Finite Group Databasebeta

← C2×#13080234 #15628889

Subgroups — C2×#13080234 #15628889

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×#66985C211yesmaximal, characteristic, complemented
2C22×#66964C211yesmaximal, characteristic, complemented
3C2×#10623130C211yesmaximal, characteristic, complemented
4C2×D4×C22⋊D11C211yesmaximal, characteristic, complemented
5#13080234C2116yesmaximal, direct product factor
6C2×#10622764C211yesmaximal, characteristic, complemented
7C2×#10622395C211yesmaximal, characteristic, complemented
8C2×#10622652C211yesmaximal, characteristic, complemented
9C2×#10622375C211yesmaximal, characteristic, complemented
10C2×#10622763C211yesmaximal, characteristic, complemented
11C2×#10622347C211yesmaximal, characteristic, complemented
12C2×#10622771C211yesmaximal, characteristic, complemented
13C2×#10622386C211yesmaximal, characteristic, complemented
14C2×#10622371C211yesmaximal, characteristic, complemented
15C2×#10622342C211yesmaximal, characteristic, complemented
16C2×C11×#447C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×C22⋊D11—21no—
19C22×#4341C2211yescharacteristic, complemented
20C22×D4×D11C2211yescharacteristic
21C22×#4339C2211yescharacteristic, complemented
22C22×C11×D8C2211yescharacteristic
23C22×C11×D8C2211yescharacteristic, complemented
24C2×C11×#121C2211yescharacteristic, complemented
25C2×#67006—21no—
26C2×#66993—21no—
27C2×#66993C2211yescharacteristic
28C2×#66993C2211yescharacteristic, complemented
29C2×#66992—21no—
30C2×#66992—21no—
31D4×C22⋊D11—24no—
32D4×C22⋊D11C2218yescomplemented
33C2×#66991C2211yescharacteristic
34C2×#66990—21no—
35C2×D4×Dic11C2211yescharacteristic
36C22×#4324C2211yescharacteristic
37C22×#4324C2211yescharacteristic, complemented
38C2×#66985—28no—
39C2×#66985C2218yescomplemented
40C22×#4323C2211yescharacteristic
41C22×#4323C2211yescharacteristic, complemented
42C22×#4323C2211yescharacteristic, complemented
43C2×#66983C2211yescharacteristic
44C2×C4×C22⋊D11C2211yescharacteristic
45C22×#4318C2211yescharacteristic, complemented
46C2×#66964—28no—
47C2×#66964C2218yescomplemented
48C22×D88C2211yescharacteristic, complemented
49C22×#4314C2211yescharacteristic, complemented
50C22×#4313C2211yescharacteristic, complemented
51#10623130—24no—
52#10623130C2218yescomplemented
53C2×#66948C2211yescharacteristic, complemented
54C2×#66940C2211yescharacteristic, complemented
55C2×#66937—21no—
56C2×(C22⋊D11)⋊C4—21no—
57C11×#447C2218yescomplemented
58C2×C11×#102C2211yescharacteristic
59C2×C11×#102C2211yescharacteristic, complemented
60C2×C11×C22⋊C8C2211yescharacteristic, complemented
61C2×#66896C2211yescharacteristic, complemented
62#10622771C2218yescomplemented
63#10622764C2218yescomplemented
64#10622763C2218yescomplemented
65C2×#66885C2211yescharacteristic, complemented
66C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
67C2×#66880C2211yescharacteristic, complemented
68C2×Dic11⋊C8C2211yescharacteristic, complemented
69C2×C8×Dic11C2211yescharacteristic, complemented
