Finite Group Databasebeta

← C2×#13080150 #15628780

Subgroups — C2×#13080150 #15628780

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×#66969C211yesmaximal, characteristic, complemented
2C2×#10623365C211yesmaximal, characteristic, complemented
3C2×#10623337C211yesmaximal, characteristic, complemented
4#13080150C2116yesmaximal, direct product factor
5C2×#10622767C211yesmaximal, characteristic, complemented
6C2×#10622747C211yesmaximal, characteristic, complemented
7C2×#10622770C211yesmaximal, characteristic, complemented
8C2×#10622779C211yesmaximal, characteristic, complemented
9C2×#10622763C211yesmaximal, characteristic, complemented
10C2×#10622852C211yesmaximal, characteristic, complemented
11C2×#10622785C211yesmaximal, characteristic, complemented
12C2×#10622771C211yesmaximal, characteristic, complemented
13C2×#10622830C211yesmaximal, characteristic, complemented
14C2×#10622777C211yesmaximal, characteristic, complemented
15C2×#10622740C211yesmaximal, characteristic, complemented
16C22×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C22×#4343C2211yescharacteristic, complemented
20C22×#4341C2211yescharacteristic
21C2×C11×AGL(1,ℤ/8)—28no—
22C2×C11×AGL(1,ℤ/8)C2218yescomplemented
23C22×C11×SD16C2211yescharacteristic
24C22×C11×SD16C2211yescharacteristic
25C22×C11×D8C2211yescharacteristic
26C22×C11×D8C2211yescharacteristic
27C22×C11×M16C2211yescharacteristic
28C2×#67006—21no—
29C22×C22⋊Dic11—21no—
30#10623365—24no—
31#10623365C2218yescomplemented
32C2×Q8×Dic11C2211yescharacteristic, complemented
33C22×#4326C2211yescharacteristic, complemented
34#10623337—24no—
35#10623337C2218yescomplemented
36C2×#66993—21no—
37C2×#66993C2211yescharacteristic, complemented
38C2×#66992—21no—
39C2×#66991—21no—
40C2×#66991C2211yescharacteristic
41C2×#66991C2211yescharacteristic, complemented
42C2×#66989C2211yescharacteristic
43C2×#66988—21no—
44C2×D4×Dic11C2211yescharacteristic
45C22×#4324C2211yescharacteristic, complemented
46C22×#4323C2211yescharacteristic
47C22×#4323C2211yescharacteristic
48C2×#66983—21no—
49C2×#66983C2211yescharacteristic
50C2×C4×C22⋊D11—21no—
51C2×C4×C22⋊D11C2211yescharacteristic
52C2×#66977C2211yescharacteristic
53C2×#66969—28no—
54C2×#66969C2218yescomplemented
55C22×#4314C2211yescharacteristic, complemented
56C22×C8×D11C2211yescharacteristic, complemented
57#10622852C2218yescomplemented
58C2×#66899C2211yescharacteristic, complemented
59#10622830C2218yescomplemented
60C2×#66896C2211yescharacteristic
61C2×#66896C2211yescharacteristic
62C2×#66896C2211yescharacteristic, complemented
63C2×C22⋊(C11⋊C8)C2211yescharacteristic
64#10622785C2218yescomplemented
65#10622779C2218yescomplemented
66#10622777C2218yescomplemented
67#10622771C2218yescomplemented
68#10622770C2218yescomplemented
69#10622767C2218yescomplemented
70#10622763C2218yescomplemented
71#10622747C2218yescomplemented
72#10622740C2218yescomplemented
