Finite Group Databasebeta

← C2×#13080157 #15628787

Subgroups — C2×#13080157 #15628787

Order 2816.

2966 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67002C211yesmaximal, characteristic, complemented
2C22×#67003C211yesmaximal, characteristic, complemented
3C2×#10623081C211yesmaximal, characteristic, complemented
4#13080157C2116yesmaximal, direct product factor
5C2×#10622687C211yesmaximal, characteristic, complemented
6C2×#10622655C211yesmaximal, characteristic, complemented
7C2×#10622651C211yesmaximal, characteristic, complemented
8C2×#10622641C211yesmaximal, characteristic, complemented
9C2×#10622685C211yesmaximal, characteristic, complemented
10C2×#10622852C211yesmaximal, characteristic, complemented
11C2×#10622851C211yesmaximal, characteristic, complemented
12C2×#10622650C211yesmaximal, characteristic, complemented
13C2×#10622649C211yesmaximal, characteristic, complemented
14C2×#10622639C211yesmaximal, characteristic, complemented
15C2×#10622624C211yesmaximal, characteristic, complemented
16C2×C11×#550C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C22×C11×#41C2211yescharacteristic, complemented
19C22×#4339C2211yescharacteristic
20C23×D44C2211yescharacteristic
21C11×#550—24no—
22C11×#550C2218yescomplemented
23C2×C11×#127—21no—
24C2×C11×#127C2211yescharacteristic, complemented
25C2×C11×#121—21no—
26C2×C11×#121—21no—
27C2×C11×#121C2211yescharacteristic
28C2×C11×#121C2211yescharacteristic, complemented
29C2×C4×Q8×C11C2211yescharacteristic, complemented
30C2×C4×D4×C11—21no—
31C2×C4×D4×C11C2211yescharacteristic
32C2×#67003—28no—
33C2×#67003C2218yescomplemented
34C2×#67002—28no—
35C2×#67002C2218yescomplemented
36C22×#4326C2211yescharacteristic, complemented
37C22×#4325C2211yescharacteristic
38C22×#4325C2211yescharacteristic
39C2×#66990—21no—
40C22×#4324C2211yescharacteristic, complemented
41C22×#4324C2211yescharacteristic, complemented
42C22×#4323C2211yescharacteristic
43C22×#4323C2211yescharacteristic
44C22×#4323C2211yescharacteristic
45C22×#4323C2211yescharacteristic
46C2×#66983C2211yescharacteristic
47C2×#66977C2211yescharacteristic
48C22×#4318C2211yescharacteristic
49C23×C11⋊C8C2211yescharacteristic, complemented
50#10623081—24no—
51#10623081C2218yescomplemented
52C2×#66947—21no—
53C2×#66937—21no—
54C2×C22⋊C4×D11—21no—
55C2×#66928C2211yescharacteristic
56C2×C4×D44C2211yescharacteristic
57#10622852C2218yescomplemented
58#10622851C2218yescomplemented
59C2×#66899C2211yescharacteristic, complemented
60C2×#66896C2211yescharacteristic, complemented
61C2×#66896C2211yescharacteristic, complemented
62C2×C22⋊(C11⋊C8)C2211yescharacteristic
63C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
64#10622687C2218yescomplemented
65#10622685C2218yescomplemented
66#10622655C2218yescomplemented
