Finite Group Databasebeta

← C2×#13079467 #15624425

Subgroups — C2×#13079467 #15624425

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×#10623364C211yesmaximal, characteristic, complemented
2C2×#10623138C211yesmaximal, characteristic, complemented
3#13079467C2116yesmaximal, direct product factor
4C2×#10622348C211yesmaximal, characteristic, complemented
5C2×#10622428C211yesmaximal, characteristic, complemented
6C2×#10622392C211yesmaximal, characteristic, complemented
7C2×#10622646C211yesmaximal, characteristic, complemented
8C2×#10622772C211yesmaximal, characteristic, complemented
9C2×#10622425C211yesmaximal, characteristic, complemented
10C2×#10622388C211yesmaximal, characteristic, complemented
11C2×#10622784C211yesmaximal, characteristic, complemented
12C2×#10622851C211yesmaximal, characteristic, complemented
13C2×#10622782C211yesmaximal, characteristic, complemented
14C2×#10622769C211yesmaximal, characteristic, complemented
15C2×#10622340C211yesmaximal, characteristic, complemented
16C2×C11×#449C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic, complemented
18C22×D4×D11C2211yescharacteristic
19C22×#4339C2211yescharacteristic
20C22×C11×SD16C2211yescharacteristic
21C22×C11×D8C2211yescharacteristic
22C2×C11×#121C2211yescharacteristic
23#10623364—24no—
24#10623364C2218yescomplemented
25C2×#66999C2211yescharacteristic
26C2×#66999C2211yescharacteristic, complemented
27C22×#4325C2211yescharacteristic
28C2×#66993—21no—
29C2×#66992—21no—
30C2×#66992—21no—
31C2×#66991C2211yescharacteristic
32C2×#66991C2211yescharacteristic
33C2×#66991C2211yescharacteristic, complemented
34C2×#66990—21no—
35C22×#4323C2211yescharacteristic
36C2×#66983—21no—
37C2×#66983C2211yescharacteristic
38C22×C4⋊Dic11C2211yescharacteristic, complemented
39C2×#66977—21no—
40C22×#4313C2211yescharacteristic, complemented
41C22×C8×D11C2211yescharacteristic, complemented
42#10623138—24no—
43#10623138C2218yescomplemented
44C2×#66948C2211yescharacteristic
45C2×#66945C2211yescharacteristic
46C2×#66938—21no—
47C2×#66935—21no—
48C11×#449C2218yescomplemented
49C2×C11×#103C2211yescharacteristic, complemented
50C2×C11×#102C2211yescharacteristic, complemented
51C2×C11×C22⋊C8C2211yescharacteristic, complemented
52#10622851C2218yescomplemented
53C2×#66899C2211yescharacteristic, complemented
54C2×#66896C2211yescharacteristic
55C2×#66896C2211yescharacteristic
56C2×#66896C2211yescharacteristic, complemented
57C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
58#10622784C2218yescomplemented
59#10622782C2218yescomplemented
60#10622772C2218yescomplemented
61#10622769C2218yescomplemented
62C2×#66885C2211yescharacteristic
63C2×#66885C2211yescharacteristic
64C2×(C2×D11)⋊C8C2211yescharacteristic
