Finite Group Databasebeta

← C2×#13080854 #15630610

Subgroups — C2×#13080854 #15630610

Order 2816.

2630 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623063C211yesmaximal, characteristic, complemented
2C2×D4×C22⋊D11C211yesmaximal, characteristic, complemented
3#13080854C2116yesmaximal, direct product factor
4C2×#10622373C211yesmaximal, characteristic, complemented
5C2×#10622616C211yesmaximal, characteristic, complemented
6C2×#10622392C211yesmaximal, characteristic, complemented
7C2×#10622374C211yesmaximal, characteristic, complemented
8C2×#10622748C211yesmaximal, characteristic, complemented
9C2×#10622395C211yesmaximal, characteristic, complemented
10C2×#10622399C211yesmaximal, characteristic, complemented
11C2×#10622386C211yesmaximal, characteristic, complemented
12C2×#10622830C211yesmaximal, characteristic, complemented
13C2×#10622369C211yesmaximal, characteristic, complemented
14C2×#10622741C211yesmaximal, characteristic, complemented
15C2×#10622383C211yesmaximal, characteristic, complemented
16C2×C11×#418C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C23×C22⋊D11—21no—
19C22×D4×D11C2211yescharacteristic
20C22×C11×M16C2211yescharacteristic, complemented
21C2×C11×#117C2211yescharacteristic, complemented
22C2×#67006—21no—
23C2×#66993C2211yescharacteristic
24C2×#66992—21no—
25D4×C22⋊D11—24no—
26D4×C22⋊D11C2218yescomplemented
27C2×#66991C2211yescharacteristic
28C2×#66990—21no—
29C2×D4×Dic11C2211yescharacteristic
30C22×#4323C2211yescharacteristic
31C22×#4323C2211yescharacteristic, complemented
32C2×#66983C2211yescharacteristic
33C2×#66983C2211yescharacteristic, complemented
34C2×C4×C22⋊D11C2211yescharacteristic
35C22×D88C2211yescharacteristic, complemented
36C22×#4313C2211yescharacteristic, complemented
37#10623063—24no—
38#10623063C2218yescomplemented
39C2×#66948C2211yescharacteristic, complemented
40C2×#66946C2211yescharacteristic, complemented
41C2×#66945C2211yescharacteristic, complemented
42C2×#66941C2211yescharacteristic, complemented
43C2×#66938—21no—
44C2×#66937—21no—
45C2×#66928—21no—
46C2×#66925—21no—
47C11×#418C2218yescomplemented
48C2×C11×#102C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic, complemented
51C2×C11×#102C2211yescharacteristic, complemented
52#10622830C2218yescomplemented
53C2×#66896C2211yescharacteristic
54C2×#66896C2211yescharacteristic, complemented
55C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
56#10622748C2218yescomplemented
57#10622741C2218yescomplemented
58C2×#66885C2211yescharacteristic, complemented
59C2×#66885C2211yescharacteristic, complemented
60C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
61C2×#66881C2211yescharacteristic, complemented