67#10622651C2218yescomplemented
68#10622650C2218yescomplemented
69#10622649C2218yescomplemented
70#10622641C2218yescomplemented
71#10622639C2218yescomplemented
72#10622624C2218yescomplemented
73C2×#66874C2211yescharacteristic, complemented
74C2×#66873C2211yescharacteristic
75C2×#66873C2211yescharacteristic
76C2×#66871C2211yescharacteristic, complemented
77C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
78C2×#66867C2211yescharacteristic, complemented
79C24×D11—21no—
80C2×C11×#41—22no—
81C2×C11×#41—22no—
82C2×C11×#41—24no—
83C2×C11×#41—24no—
84C2×C11×#41—42no—
85C2×C11×#41—42no—
86C2×C11×#41C2314yes—
87C2×C11×#41C2314yescomplemented
88C22×Q8×C11C2311yescharacteristic
89C22×D4×C11—21no—
90C22×D4×C11—21no—
91C22×D4×C11—21no—
92C22×D4×C11—21no—
93C22×D4×C11—21no—
94C22×D4×C11—21no—
95C22×D4×C11D411yescharacteristic
96C22×D4×C11C2311yescharacteristic
97C22×D4×C11C2311yescharacteristic
98C23×C4×C11—21no—
99C23×C4×C11—21no—
100C23×C4×C11C2311yescharacteristic
101C23×C4×C11C2311yescharacteristic
102C22×C22⋊D11—21no—
103C22×C22⋊D11—21no—
104C2×#4339—22no—
105C2×#4339—24no—
106C2×#4339—42no—
107C2×#4339C2314yes—
108C22×D44—24no—
109C22×D44—21no—
110C22×D44—22no—
111C22×D44—42no—
112C22×D44C2311yescharacteristic
113C22×D44C2314yes—
114C22×D44C2311yescharacteristic
115C22×C4×D11—21no—
116C22×C4×D11—21no—
117C22×Dic22C2311yescharacteristic
118C11×#127—28no—
119C11×#127—22no—
120C11×#127C2314yescomplemented
121C11×#121—22no—
122C11×#121—22no—
123C11×#121—28no—
124C11×#121—28no—
125C11×#121C2314yes—
126C11×#121C2314yescomplemented
127C4×Q8×C11—22no—
128C4×Q8×C11C2314yescomplemented
129C4×D4×C11—28no—
130C4×D4×C11D414yes—
131C4×D4×C11C2314yes—
132C2×C11×C4⋊C4—21no—
133C2×C11×C4⋊C4D411yescharacteristic
134C2×C11×C4⋊C4C2311yescharacteristic
135C2×C11×C22⋊C4—21no—
136C2×C11×C22⋊C4—21no—
137C2×C11×C22⋊C4D411yescharacteristic
138C2×C11×C22⋊C4D411yescharacteristic
139C2×C42×C11—21no—
140C2×C42×C11C2311yescharacteristic
141C2×C22⋊Dic11—21no—
142#67003—232no—
143#67002—232no—
144C2×#4326—24no—
145C2×#4326C2314yescomplemented
146C2×#4325—24no—
147C2×#4325D418yescomplemented
148C2×#4325C2314yes—
149C2×#4325C2314yes—
150#66990—28no—
151C2×#4324—24no—
152C2×#4324—42no—
153C2×#4324C2314yescomplemented
154C2×#4324C2314yescomplemented
155C2×#4323—24no—
156C2×#4323—24no—
157C2×#4323—24no—
158C2×#4323—42no—
159C2×#4323C2314yes—
160C2×#4323C2314yes—
161C2×#4323C2314yes—
162C2×#4323C2314yes—
163#66983—22no—
164#66983C2314yes—
165C2×(C2×D11)⋊C4—21no—
166C2×(C2×D11)⋊C4—21no—
167C2×(C2×D11)⋊C4—21no—
168C2×(C2×D11)⋊C4—21no—
169C2×C4⋊Dic11C2311yescharacteristic
170#66977—22no—
171#66977C2314yes—
172C2×Dic11⋊C4—21no—
173C2×#4318—24no—
174C2×#4318C2314yes—
175C22×C11⋊C8—24no—
176C22×C11⋊C8C2311yescharacteristic
177C22×C11⋊C8C2311yescharacteristic
