Finite Group Databasebeta

← C2×#13080578 #15630284

Subgroups — C2×#13080578 #15630284

Order 2816.

2514 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623038C211yesmaximal, characteristic, complemented
2C2×#10623360C211yesmaximal, characteristic, complemented
3#13080578C2116yesmaximal, direct product factor
4C2×#10622408C211yesmaximal, characteristic, complemented
5C2×#10622581C211yesmaximal, characteristic, complemented
6C2×#10622418C211yesmaximal, characteristic, complemented
7C2×#10622374C211yesmaximal, characteristic, complemented
8C2×#10622748C211yesmaximal, characteristic, complemented
9C2×#10622420C211yesmaximal, characteristic, complemented
10C2×#10622432C211yesmaximal, characteristic, complemented
11C2×#10622851C211yesmaximal, characteristic, complemented
12C2×#10622386C211yesmaximal, characteristic, complemented
13C2×#10622398C211yesmaximal, characteristic, complemented
14C2×#10622740C211yesmaximal, characteristic, complemented
15C2×D11×#102C211yesmaximal, characteristic, complemented
16C2×C11×#417C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C22×D4×D11C2211yescharacteristic
19C22×#4339—21no—
20C22×C11×M16C2211yescharacteristic, complemented
21C22×C11×C4⋊C4C2211yescharacteristic, complemented
22#10623360—24no—
23#10623360C2218yescomplemented
24C2×#67000C2211yescharacteristic
25C2×#66999C2211yescharacteristic
26C22×#4325C2211yescharacteristic, complemented
27C2×#66992—21no—
28C2×#66990—21no—
29C2×D4×Dic11C2211yescharacteristic
30C22×#4323C2211yescharacteristic
31C2×#66983C2211yescharacteristic
32C2×#66983C2211yescharacteristic, complemented
33C2×#66982—21no—
34C2×#66982—21no—
35C2×C4×C22⋊D11C2211yescharacteristic
36C22×(C2×D11)⋊C4—21no—
37C22×D88C2211yescharacteristic
38C22×C8×D11C2211yescharacteristic
39C2×#66949—21no—
40#10623038—24no—
41#10623038C2218yescomplemented
42C2×#66948C2211yescharacteristic
43C2×#66947—21no—
44C2×#66946C2211yescharacteristic, complemented
45C2×C4⋊C4×D11C2211yescharacteristic
46C2×#66941C2211yescharacteristic, complemented
47C11×#417C2218yescomplemented
48C2×C11×#103C2211yescharacteristic, complemented
49C2×C11×#103C2211yescharacteristic, complemented
50C2×C11×#102C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52#10622851C2218yescomplemented
53C2×#66899C2211yescharacteristic, complemented
54C2×#66896C2211yescharacteristic
55C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
56#10622748C2218yescomplemented
57#10622740C2218yescomplemented
58C2×#66885C2211yescharacteristic
59C2×#66885C2211yescharacteristic, complemented
60C2×(C2×D11)⋊C8C2211yescharacteristic
61C2×#66881C2211yescharacteristic, complemented
62C2×#66879C2211yescharacteristic, complemented
63C2×Dic11⋊C8C2211yescharacteristic, complemented
64#10622581C2218yescomplemented
65C2×#66873C2211yescharacteristic
66C2×#66873C2211yescharacteristic
67C2×#66872C2211yescharacteristic, complemented
68C2×#66872C2211yescharacteristic, complemented
