Finite Group Databasebeta

← C2×#13080160 #15628790

Subgroups — C2×#13080160 #15628790

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×#66964C211yesmaximal, characteristic, complemented
2C22×#67003C211yesmaximal, characteristic, complemented
3C2×#10623130C211yesmaximal, characteristic, complemented
4C2×#10623360C211yesmaximal, characteristic, complemented
5#13080160C2116yesmaximal, direct product factor
6C2×#10622789C211yesmaximal, characteristic, complemented
7C2×#10622425C211yesmaximal, characteristic, complemented
8C2×#10622651C211yesmaximal, characteristic, complemented
9C2×#10622411C211yesmaximal, characteristic, complemented
10C2×#10622763C211yesmaximal, characteristic, complemented
11C2×#10622786C211yesmaximal, characteristic, complemented
12C2×#10622347C211yesmaximal, characteristic, complemented
13C2×#10622386C211yesmaximal, characteristic, complemented
14C2×#10622370C211yesmaximal, characteristic, complemented
15C2×#10622343C211yesmaximal, characteristic, complemented
16C2×C11×#449C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C22×#4341C2211yescharacteristic
19C22×D4×D11C2211yescharacteristic
20C22×#4339C2211yescharacteristic, complemented
21C22×C11×SD16C2211yescharacteristic, complemented
22C22×C11×D8C2211yescharacteristic
23C2×C11×#121C2211yescharacteristic, complemented
24#10623360—24no—
25#10623360C2218yescomplemented
26C2×#67003—28no—
27C2×#67003C2218yescomplemented
28C2×#67000C2211yescharacteristic
29C2×#66999C2211yescharacteristic
30C22×#4326C2211yescharacteristic, complemented
31C22×#4325C2211yescharacteristic, complemented
32C2×#66993—21no—
33C2×#66993C2211yescharacteristic, complemented
34C2×#66992—21no—
35C2×#66992—21no—
36C2×#66990—21no—
37C2×D4×Dic11C2211yescharacteristic
38C22×#4324C2211yescharacteristic
39C22×#4323C2211yescharacteristic
40C22×#4323C2211yescharacteristic
41C2×#66983C2211yescharacteristic
42C2×#66982—21no—
43C2×C4×C22⋊D11C2211yescharacteristic
44C22×(C2×D11)⋊C4—21no—
45C23×C11⋊C8C2211yescharacteristic, complemented
46C2×#66964—28no—
47C2×#66964C2218yescomplemented
48C22×D88C2211yescharacteristic
49C22×#4314C2211yescharacteristic
50C22×#4313C2211yescharacteristic
51#10623130—24no—
52#10623130C2218yescomplemented
53C2×#66948C2211yescharacteristic
54C2×#66940C2211yescharacteristic, complemented
55C2×#66937—21no—
56C2×(C22⋊D11)⋊C4—21no—
57C11×#449C2218yescomplemented
58C2×C11×#103C2211yescharacteristic, complemented
59C2×C11×#102C2211yescharacteristic
60C2×C11×C22⋊C8C2211yescharacteristic, complemented
61C2×#66896C2211yescharacteristic, complemented
62#10622789C2218yescomplemented
63#10622786C2218yescomplemented
64#10622763C2218yescomplemented
65C2×#66885C2211yescharacteristic, complemented
