Finite Group Databasebeta

← C2×#13078105 #15620632

Subgroups — C2×#13078105 #15620632

Order 2816.

2918 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×#66968C211yesmaximal, characteristic, complemented
2C22×#66964C211yesmaximal, characteristic
3C2×D11×#124C211yesmaximal, characteristic, complemented
4C2×C4×#4341C211yesmaximal, characteristic, complemented
5#13078105C2116yesmaximal, direct product factor
6C2×#10622411C211yesmaximal, characteristic, complemented
7C2×#10622458C211yesmaximal, characteristic, complemented
8C2×#10622380C211yesmaximal, characteristic, complemented
9C2×#10622667C211yesmaximal, characteristic, complemented
10C2×#10622778C211yesmaximal, characteristic, complemented
11C2×#10622629C211yesmaximal, characteristic, complemented
12C2×#10622766C211yesmaximal, characteristic, complemented
13C2×#10622450C211yesmaximal, characteristic, complemented
14C2×#10622415C211yesmaximal, characteristic, complemented
15C2×#10622383C211yesmaximal, characteristic, complemented
16C2×C11×#463C211yesmaximal, characteristic, complemented
17C22×Q8×D11C2211yescharacteristic
18C22×#4341C2211yescharacteristic
19C22×D4×D11C2211yescharacteristic
20C22×C11×SD16C2211yescharacteristic, complemented
21C22×C11×D8C2211yescharacteristic
22C2×C11×#124C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic, complemented
24C2×#67000C2211yescharacteristic
25C22×#4326C2211yescharacteristic, complemented
26C2×#66989C2211yescharacteristic
27C2×D4×Dic11C2211yescharacteristic, complemented
28C22×#4324C2211yescharacteristic
29C22×#4324C2211yescharacteristic, complemented
30C22×#4323C2211yescharacteristic
31C2×C4×C22⋊D11—21no—
32C22×C4×Dic11—21no—
33C2×#66968—28no—
34C2×#66968C2218yescomplemented
35C2×#66964—28no—
36C2×#66964C2218yes—
37C22×Dic44C2211yescharacteristic, complemented
38C22×#4314C2211yescharacteristic
39C22×#4313C2211yescharacteristic
40C22×#4313C2211yescharacteristic
41D11×#124—24no—
42D11×#124C2218yescomplemented
43C4×#4341—24no—
44C4×#4341C2218yescomplemented
45C2×#66945C2211yescharacteristic
46C2×#66940C2211yescharacteristic, complemented
47C2×#66938—21no—
48C2×#66938—21no—
49C2×(C22⋊D11)⋊C4—21no—
50C2×C22⋊C4×D11—21no—
51C2×C22⋊C4×D11—21no—
52C2×#66930—21no—
53C2×#66928C2211yescharacteristic
54C2×C42×D11C2211yescharacteristic
55C2×C4×Dic22C2211yescharacteristic, complemented
56C11×#463C2218yescomplemented
57C2×C11×C4⋊C8C2211yescharacteristic, complemented
58C2×C11×#103C2211yescharacteristic, complemented
59C2×C11×#102C2211yescharacteristic
60C2×#66899C2211yescharacteristic, complemented
61C2×#66896C2211yescharacteristic
62#10622778C2218yescomplemented
63#10622766C2218yescomplemented
64C2×#66885C2211yescharacteristic
65C2×#66880C2211yescharacteristic, complemented
66C2×Dic11⋊C8C2211yescharacteristic, complemented
67C2×Dic11⋊C8C2211yescharacteristic, complemented
68#10622667C2218yescomplemented
69#10622629C2218yescomplemented
70C2×#66874C2211yescharacteristic, complemented
71C2×#66873C2211yescharacteristic
72C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
73#10622458C2218yescomplemented