70#10622652C2218yescomplemented
71C2×#66873C2211yescharacteristic, complemented
72C2×#66872C2211yescharacteristic, complemented
73#10622395C2218yescomplemented
74#10622386C2218yescomplemented
75#10622375C2218yescomplemented
76#10622371C2218yescomplemented
77#10622347C2218yescomplemented
78#10622342C2218yescomplemented
79C25×C11—21no—
80C24×D11—21no—
81C22×D4×C11—24no—
82C22×D4×C11—21no—
83C22×D4×C11—21no—
84C22×D4×C11—22no—
85C22×D4×C11—42no—
86C22×D4×C11C2311yescharacteristic
87C22×D4×C11C2311yescharacteristic
88C22×D4×C11C2314yes—
89C22×D4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C22×C22⋊D11—21no—
92C22×C22⋊D11—21no—
93C22×C22⋊D11—21no—
94C22×C22⋊D11—21no—
95C22×C22⋊D11—28no—
96C22×C22⋊D11—21no—
97C22×C22⋊D11—21no—
98C22×C22⋊D11—21no—
99C22×C22⋊D11—21no—
100C22×C22⋊D11—21no—
101C22×C22⋊D11—48no—
102C22×C22⋊D11D411yescharacteristic
103C23×Dic11—21no—
104C23×Dic11—21no—
105C2×#4341—22no—
106C2×#4341—24no—
107C2×#4341—42no—
108C2×#4341C2314yescomplemented
109C2×D4×D11—24no—
110C2×D4×D11—22no—
111C2×D4×D11—42no—
112C2×D4×D11C2314yes—
113C2×#4339—22no—
114C2×#4339—24no—
115C2×#4339—42no—
116C2×#4339C2314yescomplemented
117C22×D44—21no—
118C22×D44C2311yescharacteristic
119C22×D44C2311yescharacteristic
120C22×C4×D11—21no—
121C22×C4×D11C2311yescharacteristic
122C22×Dic22C2311yescharacteristic
123C2×C11×D8—24no—
124C2×C11×D8—42no—
125C2×C11×D8C2314yes—
126C2×C11×D8C2314yescomplemented
127C22×C8×C11C2311yescharacteristic
128C22×C8×C11C2311yescharacteristic
129C11×#121—22no—
130C11×#121C2314yescomplemented
131C2×C11×C4⋊C4C2311yescharacteristic
132C2×C11×C22⋊C4—21no—
133#67006—28no—
134C2×C22⋊Dic11—21no—
135C2×C22⋊Dic11—21no—
136C2×C22⋊Dic11D411yescharacteristic
137#66993—28no—
138#66993—22no—
139#66993—22no—
140#66993C2314yes—
141#66993C2314yescomplemented
142#66992—28no—
143#66992—28no—
144#66991—22no—
145#66991C2314yes—
146#66990—28no—
147D4×Dic11—22no—
148D4×Dic11C2314yes—
149C2×#4324—24no—
150C2×#4324D418yescomplemented
151C2×#4324C2314yes—
152C2×#4324C2314yescomplemented
153#66985—232no—
154C2×#4323—24no—
155C2×#4323—24no—
156C2×#4323—24no—
157C2×#4323C2314yes—
158C2×#4323C2314yescomplemented
159C2×#4323C2314yescomplemented
160#66983—22no—
161#66983C2314yes—
162C4×C22⋊D11D414yes—
163C4×C22⋊D11C2314yes—
164C2×(C2×D11)⋊C4—21no—
165C2×(C2×D11)⋊C4—21no—
166C2×(C2×D11)⋊C4D411yescharacteristic
167C2×C4⋊Dic11C2311yescharacteristic
168C2×Dic11⋊C4—21no—
169C2×Dic11⋊C4D411yescharacteristic
170C2×C4×Dic11—21no—
171C2×C4×Dic11C2311yescharacteristic
172C2×#4318—24no—
173C2×#4318C2314yescomplemented
174C22×C11⋊C8C2311yescharacteristic
175C22×C11⋊C8C2311yescharacteristic
176#66964—232no—
177C2×D88—42no—
178C2×D88C2314yescomplemented
179C2×#4314—24no—
180C2×#4314C2314yescomplemented
181C2×#4313—24no—
182C2×#4313C2314yescomplemented
183#66948—22no—
184#66948C2314yescomplemented
185#66940—22no—
186#66940C2314yescomplemented
187#66937—28no—
188(C22⋊D11)⋊C4—28no—
189C11×#102C2314yes—