65C2×(C2×D11)⋊C8C2211yescharacteristic
66C2×#66881C2211yescharacteristic, complemented
67C2×#66881C2211yescharacteristic, complemented
68#10622646C2218yescomplemented
69C2×#66871C2211yescharacteristic, complemented
70C2×#66871C2211yescharacteristic, complemented
71#10622428C2218yescomplemented
72#10622425C2218yescomplemented
73#10622392C2218yescomplemented
74#10622388C2218yescomplemented
75#10622348C2218yescomplemented
76#10622340C2218yescomplemented
77C24×D11—21no—
78C2×C11×#41—22no—
79C2×C11×#41—42no—
80C2×C11×#41—42no—
81C2×C11×#41C2314yescomplemented
82C22×Q8×C11C2311yescharacteristic
83C22×D4×C11—21no—
84C22×D4×C11—21no—
85C22×D4×C11C2311yescharacteristic
86C22×D4×C11C2311yescharacteristic
87C23×C4×C11—21no—
88C23×C4×C11C2311yescharacteristic
89C22×C22⋊D11—21no—
90C22×C22⋊D11—21no—
91C22×C22⋊D11—21no—
92C22×C22⋊D11—21no—
93C22×C22⋊D11—21no—
94C22×C22⋊D11D411yescharacteristic
95C22×C22⋊D11D411yescharacteristic
96C23×Dic11—21no—
97C2×D4×D11—22no—
98C2×D4×D11—42no—
99C2×D4×D11—42no—
100C2×D4×D11C2314yes—
101C2×#4339—42no—
102C2×#4339—42no—
103C2×#4339D414yes—
104C2×#4339C2314yes—
105C22×D44—21no—
106C22×D44D411yescharacteristic
107C22×D44C2311yescharacteristic
108C22×C4×D11C2311yescharacteristic
109C22×C4×D11C2311yescharacteristic
110C22×Dic22D411yescharacteristic
111C2×C11×SD16—42no—
112C2×C11×SD16C2314yes—
113C2×C11×D8—42no—
114C2×C11×D8C2314yes—
115C22×C8×C11C2311yescharacteristic
116C22×C8×C11C2311yescharacteristic
117C11×#121—22no—
118C11×#121C2314yes—
119C2×C11×C4⋊C4C2311yescharacteristic
120C2×C11×C22⋊C4—21no—
121C2×C22⋊Dic11—21no—
122C2×C22⋊Dic11—21no—
123C2×C22⋊Dic11—21no—
124#66999—22no—
125#66999—22no—
126#66999C2314yes—
127#66999C2314yescomplemented
128C2×#4325—42no—
129C2×#4325C2314yes—
130#66993—28no—
131#66992—28no—
132#66992—28no—
133#66991—22no—
134#66991—22no—
135#66991—22no—
136#66991C2314yes—
137#66991C2314yes—
138#66991C2314yescomplemented
139#66990—28no—
140C2×#4323—42no—
141C2×#4323C2314yes—
142#66983—22no—
143#66983—28no—
144#66983C2314yes—
145C2×(C2×D11)⋊C4—21no—
146C2×(C2×D11)⋊C4—21no—
147C2×(C2×D11)⋊C4—21no—
148C2×(C2×D11)⋊C4—21no—
149C2×(C2×D11)⋊C4—21no—
150C2×C4⋊Dic11—21no—
151C2×C4⋊Dic11—22no—
152C2×C4⋊Dic11C2311yescharacteristic
153C2×C4⋊Dic11C2311yescharacteristic
154C2×C4⋊Dic11C2311yescharacteristic
155C2×C4⋊Dic11C2314yescomplemented
156#66977—28no—
157C2×Dic11⋊C4—21no—
158C2×Dic11⋊C4—21no—
159C2×C4×Dic11—21no—
160C22×C11⋊C8C2311yescharacteristic
161C22×C11⋊C8C2311yescharacteristic
162C2×#4313—42no—
163C2×#4313C2314yescomplemented
164C2×C8×D11—42no—
165C2×C8×D11C2314yescomplemented
166#66948—22no—
167#66948C2314yes—
168#66945—22no—
169#66945C2314yes—
170#66938—28no—
171#66935—28no—
172C11×#103C2314yescomplemented
173C11×#102C2314yescomplemented
