Finite Group Databasebeta

← C2×#13078220 #15620903

Subgroups — C2×#13078220 #15620903

Order 2816.

2918 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66969C211yesmaximal, characteristic, complemented
2C22×M16×D11C211yesmaximal, characteristic, complemented
3C2×#10623158C211yesmaximal, characteristic, complemented
4C2×#10623137C211yesmaximal, characteristic, complemented
5#13078220C2116yesmaximal, direct product factor
6C2×#10622429C211yesmaximal, characteristic, complemented
7C2×#10622665C211yesmaximal, characteristic, complemented
8C2×#10622395C211yesmaximal, characteristic, complemented
9C2×#10622652C211yesmaximal, characteristic, complemented
10C2×#10622499C211yesmaximal, characteristic, complemented
11C2×#10622747C211yesmaximal, characteristic, complemented
12C2×#10622787C211yesmaximal, characteristic, complemented
13C2×#10622493C211yesmaximal, characteristic, complemented
14C2×#10622417C211yesmaximal, characteristic, complemented
15C2×#10622385C211yesmaximal, characteristic, complemented
16C2×C11×#468C211yesmaximal, characteristic, complemented
17C22×#4343C2211yescharacteristic
18C22×#4341C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C22×C11×SD16C2211yescharacteristic, complemented
21C22×C11×M16C2211yescharacteristic
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C11×#121C2211yescharacteristic
24C2×#66999C2211yescharacteristic
25C22×#4326C2211yescharacteristic, complemented
26C2×#66991C2211yescharacteristic
27C2×#66990—21no—
28C2×D4×Dic11—21no—
29C22×#4323C2211yescharacteristic, complemented
30C2×#66983C2211yescharacteristic
31C2×#66977C2211yescharacteristic
32C22×#4318C2211yescharacteristic
33C2×#66969—28no—
34C2×#66969C2218yescomplemented
35C2×M16×D11—28no—
36C2×M16×D11C2218yescomplemented
37C22×#4314C2211yescharacteristic, complemented
38C22×#4313C2211yescharacteristic
39C22×#4313C2211yescharacteristic
40C22×C8×D11C2211yescharacteristic
41C22×C8×D11C2211yescharacteristic
42#10623158—24no—
43#10623158C2218yescomplemented
44#10623137—24no—
45#10623137C2218yescomplemented
46C2×#66950C2211yescharacteristic
47C2×#66948C2211yescharacteristic
48C2×#66947—21no—
49C2×#66946—21no—
50C2×#66945C2211yescharacteristic
51C2×#66945C2211yescharacteristic
52C2×#66936—21no—
53C2×#66935—21no—
54C2×(C22⋊D11)⋊C4—21no—
55C2×(C22⋊D11)⋊C4—21no—
56C11×#468C2218yescomplemented
57C2×C11×#107C2211yescharacteristic, complemented
58C2×C11×#103C2211yescharacteristic, complemented
59C2×C11×#102C2211yescharacteristic, complemented
60C2×#66899C2211yescharacteristic, complemented
61C2×#66896C2211yescharacteristic, complemented
62#10622787C2218yescomplemented
63#10622747C2218yescomplemented
