Finite Group Databasebeta

← C2×#13080759 #15630333

Subgroups — C2×#13080759 #15630333

Order 2816.

2642 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×#10623096C211yesmaximal, characteristic, complemented
2C2×D4×D44C211yesmaximal, characteristic, complemented
3#13080759C2116yesmaximal, direct product factor
4C2×#10622326C211yesmaximal, characteristic, complemented
5C2×#10622348C211yesmaximal, characteristic, complemented
6C2×#10622350C211yesmaximal, characteristic, complemented
7C2×#10622460C211yesmaximal, characteristic, complemented
8C2×#10622748C211yesmaximal, characteristic, complemented
9C2×#10622728C211yesmaximal, characteristic, complemented
10C2×#10622456C211yesmaximal, characteristic, complemented
11C2×#10622345C211yesmaximal, characteristic, complemented
12C2×#10622345C211yesmaximal, characteristic, complemented
13C2×#10622324C211yesmaximal, characteristic, complemented
14C2×#10622744C211yesmaximal, characteristic, complemented
15C22×#66885C211yesmaximal, characteristic, complemented
16C2×C11×#435C211yesmaximal, characteristic, complemented
17C22×D4×D11—21no—
18C23×D44C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C22×C11×M16C2211yescharacteristic, complemented
21C23×C8×C11C2211yescharacteristic, complemented
22C2×C4×D4×C11C2211yescharacteristic
23C2×#66992—21no—
24C2×#66983C2211yescharacteristic
25C2×#66983C2211yescharacteristic
26C2×#66983C2211yescharacteristic, complemented
27C2×#66983C2211yescharacteristic, complemented
28C2×#66979C2211yescharacteristic, complemented
29C22×C4⋊Dic11C2211yescharacteristic, complemented
30C22×D88C2211yescharacteristic
31C22×D88C2211yescharacteristic, complemented
32C22×D88C2211yescharacteristic, complemented
33#10623096—24no—
34#10623096C2218yescomplemented
35D4×D44—24no—
36D4×D44C2218yescomplemented
37C2×#66951—21no—
38C2×#66948—21no—
39C2×#66936—21no—
40C2×#66935—21no—
41C2×#66935—21no—
42C2×(C22⋊D11)⋊C4—21no—
43C2×#66927C2211yescharacteristic
44C2×C4×D44C2211yescharacteristic
45C2×C4×D44C2211yescharacteristic, complemented
46C2×#66923C2211yescharacteristic, complemented
47C11×#435C2218yescomplemented
48C2×C11×C4⋊C8C2211yescharacteristic, complemented
49C2×C11×C22⋊C8C2211yescharacteristic, complemented
50C2×C11×C22⋊C8C2211yescharacteristic, complemented
51C2×C11×#97C2211yescharacteristic, complemented
52#10622748C2218yescomplemented
53#10622744C2218yescomplemented
54#10622728C2218yescomplemented
55C2×#66885C2211yescharacteristic
56C2×#66885C2211yescharacteristic
57C2×#66885C2211yescharacteristic
58C2×#66885C2218yescomplemented
59C2×#66885C2211yescharacteristic, complemented
60C2×#66885C2211yescharacteristic, complemented
61C2×#66885C2211yescharacteristic, complemented
62C2×#66885C2211yescharacteristic, complemented
63C2×#66885C2211yescharacteristic, complemented
64C2×#66885C2211yescharacteristic, complemented
65C2×#66885C2211yescharacteristic, complemented
66C2×#66882C2211yescharacteristic, complemented
