Finite Group Databasebeta

← C2×#13080571 #15630277

Subgroups — C2×#13080571 #15630277

Order 2816.

2514 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623081C211yesmaximal, characteristic, complemented
2#13080571C2116yesmaximal, direct product factor
3C2×#10622702C211yesmaximal, characteristic, complemented
4C2×#10622581C211yesmaximal, characteristic, complemented
5C2×#10622584C211yesmaximal, characteristic, complemented
6C2×#10622697C211yesmaximal, characteristic, complemented
7C2×#10622652C211yesmaximal, characteristic, complemented
8C2×#10622654C211yesmaximal, characteristic, complemented
9C2×#10622629C211yesmaximal, characteristic, complemented
10C2×#10622650C211yesmaximal, characteristic, complemented
11C2×#10622649C211yesmaximal, characteristic, complemented
12C2×#10622627C211yesmaximal, characteristic, complemented
13C2×#10622624C211yesmaximal, characteristic, complemented
14C2×#10622579C211yesmaximal, characteristic, complemented
15C22×#66873C211yesmaximal, characteristic, complemented
16C2×C11×#547C211yesmaximal, characteristic, complemented
17C22×C11×#41—21no—
18C22×#4339C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C11×#547—24no—
21C11×#547C2218yescomplemented
22C2×C11×C4⋊Q8C2211yescharacteristic, complemented
23C2×C11×#123—21no—
24C2×C11×#123—21no—
25C2×C11×C22⋊Q8—21no—
26C2×C11×#121C2211yescharacteristic
27C2×C11×#121C2211yescharacteristic, complemented
28C2×C4×D4×C11C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic, complemented
30C22×C11×C4⋊C4C2211yescharacteristic
31C22×C11×C4⋊C4C2211yescharacteristic, complemented
32C2×#66990—21no—
33C22×#4324C2211yescharacteristic, complemented
34C22×#4323C2211yescharacteristic
35C22×#4323C2211yescharacteristic
36C2×#66983C2211yescharacteristic
37C2×#66977C2211yescharacteristic
38C22×#4318C2211yescharacteristic, complemented
39C23×C11⋊C8C2211yescharacteristic
40#10623081—24no—
41#10623081C2218yescomplemented
42C2×#66947—21no—
43C2×#66937—21no—
44C2×C22⋊C4×D11—21no—
45C2×#66928C2211yescharacteristic
46C2×C4×D44C2211yescharacteristic
47C2×#66896C2211yescharacteristic, complemented
48C2×C22⋊(C11⋊C8)C2211yescharacteristic
49C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
50#10622702C2218yescomplemented
51#10622697C2218yescomplemented
52#10622654C2218yescomplemented
53#10622652C2218yescomplemented
54#10622650C2218yescomplemented
55#10622649C2218yescomplemented
56#10622629C2218yescomplemented
57#10622627C2218yescomplemented
58#10622624C2218yescomplemented
59#10622584C2218yescomplemented
60C2×#66874C2211yescharacteristic, complemented
61C2×#66874C2211yescharacteristic, complemented
62C2×#66874C2211yescharacteristic, complemented
63#10622581C2218yescomplemented
64#10622579C2218yescomplemented
65C2×#66873C2211yescharacteristic
66C2×#66873C2211yescharacteristic
67C2×#66873C2211yescharacteristic
68C2×#66873C2211yescharacteristic
69C2×#66873C2211yescharacteristic
70C2×#66873C2211yescharacteristic
71C2×#66873C2218yescomplemented