69#10622432C2218yescomplemented
70#10622420C2218yescomplemented
71#10622418C2218yescomplemented
72#10622408C2218yescomplemented
73#10622398C2218yescomplemented
74#10622386C2218yescomplemented
75D11×#102C2218yescomplemented
76#10622374C2218yescomplemented
77C24×D11—21no—
78C2×C11×#41—22no—
79C2×C11×#41—24no—
80C2×C11×#41—42no—
81C2×C11×#41C2314yes—
82C22×Q8×C11C2311yescharacteristic
83C22×D4×C11—21no—
84C22×D4×C11C2311yescharacteristic
85C23×C4×C11—21no—
86C23×C4×C11—21no—
87C23×C4×C11C2311yescharacteristic
88C22×C22⋊D11—21no—
89C22×C22⋊D11—21no—
90C22×C22⋊D11—21no—
91C22×C22⋊D11D411yescharacteristic
92C23×Dic11—21no—
93C2×D4×D11—24no—
94C2×D4×D11—22no—
95C2×D4×D11—42no—
96C2×D4×D11C2314yes—
97C2×#4339—28no—
98C2×#4339—48no—
99C22×D44—21no—
100C22×D44C2311yescharacteristic
101C22×D44C2311yescharacteristic
102C22×C4×D11—21no—
103C22×C4×D11—21no—
104C22×C4×D11C2311yescharacteristic
105C22×Dic22—21no—
106C2×C11×M16—42no—
107C2×C11×M16C2314yescomplemented
108C22×C8×C11C2311yescharacteristic
109C22×C8×C11C2311yescharacteristic
110C2×C11×C4⋊C4—21no—
111C2×C11×C4⋊C4—22no—
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2314yescomplemented
115C2×C22⋊Dic11—21no—
116C2×C22⋊Dic11D411yescharacteristic
117#67000—22no—
118#67000C2314yes—
119#66999—22no—
120#66999C2314yes—
121C2×#4325—42no—
122C2×#4325C2314yescomplemented
123#66992—28no—
124#66990—28no—
125D4×Dic11—22no—
126D4×Dic11C2314yes—
127C2×#4323—24no—
128C2×#4323C2314yes—
129#66983—22no—
130#66983—22no—
131#66983C2314yes—
132#66983C2314yescomplemented
133#66982—28no—
134#66982—28no—
135C4×C22⋊D11D414yes—
136C4×C22⋊D11C2314yes—
137C2×(C2×D11)⋊C4—21no—
138C2×(C2×D11)⋊C4—21no—
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)⋊C4—28no—
145C2×(C2×D11)⋊C4D411yescharacteristic
146C2×C4⋊Dic11C2311yescharacteristic
147C2×C4⋊Dic11C2311yescharacteristic
148C2×Dic11⋊C4—21no—
149C2×Dic11⋊C4—21no—
150C2×Dic11⋊C4—21no—
151C2×Dic11⋊C4D411yescharacteristic
152C2×C4×Dic11C2311yescharacteristic
153C22×C11⋊C8C2311yescharacteristic
154C22×C11⋊C8C2311yescharacteristic
155C2×D88—42no—
156C2×D88C2314yes—
157C2×C8×D11—42no—
158C2×C8×D11C2314yes—
159#66949—28no—
160#66948—22no—
161#66948C2314yes—
162#66947—28no—
163#66946—22no—
164#66946C2314yescomplemented
165C4⋊C4×D11—22no—
166C4⋊C4×D11C2314yes—
167#66941—22no—
168#66941C2314yescomplemented
169C11×#103C2314yescomplemented
170C11×#103C2314yescomplemented
171C11×#102C2314yes—
172C11×#102C2314yes—
173#66899C2314yescomplemented
174#66896C2314yes—
175C22⋊(C11⋊C8)C2314yescomplemented
176#66885C2314yes—
177#66885C2314yescomplemented
178(C2×D11)⋊C8C2314yes—
179#66881C2314yescomplemented
180#66879C2314yescomplemented
181Dic11⋊C8C2314yescomplemented
182#66873C2314yes—
183#66873C2314yes—
184#66872C2314yescomplemented
185#66872C2314yescomplemented
186C2×#3306—111nomaximal, Sylow
187C24×C11—21no—
188C24×C11C2×D411yescharacteristic
189C23×D11—21no—
190C23×D11—21no—
191C23×D11—24no—
192C23×D11—44no—