66C2×(C2×D11)⋊C8C2211yescharacteristic
67C2×#66880C2211yescharacteristic, complemented
68C2×#66879C2211yescharacteristic, complemented
69C2×Dic11⋊C8C2211yescharacteristic, complemented
70#10622651C2218yescomplemented
71C2×#66873C2211yescharacteristic
72C2×#66871C2211yescharacteristic, complemented
73#10622425C2218yescomplemented
74#10622411C2218yescomplemented
75#10622386C2218yescomplemented
76#10622370C2218yescomplemented
77#10622347C2218yescomplemented
78#10622343C2218yescomplemented
79C24×D11—21no—
80C2×C11×#41—22no—
81C2×C11×#41—24no—
82C2×C11×#41—42no—
83C2×C11×#41C2314yes—
84C22×Q8×C11C2311yescharacteristic
85C22×D4×C11—21no—
86C22×D4×C11—21no—
87C22×D4×C11C2311yescharacteristic
88C22×D4×C11C2311yescharacteristic
89C23×C4×C11—21no—
90C23×C4×C11C2311yescharacteristic
91C22×C22⋊D11—21no—
92C22×C22⋊D11—21no—
93C22×C22⋊D11—21no—
94C22×C22⋊D11—21no—
95C22×C22⋊D11—21no—
96C22×C22⋊D11—21no—
97C22×C22⋊D11D411yescharacteristic
98C23×Dic11—21no—
99C23×Dic11—21no—
100C2×#4341—22no—
101C2×#4341—24no—
102C2×#4341—42no—
103C2×#4341C2314yes—
104C2×D4×D11—24no—
105C2×D4×D11—22no—
106C2×D4×D11—42no—
107C2×D4×D11C2314yes—
108C2×#4339—22no—
109C2×#4339—24no—
110C2×#4339—42no—
111C2×#4339C2314yescomplemented
112C22×D44—21no—
113C22×D44C2311yescharacteristic
114C22×D44C2311yescharacteristic
115C22×C4×D11—21no—
116C22×C4×D11C2311yescharacteristic
117C22×Dic22C2311yescharacteristic
118C2×C11×SD16—42no—
119C2×C11×SD16C2314yescomplemented
120C2×C11×D8—24no—
121C2×C11×D8C2314yes—
122C22×C8×C11C2311yescharacteristic
123C22×C8×C11C2311yescharacteristic
124C11×#121—22no—
125C11×#121C2314yescomplemented
126C2×C11×C4⋊C4C2311yescharacteristic
127C2×C11×C22⋊C4—21no—
128C2×C22⋊Dic11—21no—
129C2×C22⋊Dic11D411yescharacteristic
130#67003—232no—
131#67000—22no—
132#67000C2314yes—
133#66999—22no—
134#66999C2314yes—
135C2×#4326—24no—
136C2×#4326C2314yescomplemented
137C2×#4325—24no—
138C2×#4325C2314yescomplemented
139#66993—28no—
140#66993—22no—
141#66993C2314yescomplemented
142#66992—28no—
143#66992—28no—
144#66990—28no—
145D4×Dic11—22no—
146D4×Dic11C2314yes—
147C2×#4324D418yescomplemented
148C2×#4324C2314yes—
149C2×#4323—24no—
150C2×#4323—24no—
151C2×#4323C2314yes—
152C2×#4323C2314yes—
153#66983—22no—
154#66983C2314yes—
155#66982—28no—
156C4×C22⋊D11D414yes—
157C4×C22⋊D11C2314yes—
158C2×(C2×D11)⋊C4—21no—
159C2×(C2×D11)⋊C4—21no—
160C2×(C2×D11)⋊C4—21no—
161C2×(C2×D11)⋊C4—21no—
162C2×(C2×D11)⋊C4—21no—
163C2×(C2×D11)⋊C4—28no—
164C2×(C2×D11)⋊C4D411yescharacteristic
165C2×C4⋊Dic11C2311yescharacteristic
166C2×Dic11⋊C4—21no—
167C2×Dic11⋊C4—21no—
168C2×Dic11⋊C4D411yescharacteristic
169C2×C4×Dic11—21no—
170C2×C4×Dic11C2311yescharacteristic
171C22×C11⋊C8—24no—
172C22×C11⋊C8C2311yescharacteristic
173C22×C11⋊C8C2311yescharacteristic
