Finite Group Databasebeta

← C2×#13079431 #15624374

Subgroups — C2×#13079431 #15624374

Order 2816.

2686 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623158C211yesmaximal, characteristic, complemented
2C2×D11×#121C211yesmaximal, characteristic, complemented
3#13079431C2116yesmaximal, direct product factor
4C2×#10622498C211yesmaximal, characteristic, complemented
5C2×#10622392C211yesmaximal, characteristic, complemented
6C2×#10622418C211yesmaximal, characteristic, complemented
7C2×#10622495C211yesmaximal, characteristic, complemented
8C2×#10622748C211yesmaximal, characteristic, complemented
9C2×#10622652C211yesmaximal, characteristic, complemented
10C2×#10622662C211yesmaximal, characteristic, complemented
11C2×#10622424C211yesmaximal, characteristic, complemented
12C2×#10622785C211yesmaximal, characteristic, complemented
13C2×#10622782C211yesmaximal, characteristic, complemented
14C2×#10622386C211yesmaximal, characteristic, complemented
15C2×#10622739C211yesmaximal, characteristic, complemented
16C2×C11×#468C211yesmaximal, characteristic, complemented
17C22×#4343C2211yescharacteristic, complemented
18C22×D4×D11—21no—
19C22×D4×D11C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C22×C11×SD16C2211yescharacteristic, complemented
22C22×C11×M16C2211yescharacteristic, complemented
23C2×C11×C22⋊Q8C2211yescharacteristic, complemented
24C2×C11×#121C2211yescharacteristic
25C2×#66999C2211yescharacteristic
26C22×#4325C2211yescharacteristic, complemented
27C2×#66992—21no—
28C2×#66991C2211yescharacteristic
29C22×#4323C2211yescharacteristic, complemented
30C2×#66983C2211yescharacteristic
31C2×#66983C2211yescharacteristic, complemented
32C22×#4318C2211yescharacteristic, complemented
33C22×D88C2211yescharacteristic, complemented
34#10623158—24no—
35#10623158C2218yescomplemented
36D11×#121—24no—
37D11×#121C2218yescomplemented
38C2×#66948C2211yescharacteristic
39C2×#66948C2211yescharacteristic
40C2×#66947—21no—
41C2×#66946—21no—
42C2×#66945C2211yescharacteristic, complemented
43C2×C4⋊C4×D11C2211yescharacteristic
44C2×#66937—21no—
45C2×#66935—21no—
46C2×(C22⋊D11)⋊C4—21no—
47C2×C22⋊C4×D11—21no—
48C11×#468C2218yescomplemented
49C2×C11×#107C2211yescharacteristic, complemented
50C2×C11×#103C2211yescharacteristic, complemented
51C2×C11×#102C2211yescharacteristic, complemented
52C2×#66899C2211yescharacteristic, complemented
53C2×#66896C2211yescharacteristic, complemented
54#10622785C2218yescomplemented
55#10622782C2218yescomplemented
56#10622748C2218yescomplemented
57#10622739C2218yescomplemented
58C2×#66885C2211yescharacteristic, complemented
59C2×#66885C2211yescharacteristic, complemented
60C2×(C2×D11)⋊C8C2211yescharacteristic
61C2×(C2×D11)⋊C8C2211yescharacteristic
62C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
