Finite Group Databasebeta

← C2×#13079469 #15624427

Subgroups — C2×#13079469 #15624427

Order 2816.

2378 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
1C2×#10623160C211yesmaximal, characteristic, complemented
2C2×#10623138C211yesmaximal, characteristic, complemented
3#13079469C2116yesmaximal, direct product factor
4C2×#10622390C211yesmaximal, characteristic, complemented
5C2×#10622428C211yesmaximal, characteristic, complemented
6C2×#10622498C211yesmaximal, characteristic, complemented
7C2×#10622495C211yesmaximal, characteristic, complemented
8C2×#10622748C211yesmaximal, characteristic, complemented
9C2×#10622651C211yesmaximal, characteristic, complemented
10C2×#10622661C211yesmaximal, characteristic, complemented
11C2×#10622424C211yesmaximal, characteristic, complemented
12C2×#10622785C211yesmaximal, characteristic, complemented
13C2×#10622782C211yesmaximal, characteristic, complemented
14C2×#10622386C211yesmaximal, characteristic, complemented
15C2×#10622742C211yesmaximal, characteristic, complemented
16C2×C11×#468C211yesmaximal, characteristic, complemented
17C22×#4343C2211yescharacteristic, complemented
18C22×D4×D11C2211yescharacteristic
19C22×#4339C2211yescharacteristic
20C22×C11×SD16C2211yescharacteristic
21C22×C11×M16C2211yescharacteristic, complemented
22C2×C11×C22⋊Q8C2211yescharacteristic, complemented
23C2×C11×#121C2211yescharacteristic
24C2×#66999C2211yescharacteristic
25C22×#4325C2211yescharacteristic
26C2×#66993—21no—
27C2×#66991C2211yescharacteristic
28C2×#66990—21no—
29C22×#4323C2211yescharacteristic
30C2×#66983C2211yescharacteristic
31C2×#66983C2211yescharacteristic, complemented
32C23×C11⋊C8C2211yescharacteristic, complemented
33C22×D88C2211yescharacteristic
34#10623160—24no—
35#10623160C2218yescomplemented
36#10623138—24no—
37#10623138C2218yescomplemented
38C2×#66949—21no—
39C2×#66948—21no—
40C2×#66948C2211yescharacteristic
41C2×#66948C2211yescharacteristic
42C2×#66945C2211yescharacteristic
43C2×C4⋊C4×D11C2211yescharacteristic, complemented
44C2×#66938—21no—
45C2×#66937—21no—
46C2×#66937—21no—
47C2×#66935—21no—
48C11×#468C2218yescomplemented
49C2×C11×#107C2211yescharacteristic, complemented
50C2×C11×#103C2211yescharacteristic, complemented
51C2×C11×#102C2211yescharacteristic
52C2×#66899C2211yescharacteristic, complemented
53C2×#66896C2211yescharacteristic
54#10622785C2218yescomplemented
55#10622782C2218yescomplemented
56#10622748C2218yescomplemented
57#10622742C2218yescomplemented
58C2×#66885C2211yescharacteristic
59C2×#66885C2211yescharacteristic, complemented
60C2×(C2×D11)⋊C8C2211yescharacteristic
61C2×(C2×D11)⋊C8C2211yescharacteristic
62C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
63C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
64C2×#66881C2211yescharacteristic, complemented
65#10622661C2218yescomplemented
66#10622651C2218yescomplemented
67C2×#66873C2211yescharacteristic
68C2×#66873C2211yescharacteristic, complemented
69C2×#66872C2211yescharacteristic, complemented