72C2×#66872C2211yescharacteristic, complemented
73C2×#66872C2211yescharacteristic, complemented
74C2×#66872C2211yescharacteristic, complemented
75C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
76C2×#66867C2211yescharacteristic, complemented
77C24×D11—21no—
78C2×C11×#41—28no—
79C2×C11×#41—48no—
80C22×Q8×C11—21no—
81C22×D4×C11—21no—
82C22×D4×C11—21no—
83C22×D4×C11D411yescharacteristic
84C22×D4×C11C2311yescharacteristic
85C23×C4×C11—21no—
86C23×C4×C11—21no—
87C23×C4×C11—21no—
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C22×C22⋊D11—21no—
91C22×C22⋊D11—21no—
92C2×#4339—22no—
93C2×#4339—24no—
94C2×#4339—42no—
95C2×#4339C2314yes—
96C22×D44—24no—
97C22×D44—21no—
98C22×D44—22no—
99C22×D44—42no—
100C22×D44C2311yescharacteristic
101C22×D44C2314yes—
102C22×D44C2311yescharacteristic
103C22×C4×D11—21no—
104C22×C4×D11—21no—
105C22×Dic22C2311yescharacteristic
106C11×C4⋊Q8—22no—
107C11×C4⋊Q8C2314yescomplemented
108C11×#123—28no—
109C11×#123—28no—
110C11×C22⋊Q8—28no—
111C11×#121—22no—
112C11×#121—22no—
113C11×#121C2314yes—
114C11×#121C2314yescomplemented
115C4×D4×C11—22no—
116C4×D4×C11D414yes—
117C4×D4×C11C2314yes—
118C4×D4×C11C2314yescomplemented
119C2×C11×C4⋊C4—21no—
120C2×C11×C4⋊C4—22no—
121C2×C11×C4⋊C4—21no—
122C2×C11×C4⋊C4—22no—
123C2×C11×C4⋊C4—21no—
124C2×C11×C4⋊C4D411yescharacteristic
125C2×C11×C4⋊C4C2311yescharacteristic
126C2×C11×C4⋊C4C2311yescharacteristic
127C2×C11×C4⋊C4C2311yescharacteristic
128C2×C11×C4⋊C4C2314yes—
129C2×C11×C4⋊C4C2314yescomplemented
130C2×C11×C22⋊C4—21no—
131C2×C11×C22⋊C4—21no—
132C2×C11×C22⋊C4—21no—
133C2×C11×C22⋊C4D411yescharacteristic
134C2×C11×C22⋊C4D411yescharacteristic
135C2×C42×C11C2311yescharacteristic
136C2×C22⋊Dic11—21no—
137#66990—28no—
138C2×#4324—42no—
139C2×#4324C2314yescomplemented
140C2×#4323—24no—
141C2×#4323—42no—
142C2×#4323C2314yes—
143C2×#4323C2314yes—
144#66983—22no—
145#66983C2314yes—
146C2×(C2×D11)⋊C4—21no—
147C2×(C2×D11)⋊C4—21no—
148C2×(C2×D11)⋊C4—21no—
149C2×(C2×D11)⋊C4—21no—
150C2×C4⋊Dic11C2311yescharacteristic
151#66977—22no—
152#66977C2314yes—
153C2×Dic11⋊C4—21no—
154C2×#4318—42no—
155C2×#4318C2314yescomplemented
156C22×C11⋊C8—42no—
157C22×C11⋊C8C2311yescharacteristic
158C22×C11⋊C8C2311yescharacteristic
159C22×C11⋊C8C2311yescharacteristic
160C22×C11⋊C8C2311yescharacteristic
161C22×C11⋊C8C2314yes—
162#66947—28no—
163#66937—28no—
164C22⋊C4×D11—28no—
165#66928—22no—
166#66928C2314yes—
167C4×D44—22no—
168C4×D44C2314yes—
169#66896C2314yescomplemented
170C22⋊(C11⋊C8)C2314yes—
171C22⋊(C11⋊C8)C2314yescomplemented
172#66874C2314yescomplemented
173#66874C2314yescomplemented
174#66874C2314yescomplemented
175#66873C2314yes—
176#66873C2314yes—
177#66873C2314yes—
178#66873C2314yes—
179#66873C2314yes—
180#66873C2314yes—
181#66872C2314yescomplemented
182#66872C2314yescomplemented
183#66872C2314yescomplemented
184C4⋊(C11⋊C8)C2314yescomplemented
185#66867C2314yescomplemented
186C2×#3306—111nomaximal, Sylow
187C24×C11—21no—
188C24×C11C2×D411yescharacteristic
