Finite Group Databasebeta

← C2×#13080856 #15630612

Subgroups — C2×#13080856 #15630612

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×#10623140C211yesmaximal, characteristic, complemented
3#13080856C2116yesmaximal, direct product factor
4C2×#10622373C211yesmaximal, characteristic, complemented
5C2×#10622498C211yesmaximal, characteristic, complemented
6C2×#10622483C211yesmaximal, characteristic, complemented
7C2×#10622478C211yesmaximal, characteristic, complemented
8C2×#10622652C211yesmaximal, characteristic, complemented
9C2×#10622399C211yesmaximal, characteristic, complemented
10C2×#10622345C211yesmaximal, characteristic, complemented
11C2×#10622386C211yesmaximal, characteristic, complemented
12C2×#10622485C211yesmaximal, characteristic, complemented
13C2×#10622342C211yesmaximal, characteristic, complemented
14C2×#10622614C211yesmaximal, characteristic, complemented
15C2×#10622383C211yesmaximal, characteristic, complemented
16C2×C11×#482C211yesmaximal, characteristic, complemented
17C22×D4×D11—21no—
18C22×D4×D11C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic, complemented
22C2×#66993C2211yescharacteristic
23C2×#66990—21no—
24C22×#4323C2211yescharacteristic, complemented
25C2×#66983C2211yescharacteristic, complemented
26C2×C4×C22⋊D11C2211yescharacteristic
27C22×#4318C2211yescharacteristic, complemented
28C22×D88C2211yescharacteristic
29C22×D88C2211yescharacteristic, complemented
30C22×#4313C2211yescharacteristic, complemented
31#10623140—24no—
32#10623140C2218yescomplemented
33#10623063—24no—
34#10623063C2218yescomplemented
35C2×#66948C2211yescharacteristic
36C2×#66948C2211yescharacteristic, complemented
37C2×#66946C2211yescharacteristic
38C2×#66946C2211yescharacteristic, complemented
39C2×#66945C2211yescharacteristic, complemented
40C2×#66941C2211yescharacteristic, complemented
41C2×#66938—21no—
42C2×#66937—21no—
43C2×#66937—21no—
44C2×#66935—21no—
45C2×#66928—21no—
46C2×#66925—21no—
47C11×#482C2218yescomplemented
48C2×C11×#107C2211yescharacteristic, complemented
49C2×C11×#106C2211yescharacteristic, complemented
50C2×C11×#102C2211yescharacteristic, complemented
51C2×C11×#102C2211yescharacteristic, complemented
52C2×C11×C22⋊C8C2211yescharacteristic, complemented
53C2×#66896C2211yescharacteristic, complemented
54C2×#66885C2211yescharacteristic
55C2×#66885C2211yescharacteristic, complemented
56C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
57C2×Dic11⋊C8C2211yescharacteristic, complemented
58C2×C8×Dic11C2211yescharacteristic, complemented
59#10622652C2218yescomplemented
60#10622614C2218yescomplemented
61C2×#66873C2211yescharacteristic
62C2×#66873C2211yescharacteristic
63C2×#66873C2211yescharacteristic, complemented
64C2×#66873C2211yescharacteristic, complemented
65C2×#66873C2211yescharacteristic, complemented
66C2×#66872C2211yescharacteristic, complemented
67#10622498C2218yescomplemented
68#10622485C2218yescomplemented
69#10622483C2218yescomplemented
70#10622478C2218yescomplemented
71#10622399C2218yescomplemented
72#10622386C2218yescomplemented
73#10622383C2218yescomplemented
74#10622373C2218yescomplemented
75#10622345C2218yescomplemented
76#10622342C2218yescomplemented
77C24×D11—21no—
78C24×D11—21no—
79C22×D4×C11—21no—
