Finite Group Databasebeta

← C2×#13080229 #15628884

Subgroups — C2×#13080229 #15628884

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
2C22×#67002C211yesmaximal, characteristic, complemented
3C2×#10623365C211yesmaximal, characteristic, complemented
4C2×#10623140C211yesmaximal, characteristic, complemented
5#13080229C2116yesmaximal, direct product factor
6C2×#10622764C211yesmaximal, characteristic, complemented
7C2×#10622395C211yesmaximal, characteristic, complemented
8C2×#10622652C211yesmaximal, characteristic, complemented
9C2×#10622776C211yesmaximal, characteristic, complemented
10C2×#10622399C211yesmaximal, characteristic, complemented
11C2×#10622424C211yesmaximal, characteristic, complemented
12C2×#10622345C211yesmaximal, characteristic, complemented
13C2×#10622769C211yesmaximal, characteristic, complemented
14C2×#10622401C211yesmaximal, characteristic, complemented
15C2×#10622342C211yesmaximal, characteristic, complemented
16C2×C11×#449C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic, complemented
18C22×#4343C2211yescharacteristic, complemented
19C22×D4×D11—21no—
20C22×D4×D11C2211yescharacteristic
21C23×D44C2211yescharacteristic
22C22×C11×SD16C2211yescharacteristic, complemented
23C22×C11×D8C2211yescharacteristic, complemented
24C2×C11×#121C2211yescharacteristic
25#10623365—24no—
26#10623365C2218yescomplemented
27C2×#67002—28no—
28C2×#67002C2218yescomplemented
29C2×Q8×Dic11C2211yescharacteristic, complemented
30C22×#4325C2211yescharacteristic
31C22×#4325C2211yescharacteristic, complemented
32C2×#66993—21no—
33C2×#66993C2211yescharacteristic
34C2×#66993C2211yescharacteristic, complemented
35C2×#66991—21no—
36C2×#66991C2211yescharacteristic, complemented
37C2×#66990—21no—
38C22×#4323C2211yescharacteristic
39C22×#4323C2211yescharacteristic, complemented
40C22×#4323C2211yescharacteristic, complemented
41C2×#66983—21no—
42C2×#66983C2211yescharacteristic, complemented
43C2×C4×C22⋊D11—21no—
44C2×C4×C22⋊D11C2211yescharacteristic
45C22×#4318C2211yescharacteristic, complemented
46C2×#66967—28no—
47C2×#66967C2218yescomplemented
48C22×D88C2211yescharacteristic
49C22×D88C2211yescharacteristic, complemented
50C22×#4313C2211yescharacteristic, complemented
51#10623140—24no—
52#10623140C2218yescomplemented
53C2×#66948C2211yescharacteristic
54C2×#66946C2211yescharacteristic
55C2×#66937—21no—
56C2×#66935—21no—
57C11×#449C2218yescomplemented
58C2×C11×#103C2211yescharacteristic, complemented
59C2×C11×#102C2211yescharacteristic, complemented
60C2×C11×C22⋊C8C2211yescharacteristic, complemented
61C2×#66896C2211yescharacteristic, complemented
62#10622776C2218yescomplemented
63#10622769C2218yescomplemented
64#10622764C2218yescomplemented
65C2×#66885C2211yescharacteristic
66C2×#66885C2211yescharacteristic, complemented