73C2×#66885C2211yescharacteristic, complemented
74C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
75C2×#66882C2211yescharacteristic, complemented
76C2×#66880C2211yescharacteristic, complemented
77C2×#66879C2211yescharacteristic, complemented
78C2×Dic11⋊C8C2211yescharacteristic, complemented
79C25×C11—21no—
80C2×C11×#41—22no—
81C2×C11×#41—24no—
82C2×C11×#41—42no—
83C2×C11×#41C2314yes—
84C22×Q8×C11C2311yescharacteristic
85C22×D4×C11—24no—
86C22×D4×C11—21no—
87C22×D4×C11—21no—
88C22×D4×C11—22no—
89C22×D4×C11—42no—
90C22×D4×C11C2311yescharacteristic
91C22×D4×C11C2311yescharacteristic
92C22×D4×C11C2314yes—
93C22×D4×C11C2311yescharacteristic
94C23×C4×C11—21no—
95C23×C4×C11C2311yescharacteristic
96C22×C22⋊D11—21no—
97C22×C22⋊D11—21no—
98C22×C22⋊D11—21no—
99C22×C22⋊D11—21no—
100C22×C22⋊D11—21no—
101C22×C22⋊D11—21no—
102C22×C22⋊D11D411yescharacteristic
103C23×Dic11—21no—
104C23×Dic11—21no—
105C2×#4343—22no—
106C2×#4343—24no—
107C2×#4343—42no—
108C2×#4343C2314yescomplemented
109C2×#4341—24no—
110C2×#4341—22no—
111C2×#4341—42no—
112C2×#4341C2314yes—
113C22×D44—21no—
114C22×D44C2311yescharacteristic
115C22×C4×D11—21no—
116C22×C4×D11C2311yescharacteristic
117C22×Dic22C2311yescharacteristic
118C11×AGL(1,ℤ/8)—232no—
119C2×C11×SD16—24no—
120C2×C11×SD16D418yescomplemented
121C2×C11×SD16C2314yes—
122C2×C11×SD16C2314yes—
123C2×C11×D8—24no—
124C2×C11×D8—24no—
125C2×C11×D8C2314yes—
126C2×C11×D8C2314yes—
127C2×C11×M16—24no—
128C2×C11×M16C2314yes—
129C22×C8×C11C2311yescharacteristic
130C22×C8×C11C2311yescharacteristic
131#67006—28no—
132C2×C22⋊Dic11—21no—
133C2×C22⋊Dic11—21no—
134C2×C22⋊Dic11—21no—
135C2×C22⋊Dic11—21no—
136C2×C22⋊Dic11—21no—
137C2×C22⋊Dic11—21no—
138C2×C22⋊Dic11—28no—
139C2×C22⋊Dic11D411yescharacteristic
140Q8×Dic11—22no—
141Q8×Dic11C2314yescomplemented
142C2×#4326—24no—
143C2×#4326C2314yescomplemented
144#66993—28no—
145#66993—22no—
146#66993C2314yescomplemented
147#66992—28no—
148#66991—22no—
149#66991—22no—
150#66991—28no—
151#66991C2314yes—
152#66991C2314yescomplemented
153#66989—22no—
154#66989C2314yes—
155#66988—28no—
156D4×Dic11—22no—
157D4×Dic11C2314yes—
158C2×#4324—42no—
159C2×#4324C2314yescomplemented
160C2×#4323—24no—
161C2×#4323—42no—
162C2×#4323C2314yes—
163C2×#4323C2314yes—
164#66983—22no—
165#66983—28no—
166#66983C2314yes—
167C4×C22⋊D11—28no—
168C4×C22⋊D11D414yes—
169C4×C22⋊D11C2314yes—
170C2×(C2×D11)⋊C4—21no—
171C2×(C2×D11)⋊C4D411yescharacteristic
172C2×C4⋊Dic11—21no—
173C2×C4⋊Dic11C2311yescharacteristic
174C2×C4⋊Dic11C2311yescharacteristic
175#66977—22no—
176#66977C2314yes—
177C2×Dic11⋊C4—21no—
178C2×Dic11⋊C4D411yescharacteristic
179C2×C4×Dic11—21no—
180C2×C4×Dic11C2311yescharacteristic
181C22×C11⋊C8C2311yescharacteristic
182C22×C11⋊C8C2311yescharacteristic
183#66969—232no—
184C2×#4314—24no—
185C2×#4314C2314yescomplemented
186C2×C8×D11—24no—
187C2×C8×D11C2314yescomplemented