64C2×#66885C2211yescharacteristic, complemented
65C2×#66882C2211yescharacteristic, complemented
66C2×#66880C2211yescharacteristic, complemented
67#10622665C2218yescomplemented
68#10622652C2218yescomplemented
69C2×#66874C2211yescharacteristic, complemented
70C2×#66873C2211yescharacteristic, complemented
71C2×#66872C2211yescharacteristic, complemented
72C2×#66872C2211yescharacteristic, complemented
73#10622499C2218yescomplemented
74#10622493C2218yescomplemented
75#10622429C2218yescomplemented
76#10622417C2218yescomplemented
77#10622395C2218yescomplemented
78#10622385C2218yescomplemented
79C24×D11D411yescharacteristic
80C22×Q8×C11C2311yescharacteristic
81C22×D4×C11—21no—
82C22×D4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C22×C22⋊D11—21no—
87C23×Dic11—21no—
88C23×Dic11D411yescharacteristic
89C2×#4343—22no—
90C2×#4343—24no—
91C2×#4343—24no—
92C2×#4343C2314yes—
93C2×#4341—24no—
94C2×#4341—22no—
95C2×#4341—24no—
96C2×#4341C2314yes—
97C22×D44—21no—
98C22×D44—21no—
99C22×D44C2311yescharacteristic
100C22×C4×D11—24no—
101C22×C4×D11—24no—
102C22×C4×D11—21no—
103C22×C4×D11D411yescharacteristic
104C22×C4×D11D411yescharacteristic
105C22×C4×D11D414yes—
106C22×C4×D11C2311yescharacteristic
107C22×C4×D11C2314yes—
108C22×C4×D11C2311yescharacteristic
109C22×Dic22C2311yescharacteristic
110C2×C11×SD16—24no—
111C2×C11×SD16C2314yescomplemented
112C2×C11×M16—24no—
113C2×C11×M16C2314yes—
114C22×C8×C11C2311yescharacteristic
115C22×C8×C11C2311yescharacteristic
116C11×C22⋊Q8—22no—
117C11×C22⋊Q8C2314yes—
118C11×#121—22no—
119C11×#121C2314yes—
120C2×C11×C4⋊C4—21no—
121C2×C11×C4⋊C4C2311yescharacteristic
122C2×C11×C4⋊C4C2311yescharacteristic
123C2×C11×C22⋊C4—21no—
124C2×C11×C22⋊C4—21no—
125C2×C22⋊Dic11—21no—
126C2×C22⋊Dic11—21no—
127#66999—22no—
128#66999C2314yes—
129C2×#4326—24no—
130C2×#4326C2314yescomplemented
131#66991—22no—
132#66991C2314yes—
133#66990—28no—
134D4×Dic11—28no—
135C2×#4323—24no—
136C2×#4323C2314yescomplemented
137#66983—22no—
138#66983C2314yes—
139C2×(C2×D11)⋊C4—21no—
140C2×(C2×D11)⋊C4—21no—
141C2×(C2×D11)⋊C4—21no—
142C2×(C2×D11)⋊C4—21no—
143C2×(C2×D11)⋊C4—21no—
144C2×(C2×D11)⋊C4—21no—
145C2×C4⋊Dic11—21no—
146C2×C4⋊Dic11C2311yescharacteristic
147C2×C4⋊Dic11C2311yescharacteristic
148#66977—22no—
149#66977C2314yes—
150C2×Dic11⋊C4—21no—
151C2×Dic11⋊C4—21no—
152C2×C4×Dic11—21no—
153C2×C4×Dic11—21no—
154C2×#4318—24no—
155C2×#4318C2314yes—
156C22×C11⋊C8C2311yescharacteristic
157C22×C11⋊C8C2311yescharacteristic
158#66969—232no—
159M16×D11—232no—
160C2×#4314—24no—
161C2×#4314C2314yescomplemented
162C2×#4313—24no—
163C2×#4313—24no—
164C2×#4313C2314yes—
165C2×#4313C2314yes—
166C2×C8×D11—24no—
167C2×C8×D11D418yescomplemented