67C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
68C2×Dic11⋊C8C2211yescharacteristic, complemented
69C2×C8×Dic11C2211yescharacteristic, complemented
70#10622652C2218yescomplemented
71C2×#66873C2211yescharacteristic, complemented
72C2×#66872C2211yescharacteristic, complemented
73#10622424C2218yescomplemented
74#10622401C2218yescomplemented
75#10622399C2218yescomplemented
76#10622395C2218yescomplemented
77#10622345C2218yescomplemented
78#10622342C2218yescomplemented
79C24×D11—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—21no—
87C22×D4×C11—21no—
88C22×D4×C11C2311yescharacteristic
89C22×D4×C11C2311yescharacteristic
90C23×C4×C11—21no—
91C23×C4×C11C2311yescharacteristic
92C22×C22⋊D11—21no—
93C22×C22⋊D11—21no—
94C22×C22⋊D11—21no—
95C22×C22⋊D11—21no—
96C22×C22⋊D11—21no—
97C22×C22⋊D11—21no—
98C22×C22⋊D11—21no—
99C22×C22⋊D11D411yescharacteristic
100C2×#4343—22no—
101C2×#4343—24no—
102C2×#4343—42no—
103C2×#4343C2314yescomplemented
104C2×D4×D11—28no—
105C2×D4×D11—24no—
106C2×D4×D11—22no—
107C2×D4×D11—42no—
108C2×D4×D11—48no—
109C2×D4×D11C2314yes—
110C22×D44—24no—
111C22×D44—21no—
112C22×D44—21no—
113C22×D44—21no—
114C22×D44—22no—
115C22×D44—42no—
116C22×D44C2311yescharacteristic
117C22×D44C2311yescharacteristic
118C22×D44C2314yes—
119C22×D44C2311yescharacteristic
120C22×C4×D11—21no—
121C22×C4×D11—21no—
122C22×C4×D11C2311yescharacteristic
123C2×C11×SD16—24no—
124C2×C11×SD16C2314yescomplemented
125C2×C11×D8—42no—
126C2×C11×D8C2314yescomplemented
127C22×C8×C11C2311yescharacteristic
128C22×C8×C11C2311yescharacteristic
129C11×#121—22no—
130C11×#121C2314yes—
131C2×C11×C4⋊C4C2311yescharacteristic
132C2×C11×C22⋊C4—21no—
133C2×C22⋊Dic11—21no—
134C2×C22⋊Dic11D411yescharacteristic
135#67002—232no—
136Q8×Dic11—22no—
137Q8×Dic11C2314yescomplemented
138C2×#4325—24no—
139C2×#4325D418yescomplemented
140C2×#4325C2314yes—
141C2×#4325C2314yescomplemented
142#66993—28no—
143#66993—22no—
144#66993—22no—
145#66993C2314yes—
146#66993C2314yescomplemented
147#66991—22no—
148#66991—28no—
149#66991C2314yescomplemented
150#66990—28no—
151C2×#4323—24no—
152C2×#4323—24no—
153C2×#4323—24no—
154C2×#4323C2314yes—
155C2×#4323C2314yescomplemented
156C2×#4323C2314yescomplemented
157#66983—22no—
158#66983—28no—
159#66983C2314yescomplemented
160C4×C22⋊D11—28no—
161C4×C22⋊D11D414yes—
162C4×C22⋊D11C2314yes—
163C2×(C2×D11)⋊C4—21no—
164C2×(C2×D11)⋊C4—21no—
165C2×(C2×D11)⋊C4—21no—
166C2×(C2×D11)⋊C4D411yescharacteristic
167C2×C4⋊Dic11—21no—
168C2×C4⋊Dic11C2311yescharacteristic
169C2×Dic11⋊C4D411yescharacteristic
170C2×C4×Dic11—21no—
171C2×C4×Dic11C2311yescharacteristic
172C2×#4318—24no—
173C2×#4318C2314yescomplemented
174C22×C11⋊C8C2311yescharacteristic
175C22×C11⋊C8C2311yescharacteristic
176#66967—232no—
177C2×D88—24no—