188#66899C2314yescomplemented
189#66896C2314yes—
190#66896C2314yes—
191#66896C2314yescomplemented
192C22⋊(C11⋊C8)C2314yes—
193#66885C2314yescomplemented
194(C2×D11)⋊C8C2314yescomplemented
195#66882C2314yescomplemented
196#66880C2314yescomplemented
197#66879C2314yescomplemented
198Dic11⋊C8C2314yescomplemented
199C2×#3268—111nomaximal, Sylow
200C24×C11—21no—
201C24×C11—21no—
202C24×C11—21no—
203C24×C11—24no—
204C24×C11—44no—
205C24×C11—44no—
206C24×C11—82no—
207C24×C11C2×D411yescharacteristic
208C23×D11—21no—
209C23×D11C2×D411yescharacteristic
210C11×#41—28no—
211C11×#41—44no—
212C11×#41—48no—
213C2×Q8×C11—21no—
214C2×Q8×C11—22no—
215C2×Q8×C11C2×D414yes—
216C2×Q8×C11C2412yes—
217C2×D4×C11—28no—
218C2×D4×C11—24no—
219C2×D4×C11—21no—
220C2×D4×C11—22no—
221C2×D4×C11—22no—
222C2×D4×C11—24no—
223C2×D4×C11—21no—
224C2×D4×C11—21no—
225C2×D4×C11—22no—
226C2×D4×C11—22no—
227C2×D4×C11—22no—
228C2×D4×C11—44no—
229C2×D4×C11—48no—
230C2×D4×C11—44no—
231C2×D4×C11—44no—
232C2×D4×C11C2×D414yes—
233C2×D4×C11C2412yes—
234C2×D4×C11C2412yes—
235C2×D4×C11C2412yes—
236C22×C4×C11—21no—
237C22×C4×C11—22no—
238C22×C4×C11—22no—
239C22×C4×C11—24no—
240C22×C4×C11—44no—
241C22×C4×C11C2×D411yescharacteristic
242C22×C4×C11C2×D412yes—
243C22×C4×C11C2412yes—
244C22×C4×C11C2411yescharacteristic
245C2×C22⋊D11—24no—
246C2×C22⋊D11—24no—
247C2×C22⋊D11—24no—
248C2×C22⋊D11—24no—
249C2×C22⋊D11—24no—
250C2×C22⋊D11—24no—
251C2×C22⋊D11—42no—
252C2×C22⋊D11—44no—
253C2×C22⋊D11—44no—
254C2×C22⋊D11—82no—
255C2×C22⋊D11—82no—
256C2×C22⋊D11—82no—
257C2×C22⋊D11—82no—
258C2×C22⋊D11C2×D414yes—
259C22×Dic11—24no—
260C22×Dic11—24no—
261C22×Dic11—21no—
262C22×Dic11—21no—
263C22×Dic11—21no—
264C22×Dic11—44no—
265C22×Dic11—82no—
266C22×Dic11C2×D411yescharacteristic
267C22×Dic11C2×D411yescharacteristic
268C22×Dic11C2×D411yescharacteristic
269#4343—28no—
270#4343—44no—
271#4343—48no—
272#4341—28no—
273#4341—44no—
274#4341—48no—
275C2×D44—24no—
276C2×D44—21no—
277C2×D44—22no—
278C2×D44—22no—
279C2×D44—44no—
280C2×D44C2412yes—
281C2×C4×D11—24no—
282C2×C4×D11—22no—
283C2×C4×D11—22no—
284C2×C4×D11—44no—
285C2×C4×D11C2×D412yes—
286C2×C4×D11C2412yes—
287C2×Dic22—22no—
288C2×Dic22—21no—
289C2×Dic22—22no—
290C2×Dic22C2412yes—
291C11×SD16—28no—
292C11×SD16C2×D4116yescomplemented
293C11×D8—28no—
294C11×D8—28no—
295C11×M16—28no—
296C2×C8×C11—22no—
297C2×C8×C11C2×D414yes—
298C2×C8×C11C2412yes—
299C2×C8×C11C2412yes—
300C22⋊Dic11—24no—
301C22⋊Dic11—24no—
302C22⋊Dic11—24no—
303C22⋊Dic11—24no—
304C22⋊Dic11—24no—
305C22⋊Dic11—24no—
306C22⋊Dic11C2×D414yes—
307#4326—28no—
308#4324—44no—
309#4323—28no—
310#4323—44no—
311(C2×D11)⋊C4—24no—
312(C2×D11)⋊C4C2×D414yes—
313C4⋊Dic11—24no—
314C4⋊Dic11—21no—
315C4⋊Dic11—21no—
316C4⋊Dic11C2412yes—
317C4⋊Dic11C2412yes—
318Dic11⋊C4—24no—
319Dic11⋊C4C2×D414yes—
320C4×Dic11—24no—
321C4×Dic11C2×D412yes—
322C4×Dic11C2412yes—
323C2×C11⋊C8—22no—
324C2×C11⋊C8—22no—
