Finite Group Databasebeta

← C2×#13080230 #15628885

Subgroups — C2×#13080230 #15628885

Order 2816.

3278 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66967C211yesmaximal, characteristic, complemented
2C2×#10623365C211yesmaximal, characteristic, complemented
3C2×D4×C22⋊D11C211yesmaximal, characteristic, complemented
4#13080230C2116yesmaximal, direct product factor
5C2×#10622764C211yesmaximal, characteristic, complemented
6C2×#10622748C211yesmaximal, characteristic, complemented
7C2×#10622772C211yesmaximal, characteristic, complemented
8C2×#10622776C211yesmaximal, characteristic, complemented
9C2×#10622763C211yesmaximal, characteristic, complemented
10C2×#10622851C211yesmaximal, characteristic, complemented
11C2×#10622785C211yesmaximal, characteristic, complemented
12C2×#10622830C211yesmaximal, characteristic, complemented
13C2×#10622769C211yesmaximal, characteristic, complemented
14C2×SD16×Dic11C211yesmaximal, characteristic, complemented
15C2×#10622741C211yesmaximal, characteristic, complemented
16C22×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic, complemented
18C23×D4×C11C2211yescharacteristic
19C23×C22⋊D11—21no—
20C22×#4343C2211yescharacteristic, complemented
21C22×D4×D11C2211yescharacteristic
22C2×C11×AGL(1,ℤ/8)—28no—
23C2×C11×AGL(1,ℤ/8)C2218yescomplemented
24C22×C11×SD16C2211yescharacteristic
25C22×C11×SD16C2211yescharacteristic, complemented
26C22×C11×D8C2211yescharacteristic
27C22×C11×D8C2211yescharacteristic, complemented
28C22×C11×M16C2211yescharacteristic, complemented
29C2×#67006—21no—
30#10623365—24no—
31#10623365C2218yescomplemented
32C2×Q8×Dic11C2211yescharacteristic, complemented
33C22×#4325C2211yescharacteristic, complemented
34C2×#66993—21no—
35C2×#66993C2211yescharacteristic
36C2×#66993C2211yescharacteristic, complemented
37C2×#66992—21no—
38D4×C22⋊D11—24no—
39D4×C22⋊D11C2218yescomplemented
40C2×#66991—21no—
41C2×#66991C2211yescharacteristic
42C2×#66991C2211yescharacteristic, complemented
43C2×#66990—21no—
44C2×D4×Dic11C2211yescharacteristic
45C22×#4323C2211yescharacteristic
46C22×#4323C2211yescharacteristic, complemented
47C22×#4323C2211yescharacteristic, complemented
48C2×#66983—21no—
49C2×#66983C2211yescharacteristic
50C2×#66983C2211yescharacteristic, complemented
51C2×C4×C22⋊D11—21no—
52C2×C4×C22⋊D11C2211yescharacteristic
53C2×#66967—28no—
54C2×#66967C2218yescomplemented
55C22×D88C2211yescharacteristic, complemented
56C22×#4313C2211yescharacteristic, complemented
57#10622851C2218yescomplemented
58C2×#66899C2211yescharacteristic, complemented
59#10622830C2218yescomplemented
60C2×#66896C2211yescharacteristic
61C2×#66896C2211yescharacteristic, complemented
62C2×#66896C2211yescharacteristic, complemented
63C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
64#10622785C2218yescomplemented
65#10622776C2218yescomplemented
66SD16×Dic11C2218yescomplemented
67#10622772C2218yescomplemented
68#10622769C2218yescomplemented
69#10622764C2218yescomplemented
70#10622763C2218yescomplemented
71#10622748C2218yescomplemented