74#10622450C2218yescomplemented
75#10622415C2218yescomplemented
76#10622411C2218yescomplemented
77#10622383C2218yescomplemented
78#10622380C2218yescomplemented
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—22no—
93C2×#4341—24no—
94C2×#4341D418yes—
95C2×#4341C2314yes—
96C2×D4×D11—24no—
97C2×D4×D11—22no—
98C2×D4×D11—24no—
99C2×D4×D11C2314yes—
100C22×D44C2311yescharacteristic
101C22×C4×D11—21no—
102C22×C4×D11D411yescharacteristic
103C22×C4×D11D411yescharacteristic
104C22×C4×D11C2311yescharacteristic
105C22×Dic22—21no—
106C22×Dic22C2311yescharacteristic
107C22×Dic22C2311yescharacteristic
108C2×C11×SD16—24no—
109C2×C11×SD16C2314yescomplemented
110C2×C11×D8—24no—
111C2×C11×D8C2314yes—
112C22×C8×C11C2311yescharacteristic
113C22×C8×C11C2311yescharacteristic
114C11×#124—22no—
115C11×#124C2314yes—
116C4×D4×C11—22no—
117C4×D4×C11C2314yescomplemented
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#67000—22no—
127#67000C2314yes—
128C2×#4326—24no—
129C2×#4326C2314yescomplemented
130#66989—22no—
131#66989C2314yes—
132D4×Dic11—22no—
133D4×Dic11C2314yescomplemented
134C2×#4324—24no—
135C2×#4324—24no—
136C2×#4324C2314yes—
137C2×#4324C2314yescomplemented
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—21no—
145C2×(C2×D11)⋊C4—21no—
146C2×C4⋊Dic11C2311yescharacteristic
147C2×Dic11⋊C4—21no—
148C2×Dic11⋊C4—21no—
149C2×C4×Dic11—21no—
150C2×C4×Dic11—21no—
151C2×C4×Dic11—21no—
152C2×C4×Dic11—28no—
153C2×C4×Dic11D411yescharacteristic
154C2×C4×Dic11D411yescharacteristic
155C2×C4×Dic11C2311yescharacteristic
156C22×C11⋊C8C2311yescharacteristic
157C22×C11⋊C8C2311yescharacteristic
158#66968—232no—
159#66964—232no—
160C2×Dic44—24no—
161C2×Dic44C2314yescomplemented
162C2×#4314—24no—
163C2×#4314C2314yes—
164C2×#4313—24no—
165C2×#4313—24no—
166C2×#4313C2314yes—
167C2×#4313C2314yes—
168#66945—22no—
169#66945C2314yes—
170#66940—22no—
171#66940C2314yescomplemented
172#66938—28no—
173#66938—28no—
174(C22⋊D11)⋊C4—28no—
175C22⋊C4×D11—28no—
176C22⋊C4×D11—28no—
177#66930—28no—
178#66928—22no—
179#66928C2314yes—
180C42×D11D414yes—
181C42×D11C2314yes—
182C4×Dic22—22no—
183C4×Dic22C2314yescomplemented
184C11×C4⋊C8C2314yescomplemented
185C11×#103C2314yescomplemented
186C11×#102C2314yes—
187#66899C2314yescomplemented
188#66896C2314yes—
189#66885C2314yes—
190#66880C2314yescomplemented
191Dic11⋊C8C2314yescomplemented
192Dic11⋊C8C2314yescomplemented
193#66874C2314yescomplemented
194#66873C2314yes—
195C4⋊(C11⋊C8)C2314yescomplemented
196C2×#3040—111nomaximal, Sylow
197C24×C11—21no—
198C24×C11—21no—
199C23×D11—21no—
200C23×D11—24no—
201C23×D11—44no—
202C23×D11—44no—
203C23×D11—44no—
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—44no—
221C22×C4×C11C2×D411yescharacteristic
222C22×C4×C11C2×D411yescharacteristic
223C22×C4×C11C2411yescharacteristic
224C2×C22⋊D11—24no—
225C2×C22⋊D11—28no—
226C2×C22⋊D11—24no—
227C2×C22⋊D11—44no—
228C22×Dic11—28no—
229C22×Dic11—24no—
230C22×Dic11—24no—
231C22×Dic11—21no—
232C22×Dic11—21no—
233C22×Dic11—21no—
234C22×Dic11—44no—
235C22×Dic11C2×D411yescharacteristic
236C22×Dic11C2×D411yescharacteristic