174C22×C11⋊C8C2314yescomplemented
175#66964—232no—
176C2×D88—42no—
177C2×D88C2314yes—
178C2×#4314—24no—
179C2×#4314C2314yes—
180C2×#4313—24no—
181C2×#4313C2314yes—
182#66948—22no—
183#66948C2314yes—
184#66940—22no—
185#66940C2314yescomplemented
186#66937—28no—
187(C22⋊D11)⋊C4—28no—
188C11×#103C2314yescomplemented
189C11×#102C2314yes—
190C11×C22⋊C8C2314yescomplemented
191#66896C2314yescomplemented
192#66885C2314yescomplemented
193(C2×D11)⋊C8C2314yes—
194#66880C2314yescomplemented
195#66879C2314yescomplemented
196Dic11⋊C8C2314yescomplemented
197#66873C2314yes—
198#66871C2314yescomplemented
199C2×#3268—111nomaximal, Sylow
200C24×C11—21no—
201C24×C11—21no—
202C24×C11C2×D411yescharacteristic
203C23×D11—21no—
204C23×D11—21no—
205C23×D11—24no—
206C23×D11—44no—
207C23×D11—44no—
208C23×D11—82no—
209C23×D11C2×D411yescharacteristic
210C11×#41—28no—
211C11×#41—44no—
212C11×#41—48no—
213C2×Q8×C11—21no—
214C2×Q8×C11—22no—
215C2×Q8×C11—22no—
216C2×Q8×C11C2412yes—
217C2×D4×C11—24no—
218C2×D4×C11—24no—
219C2×D4×C11—21no—
220C2×D4×C11—22no—
221C2×D4×C11—21no—
222C2×D4×C11—22no—
223C2×D4×C11—22no—
224C2×D4×C11—44no—
225C2×D4×C11—82no—
226C2×D4×C11C2×D414yes—
227C2×D4×C11C2412yes—
228C2×D4×C11C2412yes—
229C22×C4×C11—22no—
230C22×C4×C11—22no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—24no—
234C22×C4×C11—44no—
235C22×C4×C11C2×D411yescharacteristic
236C22×C4×C11C2×D412yes—
237C22×C4×C11C2412yes—
238C22×C4×C11C2411yescharacteristic
239C2×C22⋊D11—24no—
240C2×C22⋊D11—24no—
241C2×C22⋊D11—24no—
242C2×C22⋊D11—24no—
243C2×C22⋊D11—24no—
244C2×C22⋊D11—24no—
245C2×C22⋊D11—42no—
246C2×C22⋊D11—44no—
247C2×C22⋊D11—44no—
248C2×C22⋊D11—44no—
249C2×C22⋊D11—44no—
250C2×C22⋊D11—82no—
251C2×C22⋊D11—82no—
252C2×C22⋊D11C2×D414yes—
253C22×Dic11—24no—
254C22×Dic11—24no—
255C22×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11—44no—
258C22×Dic11—82no—
259C22×Dic11C2×D411yescharacteristic
260C22×Dic11C2×D411yescharacteristic
261C22×Dic11C2×D411yescharacteristic
262#4341—28no—
263#4341—44no—
264#4341—48no—
265D4×D11—28no—
266D4×D11—44no—
267D4×D11—48no—
268#4339—28no—
269#4339—44no—
270#4339—48no—
271C2×D44—24no—
272C2×D44—21no—
273C2×D44—21no—
274C2×D44—22no—
275C2×D44—22no—
276C2×D44—22no—
277C2×D44—22no—
278C2×D44—82no—
279C2×D44C2412yes—
280C2×D44C2412yes—
281C2×C4×D11—22no—
282C2×C4×D11—24no—
283C2×C4×D11—22no—
284C2×C4×D11—44no—
285C2×C4×D11C2×D412yes—
286C2×C4×D11C2412yes—
287C2×Dic22—21no—
288C2×Dic22—22no—
289C2×Dic22C2×D414yes—
290C2×Dic22C2412yes—
291C11×SD16—44no—
292C11×D8—28no—
293C2×C8×C11—22no—
294C2×C8×C11—22no—
295C2×C8×C11C2412yes—
296C2×C8×C11C2412yes—
297C11×C4⋊C4—21no—
298C11×C4⋊C4C2412yes—
299C11×C22⋊C4—24no—
300C22⋊Dic11—24no—
301C22⋊Dic11C2×D414yes—