63C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
64C2×#66881C2211yescharacteristic, complemented
65#10622662C2218yescomplemented
66#10622652C2218yescomplemented
67C2×#66873C2211yescharacteristic, complemented
68C2×#66873C2211yescharacteristic, complemented
69C2×#66872C2211yescharacteristic, complemented
70C2×#66871C2211yescharacteristic, complemented
71#10622498C2218yescomplemented
72#10622495C2218yescomplemented
73#10622424C2218yescomplemented
74#10622418C2218yescomplemented
75#10622392C2218yescomplemented
76#10622386C2218yescomplemented
77C24×D11—21no—
78C24×D11D411yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11—21no—
81C22×D4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C22×C22⋊D11—21no—
87C23×Dic11D411yescharacteristic
88C2×#4343—22no—
89C2×#4343—42no—
90C2×#4343—42no—
91C2×#4343C2314yescomplemented
92C2×D4×D11—28no—
93C2×D4×D11—22no—
94C2×D4×D11—42no—
95C2×D4×D11—42no—
96C2×D4×D11—48no—
97C2×D4×D11C2314yes—
98C22×D44—21no—
99C22×D44—21no—
100C22×D44—21no—
101C22×D44C2311yescharacteristic
102C22×D44C2311yescharacteristic
103C22×C4×D11—21no—
104C22×C4×D11—21no—
105C22×C4×D11—42no—
106C22×C4×D11—42no—
107C22×C4×D11D411yescharacteristic
108C22×C4×D11D411yescharacteristic
109C22×C4×D11D414yes—
110C22×C4×D11C2311yescharacteristic
111C22×C4×D11C2311yescharacteristic
112C22×C4×D11C2314yes—
113C2×C11×SD16—42no—
114C2×C11×SD16C2314yescomplemented
115C2×C11×M16—42no—
116C2×C11×M16C2314yescomplemented
117C22×C8×C11C2311yescharacteristic
118C22×C8×C11C2311yescharacteristic
119C11×C22⋊Q8—22no—
120C11×C22⋊Q8C2314yescomplemented
121C11×#121—22no—
122C11×#121C2314yes—
123C2×C11×C4⋊C4—21no—
124C2×C11×C4⋊C4C2311yescharacteristic
125C2×C11×C4⋊C4C2311yescharacteristic
126C2×C11×C22⋊C4—21no—
127C2×C11×C22⋊C4—21no—
128C2×C22⋊Dic11—21no—
129#66999—22no—
130#66999C2314yes—
131C2×#4325—42no—
132C2×#4325C2314yescomplemented
133#66992—28no—
134#66991—22no—
135#66991C2314yes—
136C2×#4323—42no—
137C2×#4323C2314yescomplemented
138#66983—22no—
139#66983—22no—
140#66983C2314yes—
141#66983C2314yescomplemented
142C2×(C2×D11)⋊C4—21no—
143C2×(C2×D11)⋊C4—21no—
144C2×(C2×D11)⋊C4—21no—
145C2×(C2×D11)⋊C4—21no—
146C2×(C2×D11)⋊C4—21no—
147C2×(C2×D11)⋊C4—21no—
148C2×C4⋊Dic11C2311yescharacteristic
149C2×C4⋊Dic11C2311yescharacteristic
150C2×Dic11⋊C4—21no—
151C2×Dic11⋊C4—21no—
152C2×C4×Dic11—21no—
153C2×#4318—42no—
154C2×#4318C2314yescomplemented
155C22×C11⋊C8C2311yescharacteristic
156C22×C11⋊C8C2311yescharacteristic
157C2×D88—42no—
158C2×D88C2314yescomplemented
159#66948—22no—
160#66948—22no—
161#66948C2314yes—
162#66948C2314yes—
163#66947—28no—
164#66946—28no—
165#66945—22no—
166#66945C2314yescomplemented
167C4⋊C4×D11—22no—
168C4⋊C4×D11C2314yes—
169#66937—28no—
170#66935—28no—
171(C22⋊D11)⋊C4—28no—
172C22⋊C4×D11—28no—
173C11×#107C2314yescomplemented