325C2×C11⋊C8C2412yes—
326C2×C11⋊C8C2412yes—
327#4314—28no—
328C8×D11—28no—
329C22×AGL(1,ℤ/8)D1111yescharacteristic, complemented
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×#449—111no—
342C2×#447—111no—
343C2×#440—111no—
344C2×#435—111no—
345C23×C11—24no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—22no—
352C23×C11—48no—
353C23×C11—48no—
354C23×C11—42no—
355C23×C11—42no—
356C23×C11—42no—
357C23×C11—42no—
358C23×C11—42no—
359C23×C11—42no—
360C23×C11—42no—
361C23×C11—42no—
362C23×C11—84no—
363C23×C11—816no—
364C23×C11C22×D412yes—
365C23×C11C22×D411yescharacteristic
366C22×D11—22no—
367C22×D11—22no—
368C22×D11—22no—
369C22×D11—22no—
370C22×D11—42no—
371C22×D11—42no—
372C22×D11—42no—
373C22×D11C22×D412yes—
374Q8×C11—24no—
375Q8×C11—22no—
376Q8×C11C22×D414yes—
377D4×C11—24no—
378D4×C11—22no—
379D4×C11—22no—
380D4×C11—22no—
381D4×C11—22no—
382D4×C11—22no—
383D4×C11—48no—
384D4×C11—48no—
385D4×C11—42no—
386D4×C11—42no—
387D4×C11C22×D414yes—
388C2×C4×C11—24no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—24no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—48no—
395C2×C4×C11C22×D412yes—
396C2×C4×C11C22×D411yescharacteristic
397C2×C4×C11C22×D412yes—
398C2×C4×C11H(5,𝔽2)12yes—
399C2×C4×C11C2511yescharacteristic
400C22⋊D11—44no—
401C22⋊D11—48no—
402C22⋊D11—48no—
403C22⋊D11—84no—
404C22⋊D11—84no—
405C22⋊D11—84no—
406C22⋊D11—84no—
407C2×Dic11—22no—
408C2×Dic11—22no—
409C2×Dic11—22no—
410C2×Dic11—22no—
411C2×Dic11—22no—
412C2×Dic11—22no—
413C2×Dic11—48no—
414C2×Dic11—42no—
415C2×Dic11—42no—
416C2×Dic11—42no—
417C2×Dic11—84no—
418C2×Dic11C22×D412yes—
419C2×Dic11C22×D412yes—
420C2×Dic11C22×D412yes—
421D44—22no—
422D44—22no—
423D44—48no—
424D44—42no—
425C4×D11—24no—
426C4×D11—22no—
427C4×D11—22no—
428C4×D11—48no—
429Dic22—22no—
430Dic22—22no—
431Dic22—42no—
432C8×C11—22no—
433C8×C11C22×D414yes—
434C11⋊C8—22no—
435C11⋊C8—22no—
436C22×#41—111no—
437C22×#41—111no—
438C22×#41C2×D1111yescharacteristic
439C23×D4C2×D1111yescharacteristic
440C2×AGL(1,ℤ/8)—28no—
441C2×AGL(1,ℤ/8)C2×D1118yescomplemented
442C2×#135—118no—
443C2×#135—228no—
444C22×Q16—111no—
445C22×SD16—111no—
446C22×SD16—111no—
447C22×SD16C2×D1111yescharacteristic
448C22×SD16C2×D1111yescharacteristic
449C22×D8—111no—
450C22×D8—111no—
451C22×D8C2×D1111yescharacteristic
452C22×D8C2×D1111yescharacteristic
453C22×M16C2×D1111yescharacteristic
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—111no—
467C2×#121—221no—
468C2×#121—221no—
469C2×#121—221no—
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#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—24no—
500C22×C11—22no—
501C22×C11—22no—
502C22×C11—44no—
503C22×C11—48no—
504C22×C11—42no—
505C22×C11—42no—
506C22×C11—42no—
507C22×C11—42no—
508C22×C11—42no—
509C22×C11—42no—
510C22×C11—42no—
511C22×C11—42no—
512C22×C11—816no—
513C22×C11—84no—
514C22×C11—84no—
515C22×C11D4212yes—
516C22×C11#57512yes—