70C2×#66871C2211yescharacteristic, complemented
71#10622498C2218yescomplemented
72#10622495C2218yescomplemented
73#10622428C2218yescomplemented
74#10622424C2218yescomplemented
75#10622390C2218yescomplemented
76#10622386C2218yescomplemented
77C24×D11—21no—
78C22×Q8×C11C2311yescharacteristic
79C22×D4×C11—21no—
80C22×D4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C22×C22⋊D11D411yescharacteristic
87C22×C22⋊D11D411yescharacteristic
88C2×#4343—22no—
89C2×#4343—42no—
90C2×#4343—42no—
91C2×#4343C2314yescomplemented
92C2×D4×D11—22no—
93C2×D4×D11—42no—
94C2×D4×D11—42no—
95C2×D4×D11C2314yes—
96C2×#4339—42no—
97C2×#4339—42no—
98C2×#4339D414yes—
99C2×#4339C2314yes—
100C22×D44—21no—
101C22×D44—21no—
102C22×D44—21no—
103C22×D44D411yescharacteristic
104C22×D44C2311yescharacteristic
105C22×D44C2311yescharacteristic
106C22×C4×D11—21no—
107C22×C4×D11—21no—
108C22×C4×D11C2311yescharacteristic
109C22×C4×D11C2311yescharacteristic
110C22×Dic22D411yescharacteristic
111C2×C11×SD16—42no—
112C2×C11×SD16C2314yes—
113C2×C11×M16—42no—
114C2×C11×M16C2314yescomplemented
115C22×C8×C11C2311yescharacteristic
116C22×C8×C11C2311yescharacteristic
117C11×C22⋊Q8—22no—
118C11×C22⋊Q8C2314yescomplemented
119C11×#121—22no—
120C11×#121C2314yes—
121C2×C11×C4⋊C4—21no—
122C2×C11×C4⋊C4C2311yescharacteristic
123C2×C11×C4⋊C4C2311yescharacteristic
124C2×C11×C22⋊C4—21no—
125C2×C11×C22⋊C4—21no—
126C2×C22⋊Dic11—21no—
127#66999—22no—
128#66999C2314yes—
129C2×#4325—42no—
130C2×#4325C2314yes—
131#66993—28no—
132#66991—22no—
133#66991C2314yes—
134#66990—28no—
135C2×#4323—42no—
136C2×#4323C2314yes—
137#66983—22no—
138#66983—22no—
139#66983C2314yes—
140#66983C2314yescomplemented
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×(C2×D11)⋊C4—21no—
147C2×C4⋊Dic11C2311yescharacteristic
148C2×C4⋊Dic11C2311yescharacteristic
149C2×Dic11⋊C4—21no—
150C2×Dic11⋊C4—21no—
151C2×C4×Dic11—21no—
152C22×C11⋊C8—42no—
153C22×C11⋊C8C2311yescharacteristic
154C22×C11⋊C8C2311yescharacteristic
155C22×C11⋊C8C2314yescomplemented
156C2×D88—42no—
157C2×D88C2314yes—
158#66949—28no—
159#66948—28no—
160#66948—22no—
161#66948—22no—
162#66948C2314yes—
163#66948C2314yes—
164#66945—22no—
165#66945C2314yes—
166C4⋊C4×D11—22no—
167C4⋊C4×D11C2314yescomplemented
168#66938—28no—
169#66937—28no—
170#66937—28no—
171#66935—28no—
172C11×#107C2314yescomplemented
173C11×#103C2314yescomplemented
174C11×#102C2314yes—
175#66899C2314yescomplemented
176#66896C2314yes—
177#66885C2314yes—
178#66885C2314yescomplemented
179(C2×D11)⋊C8C2314yes—
180(C2×D11)⋊C8C2314yes—
181(C2×D11)⋊C8C2314yescomplemented
182(C2×D11)⋊C8C2314yescomplemented
183#66881C2314yescomplemented
184#66873C2314yes—
185#66873C2314yescomplemented
186#66872C2314yescomplemented
187#66871C2314yescomplemented
188C2×#3198—111nomaximal, Sylow
189C24×C11—21no—
190C24×C11C2×D411yescharacteristic
191C23×D11—21no—
192C23×D11—21no—
193C23×D11—24no—
194C23×D11—44no—
195C23×D11—82no—
196C23×D11—82no—
197C23×D11C2×D411yescharacteristic