72#10622741C2218yescomplemented
73C2×#66885C2211yescharacteristic, complemented
74C2×#66885C2211yescharacteristic, complemented
75C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
76C2×#66881C2211yescharacteristic, complemented
77C2×Dic11⋊C8C2211yescharacteristic, complemented
78C2×C8×Dic11C2211yescharacteristic, complemented
79C25×C11—21no—
80C24×D11—21no—
81C2×C11×#41—22no—
82C2×C11×#41—24no—
83C2×C11×#41—42no—
84C2×C11×#41C2314yescomplemented
85C22×Q8×C11C2311yescharacteristic
86C22×D4×C11—24no—
87C22×D4×C11—21no—
88C22×D4×C11—21no—
89C22×D4×C11—22no—
90C22×D4×C11—42no—
91C22×D4×C11C2311yescharacteristic
92C22×D4×C11C2311yescharacteristic
93C22×D4×C11C2314yes—
94C22×D4×C11C2311yescharacteristic
95C23×C4×C11—21no—
96C23×C4×C11C2311yescharacteristic
97C22×C22⋊D11—21no—
98C22×C22⋊D11—21no—
99C22×C22⋊D11—21no—
100C22×C22⋊D11—21no—
101C22×C22⋊D11—28no—
102C22×C22⋊D11—21no—
103C22×C22⋊D11—21no—
104C22×C22⋊D11—21no—
105C22×C22⋊D11—21no—
106C22×C22⋊D11—21no—
107C22×C22⋊D11—48no—
108C22×C22⋊D11D411yescharacteristic
109C23×Dic11—21no—
110C2×#4343—22no—
111C2×#4343—24no—
112C2×#4343—42no—
113C2×#4343C2314yescomplemented
114C2×D4×D11—24no—
115C2×D4×D11—22no—
116C2×D4×D11—42no—
117C2×D4×D11C2314yes—
118C22×D44—21no—
119C22×D44C2311yescharacteristic
120C22×D44C2311yescharacteristic
121C22×C4×D11—21no—
122C22×C4×D11C2311yescharacteristic
123C11×AGL(1,ℤ/8)—232no—
124C2×C11×SD16—24no—
125C2×C11×SD16D418yescomplemented
126C2×C11×SD16C2314yes—
127C2×C11×SD16C2314yescomplemented
128C2×C11×D8—24no—
129C2×C11×D8—24no—
130C2×C11×D8C2314yes—
131C2×C11×D8C2314yescomplemented
132C2×C11×M16—24no—
133C2×C11×M16C2314yescomplemented
134C22×C8×C11C2311yescharacteristic
135C22×C8×C11C2311yescharacteristic
136#67006—28no—
137C2×C22⋊Dic11—21no—
138C2×C22⋊Dic11—21no—
139C2×C22⋊Dic11—21no—
140C2×C22⋊Dic11D411yescharacteristic
141Q8×Dic11—22no—
142Q8×Dic11C2314yescomplemented
143C2×#4325—24no—
144C2×#4325C2314yescomplemented
145#66993—28no—
146#66993—22no—
147#66993—22no—
148#66993C2314yes—
149#66993C2314yescomplemented
150#66992—28no—
151#66991—22no—
152#66991—22no—
153#66991—28no—
154#66991C2314yes—
155#66991C2314yescomplemented
156#66990—28no—
157D4×Dic11—22no—
158D4×Dic11C2314yes—
159C2×#4323—24no—
160C2×#4323—42no—
161C2×#4323—42no—
162C2×#4323C2314yes—
163C2×#4323C2314yescomplemented
164C2×#4323C2314yescomplemented
165#66983—22no—
166#66983—22no—
167#66983—28no—
168#66983C2314yes—
169#66983C2314yescomplemented
170C4×C22⋊D11—28no—
171C4×C22⋊D11D414yes—
172C4×C22⋊D11C2314yes—
173C2×(C2×D11)⋊C4—21no—
174C2×(C2×D11)⋊C4—21no—
175C2×(C2×D11)⋊C4D411yescharacteristic
176C2×C4⋊Dic11—21no—
177C2×C4⋊Dic11C2311yescharacteristic
178C2×C4⋊Dic11C2311yescharacteristic
179C2×Dic11⋊C4D411yescharacteristic
180C2×C4×Dic11—21no—
181C2×C4×Dic11C2311yescharacteristic
182C22×C11⋊C8C2311yescharacteristic
183C22×C11⋊C8C2311yescharacteristic
184#66967—232no—
185C2×D88—24no—
186C2×D88C2314yescomplemented
187C2×#4313—24no—
188C2×#4313C2314yescomplemented
189#66899C2314yescomplemented