174C11×#103C2314yescomplemented
175C11×#102C2314yescomplemented
176#66899C2314yescomplemented
177#66896C2314yescomplemented
178#66885C2314yescomplemented
179#66885C2314yescomplemented
180(C2×D11)⋊C8C2314yes—
181(C2×D11)⋊C8C2314yes—
182(C2×D11)⋊C8C2314yescomplemented
183(C2×D11)⋊C8C2314yescomplemented
184#66881C2314yescomplemented
185#66873C2314yescomplemented
186#66873C2314yescomplemented
187#66872C2314yescomplemented
188#66871C2314yescomplemented
189C2×#3194—111nomaximal, Sylow
190C24×C11—21no—
191C24×C11C2×D411yescharacteristic
192C23×D11—24no—
193C23×D11—21no—
194C23×D11—21no—
195C23×D11—24no—
196C23×D11—42no—
197C23×D11—42no—
198C23×D11—44no—
199C23×D11—44no—
200C23×D11—44no—
201C23×D11C2×D411yescharacteristic
202C23×D11C2×D411yescharacteristic
203C23×D11C2×D414yes—
204C2×Q8×C11—21no—
205C2×Q8×C11—22no—
206C2×Q8×C11—22no—
207C2×Q8×C11C2412yes—
208C2×D4×C11—24no—
209C2×D4×C11—21no—
210C2×D4×C11—22no—
211C2×D4×C11—22no—
212C2×D4×C11—44no—
213C2×D4×C11C2412yes—
214C22×C4×C11—22no—
215C22×C4×C11—22no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11C2×D411yescharacteristic
220C22×C4×C11C2×D412yes—
221C22×C4×C11C2412yes—
222C22×C4×C11C2411yescharacteristic
223C2×C22⋊D11—24no—
224C2×C22⋊D11—24no—
225C2×C22⋊D11—24no—
226C2×C22⋊D11—24no—
227C2×C22⋊D11—44no—
228C2×C22⋊D11—44no—
229C2×C22⋊D11—44no—
230C2×C22⋊D11—44no—
231C22×Dic11—21no—
232C22×Dic11—21no—
233C22×Dic11—42no—
234C22×Dic11C2×D411yescharacteristic
235C22×Dic11C2×D411yescharacteristic
236C22×Dic11C2×D414yes—
237#4343—44no—
238#4343—44no—
239#4343—48no—
240D4×D11—44no—
241D4×D11—44no—
242D4×D11—432no—
243D4×D11—48no—
244C2×D44—24no—
245C2×D44—24no—
246C2×D44—24no—
247C2×D44—21no—
248C2×D44—21no—
249C2×D44—22no—
250C2×D44—22no—
251C2×D44—22no—
252C2×D44—22no—
253C2×D44—44no—
254C2×D44—44no—
255C2×D44—44no—
256C2×D44C2412yes—
257C2×D44C2412yes—
258C2×C4×D11—24no—
259C2×C4×D11—24no—
260C2×C4×D11—22no—
261C2×C4×D11—22no—
262C2×C4×D11—22no—
263C2×C4×D11—22no—
264C2×C4×D11—42no—
265C2×C4×D11—42no—
266C2×C4×D11—48no—
267C2×C4×D11—44no—
268C2×C4×D11—44no—
269C2×C4×D11—44no—
270C2×C4×D11—44no—
271C2×C4×D11C2×D412yes—
272C2×C4×D11C2×D412yes—
273C2×C4×D11C2×D414yes—
274C2×C4×D11C2×D414yes—
275C2×C4×D11C2412yes—
276C2×C4×D11C2412yes—
277C11×SD16—44no—
278C11×M16—44no—
279C2×C8×C11—22no—
280C2×C8×C11—22no—
281C2×C8×C11C2412yes—
282C2×C8×C11C2412yes—
283C11×C4⋊C4—21no—
284C11×C4⋊C4—21no—
285C11×C4⋊C4—24no—
286C11×C4⋊C4C2412yes—
287C11×C4⋊C4C2412yes—
288C11×C22⋊C4—24no—
289C11×C22⋊C4—24no—
290C22⋊Dic11—24no—
291#4325—44no—
292#4323—44no—
293(C2×D11)⋊C4—24no—
294(C2×D11)⋊C4—24no—
295(C2×D11)⋊C4—24no—
296(C2×D11)⋊C4—24no—
297(C2×D11)⋊C4—24no—
298(C2×D11)⋊C4—24no—
299C4⋊Dic11—21no—
300C4⋊Dic11—21no—
301C4⋊Dic11C2412yes—
302C4⋊Dic11C2412yes—
303Dic11⋊C4—24no—