190C11×#102C2314yescomplemented
191C11×C22⋊C8C2314yescomplemented
192#66896C2314yescomplemented
193#66885C2314yescomplemented
194(C2×D11)⋊C8C2314yescomplemented
195#66880C2314yescomplemented
196Dic11⋊C8C2314yescomplemented
197C8×Dic11C2314yescomplemented
198#66873C2314yescomplemented
199#66872C2314yescomplemented
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
216C2×D4×C11—28no—
217C2×D4×C11—24no—
218C2×D4×C11—21no—
219C2×D4×C11—22no—
220C2×D4×C11—22no—
221C2×D4×C11—24no—
222C2×D4×C11—21no—
223C2×D4×C11—21no—
224C2×D4×C11—22no—
225C2×D4×C11—22no—
226C2×D4×C11—22no—
227C2×D4×C11—44no—
228C2×D4×C11—48no—
229C2×D4×C11—44no—
230C2×D4×C11—82no—
231C2×D4×C11C2×D414yes—
232C2×D4×C11C2412yes—
233C2×D4×C11C2412yes—
234C2×D4×C11C2412yes—
235C22×C4×C11—22no—
236C22×C4×C11—22no—
237C22×C4×C11—21no—
238C22×C4×C11C2×D411yescharacteristic
239C22×C4×C11C2×D412yes—
240C22×C4×C11C2412yes—
241C22×C4×C11C2411yescharacteristic
242C2×C22⋊D11—24no—
243C2×C22⋊D11—24no—
244C2×C22⋊D11—24no—
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—44no—
253C2×C22⋊D11—44no—
254C2×C22⋊D11—44no—
255C2×C22⋊D11—44no—
256C2×C22⋊D11—44no—
257C2×C22⋊D11—432no—
258C2×C22⋊D11—44no—
259C2×C22⋊D11—44no—
260C2×C22⋊D11—82no—
261C2×C22⋊D11—82no—
262C2×C22⋊D11C2×D414yes—
263C22×Dic11—24no—
264C22×Dic11—24no—
265C22×Dic11—21no—
266C22×Dic11—21no—
267C22×Dic11—44no—
268C22×Dic11—44no—
269C22×Dic11C2×D411yescharacteristic
270C22×Dic11C2×D411yescharacteristic
271C22×Dic11C2×D411yescharacteristic
272#4341—28no—
273#4341—44no—
274#4341—48no—
275D4×D11—28no—
276D4×D11—44no—
277D4×D11—48no—
278#4339—28no—
279#4339—44no—
280#4339—48no—
281C2×D44—24no—
282C2×D44—21no—
283C2×D44—21no—
284C2×D44—22no—
285C2×D44—22no—
286C2×D44—22no—
287C2×D44—22no—
288C2×D44—82no—
289C2×D44C2412yes—
290C2×D44C2412yes—
291C2×C4×D11—22no—
292C2×C4×D11—24no—
293C2×C4×D11—22no—
294C2×C4×D11—44no—
295C2×C4×D11C2×D412yes—
296C2×C4×D11C2412yes—
297C2×Dic22—21no—
298C2×Dic22—22no—
299C2×Dic22C2×D414yescomplemented
300C2×Dic22C2412yes—
301C11×D8—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⋊Dic11—24no—
312C22⋊Dic11C2×D414yes—
313#4324—28no—
314#4324C2×D4116yescomplemented
315#4323—28no—
316#4323—28no—
317#4323—28no—
318(C2×D11)⋊C4—24no—
319(C2×D11)⋊C4—24no—
320(C2×D11)⋊C4C2×D414yes—
321C4⋊Dic11—21no—
322C4⋊Dic11C2412yes—
323Dic11⋊C4—24no—
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—44no—
334#4314—28no—
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×#449—111no—
348C2×#447—111no—
349C2×#447D1111yescharacteristic, complemented
350C2×C4×SD16—111no—
351C2×#436—111no—
352C23×C11—22no—
353C23×C11—24no—
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—
389D4×C11—24no—
390D4×C11—22no—
391D4×C11—22no—
392D4×C11—22no—
393D4×C11—22no—
394D4×C11—22no—
395D4×C11—48no—
396D4×C11—42no—
397D4×C11—42no—
398D4×C11—84no—
399D4×C11C22×D414yes—
400C2×C4×C11—22no—
401C2×C4×C11—24no—
402C2×C4×C11—22no—
403C2×C4×C11—22no—
404C2×C4×C11—22no—
405C2×C4×C11—42no—