67C2×#66881C2211yescharacteristic, complemented
68C2×#66881C2211yescharacteristic, complemented
69#10622460C2218yescomplemented
70#10622456C2218yescomplemented
71#10622350C2218yescomplemented
72#10622348C2218yescomplemented
73#10622345C2218yescomplemented
74#10622345C2218yescomplemented
75#10622326C2218yescomplemented
76#10622324C2218yescomplemented
77C24×D11—21no—
78C24×D11—21no—
79C22×D4×C11D411yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C23×Dic11—21no—
87C2×D4×D11—28no—
88C2×D4×D11—48no—
89C22×D44—24no—
90C22×D44—24no—
91C22×D44—21no—
92C22×D44—21no—
93C22×D44—21no—
94C22×D44—22no—
95C22×D44—22no—
96C22×D44—21no—
97C22×D44—42no—
98C22×D44—42no—
99C22×D44C2311yescharacteristic
100C22×D44C2311yescharacteristic
101C22×D44C2311yescharacteristic
102C22×D44C2314yes—
103C22×D44C2314yes—
104C22×D44C2311yescharacteristic
105C22×C4×D11—21no—
106C22×C4×D11—21no—
107C2×C11×M16—42no—
108C2×C11×M16C2314yescomplemented
109C22×C8×C11—42no—
110C22×C8×C11C2311yescharacteristic
111C22×C8×C11C2311yescharacteristic
112C22×C8×C11C2311yescharacteristic
113C22×C8×C11C2311yescharacteristic
114C22×C8×C11C2314yescomplemented
115C4×D4×C11D414yes—
116C4×D4×C11C2314yes—
117C2×C11×C4⋊C4D411yescharacteristic
118C2×C11×C22⋊C4D411yescharacteristic
119C2×C11×C22⋊C4D411yescharacteristic
120C2×C42×C11C2311yescharacteristic
121C2×C22⋊Dic11—21no—
122#66992—28no—
123#66983—22no—
124#66983—22no—
125#66983—22no—
126#66983—22no—
127#66983C2314yes—
128#66983C2314yes—
129#66983C2314yescomplemented
130#66983C2314yescomplemented
131C2×(C2×D11)⋊C4—21no—
132C2×(C2×D11)⋊C4—21no—
133C2×(C2×D11)⋊C4—21no—
134C2×(C2×D11)⋊C4—21no—
135C2×(C2×D11)⋊C4—21no—
136C2×(C2×D11)⋊C4—21no—
137#66979—22no—
138#66979C2314yescomplemented
139C2×C4⋊Dic11—21no—
140C2×C4⋊Dic11—22no—
141C2×C4⋊Dic11C2311yescharacteristic
142C2×C4⋊Dic11C2311yescharacteristic
143C2×C4⋊Dic11C2311yescharacteristic
144C2×C4⋊Dic11C2311yescharacteristic
145C2×C4⋊Dic11C2314yescomplemented
146C2×Dic11⋊C4—21no—
147C2×Dic11⋊C4—21no—
148C2×C4×Dic11—21no—
149C2×D88—24no—
150C2×D88—42no—
151C2×D88—42no—
152C2×D88C2314yes—
153C2×D88C2314yescomplemented
154C2×D88C2314yescomplemented
155#66951—28no—
156#66948—28no—
157#66936—28no—
158#66935—28no—
159#66935—28no—
160(C22⋊D11)⋊C4—28no—
161#66927—22no—
162#66927C2314yes—
163C4×D44—22no—
164C4×D44—22no—
165C4×D44C2314yes—
166C4×D44C2314yescomplemented
167#66923—22no—
168#66923C2314yescomplemented
169C11×C4⋊C8C2314yescomplemented
170C11×C22⋊C8C2314yescomplemented
171C11×C22⋊C8C2314yescomplemented
172C11×#97C2314yescomplemented
173#66885C2314yes—
174#66885C2314yes—
175#66885C2314yes—
176#66885C2314yescomplemented
177#66885C2314yescomplemented
178#66885C2314yescomplemented
179#66885C2314yescomplemented
180#66885C2314yescomplemented
181#66885C2314yescomplemented
182#66885C2314yescomplemented
183#66882C2314yescomplemented
184#66881C2314yescomplemented
185#66881C2314yescomplemented
186C2×#3318—111nomaximal, Sylow
187C24×C11C2×D411yescharacteristic