304Dic11⋊C4—24no—
305C4×Dic11—24no—
306#4318—44no—
307C2×C11⋊C8—22no—
308C2×C11⋊C8—22no—
309C2×C11⋊C8C2412yes—
310C2×C11⋊C8C2412yes—
311D88—44no—
312C2×#525—111no—
313C22×#121—111no—
314#3194—1116no—
315C2×#482—111no—
316C2×#482—111no—
317C2×#483—111no—
318C2×#480—111no—
319C2×#469—111no—
320C2×#469—111no—
321C2×#468—111no—
322C2×#468D1111yescharacteristic, complemented
323C2×#449—111no—
324C2×#449—111no—
325C2×#450—111no—
326C2×#447—111no—
327C2×#407—111no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—42no—
333C23×C11—42no—
334C23×C11—42no—
335C23×C11C22×D412yes—
336C23×C11C22×D411yescharacteristic
337C22×D11—22no—
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—22no—
342C22×D11—28no—
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—44no—
346C22×D11—44no—
347C22×D11—416no—
348C22×D11—48no—
349C22×D11—48no—
350C22×D11—42no—
351C22×D11—42no—
352C22×D11—42no—
353C22×D11—42no—
354C22×D11—42no—
355C22×D11—42no—
356C22×D11—48no—
357C22×D11—816no—
358C22×D11AGL(1,ℤ/8)14yes—
359C22×D11C22×D412yes—
360C22×D11C22×D412yes—
361Q8×C11—22no—
362Q8×C11—22no—
363Q8×C11—42no—
364D4×C11—22no—
365D4×C11—22no—
366D4×C11—48no—
367D4×C11—42no—
368C2×C4×C11—22no—
369C2×C4×C11—24no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—42no—
376C2×C4×C11—42no—
377C2×C4×C11—42no—
378C2×C4×C11C22×D412yes—
379C2×C4×C11C22×D411yescharacteristic
380C2×C4×C11H(5,𝔽2)12yes—
381C2×C4×C11H(5,𝔽2)12yes—
382C2×C4×C11C2511yescharacteristic
383C22⋊D11—48no—
384C22⋊D11—48no—
385C22⋊D11—48no—
386C22⋊D11—48no—
387C2×Dic11—22no—
388C2×Dic11—22no—
389C2×Dic11—22no—
390C2×Dic11—22no—
391C2×Dic11—44no—
392C2×Dic11—42no—
393C2×Dic11—42no—
394C2×Dic11C22×D412yes—
395C2×Dic11C22×D412yes—
396D44—22no—
397D44—22no—
398D44—22no—
399D44—22no—
400D44—48no—
401D44—48no—
402D44—48no—
403D44—42no—
404D44—42no—
405C4×D11—24no—
406C4×D11—24no—
407C4×D11—22no—
408C4×D11—22no—
409C4×D11—22no—
410C4×D11—22no—
411C4×D11—44no—
412C4×D11—44no—
413C4×D11—48no—
414C4×D11—48no—
415C8×C11—22no—
416C8×C11—22no—
417C11⋊C8—22no—
418C11⋊C8—22no—
419C22×#41—111no—
420C23×D4—111no—
421C23×D4—221no—
422C24×C4—111no—
423C22×SD16—111no—
424C22×SD16C2×D1111yescharacteristic, complemented
425C22×D8—111no—
426C22×D8—111no—
427C22×M16—111no—
428C22×M16C2×D1111yescharacteristic, complemented
429#525—118no—
430#525—224no—
431C2×#123—221no—
432C2×C22⋊Q8—111no—
433C2×C22⋊Q8C2×D1111yescharacteristic, complemented
434C2×#121—111no—
435C2×#121—111no—
436C2×#121—111no—
437C2×#121—118no—
438C2×#121—111no—
439C2×#121—111no—
440C2×#121—221no—
441C2×#121—224no—
442C2×#121—221no—
443C2×#121C2×D1111yescharacteristic
444C2×#120—221no—
445C2×C4×D4—221no—
446C2×C4×D4—221no—
447C2×#117—111no—
448C22×C4⋊C4—111no—
449C22×C22⋊C4—221no—
450#483—118no—
451#482—118no—
452#482—118no—
453#480—118no—
454#469—118no—