189C24×C11C2×D411yescharacteristic
190C23×D11—21no—
191C23×D11—21no—
192C23×D11—24no—
193C23×D11—44no—
194C23×D11—44no—
195C23×D11—82no—
196C11×#41—432no—
197C2×Q8×C11—24no—
198C2×Q8×C11—44no—
199C2×D4×C11—24no—
200C2×D4×C11—24no—
201C2×D4×C11—24no—
202C2×D4×C11—21no—
203C2×D4×C11—22no—
204C2×D4×C11—22no—
205C2×D4×C11—44no—
206C2×D4×C11—44no—
207C2×D4×C11C2×D414yes—
208C2×D4×C11C2412yes—
209C22×C4×C11—22no—
210C22×C4×C11—22no—
211C22×C4×C11—22no—
212C22×C4×C11—22no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—24no—
217C22×C4×C11—24no—
218C22×C4×C11—24no—
219C22×C4×C11—44no—
220C22×C4×C11—44no—
221C22×C4×C11—44no—
222C22×C4×C11C2×D411yescharacteristic
223C22×C4×C11C2×D412yes—
224C22×C4×C11C2×D411yescharacteristic
225C22×C4×C11C2×D411yescharacteristic
226C22×C4×C11C2×D411yescharacteristic
227C22×C4×C11C2×D412yes—
228C22×C4×C11C2412yes—
229C22×C4×C11C2412yes—
230C22×C4×C11C2411yescharacteristic
231C2×C22⋊D11—24no—
232C2×C22⋊D11—24no—
233C2×C22⋊D11—44no—
234C2×C22⋊D11—82no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237#4339—28no—
238#4339—44no—
239#4339—48no—
240C2×D44—28no—
241C2×D44—21no—
242C2×D44—21no—
243C2×D44—24no—
244C2×D44—22no—
245C2×D44—22no—
246C2×D44—22no—
247C2×D44—44no—
248C2×D44—44no—
249C2×D44—48no—
250C2×D44#4114yescomplemented
251C2×D44C2412yes—
252C2×D44C2412yes—
253C2×C4×D11—24no—
254C2×C4×D11—24no—
255C2×C4×D11—44no—
256C2×C4×D11—82no—
257C2×Dic22—21no—
258C2×Dic22—22no—
259C2×Dic22—22no—
260C2×Dic22C2412yes—
261C11×C4⋊C4—21no—
262C11×C4⋊C4—21no—
263C11×C4⋊C4—21no—
264C11×C4⋊C4—24no—
265C11×C4⋊C4—24no—
266C11×C4⋊C4—24no—
267C11×C4⋊C4C2×D414yes—
268C11×C4⋊C4C2412yes—
269C11×C4⋊C4C2412yes—
270C11×C4⋊C4C2412yes—
271C11×C22⋊C4—24no—
272C11×C22⋊C4—24no—
273C11×C22⋊C4—24no—
274C11×C22⋊C4C2×D414yes—
275C11×C22⋊C4C2×D414yes—
276C42×C11C2×D412yes—
277C42×C11C2412yes—
278C22⋊Dic11—24no—
279#4324—44no—
280#4323—28no—
281#4323—44no—
282(C2×D11)⋊C4—24no—
283(C2×D11)⋊C4—24no—
284(C2×D11)⋊C4—24no—
285(C2×D11)⋊C4—24no—
286C4⋊Dic11—21no—
287C4⋊Dic11C2412yes—
288Dic11⋊C4—24no—
289#4318—44no—
290C2×C11⋊C8—22no—
291C2×C11⋊C8—22no—
292C2×C11⋊C8—22no—
293C2×C11⋊C8—22no—
294C2×C11⋊C8—44no—
295C2×C11⋊C8C2412yes—
296C2×C11⋊C8C2412yes—
297C2×C11⋊C8C2412yes—
298C2×C11⋊C8C2412yes—
299C2×#547D1111yescharacteristic, complemented
300C2×#546—111no—
301#3306—1116no—
302C2×#489—111no—
303C2×#481—111no—
304C2×#483—111no—
305C2×#476—111no—
306C2×#469—111no—
307C2×#465—111no—
308C2×#463—111no—
309C2×#449—111no—
310C2×#447—111no—
311C2×#442—111no—
312C2×#435—111no—
313C2×#417—111no—
314C22×#102—111no—
315C23×C11—22no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—42no—
322C23×C11—42no—
323C23×C11—42no—
324C23×C11AGL(1,ℤ/8)14yes—
325C23×C11C22×D412yes—
326C23×C11C22×D412yes—
327C23×C11C22×D411yescharacteristic
328C22×D11—24no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—48no—
332C22×D11—42no—
333C22×D11—42no—
334C22×D11—42no—
335C22×D11—48no—
336C22×D11—42no—
337C22×D11—42no—