62C2×Dic11⋊C8C2211yescharacteristic, complemented
63C2×C8×Dic11C2211yescharacteristic, complemented
64#10622616C2218yescomplemented
65C2×#66873C2211yescharacteristic, complemented
66C2×#66873C2211yescharacteristic, complemented
67C2×#66872C2211yescharacteristic, complemented
68C2×#66871C2211yescharacteristic, complemented
69#10622399C2218yescomplemented
70#10622395C2218yescomplemented
71#10622392C2218yescomplemented
72#10622386C2218yescomplemented
73#10622383C2218yescomplemented
74#10622374C2218yescomplemented
75#10622373C2218yescomplemented
76#10622369C2218yescomplemented
77C25×C11—21no—
78C24×D11—21no—
79C22×D4×C11—24no—
80C22×D4×C11—21no—
81C22×D4×C11—22no—
82C22×D4×C11—42no—
83C22×D4×C11C2311yescharacteristic
84C22×D4×C11C2314yes—
85C22×D4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C22×C22⋊D11—21no—
88C22×C22⋊D11—21no—
89C22×C22⋊D11—21no—
90C22×C22⋊D11—28no—
91C22×C22⋊D11—21no—
92C22×C22⋊D11—21no—
93C22×C22⋊D11—21no—
94C22×C22⋊D11—48no—
95C22×C22⋊D11D411yescharacteristic
96C23×Dic11—21no—
97C2×D4×D11—24no—
98C2×D4×D11—22no—
99C2×D4×D11—42no—
100C2×D4×D11C2314yes—
101C22×D44—21no—
102C22×D44C2311yescharacteristic
103C22×D44C2311yescharacteristic
104C22×C4×D11—21no—
105C22×C4×D11C2311yescharacteristic
106C22×Dic22—21no—
107C2×C11×M16—42no—
108C2×C11×M16C2314yescomplemented
109C22×C8×C11C2311yescharacteristic
110C22×C8×C11C2311yescharacteristic
111C11×#117—22no—
112C11×#117C2314yescomplemented
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C22⋊C4—21no—
116C2×C42×C11—21no—
117#67006—28no—
118C2×C22⋊Dic11—21no—
119C2×C22⋊Dic11—21no—
120C2×C22⋊Dic11D411yescharacteristic
121#66993—22no—
122#66993C2314yes—
123#66992—28no—
124#66991—22no—
125#66991C2314yes—
126#66990—28no—
127D4×Dic11—22no—
128D4×Dic11C2314yes—
129C2×#4323—24no—
130C2×#4323—42no—
131C2×#4323C2314yes—
132C2×#4323C2314yescomplemented
133#66983—22no—
134#66983—22no—
135#66983C2314yes—
136#66983C2314yescomplemented
137C4×C22⋊D11D414yes—
138C4×C22⋊D11C2314yes—
139C2×(C2×D11)⋊C4—21no—
140C2×(C2×D11)⋊C4—21no—
141C2×(C2×D11)⋊C4—21no—
142C2×(C2×D11)⋊C4—21no—
143C2×(C2×D11)⋊C4—21no—
144C2×(C2×D11)⋊C4D411yescharacteristic
145C2×C4⋊Dic11C2311yescharacteristic
146C2×C4⋊Dic11C2311yescharacteristic
147C2×Dic11⋊C4—21no—
148C2×Dic11⋊C4D411yescharacteristic
149C2×C4×Dic11—21no—
150C2×C4×Dic11C2311yescharacteristic
151C22×C11⋊C8C2311yescharacteristic
152C22×C11⋊C8C2311yescharacteristic
153C2×D88—42no—
154C2×D88C2314yescomplemented
155C2×#4313—42no—
156C2×#4313C2314yescomplemented
157#66948—22no—
158#66948C2314yescomplemented
159#66946—22no—
160#66946C2314yescomplemented
161#66945—22no—
162#66945C2314yescomplemented
163#66941—22no—
164#66941C2314yescomplemented