188C24×C11C2×D411yescharacteristic
189C23×D11—21no—
190C23×D11—21no—
191C23×D11—21no—
192C23×D11—21no—
193C23×D11—24no—
194C23×D11—24no—
195C23×D11—44no—
196C23×D11—44no—
197C23×D11—44no—
198C23×D11—44no—
199C23×D11—82no—
200C23×D11—82no—
201C2×D4×C11—24no—
202C2×D4×C11C2×D414yes—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2×D412yes—
212C22×C4×C11C2×D412yes—
213C22×C4×C11C2412yes—
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—44no—
221C2×C22⋊D11—44no—
222C2×C22⋊D11—44no—
223C2×C22⋊D11—82no—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C22×Dic11—21no—
227C22×Dic11—21no—
228C22×Dic11—24no—
229C22×Dic11—82no—
230D4×D11—432no—
231C2×D44—28no—
232C2×D44—28no—
233C2×D44—21no—
234C2×D44—21no—
235C2×D44—21no—
236C2×D44—21no—
237C2×D44—24no—
238C2×D44—24no—
239C2×D44—24no—
240C2×D44—24no—
241C2×D44—22no—
242C2×D44—22no—
243C2×D44—22no—
244C2×D44—22no—
245C2×D44—22no—
246C2×D44—22no—
247C2×D44—22no—
248C2×D44—44no—
249C2×D44—44no—
250C2×D44—44no—
251C2×D44—44no—
252C2×D44—48no—
253C2×D44—48no—
254C2×D44—44no—
255C2×D44—82no—
256C2×D44#4114yes—
257C2×D44C2412yes—
258C2×D44C2412yes—
259C2×D44C2412yes—
260C2×D44C2412yes—
261C2×C4×D11—24no—
262C2×C4×D11—24no—
263C2×C4×D11—44no—
264C2×C4×D11—82no—
265C11×M16—44no—
266C2×C8×C11—22no—
267C2×C8×C11—22no—
268C2×C8×C11—22no—
269C2×C8×C11—22no—
270C2×C8×C11—44no—
271C2×C8×C11C2412yes—
272C2×C8×C11C2412yes—
273C2×C8×C11C2412yes—
274C2×C8×C11C2412yes—
275C11×C4⋊C4C2×D414yes—
276C11×C22⋊C4C2×D414yes—
277C11×C22⋊C4C2×D414yes—
278C42×C11C2×D412yes—
279C42×C11C2412yes—
280C22⋊Dic11—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)⋊C4—24no—
287C4⋊Dic11—21no—
288C4⋊Dic11—21no—
289C4⋊Dic11—21no—
290C4⋊Dic11—21no—
291C4⋊Dic11—24no—
292C4⋊Dic11C2412yes—
293C4⋊Dic11C2412yes—
294C4⋊Dic11C2412yes—
295C4⋊Dic11C2412yes—
296Dic11⋊C4—24no—
297Dic11⋊C4—24no—
298C4×Dic11—24no—
299D88—28no—
300D88—44no—
301D88—44no—
302C2×#553—111no—
303C2×D42—111no—
304#3318—1116no—
305C2×#490—111no—
306C2×#481—111no—
307C2×#482—111no—
308C2×#478—111no—
309C2×#469—111no—
310C2×#466—111no—
311C2×#459—111no—
312C2×#447—111no—
313C2×#447—111no—
314C2×#442—111no—
315C2×#435D1111yescharacteristic, complemented
316C2×#418—111no—
317C22×#102—111no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11AGL(1,ℤ/8)14yes—
324C23×C11C22×D412yes—
325C23×C11C22×D412yes—
326C23×C11C22×D411yescharacteristic
327C22×D11—24no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—48no—
333C22×D11—48no—
334C22×D11—42no—
335C22×D11—42no—
336C22×D11—48no—
337C22×D11—42no—
338C22×D11—42no—
339C22×D11—42no—
340C22×D11—42no—
341C22×D11—42no—
342C22×D11—48no—
343C22×D11—42no—
344C22×D11—42no—
345C22×D11—42no—
346C22×D11—42no—
347C22×D11—84no—
348C22×D11—84no—
349C22×D11—816no—
350C22×D11—816no—
351D4×C11—28no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—24no—
357C2×C4×C11—24no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11C22×D412yes—
363C2×C4×C11C22×D412yes—