338C22×D11—84no—
339C22×D11—816no—
340Q8×C11—48no—
341D4×C11—28no—
342D4×C11—22no—
343D4×C11—22no—
344D4×C11—48no—
345D4×C11—48no—
346D4×C11—42no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—24no—
352C2×C4×C11—24no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—48no—
361C2×C4×C11—48no—
362C2×C4×C11—42no—
363C2×C4×C11—42no—
364C2×C4×C11—42no—
365C2×C4×C11—48no—
366C2×C4×C11C22×D412yes—
367C2×C4×C11C22×D412yes—
368C2×C4×C11C22×D412yes—
369C2×C4×C11C22×D412yes—
370C2×C4×C11C22×D411yescharacteristic
371C2×C4×C11C2×#4112yes—
372C2×C4×C11H(5,𝔽2)12yes—
373C2×C4×C11C2511yescharacteristic
374C22⋊D11—48no—
375C22⋊D11—84no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—42no—
379C2×Dic11—42no—
380D44—24no—
381D44—22no—
382D44—22no—
383D44—22no—
384D44—48no—
385D44—42no—
386D44C2×#4114yescomplemented
387C4×D11—48no—
388C4×D11—84no—
389Dic22—22no—
390Dic22—22no—
391Dic22—42no—
392C11⋊C8—22no—
393C11⋊C8—22no—
394C11⋊C8—22no—
395C11⋊C8—22no—
396C22×#41—21no—
397C22×#41—111no—
398C23×D4—111no—
399C22×SD16—111no—
400C22×D8—111no—
401C22×D8—111no—
402C22×M16—111no—
403C23×C8—111no—
404#547—24no—
405#547C2×D1118yescomplemented
406#546—118no—
407#546—224no—
408C2×C4⋊Q8C2×D1111yescharacteristic, complemented
409C2×#124—111no—
410C2×#123—21no—
411C2×#123—21no—
412C2×#123—221no—
413C2×C22⋊Q8—21no—
414C2×C22⋊Q8—111no—
415C2×#121—111no—
416C2×#121—221no—
417C2×#121C2×D1111yescharacteristic
418C2×#121C2×D1111yescharacteristic, complemented
419C2×#120—221no—
420C2×C4×D4—111no—
421C2×C4×D4C2×D1111yescharacteristic
422C2×C4×D4C2×D1111yescharacteristic, complemented
423C22×C4⋊C4C2×D1111yescharacteristic
424C22×C4⋊C4C2×D1111yescharacteristic, complemented
425C22×C22⋊C4—221no—
426#489—118no—
427#483—118no—
428#481—118no—
429#476—118no—
430#469—118no—
431#465—118no—
432#463—118no—
433#449—118no—
434#447—118no—
435#442—118no—
436#435—118no—
437C2×#106—111no—
438C2×#106—111no—
439C2×#106—111no—
440C2×C4⋊C8—111no—
441#417—118no—
442C2×#103—111no—
443C2×#103—111no—
444C2×#103—111no—
445C2×#102—111no—
446C2×#102—111no—
447C2×#102—111no—
448C2×#102—111no—
449C2×#102—111no—
450C2×#102—111no—
451C2×#102—118no—
452C2×#102—111no—
453C2×C22⋊C8—111no—
454C2×C22⋊C8—111no—
455C2×#97—111no—
456C22×C11—22no—
457C22×C11—28no—
458C22×C11—22no—
459C22×C11—22no—
460C22×C11—22no—
461C22×C11—22no—
462C22×C11—44no—
463C22×C11—42no—
464C22×C11—42no—
465C22×C11—42no—
466C22×C11—84no—
467C22×C11#54612yes—
468C22×C11C2×AGL(1,ℤ/8)14yes—
469C22×C11C2×AGL(1,ℤ/8)12yes—
470C22×C11#57712yes—
471C22×C11C23×D411yescharacteristic
472C2×D11—24no—
473C2×D11—48no—
474C2×D11—42no—
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—42no—
479C2×D11—816no—
480C2×D11—84no—
481C4×C11—22no—
482C4×C11—22no—
483C4×C11—22no—
484C4×C11—22no—
485C4×C11—42no—
486C4×C11—42no—
487C4×C11—42no—
488C4×C11#54612yes—
489C4×C11C22×#4111yescharacteristic
490C4×C11C2×H(5,𝔽2)11yescharacteristic
491Dic11—42no—
492Dic11—42no—
493C25—221no—
494C2×#41—28no—
495C2×#41—48no—