198C23×D11C2×D411yescharacteristic
199C2×Q8×C11—21no—
200C2×Q8×C11—22no—
201C2×Q8×C11—22no—
202C2×Q8×C11C2412yes—
203C2×D4×C11—24no—
204C2×D4×C11—21no—
205C2×D4×C11—22no—
206C2×D4×C11—22no—
207C2×D4×C11—82no—
208C2×D4×C11C2412yes—
209C22×C4×C11—22no—
210C22×C4×C11—22no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11C2×D411yescharacteristic
215C22×C4×C11C2×D412yes—
216C22×C4×C11C2412yes—
217C22×C4×C11C2411yescharacteristic
218C2×C22⋊D11—24no—
219C2×C22⋊D11—24no—
220C2×C22⋊D11—24no—
221C2×C22⋊D11—24no—
222C2×C22⋊D11—42no—
223C2×C22⋊D11—42no—
224C2×C22⋊D11—44no—
225C2×C22⋊D11—82no—
226C2×C22⋊D11—82no—
227C2×C22⋊D11—82no—
228C2×C22⋊D11C2×D414yes—
229C2×C22⋊D11C2×D414yes—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11C2×D411yescharacteristic
233C22×Dic11C2×D411yescharacteristic
234#4343—44no—
235#4343—44no—
236#4343—48no—
237D4×D11—44no—
238D4×D11—44no—
239D4×D11—48no—
240#4339—48no—
241#4339—44no—
242#4339—44no—
243C2×D44—24no—
244C2×D44—24no—
245C2×D44—24no—
246C2×D44—21no—
247C2×D44—21no—
248C2×D44—22no—
249C2×D44—22no—
250C2×D44—22no—
251C2×D44—22no—
252C2×D44—42no—
253C2×D44—44no—
254C2×D44—82no—
255C2×D44—82no—
256C2×D44C2×D414yes—
257C2×D44C2412yes—
258C2×D44C2412yes—
259C2×C4×D11—24no—
260C2×C4×D11—24no—
261C2×C4×D11—22no—
262C2×C4×D11—22no—
263C2×C4×D11—22no—
264C2×C4×D11—22no—
265C2×C4×D11—44no—
266C2×C4×D11—82no—
267C2×C4×D11C2×D412yes—
268C2×C4×D11C2×D412yes—
269C2×C4×D11C2412yes—
270C2×C4×D11C2412yes—
271C2×Dic22—42no—
272C2×Dic22C2×D414yes—
273C11×SD16—44no—
274C11×M16—44no—
275C2×C8×C11—22no—
276C2×C8×C11—22no—
277C2×C8×C11C2412yes—
278C2×C8×C11C2412yes—
279C11×C4⋊C4—21no—
280C11×C4⋊C4—21no—
281C11×C4⋊C4—24no—
282C11×C4⋊C4C2412yes—
283C11×C4⋊C4C2412yes—
284C11×C22⋊C4—24no—
285C11×C22⋊C4—24no—
286C22⋊Dic11—24no—
287#4325—44no—
288#4323—44no—
289(C2×D11)⋊C4—24no—
290(C2×D11)⋊C4—24no—
291(C2×D11)⋊C4—24no—
292(C2×D11)⋊C4—24no—
293(C2×D11)⋊C4—24no—
294(C2×D11)⋊C4—24no—
295C4⋊Dic11—21no—
296C4⋊Dic11—21no—
297C4⋊Dic11C2412yes—
298C4⋊Dic11C2412yes—
299Dic11⋊C4—24no—
300Dic11⋊C4—24no—
301C4×Dic11—24no—
302C2×C11⋊C8—22no—
303C2×C11⋊C8—22no—
304C2×C11⋊C8—44no—
305C2×C11⋊C8C2412yes—
306C2×C11⋊C8C2412yes—
307D88—44no—
308C2×#537—111no—
309C2×#535—111no—
310#3198—1116no—
311C2×#481—111no—
312C2×#485—111no—
313C2×#482—111no—
314C2×#480—111no—
315C2×#469—111no—
316C2×#468D1111yescharacteristic, complemented
317C2×#466—111no—
318C2×#465—111no—
319C2×#449—111no—
320C2×#449—111no—
321C2×#450—111no—
322C2×#447—111no—
323C2×#408—111no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—42no—
329C23×C11—42no—
330C23×C11—42no—
331C23×C11C22×D412yes—
332C23×C11C22×D411yescharacteristic
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—48no—
342C22×D11—42no—
343C22×D11—42no—
344C22×D11—42no—
345C22×D11—42no—
346C22×D11—42no—
347C22×D11—42no—
348C22×D11—84no—
349C22×D11—84no—
350C22×D11—816no—
351C22×D11C22×D412yes—
352C22×D11C22×D412yes—
353Q8×C11—22no—
354Q8×C11—22no—