178C2×D88—42no—
179C2×D88C2314yes—
180C2×D88C2314yescomplemented
181C2×#4313—24no—
182C2×#4313C2314yescomplemented
183#66948—22no—
184#66948C2314yes—
185#66946—22no—
186#66946C2314yes—
187#66937—28no—
188#66935—28no—
189C11×#103C2314yescomplemented
190C11×#102C2314yescomplemented
191C11×C22⋊C8C2314yescomplemented
192#66896C2314yescomplemented
193#66885C2314yes—
194#66885C2314yescomplemented
195(C2×D11)⋊C8C2314yescomplemented
196Dic11⋊C8C2314yescomplemented
197C8×Dic11C2314yescomplemented
198#66873C2314yescomplemented
199#66872C2314yescomplemented
200C2×#3274—111nomaximal, Sylow
201C24×C11—21no—
202C24×C11—21no—
203C24×C11C2×D411yescharacteristic
204C23×D11—21no—
205C23×D11—21no—
206C23×D11—21no—
207C23×D11—24no—
208C23×D11—24no—
209C23×D11—44no—
210C23×D11—44no—
211C23×D11—44no—
212C23×D11—44no—
213C23×D11—82no—
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—24no—
224C2×D4×C11—24no—
225C2×D4×C11—22no—
226C2×D4×C11—22no—
227C2×D4×C11—21no—
228C2×D4×C11—21no—
229C2×D4×C11—22no—
230C2×D4×C11—22no—
231C2×D4×C11—44no—
232C2×D4×C11—44no—
233C2×D4×C11C2412yes—
234C2×D4×C11C2412yes—
235C22×C4×C11—21no—
236C22×C4×C11—22no—
237C22×C4×C11—22no—
238C22×C4×C11—21no—
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—24no—
252C2×C22⋊D11—24no—
253C2×C22⋊D11—44no—
254C2×C22⋊D11—44no—
255C2×C22⋊D11—44no—
256C2×C22⋊D11—82no—
257C2×C22⋊D11—82no—
258C2×C22⋊D11—82no—
259C2×C22⋊D11—82no—
260C2×C22⋊D11C2×D414yes—
261C22×Dic11—21no—
262C22×Dic11C2×D411yescharacteristic
263C22×Dic11C2×D411yescharacteristic
264C22×Dic11C2×D411yescharacteristic
265#4343—28no—
266#4343—44no—
267#4343—48no—
268D4×D11—28no—
269D4×D11—44no—
270D4×D11—48no—
271D4×D11—432no—
272C2×D44—24no—
273C2×D44—24no—
274C2×D44—28no—
275C2×D44—21no—
276C2×D44—24no—
277C2×D44—21no—
278C2×D44—21no—
279C2×D44—22no—
280C2×D44—22no—
281C2×D44—22no—
282C2×D44—22no—
283C2×D44—22no—
284C2×D44—44no—
285C2×D44—44no—
286C2×D44—44no—
287C2×D44—48no—
288C2×D44—44no—
289C2×D44C2×D414yes—
290C2×D44C2412yes—
291C2×D44C2412yes—
292C2×D44C2412yes—
293C2×C4×D11—24no—
294C2×C4×D11—24no—
295C2×C4×D11—22no—
296C2×C4×D11—22no—
297C2×C4×D11—44no—
298C2×C4×D11—44no—
299C2×C4×D11C2×D412yes—
300C2×C4×D11C2412yes—
301C11×SD16—28no—
302C11×D8—44no—
303C2×C8×C11—22no—
304C2×C8×C11—22no—
305C2×C8×C11C2412yes—
306C2×C8×C11C2412yes—
307C11×C4⋊C4—21no—
308C11×C4⋊C4C2412yes—
309C11×C22⋊C4—24no—
310C22⋊Dic11—24no—
311C22⋊Dic11C2×D414yes—
312#4325—28no—
313#4325C2×D4116yescomplemented
314#4323—28no—
315#4323—28no—
316#4323—28no—
317(C2×D11)⋊C4—24no—
318(C2×D11)⋊C4—24no—
319(C2×D11)⋊C4—24no—
320(C2×D11)⋊C4C2×D414yes—
321C4⋊Dic11—24no—
322C4⋊Dic11—21no—
323C4⋊Dic11C2412yes—
324Dic11⋊C4C2×D414yes—
325C4×Dic11—24no—
326C4×Dic11C2×D412yes—
327C4×Dic11C2412yes—
328#4318—28no—
329C2×C11⋊C8—22no—