174C11×C22⋊C8C2314yescomplemented
175#66899C2314yescomplemented
176#66896C2314yes—
177#66896C2314yes—
178#66896C2314yescomplemented
179C22⋊(C11⋊C8)C2314yescomplemented
180#66885C2314yes—
181#66885C2314yes—
182(C2×D11)⋊C8C2314yes—
183(C2×D11)⋊C8C2314yes—
184#66881C2314yescomplemented
185#66881C2314yescomplemented
186#66871C2314yescomplemented
187#66871C2314yescomplemented
188C2×#3198—111nomaximal, Sylow
189C24×C11—21no—
190C24×C11—21no—
191C24×C11C2×D411yescharacteristic
192C23×D11—21no—
193C23×D11—24no—
194C23×D11—44no—
195C23×D11—82no—
196C23×D11—82no—
197C23×D11C2×D411yescharacteristic
198C23×D11C2×D411yescharacteristic
199C11×#41—44no—
200C11×#41—44no—
201C11×#41—48no—
202C2×Q8×C11—21no—
203C2×Q8×C11—22no—
204C2×Q8×C11—22no—
205C2×Q8×C11C2412yes—
206C2×D4×C11—24no—
207C2×D4×C11—24no—
208C2×D4×C11—21no—
209C2×D4×C11—21no—
210C2×D4×C11—22no—
211C2×D4×C11—22no—
212C2×D4×C11—22no—
213C2×D4×C11—22no—
214C2×D4×C11—44no—
215C2×D4×C11—82no—
216C2×D4×C11C2412yes—
217C2×D4×C11C2412yes—
218C22×C4×C11—22no—
219C22×C4×C11—22no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—24no—
223C22×C4×C11—44no—
224C22×C4×C11C2×D411yescharacteristic
225C22×C4×C11C2×D412yes—
226C22×C4×C11C2412yes—
227C22×C4×C11C2411yescharacteristic
228C2×C22⋊D11—24no—
229C2×C22⋊D11—24no—
230C2×C22⋊D11—24no—
231C2×C22⋊D11—24no—
232C2×C22⋊D11—24no—
233C2×C22⋊D11—42no—
234C2×C22⋊D11—42no—
235C2×C22⋊D11—44no—
236C2×C22⋊D11—82no—
237C2×C22⋊D11—82no—
238C2×C22⋊D11—82no—
239C2×C22⋊D11—82no—
240C2×C22⋊D11C2×D414yes—
241C2×C22⋊D11C2×D414yes—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11—21no—
245C22×Dic11—24no—
246C22×Dic11—82no—
247C22×Dic11C2×D411yescharacteristic
248C22×Dic11C2×D411yescharacteristic
249D4×D11—44no—
250D4×D11—44no—
251D4×D11—48no—
252#4339—48no—
253#4339—44no—
254#4339—44no—
255C2×D44—24no—
256C2×D44—21no—
257C2×D44—22no—
258C2×D44—22no—
259C2×D44—42no—
260C2×D44—82no—
261C2×D44C2×D414yes—
262C2×D44C2412yes—
263C2×C4×D11—22no—
264C2×C4×D11—22no—
265C2×C4×D11—22no—
266C2×C4×D11—22no—
267C2×C4×D11C2×D412yes—
268C2×C4×D11C2×D412yes—
269C2×C4×D11C2412yes—
270C2×C4×D11C2412yes—
271C2×Dic22—42no—
272C2×Dic22C2×D414yes—
273C11×SD16—44no—
274C11×D8—44no—
275C2×C8×C11—22no—
276C2×C8×C11—22no—
277C2×C8×C11C2412yes—
278C2×C8×C11C2412yes—
279C11×C4⋊C4—21no—
280C11×C4⋊C4C2412yes—
281C11×C22⋊C4—24no—
282C22⋊Dic11—24no—
283C22⋊Dic11—24no—
284C22⋊Dic11—24no—
285#4325—44no—
286#4323—44no—
287(C2×D11)⋊C4—24no—
288(C2×D11)⋊C4—24no—
289(C2×D11)⋊C4—24no—
290(C2×D11)⋊C4—24no—
291(C2×D11)⋊C4—24no—
292C4⋊Dic11—21no—
293C4⋊Dic11—24no—
294C4⋊Dic11—21no—
295C4⋊Dic11—21no—
296C4⋊Dic11C2412yes—
297C4⋊Dic11C2412yes—
298C4⋊Dic11C2412yes—
299Dic11⋊C4—24no—
300Dic11⋊C4—24no—
301C4×Dic11—24no—
302C2×C11⋊C8—22no—
