Finite Group Databasebeta

← C2×#13078853 #15622061

Subgroups — C2×#13078853 #15622061

Order 2816.

2338 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623150C211yesmaximal, characteristic, complemented
2C2×#10623329C211yesmaximal, characteristic, complemented
3#13078853C2116yesmaximal, direct product factor
4C2×#10622350C211yesmaximal, characteristic, complemented
5C2×#10622648C211yesmaximal, characteristic, complemented
6C2×#10622376C211yesmaximal, characteristic, complemented
7C2×#10622379C211yesmaximal, characteristic, complemented
8C2×#10622763C211yesmaximal, characteristic, complemented
9C2×#10622763C211yesmaximal, characteristic, complemented
10C2×#10622830C211yesmaximal, characteristic, complemented
11C2×#10622765C211yesmaximal, characteristic, complemented
12C2×#10622398C211yesmaximal, characteristic, complemented
13C2×D8×Dic11C211yesmaximal, characteristic, complemented
14C2×#10622369C211yesmaximal, characteristic, complemented
15C2×#10622333C211yesmaximal, characteristic, complemented
16C2×C11×#447C211yesmaximal, characteristic, complemented
17C23×D4×C11C2211yescharacteristic
18C22×C11×D8C2211yescharacteristic
19C22×C11×D8C2211yescharacteristic
20C2×C11×#121C2211yescharacteristic
21C22×C22⋊Dic11—21no—
22C22×C22⋊Dic11—21no—
23C2×#66993C2211yescharacteristic, complemented
24C2×#66992—21no—
25C2×#66991—21no—
26#10623329—24no—
27#10623329C2218yescomplemented
28C2×D4×Dic11—21no—
29C2×D4×Dic11—21no—
30C2×D4×Dic11C2211yescharacteristic
31C2×D4×Dic11C2211yescharacteristic
32C2×D4×Dic11C2211yescharacteristic
33C2×D4×Dic11C2211yescharacteristic
34C2×D4×Dic11C2211yescharacteristic, complemented
35C22×#4323C2211yescharacteristic
36C22×#4323C2211yescharacteristic
37C2×#66983C2211yescharacteristic
38C2×#66979C2211yescharacteristic
39C2×#66979C2211yescharacteristic
40#10623150—24no—
41#10623150C2218yescomplemented
42C2×#66946C2211yescharacteristic, complemented
43C2×#66943C2211yescharacteristic, complemented
44C2×#66939—21no—
45C2×#66936—21no—
46C11×#447C2218yescomplemented
47C2×C11×#102C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×C11×C22⋊C8C2211yescharacteristic
50#10622830C2218yescomplemented
51C2×#66896C2211yescharacteristic
52C2×#66896C2211yescharacteristic
53C2×#66896C2211yescharacteristic, complemented
54C2×#66896C2211yescharacteristic, complemented
55C2×C22⋊(C11⋊C8)C2211yescharacteristic
56#10622765C2218yescomplemented
57#10622763C2218yescomplemented
58#10622763C2218yescomplemented
59D8×Dic11C2218yescomplemented
60C2×#66885C2211yescharacteristic, complemented
61C2×#66885C2211yescharacteristic, complemented
62C2×#66882C2211yescharacteristic, complemented
63C2×#66881C2211yescharacteristic, complemented
64C2×#66879C2211yescharacteristic, complemented
65C2×Dic11⋊C8C2211yescharacteristic, complemented
66C2×Dic11⋊C8C2211yescharacteristic, complemented
