Finite Group Databasebeta

← C2×#13079804 #15625876

Subgroups — C2×#13079804 #15625876

Order 2816.

2050 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623079C211yesmaximal, characteristic
2C2×D11×#125C211yesmaximal, characteristic, complemented
3#13079804C2116yesmaximal, direct product factor
4C2×#10622489C211yesmaximal, characteristic, complemented
5C2×#10622469C211yesmaximal, characteristic, complemented
6C2×#10622377C211yesmaximal, characteristic, complemented
7C2×#10622377C211yesmaximal, characteristic, complemented
8C2×#10622476C211yesmaximal, characteristic, complemented
9C2×#10622390C211yesmaximal, characteristic, complemented
10C2×#10622495C211yesmaximal, characteristic, complemented
11C2×#10622387C211yesmaximal, characteristic, complemented
12C2×#10622460C211yesmaximal, characteristic, complemented
13C2×#10622622C211yesmaximal, characteristic, complemented
14C2×#10622679C211yesmaximal, characteristic, complemented
15C2×#10622448C211yesmaximal, characteristic, complemented
16C2×C11×#478C211yesmaximal, characteristic, complemented
17C22×#4339—21no—
18C2×C11×#125C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×#66993C2211yescharacteristic
21C2×#66991C2211yescharacteristic
22C2×C4×C22⋊D11—21no—
23D11×#125—24no—
24D11×#125C2218yescomplemented
25#10623079—24no—
26#10623079C2218yes—
27C2×#66948C2211yescharacteristic
28C2×C4⋊C4×D11—21no—
29C2×C4⋊C4×D11—21no—
30C2×C4⋊C4×D11C2211yescharacteristic
31C2×C4⋊C4×D11C2211yescharacteristic
32C2×#66943C2211yescharacteristic
33C2×#66943C2211yescharacteristic
34C2×#66942—21no—
35C2×#66942—21no—
36C2×#66941C2211yescharacteristic
37C2×#66938—21no—
38C2×#66937—21no—
39C2×C4×D44C2211yescharacteristic
40C2×C42×D11C2211yescharacteristic
41C2×#66923C2211yescharacteristic
42C11×#478C2218yescomplemented
43C2×C11×#107C2211yescharacteristic
44C2×C11×#106C2211yescharacteristic
45C2×C11×C4⋊C8C2211yescharacteristic
46C2×C11×#102C2211yescharacteristic
47C2×C11×#102C2211yescharacteristic
48C2×#66896C2211yescharacteristic
49C2×#66896C2211yescharacteristic
50C2×#66885C2211yescharacteristic
51C2×#66885C2211yescharacteristic
52C2×(C2×D11)⋊C8C2211yescharacteristic
53C2×(C2×D11)⋊C8C2211yescharacteristic
54C2×#66882C2211yescharacteristic
55C2×#66881C2211yescharacteristic
56C2×#66879C2211yescharacteristic
57C2×#66879C2211yescharacteristic
58#10622679C2218yescomplemented
59#10622622C2218yescomplemented
60C2×#66873C2211yescharacteristic
61C2×#66873C2211yescharacteristic
62C2×#66872C2211yescharacteristic
63C2×#66872C2211yescharacteristic
64C2×#66871C2211yescharacteristic
65C2×#66871C2211yescharacteristic
66C2×C4⋊(C11⋊C8)C2211yescharacteristic
67#10622495C2218yescomplemented
68#10622489C2218yescomplemented
69#10622476C2218yescomplemented
70#10622469C2218yescomplemented
71#10622460C2218yescomplemented
72#10622448C2218yescomplemented