165#66938—28no—
166#66937—28no—
167#66928—28no—
168#66925—28no—
169C11×#102C2314yes—
170C11×#102C2314yes—
171C11×#102C2314yescomplemented
172C11×#102C2314yescomplemented
173#66896C2314yes—
174#66896C2314yescomplemented
175C22⋊(C11⋊C8)C2314yescomplemented
176#66885C2314yescomplemented
177#66885C2314yescomplemented
178(C2×D11)⋊C8C2314yescomplemented
179#66881C2314yescomplemented
180Dic11⋊C8C2314yescomplemented
181C8×Dic11C2314yescomplemented
182#66873C2314yescomplemented
183#66873C2314yescomplemented
184#66872C2314yescomplemented
185#66871C2314yescomplemented
186C2×#3325—111nomaximal, Sylow
187C24×C11—21no—
188C24×C11—21no—
189C24×C11—24no—
190C24×C11—44no—
191C24×C11—44no—
192C24×C11—82no—
193C24×C11C2×D411yescharacteristic
194C23×D11—21no—
195C23×D11—21no—
196C23×D11—24no—
197C23×D11—44no—
198C23×D11—44no—
199C23×D11—82no—
200C23×D11C2×D411yescharacteristic
201C2×D4×C11—28no—
202C2×D4×C11—21no—
203C2×D4×C11—24no—
204C2×D4×C11—21no—
205C2×D4×C11—22no—
206C2×D4×C11—22no—
207C2×D4×C11—22no—
208C2×D4×C11—44no—
209C2×D4×C11—48no—
210C2×D4×C11—44no—
211C2×D4×C11#4114yes—
212C2×D4×C11C2412yes—
213C2×D4×C11C2412yes—
214C22×C4×C11—22no—
215C22×C4×C11—22no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2×D412yes—
220C22×C4×C11C2412yes—
221C22×C4×C11C2411yescharacteristic
222C2×C22⋊D11—24no—
223C2×C22⋊D11—24no—
224C2×C22⋊D11—24no—
225C2×C22⋊D11—24no—
226C2×C22⋊D11—24no—
227C2×C22⋊D11—24no—
228C2×C22⋊D11—24no—
229C2×C22⋊D11—44no—
230C2×C22⋊D11—44no—
231C2×C22⋊D11—44no—
232C2×C22⋊D11—432no—
233C2×C22⋊D11—44no—
234C2×C22⋊D11—82no—
235C2×C22⋊D11—82no—
236C2×C22⋊D11C2×D414yes—
237C22×Dic11—24no—
238C22×Dic11—21no—
239C22×Dic11—21no—
240C22×Dic11—44no—
241C22×Dic11C2×D411yescharacteristic
242C22×Dic11C2×D411yescharacteristic
243C22×Dic11C2×D411yescharacteristic
244D4×D11—28no—
245D4×D11—44no—
246D4×D11—48no—
247C2×D44—24no—
248C2×D44—21no—
249C2×D44—21no—
250C2×D44—22no—
251C2×D44—22no—
252C2×D44—22no—
253C2×D44—22no—
254C2×D44—82no—
255C2×D44C2412yes—
256C2×D44C2412yes—
257C2×C4×D11—24no—
258C2×C4×D11—22no—
259C2×C4×D11—22no—
260C2×C4×D11—44no—
261C2×C4×D11C2×D412yes—
262C2×C4×D11C2412yes—
263C2×Dic22—24no—
264C2×Dic22—82no—
265C11×M16—44no—
266C2×C8×C11—22no—
267C2×C8×C11—22no—
268C2×C8×C11C2412yes—
269C2×C8×C11C2412yes—
270C11×C4⋊C4—21no—
271C11×C4⋊C4—21no—
272C11×C4⋊C4C2412yes—
273C11×C4⋊C4C2412yes—
274C11×C22⋊C4—24no—
275C42×C11—24no—
276C22⋊Dic11—24no—
277C22⋊Dic11—24no—
278C22⋊Dic11C2×D414yes—
279#4323—28no—
280#4323—44no—
281(C2×D11)⋊C4—24no—
282(C2×D11)⋊C4—24no—
283(C2×D11)⋊C4—24no—
284(C2×D11)⋊C4—24no—
285(C2×D11)⋊C4—24no—
286(C2×D11)⋊C4C2×D414yes—
287C4⋊Dic11—21no—
288C4⋊Dic11—21no—
289C4⋊Dic11C2412yes—
290C4⋊Dic11C2412yes—