80C22×D4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C22×C22⋊D11D411yescharacteristic
87C2×D4×D11—28no—
88C2×D4×D11—24no—
89C2×D4×D11—22no—
90C2×D4×D11—42no—
91C2×D4×D11—48no—
92C2×D4×D11C2314yes—
93C22×D44—24no—
94C22×D44—21no—
95C22×D44—21no—
96C22×D44—22no—
97C22×D44—21no—
98C22×D44—42no—
99C22×D44C2311yescharacteristic
100C22×D44C2311yescharacteristic
101C22×D44C2314yes—
102C22×D44C2311yescharacteristic
103C22×C4×D11—21no—
104C22×C4×D11—21no—
105C22×C4×D11C2311yescharacteristic
106C22×Dic22—21no—
107C22×C8×C11C2311yescharacteristic
108C22×C8×C11C2311yescharacteristic
109C11×#121—22no—
110C11×#121C2314yes—
111C11×#117—22no—
112C11×#117C2314yescomplemented
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C22⋊C4—21no—
117C2×C11×C22⋊C4—21no—
118C2×C42×C11—21no—
119C2×C22⋊Dic11D411yescharacteristic
120#66993—22no—
121#66993C2314yes—
122#66990—28no—
123C2×#4323—42no—
124C2×#4323C2314yescomplemented
125#66983—22no—
126#66983C2314yescomplemented
127C4×C22⋊D11D414yes—
128C4×C22⋊D11C2314yes—
129C2×(C2×D11)⋊C4—21no—
130C2×(C2×D11)⋊C4—21no—
131C2×(C2×D11)⋊C4—21no—
132C2×(C2×D11)⋊C4—21no—
133C2×(C2×D11)⋊C4—21no—
134C2×(C2×D11)⋊C4—21no—
135C2×(C2×D11)⋊C4D411yescharacteristic
136C2×C4⋊Dic11C2311yescharacteristic
137C2×Dic11⋊C4—21no—
138C2×Dic11⋊C4D411yescharacteristic
139C2×C4×Dic11—21no—
140C2×C4×Dic11C2311yescharacteristic
141C2×#4318—42no—
142C2×#4318C2314yescomplemented
143C22×C11⋊C8C2311yescharacteristic
144C22×C11⋊C8C2311yescharacteristic
145C2×D88—24no—
146C2×D88—42no—
147C2×D88C2314yes—
148C2×D88C2314yescomplemented
149C2×#4313—42no—
150C2×#4313C2314yescomplemented
151#66948—22no—
152#66948—22no—
153#66948C2314yes—
154#66948C2314yescomplemented
155#66946—22no—
156#66946—22no—
157#66946C2314yes—
158#66946C2314yescomplemented
159#66945—22no—
160#66945C2314yescomplemented
161#66941—22no—
162#66941C2314yescomplemented
163#66938—28no—
164#66937—28no—
165#66937—28no—
166#66935—28no—
167#66928—28no—
168#66925—28no—
169C11×#107C2314yescomplemented
170C11×#106C2314yescomplemented
171C11×#102C2314yescomplemented
172C11×#102C2314yescomplemented
173C11×C22⋊C8C2314yescomplemented
174#66896C2314yescomplemented
175#66885C2314yes—
176#66885C2314yescomplemented
177(C2×D11)⋊C8C2314yescomplemented
178Dic11⋊C8C2314yescomplemented
179C8×Dic11C2314yescomplemented
180#66873C2314yes—
181#66873C2314yes—
182#66873C2314yescomplemented
183#66873C2314yescomplemented
184#66873C2314yescomplemented
185#66872C2314yescomplemented
186C2×#3325—111nomaximal, Sylow
187C24×C11—21no—
188C24×C11C2×D411yescharacteristic
189C23×D11—21no—
190C23×D11—21no—
191C23×D11—21no—
192C23×D11—24no—
193C23×D11—24no—
194C23×D11—44no—
195C23×D11—44no—
196C23×D11—44no—
197C23×D11—44no—
198C23×D11—82no—
199C23×D11—82no—
200C23×D11C2×D411yescharacteristic
201C2×D4×C11—24no—
202C2×D4×C11—21no—
203C2×D4×C11—22no—
204C2×D4×C11—22no—
205C2×D4×C11—44no—
206C2×D4×C11C2412yes—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2×D412yes—
214C22×C4×C11C2412yes—
215C22×C4×C11C2411yescharacteristic
216C2×C22⋊D11—24no—
217C2×C22⋊D11—24no—
218C2×C22⋊D11—24no—
219C2×C22⋊D11—24no—
220C2×C22⋊D11—24no—
221C2×C22⋊D11—44no—
222C2×C22⋊D11—44no—
223C2×C22⋊D11—82no—
224C2×C22⋊D11—82no—
225C2×C22⋊D11C2×D414yes—
226C22×Dic11—21no—
227C22×Dic11C2×D411yescharacteristic