496C2×#41—114no—
497C2×#41—224no—
498C2×#41—222no—
499C2×#41—442no—
500C22×Q8—21no—
501C22×Q8—111no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—111no—
505C22×D4—111no—
506C22×D4—114no—
507C22×D4—224no—
508C22×D4—221no—
509C22×D4—221no—
510C22×D4—221no—
511C22×D4—222no—
512C22×D4—442no—
513C22×D4C22⋊D1111yescharacteristic
514C22×D4C22×D1111yescharacteristic
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—221no—
519C23×C4—221no—
520C23×C4C22×D1111yescharacteristic
521C23×C4C22×D1111yescharacteristic
522C2×SD16—114no—
523C2×SD16—442no—
524C2×D8—114no—
525C2×D8—114no—
526C2×D8—224no—
527C2×D8—442no—
528C2×M16—114no—
529C2×M16—442no—
530C22×C8—111no—
531C22×C8—111no—
532C22×C8—111no—
533C22×C8—111no—
534C22×C8—114no—
535C22×C8—442no—
536C4⋊Q8—22no—
537C4⋊Q8C22×D1114yescomplemented
538#124—114no—
539#124—222no—
540#123—28no—
541#123—28no—
542#123—228no—
543C22⋊Q8—28no—
544C22⋊Q8—114no—
545C22⋊Q8—222no—
546#121—22no—
547#121—22no—
548#121—114no—
549#121—222no—
550#121—228no—
551#121C22×D1114yes—
552#121C22×D1114yescomplemented
553#120—228no—
554C4×D4—22no—
555C4×D4—114no—
556C4×D4—222no—
557C4×D4C22⋊D1114yes—
558C4×D4C22×D1114yes—
559C4×D4C22×D1114yescomplemented
560C2×C4⋊C4—21no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—22no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—111no—
566C2×C4⋊C4—221no—
567C2×C4⋊C4C22⋊D1111yescharacteristic
568C2×C4⋊C4C22×D1111yescharacteristic
569C2×C4⋊C4C22×D1111yescharacteristic
570C2×C4⋊C4C22×D1114yes—
571C2×C4⋊C4C22×D1111yescharacteristic
572C2×C4⋊C4C22×D1114yescomplemented
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—221no—
577C2×C22⋊C4—221no—
578C2×C22⋊C4—221no—
579C2×C22⋊C4—221no—
580C2×C22⋊C4—221no—
581C2×C22⋊C4—228no—
582C2×C22⋊C4C22⋊D1111yescharacteristic
583C2×C22⋊C4C22⋊D1111yescharacteristic
584C2×C42C22×D1111yescharacteristic
585#106—114no—
586#106—114no—
587#106—114no—
588C4⋊C8—114no—
589#103—114no—
590#103—114no—
591#103—114no—
592#102—114no—
593#102—114no—
594#102—114no—
595#102—114no—
596#102—114no—
597#102—114no—
598#102—114no—
599C22⋊C8—114no—
600C22⋊C8—114no—
601#97—114no—
602C2×C11—24no—
603C2×C11—42no—
604C2×C11—82no—
605C2×C11#330614yescomplemented
606C2×C11C2×#54611yescharacteristic
607C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
608C2×C11C2×#57711yescharacteristic
609D11—44no—
610D11—82no—
611C24—21no—
612C24—221no—
613C24—221no—
614C24—224no—
615C24—444no—
616C24—444no—
617C24—882no—
618C24C2×C22⋊D1111yescharacteristic
619C24C2×C22⋊D1111yescharacteristic
620#41—432no—
621#41—228no—
622#41—444no—
623#41—448no—
624C2×Q8—24no—
625C2×Q8—44no—
626C2×Q8—112no—
627C2×Q8—221no—
628C2×Q8—222no—
629C2×Q8—222no—
630C2×D4—24no—
631C2×D4—24no—
632C2×D4—24no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—21no—
636C2×D4—44no—
637C2×D4—44no—
638C2×D4—114no—
639C2×D4—112no—
640C2×D4—112no—
641C2×D4—228no—
642C2×D4—224no—
643C2×D4—224no—
644C2×D4—222no—
645C2×D4—222no—
646C2×D4—222no—
647C2×D4—221no—