168C2×C8×D11C2314yes—
169C2×C8×D11C2314yes—
170#66950—22no—
171#66950C2314yes—
172#66948—22no—
173#66948C2314yes—
174#66947—28no—
175#66946—28no—
176#66945—22no—
177#66945—22no—
178#66945C2314yes—
179#66945C2314yes—
180#66936—28no—
181#66935—28no—
182(C22⋊D11)⋊C4—28no—
183(C22⋊D11)⋊C4—28no—
184C11×#107C2314yescomplemented
185C11×#103C2314yescomplemented
186C11×#102C2314yescomplemented
187#66899C2314yescomplemented
188#66896C2314yescomplemented
189#66885C2314yescomplemented
190#66882C2314yescomplemented
191#66880C2314yescomplemented
192#66874C2314yescomplemented
193#66873C2314yescomplemented
194#66872C2314yescomplemented
195#66872C2314yescomplemented
196C2×#3054—111nomaximal, Sylow
197C24×C11—21no—
198C24×C11C2×D411yescharacteristic
199C23×D11—24no—
200C23×D11—21no—
201C23×D11—42no—
202C23×D11—42no—
203C23×D11C2×D411yescharacteristic
204C23×D11C2×D411yescharacteristic
205C23×D11C2×D414yes—
206C2×Q8×C11—21no—
207C2×Q8×C11—22no—
208C2×Q8×C11—22no—
209C2×Q8×C11C2412yes—
210C2×D4×C11—24no—
211C2×D4×C11—22no—
212C2×D4×C11—21no—
213C2×D4×C11—22no—
214C2×D4×C11—44no—
215C2×D4×C11C2412yes—
216C22×C4×C11—22no—
217C22×C4×C11—22no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11C2×D411yescharacteristic
222C22×C4×C11C2×D412yes—
223C22×C4×C11C2412yes—
224C22×C4×C11C2411yescharacteristic
225C2×C22⋊D11—24no—
226C2×C22⋊D11—24no—
227C2×C22⋊D11—24no—
228C2×C22⋊D11—44no—
229C2×C22⋊D11—44no—
230C2×C22⋊D11—44no—
231C22×Dic11—24no—
232C22×Dic11—24no—
233C22×Dic11—21no—
234C22×Dic11—21no—
235C22×Dic11—21no—
236C22×Dic11—44no—
237C22×Dic11C2×D414yes—
238C22×Dic11C2×D411yescharacteristic
239C22×Dic11C2×D411yescharacteristic
240#4343—28no—
241#4343—28no—
242#4343—48no—
243#4341—28no—
244#4341—28no—
245#4341—48no—
246C2×D44—24no—
247C2×D44—24no—
248C2×D44—21no—
249C2×D44—22no—
250C2×D44—22no—
251C2×D44—44no—
252C2×D44—44no—
253C2×D44C2412yes—
254C2×C4×D11—24no—
255C2×C4×D11—216no—
256C2×C4×D11—28no—
257C2×C4×D11—28no—
258C2×C4×D11—24no—
259C2×C4×D11—24no—
260C2×C4×D11—22no—
261C2×C4×D11—22no—
262C2×C4×D11—44no—
263C2×C4×D11C2×D414yes—
264C2×C4×D11C2×D414yes—
265C2×C4×D11C2×D414yes—
266C2×C4×D11C2×D412yes—
267C2×C4×D11C2×D412yes—
268C2×C4×D11#4114yes—
269C2×C4×D11C2412yes—
270C2×C4×D11C2412yes—
271C2×Dic22—22no—
272C2×Dic22—21no—
273C2×Dic22—22no—
274C2×Dic22C2412yes—
275C11×SD16—28no—
276C11×M16—28no—
277C2×C8×C11—22no—
278C2×C8×C11C2×D414yes—
279C2×C8×C11C2412yes—
280C2×C8×C11C2412yes—
281C11×C4⋊C4—21no—
282C11×C4⋊C4—21no—
283C11×C4⋊C4—24no—
284C11×C4⋊C4C2412yes—
285C11×C4⋊C4C2412yes—
286C11×C22⋊C4—24no—
287C11×C22⋊C4—24no—
288C22⋊Dic11—24no—
289C22⋊Dic11—24no—
290#4326—28no—
291#4323—28no—
292(C2×D11)⋊C4—24no—
293(C2×D11)⋊C4—24no—