190#66896C2314yes—
191#66896C2314yescomplemented
192#66896C2314yescomplemented
193C22⋊(C11⋊C8)C2314yescomplemented
194#66885C2314yescomplemented
195#66885C2314yescomplemented
196(C2×D11)⋊C8C2314yescomplemented
197#66881C2314yescomplemented
198Dic11⋊C8C2314yescomplemented
199C8×Dic11C2314yescomplemented
200C2×#3274—111nomaximal, Sylow
201C24×C11—21no—
202C24×C11—21no—
203C24×C11—21no—
204C24×C11—24no—
205C24×C11—44no—
206C24×C11—44no—
207C24×C11—82no—
208C24×C11C2×D411yescharacteristic
209C23×D11—21no—
210C23×D11—21no—
211C23×D11—24no—
212C23×D11—44no—
213C23×D11—44no—
214C23×D11—82no—
215C23×D11C2×D411yescharacteristic
216C11×#41—28no—
217C11×#41—44no—
218C11×#41—48no—
219C2×Q8×C11—21no—
220C2×Q8×C11—22no—
221C2×Q8×C11C2×D414yescomplemented
222C2×Q8×C11C2412yes—
223C2×D4×C11—28no—
224C2×D4×C11—24no—
225C2×D4×C11—21no—
226C2×D4×C11—22no—
227C2×D4×C11—22no—
228C2×D4×C11—24no—
229C2×D4×C11—21no—
230C2×D4×C11—21no—
231C2×D4×C11—22no—
232C2×D4×C11—22no—
233C2×D4×C11—22no—
234C2×D4×C11—44no—
235C2×D4×C11—48no—
236C2×D4×C11—44no—
237C2×D4×C11—44no—
238C2×D4×C11C2×D414yes—
239C2×D4×C11C2412yes—
240C2×D4×C11C2412yes—
241C2×D4×C11C2412yes—
242C22×C4×C11—21no—
243C22×C4×C11—22no—
244C22×C4×C11—22no—
245C22×C4×C11—24no—
246C22×C4×C11—44no—
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2×D412yes—
249C22×C4×C11C2412yes—
250C22×C4×C11C2411yescharacteristic
251C2×C22⋊D11—24no—
252C2×C22⋊D11—24no—
253C2×C22⋊D11—24no—
254C2×C22⋊D11—24no—
255C2×C22⋊D11—24no—
256C2×C22⋊D11—24no—
257C2×C22⋊D11—24no—
258C2×C22⋊D11—24no—
259C2×C22⋊D11—24no—
260C2×C22⋊D11—24no—
261C2×C22⋊D11—44no—
262C2×C22⋊D11—44no—
263C2×C22⋊D11—44no—
264C2×C22⋊D11—432no—
265C2×C22⋊D11—44no—
266C2×C22⋊D11—44no—
267C2×C22⋊D11—82no—
268C2×C22⋊D11—82no—
269C2×C22⋊D11—82no—
270C2×C22⋊D11—82no—
271C2×C22⋊D11C2×D414yes—
272C22×Dic11—24no—
273C22×Dic11—21no—
274C22×Dic11—21no—
275C22×Dic11—44no—
276C22×Dic11C2×D411yescharacteristic
277C22×Dic11C2×D411yescharacteristic
278C22×Dic11C2×D411yescharacteristic
279#4343—28no—
280#4343—44no—
281#4343—48no—
282D4×D11—28no—
283D4×D11—44no—
284D4×D11—48no—
285C2×D44—24no—
286C2×D44—21no—
287C2×D44—21no—
288C2×D44—22no—
289C2×D44—22no—
290C2×D44—22no—
291C2×D44—22no—
292C2×D44—44no—
293C2×D44C2412yes—
294C2×D44C2412yes—
295C2×C4×D11—24no—
296C2×C4×D11—22no—
297C2×C4×D11—22no—
298C2×C4×D11—44no—
299C2×C4×D11C2×D412yes—
300C2×C4×D11C2412yes—
301C11×SD16—28no—
302C11×SD16C2×D4116yescomplemented
303C11×D8—28no—
304C11×D8—28no—
305C11×M16—28no—
306C2×C8×C11—22no—
307C2×C8×C11C2×D414yescomplemented
308C2×C8×C11C2412yes—
309C2×C8×C11C2412yes—
310C22⋊Dic11—24no—
311C22⋊Dic11—24no—
312C22⋊Dic11—24no—
313C22⋊Dic11C2×D414yes—
314#4325—28no—
315#4323—28no—
316#4323—44no—
317#4323—44no—
318(C2×D11)⋊C4—24no—
319(C2×D11)⋊C4—24no—
320(C2×D11)⋊C4C2×D414yes—
321C4⋊Dic11—24no—
322C4⋊Dic11—21no—
323C4⋊Dic11—21no—
324C4⋊Dic11C2412yes—
325C4⋊Dic11C2412yes—
326Dic11⋊C4C2×D414yes—
327C4×Dic11—24no—
328C4×Dic11C2×D412yes—
329C4×Dic11C2412yes—
330C2×C11⋊C8—22no—
331C2×C11⋊C8—22no—