67C2×C8×Dic11C2211yescharacteristic, complemented
68#10622648C2218yescomplemented
69C2×#66872C2211yescharacteristic, complemented
70C2×#66871C2211yescharacteristic, complemented
71#10622398C2218yescomplemented
72#10622379C2218yescomplemented
73#10622376C2218yescomplemented
74#10622369C2218yescomplemented
75#10622350C2218yescomplemented
76#10622333C2218yescomplemented
77C25×C11—21no—
78C22×D4×C11—24no—
79C22×D4×C11—24no—
80C22×D4×C11—21no—
81C22×D4×C11—21no—
82C22×D4×C11—22no—
83C22×D4×C11C2311yescharacteristic
84C22×D4×C11C2314yes—
85C22×D4×C11C2311yescharacteristic
86C22×D4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C22×C22⋊D11—21no—
89C22×C22⋊D11—21no—
90C22×C22⋊D11—21no—
91C23×Dic11—21no—
92C23×Dic11—21no—
93C23×Dic11—21no—
94C23×Dic11—21no—
95C23×Dic11—21no—
96C22×D44C2311yescharacteristic
97C22×C4×D11—21no—
98C2×C11×D8—24no—
99C2×C11×D8—24no—
100C2×C11×D8C2314yes—
101C2×C11×D8C2314yes—
102C22×C8×C11C2311yescharacteristic
103C22×C8×C11C2311yescharacteristic
104C11×#121—22no—
105C11×#121C2314yes—
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C22⋊C4—21no—
108C2×C22⋊Dic11—21no—
109C2×C22⋊Dic11—21no—
110C2×C22⋊Dic11—21no—
111C2×C22⋊Dic11—21no—
112C2×C22⋊Dic11—21no—
113C2×C22⋊Dic11—21no—
114C2×C22⋊Dic11—28no—
115C2×C22⋊Dic11—28no—
116C2×C22⋊Dic11D411yescharacteristic
117C2×C22⋊Dic11D411yescharacteristic
118#66993—22no—
119#66993C2314yescomplemented
120#66992—28no—
121#66991—28no—
122D4×Dic11—28no—
123D4×Dic11—28no—
124D4×Dic11—22no—
125D4×Dic11—22no—
126D4×Dic11—22no—
127D4×Dic11—22no—
128D4×Dic11—22no—
129D4×Dic11C2314yes—
130D4×Dic11C2314yes—
131D4×Dic11C2314yes—
132D4×Dic11C2314yes—
133D4×Dic11C2314yescomplemented
134C2×#4323—24no—
135C2×#4323—24no—
136C2×#4323C2314yes—
137C2×#4323C2314yes—
138#66983—22no—
139#66983C2314yes—
140C2×(C2×D11)⋊C4—21no—
141C2×(C2×D11)⋊C4—21no—
142#66979—22no—
143#66979D414yes—
144#66979C2314yes—
145#66979C2314yes—
146C2×C4⋊Dic11—21no—
147C2×C4⋊Dic11D411yescharacteristic
148C2×C4⋊Dic11D411yescharacteristic
149C2×C4⋊Dic11C2311yescharacteristic
150C2×C4⋊Dic11C2311yescharacteristic
151C2×C4⋊Dic11C2311yescharacteristic
152C2×Dic11⋊C4—21no—
153C2×C4×Dic11—21no—
154C2×C4×Dic11C2311yescharacteristic
155C2×C4×Dic11C2311yescharacteristic
156C22×C11⋊C8C2311yescharacteristic
157C22×C11⋊C8C2311yescharacteristic
158#66946—22no—
159#66946C2314yescomplemented
160#66943—22no—
161#66943C2314yescomplemented
162#66939—28no—
163#66936—28no—
164C11×#102C2314yes—
165C11×#102C2314yes—
166C11×C22⋊C8C2314yes—
167#66896C2314yes—
168#66896C2314yes—
169#66896C2314yescomplemented
170#66896C2314yescomplemented
171C22⋊(C11⋊C8)C2314yes—
172#66885C2314yescomplemented
173#66885C2314yescomplemented
174#66882C2314yescomplemented
175#66881C2314yescomplemented
176#66879C2314yescomplemented
177Dic11⋊C8C2314yescomplemented
178Dic11⋊C8C2314yescomplemented
179C8×Dic11C2314yescomplemented