178C22×C11⋊C8C2311yescharacteristic
179C22×C11⋊C8C2311yescharacteristic
180C22×C11⋊C8C2314yescomplemented
181#66947—28no—
182#66937—28no—
183C22⋊C4×D11—28no—
184#66928—22no—
185#66928C2314yes—
186C4×D44—22no—
187C4×D44C2314yes—
188#66899C2314yescomplemented
189#66896C2314yescomplemented
190#66896C2314yescomplemented
191C22⋊(C11⋊C8)C2314yes—
192C22⋊(C11⋊C8)C2314yescomplemented
193#66874C2314yescomplemented
194#66873C2314yes—
195#66873C2314yes—
196#66871C2314yescomplemented
197C4⋊(C11⋊C8)C2314yescomplemented
198#66867C2314yescomplemented
199C2×#3268—111nomaximal, Sylow
200C24×C11—21no—
201C24×C11—21no—
202C24×C11C2×D411yescharacteristic
203C24×C11C2×D411yescharacteristic
204C23×D11—21no—
205C23×D11—21no—
206C23×D11—24no—
207C23×D11—44no—
208C23×D11—44no—
209C23×D11—82no—
210C11×#41—28no—
211C11×#41—28no—
212C11×#41—44no—
213C11×#41—44no—
214C11×#41—48no—
215C11×#41—48no—
216C2×Q8×C11—21no—
217C2×Q8×C11—22no—
218C2×Q8×C11C2×D414yes—
219C2×Q8×C11C2412yes—
220C2×D4×C11—24no—
221C2×D4×C11—24no—
222C2×D4×C11—24no—
223C2×D4×C11—24no—
224C2×D4×C11—22no—
225C2×D4×C11—22no—
226C2×D4×C11—24no—
227C2×D4×C11—21no—
228C2×D4×C11—21no—
229C2×D4×C11—24no—
230C2×D4×C11—22no—
231C2×D4×C11—22no—
232C2×D4×C11—42no—
233C2×D4×C11—44no—
234C2×D4×C11—44no—
235C2×D4×C11—44no—
236C2×D4×C11—82no—
237C2×D4×C11—82no—
238C2×D4×C11—82no—
239C2×D4×C11C2×D414yes—
240C2×D4×C11C2412yes—
241C2×D4×C11C2412yes—
242C22×C4×C11—21no—
243C22×C4×C11—22no—
244C22×C4×C11—22no—
245C22×C4×C11—22no—
246C22×C4×C11—22no—
247C22×C4×C11—21no—
248C22×C4×C11—24no—
249C22×C4×C11—24no—
250C22×C4×C11—44no—
251C22×C4×C11—44no—
252C22×C4×C11C2×D411yescharacteristic
253C22×C4×C11C2×D412yes—
254C22×C4×C11C2×D411yescharacteristic
255C22×C4×C11C2×D411yescharacteristic
256C22×C4×C11C2×D411yescharacteristic
257C22×C4×C11C2×D412yes—
258C22×C4×C11C2412yes—
259C22×C4×C11C2412yes—
260C22×C4×C11C2411yescharacteristic
261C2×C22⋊D11—24no—
262C2×C22⋊D11—24no—
263C2×C22⋊D11—44no—
264C2×C22⋊D11—82no—
265C22×Dic11—21no—
266C22×Dic11—21no—
267#4339—28no—
268#4339—44no—
269#4339—48no—
270C2×D44—28no—
271C2×D44—21no—
272C2×D44—21no—
273C2×D44—24no—
274C2×D44—22no—
275C2×D44—22no—
276C2×D44—22no—
277C2×D44—44no—
278C2×D44—44no—
279C2×D44—48no—
280C2×D44C2×D414yes—
281C2×D44C2412yes—
282C2×D44C2412yes—
283C2×C4×D11—24no—
284C2×C4×D11—24no—
285C2×C4×D11—44no—
286C2×C4×D11—82no—
287C2×Dic22—22no—
288C2×Dic22—21no—
289C2×Dic22—22no—
290C2×Dic22C2412yes—
291C11×C4⋊C4—24no—
292C11×C4⋊C4—21no—
293C11×C4⋊C4C2×D414yes—
294C11×C4⋊C4C2412yes—
295C11×C22⋊C4—24no—
296C11×C22⋊C4—24no—
297C11×C22⋊C4C2×D414yes—
298C11×C22⋊C4C2×D414yes—
299C42×C11—24no—
300C42×C11C2×D412yes—
301C42×C11C2412yes—
302C22⋊Dic11—24no—
303#4326—28no—
304#4325—28no—
305#4325C2×D4116yescomplemented
306#4324—28no—