332C2×C11⋊C8C2412yes—
333C2×C11⋊C8C2412yes—
334D88—28no—
335#4313—28no—
336C22×AGL(1,ℤ/8)—111no—
337C22×AGL(1,ℤ/8)D1111yescharacteristic, complemented
338C2×#550—111no—
339C2×D42—111no—
340#3274—1116no—
341C2×#493—111no—
342C2×#469—111no—
343C2×#469—111no—
344C2×#460—111no—
345C2×#459—111no—
346C2×#449—111no—
347C2×#449—111no—
348C2×#447—111no—
349C2×#447—111no—
350C2×C4×SD16—111no—
351C2×#436—111no—
352C23×C11—24no—
353C23×C11—22no—
354C23×C11—22no—
355C23×C11—22no—
356C23×C11—22no—
357C23×C11—22no—
358C23×C11—22no—
359C23×C11—48no—
360C23×C11—48no—
361C23×C11—42no—
362C23×C11—42no—
363C23×C11—42no—
364C23×C11—42no—
365C23×C11—42no—
366C23×C11—42no—
367C23×C11—42no—
368C23×C11—42no—
369C23×C11—84no—
370C23×C11—816no—
371C23×C11C22×D412yes—
372C23×C11C22×D411yescharacteristic
373C22×D11—22no—
374C22×D11—22no—
375C22×D11—22no—
376C22×D11—22no—
377C22×D11—22no—
378C22×D11—48no—
379C22×D11—48no—
380C22×D11—42no—
381C22×D11—42no—
382C22×D11—42no—
383C22×D11—42no—
384C22×D11—42no—
385C22×D11—42no—
386C22×D11—84no—
387C22×D11—816no—
388C22×D11C22×D412yes—
389Q8×C11—24no—
390Q8×C11—22no—
391Q8×C11C22×D414yescomplemented
392D4×C11—24no—
393D4×C11—22no—
394D4×C11—22no—
395D4×C11—22no—
396D4×C11—22no—
397D4×C11—22no—
398D4×C11—48no—
399D4×C11—48no—
400D4×C11—42no—
401D4×C11—42no—
402D4×C11C22×D414yes—
403C2×C4×C11—24no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—24no—
407C2×C4×C11—22no—
408C2×C4×C11—22no—
409C2×C4×C11—48no—
410C2×C4×C11C22×D412yes—
411C2×C4×C11C22×D411yescharacteristic
412C2×C4×C11C22×D412yes—
413C2×C4×C11H(5,𝔽2)12yes—
414C2×C4×C11C2511yescharacteristic
415C22⋊D11—28no—
416C22⋊D11—48no—
417C22⋊D11—48no—
418C22⋊D11—48no—
419C22⋊D11—48no—
420C22⋊D11—48no—
421C22⋊D11—84no—
422C22⋊D11—84no—
423C22⋊D11—84no—
424C22⋊D11—84no—
425C2×Dic11—22no—
426C2×Dic11—22no—
427C2×Dic11—22no—
428C2×Dic11—22no—
429C2×Dic11—42no—
430C2×Dic11—42no—
431C2×Dic11—48no—
432C2×Dic11AGL(1,ℤ/8)14yescomplemented
433C2×Dic11C22×D412yes—
434C2×Dic11C22×D412yes—
435C2×Dic11C22×D412yes—
436D44—22no—
437D44—22no—
438D44—22no—
439D44—22no—
440D44—48no—
441D44—42no—
442D44—42no—
443C4×D11—24no—
444C4×D11—22no—
445C4×D11—22no—
446C4×D11—48no—
447C8×C11—22no—
448C8×C11C22×D414yescomplemented
449C11⋊C8—22no—
450C11⋊C8—22no—
451C22×#41—111no—
452C22×#41C2×D1111yescharacteristic, complemented
453C23×D4—111no—
454C23×D4—221no—
455C23×D4C2×D1111yescharacteristic
456C2×AGL(1,ℤ/8)—28no—
457C2×AGL(1,ℤ/8)—118no—
458C2×AGL(1,ℤ/8)—228no—
459C2×AGL(1,ℤ/8)C2×D1118yescomplemented
460C22×SD16—111no—
461C22×SD16C2×D1111yescharacteristic
462C22×SD16C2×D1111yescharacteristic, complemented
463C22×D8—111no—
464C22×D8—111no—
465C22×D8—111no—
466C22×D8—111no—
467C22×D8C2×D1111yescharacteristic
468C22×D8C2×D1111yescharacteristic, complemented
469C22×M16—111no—
470C22×M16C2×D1111yescharacteristic, complemented
471#550—118no—
472#550—224no—
473D42—118no—
474D42—224no—
475C2×#127—111no—
476C2×#127—111no—
477C2×#127—221no—
478C2×#121—111no—
479C2×#121—111no—
480C2×#121—111no—
481C2×#121—111no—