237C22×Dic11C2×D411yescharacteristic
238Q8×D11—28no—
239Q8×D11—28no—
240Q8×D11—48no—
241#4341—216no—
242#4341—28no—
243#4341C2×D4116yes—
244D4×D11—28no—
245D4×D11—28no—
246D4×D11—48no—
247C2×D44—21no—
248C2×D44—22no—
249C2×D44—22no—
250C2×D44C2412yes—
251C2×C4×D11—24no—
252C2×C4×D11—42no—
253C2×C4×D11—42no—
254C2×C4×D11—44no—
255C2×C4×D11C2×D414yes—
256C2×C4×D11C2×D414yes—
257C2×C4×D11C2×D414yes—
258C2×C4×D11C2×D412yes—
259C2×C4×D11#4114yes—
260C2×C4×D11C2412yes—
261C2×Dic22—24no—
262C2×Dic22—21no—
263C2×Dic22—22no—
264C2×Dic22—21no—
265C2×Dic22—22no—
266C2×Dic22—22no—
267C2×Dic22—44no—
268C2×Dic22C2×D414yes—
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#4326—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)⋊C4—24no—
295(C2×D11)⋊C4—24no—
296C4⋊Dic11—21no—
297C4⋊Dic11C2412yes—
298Dic11⋊C4—24no—
299Dic11⋊C4—24no—
300C4×Dic11—24no—
301C4×Dic11—24no—
302C4×Dic11—24no—
303C4×Dic11C2×D412yes—
304C4×Dic11C2×D414yes—
305C4×Dic11C2×D414yes—
306C4×Dic11C2412yes—
307C2×C11⋊C8—22no—
308C2×C11⋊C8—22no—
309C2×C11⋊C8C2412yes—
310C2×C11⋊C8C2412yes—
311Dic44—28no—
312#4314—28no—
313#4313—28no—
314#4313—28no—
315C22×#137—111no—
316C22×AGL(1,ℤ/8)—111no—
317C22×#124—111no—
318C2×C4×#41—111no—
319#3040—1116no—
320C2×#464—111no—
321C2×#464—111no—
322C2×#464—111no—
323C2×#464—111no—
324C2×#463—111no—
325C2×#463—111no—
326C2×#463—111no—
327C2×#463D1111yescharacteristic, complemented
328C2×#423—111no—
329C2×#419—111no—
330C2×#418—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—22no—
343C22×D11—48no—
344C22×D11—48no—
345C22×D11—42no—
346C22×D11—42no—
347C22×D11—42no—
348C22×D11—48no—
349C22×D11—816no—
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—48no—
366C2×C4×C11—42no—
367C2×C4×C11—42no—
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—24no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—216no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—48no—
384C2×Dic11—42no—
385C2×Dic11—42no—
386C2×Dic11#12114yes—
387C2×Dic11C22×D412yes—
388C2×Dic11C22×D412yes—
389C2×Dic11C22×D412yes—
390D44—22no—
391D44—22no—
392D44—42no—
393C4×D11—44no—
394C4×D11—44no—
395C4×D11—48no—
396C4×D11#12118yes—
397C4×D11C22×D414yes—
398C4×D11C2×#4114yes—
399Dic22—24no—
400Dic22—22no—
401Dic22—22no—
402Dic22—22no—
403Dic22—42no—
404Dic22—48no—
405Dic22C22×D414yes—
406C8×C11—22no—
407C8×C11—22no—
408C11⋊C8—22no—
409C11⋊C8—22no—
410C22×#41—111no—
411C23×Q8—111no—
412C23×D4—111no—
413C2×#137—118no—
414C2×#137—228no—
415C2×AGL(1,ℤ/8)—118no—
416C2×AGL(1,ℤ/8)—228no—
417C22×Q16—111no—
418C22×Q16—111no—
419C22×SD16—111no—
420C22×SD16—111no—
421C22×SD16—111no—
422C22×SD16C2×D1111yescharacteristic, complemented
423C22×D8—111no—
424C22×D8C2×D1111yescharacteristic
425C22×M16—111no—
426C22×M16—111no—
427C2×#124—111no—
428C2×#124—111no—
429C2×#124—118no—
430C2×#124—111no—
431C2×#124—221no—
432C2×#124—221no—
433C2×#124—224no—
434C2×#124C2×D1111yescharacteristic
435C4×#41—118no—
436C4×#41—224no—
437C2×C4×Q8—111no—
438C2×C4×Q8—111no—
439C2×C4×D4—111no—
440C2×C4×D4—221no—
441C2×C4×D4—221no—
442C2×C4×D4C2×D1111yescharacteristic, complemented