307#4324—44no—
308#4323—28no—
309#4323—28no—
310#4323—28no—
311#4323—44no—
312(C2×D11)⋊C4—24no—
313(C2×D11)⋊C4—24no—
314(C2×D11)⋊C4—24no—
315(C2×D11)⋊C4—24no—
316C4⋊Dic11—21no—
317C4⋊Dic11C2412yes—
318Dic11⋊C4—24no—
319#4318—28no—
320C2×C11⋊C8—28no—
321C2×C11⋊C8—22no—
322C2×C11⋊C8—22no—
323C2×C11⋊C8—22no—
324C2×C11⋊C8C2×D414yes—
325C2×C11⋊C8C2412yes—
326C2×C11⋊C8C2412yes—
327C2×C11⋊C8C2412yes—
328C2×C11⋊C8C2412yes—
329C22×AGL(1,ℤ/8)—111no—
330C22×#135—111no—
331C2×#550D1111yescharacteristic, complemented
332C2×#546—111no—
333#3268—1116no—
334C2×#496—111no—
335C2×#468—111no—
336C2×#466—111no—
337C2×#464—111no—
338C2×#459—111no—
339C2×#452—111no—
340C2×#449—111no—
341C2×#449—111no—
342C2×#447—111no—
343C2×#440—111no—
344C2×#435—111no—
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—22no—
352C23×C11—22no—
353C23×C11—42no—
354C23×C11—42no—
355C23×C11—42no—
356C23×C11—42no—
357C23×C11—42no—
358C23×C11—42no—
359C23×C11C22×D412yes—
360C23×C11C22×D412yes—
361C23×C11C22×D411yescharacteristic
362C22×D11—24no—
363C22×D11—22no—
364C22×D11—22no—
365C22×D11—48no—
366C22×D11—42no—
367C22×D11—42no—
368C22×D11—48no—
369C22×D11—42no—
370C22×D11—42no—
371C22×D11—42no—
372C22×D11—84no—
373C22×D11—816no—
374Q8×C11—24no—
375Q8×C11—22no—
376Q8×C11C22×D414yes—
377D4×C11—22no—
378D4×C11—22no—
379D4×C11—22no—
380D4×C11—22no—
381D4×C11—44no—
382D4×C11—48no—
383D4×C11—48no—
384D4×C11—48no—
385D4×C11—42no—
386D4×C11—42no—
387D4×C11—84no—
388D4×C11—84no—
389D4×C11—84no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—24no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—22no—
396C2×C4×C11—24no—
397C2×C4×C11—24no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—48no—
404C2×C4×C11—48no—
405C2×C4×C11—42no—
406C2×C4×C11C22×D412yes—
407C2×C4×C11C22×D412yes—
408C2×C4×C11C22×D412yes—
409C2×C4×C11C22×D412yes—
410C2×C4×C11C22×D412yes—
411C2×C4×C11C22×D411yescharacteristic
412C2×C4×C11H(5,𝔽2)12yes—
413C2×C4×C11C2511yescharacteristic
414C22⋊D11—48no—
415C22⋊D11—84no—
416C2×Dic11—22no—
417C2×Dic11—22no—
418C2×Dic11—42no—
419C2×Dic11—42no—
420D44—24no—
421D44—22no—
422D44—22no—
423D44—22no—
424D44—48no—
425D44—42no—
426D44C22×D414yes—
427C4×D11—48no—
428C4×D11—84no—
429Dic22—22no—
430Dic22—22no—
431Dic22—42no—
432C11⋊C8—22no—
433C11⋊C8—22no—
434C11⋊C8—22no—
435C11⋊C8C22×D414yes—
436C22×#41—111no—
437C22×#41C2×D1111yescharacteristic
438C22×#41C2×D1111yescharacteristic, complemented
439C23×D4—111no—
440C2×AGL(1,ℤ/8)—118no—
441C2×AGL(1,ℤ/8)—228no—
442C2×#135—118no—
443C2×#135—228no—
444C22×Q16—111no—
445C22×SD16—111no—
446C22×SD16—111no—
447C22×SD16—111no—
448C22×SD16—111no—
449C22×D8—111no—
450C22×D8—111no—
451C22×D8—111no—
452C22×D8—111no—
453C22×M16—111no—
454C23×C8—111no—
455#550—24no—
456#550C2×D1118yescomplemented
457#546—118no—
