Finite Group Databasebeta

← C2×#13079471 #15624429

Subgroups — C2×#13079471 #15624429

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#13079471C2116yesmaximal, direct product factor
4C2×#10622476C211yesmaximal, characteristic, complemented
5C2×#10622427C211yesmaximal, characteristic, complemented
6C2×#10622479C211yesmaximal, characteristic, complemented
7C2×#10622387C211yesmaximal, characteristic, complemented
8C2×#10622652C211yesmaximal, characteristic, complemented
9C2×#10622662C211yesmaximal, characteristic, complemented
10C2×#10622728C211yesmaximal, characteristic, complemented
11C2×#10622424C211yesmaximal, characteristic, complemented
12C2×#10622785C211yesmaximal, characteristic, complemented
13C2×#10622782C211yesmaximal, characteristic, complemented
14C2×#10622386C211yesmaximal, characteristic, complemented
15C2×#10622723C211yesmaximal, characteristic, complemented
16C2×C11×#465C211yesmaximal, characteristic, complemented
17C22×#4343C2211yescharacteristic, complemented
18C22×D4×D11C2211yescharacteristic
19C22×#4339C2211yescharacteristic
20C22×C11×SD16C2211yescharacteristic
21C23×C8×C11C2211yescharacteristic, 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
32C22×#4318C2211yescharacteristic, 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×#465C2218yescomplemented
49C2×C11×#106C2211yescharacteristic, complemented
50C2×C11×#103C2211yescharacteristic, complemented
51C2×C11×#102C2211yescharacteristic
52C2×#66899C2211yescharacteristic, complemented
53C2×#66896C2211yescharacteristic
54#10622785C2218yescomplemented
55#10622782C2218yescomplemented
56#10622728C2218yescomplemented
57C2×#66885C2211yescharacteristic
58C2×#66885C2211yescharacteristic, complemented
59#10622723C2218yescomplemented
60C2×(C2×D11)⋊C8C2211yescharacteristic
61C2×(C2×D11)⋊C8C2211yescharacteristic
62C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
63C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
64C2×#66882C2211yescharacteristic, complemented
65#10622662C2218yescomplemented
66#10622652C2218yescomplemented
67C2×#66873C2211yescharacteristic
68C2×#66873C2211yescharacteristic, complemented
69C2×#66872C2211yescharacteristic, complemented
70C2×#66871C2211yescharacteristic, complemented
71#10622479C2218yescomplemented
72#10622476C2218yescomplemented
73#10622427C2218yescomplemented
74#10622424C2218yescomplemented
75#10622387C2218yescomplemented
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—
113C22×C8×C11—42no—
114C22×C8×C11C2311yescharacteristic
115C22×C8×C11C2311yescharacteristic
116C22×C8×C11C2314yescomplemented
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—
152C2×#4318—42no—
153C2×#4318C2314yescomplemented
154C22×C11⋊C8C2311yescharacteristic
155C22×C11⋊C8C2311yescharacteristic
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×#106C2314yescomplemented
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#66882C2314yescomplemented
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—
274C2×C8×C11—22no—
275C2×C8×C11—22no—
276C2×C8×C11—44no—
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—
302#4318—44no—
303C2×C11⋊C8—22no—
304C2×C11⋊C8—22no—
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×#468—111no—
317C2×#466—111no—
318C2×#465D1111yescharacteristic, complemented
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×M16—111no—
420C23×C8C2×D1111yescharacteristic, complemented
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#468—118no—
449#466—118no—
450#465C2×D1118yescomplemented