180#66872C2314yescomplemented
181#66871C2314yescomplemented
182C2×#3122—111nomaximal, Sylow
183C24×C11—28no—
184C24×C11—21no—
185C24×C11—21no—
186C24×C11—24no—
187C24×C11—21no—
188C24×C11—82no—
189C24×C11—82no—
190C24×C11C2×D411yescharacteristic
191C23×D11—21no—
192C2×D4×C11—28no—
193C2×D4×C11—216no—
194C2×D4×C11—28no—
195C2×D4×C11—28no—
196C2×D4×C11—24no—
197C2×D4×C11—24no—
198C2×D4×C11—21no—
199C2×D4×C11—21no—
200C2×D4×C11—21no—
201C2×D4×C11—22no—
202C2×D4×C11—22no—
203C2×D4×C11—22no—
204C2×D4×C11—22no—
205C2×D4×C11—82no—
206C2×D4×C11#4114yes—
207C2×D4×C11#4114yes—
208C2×D4×C11C2412yes—
209C2×D4×C11C2412yes—
210C2×D4×C11C2412yes—
211C22×C4×C11—22no—
212C22×C4×C11—22no—
213C22×C4×C11—21no—
214C22×C4×C11C2×D411yescharacteristic
215C22×C4×C11C2×D412yes—
216C22×C4×C11C2412yes—
217C22×C4×C11C2411yescharacteristic
218C2×C22⋊D11—24no—
219C2×C22⋊D11—24no—
220C2×C22⋊D11—24no—
221C2×C22⋊D11—82no—
222C2×C22⋊D11—82no—
223C2×C22⋊D11—82no—
224C22×Dic11—24no—
225C22×Dic11—24no—
226C22×Dic11—24no—
227C22×Dic11—24no—
228C22×Dic11—24no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—82no—
233C22×Dic11—82no—
234C22×Dic11—82no—
235C22×Dic11—82no—
236C22×Dic11—82no—
237C22×Dic11C2×D411yescharacteristic
238C22×Dic11C2×D411yescharacteristic
239C22×Dic11C2×D411yescharacteristic
240C22×Dic11C2×D411yescharacteristic
241C2×D44—21no—
242C2×D44—22no—
243C2×D44—22no—
244C2×D44C2412yes—
245C2×C4×D11—24no—
246C2×C4×D11—82no—
247C11×D8—28no—
248C11×D8—28no—
249C2×C8×C11—22no—
250C2×C8×C11—22no—
251C2×C8×C11C2412yes—
252C2×C8×C11C2412yes—
253C11×C4⋊C4—21no—
254C11×C4⋊C4C2412yes—
255C11×C22⋊C4—24no—
256C22⋊Dic11—24no—
257C22⋊Dic11—24no—
258C22⋊Dic11—24no—
259C22⋊Dic11—24no—
260C22⋊Dic11—24no—
261C22⋊Dic11—24no—
262C22⋊Dic11C2×D414yes—
263C22⋊Dic11C2×D414yes—
264#4323—28no—
265#4323—28no—
266(C2×D11)⋊C4—24no—
267(C2×D11)⋊C4—24no—
268C4⋊Dic11—24no—
269C4⋊Dic11—21no—
270C4⋊Dic11—21no—
271C4⋊Dic11—21no—
272C4⋊Dic11C2×D414yes—
273C4⋊Dic11C2×D414yes—
274C4⋊Dic11C2412yes—
275C4⋊Dic11C2412yes—
276C4⋊Dic11C2412yes—
277Dic11⋊C4—24no—
278C4×Dic11—24no—
279C4×Dic11C2×D412yes—
280C4×Dic11C2×D412yes—
281C4×Dic11C2412yes—
282C4×Dic11C2412yes—
283C2×C11⋊C8—22no—
284C2×C11⋊C8—22no—
285C2×C11⋊C8C2412yes—
286C2×C11⋊C8C2412yes—
287C2×#540—111no—
288C2×#518—111no—
289#3122—1116no—
290C2×#482—111no—
291C2×#482—111no—
292C2×#478—111no—
293C2×#478—111no—
294C2×#459—111no—
295C2×#459—111no—
296C2×#447—111no—
297C2×#447D1111yescharacteristic, complemented
298C2×#442—111no—
299C2×#442—111no—
300C2×C4×D8—111no—
301C2×C4×D8—111no—
302C2×#433—111no—
303C23×C11—216no—
304C23×C11—22no—
305C23×C11—24no—
306C23×C11—24no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—42no—
313C23×C11—42no—
314C23×C11—42no—
315C23×C11—42no—
316C23×C11—42no—
317C23×C11—42no—
318C23×C11—42no—
319C23×C11—84no—
320C23×C11—84no—
321C23×C11—816no—