455#469—118no—
456#468—118no—
457#468C2×D1118yescomplemented
458#450—118no—
459#449—118no—
460#449—118no—
461#447—118no—
462C2×#107—111no—
463C2×#107C2×D1111yescharacteristic, complemented
464C2×#106—111no—
465C2×#106—111no—
466C2×#103—111no—
467C2×#103C2×D1111yescharacteristic, complemented
468C2×#102—111no—
469C2×#102—111no—
470C2×#102—111no—
471C2×#102—111no—
472C2×#102—111no—
473C2×#102C2×D1111yescharacteristic, complemented
474#407—118no—
475C2×C22⋊C8—111no—
476C2×C22⋊C8—111no—
477C2×C22⋊C8—111no—
478C2×C22⋊C8—111no—
479C22×C11—22no—
480C22×C11—22no—
481C22×C11—22no—
482C22×C11—44no—
483C22×C11—42no—
484C22×C11—42no—
485C22×C11—42no—
486C22×C11—84no—
487C22×C11#53412yes—
488C22×C11C2×AGL(1,ℤ/8)12yes—
489C22×C11#57512yes—
490C22×C11C23×D411yescharacteristic
491C2×D11—22no—
492C2×D11—28no—
493C2×D11—22no—
494C2×D11—22no—
495C2×D11—22no—
496C2×D11—22no—
497C2×D11—416no—
498C2×D11—44no—
499C2×D11—42no—
500C2×D11—42no—
501C2×D11—42no—
502C2×D11—42no—
503C2×D11—42no—
504C2×D11—42no—
505C2×D11—816no—
506C2×D11—84no—
507C2×D11—84no—
508C2×D11C2×AGL(1,ℤ/8)14yes—
509C4×C11—22no—
510C4×C11—42no—
511C4×C11—42no—
512C4×C11—42no—
513C4×C11#53412yes—
514C4×C11C2×H(5,𝔽2)11yescharacteristic
515C4×C11C2×H(5,𝔽2)11yescharacteristic
516Dic11—22no—
517Dic11—22no—
518Dic11—42no—
519Dic11—42no—
520C25—111no—
521C25—221no—
522C2×#41—114no—
523C2×#41—222no—
524C2×#41—442no—
525C2×#41—442no—
526C22×Q8C22×D1111yescharacteristic
527C22×D4—21no—
528C22×D4—114no—
529C22×D4—111no—
530C22×D4—111no—
531C22×D4—221no—
532C22×D4—221no—
533C22×D4—221no—
534C22×D4—222no—
535C22×D4—221no—
536C22×D4—228no—
537C22×D4—221no—
538C22×D4—221no—
539C22×D4—221no—
540C22×D4—442no—
541C22×D4—442no—
542C22×D4—448no—
543C22×D4C22×D1111yescharacteristic
544C23×C4—111no—
545C23×C4—111no—
546C23×C4—111no—
547C23×C4—111no—
548C23×C4—111no—
549C23×C4—114no—
550C23×C4—114no—
551C23×C4—221no—
552C23×C4—221no—
553C23×C4—442no—
554C23×C4—442no—
555C23×C4C22×D1111yescharacteristic
556C2×SD16—42no—
557C2×SD16—114no—
558C2×SD16—442no—
559C2×SD16C22×D1114yescomplemented
560C2×D8—114no—
561C2×D8—114no—
562C2×D8—442no—
563C2×D8—442no—
564C2×M16—42no—
565C2×M16—114no—
566C2×M16—442no—
567C2×M16C22×D1114yescomplemented
568C22×C8—111no—
569C22×C8—111no—
570C22×C8C22×D1111yescharacteristic
571C22×C8C22×D1111yescharacteristic
572#123—228no—
573C22⋊Q8—22no—
574C22⋊Q8—114no—
575C22⋊Q8—222no—
576C22⋊Q8C22×D1114yescomplemented
577#121—22no—
578#121—114no—
579#121—114no—
580#121—114no—
581#121—114no—
582#121—114no—
583#121—228no—
584#121—222no—
585#121—222no—
586#121—222no—
587#121—228no—
588#121—222no—
589#121—222no—
590#121C22×D1114yes—
591#120—228no—
592C4×D4—228no—
593C4×D4—228no—
594#117—114no—
595#117—222no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—111no—
598C2×C4⋊C4—111no—