364C2×C4×C11C22×D412yes—
365C2×C4×C11C22×D412yes—
366C2×C4×C11C22×D411yescharacteristic
367C2×C4×C11C2×#4112yes—
368C2×C4×C11H(5,𝔽2)12yes—
369C2×C4×C11C2511yescharacteristic
370C22⋊D11—48no—
371C22⋊D11—48no—
372C22⋊D11—48no—
373C22⋊D11—84no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—42no—
379C2×Dic11—42no—
380C2×Dic11—42no—
381C2×Dic11—42no—
382C2×Dic11—84no—
383D44—24no—
384D44—22no—
385D44—22no—
386D44—22no—
387D44—22no—
388D44—22no—
389D44—22no—
390D44—22no—
391D44—48no—
392D44—48no—
393D44—48no—
394D44—42no—
395D44—42no—
396D44—42no—
397D44—84no—
398D44C2×#4114yes—
399C4×D11—48no—
400C4×D11—84no—
401C8×C11—22no—
402C8×C11—22no—
403C8×C11—22no—
404C8×C11—22no—
405C23×D4—111no—
406C23×D4—111no—
407C23×D4—221no—
408C22×D8—111no—
409C22×D8—111no—
410C22×D8—111no—
411C22×M16C2×D1111yescharacteristic, complemented
412C23×C8C2×D1111yescharacteristic, complemented
413#553—118no—
414#553—224no—
415D42—118no—
416D42—224no—
417C2×#127—111no—
418C2×#126—221no—
419C2×#125—111no—
420C2×#123—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—221no—
432C2×C4×D4C2×D1111yescharacteristic
433C2×#117—111no—
434C22×C4⋊C4—111no—
435#490—118no—
436#482—118no—
437#481—118no—
438#478—118no—
439#469—118no—
440#466—118no—
441#459—118no—
442#447—118no—
443#447—118no—
444#442—118no—
445#435C2×D1118yescomplemented
446C2×#107—111no—
447C2×#106—111no—
448C2×#106—111no—
449C2×C4⋊C8C2×D1111yescharacteristic, complemented
450#418—118no—
451C2×#102—111no—
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×#102—111no—
461C2×#102—118no—
462C2×C22⋊C8C2×D1111yescharacteristic, complemented
463C2×C22⋊C8C2×D1111yescharacteristic, complemented
464C2×#97C2×D1111yescharacteristic, complemented
465C22×C11—22no—
466C22×C11—28no—
467C22×C11—22no—
468C22×C11—22no—
469C22×C11—22no—
470C22×C11—22no—
471C22×C11—44no—
472C22×C11#54612yes—
473C22×C11C2×AGL(1,ℤ/8)14yes—
474C22×C11C2×AGL(1,ℤ/8)12yes—
475C22×C11#57612yes—
476C22×C11C23×D411yescharacteristic
477C2×D11—24no—
478C2×D11—48no—
479C2×D11—42no—
480C2×D11—42no—
481C2×D11—42no—
482C2×D11—42no—
483C2×D11—42no—
484C2×D11—42no—
485C2×D11—42no—
486C2×D11—42no—
487C2×D11—42no—
488C2×D11—42no—
489C2×D11—42no—
490C2×D11—816no—
491C2×D11—816no—
492C2×D11—84no—
493C2×D11—84no—
494C2×D11—84no—
495C4×C11—22no—
496C4×C11—22no—
497C4×C11—22no—
498C4×C11—22no—
499C4×C11#54612yes—
500C4×C11C22×#4111yescharacteristic
501C4×C11C2×H(5,𝔽2)11yescharacteristic
502Dic11—42no—
503Dic11—42no—
504Dic11—42no—
505Dic11—42no—
506C25—221no—
507C25—221no—
508C22×D4—111no—
509C22×D4—111no—
510C22×D4—111no—
511C22×D4—111no—
512C22×D4—114no—
513C22×D4—114no—
514C22×D4—224no—
515C22×D4—224no—
516C22×D4—221no—
517C22×D4—221no—
518C22×D4—221no—
519C22×D4—221no—
520C22×D4—228no—
521C22×D4—221no—
522C22×D4—221no—
523C22×D4—221no—
524C22×D4—222no—
525C22×D4—222no—
526C22×D4—221no—
527C22×D4—442no—
528C22×D4—442no—
529C22×D4—448no—
530C22×D4D4411yescharacteristic
531C23×C4—221no—
532C23×C4—221no—