648C2×D4—224no—
649C2×D4—221no—
650C2×D4—444no—
651C2×D4—448no—
652C2×D4—444no—
653C2×D4—444no—
654C2×D4—882no—
655C2×D4C2×C22⋊D1114yes—
656C2×D4C23×D1112yes—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—24no—
662C22×C4—24no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—24no—
667C22×C4—44no—
668C22×C4—44no—
669C22×C4—44no—
670C22×C4—221no—
671C22×C4—221no—
672C22×C4—224no—
673C22×C4—224no—
674C22×C4—444no—
675C22×C4—882no—
676C22×C4C2×C22⋊D1112yes—
677C22×C4C2×C22⋊D1112yes—
678C22×C4C2×C22⋊D1111yescharacteristic
679C22×C4C2×C22⋊D1111yescharacteristic
680C22×C4C2×C22⋊D1111yescharacteristic
681C22×C4C2×C22⋊D1111yescharacteristic
682C22×C4C23×D1112yes—
683C22×C4C23×D1112yes—
684C22×C4C23×D1111yescharacteristic
685SD16—444no—
686D8—228no—
687D8—444no—
688M16—444no—
689C2×C8—112no—
690C2×C8—112no—
691C2×C8—112no—
692C2×C8—112no—
693C2×C8—222no—
694C2×C8—222no—
695C2×C8—222no—
696C2×C8—222no—
697C2×C8—444no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—24no—
702C4⋊C4—24no—
703C4⋊C4—24no—
704C4⋊C4—112no—
705C4⋊C4—221no—
706C4⋊C4—224no—
707C4⋊C4C2×C22⋊D1114yes—
708C4⋊C4C23×D1112yes—
709C4⋊C4C23×D1112yes—
710C4⋊C4C23×D1112yes—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—224no—
715C22⋊C4—224no—
716C22⋊C4—224no—
717C22⋊C4—224no—
718C22⋊C4—224no—
719C22⋊C4C2×C22⋊D1114yes—
720C22⋊C4C2×C22⋊D1114yes—
721C42C2×C22⋊D1112yes—
722C42C23×D1112yes—
723C11C2×#330611yescharacteristic, complemented, Sylow
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—224no—
734C23—222no—
735C23—222no—
736C23—448no—
737C23—442no—
738C23—442no—
739C23—448no—
740C23—442no—
741C23—442no—
742C23—442no—
743C23—884no—
744C23—8816no—
745C23#6698514yes—
746C23C22×C22⋊D1112yes—
747C23C22×C22⋊D1112yes—
748C23C22×C22⋊D1111yescharacteristic
749Q8—48no—
750Q8—222no—
751Q8—222no—
752Q8—442no—
753D4—28no—
754D4—22no—
755D4—22no—
756D4—48no—
757D4—48no—
758D4—42no—
759D4—114no—
760D4—224no—
761D4—222no—
762D4—222no—
763D4—222no—
764D4—448no—
765D4—448no—
766D4—442no—
767D4—884no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—48no—
782C2×C4—48no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—48no—
787C2×C4—222no—
788C2×C4—222no—
789C2×C4—448no—
790C2×C4—442no—
791C2×C4—442no—
792C2×C4—884no—
793C2×C4#41×D1112yes—
794C2×C4#6704212yes—
795C2×C4C22×C22⋊D1112yes—
796C2×C4C22×C22⋊D1112yes—
797C2×C4C22×C22⋊D1112yes—
798C2×C4C22×C22⋊D1112yes—
799C2×C4C22×C22⋊D1111yescharacteristic
800C2×C4C24×D1111yescharacteristic
801C8—222no—
802C8—222no—
803C8—222no—
804C8—222no—
805C22—22no—
806C22—22no—
807C22—28no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—44no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—84no—
816C22—224no—
817C22—442no—
818C22—442no—
819C22—448no—
820C22—442no—
821C22—442no—
822C22—442no—
823C22—8816no—
824C22—884no—
825C22C2×#6698514yes—
826C22C2×#6698512yes—
827C22#1062336012yes—
828C22#1062336812yes—
829C22C23×C22⋊D1111yescharacteristic
830C4—22no—
831C4—22no—
832C4—22no—
833C4—22no—