482C2×#121—221no—
483C2×#121—221no—
484C2×#121—221no—
485C2×#120—221no—
486C2×#120—221no—
487C2×C4×Q8—111no—
488C2×C4×D4—111no—
489C2×C4×D4—111no—
490C2×C4×D4—221no—
491#493—118no—
492#469—118no—
493#469—118no—
494#460—118no—
495#459—118no—
496#449—118no—
497#449—118no—
498#447—118no—
499#447—118no—
500C4×SD16—118no—
501#436—118no—
502C2×#106—111no—
503C2×C4⋊C8—111no—
504C2×#103—111no—
505C2×#102—111no—
506C2×#102—111no—
507C2×#102—111no—
508C2×#102—111no—
509C2×#102—111no—
510C2×C22⋊C8—111no—
511C2×C22⋊C8—111no—
512C2×C4×C8—111no—
513C22×C11—22no—
514C22×C11—24no—
515C22×C11—22no—
516C22×C11—22no—
517C22×C11—48no—
518C22×C11—44no—
519C22×C11—42no—
520C22×C11—42no—
521C22×C11—42no—
522C22×C11—42no—
523C22×C11—42no—
524C22×C11—42no—
525C22×C11—42no—
526C22×C11—42no—
527C22×C11—816no—
528C22×C11—84no—
529C22×C11—84no—
530C22×C11D4212yes—
531C22×C11C2×AGL(1,ℤ/8)12yes—
532C22×C11#57612yes—
533C22×C11C23×D411yescharacteristic
534C2×D11—22no—
535C2×D11—22no—
536C2×D11—22no—
537C2×D11—44no—
538C2×D11—42no—
539C2×D11—42no—
540C2×D11—42no—
541C2×D11—42no—
542C2×D11—42no—
543C2×D11—42no—
544C2×D11—816no—
545C2×D11—84no—
546C2×D11—84no—
547C4×C11—22no—
548C4×C11—24no—
549C4×C11D4212yes—
550C4×C11C23×D411yescharacteristic
551C4×C11C2×H(5,𝔽2)11yescharacteristic
552Dic11—22no—
553Dic11—22no—
554Dic11—42no—
555Dic11—42no—
556Dic11C2×AGL(1,ℤ/8)14yescomplemented
557C25—21no—
558C25—221no—
559C2×#41—22no—
560C2×#41—24no—
561C2×#41—42no—
562C2×#41—114no—
563C2×#41—222no—
564C2×#41—224no—
565C2×#41—442no—
566C2×#41C22×D1114yescomplemented
567C22×Q8C22×D1111yescharacteristic
568C22×D4—24no—
569C22×D4—21no—
570C22×D4—21no—
571C22×D4—22no—
572C22×D4—42no—
573C22×D4—111no—
574C22×D4—114no—
575C22×D4—111no—
576C22×D4—111no—
577C22×D4—221no—
578C22×D4—222no—
579C22×D4—221no—
580C22×D4—221no—
581C22×D4—221no—
582C22×D4—221no—
583C22×D4—221no—
584C22×D4—228no—
585C22×D4—224no—
586C22×D4—221no—
587C22×D4—221no—
588C22×D4—221no—
589C22×D4—221no—
590C22×D4—442no—
591C22×D4—448no—
592C22×D4C22×D1111yescharacteristic
593C22×D4C22×D1111yescharacteristic
594C22×D4C22×D1114yes—
595C22×D4C22×D1111yescharacteristic
596C23×C4—21no—
597C23×C4—111no—
598C23×C4—221no—
599C23×C4—221no—
600C23×C4C22×D1111yescharacteristic
601AGL(1,ℤ/8)—232no—
602AGL(1,ℤ/8)—2232no—
603C2×SD16—24no—
604C2×SD16—114no—
605C2×SD16—224no—
606C2×SD16C22⋊D1118yescomplemented
607C2×SD16C22×D1114yes—
608C2×SD16C22×D1114yescomplemented
609C2×D8—24no—
610C2×D8—24no—
611C2×D8—114no—
612C2×D8—114no—
613C2×D8—114no—
614C2×D8—114no—
615C2×D8—224no—
616C2×D8—224no—
617C2×D8—442no—
618C2×D8—442no—
619C2×D8C22×D1114yes—
620C2×D8C22×D1114yescomplemented
621C2×M16—24no—
622C2×M16—114no—
623C2×M16—224no—
624C2×M16C22×D1114yescomplemented
625C22×C8—111no—
626C22×C8—111no—
627C22×C8C22×D1111yescharacteristic
628C22×C8C22×D1111yescharacteristic
629#127—114no—
630#127—114no—
631#127—222no—
632#127—222no—
633#127—228no—
634#121—114no—
635#121—114no—
636#121—114no—
637#121—114no—
638#121—228no—
639#121—228no—
640#121—228no—