302#4326—28no—
303#4325—28no—
304#4324C2×D4116yescomplemented
305#4323—28no—
306#4323—28no—
307(C2×D11)⋊C4—24no—
308(C2×D11)⋊C4—24no—
309(C2×D11)⋊C4—24no—
310(C2×D11)⋊C4—24no—
311(C2×D11)⋊C4—24no—
312(C2×D11)⋊C4C2×D414yes—
313C4⋊Dic11—21no—
314C4⋊Dic11C2412yes—
315Dic11⋊C4—24no—
316Dic11⋊C4—24no—
317Dic11⋊C4C2×D414yes—
318C4×Dic11—24no—
319C4×Dic11C2×D412yes—
320C4×Dic11C2412yes—
321C2×C11⋊C8—28no—
322C2×C11⋊C8—22no—
323C2×C11⋊C8C2×D414yes—
324C2×C11⋊C8C2412yes—
325C2×C11⋊C8C2412yes—
326D88—44no—
327#4314—28no—
328#4313—28no—
329C22×AGL(1,ℤ/8)—111no—
330C22×#135—111no—
331C2×#550—111no—
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×#449D1111yescharacteristic, complemented
342C2×#447—111no—
343C2×#440—111no—
344C2×#435—111no—
345C23×C11—22no—
346C23×C11—24no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—42no—
352C23×C11—42no—
353C23×C11—42no—
354C23×C11—42no—
355C23×C11—42no—
356C23×C11C22×D412yes—
357C23×C11C22×D411yescharacteristic
358C22×D11—22no—
359C22×D11—22no—
360C22×D11—22no—
361C22×D11—22no—
362C22×D11—22no—
363C22×D11—48no—
364C22×D11—48no—
365C22×D11—42no—
366C22×D11—42no—
367C22×D11—42no—
368C22×D11—42no—
369C22×D11—42no—
370C22×D11—42no—
371C22×D11—84no—
372C22×D11—816no—
373C22×D11C22×D412yes—
374Q8×C11—22no—
375Q8×C11—22no—
376Q8×C11—42no—
377D4×C11—24no—
378D4×C11—22no—
379D4×C11—22no—
380D4×C11—22no—
381D4×C11—48no—
382D4×C11—42no—
383D4×C11—84no—
384D4×C11C22×D414yes—
385C2×C4×C11—22no—
386C2×C4×C11—24no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—48no—
392C2×C4×C11—42no—
393C2×C4×C11—42no—
394C2×C4×C11C22×D412yes—
395C2×C4×C11C22×D411yescharacteristic
396C2×C4×C11C22×D412yes—
397C2×C4×C11H(5,𝔽2)12yes—
398C2×C4×C11C2511yescharacteristic
399C22⋊D11—44no—
400C22⋊D11—48no—
401C22⋊D11—48no—
402C22⋊D11—48no—
403C22⋊D11—48no—
404C22⋊D11—84no—
405C22⋊D11—84no—
406C2×Dic11—24no—
407C2×Dic11—22no—
408C2×Dic11—22no—
409C2×Dic11—22no—
410C2×Dic11—22no—
411C2×Dic11—22no—
412C2×Dic11—48no—
413C2×Dic11—42no—
414C2×Dic11—84no—
415C2×Dic11C22×D412yes—
416C2×Dic11C22×D412yes—
417C2×Dic11C22×D412yes—
418D44—22no—
419D44—22no—
420D44—22no—
421D44—22no—
422D44—42no—
423D44—42no—
424D44—84no—
425C4×D11—24no—
426C4×D11—22no—
427C4×D11—22no—
428C4×D11—48no—
429Dic22—24no—
430Dic22—22no—
431Dic22C22×D414yes—
432C8×C11—22no—
433C8×C11—22no—
434C11⋊C8—22no—
435C11⋊C8C22×D414yes—
436C22×#41—111no—
437C22×#41—111no—
438C22×#41C2×D1111yescharacteristic
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×SD16C2×D1111yescharacteristic, complemented
449C22×D8—111no—
450C22×D8—111no—
451C22×D8—111no—
452C22×D8C2×D1111yescharacteristic
453C22×M16—111no—
454C23×C8—111no—
455#550—118no—
456#550—224no—
457#546—118no—
458#546—224no—
459C2×#127—111no—