294(C2×D11)⋊C4—24no—
295(C2×D11)⋊C4—24no—
296(C2×D11)⋊C4—24no—
297(C2×D11)⋊C4—24no—
298C4⋊Dic11—24no—
299C4⋊Dic11—21no—
300C4⋊Dic11—21no—
301C4⋊Dic11C2412yes—
302C4⋊Dic11C2412yes—
303Dic11⋊C4—24no—
304Dic11⋊C4—24no—
305C4×Dic11—24no—
306C4×Dic11—24no—
307#4318—28no—
308C2×C11⋊C8—22no—
309C2×C11⋊C8C2×D414yes—
310C2×C11⋊C8C2412yes—
311C2×C11⋊C8C2412yes—
312#4314—28no—
313#4313—28no—
314#4313—28no—
315C8×D11—28no—
316C8×D11C2×D4116yescomplemented
317C22×#135—111no—
318C23×M16—111no—
319C2×#525—111no—
320C2×#525—111no—
321#3054—1116no—
322C2×#470—111no—
323C2×#470—111no—
324C2×#469—111no—
325C2×#469—111no—
326C2×#468—111no—
327C2×#468—111no—
328C2×#468—111no—
329C2×#468D1111yescharacteristic, complemented
330C2×#427—111no—
331C2×#416—111no—
332C2×#416—111no—
333C23×C11—22no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—22no—
337C23×C11—42no—
338C23×C11—42no—
339C23×C11—42no—
340C23×C11C22×D412yes—
341C23×C11C22×D411yescharacteristic
342C22×D11—22no—
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—22no—
346C22×D11—22no—
347C22×D11—28no—
348C22×D11—22no—
349C22×D11—44no—
350C22×D11—44no—
351C22×D11—416no—
352C22×D11—42no—
353C22×D11—42no—
354C22×D11—42no—
355C22×D11#12114yes—
356C22×D11C22×D412yes—
357C22×D11C22×D412yes—
358Q8×C11—22no—
359Q8×C11—22no—
360Q8×C11—42no—
361D4×C11—22no—
362D4×C11—22no—
363D4×C11—48no—
364D4×C11—42no—
365C2×C4×C11—22no—
366C2×C4×C11—24no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—42no—
373C2×C4×C11—42no—
374C2×C4×C11—42no—
375C2×C4×C11C22×D412yes—
376C2×C4×C11C22×D411yescharacteristic
377C2×C4×C11C22×D412yes—
378C2×C4×C11C2×#4112yes—
379C2×C4×C11C2511yescharacteristic
380C22⋊D11—48no—
381C22⋊D11—48no—
382C22⋊D11—48no—
383C2×Dic11—22no—
384C2×Dic11—28no—
385C2×Dic11—22no—
386C2×Dic11—22no—
387C2×Dic11—22no—
388C2×Dic11—42no—
389C2×Dic11—42no—
390C2×Dic11—42no—
391C2×Dic11—48no—
392C2×Dic11#12114yes—
393C2×Dic11C22×D412yes—
394C2×Dic11C22×D412yes—
395D44—22no—
396D44—22no—
397D44—48no—
398D44—48no—
399D44—42no—
400C4×D11—28no—
401C4×D11—24no—
402C4×D11—22no—
403C4×D11—22no—
404C4×D11—28no—
405C4×D11—48no—
406C4×D11#12118yes—
407C4×D11C22×D414yes—
408C4×D11C2×#4114yes—
409Dic22—22no—
410Dic22—22no—
411Dic22—42no—
412C8×C11—22no—
413C8×C11C22×D414yes—
414C11⋊C8—22no—
415C11⋊C8C22×D414yes—
416C22×#41—111no—
417C22×#41—111no—
418C24×C4—111no—
419C2×#135—118no—
420C2×#135—228no—
421C22×Q16—111no—
422C22×SD16—111no—
423C22×SD16C2×D1111yescharacteristic, complemented
424C22×D8—111no—
425C22×M16—111no—
426C22×M16—118no—
427C22×M16—111no—
428C22×M16—111no—
429C22×M16—228no—
430C22×M16C2×D1111yescharacteristic
431C23×C8—111no—
432C23×C8—111no—
433#525—118no—