291Dic11⋊C4—24no—
292Dic11⋊C4C2×D414yes—
293C4×Dic11—24no—
294C4×Dic11C2×D412yes—
295C4×Dic11C2412yes—
296C2×C11⋊C8—22no—
297C2×C11⋊C8—22no—
298C2×C11⋊C8C2412yes—
299C2×C11⋊C8C2412yes—
300D88—44no—
301#4313—44no—
302C2×#555—111no—
303C2×D42—111no—
304#3325—1116no—
305C2×#486—111no—
306C2×#482—111no—
307C2×#482—111no—
308C2×#476—111no—
309C2×#469—111no—
310C2×#469—111no—
311C2×#459—111no—
312C2×#447—111no—
313C2×#447—111no—
314C2×C4×D8—111no—
315C2×#436—111no—
316C2×#418—111no—
317C2×#418D1111yescharacteristic, complemented
318C23×C11—24no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—48no—
325C23×C11—48no—
326C23×C11—42no—
327C23×C11—42no—
328C23×C11—42no—
329C23×C11—42no—
330C23×C11—42no—
331C23×C11—84no—
332C23×C11—816no—
333C23×C11C22×D412yes—
334C23×C11C22×D411yescharacteristic
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—48no—
341C22×D11—48no—
342C22×D11—42no—
343C22×D11—42no—
344C22×D11—42no—
345C22×D11—42no—
346C22×D11—42no—
347C22×D11—42no—
348C22×D11—84no—
349C22×D11—816no—
350C22×D11C22×D412yes—
351D4×C11—24no—
352D4×C11—22no—
353D4×C11—22no—
354D4×C11—22no—
355D4×C11—48no—
356D4×C11—42no—
357D4×C11C2×#4114yes—
358C2×C4×C11—22no—
359C2×C4×C11—24no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—42no—
365C2×C4×C11—42no—
366C2×C4×C11C22×D412yes—
367C2×C4×C11C22×D411yescharacteristic
368C2×C4×C11C2×#4112yes—
369C2×C4×C11H(5,𝔽2)12yes—
370C2×C4×C11C2511yescharacteristic
371C22⋊D11—28no—
372C22⋊D11—48no—
373C22⋊D11—48no—
374C22⋊D11—48no—
375C22⋊D11—48no—
376C22⋊D11—84no—
377C22⋊D11—84no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—42no—
383C2×Dic11—42no—
384C2×Dic11—48no—
385C2×Dic11AGL(1,ℤ/8)14yes—
386C2×Dic11C22×D412yes—
387C2×Dic11C22×D412yes—
388C2×Dic11C22×D412yes—
389D44—22no—
390D44—22no—
391D44—22no—
392D44—22no—
393D44—42no—
394D44—42no—
395D44—84no—
396C4×D11—24no—
397C4×D11—22no—
398C4×D11—22no—
399C4×D11—48no—
400Dic22—84no—
401C8×C11—22no—
402C8×C11—22no—
403C11⋊C8—22no—
404C11⋊C8—22no—
405C23×D4—111no—
406C23×D4—221no—
407C23×D4C2×D1111yescharacteristic
408C22×D8—111no—
409C22×D8—111no—
410C22×D8—111no—
411C22×M16—111no—
412C22×M16C2×D1111yescharacteristic, complemented
413#555—118no—
414#555—224no—
415D42—118no—
416D42—224no—
417C2×C4⋊Q8—111no—
418C2×#127—111no—
419C2×#124—221no—
420C2×#124—221no—
421C2×#121—111no—
422C2×#121—111no—
423C2×#121—111no—
424C2×#121—111no—
425C2×#121—221no—
426C2×#121—221no—
427C2×#120—221no—
428C2×#120—221no—
429C2×C4×D4—111no—
430C2×C4×D4—111no—
431C2×C4×D4—111no—
432C2×#117—111no—
433C2×#117—221no—
434C2×#117C2×D1111yescharacteristic, complemented
435#486—118no—
436#482—118no—
437#482—118no—
438#476—118no—
439#469—118no—
440#469—118no—