73#10622390C2218yescomplemented
74#10622387C2218yescomplemented
75#10622377C2218yescomplemented
76#10622377C2218yescomplemented
77C22×D4×C11C2311yescharacteristic
78C23×C4×C11—21no—
79C22×C22⋊D11—21no—
80C22×C22⋊D11—21no—
81C22×C22⋊D11—21no—
82C2×#4339—28no—
83C2×#4339—48no—
84C22×D44—21no—
85C22×D44C2311yescharacteristic
86C22×C4×D11—21no—
87C22×C4×D11—21no—
88C22×C4×D11—21no—
89C22×C4×D11D411yescharacteristic
90C22×C4×D11D411yescharacteristic
91C22×C4×D11C2311yescharacteristic
92C22×Dic22—21no—
93C22×C8×C11C2311yescharacteristic
94C22×C8×C11C2311yescharacteristic
95C11×#125—22no—
96C11×#125C2314yes—
97C4×D4×C11—22no—
98C4×D4×C11C2314yes—
99C2×C11×C4⋊C4—21no—
100C2×C11×C4⋊C4—21no—
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C22⋊C4—21no—
105C2×C42×C11C2311yescharacteristic
106C2×C22⋊Dic11—21no—
107#66993—22no—
108#66993C2314yes—
109#66991—22no—
110#66991C2314yes—
111C4×C22⋊D11—28no—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4—21no—
114C2×C4⋊Dic11—21no—
115C2×C4⋊Dic11—21no—
116C2×C4⋊Dic11C2311yescharacteristic
117C2×C4⋊Dic11C2311yescharacteristic
118C2×C4⋊Dic11C2311yescharacteristic
119C2×Dic11⋊C4—21no—
120C2×Dic11⋊C4—21no—
121C2×Dic11⋊C4—21no—
122C2×Dic11⋊C4—21no—
123C2×Dic11⋊C4—21no—
124C2×Dic11⋊C4—21no—
125C2×Dic11⋊C4—21no—
126C2×C4×Dic11D411yescharacteristic
127C2×C4×Dic11D411yescharacteristic
128C2×C4×Dic11C2311yescharacteristic
129C22×C11⋊C8C2311yescharacteristic
130C22×C11⋊C8C2311yescharacteristic
131#66948—22no—
132#66948C2314yes—
133C4⋊C4×D11—28no—
134C4⋊C4×D11—28no—
135C4⋊C4×D11—22no—
136C4⋊C4×D11—22no—
137C4⋊C4×D11C2314yes—
138C4⋊C4×D11C2314yes—
139#66943—22no—
140#66943—22no—
141#66943C2314yes—
142#66943C2314yes—
143#66942—28no—
144#66942—28no—
145#66941—22no—
146#66941C2314yes—
147#66938—28no—
148#66937—28no—
149C4×D44—22no—
150C4×D44C2314yes—
151C42×D11D414yes—
152C42×D11C2314yes—
153#66923—22no—
154#66923C2314yes—
155C11×#107C2314yes—
156C11×#106C2314yes—
157C11×C4⋊C8C2314yes—
158C11×#102C2314yes—
159C11×#102C2314yes—
160#66896C2314yes—
161#66896C2314yes—
162#66885C2314yes—
163#66885C2314yes—
164(C2×D11)⋊C8C2314yes—
165(C2×D11)⋊C8C2314yes—
166#66882C2314yes—
167#66881C2314yes—
168#66879C2314yes—
169#66879C2314yes—
170#66873C2314yes—
171#66873C2314yes—
172#66872C2314yes—
173#66872C2314yes—
174#66871C2314yes—
175#66871C2314yes—
176C4⋊(C11⋊C8)C2314yes—
177C2×#3234—111nomaximal, Sylow
178C24×C11—21no—
179C23×D11—21no—
180C23×D11C2×D411yescharacteristic
181C2×D4×C11—21no—
182C2×D4×C11—22no—
183C2×D4×C11—22no—
184C2×D4×C11C2412yes—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—24no—
189C22×C4×C11—44no—
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2411yescharacteristic
193C2×C22⋊D11—24no—
194C2×C22⋊D11—24no—
195C2×C22⋊D11—24no—
196C2×C22⋊D11—44no—
197C2×C22⋊D11—44no—
198C2×C22⋊D11—44no—
199C22×Dic11—21no—
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11C2×D411yescharacteristic