193C23×D11—44no—
194C23×D11—82no—
195C23×D11C2×D411yescharacteristic
196C11×#41—28no—
197C11×#41—44no—
198C11×#41—48no—
199C2×Q8×C11—21no—
200C2×Q8×C11—22no—
201C2×Q8×C11—22no—
202C2×Q8×C11C2412yes—
203C2×D4×C11—24no—
204C2×D4×C11—21no—
205C2×D4×C11—22no—
206C2×D4×C11—44no—
207C2×D4×C11#4114yescomplemented
208C2×D4×C11C2412yes—
209C22×C4×C11—22no—
210C22×C4×C11—22no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—24no—
215C22×C4×C11—24no—
216C22×C4×C11—44no—
217C22×C4×C11—44no—
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—44no—
227C2×C22⋊D11—44no—
228C2×C22⋊D11—82no—
229C2×C22⋊D11C2×D414yes—
230C22×Dic11—24no—
231C22×Dic11—21no—
232C22×Dic11—21no—
233C22×Dic11—82no—
234C22×Dic11C2×D411yescharacteristic
235C22×Dic11C2×D411yescharacteristic
236C22×Dic11C2×D411yescharacteristic
237D4×D11—28no—
238D4×D11—44no—
239D4×D11—48no—
240#4339—432no—
241C2×D44—24no—
242C2×D44—21no—
243C2×D44—21no—
244C2×D44—22no—
245C2×D44—22no—
246C2×D44—22no—
247C2×D44—22no—
248C2×D44—44no—
249C2×D44C2412yes—
250C2×D44C2412yes—
251C2×C4×D11—24no—
252C2×C4×D11—24no—
253C2×C4×D11—22no—
254C2×C4×D11—22no—
255C2×C4×D11—44no—
256C2×C4×D11—44no—
257C2×C4×D11C2×D412yes—
258C2×C4×D11C2412yes—
259C2×Dic22—24no—
260C2×Dic22—44no—
261C11×M16—44no—
262C2×C8×C11—22no—
263C2×C8×C11—22no—
264C2×C8×C11C2412yes—
265C2×C8×C11C2412yes—
266C11×C4⋊C4—21no—
267C11×C4⋊C4—21no—
268C11×C4⋊C4—24no—
269C11×C4⋊C4C2412yes—
270C11×C4⋊C4C2412yes—
271C22⋊Dic11—24no—
272C22⋊Dic11C2×D414yes—
273#4325—44no—
274#4323—28no—
275(C2×D11)⋊C4—24no—
276(C2×D11)⋊C4—24no—
277(C2×D11)⋊C4—24no—
278(C2×D11)⋊C4—24no—
279(C2×D11)⋊C4—24no—
280(C2×D11)⋊C4—24no—
281(C2×D11)⋊C4—24no—
282(C2×D11)⋊C4C2×D414yes—
283C4⋊Dic11—21no—
284C4⋊Dic11—21no—
285C4⋊Dic11C2412yes—
286C4⋊Dic11C2412yes—
287Dic11⋊C4—24no—
288Dic11⋊C4—24no—
289Dic11⋊C4—24no—
290Dic11⋊C4C2×D414yes—
291C4×Dic11C2×D412yes—
292C4×Dic11C2412yes—
293C2×C11⋊C8—22no—
294C2×C11⋊C8—22no—
295C2×C11⋊C8C2412yes—
296C2×C11⋊C8C2412yes—
297D88—44no—
298C8×D11—44no—
299C2×#547—111no—
300C2×#546—111no—
301#3306—1116no—
302C2×#489—111no—
303C2×#481—111no—
304C2×#483—111no—
305C2×#476—111no—
306C2×#469—111no—
307C2×#465—111no—
308C2×#463—111no—
309C2×#449—111no—
310C2×#447—111no—
311C2×#442—111no—
312C2×#435—111no—
313C2×#417D1111yescharacteristic, complemented
314C22×#102—111no—
315C23×C11—24no—
316C23×C11—22no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—42no—
321C23×C11—42no—
322C23×C11C22×D412yes—
323C23×C11C22×D411yescharacteristic
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—48no—
329C22×D11—42no—
330C22×D11—42no—
331C22×D11—42no—
332C22×D11—42no—
333C22×D11—42no—
334C22×D11—42no—
335C22×D11—48no—
336C22×D11—84no—
337C22×D11—816no—
338C22×D11AGL(1,ℤ/8)14yes—
339C22×D11C22×D412yes—
340Q8×C11—22no—
341Q8×C11—22no—
342Q8×C11—42no—
343D4×C11—24no—
344D4×C11—22no—
345D4×C11—48no—
346D4×C11C2×#4114yescomplemented
347C2×C4×C11—22no—