441#459—118no—
442#447—118no—
443#447—118no—
444C4×D8—118no—
445#436—118no—
446C2×#107—111no—
447C2×#106—111no—
448C2×#106—111no—
449C2×C4⋊C8—111no—
450#418—118no—
451#418C2×D1118yescomplemented
452C2×#102—111no—
453C2×#102—111no—
454C2×#102—111no—
455C2×#102—111no—
456C2×#102—111no—
457C2×#102—111no—
458C2×#102C2×D1111yescharacteristic
459C2×#102C2×D1111yescharacteristic
460C2×#102C2×D1111yescharacteristic, complemented
461C2×#102C2×D1111yescharacteristic, complemented
462C2×C22⋊C8—111no—
463C2×C22⋊C8—111no—
464C2×C4×C8—111no—
465C22×C11—22no—
466C22×C11—24no—
467C22×C11—22no—
468C22×C11—22no—
469C22×C11—42no—
470C22×C11—48no—
471C22×C11—44no—
472C22×C11—42no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—42no—
476C22×C11—816no—
477C22×C11—84no—
478C22×C11#54612yes—
479C22×C11C2×AGL(1,ℤ/8)12yes—
480C22×C11#57612yes—
481C22×C11C23×D411yescharacteristic
482C2×D11—22no—
483C2×D11—22no—
484C2×D11—22no—
485C2×D11—44no—
486C2×D11—42no—
487C2×D11—42no—
488C2×D11—42no—
489C2×D11—42no—
490C2×D11—42no—
491C2×D11—42no—
492C2×D11—816no—
493C2×D11—84no—
494C2×D11—84no—
495C4×C11—22no—
496C4×C11—42no—
497C4×C11—42no—
498C4×C11#54612yes—
499C4×C11C22×#4111yescharacteristic
500C4×C11C2×H(5,𝔽2)11yescharacteristic
501Dic11—22no—
502Dic11—22no—
503Dic11—42no—
504Dic11—42no—
505Dic11C2×AGL(1,ℤ/8)14yes—
506C25—21no—
507C25—221no—
508C22×Q8—221no—
509C22×D4—24no—
510C22×D4—21no—
511C22×D4—22no—
512C22×D4—42no—
513C22×D4—111no—
514C22×D4—114no—
515C22×D4—111no—
516C22×D4—111no—
517C22×D4—221no—
518C22×D4—222no—
519C22×D4—221no—
520C22×D4—221no—
521C22×D4—221no—
522C22×D4—228no—
523C22×D4—224no—
524C22×D4—221no—
525C22×D4—221no—
526C22×D4—221no—
527C22×D4—442no—
528C22×D4—448no—
529C22×D4C22×D1111yescharacteristic
530C22×D4C22×D1114yes—
531C22×D4C22×D1111yescharacteristic
532C23×C4—111no—
533C23×C4—221no—
534C23×C4—221no—
535C23×C4C22×D1111yescharacteristic
536C2×D8—114no—
537C2×D8—114no—
538C2×D8—114no—
539C2×D8—224no—
540C2×D8—442no—
541C2×D8—442no—
542C2×M16—42no—
543C2×M16—114no—
544C2×M16—442no—
545C2×M16C22×D1114yescomplemented
546C22×C8—111no—
547C22×C8—111no—
548C22×C8C22×D1111yescharacteristic
549C22×C8C22×D1111yescharacteristic
550C4⋊Q8—114no—
551C4⋊Q8—222no—
552#127—114no—
553#127—222no—
554#124—228no—
555#124—228no—
556#121—114no—
557#121—114no—
558#121—114no—
559#121—114no—
560#121—228no—
561#121—222no—
562#121—228no—
563#121—222no—
564#121—222no—
565#121—222no—
566#120—228no—
567#120—228no—
568C4×D4—114no—
569C4×D4—114no—
570C4×D4—114no—
571C4×D4—114no—
572C4×D4—222no—
573C4×D4—222no—
574#117—22no—
575#117—114no—
576#117—228no—
577#117—222no—
578#117C22×D1114yescomplemented
579C2×C4⋊C4—111no—
580C2×C4⋊C4—111no—