641#121—222no—
642#121—222no—
643#121—222no—
644#121—222no—
645#120—228no—
646#120—228no—
647C4×Q8—114no—
648C4×Q8—222no—
649C4×D4—114no—
650C4×D4—114no—
651C4×D4—114no—
652C4×D4—222no—
653C4×D4—228no—
654C2×C4⋊C4—111no—
655C2×C4⋊C4—111no—
656C2×C4⋊C4—111no—
657C2×C4⋊C4—221no—
658C2×C22⋊C4—111no—
659C2×C22⋊C4—111no—
660C2×C22⋊C4—221no—
661C2×C22⋊C4—221no—
662C2×C22⋊C4—221no—
663C2×C22⋊C4—221no—
664C2×C22⋊C4—221no—
665C2×C42—111no—
666C2×C42—221no—
667#106—114no—
668C4⋊C8—114no—
669#103—114no—
670#102—114no—
671#102—114no—
672#102—114no—
673#102—114no—
674#102—114no—
675C22⋊C8—114no—
676C22⋊C8—114no—
677C4×C8—114no—
678C2×C11—44no—
679C2×C11—42no—
680C2×C11—82no—
681C2×C11—82no—
682C2×C11#327414yescomplemented
683C2×C11C2×D4211yescharacteristic
684C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
685C2×C11C2×#57611yescharacteristic
686D11—42no—
687D11—82no—
688D11—82no—
689C24—21no—
690C24—21no—
691C24—21no—
692C24—24no—
693C24—44no—
694C24—44no—
695C24—82no—
696C24—111no—
697C24—224no—
698C24—221no—
699C24—221no—
700C24—444no—
701C24—444no—
702C24—882no—
703C24D4×D1111yescharacteristic
704#41—28no—
705#41—44no—
706#41—48no—
707#41—228no—
708#41—444no—
709#41—448no—
710C2×Q8—21no—
711C2×Q8—22no—
712C2×Q8C2×C22⋊D1114yescomplemented
713C2×Q8C23×D1112yes—
714C2×D4—28no—
715C2×D4—24no—
716C2×D4—21no—
717C2×D4—24no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—22no—
721C2×D4—22no—
722C2×D4—22no—
723C2×D4—22no—
724C2×D4—22no—
725C2×D4—44no—
726C2×D4—48no—
727C2×D4—44no—
728C2×D4—44no—
729C2×D4—114no—
730C2×D4—112no—
731C2×D4—112no—
732C2×D4—224no—
733C2×D4—224no—
734C2×D4—224no—
735C2×D4—224no—
736C2×D4—224no—
737C2×D4—224no—
738C2×D4—224no—
739C2×D4—228no—
740C2×D4—224no—
741C2×D4—224no—
742C2×D4—224no—
743C2×D4—224no—
744C2×D4—221no—
745C2×D4—221no—
746C2×D4—222no—
747C2×D4—222no—
748C2×D4—222no—
749C2×D4—222no—
750C2×D4—444no—
751C2×D4—444no—
752C2×D4—444no—
753C2×D4—444no—
754C2×D4—448no—
755C2×D4—444no—
756C2×D4—4432no—
757C2×D4—444no—
758C2×D4—444no—
759C2×D4—882no—
760C2×D4—882no—
761C2×D4—882no—
762C2×D4—882no—
763C2×D4C2×C22⋊D1114yes—
764C2×D4C23×D1112yes—
765C2×D4C23×D1112yes—
766C2×D4C23×D1112yes—
767C22×C4—21no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—24no—
771C22×C4—44no—
772C22×C4—111no—
773C22×C4—111no—
774C22×C4—111no—
775C22×C4—112no—
776C22×C4—112no—
777C22×C4—224no—
778C22×C4—224no—
779C22×C4—222no—
780C22×C4—222no—
781C22×C4—221no—
782C22×C4—221no—
783C22×C4—444no—
784C22×C4—444no—
785C22×C4D4×D1112yes—
786C22×C4D4×D1111yescharacteristic
787C22×C4C23×D1112yes—
788C22×C4C23×D1111yescharacteristic
789SD16—28no—
790SD16—228no—
791SD16C2×C22⋊D11116yescomplemented
792D8—28no—
793D8—28no—
794D8—228no—
795D8—228no—
796D8—444no—
797D8—444no—
798M16—28no—
799M16—228no—
800C2×C8—22no—
801C2×C8—112no—
802C2×C8—112no—
803C2×C8—222no—
804C2×C8—222no—
805C2×C8C2×C22⋊D1114yescomplemented
806C2×C8C23×D1112yes—
807C2×C8C23×D1112yes—
808C4⋊C4—114no—
809C4⋊C4—112no—
810C4⋊C4—112no—
811C4⋊C4—224no—
812C4⋊C4—221no—
813C4⋊C4—221no—