443C2×#117—111no—
444C2×#117—221no—
445C22×C22⋊C4—221no—
446C22×C22⋊C4—221no—
447C22×C42—111no—
448C22×C42—221no—
449#464—118no—
450#464—118no—
451#464—118no—
452#464—118no—
453#463—118no—
454#463—118no—
455#463—118no—
456#463C2×D1118yescomplemented
457#423—118no—
458C2×C4⋊C8—111no—
459C2×C4⋊C8—111no—
460C2×C4⋊C8—111no—
461C2×C4⋊C8C2×D1111yescharacteristic, complemented
462#419—118no—
463#418—118no—
464C2×#103—111no—
465C2×#103—111no—
466C2×#103—111no—
467C2×#103C2×D1111yescharacteristic, complemented
468C2×#102—111no—
469C2×#102—111no—
470C2×#102—111no—
471C2×#102C2×D1111yescharacteristic
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#57512yes—
482C22×C11#57512yes—
483C22×C11C23×D411yescharacteristic
484C2×D11—28no—
485C2×D11—22no—
486C2×D11—22no—
487C2×D11—42no—
488C2×D11—42no—
489C2×D11—42no—
490C2×D11—816no—
491C2×D11—84no—
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—24no—
501Dic11—22no—
502Dic11—22no—
503Dic11—42no—
504Dic11—42no—
505Dic11C2×#12114yes—
506C25—221no—
507C2×#41—118no—
508C2×#41—114no—
509C2×#41—222no—
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—114no—
520C22×D4—111no—
521C22×D4—224no—
522C22×D4—224no—
523C22×D4—222no—
524C22×D4—221no—
525C22×D4—221no—
526C22×D4C22×D1111yescharacteristic
527C22×D4C22×D1111yescharacteristic
528C23×C4—21no—
529C23×C4—111no—
530C23×C4—111no—
531C23×C4—111no—
532C23×C4—221no—
533C23×C4—221no—
534C23×C4—221no—
535#137—2232no—
536AGL(1,ℤ/8)—2232no—
537C2×Q16—114no—
538C2×Q16—114no—
539C2×Q16—224no—
540C2×Q16—224no—
541C2×SD16—24no—
542C2×SD16—114no—
543C2×SD16—114no—
544C2×SD16—114no—
545C2×SD16—224no—
546C2×SD16—224no—
547C2×SD16—224no—
548C2×SD16C22×D1114yescomplemented
549C2×D8—24no—
550C2×D8—114no—
551C2×D8—224no—
552C2×D8C22×D1114yes—
553C2×M16—114no—
554C2×M16—114no—
555C2×M16—224no—
556C2×M16—224no—
557C22×C8—111no—
558C22×C8—111no—
559C22×C8C22×D1111yescharacteristic
560C22×C8C22×D1111yescharacteristic
561#124—22no—
562#124—114no—
563#124—114no—
564#124—114no—
565#124—228no—
566#124—228no—
567#124—222no—
568#124—222no—
569#124—222no—
570#124C22×D1114yes—
571C4×Q8—114no—
572C4×Q8—114no—
573C4×Q8—222no—
574C4×Q8—222no—
575C4×D4—22no—
576C4×D4—114no—
577C4×D4—222no—
578C4×D4—228no—
579C4×D4—228no—
580C4×D4C22×D1114yescomplemented
581#117—114no—
582#117—228no—
583#117—222no—
584C2×C4⋊C4—111no—
585C2×C4⋊C4—221no—
586C2×C4⋊C4—221no—
587C2×C4⋊C4C22×D1111yescharacteristic
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—228no—
592C2×C22⋊C4—228no—
593C2×C22⋊C4—221no—
594C2×C22⋊C4—221no—
595C2×C22⋊C4—221no—
596C2×C22⋊C4—221no—
597C2×C22⋊C4—221no—
598C2×C22⋊C4—221no—
599C2×C22⋊C4—221no—
600C2×C22⋊C4—221no—
601C2×C42—111no—
602C2×C42—111no—
603C2×C42—111no—
604C2×C42—114no—
605C2×C42—114no—
606C2×C42—228no—
607C2×C42—221no—
608C2×C42—221no—
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#103C22×D1114yescomplemented
619#102—114no—
620#102—114no—
621#102—114no—
622#102C22×D1114yes—
623C2×C11—44no—
624C2×C11—82no—
625C2×C11#304014yescomplemented
626C2×C11C22×#12111yescharacteristic