460C2×#127—221no—
461C2×#124—111no—
462C2×#123—221no—
463C2×C22⋊Q8—111no—
464C2×#121—111no—
465C2×#121—111no—
466C2×#121—221no—
467C2×#121—221no—
468C2×#121—221no—
469C2×#121C2×D1111yescharacteristic, complemented
470C2×#120—221no—
471C2×C4×Q8—111no—
472C2×C4×D4—111no—
473C2×C4×D4—111no—
474C2×C4×D4—221no—
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#449C2×D1118yescomplemented
484#447—118no—
485#440—118no—
486#435—118no—
487C2×#107—111no—
488C2×C4⋊C8—111no—
489C2×#103—111no—
490C2×#103C2×D1111yescharacteristic, complemented
491C2×#102—111no—
492C2×#102—111no—
493C2×#102—111no—
494C2×#102C2×D1111yescharacteristic
495C2×C22⋊C8—111no—
496C2×C22⋊C8C2×D1111yescharacteristic, complemented
497C2×#97—111no—
498C22×C11—22no—
499C22×C11—24no—
500C22×C11—22no—
501C22×C11—22no—
502C22×C11—48no—
503C22×C11—44no—
504C22×C11—42no—
505C22×C11—42no—
506C22×C11—42no—
507C22×C11—42no—
508C22×C11—42no—
509C22×C11—84no—
510C22×C11D4212yes—
511C22×C11#57512yes—
512C22×C11#57612yes—
513C22×C11C23×D411yescharacteristic
514C2×D11—22no—
515C2×D11—22no—
516C2×D11—22no—
517C2×D11—44no—
518C2×D11—42no—
519C2×D11—42no—
520C2×D11—42no—
521C2×D11—42no—
522C2×D11—42no—
523C2×D11—42no—
524C2×D11—816no—
525C2×D11—84no—
526C2×D11—84no—
527C4×C11—22no—
528C4×C11—42no—
529C4×C11—42no—
530C4×C11D4212yes—
531C4×C11C23×D411yescharacteristic
532C4×C11C2×H(5,𝔽2)11yescharacteristic
533Dic11—24no—
534Dic11—22no—
535Dic11—22no—
536Dic11—22no—
537Dic11—42no—
538C25—221no—
539C2×#41—22no—
540C2×#41—24no—
541C2×#41—42no—
542C2×#41—114no—
543C2×#41—114no—
544C2×#41—224no—
545C2×#41—222no—
546C2×#41—222no—
547C2×#41—224no—
548C2×#41—442no—
549C2×#41—442no—
550C2×#41C22×D1114yes—
551C22×Q8—111no—
552C22×Q8C22×D1111yescharacteristic
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—111no—
556C22×D4—114no—
557C22×D4—111no—
558C22×D4—111no—
559C22×D4—221no—
560C22×D4—222no—
561C22×D4—221no—
562C22×D4—221no—
563C22×D4—221no—
564C22×D4—224no—
565C22×D4—221no—
566C22×D4—221no—
567C22×D4—221no—
568C22×D4—442no—
569C22×D4C22×D1111yescharacteristic
570C22×D4C22×D1111yescharacteristic
571C23×C4—21no—
572C23×C4—111no—
573C23×C4—221no—
574C23×C4—221no—
575C23×C4—221no—
576C23×C4C22×D1111yescharacteristic
577AGL(1,ℤ/8)—2232no—
578#135—2232no—
579C2×Q16—114no—
580C2×Q16—224no—
581C2×SD16—42no—
582C2×SD16—118no—
583C2×SD16—114no—
584C2×SD16—114no—
585C2×SD16—114no—
586C2×SD16—224no—
587C2×SD16—224no—
588C2×SD16C22×D1114yescomplemented
589C2×D8—24no—
590C2×D8—114no—
591C2×D8—114no—
592C2×D8—114no—
593C2×D8—224no—
594C2×D8—224no—
595C2×D8—442no—
596C2×D8C22×D1114yes—
597C2×M16—114no—
598C2×M16—224no—
599C22×C8—111no—
600C22×C8—111no—
601C22×C8—114no—
602C22×C8—224no—
603C22×C8C22×D1111yescharacteristic