814C22⋊C4—114no—
815C22⋊C4—114no—
816C22⋊C4—224no—
817C22⋊C4—224no—
818C22⋊C4—224no—
819C22⋊C4—224no—
820C22⋊C4—224no—
821C42—112no—
822C42—112no—
823C42—224no—
824C11C2×#327411yescharacteristic, complemented, Sylow
825C23—22no—
826C23—22no—
827C23—22no—
828C23—24no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—48no—
833C23—48no—
834C23—42no—
835C23—42no—
836C23—42no—
837C23—42no—
838C23—42no—
839C23—42no—
840C23—42no—
841C23—42no—
842C23—84no—
843C23—816no—
844C23—112no—
845C23—222no—
846C23—222no—
847C23—222no—
848C23—222no—
849C23—222no—
850C23—448no—
851C23—448no—
852C23—442no—
853C23—442no—
854C23—442no—
855C23—442no—
856C23—442no—
857C23—442no—
858C23—884no—
859C23—8816no—
860C23C2×D4×D1112yes—
861C23C2×D4×D1111yescharacteristic
862Q8—24no—
863Q8—22no—
864Q8C22×C22⋊D1114yescomplemented
865D4—24no—
866D4—22no—
867D4—22no—
868D4—22no—
869D4—22no—
870D4—22no—
871D4—48no—
872D4—48no—
873D4—42no—
874D4—42no—
875D4—228no—
876D4—222no—
877D4—222no—
878D4—222no—
879D4—222no—
880D4—448no—
881D4—448no—
882D4—448no—
883D4—448no—
884D4—448no—
885D4—448no—
886D4—442no—
887D4—442no—
888D4—884no—
889D4—884no—
890D4—884no—
891D4—884no—
892D4C22×C22⋊D1114yes—
893C2×C4—22no—
894C2×C4—24no—
895C2×C4—22no—
896C2×C4—24no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—48no—
900C2×C4—114no—
901C2×C4—112no—
902C2×C4—112no—
903C2×C4—112no—
904C2×C4—222no—
905C2×C4—222no—
906C2×C4—224no—
907C2×C4—222no—
908C2×C4—222no—
909C2×C4—222no—
910C2×C4—222no—
911C2×C4—448no—
912C2×C4—448no—
913C2×C4—442no—
914C2×C4—442no—
915C2×C4C2×D4×D1112yes—
916C2×C4C2×D4×D1111yescharacteristic
917C2×C4#6703712yes—
918C2×C4C22×C22⋊D1112yes—
919C2×C4C24×D1111yescharacteristic
920C8—22no—
921C8—222no—
922C8—222no—
923C8C22×C22⋊D1114yescomplemented
924C22—22no—
925C22—24no—
926C22—22no—
927C22—22no—
928C22—44no—
929C22—48no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—816no—
939C22—84no—
940C22—84no—
941C22—222no—
942C22—222no—
943C22—222no—
944C22—444no—
945C22—442no—
946C22—442no—
947C22—442no—
948C22—442no—
949C22—442no—
950C22—442no—
951C22—8816no—
952C22—884no—
953C22—884no—
954C22D11×AGL(1,ℤ/8)12yes—
955C22#1062330512yes—
956C22D4×C22⋊D1112yes—
957C22C22×D4×D1111yescharacteristic
958C4—22no—
959C4—24no—
960C4—114no—
961C4—222no—
962C4—222no—
963C4—442no—
964C4—442no—
965C4D4×C22⋊D1112yes—
966C4C2×#6703711yescharacteristic
967C4C23×C22⋊D1111yescharacteristic
968C2—42no—
969C2—44no—
970C2—82no—
971C2—82no—
972C2—442no—
973C2—882no—
974C2—882no—
975C2#1308023014yesdirect product factor
976C2C2×D4×C22⋊D1111yescharacteristic
977C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
978C2C2×#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×#3274
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×#66967C2semidirect
2. C2×#10623365C2semidirect
3. C2×D4×C22⋊D11C2semidirect
4. #13080230C2direct (N × H)
5. C2×#10622764C2semidirect
6. C2×#10622748C2semidirect
7. C2×#10622772C2semidirect
8. C2×#10622776C2semidirect
9. C2×#10622763C2semidirect
10. C2×#10622851C2semidirect