348C2×C4×C11—24no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—48no—
355C2×C4×C11—48no—
356C2×C4×C11—42no—
357C2×C4×C11—42no—
358C2×C4×C11—42no—
359C2×C4×C11C22×D412yes—
360C2×C4×C11C22×D411yescharacteristic
361C2×C4×C11C2×#4112yes—
362C2×C4×C11H(5,𝔽2)12yes—
363C2×C4×C11C2511yescharacteristic
364C22⋊D11—28no—
365C22⋊D11—48no—
366C22⋊D11—48no—
367C22⋊D11—84no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—42no—
374C2×Dic11—42no—
375C2×Dic11—84no—
376C2×Dic11C22×D412yes—
377C2×Dic11C22×D412yes—
378C2×Dic11C22×D412yes—
379D44—22no—
380D44—22no—
381D44—22no—
382D44—22no—
383D44—48no—
384D44—42no—
385D44—42no—
386C4×D11—24no—
387C4×D11—22no—
388C4×D11—22no—
389C4×D11—48no—
390C4×D11—48no—
391Dic22—48no—
392C8×C11—22no—
393C8×C11—22no—
394C11⋊C8—22no—
395C11⋊C8—22no—
396C22×#41—221no—
397C22×#41C2×D1111yescharacteristic
398C23×D4—111no—
399C22×SD16—111no—
400C22×D8—111no—
401C22×D8—111no—
402C22×M16C2×D1111yescharacteristic, complemented
403C23×C8—111no—
404#547—118no—
405#547—224no—
406#546—118no—
407#546—224no—
408C2×C4⋊Q8—111no—
409C2×#124—111no—
410C2×#123—221no—
411C2×#123—221no—
412C2×#123—221no—
413C2×C22⋊Q8—111no—
414C2×C22⋊Q8—221no—
415C2×#121—111no—
416C2×#121—111no—
417C2×#121—111no—
418C2×#121—221no—
419C2×#120—221no—
420C2×C4×D4—111no—
421C2×C4×D4—111no—
422C2×C4×D4—111no—
423C22×C4⋊C4—111no—
424C22×C4⋊C4C2×D1111yescharacteristic, complemented
425C22×C22⋊C4—221no—
426#489—118no—
427#483—118no—
428#481—118no—
429#476—118no—
430#469—118no—
431#465—118no—
432#463—118no—
433#449—118no—
434#447—118no—
435#442—118no—
436#435—118no—
437C2×#106—111no—
438C2×#106—111no—
439C2×#106—111no—
440C2×C4⋊C8—111no—
441#417C2×D1118yescomplemented
442C2×#103—111no—
443C2×#103C2×D1111yescharacteristic, complemented
444C2×#103C2×D1111yescharacteristic, complemented
445C2×#102—111no—
446C2×#102—111no—
447C2×#102—111no—
448C2×#102—111no—
449C2×#102—111no—
450C2×#102—118no—
451C2×#102C2×D1111yescharacteristic
452C2×#102C2×D1111yescharacteristic
453C2×C22⋊C8—111no—
454C2×C22⋊C8—111no—
455C2×#97—111no—
456C22×C11—22no—
457C22×C11—24no—
458C22×C11—22no—
459C22×C11—22no—
460C22×C11—48no—
461C22×C11—44no—
462C22×C11—42no—
463C22×C11—42no—
464C22×C11#54612yes—
465C22×C11C2×AGL(1,ℤ/8)12yes—
466C22×C11#57712yes—
467C22×C11C23×D411yescharacteristic
468C2×D11—22no—
469C2×D11—28no—
470C2×D11—22no—
471C2×D11—42no—
472C2×D11—42no—
473C2×D11—42no—
474C2×D11—42no—
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—816no—
478C2×D11—84no—
479C2×D11—84no—
480C2×D11C2×AGL(1,ℤ/8)14yes—
481C4×C11—22no—
482C4×C11—42no—
483C4×C11—42no—
484C4×C11—42no—
485C4×C11#54612yes—
486C4×C11C22×#4111yescharacteristic
487C4×C11C2×H(5,𝔽2)11yescharacteristic
488Dic11—22no—
489Dic11—22no—
490Dic11—22no—
491Dic11—42no—
492Dic11—42no—
493C25—221no—
494C2×#41—22no—
495C2×#41—24no—
496C2×#41—42no—
497C2×#41—228no—
498C2×#41—448no—
499C2×#41C22×D1114yes—
500C22×Q8—221no—
501C22×Q8C22×D1111yescharacteristic
502C22×D4—21no—
503C22×D4—111no—