330C2×C11⋊C8C2×D414yescomplemented
331C2×C11⋊C8C2412yes—
332C2×C11⋊C8C2412yes—
333D88—28no—
334D88—44no—
335#4313—28no—
336C22×AGL(1,ℤ/8)—111no—
337C22×AGL(1,ℤ/8)—111no—
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×#449D1111yescharacteristic, complemented
348C2×#447—111no—
349C2×#447—111no—
350C2×C4×SD16—111no—
351C2×#436—111no—
352C23×C11—22no—
353C23×C11—22no—
354C23×C11—22no—
355C23×C11—22no—
356C23×C11—22no—
357C23×C11—42no—
358C23×C11—42no—
359C23×C11—42no—
360C23×C11—42no—
361C23×C11—42no—
362C23×C11—42no—
363C23×C11C22×D412yes—
364C23×C11C22×D411yescharacteristic
365C22×D11—22no—
366C22×D11—24no—
367C22×D11—22no—
368C22×D11—22no—
369C22×D11—22no—
370C22×D11—22no—
371C22×D11—22no—
372C22×D11—48no—
373C22×D11—48no—
374C22×D11—48no—
375C22×D11—42no—
376C22×D11—42no—
377C22×D11—48no—
378C22×D11—42no—
379C22×D11—42no—
380C22×D11—42no—
381C22×D11—42no—
382C22×D11—42no—
383C22×D11—42no—
384C22×D11—84no—
385C22×D11—84no—
386C22×D11—816no—
387C22×D11—816no—
388C22×D11C22×D412yes—
389Q8×C11—24no—
390Q8×C11—22no—
391Q8×C11C22×D414yescomplemented
392D4×C11—22no—
393D4×C11—22no—
394D4×C11—22no—
395D4×C11—22no—
396D4×C11—48no—
397D4×C11—48no—
398D4×C11—42no—
399D4×C11—42no—
400C2×C4×C11—24no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—24no—
404C2×C4×C11—22no—
405C2×C4×C11—22no—
406C2×C4×C11—22no—
407C2×C4×C11—48no—
408C2×C4×C11—42no—
409C2×C4×C11C22×D412yes—
410C2×C4×C11C22×D411yescharacteristic
411C2×C4×C11C22×D412yes—
412C2×C4×C11H(5,𝔽2)12yes—
413C2×C4×C11C2511yescharacteristic
414C22⋊D11—28no—
415C22⋊D11—48no—
416C22⋊D11—48no—
417C22⋊D11—48no—
418C22⋊D11—84no—
419C22⋊D11—84no—
420C22⋊D11—84no—
421C22⋊D11—84no—
422C2×Dic11—22no—
423C2×Dic11—22no—
424C2×Dic11—22no—
425C2×Dic11—42no—
426C2×Dic11AGL(1,ℤ/8)14yescomplemented
427C2×Dic11C22×D412yes—
428C2×Dic11C22×D412yes—
429C2×Dic11C22×D412yes—
430D44—24no—
431D44—22no—
432D44—22no—
433D44—22no—
434D44—22no—
435D44—22no—
436D44—48no—
437D44—48no—
438D44—48no—
439D44—42no—
440D44—42no—
441D44C22×D414yes—
442C4×D11—24no—
443C4×D11—22no—
444C4×D11—22no—
445C4×D11—48no—
446C4×D11—48no—
447C8×C11—22no—
448C8×C11—22no—
449C11⋊C8—22no—
450C11⋊C8C22×D414yescomplemented
451C22×#41—111no—
452C22×#41C2×D1111yescharacteristic, complemented
453C23×D4—111no—
454C23×D4—111no—
455C23×D4—221no—
456C2×AGL(1,ℤ/8)—118no—
457C2×AGL(1,ℤ/8)—118no—
458C2×AGL(1,ℤ/8)—228no—
459C2×AGL(1,ℤ/8)—228no—
460C22×SD16—111no—
461C22×SD16—111no—
462C22×SD16C2×D1111yescharacteristic, complemented
463C22×D8—111no—
464C22×D8—111no—
465C22×D8—111no—
466C22×D8—111no—
467C22×D8—111no—
468C22×D8C2×D1111yescharacteristic, complemented
469C22×M16—111no—
470C22×M16—111no—
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—221no—
482C2×#121—221no—
483C2×#121—221no—
484C2×#121C2×D1111yescharacteristic