303C2×C11⋊C8—22no—
304C2×C11⋊C8C2412yes—
305C2×C11⋊C8C2412yes—
306#4313—44no—
307C8×D11—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×#465—111no—
319C2×#449—111no—
320C2×#449D1111yescharacteristic, complemented
321C2×#450—111no—
322C2×#447—111no—
323C2×#408—111no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—42no—
330C23×C11—42no—
331C23×C11—42no—
332C23×C11—42no—
333C23×C11—42no—
334C23×C11—42no—
335C23×C11C22×D412yes—
336C23×C11C22×D411yescharacteristic
337C22×D11—22no—
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—22no—
342C22×D11—22no—
343C22×D11—22no—
344C22×D11—48no—
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—22no—
359D4×C11—22no—
360D4×C11—48no—
361D4×C11—42no—
362D4×C11—42no—
363D4×C11—84no—
364C2×C4×C11—22no—
365C2×C4×C11—24no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—48no—
371C2×C4×C11—42no—
372C2×C4×C11—42no—
373C2×C4×C11C22×D412yes—
374C2×C4×C11C22×D411yescharacteristic
375C2×C4×C11H(5,𝔽2)12yes—
376C2×C4×C11H(5,𝔽2)12yes—
377C2×C4×C11C2511yescharacteristic
378C22⋊D11—44no—
379C22⋊D11—44no—
380C22⋊D11—48no—
381C22⋊D11—84no—
382C22⋊D11—84no—
383C22⋊D11—84no—
384C22⋊D11—84no—
385C2×Dic11—22no—
386C2×Dic11—22no—
387C2×Dic11—22no—
388C2×Dic11—22no—
389C2×Dic11—22no—
390C2×Dic11—42no—
391C2×Dic11—42no—
392C2×Dic11—42no—
393C2×Dic11—84no—
394C2×Dic11C22×D412yes—
395C2×Dic11C22×D412yes—
396D44—22no—
397D44—22no—
398D44—44no—
399D44—42no—
400D44—84no—
401C4×D11—24no—
402C4×D11—24no—
403C4×D11—22no—
404C4×D11—22no—
405C4×D11—22no—
406C4×D11—22no—
407Dic22—44no—
408C8×C11—22no—
409C8×C11—22no—
410C11⋊C8—22no—
411C11⋊C8—22no—
412C22×#41—111no—
413C22×#41C2×D1111yescharacteristic, complemented
414C23×D4—111no—
415C22×SD16—111no—
416C22×SD16C2×D1111yescharacteristic
417C22×D8—111no—
418C22×D8C2×D1111yescharacteristic
419C22×M16—111no—
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—111no—
429C2×C22⋊Q8—221no—
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#465—118no—
451#450—118no—
452#449—118no—
453#449C2×D1118yescomplemented
454#447—118no—
455C2×#107—111no—
456C2×#107—111no—
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, complemented
467#408—118no—
468C2×C22⋊C8—111no—
469C2×C22⋊C8—111no—
470C2×C22⋊C8—111no—
471C2×C22⋊C8C2×D1111yescharacteristic, complemented
472C22×C11—22no—
473C22×C11—22no—
474C22×C11—22no—
475C22×C11—44no—
476C22×C11—42no—
477C22×C11—42no—
478C22×C11—42no—
479C22×C11—42no—
480C22×C11—42no—
481C22×C11—42no—
482C22×C11—84no—
483C22×C11—84no—
484C22×C11#53412yes—
485C22×C11#57612yes—
486C22×C11#57712yes—
487C22×C11C23×D411yescharacteristic
488C2×D11—22no—
489C2×D11—22no—
490C2×D11—22no—
491C2×D11—22no—
492C2×D11—22no—
493C2×D11—22no—
494C2×D11—44no—
495C2×D11—44no—
496C2×D11—42no—
497C2×D11—42no—