517C22×C11#57612yes—
518C22×C11C23×D411yescharacteristic
519C2×D11—22no—
520C2×D11—22no—
521C2×D11—22no—
522C2×D11—44no—
523C2×D11—42no—
524C2×D11—42no—
525C2×D11—42no—
526C2×D11—84no—
527C4×C11—22no—
528C4×C11—24no—
529C4×C11D4212yes—
530C4×C11C23×D411yescharacteristic
531C4×C11C2×H(5,𝔽2)11yescharacteristic
532Dic11—22no—
533Dic11—22no—
534Dic11—22no—
535Dic11—42no—
536Dic11—42no—
537Dic11—42no—
538C25—21no—
539C2×#41—22no—
540C2×#41—24no—
541C2×#41—42no—
542C2×#41—114no—
543C2×#41—114no—
544C2×#41—222no—
545C2×#41—222no—
546C2×#41—224no—
547C2×#41—224no—
548C2×#41—442no—
549C2×#41—442no—
550C2×#41C22×D1114yes—
551C22×Q8—111no—
552C22×Q8C22×D1111yescharacteristic
553C22×D4—24no—
554C22×D4—21no—
555C22×D4—21no—
556C22×D4—22no—
557C22×D4—42no—
558C22×D4—111no—
559C22×D4—111no—
560C22×D4—221no—
561C22×D4—221no—
562C22×D4—221no—
563C22×D4—221no—
564C22×D4—221no—
565C22×D4—221no—
566C22×D4—221no—
567C22×D4C22×D1111yescharacteristic
568C22×D4C22×D1111yescharacteristic
569C22×D4C22×D1114yes—
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)—232no—
578#135—2232no—
579C2×Q16—114no—
580C2×Q16—224no—
581C2×SD16—24no—
582C2×SD16—114no—
583C2×SD16—114no—
584C2×SD16—224no—
585C2×SD16—442no—
586C2×SD16C22⋊D1118yescomplemented
587C2×SD16C22×D1114yes—
588C2×SD16C22×D1114yes—
589C2×D8—24no—
590C2×D8—24no—
591C2×D8—114no—
592C2×D8—114no—
593C2×D8—224no—
594C2×D8—442no—
595C2×D8C22×D1114yes—
596C2×D8C22×D1114yes—
597C2×M16—24no—
598C2×M16C22×D1114yes—
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—114no—
614#121—114no—
615#121—114no—
616#121—228no—
617#121—228no—
618#121—228no—
619#121—222no—
620#121—222no—
621#121—222no—
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—111no—
633C2×C4⋊C4—221no—
634C2×C4⋊C4—221no—
635C2×C22⋊C4—111no—
636C2×C22⋊C4—111no—
637C2×C22⋊C4—228no—
638C2×C22⋊C4—221no—
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#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—44no—
660C2×C11—82no—
661C2×C11—82no—
662C2×C11#326814yescomplemented
663C2×C11C2×D4211yescharacteristic
664C2×C11C2×#57511yescharacteristic
665C2×C11C2×#57611yescharacteristic
666D11—42no—
667D11—82no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—24no—
672C24—44no—
673C24—44no—
674C24—82no—
675C24—111no—
676C24—221no—
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—112no—
690C2×Q8—221no—
691C2×Q8—222no—
692C2×Q8—222no—
693C2×Q8C2×C22⋊D1114yes—
694C2×Q8C23×D1112yes—
695C2×D4—28no—
696C2×D4—24no—
697C2×D4—21no—
698C2×D4—24no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—22no—
702C2×D4—22no—
703C2×D4—22no—
704C2×D4—22no—
705C2×D4—22no—
706C2×D4—44no—
707C2×D4—48no—
708C2×D4—44no—
709C2×D4—44no—
710C2×D4—114no—
711C2×D4—112no—
712C2×D4—224no—
713C2×D4—224no—
714C2×D4—224no—
715C2×D4—224no—
716C2×D4—224no—
717C2×D4—224no—
718C2×D4—224no—
719C2×D4—221no—
720C2×D4—222no—
721C2×D4—222no—