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#449C2×D1118yescomplemented
498#447—118no—
499#447—118no—
500C4×SD16—118no—
501#436—118no—
502C2×#106—111no—
503C2×C4⋊C8—111no—
504C2×#103C2×D1111yescharacteristic, complemented
505C2×#102—111no—
506C2×#102—111no—
507C2×#102—111no—
508C2×#102—111no—
509C2×#102C2×D1111yescharacteristic, complemented
510C2×C22⋊C8—111no—
511C2×C22⋊C8C2×D1111yescharacteristic, complemented
512C2×C4×C8—111no—
513C22×C11—22no—
514C22×C11—22no—
515C22×C11—22no—
516C22×C11—44no—
517C22×C11—42no—
518C22×C11—42no—
519C22×C11—42no—
520C22×C11—42no—
521C22×C11—42no—
522C22×C11—42no—
523C22×C11—84no—
524C22×C11—84no—
525C22×C11D4212yes—
526C22×C11C2×AGL(1,ℤ/8)12yes—
527C22×C11#57612yes—
528C22×C11C23×D411yescharacteristic
529C2×D11—24no—
530C2×D11—22no—
531C2×D11—22no—
532C2×D11—22no—
533C2×D11—44no—
534C2×D11—48no—
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—42no—
538C2×D11—42no—
539C2×D11—42no—
540C2×D11—42no—
541C2×D11—42no—
542C2×D11—42no—
543C2×D11—816no—
544C2×D11—816no—
545C2×D11—84no—
546C2×D11—84no—
547C4×C11—22no—
548C4×C11—24no—
549C4×C11—42no—
550C4×C11D4212yes—
551C4×C11C23×D411yescharacteristic
552C4×C11C2×H(5,𝔽2)11yescharacteristic
553Dic11—22no—
554Dic11—22no—
555Dic11—42no—
556Dic11C2×AGL(1,ℤ/8)14yescomplemented
557C25—221no—
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—21no—
569C22×D4—21no—
570C22×D4—111no—
571C22×D4—114no—
572C22×D4—111no—
573C22×D4—111no—
574C22×D4—111no—
575C22×D4—114no—
576C22×D4—224no—
577C22×D4—221no—
578C22×D4—221no—
579C22×D4—222no—
580C22×D4—221no—
581C22×D4—221no—
582C22×D4—221no—
583C22×D4—221no—
584C22×D4—221no—
585C22×D4—224no—
586C22×D4—228no—
587C22×D4—221no—
588C22×D4—221no—
589C22×D4—221no—
590C22×D4—222no—
591C22×D4—442no—
592C22×D4—442no—
593C22×D4—448no—
594C22×D4C22×D1111yescharacteristic
595C22×D4C22×D1111yescharacteristic
596C23×C4—21no—
597C23×C4—111no—
598C23×C4—221no—
599C23×C4—221no—
600C23×C4C22×D1111yescharacteristic
601AGL(1,ℤ/8)—2232no—
602AGL(1,ℤ/8)—2232no—
603C2×SD16—24no—
604C2×SD16—118no—
605C2×SD16—114no—
606C2×SD16—114no—
607C2×SD16—224no—
608C2×SD16C22×D1114yescomplemented
609C2×D8—42no—
610C2×D8—114no—
611C2×D8—114no—
612C2×D8—114no—
613C2×D8—114no—
614C2×D8—114no—
615C2×D8—224no—
616C2×D8—224no—
617C2×D8—224no—
618C2×D8—224no—
619C2×D8—442no—
620C2×D8C22×D1114yescomplemented
621C2×M16—114no—
622C2×M16—114no—
623C2×M16—224no—
624C2×M16—224no—
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—22no—
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#121C22×D1114yes—
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—221no—
657C2×C4⋊C4C22×D1111yescharacteristic
658C2×C22⋊C4—21no—
659C2×C22⋊C4—111no—
660C2×C22⋊C4—111no—
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#103C22×D1114yescomplemented