604C22×C8C22×D1111yescharacteristic
605#127—114no—
606#127—222no—
607#127—228no—
608#124—114no—
609#124—222no—
610#123—228no—
611C22⋊Q8—114no—
612C22⋊Q8—222no—
613#121—22no—
614#121—114no—
615#121—114no—
616#121—228no—
617#121—228no—
618#121—228no—
619#121—222no—
620#121—222no—
621#121C22×D1114yescomplemented
622#120—228no—
623C4×Q8—114no—
624C4×Q8—222no—
625C4×D4—114no—
626C4×D4—114no—
627C4×D4—114no—
628C4×D4—222no—
629C4×D4—228no—
630C2×C4⋊C4—111no—
631C2×C4⋊C4—111no—
632C2×C4⋊C4—221no—
633C2×C4⋊C4—221no—
634C2×C4⋊C4C22×D1111yescharacteristic
635C2×C22⋊C4—21no—
636C2×C22⋊C4—111no—
637C2×C22⋊C4—111no—
638C2×C22⋊C4—228no—
639C2×C22⋊C4—221no—
640C2×C22⋊C4—221no—
641C2×C22⋊C4—221no—
642C2×C22⋊C4—221no—
643C2×C22⋊C4—221no—
644C2×C22⋊C4—221no—
645C2×C42—111no—
646C2×C42—221no—
647#107—114no—
648C4⋊C8—114no—
649#103—114no—
650#103C22×D1114yescomplemented
651#102—114no—
652#102—114no—
653#102—114no—
654#102C22×D1114yes—
655C22⋊C8—114no—
656C22⋊C8C22×D1114yescomplemented
657#97—114no—
658C2×C11—44no—
659C2×C11—42no—
660C2×C11—82no—
661C2×C11#326814yescomplemented
662C2×C11C2×D4211yescharacteristic
663C2×C11C2×#57511yescharacteristic
664C2×C11C2×#57611yescharacteristic
665D11—42no—
666D11—82no—
667D11—82no—
668C24—21no—
669C24—21no—
670C24—111no—
671C24—224no—
672C24—221no—
673C24—221no—
674C24—444no—
675C24—444no—
676C24—882no—
677C24D4×D1111yescharacteristic
678#41—28no—
679#41—44no—
680#41—48no—
681#41—228no—
682#41—228no—
683#41—444no—
684#41—448no—
685#41—444no—
686#41—448no—
687C2×Q8—21no—
688C2×Q8—22no—
689C2×Q8—22no—
690C2×Q8—114no—
691C2×Q8—112no—
692C2×Q8—221no—
693C2×Q8—222no—
694C2×Q8C23×D1112yes—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—21no—
698C2×D4—22no—
699C2×D4—21no—
700C2×D4—22no—
701C2×D4—22no—
702C2×D4—44no—
703C2×D4—82no—
704C2×D4—114no—
705C2×D4—112no—
706C2×D4—112no—
707C2×D4—224no—
708C2×D4—224no—
709C2×D4—224no—
710C2×D4—224no—
711C2×D4—228no—
712C2×D4—224no—
713C2×D4—224no—
714C2×D4—224no—
715C2×D4—222no—
716C2×D4—222no—
717C2×D4—221no—
718C2×D4—221no—
719C2×D4—222no—
720C2×D4—222no—
721C2×D4—444no—
722C2×D4—448no—
723C2×D4—442no—
724C2×D4—444no—
725C2×D4—444no—
726C2×D4—444no—
727C2×D4—444no—
728C2×D4—882no—
729C2×D4—882no—
730C2×D4—882no—
731C2×D4D4×D1114yes—
732C2×D4C23×D1112yes—
733C2×D4C23×D1112yes—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—24no—
739C22×C4—44no—
740C22×C4—111no—
741C22×C4—111no—
742C22×C4—111no—
743C22×C4—112no—
744C22×C4—112no—
745C22×C4—224no—
746C22×C4—224no—
747C22×C4—221no—
748C22×C4—222no—
749C22×C4—222no—
750C22×C4—221no—
751C22×C4—224no—
752C22×C4—444no—
753C22×C4—444no—
754C22×C4—882no—
755C22×C4D4×D1112yes—
756C22×C4D4×D1111yescharacteristic
757C22×C4C23×D1112yes—
758C22×C4C23×D1111yescharacteristic