355Q8×C11—42no—
356D4×C11—22no—
357D4×C11—22no—
358D4×C11—42no—
359D4×C11—84no—
360C2×C4×C11—22no—
361C2×C4×C11—24no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—42no—
368C2×C4×C11—42no—
369C2×C4×C11—42no—
370C2×C4×C11C22×D412yes—
371C2×C4×C11C22×D411yescharacteristic
372C2×C4×C11H(5,𝔽2)12yes—
373C2×C4×C11H(5,𝔽2)12yes—
374C2×C4×C11C2511yescharacteristic
375C22⋊D11—44no—
376C22⋊D11—44no—
377C22⋊D11—48no—
378C22⋊D11—84no—
379C22⋊D11—84no—
380C22⋊D11—84no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—42no—
386C2×Dic11—42no—
387C2×Dic11C22×D412yes—
388C2×Dic11C22×D412yes—
389D44—22no—
390D44—22no—
391D44—22no—
392D44—22no—
393D44—44no—
394D44—48no—
395D44—42no—
396D44—42no—
397D44—84no—
398D44—84no—
399C4×D11—24no—
400C4×D11—24no—
401C4×D11—22no—
402C4×D11—22no—
403C4×D11—22no—
404C4×D11—22no—
405C4×D11—48no—
406C4×D11—84no—
407Dic22—44no—
408C8×C11—22no—
409C8×C11—22no—
410C11⋊C8—22no—
411C11⋊C8—22no—
412C22×#41—111no—
413C22×#41—111no—
414C23×D4—111no—
415C22×SD16—111no—
416C22×SD16C2×D1111yescharacteristic
417C22×D8—111no—
418C22×D8—111no—
419C22×M16C2×D1111yescharacteristic, complemented
420C23×C8—111no—
421#537—118no—
422#537—224no—
423#535—118no—
424#535—224no—
425C2×#127—221no—
426C2×#124—221no—
427C2×C22⋊Q8—111no—
428C2×C22⋊Q8—221no—
429C2×C22⋊Q8C2×D1111yescharacteristic, complemented
430C2×#121—111no—
431C2×#121—111no—
432C2×#121—111no—
433C2×#121—111no—
434C2×#121—111no—
435C2×#121—221no—
436C2×#121—221no—
437C2×#121—221no—
438C2×#121C2×D1111yescharacteristic
439C2×#120—221no—
440C2×#120—221no—
441C2×#117—111no—
442C22×C4⋊C4—111no—
443#485—118no—
444#482—118no—
445#481—118no—
446#480—118no—
447#469—118no—
448#468C2×D1118yescomplemented
449#466—118no—
450#465—118no—
451#450—118no—
452#449—118no—
453#449—118no—
454#447—118no—
455C2×#107—111no—
456C2×#107C2×D1111yescharacteristic, complemented
457C2×#106—111no—
458C2×#106—111no—
459C2×#103—111no—
460C2×#103C2×D1111yescharacteristic, complemented
461C2×#102—111no—
462C2×#102—111no—
463C2×#102—111no—
464C2×#102—111no—
465C2×#102—111no—
466C2×#102C2×D1111yescharacteristic
467#408—118no—
468C2×C22⋊C8—111no—
469C2×C22⋊C8—111no—
470C2×C22⋊C8—111no—
471C2×C22⋊C8—111no—
472C22×C11—22no—
473C22×C11—22no—
474C22×C11—22no—
475C22×C11—44no—
476C22×C11—42no—
477C22×C11—42no—
478C22×C11—42no—
479C22×C11—84no—
480C22×C11#53412yes—
481C22×C11#57612yes—
482C22×C11#57712yes—
483C22×C11C23×D411yescharacteristic
484C2×D11—22no—
485C2×D11—22no—
486C2×D11—22no—
487C2×D11—22no—
488C2×D11—22no—
489C2×D11—22no—
490C2×D11—44no—
491C2×D11—44no—
492C2×D11—42no—
493C2×D11—42no—
494C2×D11—42no—
495C2×D11—42no—
496C2×D11—42no—
497C2×D11—42no—
498C2×D11—816no—
499C2×D11—84no—
500C2×D11—84no—
501C4×C11—22no—
502C4×C11—42no—
503C4×C11—42no—
504C4×C11—42no—
505C4×C11#53412yes—
506C4×C11C2×H(5,𝔽2)11yescharacteristic
507C4×C11C2×H(5,𝔽2)11yescharacteristic
508Dic11—22no—
509Dic11—22no—
510Dic11—42no—
511Dic11—42no—
512C25—221no—
513C2×#41—114no—
514C2×#41—114no—