533C23×C4—221no—
534C23×C4C22×D1111yescharacteristic
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×M16C22×D1114yescomplemented
544C22×C8—42no—
545C22×C8C22×D1111yescharacteristic
546C22×C8C22×D1111yescharacteristic
547C22×C8C22×D1111yescharacteristic
548C22×C8C22×D1111yescharacteristic
549C22×C8C22×D1114yescomplemented
550#127—114no—
551#127—222no—
552#126—228no—
553#125—114no—
554#125—222no—
555#123—228no—
556#121—114no—
557#121—114no—
558#121—114no—
559#121—114no—
560#121—228no—
561#121—222no—
562#121—222no—
563#121—222no—
564#121—222no—
565#121—228no—
566#120—228no—
567#120—228no—
568C4×D4—114no—
569C4×D4—114no—
570C4×D4—228no—
571C4×D4—222no—
572C4×D4—222no—
573C4×D4D4414yes—
574C4×D4C22×D1114yes—
575#117—114no—
576#117—222no—
577C2×C4⋊C4—111no—
578C2×C4⋊C4—111no—
579C2×C4⋊C4—114no—
580C2×C4⋊C4—111no—
581C2×C4⋊C4—111no—
582C2×C4⋊C4—221no—
583C2×C4⋊C4—222no—
584C2×C4⋊C4—221no—
585C2×C4⋊C4—221no—
586C2×C4⋊C4D4411yescharacteristic
587C2×C22⋊C4—221no—
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⋊C4D4411yescharacteristic
595C2×C22⋊C4D4411yescharacteristic
596C2×C42—221no—
597C2×C42C22×D1111yescharacteristic
598#107—114no—
599#106—114no—
600#106—114no—
601C4⋊C8C22×D1114yescomplemented
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#102—114no—
611#102—114no—
612C22⋊C8C22×D1114yescomplemented
613C22⋊C8C22×D1114yescomplemented
614#97C22×D1114yescomplemented
615C2×C11—24no—
616C2×C11—42no—
617C2×C11#331814yescomplemented
618C2×C11C2×#54611yescharacteristic
619C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
620C2×C11C2×#57611yescharacteristic
621D11—44no—
622D11—82no—
623D11—82no—
624D11—82no—
625C24—221no—
626C24—221no—
627C24—221no—
628C24—221no—
629C24—224no—
630C24—224no—
631C24—444no—
632C24—444no—
633C24—444no—
634C24—444no—
635C24—882no—
636C24—882no—
637C24C2×D4411yescharacteristic
638C24C2×D4411yescharacteristic
639C2×D4—24no—
640C2×D4—114no—
641C2×D4—112no—
642C2×D4—112no—
643C2×D4—112no—
644C2×D4—112no—
645C2×D4—228no—
646C2×D4—228no—
647C2×D4—224no—
648C2×D4—224no—
649C2×D4—224no—
650C2×D4—224no—
651C2×D4—221no—
652C2×D4—221no—
653C2×D4—224no—
654C2×D4—224no—
655C2×D4—224no—
656C2×D4—221no—
657C2×D4—221no—
658C2×D4—224no—
659C2×D4—222no—
660C2×D4—222no—
661C2×D4—222no—
662C2×D4—222no—
663C2×D4—222no—
664C2×D4—222no—
665C2×D4—222no—
666C2×D4—444no—
667C2×D4—444no—
668C2×D4—448no—
669C2×D4—448no—
670C2×D4—444no—
671C2×D4—444no—
672C2×D4—444no—
673C2×D4—4432no—
674C2×D4—444no—
675C2×D4—444no—
676C2×D4—444no—
677C2×D4—882no—
678C2×D4—882no—
679C2×D4C2×D4414yes—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—221no—
685C22×C4—221no—
686C22×C4—221no—
687C22×C4—221no—
688C22×C4—224no—
689C22×C4—224no—
690C22×C4—224no—
691C22×C4—444no—
692C22×C4—882no—
693C22×C4—882no—
694C22×C4C2×D4412yes—
695C22×C4C2×D4412yes—
696C22×C4C2×D4411yescharacteristic
697C22×C4C2×D4411yescharacteristic
698C22×C4C2×D4411yescharacteristic
699C22×C4C2×D4411yescharacteristic