759Q16—228no—
760SD16—44no—
761SD16—1116no—
762SD16—228no—
763SD16—228no—
764D8—28no—
765D8—228no—
766D8—228no—
767D8—444no—
768M16—228no—
769C2×C8—22no—
770C2×C8—22no—
771C2×C8—114no—
772C2×C8—112no—
773C2×C8—112no—
774C2×C8—228no—
775C2×C8—222no—
776C2×C8C23×D1112yes—
777C2×C8C23×D1112yes—
778C4⋊C4—21no—
779C4⋊C4—114no—
780C4⋊C4—112no—
781C4⋊C4—224no—
782C4⋊C4—224no—
783C4⋊C4—221no—
784C4⋊C4C23×D1112yes—
785C22⋊C4—24no—
786C22⋊C4—114no—
787C22⋊C4—114no—
788C22⋊C4—224no—
789C22⋊C4—224no—
790C22⋊C4—224no—
791C22⋊C4—224no—
792C22⋊C4—224no—
793C22⋊C4—224no—
794C42—112no—
795C42—112no—
796C42—224no—
797C11C2×#326811yescharacteristic, complemented, Sylow
798C23—22no—
799C23—22no—
800C23—22no—
801C23—24no—
802C23—22no—
803C23—22no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—112no—
810C23—222no—
811C23—222no—
812C23—222no—
813C23—222no—
814C23—222no—
815C23—448no—
816C23—448no—
817C23—442no—
818C23—442no—
819C23—442no—
820C23—442no—
821C23—442no—
822C23—442no—
823C23—884no—
824C23—8816no—
825C23C2×D4×D1112yes—
826C23C2×D4×D1111yescharacteristic
827Q8—22no—
828Q8—22no—
829Q8—42no—
830Q8—114no—
831Q8—224no—
832Q8—222no—
833D4—24no—
834D4—22no—
835D4—22no—
836D4—22no—
837D4—48no—
838D4—42no—
839D4—84no—
840D4—222no—
841D4—222no—
842D4—222no—
843D4—222no—
844D4—444no—
845D4—448no—
846D4—448no—
847D4—448no—
848D4—448no—
849D4—442no—
850D4—442no—
851D4—884no—
852D4—884no—
853D4—884no—
854D4C2×D4×D1114yes—
855C2×C4—22no—
856C2×C4—24no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—48no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—112no—
865C2×C4—112no—
866C2×C4—112no—
867C2×C4—222no—
868C2×C4—222no—
869C2×C4—222no—
870C2×C4—224no—
871C2×C4—222no—
872C2×C4—224no—
873C2×C4—222no—
874C2×C4—222no—
875C2×C4—222no—
876C2×C4—448no—
877C2×C4—448no—
878C2×C4—442no—
879C2×C4—884no—
880C2×C4C2×D4×D1112yes—
881C2×C4C2×D4×D1111yescharacteristic
882C2×C4C2×D4×D1112yes—
883C2×C4#6703712yes—
884C2×C4C24×D1111yescharacteristic
885C8—22no—
886C8—22no—
887C8—114no—
888C8—222no—
889C22—22no—
890C22—24no—
891C22—22no—
892C22—22no—
893C22—44no—
894C22—48no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—84no—
901C22—222no—
902C22—222no—
903C22—222no—
904C22—444no—
905C22—442no—
906C22—442no—
907C22—442no—
908C22—442no—
909C22—442no—
910C22—442no—
911C22—8816no—
912C22—884no—
913C22—884no—
914C22#1062312112yes—
915C22#1062329912yes—
916C22#1062330512yes—
917C22C22×D4×D1111yescharacteristic
918C4—22no—
919C4—42no—
920C4—42no—
921C4—222no—
922C4—224no—
923C4—222no—
924C4—222no—
925C4—442no—
926C4#1062312112yes—
927C4C22×D4×D1111yescharacteristic
928C4C2×#6703711yescharacteristic
929C2—42no—
930C2—44no—
931C2—82no—
932C2—442no—
933C2—882no—
934C2—882no—