434#525—118no—
435#525—224no—
436#525—224no—
437C2×#123—221no—
438C2×#123—221no—
439C2×C22⋊Q8—111no—
440C2×C22⋊Q8—111no—
441C2×C22⋊Q8—111no—
442C2×C22⋊Q8C2×D1111yescharacteristic
443C2×#121—111no—
444C2×#121—111no—
445C2×#121—111no—
446C2×#121C2×D1111yescharacteristic
447C2×#120—221no—
448C2×#120—221no—
449C2×C4×D4—221no—
450C2×C4×D4—221no—
451C2×C4×D4—221no—
452C2×C4×D4—221no—
453C2×#117—111no—
454C2×#117—111no—
455#470—118no—
456#470—118no—
457#469—118no—
458#469—118no—
459#468—118no—
460#468—118no—
461#468—118no—
462#468C2×D1118yescomplemented
463#427—118no—
464C2×#107—111no—
465C2×#107C2×D1111yescharacteristic, complemented
466C2×#106—111no—
467C2×#106—111no—
468#416—118no—
469#416—118no—
470C2×#103—111no—
471C2×#103—111no—
472C2×#103—111no—
473C2×#103C2×D1111yescharacteristic, complemented
474C2×#102—111no—
475C2×#102—111no—
476C2×#102—111no—
477C2×#102C2×D1111yescharacteristic, complemented
478C22×C11—22no—
479C22×C11—22no—
480C22×C11—22no—
481C22×C11—44no—
482C22×C11—42no—
483C22×C11—42no—
484C22×C11—42no—
485C22×C11—84no—
486C22×C11C2×#12112yes—
487C22×C11#57512yes—
488C22×C11#57512yes—
489C22×C11C23×D411yescharacteristic
490C2×D11—28no—
491C2×D11—22no—
492C2×D11—22no—
493C2×D11—22no—
494C2×D11—22no—
495C2×D11—22no—
496C2×D11—416no—
497C2×D11—44no—
498C2×D11—42no—
499C2×D11—42no—
500C2×D11—42no—
501C2×D11—84no—
502C2×D11C2×#12114yes—
503C4×C11—22no—
504C4×C11—42no—
505C4×C11—42no—
506C4×C11—42no—
507C4×C11C2×#12112yes—
508C4×C11C23×D411yescharacteristic
509C4×C11C22×#4111yescharacteristic
510Dic11—22no—
511Dic11—42no—
512Dic11—42no—
513Dic11—42no—
514Dic11C2×#12114yes—
515C25—111no—
516C2×#41—114no—
517C2×#41—114no—
518C2×#41—222no—
519C2×#41—222no—
520C2×#41—224no—
521C2×#41—224no—
522C2×#41—224no—
523C2×#41—224no—
524C22×Q8—111no—
525C22×Q8C22×D1111yescharacteristic
526C22×D4—21no—
527C22×D4—111no—
528C22×D4—221no—
529C22×D4—221no—
530C22×D4—221no—
531C22×D4—221no—
532C22×D4—221no—
533C22×D4C22×D1111yescharacteristic
534C23×C4—111no—
535C23×C4—111no—
536C23×C4—111no—
537C23×C4—111no—
538C23×C4—114no—
539C23×C4—111no—
540C23×C4—114no—
541C23×C4—224no—
542C23×C4—224no—
543C23×C4—221no—
544C23×C4—221no—
545C23×C4C22×D1111yescharacteristic
546#135—2232no—
547C2×Q16—114no—
548C2×Q16—224no—
549C2×SD16—24no—
550C2×SD16—114no—
551C2×SD16—224no—
552C2×SD16C22×D1114yescomplemented
553C2×D8—114no—
554C2×D8—224no—
555C2×M16—24no—
556C2×M16—114no—
557C2×M16—114no—
558C2×M16—114no—
559C2×M16—224no—
560C2×M16—2232no—
561C2×M16—224no—
562C2×M16—224no—
563C2×M16C22×D1114yes—
564C22×C8—111no—
565C22×C8—118no—
566C22×C8—114no—
567C22×C8—111no—
568C22×C8—114no—
569C22×C8—224no—
570C22×C8C22×D1111yescharacteristic