322C23×C11C22×D412yes—
323C23×C11C22×D411yescharacteristic
324C22×D11—22no—
325C22×D11—42no—
326C22×D11—42no—
327C22×D11—42no—
328D4×C11—216no—
329D4×C11—24no—
330D4×C11—24no—
331D4×C11—22no—
332D4×C11—22no—
333D4×C11—22no—
334D4×C11—22no—
335D4×C11—42no—
336D4×C11—84no—
337D4×C11C2×#4114yes—
338D4×C11C2×#4114yes—
339C2×C4×C11—22no—
340C2×C4×C11—24no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—42no—
345C2×C4×C11C22×D412yes—
346C2×C4×C11C22×D411yescharacteristic
347C2×C4×C11C2×#4112yes—
348C2×C4×C11C2×#4112yes—
349C2×C4×C11C2511yescharacteristic
350C22⋊D11—84no—
351C22⋊D11—84no—
352C22⋊D11—84no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—42no—
361C2×Dic11—42no—
362C2×Dic11—42no—
363C2×Dic11—84no—
364C2×Dic11—84no—
365C2×Dic11—84no—
366C2×Dic11—84no—
367C2×Dic11—84no—
368C2×Dic11C22×D412yes—
369C2×Dic11C22×D412yes—
370C2×Dic11C22×D412yes—
371C2×Dic11C22×D412yes—
372D44—22no—
373D44—22no—
374D44—42no—
375C4×D11—84no—
376C8×C11—22no—
377C8×C11—22no—
378C11⋊C8—22no—
379C11⋊C8—22no—
380C23×D4C2×D1111yescharacteristic
381C22×D8—111no—
382C22×D8—111no—
383C22×D8C2×D1111yescharacteristic
384C22×D8C2×D1111yescharacteristic
385#540—118no—
386#540—224no—
387C2×#127—111no—
388C2×#125—111no—
389C2×#123—221no—
390C2×#123—221no—
391C2×#121—111no—
392C2×#121—221no—
393C2×#121—221no—
394C2×#121C2×D1111yescharacteristic
395#518—118no—
396#518—224no—
397C2×C4×D4—111no—
398C2×C4×D4—111no—
399C2×C4×D4—111no—
400C2×C4×D4—111no—
401C2×C4×D4—111no—
402C2×C4×D4—111no—
403C2×C4×D4—221no—
404C2×C4×D4—221no—
405C2×#117—111no—
406C2×#117—111no—
407C22×C22⋊C4—221no—
408C22×C22⋊C4—221no—
409#482—118no—
410#482—118no—
411#478—118no—
412#478—118no—
413#459—118no—
414#459—118no—
415#447—118no—
416#447C2×D1118yescomplemented
417#442—118no—
418#442—118no—
419C4×D8—118no—
420C4×D8—118no—
421#433—118no—
422C2×#107—111no—
423C2×#107—111no—
424C2×#106—111no—
425C2×#106—111no—
426C2×C4⋊C8—111no—
427C2×C4⋊C8—111no—
428C2×#102—111no—
429C2×#102—111no—
430C2×#102—111no—
431C2×#102—111no—
432C2×#102—111no—
433C2×#102—111no—
434C2×#102C2×D1111yescharacteristic
435C2×#102C2×D1111yescharacteristic
436C2×C22⋊C8—111no—
437C2×C22⋊C8C2×D1111yescharacteristic
438C2×#97—111no—
439C2×C4×C8—111no—
440C22×C11—22no—
441C22×C11—24no—
442C22×C11—24no—
443C22×C11—22no—
444C22×C11—22no—
445C22×C11—44no—
446C22×C11—48no—
447C22×C11—48no—
448C22×C11—42no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—42no—
455C22×C11—816no—
456C22×C11—84no—
457C22×C11#52512yes—
458C22×C11#57612yes—
459C22×C11#57612yes—
460C22×C11C23×D411yescharacteristic
461C2×D11—42no—
462C2×D11—42no—
463C2×D11—42no—
464C2×D11—84no—
465C4×C11—22no—
466C4×C11—42no—
467C4×C11#52512yes—
468C4×C11C22×#4111yescharacteristic
469C4×C11C22×#4111yescharacteristic
470Dic11—22no—
471Dic11—22no—
472Dic11—22no—
473Dic11—22no—
474Dic11—42no—
475Dic11—42no—