627C2×C11C2×#57511yescharacteristic
628C2×C11C2×#57511yescharacteristic
629D11—24no—
630D11—82no—
631C24—21no—
632C24—21no—
633C24—111no—
634C24—224no—
635C24—221no—
636C24—444no—
637C24—444no—
638C24—444no—
639#41—1116no—
640#41—2216no—
641#41—228no—
642C2×Q8—21no—
643C2×Q8—22no—
644C2×Q8—22no—
645C2×Q8—114no—
646C2×Q8—112no—
647C2×Q8—112no—
648C2×Q8—224no—
649C2×Q8—228no—
650C2×Q8—228no—
651C2×Q8—221no—
652C2×Q8—221no—
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—112no—
665C2×D4—228no—
666C2×D4—228no—
667C2×D4—224no—
668C2×D4—224no—
669C2×D4—228no—
670C2×D4—222no—
671C2×D4—221no—
672C2×D4—222no—
673C2×D4—448no—
674C2×D4—444no—
675C2×D4D4×D1114yes—
676C2×D4C23×D1112yes—
677C2×D4C23×D1112yes—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—24no—
681C22×C4—44no—
682C22×C4—111no—
683C22×C4—112no—
684C22×C4—114no—
685C22×C4—114no—
686C22×C4—112no—
687C22×C4—111no—
688C22×C4—111no—
689C22×C4—114no—
690C22×C4—114no—
691C22×C4—224no—
692C22×C4—224no—
693C22×C4—228no—
694C22×C4—224no—
695C22×C4—221no—
696C22×C4—221no—
697C22×C4—221no—
698C22×C4—442no—
699C22×C4—442no—
700C22×C4—444no—
701C22×C4—444no—
702C22×C4D4×D1111yescharacteristic
703C22×C4D4×D1111yescharacteristic
704C22×C4C23×D1111yescharacteristic
705Q16—228no—
706Q16—228no—
707SD16—28no—
708SD16—228no—
709SD16—228no—
710SD16—228no—
711D8—28no—
712D8—228no—
713M16—228no—
714M16—228no—
715C2×C8—22no—
716C2×C8—22no—
717C2×C8—112no—
718C2×C8—112no—
719C2×C8—222no—
720C2×C8—222no—
721C2×C8C23×D1112yes—
722C2×C8C23×D1112yes—
723C4⋊C4—21no—
724C4⋊C4—112no—
725C4⋊C4—224no—
726C4⋊C4—221no—
727C4⋊C4—224no—
728C4⋊C4C23×D1112yes—
729C22⋊C4—24no—
730C22⋊C4—24no—
731C22⋊C4—24no—
732C22⋊C4—224no—
733C22⋊C4—224no—
734C22⋊C4—224no—
735C22⋊C4—224no—
736C22⋊C4—224no—
737C22⋊C4—224no—
738C22⋊C4—224no—
739C22⋊C4—224no—
740C42—114no—
741C42—114no—
742C42—112no—
743C42—112no—
744C42—224no—
745C42—224no—
746C42—224no—
747C42D4×D1112yes—
748C42C23×D1112yes—
749C11C2×#304011yescharacteristic, complemented, Sylow
750C23—24no—
751C23—22no—
752C23—22no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—114no—
759C23—112no—
760C23—222no—
761C23—222no—
762C23—222no—
763C23—448no—
764C23—448no—
765C23—448no—
766C23—442no—
767C23—442no—
768C23—442no—
769C23—8816no—
770C23C2×D4×D1111yescharacteristic
771Q8—22no—
772Q8—22no—
773Q8—42no—
774Q8—114no—
775Q8—224no—
776Q8—222no—
777Q8—222no—
778Q8—222no—
779Q8—448no—
780Q8—442no—
781D4—24no—
782D4—22no—
783D4—22no—
784D4—22no—
785D4—42no—
786D4—2216no—
787D4—222no—
788D4—222no—
789D4—448no—
790D4—442no—
791D4C2×D4×D1114yes—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—48no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—114no—
800C2×C4—112no—
801C2×C4—118no—
802C2×C4—114no—
803C2×C4—114no—
804C2×C4—112no—
805C2×C4—112no—
806C2×C4—2216no—
807C2×C4—222no—
808C2×C4—222no—
809C2×C4—224no—
810C2×C4—222no—
811C2×C4—222no—
812C2×C4—222no—
813C2×C4—444no—
814C2×C4—444no—
815C2×C4—448no—
816C2×C4—448no—
817C2×C4—442no—
818C2×C4—442no—
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—442no—
842C22—442no—
843C22—442no—