515C2×#41—114no—
516C2×#41—222no—
517C2×#41—442no—
518C2×#41—442no—
519C2×#41—442no—
520C2×#41—442no—
521C22×Q8—111no—
522C22×Q8C22×D1111yescharacteristic
523C22×D4—21no—
524C22×D4—111no—
525C22×D4—111no—
526C22×D4—114no—
527C22×D4—111no—
528C22×D4—111no—
529C22×D4—111no—
530C22×D4—221no—
531C22×D4—221no—
532C22×D4—221no—
533C22×D4—222no—
534C22×D4—221no—
535C22×D4—221no—
536C22×D4—221no—
537C22×D4—221no—
538C22×D4—442no—
539C22×D4—442no—
540C22×D4C22×D1111yescharacteristic
541C23×C4—111no—
542C23×C4—111no—
543C23×C4—221no—
544C23×C4—221no—
545C23×C4C22×D1111yescharacteristic
546C2×SD16—42no—
547C2×SD16—114no—
548C2×SD16—442no—
549C2×SD16C22×D1114yes—
550C2×D8—114no—
551C2×D8—114no—
552C2×D8—442no—
553C2×D8—442no—
554C2×M16—42no—
555C2×M16C22×D1114yescomplemented
556C22×C8—111no—
557C22×C8—111no—
558C22×C8—114no—
559C22×C8—442no—
560C22×C8C22×D1111yescharacteristic
561C22×C8C22×D1111yescharacteristic
562#127—228no—
563#124—228no—
564C22⋊Q8—22no—
565C22⋊Q8—114no—
566C22⋊Q8—228no—
567C22⋊Q8—222no—
568C22⋊Q8C22×D1114yescomplemented
569#121—22no—
570#121—114no—
571#121—114no—
572#121—114no—
573#121—114no—
574#121—114no—
575#121—228no—
576#121—228no—
577#121—222no—
578#121—222no—
579#121—228no—
580#121—222no—
581#121—222no—
582#121—222no—
583#121C22×D1114yes—
584#120—228no—
585#120—228no—
586#117—114no—
587#117—222no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—111no—
590C2×C4⋊C4—111no—
591C2×C4⋊C4—114no—
592C2×C4⋊C4—222no—
593C2×C4⋊C4—221no—
594C2×C4⋊C4—221no—
595C2×C4⋊C4C22×D1111yescharacteristic
596C2×C4⋊C4C22×D1111yescharacteristic
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—221no—
600C2×C22⋊C4—221no—
601C2×C22⋊C4—221no—
602C2×C22⋊C4—221no—
603C2×C22⋊C4—221no—
604C2×C22⋊C4—221no—
605C2×C22⋊C4—221no—
606C2×C42—221no—
607#107—114no—
608#107C22×D1114yescomplemented
609#106—114no—
610#106—114no—
611#103—114no—
612#103C22×D1114yescomplemented
613#102—114no—
614#102—114no—
615#102—114no—
616#102—114no—
617#102—114no—
618#102C22×D1114yes—
619C22⋊C8—114no—
620C22⋊C8—114no—
621C22⋊C8—114no—
622C22⋊C8—114no—
623C2×C11—42no—
624C2×C11—82no—
625C2×C11#319814yescomplemented
626C2×C11C2×#53411yescharacteristic
627C2×C11C2×#57611yescharacteristic
628C2×C11C2×#57711yescharacteristic
629D11—42no—
630D11—42no—
631D11—82no—
632D11—82no—
633C24—21no—
634C24—111no—
635C24—111no—
636C24—224no—
637C24—221no—
638C24—221no—
639C24—444no—
640C24—882no—
641C24—882no—
642C24D4×D1111yescharacteristic
643#41—448no—
644#41—444no—
645#41—444no—
646#41—444no—
647#41—444no—
648#41—448no—
649C2×Q8—21no—
650C2×Q8—22no—
651C2×Q8—22no—
652C2×Q8—114no—
653C2×Q8—442no—
654C2×Q8C23×D1112yes—
655C2×D4—24no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—82no—
660C2×D4—114no—
661C2×D4—114no—
662C2×D4—114no—
663C2×D4—112no—
664C2×D4—112no—
665C2×D4—224no—
666C2×D4—224no—
667C2×D4—224no—
668C2×D4—224no—
669C2×D4—224no—
670C2×D4—224no—
671C2×D4—224no—
672C2×D4—221no—
673C2×D4—221no—
674C2×D4—222no—
675C2×D4—222no—