498C2×D11—42no—
499C2×D11—816no—
500C2×D11—84no—
501C4×C11—22no—
502C4×C11—42no—
503C4×C11—42no—
504C4×C11#53412yes—
505C4×C11C2×H(5,𝔽2)11yescharacteristic
506C4×C11C2×H(5,𝔽2)11yescharacteristic
507Dic11—22no—
508Dic11—22no—
509Dic11—42no—
510Dic11—42no—
511Dic11—42no—
512C25—221no—
513C2×#41—22no—
514C2×#41—42no—
515C2×#41—42no—
516C2×#41—114no—
517C2×#41—114no—
518C2×#41—442no—
519C2×#41—442no—
520C2×#41C22×D1114yescomplemented
521C22×Q8—111no—
522C22×Q8C22×D1111yescharacteristic
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—111no—
526C22×D4—111no—
527C22×D4—114no—
528C22×D4—111no—
529C22×D4—111no—
530C22×D4—221no—
531C22×D4—222no—
532C22×D4—221no—
533C22×D4—221no—
534C22×D4—221no—
535C22×D4—221no—
536C22×D4—221no—
537C22×D4—442no—
538C22×D4—442no—
539C22×D4C22×D1111yescharacteristic
540C22×D4C22×D1111yescharacteristic
541C23×C4—21no—
542C23×C4—111no—
543C23×C4—111no—
544C23×C4—221no—
545C23×C4C22×D1111yescharacteristic
546C2×SD16—42no—
547C2×SD16—114no—
548C2×SD16—442no—
549C2×SD16C22×D1114yes—
550C2×D8—42no—
551C2×D8—114no—
552C2×D8—442no—
553C2×D8C22×D1114yes—
554C2×M16—114no—
555C2×M16—442no—
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—114no—
565C22⋊Q8—114no—
566C22⋊Q8—228no—
567C22⋊Q8—222no—
568C22⋊Q8—222no—
569#121—22no—
570#121—114no—
571#121—114no—
572#121—114no—
573#121—114no—
574#121—114no—
575#121—222no—
576#121—228no—
577#121—222no—
578#121—222no—
579#121—222no—
580#121—228no—
581#121—228no—
582#121—222no—
583#121C22×D1114yes—
584#120—228no—
585#120—228no—
586#117—114no—
587#117—222no—
588C2×C4⋊C4—111no—
589C2×C4⋊C4—111no—
590C2×C4⋊C4—114no—
591C2×C4⋊C4—111no—
592C2×C4⋊C4—221no—
593C2×C4⋊C4—221no—
594C2×C4⋊C4—221no—
595C2×C4⋊C4—222no—
596C2×C4⋊C4C22×D1111yescharacteristic
597C2×C22⋊C4—21no—
598C2×C22⋊C4—221no—
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#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×D1114yescomplemented
619C22⋊C8—114no—
620C22⋊C8—114no—
621C22⋊C8—114no—
622C22⋊C8C22×D1114yescomplemented
623C2×C11—42no—
624C2×C11—82no—
625C2×C11—82no—
626C2×C11#319814yescomplemented
627C2×C11C2×#53411yescharacteristic
628C2×C11C2×#57611yescharacteristic
629C2×C11C2×#57711yescharacteristic
630D11—42no—
631D11—42no—
632D11—82no—
633C24—21no—
634C24—21no—
635C24—111no—
636C24—111no—
637C24—224no—
638C24—221no—
639C24—444no—
640C24—882no—
641C24—882no—
642C24D4×D1111yescharacteristic
643#41—44no—
644#41—44no—
645#41—48no—
646#41—448no—
647#41—444no—
648#41—444no—
649C2×Q8—21no—
650C2×Q8—22no—
651C2×Q8—22no—
652C2×Q8—114no—
653C2×Q8—442no—
654C2×Q8C23×D1112yes—
655C2×D4—24no—
656C2×D4—24no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—22no—
663C2×D4—44no—
664C2×D4—82no—
665C2×D4—114no—
666C2×D4—114no—
667C2×D4—114no—