504C22×D4—114no—
505C22×D4—111no—
506C22×D4—111no—
507C22×D4—221no—
508C22×D4—222no—
509C22×D4—221no—
510C22×D4—224no—
511C22×D4—221no—
512C22×D4—221no—
513C22×D4—442no—
514C22×D4C22×D1111yescharacteristic
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—111no—
518C23×C4—221no—
519C23×C4—221no—
520C23×C4—221no—
521C23×C4C22×D1111yescharacteristic
522C2×SD16—114no—
523C2×SD16—442no—
524C2×D8—114no—
525C2×D8—114no—
526C2×D8—224no—
527C2×D8—442no—
528C2×M16—42no—
529C2×M16C22×D1114yescomplemented
530C22×C8—111no—
531C22×C8—111no—
532C22×C8—114no—
533C22×C8—442no—
534C22×C8C22×D1111yescharacteristic
535C22×C8C22×D1111yescharacteristic
536C4⋊Q8—114no—
537C4⋊Q8—222no—
538#124—114no—
539#124—222no—
540#123—228no—
541#123—228no—
542#123—228no—
543C22⋊Q8—114no—
544C22⋊Q8—228no—
545C22⋊Q8—222no—
546#121—114no—
547#121—114no—
548#121—114no—
549#121—228no—
550#121—222no—
551#121—222no—
552#121—222no—
553#120—228no—
554C4×D4—114no—
555C4×D4—114no—
556C4×D4—114no—
557C4×D4—114no—
558C4×D4—222no—
559C4×D4—222no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—111no—
563C2×C4⋊C4—111no—
564C2×C4⋊C4—111no—
565C2×C4⋊C4—114no—
566C2×C4⋊C4—222no—
567C2×C4⋊C4—221no—
568C2×C4⋊C4—221no—
569C2×C4⋊C4—221no—
570C2×C4⋊C4C22×D1111yescharacteristic
571C2×C4⋊C4C22×D1111yescharacteristic
572C2×C4⋊C4C22×D1114yescomplemented
573C2×C22⋊C4—111no—
574C2×C22⋊C4—111no—
575C2×C22⋊C4—228no—
576C2×C22⋊C4—221no—
577C2×C22⋊C4—221no—
578C2×C22⋊C4—221no—
579C2×C22⋊C4—221no—
580C2×C22⋊C4—221no—
581C2×C22⋊C4—221no—
582C2×C22⋊C4—221no—
583C2×C22⋊C4—221no—
584C2×C42—111no—
585#106—114no—
586#106—114no—
587#106—114no—
588C4⋊C8—114no—
589#103—114no—
590#103C22×D1114yescomplemented
591#103C22×D1114yescomplemented
592#102—114no—
593#102—114no—
594#102—114no—
595#102—114no—
596#102—114no—
597#102C22×D1114yes—
598#102C22×D1114yes—
599C22⋊C8—114no—
600C22⋊C8—114no—
601#97—114no—
602C2×C11—44no—
603C2×C11—42no—
604C2×C11#330614yescomplemented
605C2×C11C2×#54611yescharacteristic
606C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
607C2×C11C2×#57711yescharacteristic
608D11—24no—
609D11—82no—
610D11—82no—
611C24—21no—
612C24—111no—
613C24—224no—
614C24—221no—
615C24—221no—
616C24—444no—
617C24—444no—
618C24—882no—
619C24D4×D1111yescharacteristic
620#41—28no—
621#41—44no—
622#41—48no—
623#41—4432no—
624C2×Q8—21no—
625C2×Q8—22no—
626C2×Q8—22no—
627C2×Q8—224no—
628C2×Q8—444no—
629C2×Q8C23×D1112yes—
630C2×D4—24no—
631C2×D4—21no—
632C2×D4—22no—
633C2×D4—44no—
634C2×D4—114no—
635C2×D4—112no—
636C2×D4—112no—
637C2×D4—224no—
638C2×D4—224no—
639C2×D4—224no—
640C2×D4—228no—
641C2×D4—224no—
642C2×D4—224no—
643C2×D4—222no—
644C2×D4—222no—
645C2×D4—221no—
646C2×D4—221no—
647C2×D4—222no—
648C2×D4—222no—
649C2×D4—444no—
650C2×D4—444no—
651C2×D4—448no—
652C2×D4—444no—
653C2×D4—444no—
654C2×D4—882no—
655C2×D4#433914yescomplemented
656C2×D4C23×D1112yes—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—24no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—24no—