670#102—114no—
671#102—114no—
672#102—114no—
673#102—114no—
674#102C22×D1114yescomplemented
675C22⋊C8—114no—
676C22⋊C8C22×D1114yescomplemented
677C4×C8—114no—
678C2×C11—42no—
679C2×C11—82no—
680C2×C11—82no—
681C2×C11#327414yescomplemented
682C2×C11C2×D4211yescharacteristic
683C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
684C2×C11C2×#57611yescharacteristic
685D11—42no—
686D11—44no—
687D11—82no—
688D11—82no—
689C24—21no—
690C24—21no—
691C24—111no—
692C24—224no—
693C24—221no—
694C24—221no—
695C24—221no—
696C24—224no—
697C24—444no—
698C24—444no—
699C24—444no—
700C24—444no—
701C24—882no—
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×Q8D4×D1114yescomplemented
713C2×Q8C23×D1112yes—
714C2×D4—24no—
715C2×D4—24no—
716C2×D4—22no—
717C2×D4—22no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—22no—
721C2×D4—22no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—114no—
725C2×D4—114no—
726C2×D4—112no—
727C2×D4—112no—
728C2×D4—112no—
729C2×D4—228no—
730C2×D4—224no—
731C2×D4—224no—
732C2×D4—224no—
733C2×D4—224no—
734C2×D4—224no—
735C2×D4—224no—
736C2×D4—224no—
737C2×D4—224no—
738C2×D4—228no—
739C2×D4—224no—
740C2×D4—224no—
741C2×D4—221no—
742C2×D4—222no—
743C2×D4—222no—
744C2×D4—224no—
745C2×D4—221no—
746C2×D4—221no—
747C2×D4—222no—
748C2×D4—222no—
749C2×D4—222no—
750C2×D4—444no—
751C2×D4—448no—
752C2×D4—444no—
753C2×D4—444no—
754C2×D4—444no—
755C2×D4—444no—
756C2×D4—444no—
757C2×D4—444no—
758C2×D4—448no—
759C2×D4—444no—
760C2×D4—4432no—
761C2×D4—882no—
762C2×D4—882no—
763C2×D4—882no—
764C2×D4—882no—
765C2×D4C23×D1112yes—
766C2×D4C23×D1112yes—
767C22×C4—21no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—21no—
771C22×C4—24no—
772C22×C4—44no—
773C22×C4—111no—
774C22×C4—111no—
775C22×C4—111no—
776C22×C4—112no—
777C22×C4—112no—
778C22×C4—224no—
779C22×C4—224no—
780C22×C4—222no—
781C22×C4—222no—
782C22×C4—221no—
783C22×C4—444no—
784C22×C4—444no—
785C22×C4D4×D1112yes—
786C22×C4D4×D1111yescharacteristic
787C22×C4C23×D1112yes—
788C22×C4C23×D1111yescharacteristic
789SD16—28no—
790SD16—1116no—
791SD16—228no—
792D8—44no—
793D8—228no—
794D8—228no—
795D8—228no—
796D8—228no—
797D8—444no—
798M16—228no—
799M16—228no—
800C2×C8—22no—
801C2×C8—22no—
802C2×C8—114no—
803C2×C8—112no—
804C2×C8—112no—
805C2×C8—222no—
806C2×C8C23×D1112yes—
807C2×C8C23×D1112yes—
808C4⋊C4—21no—
809C4⋊C4—114no—
810C4⋊C4—112no—
811C4⋊C4—224no—
812C4⋊C4—221no—
813C4⋊C4C23×D1112yes—
814C22⋊C4—24no—
815C22⋊C4—114no—
816C22⋊C4—114no—
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—22no—
829C23—22no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—42no—
834C23—42no—
835C23—42no—
836C23—112no—
837C23—222no—
838C23—222no—
839C23—222no—
840C23—224no—
841C23—222no—
842C23—222no—
843C23—222no—