203C22×Dic11C2×D411yescharacteristic
204C22×Dic11C2×D411yescharacteristic
205#4339—432no—
206C2×D44—24no—
207C2×D44—21no—
208C2×D44—22no—
209C2×D44—22no—
210C2×D44—44no—
211C2×D44C2412yes—
212C2×C4×D11—24no—
213C2×C4×D11—24no—
214C2×C4×D11—24no—
215C2×C4×D11—24no—
216C2×C4×D11—22no—
217C2×C4×D11—22no—
218C2×C4×D11—42no—
219C2×C4×D11—44no—
220C2×C4×D11—44no—
221C2×C4×D11—44no—
222C2×C4×D11C2×D412yes—
223C2×C4×D11C2×D414yes—
224C2×C4×D11C2×D414yes—
225C2×C4×D11C2412yes—
226C2×Dic22—24no—
227C2×Dic22—44no—
228C2×C8×C11—22no—
229C2×C8×C11—22no—
230C2×C8×C11C2412yes—
231C2×C8×C11C2412yes—
232C11×C4⋊C4—21no—
233C11×C4⋊C4—24no—
234C11×C4⋊C4—24no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4—21no—
237C11×C4⋊C4C2412yes—
238C11×C4⋊C4C2412yes—
239C11×C4⋊C4C2412yes—
240C11×C22⋊C4—24no—
241C42×C11C2×D412yes—
242C42×C11C2412yes—
243C22⋊Dic11—24no—
244(C2×D11)⋊C4—24no—
245(C2×D11)⋊C4—24no—
246C4⋊Dic11—24no—
247C4⋊Dic11—24no—
248C4⋊Dic11—21no—
249C4⋊Dic11—21no—
250C4⋊Dic11—21no—
251C4⋊Dic11C2412yes—
252C4⋊Dic11C2412yes—
253C4⋊Dic11C2412yes—
254Dic11⋊C4—24no—
255Dic11⋊C4—24no—
256Dic11⋊C4—24no—
257Dic11⋊C4—24no—
258Dic11⋊C4—24no—
259Dic11⋊C4—24no—
260Dic11⋊C4—24no—
261C4×Dic11C2×D412yes—
262C4×Dic11C2×D414yes—
263C4×Dic11C2×D414yes—
264C4×Dic11C2412yes—
265C2×C11⋊C8—22no—
266C2×C11⋊C8—22no—
267C2×C11⋊C8C2412yes—
268C2×C11⋊C8C2412yes—
269C2×#532—111no—
270C22×#125—111no—
271#3234—1116no—
272C2×#501—111no—
273C2×#501—111no—
274C2×#490—111no—
275C2×#490—111no—
276C2×#481—111no—
277C2×#481—111no—
278C2×#480—111no—
279C2×#480—111no—
280C2×#478—111no—
281C2×#478—111no—
282C2×#478—111no—
283C2×#478D1111yescharacteristic, complemented
284C2×#432—111no—
285C23×C11—22no—
286C23×C11—42no—
287C23×C11—42no—
288C23×C11—42no—
289C23×C11C22×D411yescharacteristic
290C22×D11—22no—
291C22×D11—22no—
292C22×D11—22no—
293C22×D11—42no—
294C22×D11—42no—
295C22×D11—42no—
296C22×D11AGL(1,ℤ/8)14yes—
297C22×D11C22×D412yes—
298D4×C11—22no—
299D4×C11—22no—
300D4×C11—42no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—48no—
307C2×C4×C11—42no—
308C2×C4×C11—42no—
309C2×C4×C11—42no—
310C2×C4×C11C22×D412yes—
311C2×C4×C11C22×D412yes—
312C2×C4×C11C22×D411yescharacteristic
313C2×C4×C112−1+412yes—
314C2×C4×C112−1+412yes—
315C2×C4×C11C2511yescharacteristic
316C22⋊D11—48no—
317C22⋊D11—48no—
318C22⋊D11—48no—
319C2×Dic11—22no—
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—42no—
326C2×Dic11—42no—
327C2×Dic11—42no—
328C2×Dic11C22×D412yes—
329C2×Dic11C22×D412yes—
330C2×Dic11C22×D412yes—
331D44—22no—
332D44—22no—
333D44—48no—
334D44—42no—
335C4×D11—28no—
336C4×D11—24no—
337C4×D11—22no—
338C4×D11—22no—
339C4×D11—44no—
340C4×D11—48no—
341C4×D11—48no—
342C4×D11—48no—
343Dic22—48no—
344C8×C11—22no—
345C8×C11—22no—
346C11⋊C8—22no—
347C11⋊C8—22no—
348C22×#41—221no—
349#532—118no—