834C4—42no—
835C4—42no—
836C4—42no—
837C4—442no—
838C4—442no—
839C4#1062336012yes—
840C4C2×#41×D1111yescharacteristic
841C4C2×#6704211yescharacteristic
842C2—24no—
843C2—42no—
844C2—82no—
845C2—444no—
846C2—882no—
847C2#1308057114yesdirect product factor
848C2C2×#1062336011yescharacteristic
849C2C22×#6698511yescharacteristic
850C2C2×#1062336811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#547C2
socleC23×C11C22×D4
hypercenterC2×#547D11
hypocenterC11C2×#3306
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#10623081C2semidirect
2. #13080571C2direct (N × H)
3. C2×#10622702C2semidirect
4. C2×#10622581C2semidirect
5. C2×#10622584C2semidirect
6. C2×#10622697C2semidirect
7. C2×#10622652C2semidirect
8. C2×#10622654C2semidirect
9. C2×#10622629C2semidirect
10. C2×#10622650C2semidirect
11. C2×#10622649C2semidirect
12. C2×#10622627C2semidirect
13. C2×#10622624C2semidirect
14. C2×#10622579C2semidirect
15. C22×#66873C2semidirect
16. C2×C11×#547C2semidirect
21. C11×#547C22semidirect
22. C2×C11×C4⋊Q8C22semidirect
27. C2×C11×#121C22semidirect
29. C2×C4×D4×C11C22semidirect
31. C22×C11×C4⋊C4C22semidirect
33. C22×#4324C22semidirect
38. C22×#4318C22semidirect
41. #10623081C22semidirect
47. C2×#66896C22semidirect
49. C2×C22⋊(C11⋊C8)C22semidirect
50. #10622702C22semidirect
51. #10622697C22semidirect
52. #10622654C22semidirect
53. #10622652C22semidirect
54. #10622650C22semidirect
55. #10622649C22semidirect
56. #10622629C22semidirect
57. #10622627C22semidirect
58. #10622624C22semidirect
59. #10622584C22semidirect
60. C2×#66874C22semidirect
61. C2×#66874C22semidirect
62. C2×#66874C22semidirect
63. #10622581C22semidirect
64. #10622579C22semidirect
71. C2×#66873C22semidirect
72. C2×#66872C22semidirect
73. C2×#66872C22semidirect
74. C2×#66872C22semidirect
75. C2×C4⋊(C11⋊C8)C22semidirect
76. C2×#66867C22semidirect
107. C11×C4⋊Q8C23semidirect
114. C11×#121C23semidirect
118. C4×D4×C11C23semidirect
129. C2×C11×C4⋊C4C23semidirect
139. C2×#4324C23semidirect
155. C2×#4318C23semidirect
169. #66896C23semidirect
171. C22⋊(C11⋊C8)C23semidirect
172. #66874C23semidirect
173. #66874C23semidirect
174. #66874C23semidirect
181. #66872C23semidirect
182. #66872C23semidirect
183. #66872C23semidirect
184. C4⋊(C11⋊C8)C23semidirect
185. #66867C23semidirect
250. C2×D44#41semidirect
299. C2×#547D11semidirect
386. D44C2×#41semidirect
405. #547C2×D11semidirect
408. C2×C4⋊Q8C2×D11semidirect
418. C2×#121C2×D11semidirect
422. C2×C4×D4C2×D11semidirect
424. C22×C4⋊C4C2×D11semidirect
537. C4⋊Q8C22×D11semidirect
552. #121C22×D11semidirect
559. C4×D4C22×D11semidirect
572. C2×C4⋊C4C22×D11semidirect
605. C2×C11#3306semidirect
723. C11C2×#3306semidirect
847. C2#13080571direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230812
#130805712
C2×#106227022
C2×#106225812
C2×#106225842
C2×#106226972
C2×#106226522
C2×#106226542
C2×#106226292
C2×#106226502
C2×#106226492
C2×#106226272
C2×#106226242
C2×#106225792
C22×#668732
C2×C11×#5472
C2×#330611