599C2×C4⋊C4—114no—
600C2×C4⋊C4—222no—
601C2×C4⋊C4—221no—
602C2×C4⋊C4—221no—
603C2×C4⋊C4C22×D1111yescharacteristic
604C2×C4⋊C4C22×D1111yescharacteristic
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—228no—
608C2×C22⋊C4—221no—
609C2×C22⋊C4—221no—
610C2×C22⋊C4—221no—
611C2×C22⋊C4—221no—
612C2×C22⋊C4—221no—
613C2×C22⋊C4—221no—
614C2×C22⋊C4—221no—
615C2×C42—221no—
616#107—114no—
617#107C22×D1114yescomplemented
618#106—114no—
619#106—114no—
620#103—114no—
621#103C22×D1114yescomplemented
622#102—114no—
623#102—114no—
624#102—114no—
625#102—114no—
626#102—114no—
627#102C22×D1114yescomplemented
628C22⋊C8—114no—
629C22⋊C8—114no—
630C22⋊C8—114no—
631C22⋊C8—114no—
632C2×C11—42no—
633C2×C11—82no—
634C2×C11#319414yescomplemented
635C2×C11C2×#53411yescharacteristic
636C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
637C2×C11C2×#57511yescharacteristic
638D11—24no—
639D11—42no—
640D11—82no—
641D11—82no—
642C24—21no—
643C24—111no—
644C24—111no—
645C24—114no—
646C24—224no—
647C24—224no—
648C24—221no—
649C24—221no—
650C24—442no—
651C24—442no—
652C24—444no—
653C24—444no—
654C24—444no—
655C24D4×D1111yescharacteristic
656#41—444no—
657#41—444no—
658#41—448no—
659C2×Q8—21no—
660C2×Q8—22no—
661C2×Q8—22no—
662C2×Q8C23×D1112yes—
663C2×D4—24no—
664C2×D4—21no—
665C2×D4—22no—
666C2×D4—22no—
667C2×D4—44no—
668C2×D4—112no—
669C2×D4—112no—
670C2×D4—224no—
671C2×D4—224no—
672C2×D4—224no—
673C2×D4—224no—
674C2×D4—224no—
675C2×D4—224no—
676C2×D4—224no—
677C2×D4—221no—
678C2×D4—221no—
679C2×D4—222no—
680C2×D4—222no—
681C2×D4—222no—
682C2×D4—222no—
683C2×D4—444no—
684C2×D4—444no—
685C2×D4—444no—
686C2×D4—444no—
687C2×D4—444no—
688C2×D4—448no—
689C2×D4—444no—
690C2×D4—4432no—
691C2×D4—444no—
692C2×D4—444no—
693C2×D4—444no—
694C2×D4C23×D1112yes—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—111no—
701C22×C4—111no—
702C22×C4—114no—
703C22×C4—112no—
704C22×C4—112no—
705C22×C4—112no—
706C22×C4—112no—
707C22×C4—114no—
708C22×C4—114no—
709C22×C4—224no—
710C22×C4—224no—
711C22×C4—222no—
712C22×C4—222no—
713C22×C4—222no—
714C22×C4—222no—
715C22×C4—221no—
716C22×C4—221no—
717C22×C4—448no—
718C22×C4—444no—
719C22×C4—444no—
720C22×C4—442no—
721C22×C4—442no—
722C22×C4—444no—
723C22×C4—444no—
724C22×C4—442no—
725C22×C4D4×D1112yes—
726C22×C4D4×D1111yescharacteristic
727C22×C4C23×D1112yes—
728C22×C4C23×D1111yescharacteristic
729SD16—44no—
730SD16—444no—
731D8—444no—
732D8—444no—
733M16—44no—
734M16—444no—
735C2×C8—22no—
736C2×C8—22no—
737C2×C8—112no—
738C2×C8—112no—
739C2×C8—222no—
740C2×C8—222no—
741C2×C8C23×D1112yes—
742C2×C8C23×D1112yes—
743C4⋊C4—24no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—112no—
747C4⋊C4—112no—
748C4⋊C4—224no—
749C4⋊C4—224no—
750C4⋊C4—221no—
751C4⋊C4—221no—
752C4⋊C4C23×D1112yes—
753C4⋊C4C23×D1112yes—