228C22×Dic11C2×D411yescharacteristic
229C22×Dic11C2×D411yescharacteristic
230D4×D11—28no—
231D4×D11—44no—
232D4×D11—48no—
233D4×D11—432no—
234C2×D44—24no—
235C2×D44—24no—
236C2×D44—28no—
237C2×D44—21no—
238C2×D44—24no—
239C2×D44—21no—
240C2×D44—21no—
241C2×D44—22no—
242C2×D44—22no—
243C2×D44—22no—
244C2×D44—22no—
245C2×D44—22no—
246C2×D44—44no—
247C2×D44—44no—
248C2×D44—48no—
249C2×D44—44no—
250C2×D44—82no—
251C2×D44#4114yes—
252C2×D44C2412yes—
253C2×D44C2412yes—
254C2×D44C2412yes—
255C2×C4×D11—24no—
256C2×C4×D11—24no—
257C2×C4×D11—22no—
258C2×C4×D11—22no—
259C2×C4×D11—44no—
260C2×C4×D11—44no—
261C2×C4×D11C2×D412yes—
262C2×C4×D11C2412yes—
263C2×Dic22—24no—
264C2×Dic22—82no—
265C2×C8×C11—22no—
266C2×C8×C11—22no—
267C2×C8×C11C2412yes—
268C2×C8×C11C2412yes—
269C11×C4⋊C4—21no—
270C11×C4⋊C4—21no—
271C11×C4⋊C4—21no—
272C11×C4⋊C4C2412yes—
273C11×C4⋊C4C2412yes—
274C11×C4⋊C4C2412yes—
275C11×C22⋊C4—24no—
276C11×C22⋊C4—24no—
277C42×C11—24no—
278C22⋊Dic11C2×D414yes—
279#4323—44no—
280(C2×D11)⋊C4—24no—
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⋊Dic11C2412yes—
289Dic11⋊C4—24no—
290Dic11⋊C4C2×D414yes—
291C4×Dic11—24no—
292C4×Dic11C2×D412yes—
293C4×Dic11C2412yes—
294#4318—44no—
295C2×C11⋊C8—22no—
296C2×C11⋊C8—22no—
297C2×C11⋊C8C2412yes—
298C2×C11⋊C8C2412yes—
299D88—28no—
300D88—44no—
301#4313—44no—
302C2×#555—111no—
303C2×D42—111no—
304#3325—1116no—
305C2×#486—111no—
306C2×#482—111no—
307C2×#482D1111yescharacteristic, complemented
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×#418—111no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—42no—
323C23×C11—42no—
324C23×C11—42no—
325C23×C11C22×D412yes—
326C23×C11C22×D411yescharacteristic
327C22×D11—22no—
328C22×D11—24no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—48no—
335C22×D11—48no—
336C22×D11—48no—
337C22×D11—42no—
338C22×D11—42no—
339C22×D11—48no—
340C22×D11—42no—
341C22×D11—42no—
342C22×D11—42no—
343C22×D11—42no—
344C22×D11—42no—
345C22×D11—42no—
346C22×D11—84no—
347C22×D11—84no—
348C22×D11—816no—
349C22×D11—816no—
350C22×D11C22×D412yes—
351D4×C11—22no—
352D4×C11—22no—
353D4×C11—48no—
354D4×C11—42no—
355C2×C4×C11—22no—
356C2×C4×C11—24no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—42no—
363C2×C4×C11—42no—
364C2×C4×C11—42no—
365C2×C4×C11C22×D412yes—
366C2×C4×C11C22×D411yescharacteristic
367C2×C4×C11C2×#4112yes—
368C2×C4×C11H(5,𝔽2)12yes—
369C2×C4×C11C2511yescharacteristic
370C22⋊D11—28no—
371C22⋊D11—48no—
372C22⋊D11—48no—
373C22⋊D11—84no—
374C22⋊D11—84no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—42no—
379C2×Dic11AGL(1,ℤ/8)14yes—
380C2×Dic11C22×D412yes—
381C2×Dic11C22×D412yes—
382C2×Dic11C22×D412yes—
383D44—24no—
384D44—22no—
385D44—22no—
386D44—22no—
387D44—22no—
388D44—22no—
389D44—48no—
390D44—48no—
391D44—42no—
392D44—42no—
393D44—84no—
394D44C2×#4114yes—
395C4×D11—24no—
396C4×D11—22no—
397C4×D11—22no—
398C4×D11—48no—
399C4×D11—48no—
400Dic22—84no—
401C8×C11—22no—
402C8×C11—22no—
403C11⋊C8—22no—
404C11⋊C8—22no—
405C23×D4—111no—
406C23×D4—111no—
407C23×D4—221no—
408C22×D8—111no—
409C22×D8—111no—
410C22×D8—111no—
411C22×M16—111no—
412C22×M16—111no—
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—221no—
425C2×#121—221no—
426C2×#121C2×D1111yescharacteristic