668C2×D4—112no—
669C2×D4—224no—
670C2×D4—224no—
671C2×D4—224no—
672C2×D4—224no—
673C2×D4—224no—
674C2×D4—224no—
675C2×D4—221no—
676C2×D4—222no—
677C2×D4—222no—
678C2×D4—442no—
679C2×D4—444no—
680C2×D4—444no—
681C2×D4—448no—
682C2×D4—442no—
683C2×D4—442no—
684C2×D4—444no—
685C2×D4—882no—
686C2×D4—882no—
687C2×D4—882no—
688C2×D4—882no—
689C2×D4—882no—
690C2×D4C23×D1112yes—
691C2×D4C23×D1112yes—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—24no—
697C22×C4—44no—
698C22×C4—111no—
699C22×C4—111no—
700C22×C4—112no—
701C22×C4—112no—
702C22×C4—112no—
703C22×C4—112no—
704C22×C4—222no—
705C22×C4—222no—
706C22×C4—222no—
707C22×C4—222no—
708C22×C4—221no—
709C22×C4—221no—
710C22×C4—221no—
711C22×C4—224no—
712C22×C4—882no—
713C22×C4D4×D1112yes—
714C22×C4D4×D1111yescharacteristic
715C22×C4C23×D1112yes—
716C22×C4C23×D1111yescharacteristic
717SD16—44no—
718SD16—444no—
719D8—44no—
720D8—444no—
721M16—444no—
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—21no—
732C4⋊C4—112no—
733C4⋊C4—112no—
734C4⋊C4—112no—
735C4⋊C4—224no—
736C4⋊C4—224no—
737C4⋊C4—224no—
738C4⋊C4—221no—
739C4⋊C4—221no—
740C4⋊C4—221no—
741C4⋊C4C23×D1112yes—
742C22⋊C4—24no—
743C22⋊C4—224no—
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—22no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—112no—
765C23—112no—
766C23—222no—
767C23—222no—
768C23—222no—
769C23—222no—
770C23—222no—
771C23—222no—
772C23—222no—
773C23—448no—
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—22no—
789D4—22no—
790D4—48no—
791D4—42no—
792D4—42no—
793D4—84no—
794D4—222no—
795D4—222no—
796D4—444no—
797D4—444no—
798D4—444no—
799D4—448no—
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—48no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—112no—
816C2×C4—112no—
817C2×C4—222no—
818C2×C4—222no—
819C2×C4—224no—
820C2×C4—224no—
821C2×C4—222no—
822C2×C4—222no—
823C2×C4—222no—
824C2×C4—222no—
825C2×C4—222no—
826C2×C4—222no—
827C2×C4—222no—
828C2×C4—442no—
829C2×C4—442no—
830C2×C4—442no—
831C2×C4—884no—
832C2×C4C2×D4×D1112yes—
833C2×C4C2×D4×D1111yescharacteristic
834C2×C4#6703712yes—
835C2×C4#6703712yes—
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—42no—
849C22—42no—
850C22—42no—
851C22—84no—
852C22—84no—
853C22—222no—
854C22—222no—
855C22—222no—
856C22—222no—
857C22—222no—
858C22—222no—
859C22—444no—
860C22—444no—
861C22—442no—
862C22—442no—
863C22—442no—
864C22—8816no—
865C22—884no—
866C22#1062312012yes—
867C22#1062330112yes—
868C22#1062330512yes—
869C22C22×D4×D1111yescharacteristic
870C4—22no—
871C4—42no—
872C4—42no—
873C4—222no—
874C4—222no—
875C4—442no—
876C4—442no—
877C4—442no—
878C4#1062312012yes—
879C4C2×#6703711yescharacteristic
880C4C2×#6703711yescharacteristic
881C2—42no—
882C2—82no—
883C2—82no—