458#546—224no—
459C2×#127—21no—
460C2×#127C2×D1111yescharacteristic, complemented
461C2×#124—111no—
462C2×#123—221no—
463C2×C22⋊Q8—111no—
464C2×#121—21no—
465C2×#121—21no—
466C2×#121—111no—
467C2×#121—221no—
468C2×#121C2×D1111yescharacteristic
469C2×#121C2×D1111yescharacteristic, complemented
470C2×#120—221no—
471C2×C4×Q8C2×D1111yescharacteristic, complemented
472C2×C4×D4—21no—
473C2×C4×D4—111no—
474C2×C4×D4C2×D1111yescharacteristic
475C22×C22⋊C4—221no—
476#496—118no—
477#468—118no—
478#466—118no—
479#464—118no—
480#459—118no—
481#452—118no—
482#449—118no—
483#449—118no—
484#447—118no—
485#440—118no—
486#435—118no—
487C2×#107—111no—
488C2×C4⋊C8—111no—
489C2×#103—111no—
490C2×#103—111no—
491C2×#102—111no—
492C2×#102—111no—
493C2×#102—111no—
494C2×#102—111no—
495C2×C22⋊C8—111no—
496C2×C22⋊C8—111no—
497C2×#97—111no—
498C22×C11—22no—
499C22×C11—22no—
500C22×C11—22no—
501C22×C11—22no—
502C22×C11—22no—
503C22×C11—22no—
504C22×C11—44no—
505C22×C11—44no—
506C22×C11—42no—
507C22×C11—42no—
508C22×C11—42no—
509C22×C11—42no—
510C22×C11—42no—
511C22×C11—42no—
512C22×C11—84no—
513C22×C11—84no—
514C22×C11D4212yes—
515C22×C11#57512yes—
516C22×C11#57612yes—
517C22×C11C23×D411yescharacteristic
518C2×D11—24no—
519C2×D11—48no—
520C2×D11—42no—
521C2×D11—42no—
522C2×D11—42no—
523C2×D11—42no—
524C2×D11—42no—
525C2×D11—816no—
526C2×D11—84no—
527C4×C11—22no—
528C4×C11—22no—
529C4×C11—24no—
530C4×C11—22no—
531C4×C11—22no—
532C4×C11—42no—
533C4×C11D4212yes—
534C4×C11C23×D411yescharacteristic
535C4×C11C2×H(5,𝔽2)11yescharacteristic
536Dic11—42no—
537Dic11—42no—
538C25—221no—
539C2×#41—22no—
540C2×#41—22no—
541C2×#41—24no—
542C2×#41—24no—
543C2×#41—42no—
544C2×#41—42no—
545C2×#41—114no—
546C2×#41—224no—
547C2×#41—222no—
548C2×#41—442no—
549C2×#41C22×D1114yes—
550C2×#41C22×D1114yescomplemented
551C22×Q8—111no—
552C22×Q8C22×D1111yescharacteristic
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—111no—
560C22×D4—111no—
561C22×D4—114no—
562C22×D4—224no—
563C22×D4—221no—
564C22×D4—221no—
565C22×D4—221no—
566C22×D4—222no—
567C22×D4—442no—
568C22×D4C22⋊D1111yescharacteristic
569C22×D4C22×D1111yescharacteristic
570C22×D4C22×D1111yescharacteristic
571C23×C4—21no—
572C23×C4—21no—
573C23×C4—221no—
574C23×C4—221no—
575C23×C4C22×D1111yescharacteristic
576C23×C4C22×D1111yescharacteristic
577AGL(1,ℤ/8)—2232no—
578#135—2232no—
579C2×Q16—114no—
580C2×Q16—224no—
581C2×SD16—118no—
582C2×SD16—114no—
583C2×SD16—114no—
584C2×SD16—114no—
585C2×SD16—114no—
586C2×SD16—224no—
587C2×SD16—224no—
588C2×SD16—442no—
589C2×D8—114no—
590C2×D8—114no—
591C2×D8—114no—
592C2×D8—114no—
593C2×D8—224no—
594C2×D8—224no—
595C2×D8—224no—
596C2×D8—442no—
597C2×M16—114no—
598C2×M16—224no—
599C22×C8—111no—
600C22×C8—111no—
601C22×C8—114no—
602C22×C8—111no—
603C22×C8—111no—