844C22—8816no—
845C22—884no—
846C22D11×#12112yes—
847C22#1062329912yes—
848C22#1062330412yes—
849C22C22×D4×D1111yescharacteristic
850C4—22no—
851C4—22no—
852C4—42no—
853C4—42no—
854C4—114no—
855C4—222no—
856C4—222no—
857C4—224no—
858C4—442no—
859C4—442no—
860C4D11×#12112yes—
861C4C22×D4×D1111yescharacteristic
862C4C2×#41×D1111yescharacteristic
863C2—44no—
864C2—82no—
865C2—224no—
866C2—882no—
867C2#1307810514yesdirect product factor
868C2C2×D11×#12111yescharacteristic
869C2C2×#1062330411yescharacteristic
870C2C2×#1062329911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#463C2
socleC23×C11C22×D4
prime radicalC22×#66964C2
hypercenterC2×#463D11
hypocenterC11C2×#3040
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
1. C22×#66968C2semidirect
3. C2×D11×#124C2semidirect
4. C2×C4×#4341C2semidirect
5. #13078105C2direct (N × H)
6. C2×#10622411C2semidirect
7. C2×#10622458C2semidirect
8. C2×#10622380C2semidirect
9. C2×#10622667C2semidirect
10. C2×#10622778C2semidirect
11. C2×#10622629C2semidirect
12. C2×#10622766C2semidirect
13. C2×#10622450C2semidirect
14. C2×#10622415C2semidirect
15. C2×#10622383C2semidirect
16. C2×C11×#463C2semidirect
20. C22×C11×SD16C22semidirect
23. C2×C4×D4×C11C22semidirect
25. C22×#4326C22semidirect
27. C2×D4×Dic11C22semidirect
29. C22×#4324C22semidirect
34. C2×#66968C22semidirect
37. C22×Dic44C22semidirect
42. D11×#124C22semidirect
44. C4×#4341C22semidirect
46. C2×#66940C22semidirect
55. C2×C4×Dic22C22semidirect
56. C11×#463C22semidirect
57. C2×C11×C4⋊C8C22semidirect
58. C2×C11×#103C22semidirect
60. C2×#66899C22semidirect
62. #10622778C22semidirect
63. #10622766C22semidirect
65. C2×#66880C22semidirect
66. C2×Dic11⋊C8C22semidirect
67. C2×Dic11⋊C8C22semidirect
68. #10622667C22semidirect
69. #10622629C22semidirect
70. C2×#66874C22semidirect
72. C2×C4⋊(C11⋊C8)C22semidirect
73. #10622458C22semidirect
74. #10622450C22semidirect
75. #10622415C22semidirect
76. #10622411C22semidirect
77. #10622383C22semidirect
78. #10622380C22semidirect
109. C2×C11×SD16C23semidirect
117. C4×D4×C11C23semidirect
129. C2×#4326C23semidirect
133. D4×Dic11C23semidirect
137. C2×#4324C23semidirect
161. C2×Dic44C23semidirect
171. #66940C23semidirect
183. C4×Dic22C23semidirect
184. C11×C4⋊C8C23semidirect
185. C11×#103C23semidirect
187. #66899C23semidirect
190. #66880C23semidirect
191. Dic11⋊C8C23semidirect
192. Dic11⋊C8C23semidirect
193. #66874C23semidirect
195. C4⋊(C11⋊C8)C23semidirect
327. C2×#463D11semidirect
422. C22×SD16C2×D11semidirect
442. C2×C4×D4C2×D11semidirect
456. #463C2×D11semidirect
461. C2×C4⋊C8C2×D11semidirect
467. C2×#103C2×D11semidirect
548. C2×SD16C22×D11semidirect
580. C4×D4C22×D11semidirect
614. C4⋊C8C22×D11semidirect
618. #103C22×D11semidirect
625. C2×C11#3040semidirect
749. C11C2×#3040semidirect
867. C2#13078105direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669682
C22×#669642
C2×D11×#1242
C2×C4×#43412
#130781052
C2×#106224112
C2×#106224582
C2×#106223802
C2×#106226672
C2×#106227782
C2×#106226292
C2×#106227662
C2×#106224502
C2×#106224152
C2×#106223832
C2×C11×#4632
C2×#304011