×SD16—114no—
541C2×SD16—114no—
542C2×SD16—224no—
543C2×SD16—224no—
544C2×SD16—2232no—
545C2×SD16—224no—
546C2×SD16—224no—
547C2×SD16—224no—
548C2×SD16C22×D1114yes—
549C2×D8—24no—
550C2×D8—114no—
551C2×D8—224no—
552C2×D8C22×D1114yes—
553C2×M16—114no—
554C2×M16—224no—
555C22×C8—111no—
556C22×C8—111no—
557C22×C8—114no—
558C22×C8—224no—
559C22×C8C22×D1111yescharacteristic
560C22×C8C22×D1111yescharacteristic
561C4⋊Q8—114no—
562C4⋊Q8—114no—
563C4⋊Q8—222no—
564C4⋊Q8—222no—
565#124—22no—
566#124—114no—
567#124—222no—
568#124C22×D1114yescomplemented
569#123—228no—
570#123—228no—
571C22⋊Q8—228no—
572C22⋊Q8—228no—
573C4×D4—22no—
574C4×D4—114no—
575C4×D4—114no—
576C4×D4—114no—
577C4×D4—222no—
578C4×D4—222no—
579C4×D4—228no—
580C4×D4—228no—
581C4×D4—222no—
582C4×D4C22×D1114yes—
583#117—114no—
584#117—114no—
585#117—114no—
586#117—222no—
587C2×C4⋊C4—111no—
588C2×C4⋊C4—111no—
589C2×C4⋊C4—111no—
590C2×C4⋊C4—221no—
591C2×C4⋊C4—221no—
592C2×C4⋊C4—221no—
593C2×C4⋊C4—221no—
594C2×C4⋊C4C22×D1111yescharacteristic
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—111no—
599C2×C22⋊C4—111no—
600C2×C22⋊C4—228no—
601C2×C22⋊C4—228no—
602C2×C22⋊C4—221no—
603C2×C22⋊C4—221no—
604C2×C22⋊C4—221no—
605C2×C22⋊C4—221no—
606C2×C22⋊C4—221no—
607C2×C22⋊C4—221no—
608C2×C42—111no—
609C2×C42—221no—
610C2×C42C22×D1111yescharacteristic
611C4⋊C8—114no—
612C4⋊C8—114no—
613C4⋊C8—114no—
614C4⋊C8C22×D1114yescomplemented
615#103—114no—
616#103—114no—
617#103—114no—
618#103—114no—
619#103—114no—
620#103C22×D1114yescomplemented
621#102—114no—
622#102C22×D1114yescomplemented
623C2×C11—44no—
624C2×C11—82no—
625C2×C11#304214yescomplemented
626C2×C11C22×#12111yescharacteristic
627C2×C11C2×#57711yescharacteristic
628C2×C11C2×#57711yescharacteristic
629D11—24no—
630D11—44no—
631C24—21no—
632C24—21no—
633C24—111no—
634C24—224no—
635C24—228no—
636C24—221no—
637C24—882no—
638C24—882no—
639#41—228no—
640#41—228no—
641#41—448no—
642C2×Q8—21no—
643C2×Q8—22no—
644C2×Q8—22no—
645C2×Q8—112no—
646C2×Q8—112no—
647C2×Q8—224no—
648C2×Q8—228no—
649C2×Q8—228no—
650C2×Q8—221no—
651C2×Q8—221no—
652C2×Q8—222no—
653C2×Q8—222no—
654C2×Q8—222no—
655C2×Q8—222no—
656C2×Q8—444no—
657C2×Q8—448no—
658C2×Q8C23×D1112yes—
659C2×D4—21no—
660C2×D4—22no—
661C2×D4—21no—
662C2×D4—22no—
663C2×D4—22no—
664C2×D4—1116no—
665C2×D4—114no—
666C2×D4—112no—
667C2×D4—2216no—
668C2×D4—228no—
669C2×D4—224no—
670C2×D4—228no—
671C2×D4—224no—
672C2×D4—221no—
673C2×D4—222no—
674C2×D4—444no—
675C2×D4D4×D1114yes—
676C2×D4C23×D1112yes—
677C2×D4C23×D1112yes—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—24no—
681C22×C4—82no—
682C22×C4—111no—
683C22×C4—112no—
684C22×C4—114no—
685C22×C4—114no—
686C22×C4—112no—
687C22×C4—111no—
688C22×C4—111no—
689C22×C4—224no—