476Dic11—42no—
477C25—21no—
478C22×D4—24no—
479C22×D4—24no—
480C22×D4—21no—
481C22×D4—21no—
482C22×D4—22no—
483C22×D4—111no—
484C22×D4—221no—
485C22×D4—221no—
486C22×D4—221no—
487C22×D4C22×D1111yescharacteristic
488C22×D4C22×D1114yes—
489C22×D4C22×D1111yescharacteristic
490C22×D4C22×D1111yescharacteristic
491C23×C4—221no—
492C23×C4—221no—
493C23×C4—221no—
494C23×C4—221no—
495C23×C4—221no—
496C23×C4—221no—
497C23×C4C22×D1111yescharacteristic
498C2×D8—24no—
499C2×D8—24no—
500C2×D8—114no—
501C2×D8—114no—
502C2×D8—224no—
503C2×D8—224no—
504C2×D8C22×D1114yes—
505C2×D8C22×D1114yes—
506C22×C8—111no—
507C22×C8—111no—
508C22×C8C22×D1111yescharacteristic
509C22×C8C22×D1111yescharacteristic
510#127—114no—
511#127—222no—
512#125—114no—
513#125—222no—
514#123—228no—
515#123—228no—
516#121—22no—
517#121—114no—
518#121—228no—
519#121—228no—
520#121—222no—
521#121C22×D1114yes—
522C4×D4—114no—
523C4×D4—114no—
524C4×D4—114no—
525C4×D4—114no—
526C4×D4—114no—
527C4×D4—114no—
528C4×D4—222no—
529C4×D4—222no—
530C4×D4—222no—
531C4×D4—222no—
532C4×D4—222no—
533C4×D4—222no—
534C4×D4—228no—
535C4×D4—228no—
536#117—114no—
537#117—114no—
538#117—114no—
539#117—222no—
540C2×C4⋊C4—111no—
541C2×C4⋊C4—111no—
542C2×C4⋊C4—111no—
543C2×C4⋊C4—111no—
544C2×C4⋊C4—111no—
545C2×C4⋊C4—221no—
546C2×C4⋊C4—221no—
547C2×C4⋊C4C22×D1111yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—111no—
550C2×C22⋊C4—111no—
551C2×C22⋊C4—228no—
552C2×C22⋊C4—228no—
553C2×C22⋊C4—221no—
554C2×C22⋊C4—221no—
555C2×C22⋊C4—221no—
556C2×C22⋊C4—221no—
557C2×C22⋊C4—221no—
558C2×C22⋊C4—221no—
559C2×C22⋊C4—221no—
560C2×C22⋊C4—221no—
561C2×C42—111no—
562C2×C42—111no—
563C2×C42—221no—
564#107—114no—
565#107—114no—
566#106—114no—
567#106—114no—
568C4⋊C8—114no—
569C4⋊C8—114no—
570#102—114no—
571#102—114no—
572#102—114no—
573#102—114no—
574#102—114no—
575#102—114no—
576#102C22×D1114yes—
577#102C22×D1114yes—
578C22⋊C8—114no—
579C22⋊C8C22×D1114yes—
580#97—114no—
581C4×C8—114no—
582C2×C11—42no—
583C2×C11—44no—
584C2×C11—44no—
585C2×C11—82no—
586C2×C11#312214yescomplemented
587C2×C11C2×#52511yescharacteristic
588C2×C11C2×#57611yescharacteristic
589C2×C11C2×#57611yescharacteristic
590D11—82no—
591C24—28no—
592C24—21no—
593C24—21no—
594C24—24no—
595C24—21no—
596C24—82no—
597C24—82no—
598C24—221no—
599C24D4×D1111yescharacteristic
600C2×D4—28no—
601C2×D4—216no—
602C2×D4—28no—
603C2×D4—28no—
604C2×D4—24no—
605C2×D4—24no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—82no—
614C2×D4—112no—
615C2×D4—224no—
616C2×D4—224no—
617C2×D4—224no—
618C2×D4—221no—
619C2×D4—222no—
620C2×D4—222no—
621C2×D4—882no—
622C2×D4—882no—
623C2×D4—882no—
624C2×D4#434114yes—
625C2×D4#434114yes—
626C2×D4C23×D1112yes—
627C2×D4C23×D1112yes—
628C2×D4C23×D1112yes—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—21no—
632C22×C4—111no—
633C22×C4—111no—
634C22×C4—111no—