844C23—448no—
845C23—448no—
846C23—448no—
847C23—448no—
848C23—442no—
849C23—442no—
850C23—442no—
851C23—442no—
852C23—442no—
853C23—442no—
854C23—442no—
855C23—442no—
856C23—884no—
857C23—884no—
858C23—8816no—
859C23—8816no—
860C23C2×D4×D1112yes—
861C23C2×D4×D1111yescharacteristic
862Q8—24no—
863Q8—22no—
864Q8C2×D4×D1114yescomplemented
865D4—22no—
866D4—22no—
867D4—22no—
868D4—22no—
869D4—48no—
870D4—48no—
871D4—42no—
872D4—42no—
873D4—114no—
874D4—228no—
875D4—224no—
876D4—222no—
877D4—222no—
878D4—222no—
879D4—222no—
880D4—222no—
881D4—448no—
882D4—448no—
883D4—448no—
884D4—448no—
885D4—448no—
886D4—448no—
887D4—442no—
888D4—442no—
889D4—884no—
890D4—884no—
891D4—884no—
892D4—884no—
893C2×C4—22no—
894C2×C4—24no—
895C2×C4—22no—
896C2×C4—24no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—48no—
901C2×C4—42no—
902C2×C4—114no—
903C2×C4—112no—
904C2×C4—112no—
905C2×C4—112no—
906C2×C4—222no—
907C2×C4—222no—
908C2×C4—224no—
909C2×C4—222no—
910C2×C4—222no—
911C2×C4—222no—
912C2×C4—448no—
913C2×C4—448no—
914C2×C4—442no—
915C2×C4C2×D4×D1112yes—
916C2×C4C2×D4×D1111yescharacteristic
917C2×C4C2×D4×D1112yes—
918C2×C4#6703712yes—
919C2×C4C24×D1111yescharacteristic
920C8—22no—
921C8—22no—
922C8—114no—
923C8—222no—
924C22—22no—
925C22—22no—
926C22—22no—
927C22—44no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—84no—
935C22—84no—
936C22—222no—
937C22—224no—
938C22—222no—
939C22—222no—
940C22—444no—
941C22—448no—
942C22—442no—
943C22—442no—
944C22—442no—
945C22—442no—
946C22—442no—
947C22—442no—
948C22—442no—
949C22—442no—
950C22—8816no—
951C22—8816no—
952C22—884no—
953C22—884no—
954C22#1062312112yes—
955C22#1062330012yes—
956C22D11×AGL(1,ℤ/8)12yes—
957C22C22×D4×D1111yescharacteristic
958C4—22no—
959C4—24no—
960C4—42no—
961C4—114no—
962C4—222no—
963C4—222no—
964C4—442no—
965C4#1062312112yes—
966C4C22×D4×D1111yescharacteristic
967C4C2×#6703711yescharacteristic
968C2—42no—
969C2—82no—
970C2—82no—
971C2—442no—
972C2—444no—
973C2—882no—
974C2—882no—
975C2#1308022914yesdirect product factor
976C2C2×#1062312111yescharacteristic
977C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
978C2C2×#1062330011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#449C2
socleC23×C11C22×D4
hypercenterC2×#449D11
hypocenterC11C2×#3274
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×#66967C2semidirect
2. C22×#67002C2semidirect
3. C2×#10623365C2semidirect
4. C2×#10623140C2semidirect
5. #13080229C2direct (N × H)
6. C2×#10622764C2semidirect
7. C2×#10622395C2semidirect
8. C2×#10622652C2semidirect
9. C2×#10622776C2semidirect
10. C2×#10622399C2semidirect
11. C2×#10622424C2semidirect
12. C2×#10622345C2semidirect
13. C2×#10622769C2semidirect
14. C2×#10622401C2semidirect
15. C2×#10622342C2semidirect
16. C2×C11×#449C2semidirect