884C2—442no—
885C2—442no—
886C2—882no—
887C2#1307946714yesdirect product factor
888C2C2×#1062312011yescharacteristic
889C2C2×#1062330511yescharacteristic
890C2C2×#1062330111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#449C2
socleC23×C11C22×D4
hypercenterC2×#449D11
hypocenterC11C2×#3198
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#10623364C2semidirect
2. C2×#10623138C2semidirect
3. #13079467C2direct (N × H)
4. C2×#10622348C2semidirect
5. C2×#10622428C2semidirect
6. C2×#10622392C2semidirect
7. C2×#10622646C2semidirect
8. C2×#10622772C2semidirect
9. C2×#10622425C2semidirect
10. C2×#10622388C2semidirect
11. C2×#10622784C2semidirect
12. C2×#10622851C2semidirect
13. C2×#10622782C2semidirect
14. C2×#10622769C2semidirect
15. C2×#10622340C2semidirect
16. C2×C11×#449C2semidirect
17. C22×C11×#41C22semidirect
24. #10623364C22semidirect
26. C2×#66999C22semidirect
33. C2×#66991C22semidirect
38. C22×C4⋊Dic11C22semidirect
40. C22×#4313C22semidirect
41. C22×C8×D11C22semidirect
43. #10623138C22semidirect
48. C11×#449C22semidirect
49. C2×C11×#103C22semidirect
50. C2×C11×#102C22semidirect
51. C2×C11×C22⋊C8C22semidirect
52. #10622851C22semidirect
53. C2×#66899C22semidirect
56. C2×#66896C22semidirect
57. C2×C22⋊(C11⋊C8)C22semidirect
58. #10622784C22semidirect
59. #10622782C22semidirect
60. #10622772C22semidirect
61. #10622769C22semidirect
66. C2×#66881C22semidirect
67. C2×#66881C22semidirect
68. #10622646C22semidirect
69. C2×#66871C22semidirect
70. C2×#66871C22semidirect
71. #10622428C22semidirect
72. #10622425C22semidirect
73. #10622392C22semidirect
74. #10622388C22semidirect
75. #10622348C22semidirect
76. #10622340C22semidirect
81. C2×C11×#41C23semidirect
127. #66999C23semidirect
138. #66991C23semidirect
155. C2×C4⋊Dic11C23semidirect
163. C2×#4313C23semidirect
165. C2×C8×D11C23semidirect
172. C11×#103C23semidirect
173. C11×#102C23semidirect
174. C11×C22⋊C8C23semidirect
175. #66899C23semidirect
178. #66896C23semidirect
179. C22⋊(C11⋊C8)C23semidirect
184. #66881C23semidirect
185. #66881C23semidirect
186. #66871C23semidirect
187. #66871C23semidirect
320. C2×#449D11semidirect
413. C22×#41C2×D11semidirect
453. #449C2×D11semidirect
460. C2×#103C2×D11semidirect
466. C2×#102C2×D11semidirect
471. C2×C22⋊C8C2×D11semidirect
520. C2×#41C22×D11semidirect
612. #103C22×D11semidirect
618. #102C22×D11semidirect
622. C22⋊C8C22×D11semidirect
626. C2×C11#3198semidirect
752. C11C2×#3198semidirect
887. C2#13079467direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233642
C2×#106231382
#130794672
C2×#106223482
C2×#106224282
C2×#106223922
C2×#106226462
C2×#106227722
C2×#106224252
C2×#106223882
C2×#106227842
C2×#106228512
C2×#106227822
C2×#106227692
C2×#106223402
C2×C11×#4492
C2×#319811