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#482C2×D1118yescomplemented
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×#107C2×D1111yescharacteristic, complemented
447C2×#106—111no—
448C2×#106C2×D1111yescharacteristic, complemented
449C2×C4⋊C8—111no—
450#418—118no—
451#418—118no—
452C2×#102—111no—
453C2×#102—111no—
454C2×#102—111no—
455C2×#102—111no—
456C2×#102—111no—
457C2×#102—111no—
458C2×#102—111no—
459C2×#102—111no—
460C2×#102C2×D1111yescharacteristic, complemented
461C2×#102C2×D1111yescharacteristic, complemented
462C2×C22⋊C8—111no—
463C2×C22⋊C8C2×D1111yescharacteristic, complemented
464C2×C4×C8—111no—
465C22×C11—22no—
466C22×C11—22no—
467C22×C11—22no—
468C22×C11—44no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—42no—
472C22×C11—84no—
473C22×C11#54612yes—
474C22×C11C2×AGL(1,ℤ/8)12yes—
475C22×C11#57612yes—
476C22×C11C23×D411yescharacteristic
477C2×D11—24no—
478C2×D11—22no—
479C2×D11—22no—
480C2×D11—22no—
481C2×D11—42no—
482C2×D11—44no—
483C2×D11—48no—
484C2×D11—42no—
485C2×D11—42no—
486C2×D11—42no—
487C2×D11—42no—
488C2×D11—42no—
489C2×D11—42no—
490C2×D11—42no—
491C2×D11—816no—
492C2×D11—816no—
493C2×D11—84no—
494C2×D11—84no—
495C4×C11—22no—
496C4×C11—42no—
497C4×C11—42no—
498C4×C11—42no—
499C4×C11#54612yes—
500C4×C11C22×#4111yescharacteristic
501C4×C11C2×H(5,𝔽2)11yescharacteristic
502Dic11—22no—
503Dic11—22no—
504Dic11—42no—
505Dic11C2×AGL(1,ℤ/8)14yes—
506C25—221no—
507C25—221no—
508C22×Q8—221no—
509C22×D4—21no—
510C22×D4—111no—
511C22×D4—114no—
512C22×D4—111no—
513C22×D4—111no—
514C22×D4—111no—
515C22×D4—114no—
516C22×D4—224no—
517C22×D4—221no—
518C22×D4—221no—
519C22×D4—222no—
520C22×D4—221no—
521C22×D4—221no—
522C22×D4—221no—
523C22×D4—224no—
524C22×D4—228no—
525C22×D4—221no—
526C22×D4—221no—
527C22×D4—222no—
528C22×D4—442no—
529C22×D4—442no—
530C22×D4—448no—
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—114no—
543C2×M16—114no—
544C2×M16—442no—
545C2×M16—442no—
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—22no—
557#121—114no—
558#121—114no—
559#121—114no—
560#121—228no—
561#121—228no—
562#121—222no—
563#121—222no—
564#121—222no—
565#121C22×D1114yes—
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—221no—
582C2×C4⋊C4C22×D1111yescharacteristic
583C2×C4⋊C4C22×D1111yescharacteristic
584C2×C4⋊C4C22×D1111yescharacteristic
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—111no—
588C2×C22⋊C4—111no—
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#107C22×D1114yescomplemented
599#106—114no—
600#106C22×D1114yescomplemented
601C4⋊C8—114no—
602#102—114no—
603#102—114no—
604#102—114no—
605#102—114no—
606#102—114no—
607#102—114no—
608#102—114no—
609#102—114no—
610#102C22×D1114yescomplemented
611#102C22×D1114yescomplemented
612C22⋊C8—114no—
613C22⋊C8C22×D1114yescomplemented
614C4×C8—114no—
615C2×C11—42no—
616C2×C11—82no—
617C2×C11#332514yescomplemented
618C2×C11C2×#54611yescharacteristic
619C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
620C2×C11C2×#57611yescharacteristic
621D11—42no—
622D11—44no—
623D11—82no—
624D11—82no—
625C24—21no—
626C24—111no—
627C24—224no—
628C24—221no—
629C24—221no—
630C24—221no—
631C24—224no—
632C24—444no—
633C24—444no—
634C24—444no—
635C24—444no—
636C24—882no—
637C24—882no—