571C22×C8C22×D1111yescharacteristic
572#123—228no—
573#123—228no—
574C22⋊Q8—22no—
575C22⋊Q8—114no—
576C22⋊Q8—114no—
577C22⋊Q8—114no—
578C22⋊Q8—222no—
579C22⋊Q8—222no—
580C22⋊Q8—222no—
581C22⋊Q8C22×D1114yes—
582#121—22no—
583#121—114no—
584#121—114no—
585#121—114no—
586#121—222no—
587#121—222no—
588#121—222no—
589#121C22×D1114yes—
590#120—228no—
591#120—228no—
592C4×D4—228no—
593C4×D4—228no—
594C4×D4—228no—
595C4×D4—228no—
596#117—114no—
597#117—114no—
598#117—222no—
599#117—222no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—111no—
602C2×C4⋊C4—111no—
603C2×C4⋊C4—221no—
604C2×C4⋊C4—221no—
605C2×C4⋊C4—221no—
606C2×C4⋊C4C22×D1111yescharacteristic
607C2×C4⋊C4C22×D1111yescharacteristic
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—221no—
611C2×C22⋊C4—221no—
612C2×C22⋊C4—221no—
613C2×C22⋊C4—221no—
614C2×C22⋊C4—221no—
615C2×C22⋊C4—221no—
616C2×C22⋊C4—221no—
617C2×C22⋊C4—221no—
618C2×C42—221no—
619C2×C42—221no—
620#107—114no—
621#107C22×D1114yescomplemented
622#106—114no—
623#106—114no—
624#103—114no—
625#103—114no—
626#103—114no—
627#103C22×D1114yescomplemented
628#102—114no—
629#102—114no—
630#102—114no—
631#102C22×D1114yescomplemented
632C2×C11—42no—
633C2×C11—82no—
634C2×C11#305414yescomplemented
635C2×C11C22×#12111yescharacteristic
636C2×C11C2×#57511yescharacteristic
637C2×C11C2×#57511yescharacteristic
638D11—24no—
639D11—42no—
640D11—82no—
641C24—21no—
642C24—111no—
643C24—111no—
644C24—114no—
645C24—224no—
646C24—221no—
647C24—442no—
648C24—442no—
649C24D4×D1111yescharacteristic
650#41—228no—
651#41—228no—
652#41—228no—
653#41—228no—
654#41—448no—
655#41—448no—
656C2×Q8—21no—
657C2×Q8—22no—
658C2×Q8—22no—
659C2×Q8—112no—
660C2×Q8—221no—
661C2×Q8—222no—
662C2×Q8—222no—
663C2×Q8C23×D1112yes—
664C2×D4—24no—
665C2×D4—22no—
666C2×D4—21no—
667C2×D4—22no—
668C2×D4—44no—
669C2×D4—112no—
670C2×D4—224no—
671C2×D4—224no—
672C2×D4—224no—
673C2×D4—224no—
674C2×D4—224no—
675C2×D4—222no—
676C2×D4—221no—
677C2×D4—222no—
678C2×D4—444no—
679C2×D4—444no—
680C2×D4—444no—
681C2×D4—444no—
682C2×D4—444no—
683C2×D4C23×D1112yes—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—111no—
690C22×C4—112no—
691C22×C4—114no—
692C22×C4—114no—
693C22×C4—112no—
694C22×C4—114no—
695C22×C4—111no—
696C22×C4—114no—
697C22×C4—112no—
698C22×C4—114no—
699C22×C4—112no—
700C22×C4—228no—
701C22×C4—224no—
702C22×C4—2216no—
703C22×C4—228no—
704C22×C4—224no—
705C22×C4—224no—
706C22×C4—224no—
707C22×C4—224no—
708C22×C4—222no—
709C22×C4—222no—
710C22×C4—221no—
711C22×C4—221no—
712C22×C4—221no—
713C22×C4—444no—
714C22×C4—444no—
715C22×C4D4×D1112yes—
716C22×C4D4×D1111yescharacteristic
717C22×C4C23×D1112yes—
718C22×C4C23×D1111yescharacteristic