11. C2×#10622785C2semidirect
12. C2×#10622830C2semidirect
13. C2×#10622769C2semidirect
14. C2×SD16×Dic11C2semidirect
15. C2×#10622741C2semidirect
16. C22×C11×AGL(1,ℤ/8)C2semidirect
17. C22×C11×#41C22semidirect
20. C22×#4343C22semidirect
23. C2×C11×AGL(1,ℤ/8)C22semidirect
25. C22×C11×SD16C22semidirect
27. C22×C11×D8C22semidirect
28. C22×C11×M16C22semidirect
31. #10623365C22semidirect
32. C2×Q8×Dic11C22semidirect
33. C22×#4325C22semidirect
36. C2×#66993C22semidirect
39. D4×C22⋊D11C22semidirect
42. C2×#66991C22semidirect
46. C22×#4323C22semidirect
47. C22×#4323C22semidirect
50. C2×#66983C22semidirect
54. C2×#66967C22semidirect
55. C22×D88C22semidirect
56. C22×#4313C22semidirect
57. #10622851C22semidirect
58. C2×#66899C22semidirect
59. #10622830C22semidirect
61. C2×#66896C22semidirect
62. C2×#66896C22semidirect
63. C2×C22⋊(C11⋊C8)C22semidirect
64. #10622785C22semidirect
65. #10622776C22semidirect
66. SD16×Dic11C22semidirect
67. #10622772C22semidirect
68. #10622769C22semidirect
69. #10622764C22semidirect
70. #10622763C22semidirect
71. #10622748C22semidirect
72. #10622741C22semidirect
73. C2×#66885C22semidirect
74. C2×#66885C22semidirect
75. C2×(C2×D11)⋊C8C22semidirect
76. C2×#66881C22semidirect
77. C2×Dic11⋊C8C22semidirect
78. C2×C8×Dic11C22semidirect
84. C2×C11×#41C23semidirect
113. C2×#4343C23semidirect
125. C2×C11×SD16D4semidirect
127. C2×C11×SD16C23semidirect
131. C2×C11×D8C23semidirect
133. C2×C11×M16C23semidirect
142. Q8×Dic11C23semidirect
144. C2×#4325C23semidirect
149. #66993C23semidirect
155. #66991C23semidirect
163. C2×#4323C23semidirect
164. C2×#4323C23semidirect
169. #66983C23semidirect
186. C2×D88C23semidirect
188. C2×#4313C23semidirect
189. #66899C23semidirect
191. #66896C23semidirect
192. #66896C23semidirect
193. C22⋊(C11⋊C8)C23semidirect
194. #66885C23semidirect
195. #66885C23semidirect
196. (C2×D11)⋊C8C23semidirect
197. #66881C23semidirect
198. Dic11⋊C8C23semidirect
199. C8×Dic11C23semidirect
221. C2×Q8×C11C2×D4semidirect
302. C11×SD16C2×D4semidirect
307. C2×C8×C11C2×D4semidirect
337. C22×AGL(1,ℤ/8)D11semidirect
391. Q8×C11C22×D4semidirect
432. C2×Dic11AGL(1,ℤ/8)semidirect
448. C8×C11C22×D4semidirect
452. C22×#41C2×D11semidirect
459. C2×AGL(1,ℤ/8)C2×D11semidirect
462. C22×SD16C2×D11semidirect
468. C22×D8C2×D11semidirect
470. C22×M16C2×D11semidirect
556. Dic11C2×AGL(1,ℤ/8)semidirect
566. C2×#41C22×D11semidirect
606. C2×SD16C22⋊D11semidirect
608. C2×SD16C22×D11semidirect
620. C2×D8C22×D11semidirect
624. C2×M16C22×D11semidirect
682. C2×C11#3274semidirect
712. C2×Q8C2×C22⋊D11semidirect
791. SD16C2×C22⋊D11semidirect
805. C2×C8C2×C22⋊D11semidirect
824. C11C2×#3274semidirect
864. Q8C22×C22⋊D11semidirect
923. C8C22×C22⋊D11semidirect
975. C2#13080230direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669672
C2×#106233652
C2×D4×C22⋊D112
#130802302
C2×#106227642
C2×#106227482
C2×#106227722
C2×#106227762
C2×#106227632
C2×#106228512
C2×#106227852
C2×#106228302
C2×#106227692
C2×SD16×Dic112
C2×#106227412
C22×C11×AGL(1,ℤ/8)2
C2×#327411