581C2×C4⋊C4—111no—
582C2×C4⋊C4—221no—
583C2×C4⋊C4C22×D1111yescharacteristic
584C2×C4⋊C4C22×D1111yescharacteristic
585C2×C22⋊C4—21no—
586C2×C22⋊C4—111no—
587C2×C22⋊C4—111no—
588C2×C22⋊C4—221no—
589C2×C22⋊C4—221no—
590C2×C22⋊C4—221no—
591C2×C22⋊C4—221no—
592C2×C22⋊C4—221no—
593C2×C22⋊C4—221no—
594C2×C22⋊C4—221no—
595C2×C42—21no—
596C2×C42—111no—
597C2×C42—221no—
598#107—114no—
599#106—114no—
600#106—114no—
601C4⋊C8—114no—
602#102—114no—
603#102—114no—
604#102—114no—
605#102—114no—
606#102—114no—
607#102—114no—
608#102C22×D1114yes—
609#102C22×D1114yes—
610#102C22×D1114yescomplemented
611#102C22×D1114yescomplemented
612C22⋊C8—114no—
613C22⋊C8—114no—
614C4×C8—114no—
615C2×C11—44no—
616C2×C11—42no—
617C2×C11—82no—
618C2×C11#332514yescomplemented
619C2×C11C2×#54611yescharacteristic
620C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
621C2×C11C2×#57611yescharacteristic
622D11—42no—
623D11—82no—
624D11—82no—
625C24—21no—
626C24—21no—
627C24—24no—
628C24—44no—
629C24—44no—
630C24—82no—
631C24—111no—
632C24—224no—
633C24—221no—
634C24—221no—
635C24—444no—
636C24—444no—
637C24—882no—
638C24D4×D1111yescharacteristic
639C2×Q8—224no—
640C2×Q8—882no—
641C2×D4—28no—
642C2×D4—22no—
643C2×D4—21no—
644C2×D4—24no—
645C2×D4—21no—
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—44no—
649C2×D4—48no—
650C2×D4—44no—
651C2×D4—114no—
652C2×D4—112no—
653C2×D4—112no—
654C2×D4—224no—
655C2×D4—224no—
656C2×D4—224no—
657C2×D4—224no—
658C2×D4—224no—
659C2×D4—228no—
660C2×D4—224no—
661C2×D4—224no—
662C2×D4—224no—
663C2×D4—222no—
664C2×D4—222no—
665C2×D4—221no—
666C2×D4—221no—
667C2×D4—222no—
668C2×D4—222no—
669C2×D4—444no—
670C2×D4—444no—
671C2×D4—448no—
672C2×D4—444no—
673C2×D4—4432no—
674C2×D4—444no—
675C2×D4—444no—
676C2×D4—882no—
677C2×D4—882no—
678C2×D4—882no—
679C2×D4#433914yes—
680C2×D4C23×D1112yes—
681C2×D4C23×D1112yes—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—111no—
687C22×C4—111no—
688C22×C4—111no—
689C22×C4—112no—
690C22×C4—112no—
691C22×C4—224no—
692C22×C4—224no—
693C22×C4—222no—
694C22×C4—222no—
695C22×C4—221no—
696C22×C4—221no—
697C22×C4—444no—
698C22×C4—444no—
699C22×C4D4×D1112yes—
700C22×C4D4×D1111yescharacteristic
701C22×C4C23×D1112yes—
702C22×C4C23×D1111yescharacteristic
703D8—228no—
704D8—444no—
705D8—444no—
706M16—44no—
707M16—444no—
708C2×C8—22no—
709C2×C8—22no—
710C2×C8—112no—
711C2×C8—112no—
712C2×C8—222no—
713C2×C8—222no—
714C2×C8C23×D1112yes—
715C2×C8C23×D1112yes—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—114no—
719C4⋊C4—112no—
720C4⋊C4—112no—
721C4⋊C4—224no—
722C4⋊C4—221no—
723C4⋊C4—221no—
724C4⋊C4C23×D1112yes—
725C4⋊C4C23×D1112yes—
726C22⋊C4—24no—
727C22⋊C4—114no—
728C22⋊C4—114no—
729C22⋊C4—224no—