754C22⋊C4—24no—
755C22⋊C4—24no—
756C22⋊C4—224no—
757C22⋊C4—224no—
758C22⋊C4—224no—
759C22⋊C4—224no—
760C22⋊C4—224no—
761C22⋊C4—224no—
762C22⋊C4—224no—
763C42—224no—
764C11C2×#319411yescharacteristic, complemented, Sylow
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—114no—
773C23—112no—
774C23—112no—
775C23—228no—
776C23—222no—
777C23—222no—
778C23—222no—
779C23—222no—
780C23—222no—
781C23—222no—
782C23—222no—
783C23—444no—
784C23—444no—
785C23—448no—
786C23—4416no—
787C23—448no—
788C23—448no—
789C23—442no—
790C23—442no—
791C23—442no—
792C23—442no—
793C23—442no—
794C23—442no—
795C23—8816no—
796C23C2×D4×D1112yes—
797C23C2×D4×D1111yescharacteristic
798Q8—22no—
799Q8—22no—
800Q8—42no—
801D4—22no—
802D4—22no—
803D4—48no—
804D4—42no—
805D4—222no—
806D4—222no—
807D4—222no—
808D4—222no—
809D4—448no—
810D4—448no—
811D4—448no—
812D4—448no—
813D4—448no—
814D4—448no—
815D4—448no—
816D4—442no—
817D4—442no—
818C2×C4—22no—
819C2×C4—24no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—112no—
829C2×C4—112no—
830C2×C4—222no—
831C2×C4—222no—
832C2×C4—224no—
833C2×C4—224no—
834C2×C4—222no—
835C2×C4—222no—
836C2×C4—222no—
837C2×C4—222no—
838C2×C4—222no—
839C2×C4—222no—
840C2×C4—444no—
841C2×C4—444no—
842C2×C4—448no—
843C2×C4—448no—
844C2×C4—444no—
845C2×C4—442no—
846C2×C4—442no—
847C2×C4C2×D4×D1112yes—
848C2×C4C2×D4×D1111yescharacteristic
849C2×C4#6703712yes—
850C2×C4#6704212yes—
851C2×C4C24×D1111yescharacteristic
852C8—22no—
853C8—22no—
854C8—222no—
855C8—222no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—44no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—84no—
864C22—114no—
865C22—222no—
866C22—228no—
867C22—222no—
868C22—222no—
869C22—222no—
870C22—222no—
871C22—4416no—
872C22—444no—
873C22—442no—
874C22—442no—
875C22—442no—
876C22—442no—
877C22—442no—
878C22—442no—
879C22—8816no—
880C22—884no—
881C22—884no—
882C22#1062313612yes—
883C22D11×AGL(1,ℤ/8)12yes—
884C22#1062330812yes—
885C22C22×D4×D1111yescharacteristic
886C4—22no—
887C4—42no—
888C4—42no—
889C4—42no—
890C4—222no—
891C4—222no—
892C4—442no—
893C4—442no—
894C4#1062313612yes—
895C4C2×#6703711yescharacteristic
896C4C2×#6704211yescharacteristic
897C2—42no—
898C2—82no—
899C2—224no—
900C2—442no—
901C2—882no—
902C2—882no—
903C2#1307943114yesdirect product factor
904C2C2×#1062313611yescharacteristic
905C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
906C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#468C2
socleC23×C11C22×D4
hypercenterC2×#468D11
hypocenterC11C2×#3194
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#468

Complements

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

NH ≅ G/Ntype
1. C2×#10623158C2semidirect
2. C2×D11×#121C2semidirect
3. #13079431C2direct (N × H)
4. C2×#10622498C2semidirect
5. C2×#10622392C2semidirect