406C2×C4×C11C22×D412yes—
407C2×C4×C11C22×D411yescharacteristic
408C2×C4×C11C22×D412yes—
409C2×C4×C11H(5,𝔽2)12yes—
410C2×C4×C11C2511yescharacteristic
411C22⋊D11—28no—
412C22⋊D11—48no—
413C22⋊D11—48no—
414C22⋊D11—48no—
415C22⋊D11—48no—
416C22⋊D11—48no—
417C22⋊D11—48no—
418C22⋊D11—48no—
419C22⋊D11—84no—
420C22⋊D11—84no—
421C2×Dic11—24no—
422C2×Dic11—22no—
423C2×Dic11—22no—
424C2×Dic11—22no—
425C2×Dic11—22no—
426C2×Dic11—48no—
427C2×Dic11—42no—
428C2×Dic11—48no—
429C2×Dic11AGL(1,ℤ/8)14yescomplemented
430C2×Dic11C22×D412yes—
431C2×Dic11C22×D412yes—
432C2×Dic11C22×D412yes—
433D44—22no—
434D44—22no—
435D44—22no—
436D44—22no—
437D44—42no—
438D44—42no—
439D44—84no—
440C4×D11—24no—
441C4×D11—22no—
442C4×D11—22no—
443C4×D11—48no—
444Dic22—24no—
445Dic22—22no—
446Dic22C22×D414yescomplemented
447C8×C11—22no—
448C8×C11—22no—
449C11⋊C8—22no—
450C11⋊C8C22×D414yescomplemented
451C22×#41—111no—
452C22×#41—111no—
453C23×D4—111no—
454C23×D4—221no—
455C23×D4C2×D1111yescharacteristic
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×SD16—111no—
463C22×D8—111no—
464C22×D8—111no—
465C22×D8—111no—
466C22×D8—111no—
467C22×D8C2×D1111yescharacteristic
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, complemented
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#447C2×D1118yescomplemented
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×#102C2×D1111yescharacteristic
509C2×#102C2×D1111yescharacteristic, complemented
510C2×C22⋊C8—111no—
511C2×C22⋊C8C2×D1111yescharacteristic, complemented
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—42no—
549C4×C11D4212yes—
550C4×C11C23×D411yescharacteristic
551C4×C11C2×H(5,𝔽2)11yescharacteristic
552Dic11—24no—
553Dic11—22no—
554Dic11—22no—
555Dic11—42no—
556Dic11C2×AGL(1,ℤ/8)14yescomplemented
557C25—21no—
558C25—221no—
559C2×#41—114no—
560C2×#41—114no—
561C2×#41—224no—
562C2×#41—222no—
563C2×#41—222no—
564C2×#41—224no—
565C2×#41—442no—
566C2×#41—442no—
567C22×Q8—111no—
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—111no—
597C23×C4—221no—
598C23×C4—221no—
599C23×C4—221no—
600C23×C4C22×D1111yescharacteristic
601AGL(1,ℤ/8)—2232no—
602AGL(1,ℤ/8)—2232no—
603C2×SD16—118no—
604C2×SD16—114no—
605C2×SD16—114no—
606C2×SD16—114no—
607C2×SD16—224no—
608C2×SD16—224no—
609C2×D8—24no—
610C2×D8—42no—
611C2×D8—114no—
612C2×D8—114no—
613C2×D8—114no—
614C2×D8—114no—
615C2×D8—224no—
616C2×D8—224no—
617C2×D8—224no—
618C2×D8—442no—
619C2×D8C22×D1114yes—
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—222no—
641#121—228no—
642#121—222no—
643#121—222no—
644#121C22×D1114yescomplemented
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#103—114no—
670#102—114no—
671#102—114no—
672#102—114no—
673#102C22×D1114yes—
674#102C22×D1114yescomplemented
675C22⋊C8—114no—
676C22⋊C8C22×D1114yescomplemented
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—228no—
705#41—228no—
706#41—444no—
707#41—448no—
708#41—444no—
709#41—448no—
710C2×Q8—114no—
711C2×Q8—112no—
712C2×Q8—221no—
713C2×Q8—222no—