604C22×C8—224no—
605#127—28no—
606#127—22no—
607#127C22×D1114yescomplemented
608#124—114no—
609#124—222no—
610#123—228no—
611C22⋊Q8—114no—
612C22⋊Q8—222no—
613#121—22no—
614#121—22no—
615#121—28no—
616#121—28no—
617#121—114no—
618#121—222no—
619#121—228no—
620#121C22×D1114yes—
621#121C22×D1114yescomplemented
622#120—228no—
623C4×Q8—22no—
624C4×Q8C22×D1114yescomplemented
625C4×D4—28no—
626C4×D4—114no—
627C4×D4—222no—
628C4×D4C22⋊D1114yes—
629C4×D4C22×D1114yes—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—111no—
632C2×C4⋊C4—221no—
633C2×C4⋊C4C22⋊D1111yescharacteristic
634C2×C4⋊C4C22×D1111yescharacteristic
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—221no—
638C2×C22⋊C4—221no—
639C2×C22⋊C4—221no—
640C2×C22⋊C4—221no—
641C2×C22⋊C4—221no—
642C2×C22⋊C4—228no—
643C2×C22⋊C4C22⋊D1111yescharacteristic
644C2×C22⋊C4C22⋊D1111yescharacteristic
645C2×C42—21no—
646C2×C42C22×D1111yescharacteristic
647#107—114no—
648C4⋊C8—114no—
649#103—114no—
650#103—114no—
651#102—114no—
652#102—114no—
653#102—114no—
654#102—114no—
655C22⋊C8—114no—
656C22⋊C8—114no—
657#97—114no—
658C2×C11—42no—
659C2×C11—42no—
660C2×C11—82no—
661C2×C11—82no—
662C2×C11#326814yescomplemented
663C2×C11C2×D4211yescharacteristic
664C2×C11C2×#57511yescharacteristic
665C2×C11C2×#57611yescharacteristic
666D11—44no—
667D11—82no—
668C24—21no—
669C24—21no—
670C24—221no—
671C24—221no—
672C24—224no—
673C24—444no—
674C24—444no—
675C24—882no—
676C24C2×C22⋊D1111yescharacteristic
677C24C2×C22⋊D1111yescharacteristic
678#41—28no—
679#41—28no—
680#41—44no—
681#41—44no—
682#41—48no—
683#41—48no—
684#41—228no—
685#41—444no—
686#41—448no—
687C2×Q8—22no—
688C2×Q8—21no—
689C2×Q8—112no—
690C2×Q8—221no—
691C2×Q8—222no—
692C2×Q8—222no—
693C2×Q8D4×D1114yes—
694C2×Q8C23×D1112yes—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—24no—
698C2×D4—24no—
699C2×D4—22no—
700C2×D4—22no—
701C2×D4—22no—
702C2×D4—22no—
703C2×D4—24no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—24no—
707C2×D4—42no—
708C2×D4—44no—
709C2×D4—44no—
710C2×D4—44no—
711C2×D4—82no—
712C2×D4—82no—
713C2×D4—82no—
714C2×D4—114no—
715C2×D4—112no—
716C2×D4—112no—
717C2×D4—228no—
718C2×D4—224no—
719C2×D4—224no—
720C2×D4—222no—
721C2×D4—222no—
722C2×D4—222no—
723C2×D4—221no—
724C2×D4—224no—
725C2×D4—221no—
726C2×D4—444no—
727C2×D4—448no—
728C2×D4—444no—
729C2×D4—444no—
730C2×D4—882no—
731C2×D4C2×C22⋊D1114yes—
732C2×D4C23×D1112yes—
733C2×D4C23×D1112yes—
734C22×C4—21no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—21no—
740C22×C4—24no—
741C22×C4—24no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4—221no—
745C22×C4—221no—
746C22×C4—224no—
747C22×C4—224no—
748C22×C4—444no—
749C22×C4—882no—
750C22×C4C2×C22⋊D1112yes—
751C22×C4C2×C22⋊D1112yes—
752C22×C4C2×C22⋊D1111yescharacteristic