17. C22×C11×#41C22semidirect
18. C22×#4343C22semidirect
22. C22×C11×SD16C22semidirect
23. C22×C11×D8C22semidirect
26. #10623365C22semidirect
28. C2×#67002C22semidirect
29. C2×Q8×Dic11C22semidirect
31. C22×#4325C22semidirect
34. C2×#66993C22semidirect
36. C2×#66991C22semidirect
39. C22×#4323C22semidirect
40. C22×#4323C22semidirect
42. C2×#66983C22semidirect
45. C22×#4318C22semidirect
47. C2×#66967C22semidirect
49. C22×D88C22semidirect
50. C22×#4313C22semidirect
52. #10623140C22semidirect
57. C11×#449C22semidirect
58. C2×C11×#103C22semidirect
59. C2×C11×#102C22semidirect
60. C2×C11×C22⋊C8C22semidirect
61. C2×#66896C22semidirect
62. #10622776C22semidirect
63. #10622769C22semidirect
64. #10622764C22semidirect
66. C2×#66885C22semidirect
67. C2×(C2×D11)⋊C8C22semidirect
68. C2×Dic11⋊C8C22semidirect
69. C2×C8×Dic11C22semidirect
70. #10622652C22semidirect
71. C2×#66873C22semidirect
72. C2×#66872C22semidirect
73. #10622424C22semidirect
74. #10622401C22semidirect
75. #10622399C22semidirect
76. #10622395C22semidirect
77. #10622345C22semidirect
78. #10622342C22semidirect
84. C2×C11×#41C23semidirect
103. C2×#4343C23semidirect
124. C2×C11×SD16C23semidirect
126. C2×C11×D8C23semidirect
137. Q8×Dic11C23semidirect
139. C2×#4325D4semidirect
141. C2×#4325C23semidirect
146. #66993C23semidirect
149. #66991C23semidirect
155. C2×#4323C23semidirect
156. C2×#4323C23semidirect
159. #66983C23semidirect
173. C2×#4318C23semidirect
180. C2×D88C23semidirect
182. C2×#4313C23semidirect
189. C11×#103C23semidirect
190. C11×#102C23semidirect
191. C11×C22⋊C8C23semidirect
192. #66896C23semidirect
194. #66885C23semidirect
195. (C2×D11)⋊C8C23semidirect
196. Dic11⋊C8C23semidirect
197. C8×Dic11C23semidirect
198. #66873C23semidirect
199. #66872C23semidirect
221. C2×Q8×C11C2×D4semidirect
313. #4325C2×D4semidirect
330. C2×C11⋊C8C2×D4semidirect
347. C2×#449D11semidirect
391. Q8×C11C22×D4semidirect
426. C2×Dic11AGL(1,ℤ/8)semidirect
450. C11⋊C8C22×D4semidirect
452. C22×#41C2×D11semidirect
462. C22×SD16C2×D11semidirect
468. C22×D8C2×D11semidirect
497. #449C2×D11semidirect
504. C2×#103C2×D11semidirect
509. C2×#102C2×D11semidirect
511. C2×C22⋊C8C2×D11semidirect
556. Dic11C2×AGL(1,ℤ/8)semidirect
566. C2×#41C22×D11semidirect
608. C2×SD16C22×D11semidirect
620. C2×D8C22×D11semidirect
669. #103C22×D11semidirect
674. #102C22×D11semidirect
676. C22⋊C8C22×D11semidirect
681. C2×C11#3274semidirect
712. C2×Q8D4×D11semidirect
824. C11C2×#3274semidirect
864. Q8C2×D4×D11semidirect
975. C2#13080229direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669672
C22×#670022
C2×#106233652
C2×#106231402
#130802292
C2×#106227642
C2×#106223952
C2×#106226522
C2×#106227762
C2×#106223992
C2×#106224242
C2×#106223452
C2×#106227692
C2×#106224012
C2×#106223422
C2×C11×#4492
C2×#327411