714C2×D4—28no—
715C2×D4—24no—
716C2×D4—21no—
717C2×D4—22no—
718C2×D4—22no—
719C2×D4—24no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—22no—
723C2×D4—22no—
724C2×D4—22no—
725C2×D4—44no—
726C2×D4—48no—
727C2×D4—44no—
728C2×D4—82no—
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—222no—
745C2×D4—222no—
746C2×D4—221no—
747C2×D4—221no—
748C2×D4—222no—
749C2×D4—222no—
750C2×D4—444no—
751C2×D4—444no—
752C2×D4—444no—
753C2×D4—448no—
754C2×D4—444no—
755C2×D4—444no—
756C2×D4—444no—
757C2×D4—4432no—
758C2×D4—444no—
759C2×D4—444no—
760C2×D4—882no—
761C2×D4—882no—
762C2×D4—882no—
763C2×D4D4×D1114yes—
764C2×D4C23×D1112yes—
765C2×D4C23×D1112yes—
766C2×D4C23×D1112yes—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—21no—
770C22×C4—111no—
771C22×C4—111no—
772C22×C4—111no—
773C22×C4—112no—
774C22×C4—112no—
775C22×C4—224no—
776C22×C4—224no—
777C22×C4—221no—
778C22×C4—222no—
779C22×C4—222no—
780C22×C4—221no—
781C22×C4—224no—
782C22×C4—444no—
783C22×C4—444no—
784C22×C4—444no—
785C22×C4D4×D1112yes—
786C22×C4D4×D1111yescharacteristic
787C22×C4C23×D1112yes—
788C22×C4C23×D1111yescharacteristic
789SD16—1116no—
790SD16—228no—
791SD16—228no—
792D8—28no—
793D8—44no—
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—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—114no—
863Q8—224no—
864Q8—222no—
865D4—24no—
866D4—22no—
867D4—22no—
868D4—22no—
869D4—22no—
870D4—22no—
871D4—48no—
872D4—42no—
873D4—42no—
874D4—84no—
875D4—228no—
876D4—222no—
877D4—222no—
878D4—222no—
879D4—222no—
880D4—448no—
881D4—448no—
882D4—448no—
883D4—448no—
884D4—448no—
885D4—448no—
886D4—448no—
887D4—442no—
888D4—442no—
889D4—884no—
890D4—884no—
891D4—884no—
892D4C2×D4×D1114yes—
893C2×C4—22no—
894C2×C4—24no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—42no—
899C2×C4—114no—
900C2×C4—112no—
901C2×C4—112no—
902C2×C4—112no—
903C2×C4—222no—
904C2×C4—222no—
905C2×C4—224no—
906C2×C4—222no—
907C2×C4—224no—
908C2×C4—222no—
909C2×C4—222no—
910C2×C4—222no—
911C2×C4—448no—
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—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—
954C22#1062312112yes—
955C22#1062328812yes—
956C22D11×AGL(1,ℤ/8)12yes—
957C22C22×D4×D1111yescharacteristic
958C4—22no—
959C4—42no—
960C4—114no—
961C4—222no—
962C4—224no—
963C4—222no—
964C4—442no—
965C4#1062312112yes—
966C4C22×D4×D1111yescharacteristic
967C4C2×#6703711yescharacteristic
968C2—42no—
969C2—44no—
970C2—82no—
971C2—82no—
972C2—442no—
973C2—882no—
974C2—882no—
975C2#1308023414yesdirect product factor
976C2C2×#1062312111yescharacteristic
977C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
978C2C2×#1062328811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#447C2
socleC23×C11C22×D4
hypercenterC2×#447D11
hypocenterC11C2×#3274
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#447

Complements

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

NH ≅ G/Ntype
1. C22×#66985C2semidirect
2. C22×#66964C2semidirect
3. C2×#10623130C2semidirect