451#450—118no—
452#449—118no—
453#449—118no—
454#447—118no—
455C2×#107—111no—
456C2×#107—111no—
457C2×#106—111no—
458C2×#106C2×D1111yescharacteristic, complemented
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—114no—
555C2×M16—442no—
556C22×C8—42no—
557C22×C8—111no—
558C22×C8—111no—
559C22×C8C22×D1111yescharacteristic
560C22×C8C22×D1111yescharacteristic
561C22×C8C22×D1114yescomplemented
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#107—114no—
609#106—114no—
610#106C22×D1114yescomplemented
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—444no—
722C2×C8—22no—
723C2×C8—22no—
724C2×C8—44no—
725C2×C8—112no—
726C2×C8—112no—
727C2×C8—222no—
728C2×C8—222no—
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#1062329312yes—
868C22#1062330012yes—
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#1307947114yesdirect product factor
888C2C2×#1062313611yescharacteristic
889C2C2×#1062330011yescharacteristic
890C2C2×#1062329311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#465C2
socleC23×C11C22×D4
hypercenterC2×#465D11
hypocenterC11C2×#3198
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C2×#10623160C2semidirect
2. C2×#10623138C2semidirect
3. #13079471C2direct (N × H)
4. C2×#10622476C2semidirect
5. C2×#10622427C2semidirect
6. C2×#10622479C2semidirect
7. C2×#10622387C2semidirect
8. C2×#10622652C2semidirect
9. C2×#10622662C2semidirect
10. C2×#10622728C2semidirect
11. C2×#10622424C2semidirect
12. C2×#10622785C2semidirect
13. C2×#10622782C2semidirect
14. C2×#10622386C2semidirect
15. C2×#10622723C2semidirect
16. C2×C11×#465C2semidirect
17. C22×#4343C22semidirect
21. C23×C8×C11C22semidirect
22. C2×C11×C22⋊Q8C22semidirect
31. C2×#66983C22semidirect
32. C22×#4318C22semidirect
35. #10623160C22semidirect
37. #10623138C22semidirect
43. C2×C4⋊C4×D11C22semidirect
48. C11×#465C22semidirect
49. C2×C11×#106C22semidirect
50. C2×C11×#103C22semidirect
52. C2×#66899C22semidirect
54. #10622785C22semidirect
55. #10622782C22semidirect
56. #10622728C22semidirect
58. C2×#66885C22semidirect
59. #10622723C22semidirect
62. C2×(C2×D11)⋊C8C22semidirect
63. C2×(C2×D11)⋊C8C22semidirect
64. C2×#66882C22semidirect
65. #10622662C22semidirect
66. #10622652C22semidirect
68. C2×#66873C22semidirect
69. C2×#66872C22semidirect
70. C2×#66871C22semidirect
71. #10622479C22semidirect
72. #10622476C22semidirect
73. #10622427C22semidirect
74. #10622424C22semidirect
75. #10622387C22semidirect
76. #10622386C22semidirect
91. C2×#4343C23semidirect
116. C22×C8×C11C23semidirect
118. C11×C22⋊Q8C23semidirect
140. #66983C23semidirect
153. C2×#4318C23semidirect
167. C4⋊C4×D11C23semidirect
172. C11×#106C23semidirect
173. C11×#103C23semidirect
175. #66899C23semidirect
178. #66885C23semidirect
181. (C2×D11)⋊C8C23semidirect
182. (C2×D11)⋊C8C23semidirect
183. #66882C23semidirect
185. #66873C23semidirect
186. #66872C23semidirect
187. #66871C23semidirect
318. C2×#465D11semidirect
420. C23×C8C2×D11semidirect
429. C2×C22⋊Q8C2×D11semidirect
450. #465C2×D11semidirect
458. C2×#106C2×D11semidirect
460. C2×#103C2×D11semidirect
561. C22×C8C22×D11semidirect
568. C22⋊Q8C22×D11semidirect
610. #106C22×D11semidirect
612. #103C22×D11semidirect
625. C2×C11#3198semidirect
752. C11C2×#3198semidirect
887. C2#13079471direct (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
#130794712
C2×#106224762
C2×#106224272
C2×#106224792
C2×#106223872
C2×#106226522
C2×#106226622
C2×#106227282
C2×#106224242
C2×#106227852
C2×#106227822
C2×#106223862
C2×#106227232
C2×C11×#4652
C2×#319811