935C2#1308016014yesdirect product factor
936C2C2×#1062312111yescharacteristic
937C2C2×#1062329911yescharacteristic
938C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#449C2
socleC23×C11C22×D4
hypercenterC2×#449D11
hypocenterC11C2×#3268
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. C22×#66964C2semidirect
2. C22×#67003C2semidirect
3. C2×#10623130C2semidirect
4. C2×#10623360C2semidirect
5. #13080160C2direct (N × H)
6. C2×#10622789C2semidirect
7. C2×#10622425C2semidirect
8. C2×#10622651C2semidirect
9. C2×#10622411C2semidirect
10. C2×#10622763C2semidirect
11. C2×#10622786C2semidirect
12. C2×#10622347C2semidirect
13. C2×#10622386C2semidirect
14. C2×#10622370C2semidirect
15. C2×#10622343C2semidirect
16. C2×C11×#449C2semidirect
20. C22×#4339C22semidirect
21. C22×C11×SD16C22semidirect
23. C2×C11×#121C22semidirect
25. #10623360C22semidirect
27. C2×#67003C22semidirect
30. C22×#4326C22semidirect
31. C22×#4325C22semidirect
33. C2×#66993C22semidirect
45. C23×C11⋊C8C22semidirect
47. C2×#66964C22semidirect
52. #10623130C22semidirect
54. C2×#66940C22semidirect
57. C11×#449C22semidirect
58. C2×C11×#103C22semidirect
60. C2×C11×C22⋊C8C22semidirect
61. C2×#66896C22semidirect
62. #10622789C22semidirect
63. #10622786C22semidirect
64. #10622763C22semidirect
65. C2×#66885C22semidirect
67. C2×#66880C22semidirect
68. C2×#66879C22semidirect
69. C2×Dic11⋊C8C22semidirect
70. #10622651C22semidirect
72. C2×#66871C22semidirect
73. #10622425C22semidirect
74. #10622411C22semidirect
75. #10622386C22semidirect
76. #10622370C22semidirect
77. #10622347C22semidirect
78. #10622343C22semidirect
111. C2×#4339C23semidirect
119. C2×C11×SD16C23semidirect
125. C11×#121C23semidirect
136. C2×#4326C23semidirect
138. C2×#4325C23semidirect
141. #66993C23semidirect
147. C2×#4324D4semidirect
174. C22×C11⋊C8C23semidirect
185. #66940C23semidirect
188. C11×#103C23semidirect
190. C11×C22⋊C8C23semidirect
191. #66896C23semidirect
192. #66885C23semidirect
194. #66880C23semidirect
195. #66879C23semidirect
196. Dic11⋊C8C23semidirect
198. #66871C23semidirect
304. #4324C2×D4semidirect
341. C2×#449D11semidirect
448. C22×SD16C2×D11semidirect
469. C2×#121C2×D11semidirect
483. #449C2×D11semidirect
490. C2×#103C2×D11semidirect
496. C2×C22⋊C8C2×D11semidirect
588. C2×SD16C22×D11semidirect
621. #121C22×D11semidirect
650. #103C22×D11semidirect
656. C22⋊C8C22×D11semidirect
661. C2×C11#3268semidirect
797. C11C2×#3268semidirect
935. C2#13080160direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669642
C22×#670032
C2×#106231302
C2×#106233602
#130801602
C2×#106227892
C2×#106224252
C2×#106226512
C2×#106224112
C2×#106227632
C2×#106227862
C2×#106223472
C2×#106223862
C2×#106223702
C2×#106223432
C2×C11×#4492
C2×#326811