722C2×D4—444no—
723C2×D4—442no—
724C2×D4—444no—
725C2×D4—444no—
726C2×D4—882no—
727C2×D4—882no—
728C2×D4—882no—
729C2×D4—882no—
730C2×D4C2×C22⋊D1114yes—
731C2×D4C23×D1112yes—
732C2×D4C23×D1112yes—
733C2×D4C23×D1112yes—
734C22×C4—21no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—24no—
738C22×C4—44no—
739C22×C4—111no—
740C22×C4—111no—
741C22×C4—111no—
742C22×C4—112no—
743C22×C4—112no—
744C22×C4—224no—
745C22×C4—224no—
746C22×C4—224no—
747C22×C4—222no—
748C22×C4—222no—
749C22×C4—221no—
750C22×C4—221no—
751C22×C4—221no—
752C22×C4—444no—
753C22×C4—444no—
754C22×C4—882no—
755C22×C4D4×D1112yes—
756C22×C4D4×D1111yescharacteristic
757C22×C4C23×D1112yes—
758C22×C4C23×D1111yescharacteristic
759Q16—228no—
760SD16—28no—
761SD16—228no—
762SD16—444no—
763SD16C2×C22⋊D11116yescomplemented
764D8—28no—
765D8—28no—
766D8—228no—
767D8—444no—
768M16—28no—
769C2×C8—22no—
770C2×C8—112no—
771C2×C8—112no—
772C2×C8—222no—
773C2×C8—222no—
774C2×C8—228no—
775C2×C8C2×C22⋊D1114yes—
776C2×C8C23×D1112yes—
777C2×C8C23×D1112yes—
778C4⋊C4—114no—
779C4⋊C4—112no—
780C4⋊C4—112no—
781C4⋊C4—224no—
782C4⋊C4—221no—
783C4⋊C4—221no—
784C4⋊C4—224no—
785C22⋊C4—114no—
786C22⋊C4—114no—
787C22⋊C4—224no—
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—22no—
805C23—48no—
806C23—48no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—84no—
816C23—816no—
817C23—112no—
818C23—222no—
819C23—222no—
820C23—222no—
821C23—222no—
822C23—442no—
823C23—442no—
824C23—442no—
825C23C2×D4×D1112yes—
826C23C2×D4×D1111yescharacteristic
827Q8—24no—
828Q8—22no—
829Q8—222no—
830Q8—222no—
831Q8—442no—
832Q8C22×C22⋊D1114yes—
833D4—24no—
834D4—22no—
835D4—22no—
836D4—22no—
837D4—22no—
838D4—22no—
839D4—48no—
840D4—48no—
841D4—42no—
842D4—42no—
843D4—222no—
844D4—222no—
845D4—448no—
846D4—444no—
847D4—448no—
848D4—448no—
849D4—442no—
850D4—884no—
851D4—884no—
852D4—884no—
853D4—884no—
854D4C22×C22⋊D1114yes—
855C2×C4—22no—
856C2×C4—24no—
857C2×C4—22no—
858C2×C4—24no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—48no—
862C2×C4—112no—
863C2×C4—112no—
864C2×C4—112no—
865C2×C4—222no—
866C2×C4—222no—
867C2×C4—222no—
868C2×C4—224no—
869C2×C4—222no—
870C2×C4—222no—
871C2×C4—222no—
872C2×C4—222no—
873C2×C4—222no—
874C2×C4—448no—
875C2×C4—448no—
876C2×C4—442no—
877C2×C4—442no—
878C2×C4—442no—
879C2×C4—884no—
880C2×C4C2×D4×D1112yes—
881C2×C4C2×D4×D1111yescharacteristic
882C2×C4#6703712yes—
883C2×C4C22×C22⋊D1112yes—
884C2×C4C24×D1111yescharacteristic
885C8—22no—
886C8—222no—
887C8—222no—
888C8C22×C22⋊D1114yes—
889C22—22no—
890C22—24no—
891C22—22no—
892C22—22no—
893C22—44no—
894C22—48no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—816no—
904C22—84no—
905C22—84no—
906C22—222no—
907C22—222no—
908C22—222no—
909C22—444no—
910C22—442no—
911C22—442no—
912C22—442no—
913C22—884no—
914C22#1062330412yes—
915C22#1062330512yes—
916C22D4×C22⋊D1112yes—
917C22C22×D4×D1111yescharacteristic