664C22×C4—44no—
665C22×C4—44no—
666C22×C4—111no—
667C22×C4—111no—
668C22×C4—111no—
669C22×C4—112no—
670C22×C4—112no—
671C22×C4—224no—
672C22×C4—224no—
673C22×C4—224no—
674C22×C4—222no—
675C22×C4—222no—
676C22×C4—221no—
677C22×C4—221no—
678C22×C4—444no—
679C22×C4—444no—
680C22×C4—882no—
681C22×C4D4×D1112yes—
682C22×C4D4×D1111yescharacteristic
683C22×C4C23×D1112yes—
684C22×C4C23×D1111yescharacteristic
685SD16—444no—
686D8—228no—
687D8—444no—
688M16—44no—
689C2×C8—22no—
690C2×C8—22no—
691C2×C8—112no—
692C2×C8—112no—
693C2×C8—222no—
694C2×C8—222no—
695C2×C8—444no—
696C2×C8C23×D1112yes—
697C2×C8C23×D1112yes—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—24no—
701C4⋊C4—114no—
702C4⋊C4—112no—
703C4⋊C4—112no—
704C4⋊C4—224no—
705C4⋊C4—224no—
706C4⋊C4—224no—
707C4⋊C4—221no—
708C4⋊C4—221no—
709C4⋊C4C23×D1112yes—
710C4⋊C4C23×D1112yes—
711C22⋊C4—114no—
712C22⋊C4—114no—
713C22⋊C4—224no—
714C22⋊C4—224no—
715C22⋊C4—224no—
716C22⋊C4—224no—
717C22⋊C4—224no—
718C22⋊C4—224no—
719C22⋊C4—224no—
720C22⋊C4—224no—
721C42—112no—
722C42—112no—
723C11C2×#330611yescharacteristic, complemented, Sylow
724C23—22no—
725C23—24no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—42no—
730C23—42no—
731C23—114no—
732C23—112no—
733C23—222no—
734C23—222no—
735C23—222no—
736C23—222no—
737C23—448no—
738C23—448no—
739C23—442no—
740C23—442no—
741C23—442no—
742C23—442no—
743C23—442no—
744C23—442no—
745C23—884no—
746C23—8816no—
747C23C2×D4×D1112yes—
748C23C2×D4×D1111yescharacteristic
749Q8—22no—
750Q8—22no—
751Q8—42no—
752Q8—448no—
753D4—24no—
754D4—22no—
755D4—48no—
756D4—228no—
757D4—222no—
758D4—222no—
759D4—222no—
760D4—222no—
761D4—448no—
762D4—448no—
763D4—448no—
764D4—442no—
765D4—442no—
766D4—884no—
767D4C2×#433914yescomplemented
768C2×C4—22no—
769C2×C4—24no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—48no—
776C2×C4—48no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—112no—
781C2×C4—112no—
782C2×C4—112no—
783C2×C4—222no—
784C2×C4—222no—
785C2×C4—222no—
786C2×C4—224no—
787C2×C4—222no—
788C2×C4—222no—
789C2×C4—222no—
790C2×C4—222no—
791C2×C4—448no—
792C2×C4—448no—
793C2×C4—442no—
794C2×C4—442no—
795C2×C4—884no—
796C2×C4C2×#433912yes—
797C2×C4C2×D4×D1112yes—
798C2×C4C2×D4×D1111yescharacteristic
799C2×C4#6703712yes—
800C2×C4C24×D1111yescharacteristic
801C8—22no—
802C8—22no—
803C8—222no—
804C8—222no—
805C22—22no—
806C22—24no—
807C22—22no—
808C22—22no—
809C22—44no—
810C22—48no—
811C22—42no—
812C22—42no—
813C22—114no—
814C22—228no—
815C22—222no—
816C22—222no—
817C22—442no—
818C22—442no—
819C22—442no—
820C22—442no—
821C22—442no—
822C22—442no—
823C22—8816no—
824C22—884no—
825C22—884no—
826C22#1062302112yes—
827C22D11×AGL(1,ℤ/8)12yes—
828C22#1062330912yes—
829C22C22×D4×D1111yescharacteristic
830C4—22no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—222no—
835C4—222no—
836C4—222no—
837C4—442no—
838C4—442no—
839C4#1062302112yes—