638C24D4×D1111yescharacteristic
639C2×Q8—224no—
640C2×Q8—882no—
641C2×D4—24no—
642C2×D4—21no—
643C2×D4—22no—
644C2×D4—22no—
645C2×D4—44no—
646C2×D4—114no—
647C2×D4—114no—
648C2×D4—112no—
649C2×D4—112no—
650C2×D4—112no—
651C2×D4—228no—
652C2×D4—224no—
653C2×D4—224no—
654C2×D4—224no—
655C2×D4—224no—
656C2×D4—224no—
657C2×D4—224no—
658C2×D4—228no—
659C2×D4—224no—
660C2×D4—221no—
661C2×D4—221no—
662C2×D4—224no—
663C2×D4—221no—
664C2×D4—222no—
665C2×D4—222no—
666C2×D4—222no—
667C2×D4—222no—
668C2×D4—222no—
669C2×D4—444no—
670C2×D4—448no—
671C2×D4—444no—
672C2×D4—444no—
673C2×D4—444no—
674C2×D4—444no—
675C2×D4—448no—
676C2×D4—444no—
677C2×D4—4432no—
678C2×D4—882no—
679C2×D4—882no—
680C2×D4—882no—
681C2×D4C23×D1112yes—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—111no—
688C22×C4—111no—
689C22×C4—111no—
690C22×C4—112no—
691C22×C4—112no—
692C22×C4—224no—
693C22×C4—224no—
694C22×C4—222no—
695C22×C4—222no—
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—444no—
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—21no—
719C4⋊C4—114no—
720C4⋊C4—112no—
721C4⋊C4—224no—
722C4⋊C4—221no—
723C4⋊C4C23×D1112yes—
724C4⋊C4C23×D1112yes—
725C4⋊C4C23×D1112yes—
726C22⋊C4—24no—
727C22⋊C4—24no—
728C22⋊C4—114no—
729C22⋊C4—114no—
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—22no—
743C23—22no—
744C23—22no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—112no—
749C23—222no—
750C23—222no—
751C23—222no—
752C23—224no—
753C23—222no—
754C23—222no—
755C23—222no—
756C23—448no—
757C23—448no—
758C23—448no—
759C23—448no—
760C23—442no—
761C23—442no—
762C23—442no—
763C23—442no—
764C23—442no—
765C23—442no—
766C23—442no—
767C23—442no—
768C23—884no—
769C23—884no—
770C23—8816no—
771C23—8816no—
772C23C2×D4×D1112yes—
773C23C2×D4×D1111yescharacteristic
774Q8—884no—
775D4—22no—
776D4—22no—
777D4—48no—
778D4—42no—
779D4—114no—
780D4—228no—
781D4—224no—
782D4—222no—
783D4—222no—
784D4—222no—
785D4—222no—
786D4—222no—
787D4—448no—
788D4—448no—
789D4—448no—
790D4—448no—
791D4—442no—
792D4—442no—
793D4—884no—
794D4—884no—
795D4—884no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—114no—
807C2×C4—112no—
808C2×C4—112no—
809C2×C4—112no—
810C2×C4—222no—
811C2×C4—222no—
812C2×C4—224no—
813C2×C4—222no—
814C2×C4—222no—
815C2×C4—222no—
816C2×C4—448no—
817C2×C4—448no—
818C2×C4—442no—
819C2×C4C2×D4×D1112yes—
820C2×C4C2×D4×D1111yescharacteristic
821C2×C4#41×D1112yes—
822C2×C4#6704212yes—
823C2×C4C24×D1111yescharacteristic
824C8—22no—
825C8—22no—
826C8—222no—
827C8—222no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—44no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—84no—
836C22—222no—
837C22—224no—
838C22—222no—
839C22—222no—
840C22—444no—
841C22—448no—
842C22—442no—
843C22—442no—
844C22—442no—
845C22—442no—
846C22—442no—
847C22—442no—
848C22—442no—
849C22—442no—
850C22—8816no—
851C22—8816no—
852C22—884no—
853C22—884no—
854C22#1062318512yes—
855C22#1062330012yes—
856C22D11×AGL(1,ℤ/8)12yes—
857C22C22×D4×D1111yescharacteristic
858C4—22no—
859C4—42no—
860C4—42no—
861C4—42no—
862C4—114no—
863C4—222no—
864C4—222no—
865C4—442no—
866C4#1062318512yes—
867C4C2×#41×D1111yescharacteristic
868C4C2×#6704211yescharacteristic
869C2—42no—
870C2—82no—
871C2—442no—
872C2—444no—
873C2—882no—
874C2—882no—