676C2×D4—222no—
677C2×D4—222no—
678C2×D4—442no—
679C2×D4—444no—
680C2×D4—444no—
681C2×D4—444no—
682C2×D4—448no—
683C2×D4—442no—
684C2×D4—442no—
685C2×D4—444no—
686C2×D4—882no—
687C2×D4—882no—
688C2×D4—882no—
689C2×D4—882no—
690C2×D4—882no—
691C2×D4C23×D1112yes—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—111no—
698C22×C4—111no—
699C22×C4—112no—
700C22×C4—112no—
701C22×C4—112no—
702C22×C4—112no—
703C22×C4—224no—
704C22×C4—224no—
705C22×C4—222no—
706C22×C4—222no—
707C22×C4—222no—
708C22×C4—222no—
709C22×C4—221no—
710C22×C4—221no—
711C22×C4—444no—
712C22×C4—882no—
713C22×C4D4×D1112yes—
714C22×C4D4×D1111yescharacteristic
715C22×C4C23×D1112yes—
716C22×C4C23×D1111yescharacteristic
717SD16—44no—
718SD16—444no—
719D8—444no—
720D8—444no—
721M16—44no—
722C2×C8—22no—
723C2×C8—22no—
724C2×C8—112no—
725C2×C8—112no—
726C2×C8—222no—
727C2×C8—222no—
728C2×C8—444no—
729C2×C8C23×D1112yes—
730C2×C8C23×D1112yes—
731C4⋊C4—24no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—112no—
735C4⋊C4—112no—
736C4⋊C4—224no—
737C4⋊C4—224no—
738C4⋊C4—221no—
739C4⋊C4—221no—
740C4⋊C4C23×D1112yes—
741C4⋊C4C23×D1112yes—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—224no—
745C22⋊C4—224no—
746C22⋊C4—224no—
747C22⋊C4—224no—
748C22⋊C4—224no—
749C22⋊C4—224no—
750C22⋊C4—224no—
751C42—224no—
752C11C2×#319811yescharacteristic, complemented, Sylow
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—112no—
761C23—112no—
762C23—222no—
763C23—222no—
764C23—222no—
765C23—222no—
766C23—222no—
767C23—222no—
768C23—222no—
769C23—222no—
770C23—448no—
771C23—442no—
772C23—442no—
773C23—442no—
774C23—442no—
775C23—442no—
776C23—442no—
777C23—884no—
778C23—884no—
779C23—8816no—
780C23C2×D4×D1112yes—
781C23C2×D4×D1111yescharacteristic
782Q8—22no—
783Q8—22no—
784Q8—42no—
785Q8—444no—
786D4—22no—
787D4—22no—
788D4—42no—
789D4—84no—
790D4—222no—
791D4—222no—
792D4—222no—
793D4—222no—
794D4—444no—
795D4—448no—
796D4—444no—
797D4—444no—
798D4—448no—
799D4—442no—
800D4—442no—
801D4—884no—
802D4—884no—
803D4—884no—
804D4—884no—
805D4—884no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—112no—
817C2×C4—112no—
818C2×C4—222no—
819C2×C4—222no—
820C2×C4—224no—
821C2×C4—224no—
822C2×C4—222no—
823C2×C4—222no—
824C2×C4—222no—
825C2×C4—222no—
826C2×C4—222no—
827C2×C4—222no—
828C2×C4—448no—
829C2×C4—442no—
830C2×C4—442no—
831C2×C4—884no—
832C2×C4C2×D4×D1112yes—
833C2×C4C2×D4×D1111yescharacteristic
834C2×C4#6703712yes—
835C2×C4#6704212yes—
836C2×C4C24×D1111yescharacteristic
837C8—22no—
838C8—22no—
839C8—222no—
840C8—222no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—44no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—84no—
849C22—222no—
850C22—222no—
851C22—222no—
852C22—222no—
853C22—222no—
854C22—222no—
855C22—444no—
856C22—444no—
857C22—442no—
858C22—442no—
859C22—442no—
860C22—442no—
861C22—442no—
862C22—442no—
863C22—8816no—
864C22—884no—
865C22—884no—
866C22#1062313612yes—
867C22#1062330512yes—
868C22#1062330912yes—