753C22×C4C2×C22⋊D1111yescharacteristic
754C22×C4C2×C22⋊D1111yescharacteristic
755C22×C4C2×C22⋊D1111yescharacteristic
756C22×C4C23×D1112yes—
757C22×C4C23×D1112yes—
758C22×C4C23×D1111yescharacteristic
759Q16—228no—
760SD16—1116no—
761SD16—228no—
762SD16—228no—
763SD16—444no—
764D8—228no—
765D8—228no—
766D8—228no—
767D8—444no—
768M16—228no—
769C2×C8—114no—
770C2×C8—112no—
771C2×C8—112no—
772C2×C8—112no—
773C2×C8—112no—
774C2×C8—228no—
775C2×C8—222no—
776C2×C8—222no—
777C2×C8—222no—
778C4⋊C4—24no—
779C4⋊C4—21no—
780C4⋊C4—112no—
781C4⋊C4—221no—
782C4⋊C4—224no—
783C4⋊C4C2×C22⋊D1114yes—
784C4⋊C4C23×D1112yes—
785C22⋊C4—24no—
786C22⋊C4—24no—
787C22⋊C4—224no—
788C22⋊C4—224no—
789C22⋊C4—224no—
790C22⋊C4—224no—
791C22⋊C4—224no—
792C22⋊C4C2×C22⋊D1114yes—
793C22⋊C4C2×C22⋊D1114yes—
794C42—24no—
795C42C2×C22⋊D1112yes—
796C42C23×D1112yes—
797C11C2×#326811yescharacteristic, complemented, Sylow
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—224no—
813C23—222no—
814C23—222no—
815C23—448no—
816C23—448no—
817C23—442no—
818C23—442no—
819C23—442no—
820C23—442no—
821C23—442no—
822C23—884no—
823C23—8816no—
824C23C22×C22⋊D1112yes—
825C23C22×C22⋊D1112yes—
826C23C22×C22⋊D1111yescharacteristic
827Q8—24no—
828Q8—22no—
829Q8—222no—
830Q8—222no—
831Q8—442no—
832Q8C2×D4×D1114yes—
833D4—22no—
834D4—22no—
835D4—22no—
836D4—22no—
837D4—44no—
838D4—48no—
839D4—48no—
840D4—48no—
841D4—42no—
842D4—42no—
843D4—84no—
844D4—84no—
845D4—84no—
846D4—114no—
847D4—224no—
848D4—222no—
849D4—222no—
850D4—222no—
851D4—448no—
852D4—448no—
853D4—442no—
854D4—884no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—24no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—24no—
862C2×C4—24no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—48no—
869C2×C4—48no—
870C2×C4—42no—
871C2×C4—222no—
872C2×C4—222no—
873C2×C4—448no—
874C2×C4—442no—
875C2×C4—442no—
876C2×C4—884no—
877C2×C4C2×D4×D1112yes—
878C2×C4#6703712yes—
879C2×C4C22×C22⋊D1112yes—
880C2×C4C22×C22⋊D1112yes—
881C2×C4C22×C22⋊D1112yes—
882C2×C4C22×C22⋊D1112yes—
883C2×C4C22×C22⋊D1111yescharacteristic
884C2×C4C24×D1111yescharacteristic
885C8—114no—
886C8—222no—
887C8—222no—
888C8—222no—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—44no—
896C22—44no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—84no—
904C22—84no—
905C22—224no—
906C22—448no—
907C22—442no—
908C22—442no—
909C22—442no—
910C22—442no—
911C22—442no—
912C22—8816no—
913C22—884no—
914C22D4×C22⋊D1112yes—
915C22#1062335312yes—
916C22#1062336612yes—
917C22C23×C22⋊D1111yescharacteristic
918C4—22no—
919C4—22no—
920C4—24no—
921C4—22no—
922C4—22no—
923C4—42no—
924C4—442no—
925C4—442no—
926C4D4×C22⋊D1112yes—
927C4C22×D4×D1111yescharacteristic
928C4C2×#6703711yescharacteristic
929C2—42no—
930C2—42no—
931C2—82no—
932C2—82no—