700C22×C4C23×D1112yes—
701C22×C4C23×D1112yes—
702C22×C4C23×D1111yescharacteristic
703D8—228no—
704D8—444no—
705D8—444no—
706M16—44no—
707C2×C8—22no—
708C2×C8—22no—
709C2×C8—22no—
710C2×C8—22no—
711C2×C8—44no—
712C2×C8C23×D1112yes—
713C2×C8C23×D1112yes—
714C2×C8C23×D1112yes—
715C2×C8C23×D1112yes—
716C4⋊C4—112no—
717C4⋊C4—112no—
718C4⋊C4—112no—
719C4⋊C4—112no—
720C4⋊C4—221no—
721C4⋊C4—221no—
722C4⋊C4—224no—
723C4⋊C4—221no—
724C4⋊C4—221no—
725C4⋊C4—224no—
726C4⋊C4—224no—
727C4⋊C4C2×D4414yes—
728C22⋊C4—224no—
729C22⋊C4—224no—
730C22⋊C4—224no—
731C22⋊C4—224no—
732C22⋊C4—224no—
733C22⋊C4—224no—
734C22⋊C4—224no—
735C22⋊C4C2×D4414yes—
736C22⋊C4C2×D4414yes—
737C42—224no—
738C42C2×D4412yes—
739C42C23×D1112yes—
740C11C2×#331811yescharacteristic, complemented, Sylow
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—224no—
747C23—222no—
748C23—222no—
749C23—222no—
750C23—222no—
751C23—448no—
752C23—448no—
753C23—448no—
754C23—442no—
755C23—442no—
756C23—448no—
757C23—442no—
758C23—442no—
759C23—442no—
760C23—442no—
761C23—442no—
762C23—442no—
763C23—442no—
764C23—442no—
765C23—442no—
766C23—884no—
767C23—884no—
768C23—8816no—
769C23—8816no—
770C23#6696114yes—
771C23C22×D4412yes—
772C23C22×D4412yes—
773C23C22×D4411yescharacteristic
774D4—28no—
775D4—114no—
776D4—224no—
777D4—222no—
778D4—222no—
779D4—222no—
780D4—222no—
781D4—222no—
782D4—222no—
783D4—222no—
784D4—448no—
785D4—448no—
786D4—448no—
787D4—448no—
788D4—448no—
789D4—448no—
790D4—442no—
791D4—442no—
792D4—442no—
793D4—884no—
794D4—884no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—222no—
806C2×C4—222no—
807C2×C4—222no—
808C2×C4—222no—
809C2×C4—448no—
810C2×C4—442no—
811C2×C4—442no—
812C2×C4—442no—
813C2×C4—442no—
814C2×C4—884no—
815C2×C4—884no—
816C2×C4C22×D4412yes—
817C2×C4C22×D4412yes—
818C2×C4C22×D4412yes—
819C2×C4C22×D4412yes—
820C2×C4C22×D4411yescharacteristic
821C2×C4#6703712yes—
822C2×C4#41×D1112yes—
823C2×C4C24×D1111yescharacteristic
824C8—22no—
825C8—22no—
826C8—22no—
827C8—22no—
828C22—28no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—44no—
835C22—224no—
836C22—448no—
837C22—442no—
838C22—442no—
839C22—442no—
840C22—442no—
841C22—442no—
842C22—442no—
843C22—442no—
844C22—442no—
845C22—442no—
846C22—442no—
847C22—442no—
848C22—8816no—
849C22—8816no—
850C22—884no—
851C22—884no—
852C22—884no—
853C22#1062308512yes—
854C22C2×#6696114yes—
855C22C2×#6696112yes—
856C22#1062328312yes—
857C22C23×D4411yescharacteristic
858C4—22no—
859C4—22no—
860C4—22no—
861C4—22no—
862C4—442no—
863C4—442no—
864C4—442no—
865C4—442no—
866C4#1062308512yes—
867C4C2×#6703711yescharacteristic
868C4C2×#41×D1111yescharacteristic
869C2—24no—
870C2—42no—
871C2—444no—
872C2—882no—
873C2—882no—
874C2—882no—
875C2#1308075914yesdirect product factor
876C2C2×#1062308511yescharacteristic
877C2C22×#6696111yescharacteristic
878C2C2×#1062328311yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#435C2
socleC23×C11C22×D4
hypercenterC2×#435D11