719Q16—228no—
720SD16—28no—
721SD16—228no—
722D8—228no—
723M16—28no—
724M16—228no—
725M16—228no—
726M16—228no—
727C2×C8—22no—
728C2×C8—114no—
729C2×C8—112no—
730C2×C8—1116no—
731C2×C8—112no—
732C2×C8—228no—
733C2×C8—222no—
734C2×C8D4×D1114yes—
735C2×C8C23×D1112yes—
736C2×C8C23×D1112yes—
737C4⋊C4—24no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—112no—
741C4⋊C4—112no—
742C4⋊C4—224no—
743C4⋊C4—224no—
744C4⋊C4—221no—
745C4⋊C4—221no—
746C4⋊C4—224no—
747C4⋊C4C23×D1112yes—
748C4⋊C4C23×D1112yes—
749C22⋊C4—24no—
750C22⋊C4—24no—
751C22⋊C4—224no—
752C22⋊C4—224no—
753C22⋊C4—224no—
754C22⋊C4—224no—
755C22⋊C4—224no—
756C22⋊C4—224no—
757C22⋊C4—224no—
758C22⋊C4—224no—
759C42—224no—
760C42—224no—
761C11C2×#305411yescharacteristic, complemented, Sylow
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—42no—
767C23—42no—
768C23—42no—
769C23—114no—
770C23—112no—
771C23—112no—
772C23—228no—
773C23—222no—
774C23—222no—
775C23—222no—
776C23—222no—
777C23—222no—
778C23—222no—
779C23—444no—
780C23—444no—
781C23—4416no—
782C23—442no—
783C23—442no—
784C23—442no—
785C23C2×D4×D1112yes—
786C23C2×D4×D1111yescharacteristic
787Q8—22no—
788Q8—22no—
789Q8—42no—
790Q8—222no—
791Q8—222no—
792Q8—442no—
793D4—22no—
794D4—22no—
795D4—48no—
796D4—42no—
797D4—222no—
798D4—222no—
799D4—448no—
800D4—448no—
801D4—448no—
802D4—448no—
803D4—448no—
804D4—442no—
805C2×C4—22no—
806C2×C4—24no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—114no—
816C2×C4—112no—
817C2×C4—118no—
818C2×C4—114no—
819C2×C4—114no—
820C2×C4—112no—
821C2×C4—228no—
822C2×C4—228no—
823C2×C4—228no—
824C2×C4—222no—
825C2×C4—224no—
826C2×C4—222no—
827C2×C4—222no—
828C2×C4—222no—
829C2×C4—222no—
830C2×C4—222no—
831C2×C4—448no—
832C2×C4—448no—
833C2×C4—442no—
834C2×C4—442no—
835C2×C4—442no—
836C2×C4C2×D4×D1112yes—
837C2×C4C2×D4×D1111yescharacteristic
838C2×C4C2×D4×D1112yes—
839C2×C4#41×D1112yes—
840C2×C4C24×D1111yescharacteristic
841C8—22no—
842C8—114no—
843C8—222no—
844C8C2×D4×D1114yes—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—44no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—84no—
853C22—114no—
854C22—228no—
855C22—222no—
856C22—222no—
857C22—222no—
858C22—222no—
859C22—222no—
860C22—4416no—
861C22—444no—
862C22—442no—
863C22—442no—
864C22—442no—
865C22—884no—
866C22D11×#12112yes—
867C22#1062330412yes—
868C22#1062330812yes—
869C22C22×D4×D1111yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—114no—
875C4—222no—
876C4—442no—
877C4—442no—
878C4—442no—
879C4D11×#12112yes—
880C4C22×D4×D1111yescharacteristic
881C4C2×#41×D1111yescharacteristic
882C2—42no—
883C2—82no—
884C2—224no—
885C2—442no—
886C2—882no—
887C2#1307822014yesdirect product factor