350#532—224no—
351C2×C4⋊Q8—111no—
352C2×#127—111no—
353C2×#125—118no—
354C2×#125—111no—
355C2×#125—111no—
356C2×#125—111no—
357C2×#125—221no—
358C2×#125—221no—
359C2×#125—224no—
360C2×#125C2×D1111yescharacteristic
361C2×#124—221no—
362C2×#121—111no—
363C2×#121—111no—
364C2×#121—221no—
365C2×C4×D4—111no—
366C2×C4×D4—221no—
367C2×C4×D4C2×D1111yescharacteristic
368C22×C4⋊C4—111no—
369C22×C4⋊C4—111no—
370C22×C4⋊C4—221no—
371C22×C4⋊C4—221no—
372C22×C42—111no—
373#501—118no—
374#501—118no—
375#490—118no—
376#490—118no—
377#481—118no—
378#481—118no—
379#480—118no—
380#480—118no—
381#478—118no—
382#478—118no—
383#478—118no—
384#478C2×D1118yescomplemented
385#432—118no—
386C2×#107—111no—
387C2×#107—111no—
388C2×#107—111no—
389C2×#107C2×D1111yescharacteristic
390C2×#106—111no—
391C2×#106—111no—
392C2×#106—111no—
393C2×#106C2×D1111yescharacteristic
394C2×C4⋊C8—111no—
395C2×C4⋊C8C2×D1111yescharacteristic
396C2×#102—111no—
397C2×#102—111no—
398C2×#102—111no—
399C2×#102—111no—
400C2×#102—111no—
401C2×#102—111no—
402C2×#102C2×D1111yescharacteristic
403C2×#102C2×D1111yescharacteristic
404C2×C22⋊C8—111no—
405C2×C22⋊C8—111no—
406C2×#97—111no—
407C2×#97—111no—
408C22×C11—42no—
409C22×C11—42no—
410C22×C11—42no—
411C22×C11—84no—
412C22×C11#53612yes—
413C22×C11C2×AGL(1,ℤ/8)12yes—
414C22×C11#57512yes—
415C22×C11C23×D411yescharacteristic
416C2×D11—22no—
417C2×D11—28no—
418C2×D11—22no—
419C2×D11—42no—
420C2×D11—42no—
421C2×D11—42no—
422C2×D11—84no—
423C2×D11C2×AGL(1,ℤ/8)14yes—
424C4×C11—22no—
425C4×C11—22no—
426C4×C11—42no—
427C4×C11—42no—
428C4×C11—42no—
429C4×C11#53612yes—
430C4×C11C2×2−1+411yescharacteristic
431C4×C11C2×2−1+411yescharacteristic
432Dic11—22no—
433Dic11—22no—
434Dic11—22no—
435Dic11—42no—
436Dic11—42no—
437Dic11—42no—
438C2×#41—228no—
439C2×#41—448no—
440C22×Q8—221no—
441C22×D4—111no—
442C22×D4—221no—
443C22×D4—221no—
444C22×D4—221no—
445C22×D4—221no—
446C22×D4C22×D1111yescharacteristic
447C23×C4—21no—
448C23×C4—111no—
449C23×C4—111no—
450C23×C4—111no—
451C23×C4—221no—
452C23×C4—221no—
453C23×C4—221no—
454C22×C8—111no—
455C22×C8—111no—
456C22×C8C22×D1111yescharacteristic
457C22×C8C22×D1111yescharacteristic
458C4⋊Q8—114no—
459C4⋊Q8—222no—
460#127—114no—
461#127—222no—
462#125—22no—
463#125—114no—
464#125—114no—
465#125—114no—
466#125—228no—
467#125—228no—
468#125—222no—
469#125—222no—
470#125—222no—
471#125C22×D1114yes—
472#124—228no—
473#121—114no—
474#121—114no—
475#121—228no—
476#121—222no—
477#121—222no—
478C4×D4—22no—
479C4×D4—114no—
480C4×D4—228no—
481C4×D4—222no—
482C4×D4C22×D1114yes—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—111no—
486C2×C4⋊C4—111no—
487C2×C4⋊C4—111no—
488C2×C4⋊C4—114no—
489C2×C4⋊C4—114no—
490C2×C4⋊C4—222no—
491C2×C4⋊C4—222no—
492C2×C4⋊C4—228no—
493C2×C4⋊C4—228no—
494C2×C4⋊C4—221no—
495C2×C4⋊C4—221no—
496C2×C4⋊C4—221no—
497C2×C4⋊C4—221no—
498C2×C4⋊C4—221no—