875C2#1308085614yesdirect product factor
876C2C2×#1062318511yescharacteristic
877C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
878C2C2×#1062330011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#482C2
socleC23×C11C22×D4
hypercenterC2×#482D11
hypocenterC11C2×#3325
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#10623063C2semidirect
2. C2×#10623140C2semidirect
3. #13080856C2direct (N × H)
4. C2×#10622373C2semidirect
5. C2×#10622498C2semidirect
6. C2×#10622483C2semidirect
7. C2×#10622478C2semidirect
8. C2×#10622652C2semidirect
9. C2×#10622399C2semidirect
10. C2×#10622345C2semidirect
11. C2×#10622386C2semidirect
12. C2×#10622485C2semidirect
13. C2×#10622342C2semidirect
14. C2×#10622614C2semidirect
15. C2×#10622383C2semidirect
16. C2×C11×#482C2semidirect
21. C2×C11×#117C22semidirect
24. C22×#4323C22semidirect
25. C2×#66983C22semidirect
27. C22×#4318C22semidirect
29. C22×D88C22semidirect
30. C22×#4313C22semidirect
32. #10623140C22semidirect
34. #10623063C22semidirect
36. C2×#66948C22semidirect
38. C2×#66946C22semidirect
39. C2×#66945C22semidirect
40. C2×#66941C22semidirect
47. C11×#482C22semidirect
48. C2×C11×#107C22semidirect
49. C2×C11×#106C22semidirect
50. C2×C11×#102C22semidirect
51. C2×C11×#102C22semidirect
52. C2×C11×C22⋊C8C22semidirect
53. C2×#66896C22semidirect
55. C2×#66885C22semidirect
56. C2×(C2×D11)⋊C8C22semidirect
57. C2×Dic11⋊C8C22semidirect
58. C2×C8×Dic11C22semidirect
59. #10622652C22semidirect
60. #10622614C22semidirect
63. C2×#66873C22semidirect
64. C2×#66873C22semidirect
65. C2×#66873C22semidirect
66. C2×#66872C22semidirect
67. #10622498C22semidirect
68. #10622485C22semidirect
69. #10622483C22semidirect
70. #10622478C22semidirect
71. #10622399C22semidirect
72. #10622386C22semidirect
73. #10622383C22semidirect
74. #10622373C22semidirect
75. #10622345C22semidirect
76. #10622342C22semidirect
112. C11×#117C23semidirect
124. C2×#4323C23semidirect
126. #66983C23semidirect
142. C2×#4318C23semidirect
148. C2×D88C23semidirect
150. C2×#4313C23semidirect
154. #66948C23semidirect
158. #66946C23semidirect
160. #66945C23semidirect
162. #66941C23semidirect
169. C11×#107C23semidirect
170. C11×#106C23semidirect
171. C11×#102C23semidirect
172. C11×#102C23semidirect
173. C11×C22⋊C8C23semidirect
174. #66896C23semidirect
176. #66885C23semidirect
177. (C2×D11)⋊C8C23semidirect
178. Dic11⋊C8C23semidirect
179. C8×Dic11C23semidirect
182. #66873C23semidirect
183. #66873C23semidirect
184. #66873C23semidirect
185. #66872C23semidirect
307. C2×#482D11semidirect
434. C2×#117C2×D11semidirect
437. #482C2×D11semidirect
446. C2×#107C2×D11semidirect
448. C2×#106C2×D11semidirect
460. C2×#102C2×D11semidirect
461. C2×#102C2×D11semidirect
463. C2×C22⋊C8C2×D11semidirect
578. #117C22×D11semidirect
598. #107C22×D11semidirect
600. #106C22×D11semidirect
610. #102C22×D11semidirect
611. #102C22×D11semidirect
613. C22⋊C8C22×D11semidirect
617. C2×C11#3325semidirect
740. C11C2×#3325semidirect
875. C2#13080856direct (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×#106231402
#130808562
C2×#106223732
C2×#106224982
C2×#106224832
C2×#106224782
C2×#106226522
C2×#106223992
C2×#106223452
C2×#106223862
C2×#106224852
C2×#106223422
C2×#106226142
C2×#106223832
C2×C11×#4822
C2×#332511