933C2—444no—
934C2—882no—
935C2#1308015714yesdirect product factor
936C2C2×D4×C22⋊D1111yescharacteristic
937C2C2×#1062335311yescharacteristic
938C2C2×#1062336611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#550C2
socleC23×C11C22×D4
hypercenterC2×#550D11
hypocenterC11C2×#3268
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C22×#67002C2semidirect
2. C22×#67003C2semidirect
3. C2×#10623081C2semidirect
4. #13080157C2direct (N × H)
5. C2×#10622687C2semidirect
6. C2×#10622655C2semidirect
7. C2×#10622651C2semidirect
8. C2×#10622641C2semidirect
9. C2×#10622685C2semidirect
10. C2×#10622852C2semidirect
11. C2×#10622851C2semidirect
12. C2×#10622650C2semidirect
13. C2×#10622649C2semidirect
14. C2×#10622639C2semidirect
15. C2×#10622624C2semidirect
16. C2×C11×#550C2semidirect
18. C22×C11×#41C22semidirect
22. C11×#550C22semidirect
24. C2×C11×#127C22semidirect
28. C2×C11×#121C22semidirect
29. C2×C4×Q8×C11C22semidirect
33. C2×#67003C22semidirect
35. C2×#67002C22semidirect
36. C22×#4326C22semidirect
40. C22×#4324C22semidirect
41. C22×#4324C22semidirect
49. C23×C11⋊C8C22semidirect
51. #10623081C22semidirect
57. #10622852C22semidirect
58. #10622851C22semidirect
59. C2×#66899C22semidirect
60. C2×#66896C22semidirect
61. C2×#66896C22semidirect
63. C2×C22⋊(C11⋊C8)C22semidirect
64. #10622687C22semidirect
65. #10622685C22semidirect
66. #10622655C22semidirect
67. #10622651C22semidirect
68. #10622650C22semidirect
69. #10622649C22semidirect
70. #10622641C22semidirect
71. #10622639C22semidirect
72. #10622624C22semidirect
73. C2×#66874C22semidirect
76. C2×#66871C22semidirect
77. C2×C4⋊(C11⋊C8)C22semidirect
78. C2×#66867C22semidirect
87. C2×C11×#41C23semidirect
120. C11×#127C23semidirect
126. C11×#121C23semidirect
128. C4×Q8×C11C23semidirect
145. C2×#4326C23semidirect
147. C2×#4325D4semidirect
153. C2×#4324C23semidirect
154. C2×#4324C23semidirect
180. C22×C11⋊C8C23semidirect
188. #66899C23semidirect
189. #66896C23semidirect
190. #66896C23semidirect
192. C22⋊(C11⋊C8)C23semidirect
193. #66874C23semidirect
196. #66871C23semidirect
197. C4⋊(C11⋊C8)C23semidirect
198. #66867C23semidirect
305. #4325C2×D4semidirect
331. C2×#550D11semidirect
438. C22×#41C2×D11semidirect
456. #550C2×D11semidirect
460. C2×#127C2×D11semidirect
469. C2×#121C2×D11semidirect
471. C2×C4×Q8C2×D11semidirect
550. C2×#41C22×D11semidirect
607. #127C22×D11semidirect
621. #121C22×D11semidirect
624. C4×Q8C22×D11semidirect
662. C2×C11#3268semidirect
797. C11C2×#3268semidirect
935. C2#13080157direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670022
C22×#670032
C2×#106230812
#130801572
C2×#106226872
C2×#106226552
C2×#106226512
C2×#106226412
C2×#106226852
C2×#106228522
C2×#106228512
C2×#106226502
C2×#106226492
C2×#106226392
C2×#106226242
C2×C11×#5502
C2×#326811