690C22×C4—224no—
691C22×C4—224no—
692C22×C4—224no—
693C22×C4—221no—
694C22×C4—221no—
695C22×C4—221no—
696C22×C4—224no—
697C22×C4—444no—
698C22×C4—444no—
699C22×C4—882no—
700C22×C4—882no—
701C22×C4—882no—
702C22×C4D4×D1111yescharacteristic
703C22×C4D4×D1111yescharacteristic
704C22×C4C23×D1111yescharacteristic
705SD16—28no—
706SD16—228no—
707SD16—228no—
708SD16—228no—
709SD16—228no—
710SD16—228no—
711D8—28no—
712D8—228no—
713M16—228no—
714C2×C8—22no—
715C2×C8—22no—
716C2×C8—112no—
717C2×C8—112no—
718C2×C8—228no—
719C2×C8—222no—
720C2×C8—222no—
721C2×C8C23×D1112yes—
722C2×C8C23×D1112yes—
723C4⋊C4—21no—
724C4⋊C4—114no—
725C4⋊C4—114no—
726C4⋊C4—112no—
727C4⋊C4—224no—
728C4⋊C4—224no—
729C4⋊C4—221no—
730C4⋊C4—224no—
731C4⋊C4—224no—
732C4⋊C4C23×D1112yes—
733C22⋊C4—24no—
734C22⋊C4—24no—
735C22⋊C4—24no—
736C22⋊C4—114no—
737C22⋊C4—114no—
738C22⋊C4—224no—
739C22⋊C4—224no—
740C22⋊C4—224no—
741C22⋊C4—224no—
742C22⋊C4—224no—
743C22⋊C4—224no—
744C42—112no—
745C42—112no—
746C42—224no—
747C42D4×D1112yes—
748C42C23×D1112yes—
749C11C2×#304211yescharacteristic, complemented, Sylow
750C23—24no—
751C23—22no—
752C23—22no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—114no—
759C23—112no—
760C23—2216no—
761C23—222no—
762C23—222no—
763C23—224no—
764C23—222no—
765C23—442no—
766C23—442no—
767C23—8816no—
768C23—884no—
769C23—884no—
770C23C2×D4×D1111yescharacteristic
771Q8—22no—
772Q8—22no—
773Q8—42no—
774Q8—222no—
775Q8—222no—
776Q8—222no—
777Q8—222no—
778Q8—448no—
779Q8—442no—
780Q8—442no—
781D4—24no—
782D4—22no—
783D4—22no—
784D4—22no—
785D4—42no—
786D4—114no—
787D4—2216no—
788D4—224no—
789D4—222no—
790D4—448no—
791D4C2×D4×D1114yes—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—84no—
799C2×C4—114no—
800C2×C4—112no—
801C2×C4—118no—
802C2×C4—114no—
803C2×C4—114no—
804C2×C4—112no—
805C2×C4—112no—
806C2×C4—222no—
807C2×C4—222no—
808C2×C4—222no—
809C2×C4—222no—
810C2×C4—222no—
811C2×C4—448no—
812C2×C4—448no—
813C2×C4—442no—
814C2×C4—442no—
815C2×C4—442no—
816C2×C4—884no—
817C2×C4—884no—
818C2×C4—884no—
819C2×C4C2×D4×D1112yes—
820C2×C4C2×D4×D1112yes—
821C2×C4C2×D4×D1111yescharacteristic
822C2×C4C2×D4×D1112yes—
823C2×C4#41×D1112yes—
824C2×C4C24×D1111yescharacteristic
825C8—22no—
826C8—22no—
827C8—222no—
828C8—222no—
829C22—24no—
830C22—48no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—84no—
837C22—114no—
838C22—228no—
839C22—222no—
840C22—222no—
841C22—224no—
842C22—448no—
843C22—442no—
844C22—442no—
845C22—8816no—
846C22D11×#12112yes—
847C22#1062330112yes—
848C22#1062330612yes—
849C22C22×D4×D1111yescharacteristic
850C4—22no—
851C4—22no—
852C4—42no—
853C4—42no—
854C4—114no—
855C4—222no—
856C4—222no—
857C4—442no—
858C4—442no—
859C4—442no—
860C4D11×#12112yes—
861C4C22×D4×D1111yescharacteristic