499C2×C4⋊C4—221no—
500C2×C4⋊C4—221no—
501C2×C4⋊C4—221no—
502C2×C4⋊C4—221no—
503C2×C4⋊C4C22×D1111yescharacteristic
504C2×C4⋊C4C22×D1111yescharacteristic
505C2×C4⋊C4C22×D1111yescharacteristic
506C2×C22⋊C4—21no—
507C2×C22⋊C4—221no—
508C2×C22⋊C4—221no—
509C2×C22⋊C4—221no—
510C2×C42—111no—
511C2×C42—111no—
512C2×C42—111no—
513C2×C42—114no—
514C2×C42—114no—
515C2×C42C22×D1111yescharacteristic
516#107—114no—
517#107—114no—
518#107—114no—
519#107C22×D1114yes—
520#106—114no—
521#106—114no—
522#106—114no—
523#106C22×D1114yes—
524C4⋊C8—114no—
525C4⋊C8C22×D1114yes—
526#102—114no—
527#102—114no—
528#102—114no—
529#102—114no—
530#102—114no—
531#102—114no—
532#102C22×D1114yes—
533#102C22×D1114yes—
534C22⋊C8—114no—
535C22⋊C8—114no—
536#97—114no—
537#97—114no—
538C2×C11—82no—
539C2×C11#323414yescomplemented
540C2×C11C2×#53611yescharacteristic
541C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
542C2×C11C2×#57511yescharacteristic
543D11—24no—
544D11—82no—
545C24—21no—
546C24—111no—
547C24—221no—
548#41—4432no—
549C2×Q8—224no—
550C2×Q8—444no—
551C2×D4—21no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—112no—
555C2×D4—224no—
556C2×D4—224no—
557C2×D4—224no—
558C2×D4—224no—
559C2×D4—221no—
560C2×D4—222no—
561C2×D4—222no—
562C2×D4—444no—
563C2×D4—444no—
564C2×D4—444no—
565C2×D4—444no—
566C2×D4C23×D1112yes—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—24no—
571C22×C4—44no—
572C22×C4—111no—
573C22×C4—111no—
574C22×C4—111no—
575C22×C4—112no—
576C22×C4—114no—
577C22×C4—112no—
578C22×C4—114no—
579C22×C4—224no—
580C22×C4—224no—
581C22×C4—224no—
582C22×C4—222no—
583C22×C4—222no—
584C22×C4—221no—
585C22×C4—221no—
586C22×C4—221no—
587C22×C4—224no—
588C22×C4—442no—
589C22×C4—444no—
590C22×C4—444no—
591C22×C4—444no—
592C22×C4D4×D1111yescharacteristic
593C22×C4D4×D1111yescharacteristic
594C22×C4C23×D1111yescharacteristic
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—112no—
598C2×C8—112no—
599C2×C8—222no—
600C2×C8—222no—
601C2×C8C23×D1112yes—
602C2×C8C23×D1112yes—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—112no—
609C4⋊C4—112no—
610C4⋊C4—112no—
611C4⋊C4—224no—
612C4⋊C4—224no—
613C4⋊C4—224no—
614C4⋊C4—224no—
615C4⋊C4—224no—
616C4⋊C4—224no—
617C4⋊C4—224no—
618C4⋊C4—221no—
619C4⋊C4—221no—
620C4⋊C4—221no—
621C4⋊C4—224no—
622C4⋊C4—224no—
623C4⋊C4C23×D1112yes—
624C4⋊C4C23×D1112yes—
625C4⋊C4C23×D1112yes—
626C22⋊C4—24no—
627C22⋊C4—224no—
628C22⋊C4—224no—
629C22⋊C4—224no—
630C42—114no—
631C42—114no—
632C42—112no—
633C42—112no—
634C42D4×D1112yes—
635C42C23×D1112yes—
636C11C2×#323411yescharacteristic, complemented, Sylow
637C23—22no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—114no—
642C23—112no—
643C23—222no—
644C23—222no—
645C23—222no—
646C23—442no—
647C23—442no—
648C23—442no—
649C23C2×D4×D1111yescharacteristic
650Q8—448no—
651D4—22no—
652D4—22no—
653D4—42no—