869C22C22×D4×D1111yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—222no—
875C4—222no—
876C4—442no—
877C4—442no—
878C4#1062313612yes—
879C4C2×#6703711yescharacteristic
880C4C2×#6704211yescharacteristic
881C2—42no—
882C2—82no—
883C2—442no—
884C2—442no—
885C2—882no—
886C2—882no—
887C2#1307946914yesdirect product factor
888C2C2×#1062313611yescharacteristic
889C2C2×#1062330511yescharacteristic
890C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#468C2
socleC23×C11C22×D4
hypercenterC2×#468D11
hypocenterC11C2×#3198
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. C2×#10623160C2semidirect
2. C2×#10623138C2semidirect
3. #13079469C2direct (N × H)
4. C2×#10622390C2semidirect
5. C2×#10622428C2semidirect
6. C2×#10622498C2semidirect
7. C2×#10622495C2semidirect
8. C2×#10622748C2semidirect
9. C2×#10622651C2semidirect
10. C2×#10622661C2semidirect
11. C2×#10622424C2semidirect
12. C2×#10622785C2semidirect
13. C2×#10622782C2semidirect
14. C2×#10622386C2semidirect
15. C2×#10622742C2semidirect
16. C2×C11×#468C2semidirect
17. C22×#4343C22semidirect
21. C22×C11×M16C22semidirect
22. C2×C11×C22⋊Q8C22semidirect
31. C2×#66983C22semidirect
32. C23×C11⋊C8C22semidirect
35. #10623160C22semidirect
37. #10623138C22semidirect
43. C2×C4⋊C4×D11C22semidirect
48. C11×#468C22semidirect
49. C2×C11×#107C22semidirect
50. C2×C11×#103C22semidirect
52. C2×#66899C22semidirect
54. #10622785C22semidirect
55. #10622782C22semidirect
56. #10622748C22semidirect
57. #10622742C22semidirect
59. C2×#66885C22semidirect
62. C2×(C2×D11)⋊C8C22semidirect
63. C2×(C2×D11)⋊C8C22semidirect
64. C2×#66881C22semidirect
65. #10622661C22semidirect
66. #10622651C22semidirect
68. C2×#66873C22semidirect
69. C2×#66872C22semidirect
70. C2×#66871C22semidirect
71. #10622498C22semidirect
72. #10622495C22semidirect
73. #10622428C22semidirect
74. #10622424C22semidirect
75. #10622390C22semidirect
76. #10622386C22semidirect
91. C2×#4343C23semidirect
114. C2×C11×M16C23semidirect
118. C11×C22⋊Q8C23semidirect
140. #66983C23semidirect
155. C22×C11⋊C8C23semidirect
167. C4⋊C4×D11C23semidirect
172. C11×#107C23semidirect
173. C11×#103C23semidirect
175. #66899C23semidirect
178. #66885C23semidirect
181. (C2×D11)⋊C8C23semidirect
182. (C2×D11)⋊C8C23semidirect
183. #66881C23semidirect
185. #66873C23semidirect
186. #66872C23semidirect
187. #66871C23semidirect
316. C2×#468D11semidirect
419. C22×M16C2×D11semidirect
429. C2×C22⋊Q8C2×D11semidirect
448. #468C2×D11semidirect
456. C2×#107C2×D11semidirect
460. C2×#103C2×D11semidirect
555. C2×M16C22×D11semidirect
568. C22⋊Q8C22×D11semidirect
608. #107C22×D11semidirect
612. #103C22×D11semidirect
625. C2×C11#3198semidirect
752. C11C2×#3198semidirect
887. C2#13079469direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231602
C2×#106231382
#130794692
C2×#106223902
C2×#106224282
C2×#106224982
C2×#106224952
C2×#106227482
C2×#106226512
C2×#106226612
C2×#106224242
C2×#106227852
C2×#106227822
C2×#106223862
C2×#106227422
C2×C11×#4682
C2×#319811