862C4C2×#41×D1111yescharacteristic
863C2—44no—
864C2—82no—
865C2—224no—
866C2—444no—
867C2#1307812614yesdirect product factor
868C2C2×D11×#12111yescharacteristic
869C2C2×#1062330111yescharacteristic
870C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#463C2
socleC23×C11C22×D4
prime radicalC22×#66964C2
hypercenterC2×#463D11
hypocenterC11C2×#3042
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
2. C22×SD16×D11C2semidirect
3. C2×#10623206C2semidirect
4. C2×#10623076C2semidirect
5. #13078126C2direct (N × H)
6. C2×#10622400C2semidirect
7. C2×#10622766C2semidirect
8. C2×#10622670C2semidirect
9. C2×#10622454C2semidirect
10. C2×#10622632C2semidirect
11. C2×#10622431C2semidirect
12. C2×#10622775C2semidirect
13. C2×#10622452C2semidirect
14. C2×#10622415C2semidirect
15. C2×#10622385C2semidirect
16. C2×C11×#463C2semidirect
22. C2×C11×#124C22semidirect
24. C2×#66997C22semidirect
26. C2×#66989C22semidirect
34. C2×SD16×D11C22semidirect
42. #10623206C22semidirect
44. #10623076C22semidirect
55. C2×#66922C22semidirect
56. C11×#463C22semidirect
57. C2×C11×C4⋊C8C22semidirect
58. C2×C11×#103C22semidirect
59. C2×C11×#102C22semidirect
60. C2×#66899C22semidirect
61. C2×#66896C22semidirect
62. #10622775C22semidirect
63. #10622766C22semidirect
64. C2×#66880C22semidirect
65. C2×#66880C22semidirect
66. C2×Dic11⋊C8C22semidirect
67. C2×Dic11⋊C8C22semidirect
68. #10622670C22semidirect
69. #10622632C22semidirect
70. C2×#66874C22semidirect
71. C2×#66874C22semidirect
72. C2×C4⋊(C11⋊C8)C22semidirect
73. #10622454C22semidirect
74. #10622452C22semidirect
75. #10622431C22semidirect
76. #10622415C22semidirect
77. #10622400C22semidirect
78. #10622385C22semidirect
115. C11×#124C23semidirect
127. #66997C23semidirect
131. #66989C23semidirect
183. #66922C23semidirect
184. C11×C4⋊C8C23semidirect
185. C11×#103C23semidirect
186. C11×#102C23semidirect
187. #66899C23semidirect
188. #66896C23semidirect
189. #66880C23semidirect
190. #66880C23semidirect
191. Dic11⋊C8C23semidirect
192. Dic11⋊C8C23semidirect
193. #66874C23semidirect
194. #66874C23semidirect
195. C4⋊(C11⋊C8)C23semidirect
323. C2×#463D11semidirect
432. C2×#124C2×D11semidirect
452. #463C2×D11semidirect
461. C2×C4⋊C8C2×D11semidirect
469. C2×#103C2×D11semidirect
471. C2×#102C2×D11semidirect
568. #124C22×D11semidirect
614. C4⋊C8C22×D11semidirect
620. #103C22×D11semidirect
622. #102C22×D11semidirect
625. C2×C11#3042semidirect
749. C11C2×#3042semidirect
867. C2#13078126direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669642
C22×SD16×D112
C2×#106232062
C2×#106230762
#130781262
C2×#106224002
C2×#106227662
C2×#106226702
C2×#106224542
C2×#106226322
C2×#106224312
C2×#106227752
C2×#106224522
C2×#106224152
C2×#106223852
C2×C11×#4632
C2×#304211