840C4C22×#433911yescharacteristic
841C4C2×#6703711yescharacteristic
842C2—42no—
843C2—44no—
844C2—224no—
845C2—882no—
846C2—882no—
847C2#1308057814yesdirect product factor
848C2C2×#1062302111yescharacteristic
849C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
850C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#417C2
socleC23×C11C22×D4
hypercenterC2×#417D11
hypocenterC11C2×#3306
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#10623038C2semidirect
2. C2×#10623360C2semidirect
3. #13080578C2direct (N × H)
4. C2×#10622408C2semidirect
5. C2×#10622581C2semidirect
6. C2×#10622418C2semidirect
7. C2×#10622374C2semidirect
8. C2×#10622748C2semidirect
9. C2×#10622420C2semidirect
10. C2×#10622432C2semidirect
11. C2×#10622851C2semidirect
12. C2×#10622386C2semidirect
13. C2×#10622398C2semidirect
14. C2×#10622740C2semidirect
15. C2×D11×#102C2semidirect
16. C2×C11×#417C2semidirect
20. C22×C11×M16C22semidirect
21. C22×C11×C4⋊C4C22semidirect
23. #10623360C22semidirect
26. C22×#4325C22semidirect
32. C2×#66983C22semidirect
41. #10623038C22semidirect
44. C2×#66946C22semidirect
46. C2×#66941C22semidirect
47. C11×#417C22semidirect
48. C2×C11×#103C22semidirect
49. C2×C11×#103C22semidirect
52. #10622851C22semidirect
53. C2×#66899C22semidirect
55. C2×C22⋊(C11⋊C8)C22semidirect
56. #10622748C22semidirect
57. #10622740C22semidirect
59. C2×#66885C22semidirect
61. C2×#66881C22semidirect
62. C2×#66879C22semidirect
63. C2×Dic11⋊C8C22semidirect
64. #10622581C22semidirect
67. C2×#66872C22semidirect
68. C2×#66872C22semidirect
69. #10622432C22semidirect
70. #10622420C22semidirect
71. #10622418C22semidirect
72. #10622408C22semidirect
73. #10622398C22semidirect
74. #10622386C22semidirect
75. D11×#102C22semidirect
76. #10622374C22semidirect
107. C2×C11×M16C23semidirect
114. C2×C11×C4⋊C4C23semidirect
122. C2×#4325C23semidirect
132. #66983C23semidirect
164. #66946C23semidirect
168. #66941C23semidirect
169. C11×#103C23semidirect
170. C11×#103C23semidirect
173. #66899C23semidirect
175. C22⋊(C11⋊C8)C23semidirect
177. #66885C23semidirect
179. #66881C23semidirect
180. #66879C23semidirect
181. Dic11⋊C8C23semidirect
184. #66872C23semidirect
185. #66872C23semidirect
207. C2×D4×C11#41semidirect
313. C2×#417D11semidirect
346. D4×C11C2×#41semidirect
402. C22×M16C2×D11semidirect
424. C22×C4⋊C4C2×D11semidirect
441. #417C2×D11semidirect
443. C2×#103C2×D11semidirect
444. C2×#103C2×D11semidirect
529. C2×M16C22×D11semidirect
572. C2×C4⋊C4C22×D11semidirect
590. #103C22×D11semidirect
591. #103C22×D11semidirect
604. C2×C11#3306semidirect
655. C2×D4#4339semidirect
723. C11C2×#3306semidirect
767. D4C2×#4339semidirect
847. C2#13080578direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230382
C2×#106233602
#130805782
C2×#106224082
C2×#106225812
C2×#106224182
C2×#106223742
C2×#106227482
C2×#106224202
C2×#106224322
C2×#106228512
C2×#106223862
C2×#106223982
C2×#106227402
C2×D11×#1022
C2×C11×#4172
C2×#330611