730C22⋊C4—224no—
731C22⋊C4—224no—
732C22⋊C4—224no—
733C22⋊C4—224no—
734C22⋊C4—224no—
735C22⋊C4—224no—
736C42—24no—
737C42—112no—
738C42—112no—
739C42—224no—
740C11C2×#332511yescharacteristic, complemented, Sylow
741C23—22no—
742C23—24no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—48no—
748C23—48no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—84no—
755C23—816no—
756C23—112no—
757C23—222no—
758C23—222no—
759C23—222no—
760C23—222no—
761C23—222no—
762C23—448no—
763C23—448no—
764C23—442no—
765C23—442no—
766C23—442no—
767C23—442no—
768C23—442no—
769C23—442no—
770C23—884no—
771C23—8816no—
772C23C2×D4×D1112yes—
773C23C2×D4×D1111yescharacteristic
774Q8—884no—
775D4—24no—
776D4—22no—
777D4—22no—
778D4—22no—
779D4—48no—
780D4—42no—
781D4—228no—
782D4—222no—
783D4—222no—
784D4—222no—
785D4—222no—
786D4—448no—
787D4—448no—
788D4—448no—
789D4—448no—
790D4—442no—
791D4—442no—
792D4—884no—
793D4—884no—
794D4—884no—
795D4C2×#433914yes—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—114no—
805C2×C4—112no—
806C2×C4—112no—
807C2×C4—112no—
808C2×C4—222no—
809C2×C4—222no—
810C2×C4—224no—
811C2×C4—222no—
812C2×C4—222no—
813C2×C4—222no—
814C2×C4—222no—
815C2×C4—448no—
816C2×C4—448no—
817C2×C4—442no—
818C2×C4—442no—
819C2×C4C2×#433912yes—
820C2×C4C2×D4×D1112yes—
821C2×C4C2×D4×D1111yescharacteristic
822C2×C4#6703712yes—
823C2×C4C24×D1111yescharacteristic
824C8—22no—
825C8—22no—
826C8—222no—
827C8—222no—
828C22—22no—
829C22—24no—
830C22—22no—
831C22—22no—
832C22—44no—
833C22—48no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—816no—
840C22—84no—
841C22—222no—
842C22—222no—
843C22—222no—
844C22—444no—
845C22—442no—
846C22—442no—
847C22—442no—
848C22—442no—
849C22—442no—
850C22—442no—
851C22—8816no—
852C22—884no—
853C22—884no—
854C22#1062302112yes—
855C22D11×AGL(1,ℤ/8)12yes—
856C22#1062330512yes—
857C22C22×D4×D1111yescharacteristic
858C4—22no—
859C4—42no—
860C4—42no—
861C4—114no—
862C4—222no—
863C4—222no—
864C4—442no—
865C4—442no—
866C4#1062302112yes—
867C4C22×#433911yescharacteristic
868C4C2×#6703711yescharacteristic
869C2—42no—
870C2—44no—
871C2—82no—
872C2—442no—
873C2—882no—
874C2—882no—
875C2#1308085414yesdirect product factor
876C2C2×#1062302111yescharacteristic
877C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
878C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#418C2
socleC23×C11C22×D4
hypercenterC2×#418D11
hypocenterC11C2×#3325
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#418

Complements

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

NH ≅ G/Ntype
1. C2×#10623063C2semidirect
2. C2×D4×C22⋊D11C2semidirect
3. #13080854C2direct (N × H)
4. C2×#10622373C2semidirect