918C4—22no—
919C4—24no—
920C4—222no—
921C4—222no—
922C4—222no—
923C4—442no—
924C4—442no—
925C4—442no—
926C4D4×C22⋊D1112yes—
927C4C2×#6703711yescharacteristic
928C4C23×C22⋊D1111yescharacteristic
929C2—42no—
930C2—44no—
931C2—82no—
932C2—82no—
933C2—442no—
934C2—882no—
935C2#1308015014yesdirect product factor
936C2C2×D4×C22⋊D1111yescharacteristic
937C2C2×#1062330411yescharacteristic
938C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×AGL(1,ℤ/8)C2
socleC23×C11C22×D4
hypercenterC22×AGL(1,ℤ/8)D11
hypocenterC11C2×#3268
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C22×#66969C2semidirect
2. C2×#10623365C2semidirect
3. C2×#10623337C2semidirect
4. #13080150C2direct (N × H)
5. C2×#10622767C2semidirect
6. C2×#10622747C2semidirect
7. C2×#10622770C2semidirect
8. C2×#10622779C2semidirect
9. C2×#10622763C2semidirect
10. C2×#10622852C2semidirect
11. C2×#10622785C2semidirect
12. C2×#10622771C2semidirect
13. C2×#10622830C2semidirect
14. C2×#10622777C2semidirect
15. C2×#10622740C2semidirect
16. C22×C11×AGL(1,ℤ/8)C2semidirect
19. C22×#4343C22semidirect
22. C2×C11×AGL(1,ℤ/8)C22semidirect
31. #10623365C22semidirect
32. C2×Q8×Dic11C22semidirect
33. C22×#4326C22semidirect
35. #10623337C22semidirect
37. C2×#66993C22semidirect
41. C2×#66991C22semidirect
45. C22×#4324C22semidirect
54. C2×#66969C22semidirect
55. C22×#4314C22semidirect
56. C22×C8×D11C22semidirect
57. #10622852C22semidirect
58. C2×#66899C22semidirect
59. #10622830C22semidirect
62. C2×#66896C22semidirect
64. #10622785C22semidirect
65. #10622779C22semidirect
66. #10622777C22semidirect
67. #10622771C22semidirect
68. #10622770C22semidirect
69. #10622767C22semidirect
70. #10622763C22semidirect
71. #10622747C22semidirect
72. #10622740C22semidirect
73. C2×#66885C22semidirect
74. C2×(C2×D11)⋊C8C22semidirect
75. C2×#66882C22semidirect
76. C2×#66880C22semidirect
77. C2×#66879C22semidirect
78. C2×Dic11⋊C8C22semidirect
108. C2×#4343C23semidirect
120. C2×C11×SD16D4semidirect
141. Q8×Dic11C23semidirect
143. C2×#4326C23semidirect
146. #66993C23semidirect
152. #66991C23semidirect
159. C2×#4324C23semidirect
185. C2×#4314C23semidirect
187. C2×C8×D11C23semidirect
188. #66899C23semidirect
191. #66896C23semidirect
193. #66885C23semidirect
194. (C2×D11)⋊C8C23semidirect
195. #66882C23semidirect
196. #66880C23semidirect
197. #66879C23semidirect
198. Dic11⋊C8C23semidirect
292. C11×SD16C2×D4semidirect
329. C22×AGL(1,ℤ/8)D11semidirect
441. C2×AGL(1,ℤ/8)C2×D11semidirect
586. C2×SD16C22⋊D11semidirect
662. C2×C11#3268semidirect
763. SD16C2×C22⋊D11semidirect
797. C11C2×#3268semidirect
935. C2#13080150direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669692
C2×#106233652
C2×#106233372
#130801502
C2×#106227672
C2×#106227472
C2×#106227702
C2×#106227792
C2×#106227632
C2×#106228522
C2×#106227852
C2×#106227712
C2×#106228302
C2×#106227772
C2×#106227402
C22×C11×AGL(1,ℤ/8)2
C2×#326811