hypocenterC11C2×#3318
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#10623096C2semidirect
2. C2×D4×D44C2semidirect
3. #13080759C2direct (N × H)
4. C2×#10622326C2semidirect
5. C2×#10622348C2semidirect
6. C2×#10622350C2semidirect
7. C2×#10622460C2semidirect
8. C2×#10622748C2semidirect
9. C2×#10622728C2semidirect
10. C2×#10622456C2semidirect
11. C2×#10622345C2semidirect
12. C2×#10622345C2semidirect
13. C2×#10622324C2semidirect
14. C2×#10622744C2semidirect
15. C22×#66885C2semidirect
16. C2×C11×#435C2semidirect
20. C22×C11×M16C22semidirect
21. C23×C8×C11C22semidirect
26. C2×#66983C22semidirect
27. C2×#66983C22semidirect
28. C2×#66979C22semidirect
29. C22×C4⋊Dic11C22semidirect
31. C22×D88C22semidirect
32. C22×D88C22semidirect
34. #10623096C22semidirect
36. D4×D44C22semidirect
45. C2×C4×D44C22semidirect
46. C2×#66923C22semidirect
47. C11×#435C22semidirect
48. C2×C11×C4⋊C8C22semidirect
49. C2×C11×C22⋊C8C22semidirect
50. C2×C11×C22⋊C8C22semidirect
51. C2×C11×#97C22semidirect
52. #10622748C22semidirect
53. #10622744C22semidirect
54. #10622728C22semidirect
58. C2×#66885C22semidirect
59. C2×#66885C22semidirect
60. C2×#66885C22semidirect
61. C2×#66885C22semidirect
62. C2×#66885C22semidirect
63. C2×#66885C22semidirect
64. C2×#66885C22semidirect
65. C2×#66885C22semidirect
66. C2×#66882C22semidirect
67. C2×#66881C22semidirect
68. C2×#66881C22semidirect
69. #10622460C22semidirect
70. #10622456C22semidirect
71. #10622350C22semidirect
72. #10622348C22semidirect
73. #10622345C22semidirect
74. #10622345C22semidirect
75. #10622326C22semidirect
76. #10622324C22semidirect
108. C2×C11×M16C23semidirect
114. C22×C8×C11C23semidirect
129. #66983C23semidirect
130. #66983C23semidirect
138. #66979C23semidirect
145. C2×C4⋊Dic11C23semidirect
153. C2×D88C23semidirect
154. C2×D88C23semidirect
166. C4×D44C23semidirect
168. #66923C23semidirect
169. C11×C4⋊C8C23semidirect
170. C11×C22⋊C8C23semidirect
171. C11×C22⋊C8C23semidirect
172. C11×#97C23semidirect
176. #66885C23semidirect
177. #66885C23semidirect
178. #66885C23semidirect
179. #66885C23semidirect
180. #66885C23semidirect
181. #66885C23semidirect
182. #66885C23semidirect
183. #66882C23semidirect
184. #66881C23semidirect
185. #66881C23semidirect
315. C2×#435D11semidirect
411. C22×M16C2×D11semidirect
412. C23×C8C2×D11semidirect
445. #435C2×D11semidirect
449. C2×C4⋊C8C2×D11semidirect
462. C2×C22⋊C8C2×D11semidirect
463. C2×C22⋊C8C2×D11semidirect
464. C2×#97C2×D11semidirect
543. C2×M16C22×D11semidirect
549. C22×C8C22×D11semidirect
601. C4⋊C8C22×D11semidirect
612. C22⋊C8C22×D11semidirect
613. C22⋊C8C22×D11semidirect
614. #97C22×D11semidirect
617. C2×C11#3318semidirect
740. C11C2×#3318semidirect
875. C2#13080759direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230962
C2×D4×D442
#130807592
C2×#106223262
C2×#106223482
C2×#106223502
C2×#106224602
C2×#106227482
C2×#106227282
C2×#106224562
C2×#106223452
C2×#106223242
C2×#106227442
C22×#668852
C2×C11×#4352
C2×#331811