4. C2×D4×C22⋊D11C2semidirect
5. #13080234C2direct (N × H)
6. C2×#10622764C2semidirect
7. C2×#10622395C2semidirect
8. C2×#10622652C2semidirect
9. C2×#10622375C2semidirect
10. C2×#10622763C2semidirect
11. C2×#10622347C2semidirect
12. C2×#10622771C2semidirect
13. C2×#10622386C2semidirect
14. C2×#10622371C2semidirect
15. C2×#10622342C2semidirect
16. C2×C11×#447C2semidirect
19. C22×#4341C22semidirect
21. C22×#4339C22semidirect
23. C22×C11×D8C22semidirect
24. C2×C11×#121C22semidirect
28. C2×#66993C22semidirect
32. D4×C22⋊D11C22semidirect
37. C22×#4324C22semidirect
39. C2×#66985C22semidirect
41. C22×#4323C22semidirect
42. C22×#4323C22semidirect
45. C22×#4318C22semidirect
47. C2×#66964C22semidirect
48. C22×D88C22semidirect
49. C22×#4314C22semidirect
50. C22×#4313C22semidirect
52. #10623130C22semidirect
53. C2×#66948C22semidirect
54. C2×#66940C22semidirect
57. C11×#447C22semidirect
59. C2×C11×#102C22semidirect
60. C2×C11×C22⋊C8C22semidirect
61. C2×#66896C22semidirect
62. #10622771C22semidirect
63. #10622764C22semidirect
64. #10622763C22semidirect
65. C2×#66885C22semidirect
66. C2×(C2×D11)⋊C8C22semidirect
67. C2×#66880C22semidirect
68. C2×Dic11⋊C8C22semidirect
69. C2×C8×Dic11C22semidirect
70. #10622652C22semidirect
71. C2×#66873C22semidirect
72. C2×#66872C22semidirect
73. #10622395C22semidirect
74. #10622386C22semidirect
75. #10622375C22semidirect
76. #10622371C22semidirect
77. #10622347C22semidirect
78. #10622342C22semidirect
108. C2×#4341C23semidirect
116. C2×#4339C23semidirect
126. C2×C11×D8C23semidirect
130. C11×#121C23semidirect
141. #66993C23semidirect
150. C2×#4324D4semidirect
152. C2×#4324C23semidirect
158. C2×#4323C23semidirect
159. C2×#4323C23semidirect
173. C2×#4318C23semidirect
178. C2×D88C23semidirect
180. C2×#4314C23semidirect
182. C2×#4313C23semidirect
184. #66948C23semidirect
186. #66940C23semidirect
190. C11×#102C23semidirect
191. C11×C22⋊C8C23semidirect
192. #66896C23semidirect
193. #66885C23semidirect
194. (C2×D11)⋊C8C23semidirect
195. #66880C23semidirect
196. Dic11⋊C8C23semidirect
197. C8×Dic11C23semidirect
198. #66873C23semidirect
199. #66872C23semidirect
299. C2×Dic22C2×D4semidirect
314. #4324C2×D4semidirect
330. C2×C11⋊C8C2×D4semidirect
349. C2×#447D11semidirect
429. C2×Dic11AGL(1,ℤ/8)semidirect
446. Dic22C22×D4semidirect
450. C11⋊C8C22×D4semidirect
468. C22×D8C2×D11semidirect
484. C2×#121C2×D11semidirect
499. #447C2×D11semidirect
509. C2×#102C2×D11semidirect
511. C2×C22⋊C8C2×D11semidirect
556. Dic11C2×AGL(1,ℤ/8)semidirect
620. C2×D8C22×D11semidirect
644. #121C22×D11semidirect
674. #102C22×D11semidirect
676. C22⋊C8C22×D11semidirect
682. C2×C11#3274semidirect
824. C11C2×#3274semidirect
975. C2#13080234direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669852
C22×#669642
C2×#106231302
C2×D4×C22⋊D112
#130802342
C2×#106227642
C2×#106223952
C2×#106226522
C2×#106223752
C2×#106227632
C2×#106223472
C2×#106227712
C2×#106223862
C2×#106223712
C2×#106223422
C2×C11×#4472
C2×#327411