6. C2×#10622418C2semidirect
7. C2×#10622495C2semidirect
8. C2×#10622748C2semidirect
9. C2×#10622652C2semidirect
10. C2×#10622662C2semidirect
11. C2×#10622424C2semidirect
12. C2×#10622785C2semidirect
13. C2×#10622782C2semidirect
14. C2×#10622386C2semidirect
15. C2×#10622739C2semidirect
16. C2×C11×#468C2semidirect
17. C22×#4343C22semidirect
21. C22×C11×SD16C22semidirect
22. C22×C11×M16C22semidirect
23. C2×C11×C22⋊Q8C22semidirect
26. C22×#4325C22semidirect
29. C22×#4323C22semidirect
31. C2×#66983C22semidirect
32. C22×#4318C22semidirect
33. C22×D88C22semidirect
35. #10623158C22semidirect
37. D11×#121C22semidirect
42. C2×#66945C22semidirect
48. C11×#468C22semidirect
49. C2×C11×#107C22semidirect
50. C2×C11×#103C22semidirect
51. C2×C11×#102C22semidirect
52. C2×#66899C22semidirect
53. C2×#66896C22semidirect
54. #10622785C22semidirect
55. #10622782C22semidirect
56. #10622748C22semidirect
57. #10622739C22semidirect
58. C2×#66885C22semidirect
59. C2×#66885C22semidirect
62. C2×(C2×D11)⋊C8C22semidirect
63. C2×(C2×D11)⋊C8C22semidirect
64. C2×#66881C22semidirect
65. #10622662C22semidirect
66. #10622652C22semidirect
67. C2×#66873C22semidirect
68. C2×#66873C22semidirect
69. C2×#66872C22semidirect
70. C2×#66871C22semidirect
71. #10622498C22semidirect
72. #10622495C22semidirect
73. #10622424C22semidirect
74. #10622418C22semidirect
75. #10622392C22semidirect
76. #10622386C22semidirect
91. C2×#4343C23semidirect
114. C2×C11×SD16C23semidirect
116. C2×C11×M16C23semidirect
120. C11×C22⋊Q8C23semidirect
132. C2×#4325C23semidirect
137. C2×#4323C23semidirect
141. #66983C23semidirect
154. C2×#4318C23semidirect
158. C2×D88C23semidirect
166. #66945C23semidirect
173. C11×#107C23semidirect
174. C11×#103C23semidirect
175. C11×#102C23semidirect
176. #66899C23semidirect
177. #66896C23semidirect
178. #66885C23semidirect
179. #66885C23semidirect
182. (C2×D11)⋊C8C23semidirect
183. (C2×D11)⋊C8C23semidirect
184. #66881C23semidirect
185. #66873C23semidirect
186. #66873C23semidirect
187. #66872C23semidirect
188. #66871C23semidirect
322. C2×#468D11semidirect
424. C22×SD16C2×D11semidirect
428. C22×M16C2×D11semidirect
433. C2×C22⋊Q8C2×D11semidirect
457. #468C2×D11semidirect
463. C2×#107C2×D11semidirect
467. C2×#103C2×D11semidirect
473. C2×#102C2×D11semidirect
559. C2×SD16C22×D11semidirect
567. C2×M16C22×D11semidirect
576. C22⋊Q8C22×D11semidirect
617. #107C22×D11semidirect
621. #103C22×D11semidirect
627. #102C22×D11semidirect
634. C2×C11#3194semidirect
764. C11C2×#3194semidirect
903. C2#13079431direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231582
C2×D11×#1212
#130794312
C2×#106224982
C2×#106223922
C2×#106224182
C2×#106224952
C2×#106227482
C2×#106226522
C2×#106226622
C2×#106224242
C2×#106227852
C2×#106227822
C2×#106223862
C2×#106227392
C2×C11×#4682
C2×#319411