888C2C2×D11×#12111yescharacteristic
889C2C2×#1062330411yescharacteristic
890C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#468C2
socleC23×C11C22×D4
hypercenterC2×#468D11
hypocenterC11C2×#3054
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C22×#66969C2semidirect
2. C22×M16×D11C2semidirect
3. C2×#10623158C2semidirect
4. C2×#10623137C2semidirect
5. #13078220C2direct (N × H)
6. C2×#10622429C2semidirect
7. C2×#10622665C2semidirect
8. C2×#10622395C2semidirect
9. C2×#10622652C2semidirect
10. C2×#10622499C2semidirect
11. C2×#10622747C2semidirect
12. C2×#10622787C2semidirect
13. C2×#10622493C2semidirect
14. C2×#10622417C2semidirect
15. C2×#10622385C2semidirect
16. C2×C11×#468C2semidirect
20. C22×C11×SD16C22semidirect
25. C22×#4326C22semidirect
29. C22×#4323C22semidirect
34. C2×#66969C22semidirect
36. C2×M16×D11C22semidirect
37. C22×#4314C22semidirect
43. #10623158C22semidirect
45. #10623137C22semidirect
56. C11×#468C22semidirect
57. C2×C11×#107C22semidirect
58. C2×C11×#103C22semidirect
59. C2×C11×#102C22semidirect
60. C2×#66899C22semidirect
61. C2×#66896C22semidirect
62. #10622787C22semidirect
63. #10622747C22semidirect
64. C2×#66885C22semidirect
65. C2×#66882C22semidirect
66. C2×#66880C22semidirect
67. #10622665C22semidirect
68. #10622652C22semidirect
69. C2×#66874C22semidirect
70. C2×#66873C22semidirect
71. C2×#66872C22semidirect
72. C2×#66872C22semidirect
73. #10622499C22semidirect
74. #10622493C22semidirect
75. #10622429C22semidirect
76. #10622417C22semidirect
77. #10622395C22semidirect
78. #10622385C22semidirect
111. C2×C11×SD16C23semidirect
130. C2×#4326C23semidirect
136. C2×#4323C23semidirect
161. C2×#4314C23semidirect
167. C2×C8×D11D4semidirect
184. C11×#107C23semidirect
185. C11×#103C23semidirect
186. C11×#102C23semidirect
187. #66899C23semidirect
188. #66896C23semidirect
189. #66885C23semidirect
190. #66882C23semidirect
191. #66880C23semidirect
192. #66874C23semidirect
193. #66873C23semidirect
194. #66872C23semidirect
195. #66872C23semidirect
316. C8×D11C2×D4semidirect
329. C2×#468D11semidirect
423. C22×SD16C2×D11semidirect
462. #468C2×D11semidirect
465. C2×#107C2×D11semidirect
473. C2×#103C2×D11semidirect
477. C2×#102C2×D11semidirect
552. C2×SD16C22×D11semidirect
621. #107C22×D11semidirect
627. #103C22×D11semidirect
631. #102C22×D11semidirect
634. C2×C11#3054semidirect
761. C11C2×#3054semidirect
887. C2#13078220direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669692
C22×M16×D112
C2×#106231582
C2×#106231372
#130782202
C2×#106224292
C2×#106226652
C2×#106223952
C2×#106226522
C2×#106224992
C2×#106227472
C2×#106227872
C2×#106224932
C2×#106224172
C2×#106223852
C2×C11×#4682
C2×#305411