5. C2×#10622616C2semidirect
6. C2×#10622392C2semidirect
7. C2×#10622374C2semidirect
8. C2×#10622748C2semidirect
9. C2×#10622395C2semidirect
10. C2×#10622399C2semidirect
11. C2×#10622386C2semidirect
12. C2×#10622830C2semidirect
13. C2×#10622369C2semidirect
14. C2×#10622741C2semidirect
15. C2×#10622383C2semidirect
16. C2×C11×#418C2semidirect
20. C22×C11×M16C22semidirect
21. C2×C11×#117C22semidirect
26. D4×C22⋊D11C22semidirect
31. C22×#4323C22semidirect
33. C2×#66983C22semidirect
35. C22×D88C22semidirect
36. C22×#4313C22semidirect
38. #10623063C22semidirect
39. C2×#66948C22semidirect
40. C2×#66946C22semidirect
41. C2×#66945C22semidirect
42. C2×#66941C22semidirect
47. C11×#418C22semidirect
50. C2×C11×#102C22semidirect
51. C2×C11×#102C22semidirect
52. #10622830C22semidirect
54. C2×#66896C22semidirect
55. C2×C22⋊(C11⋊C8)C22semidirect
56. #10622748C22semidirect
57. #10622741C22semidirect
58. C2×#66885C22semidirect
59. C2×#66885C22semidirect
60. C2×(C2×D11)⋊C8C22semidirect
61. C2×#66881C22semidirect
62. C2×Dic11⋊C8C22semidirect
63. C2×C8×Dic11C22semidirect
64. #10622616C22semidirect
65. C2×#66873C22semidirect
66. C2×#66873C22semidirect
67. C2×#66872C22semidirect
68. C2×#66871C22semidirect
69. #10622399C22semidirect
70. #10622395C22semidirect
71. #10622392C22semidirect
72. #10622386C22semidirect
73. #10622383C22semidirect
74. #10622374C22semidirect
75. #10622373C22semidirect
76. #10622369C22semidirect
108. C2×C11×M16C23semidirect
112. C11×#117C23semidirect
132. C2×#4323C23semidirect
136. #66983C23semidirect
154. C2×D88C23semidirect
156. C2×#4313C23semidirect
158. #66948C23semidirect
160. #66946C23semidirect
162. #66945C23semidirect
164. #66941C23semidirect
171. C11×#102C23semidirect
172. C11×#102C23semidirect
174. #66896C23semidirect
175. C22⋊(C11⋊C8)C23semidirect
176. #66885C23semidirect
177. #66885C23semidirect
178. (C2×D11)⋊C8C23semidirect
179. #66881C23semidirect
180. Dic11⋊C8C23semidirect
181. C8×Dic11C23semidirect
182. #66873C23semidirect
183. #66873C23semidirect
184. #66872C23semidirect
185. #66871C23semidirect
317. C2×#418D11semidirect
412. C22×M16C2×D11semidirect
434. C2×#117C2×D11semidirect
451. #418C2×D11semidirect
460. C2×#102C2×D11semidirect
461. C2×#102C2×D11semidirect
545. C2×M16C22×D11semidirect
578. #117C22×D11semidirect
610. #102C22×D11semidirect
611. #102C22×D11semidirect
618. C2×C11#3325semidirect
740. C11C2×#3325semidirect
875. C2#13080854direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230632
C2×D4×C22⋊D112
#130808542
C2×#106223732
C2×#106226162
C2×#106223922
C2×#106223742
C2×#106227482
C2×#106223952
C2×#106223992
C2×#106223862
C2×#106228302
C2×#106223692
C2×#106227412
C2×#106223832
C2×C11×#4182
C2×#332511