654D4—222no—
655D4—222no—
656D4—448no—
657D4—448no—
658D4—448no—
659D4—448no—
660D4—442no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—48no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—112no—
671C2×C4—112no—
672C2×C4—112no—
673C2×C4—228no—
674C2×C4—222no—
675C2×C4—222no—
676C2×C4—222no—
677C2×C4—224no—
678C2×C4—222no—
679C2×C4—222no—
680C2×C4—222no—
681C2×C4—222no—
682C2×C4—222no—
683C2×C4—444no—
684C2×C4—448no—
685C2×C4—448no—
686C2×C4—448no—
687C2×C4—442no—
688C2×C4—442no—
689C2×C4—442no—
690C2×C4C2×D4×D1112yes—
691C2×C4C2×D4×D1112yes—
692C2×C4C2×D4×D1111yescharacteristic
693C2×C4#6704012yes—
694C2×C4#6704312yes—
695C2×C4C24×D1111yescharacteristic
696C8—22no—
697C8—22no—
698C8—222no—
699C8—222no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—84no—
704C22—114no—
705C22—222no—
706C22—222no—
707C22—228no—
708C22—442no—
709C22—442no—
710C22—442no—
711C22—884no—
712C22#1062315912yes—
713C22#1062329912yes—
714C22D11×AGL(1,ℤ/8)12yes—
715C22C22×D4×D1111yescharacteristic
716C4—22no—
717C4—22no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—222no—
722C4—222no—
723C4—222no—
724C4—442no—
725C4—442no—
726C4—442no—
727C4#1062315912yes—
728C4C2×#6704011yescharacteristic
729C4C2×#6704311yescharacteristic
730C2—82no—
731C2—224no—
732C2—882no—
733C2#1307980414yesdirect product factor
734C2C2×#1062315911yescharacteristic
735C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
736C2C2×#1062329911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#478C2
socleC23×C11C22×D4
prime radicalC2×#10623079C2
hypercenterC2×#478D11
hypocenterC11C2×#3234
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
2. C2×D11×#125C2semidirect
3. #13079804C2direct (N × H)
4. C2×#10622489C2semidirect
5. C2×#10622469C2semidirect
6. C2×#10622377C2semidirect
7. C2×#10622377C2semidirect
8. C2×#10622476C2semidirect
9. C2×#10622390C2semidirect
10. C2×#10622495C2semidirect
11. C2×#10622387C2semidirect
12. C2×#10622460C2semidirect
13. C2×#10622622C2semidirect
14. C2×#10622679C2semidirect
15. C2×#10622448C2semidirect
16. C2×C11×#478C2semidirect
24. D11×#125C22semidirect
42. C11×#478C22semidirect
58. #10622679C22semidirect
59. #10622622C22semidirect
67. #10622495C22semidirect
68. #10622489C22semidirect
69. #10622476C22semidirect
70. #10622469C22semidirect
71. #10622460C22semidirect
72. #10622448C22semidirect
73. #10622390C22semidirect
74. #10622387C22semidirect
75. #10622377C22semidirect
76. #10622377C22semidirect
283. C2×#478D11semidirect
384. #478C2×D11semidirect
539. C2×C11#3234semidirect
636. C11C2×#3234semidirect
733. C2#13079804direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230792
C2×D11×#1252
#130798042
C2×#106224892
C2×#106224692
C2×#106223772
C2×#106224762
C2×#106223902
C2×#106224952
C2×#106223872
C2×#106224602
C2×#106226222
C2×#106226792
C2×#106224482
C2×C11×#4782
C2×#323411