635C22×C4—111no—
636C22×C4—224no—
637C22×C4—224no—
638C22×C4—224no—
639C22×C4—224no—
640C22×C4—224no—
641C22×C4—224no—
642C22×C4—221no—
643C22×C4—221no—
644C22×C4—221no—
645C22×C4—882no—
646C22×C4—882no—
647C22×C4—882no—
648C22×C4—882no—
649C22×C4—882no—
650C22×C4—882no—
651C22×C4D4×D1112yes—
652C22×C4D4×D1111yescharacteristic
653C22×C4C23×D1112yes—
654C22×C4C23×D1111yescharacteristic
655D8—28no—
656D8—28no—
657D8—228no—
658D8—228no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—112no—
662C2×C8—112no—
663C2×C8—222no—
664C2×C8—222no—
665C2×C8C23×D1112yes—
666C2×C8C23×D1112yes—
667C4⋊C4—21no—
668C4⋊C4—114no—
669C4⋊C4—114no—
670C4⋊C4—112no—
671C4⋊C4—112no—
672C4⋊C4—112no—
673C4⋊C4—224no—
674C4⋊C4—224no—
675C4⋊C4—221no—
676C4⋊C4—221no—
677C4⋊C4—221no—
678C4⋊C4C23×D1112yes—
679C22⋊C4—24no—
680C22⋊C4—114no—
681C22⋊C4—114no—
682C22⋊C4—224no—
683C22⋊C4—224no—
684C22⋊C4—224no—
685C22⋊C4—224no—
686C22⋊C4—224no—
687C22⋊C4—224no—
688C22⋊C4—224no—
689C22⋊C4—224no—
690C42—112no—
691C42—112no—
692C42—112no—
693C42—112no—
694C42—224no—
695C11C2×#312211yescharacteristic, complemented, Sylow
696C23—216no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—24no—
701C23—24no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—84no—
713C23—84no—
714C23—816no—
715C23—222no—
716C23—442no—
717C23—442no—
718C23—442no—
719C23C2×D4×D1112yes—
720C23C2×D4×D1111yescharacteristic
721D4—216no—
722D4—24no—
723D4—24no—
724D4—22no—
725D4—22no—
726D4—22no—
727D4—22no—
728D4—42no—
729D4—84no—
730D4—222no—
731D4—222no—
732D4—442no—
733D4—884no—
734D4—884no—
735D4—884no—
736D4C2×#434114yes—
737D4C2×#434114yes—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—42no—
744C2×C4—112no—
745C2×C4—112no—
746C2×C4—112no—
747C2×C4—112no—
748C2×C4—222no—
749C2×C4—222no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—442no—
756C2×C4—442no—
757C2×C4—442no—
758C2×C4—884no—
759C2×C4—884no—
760C2×C4—884no—
761C2×C4—884no—
762C2×C4—884no—
763C2×C4—884no—
764C2×C4C2×D4×D1112yes—
765C2×C4C2×D4×D1111yescharacteristic
766C2×C4C2×#434112yes—
767C2×C4C2×#434112yes—
768C2×C4C24×D1111yescharacteristic
769C8—22no—
770C8—22no—
771C8—222no—
772C8—222no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—24no—
777C22—24no—
778C22—44no—
779C22—48no—
780C22—48no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—816no—
789C22—84no—
790C22—442no—
791C22—442no—
792C22—442no—
793C22—884no—
794C22#1062311712yes—
795C22#1062328812yes—
796C22#1062330512yes—
797C22C22×D4×D1111yescharacteristic
798C4—22no—
799C4—42no—
800C4—222no—
801C4—222no—
802C4—222no—
803C4—222no—
804C4—442no—
805C4—442no—
806C4—442no—
807C4#1062311712yes—
808C4C22×#434111yescharacteristic
809C4C22×#434111yescharacteristic
810C2—42no—
811C2—44no—
812C2—44no—
813C2—82no—
814C2—882no—
815C2#1307885314yesdirect product factor
816C2C2×#1062311711yescharacteristic
817C2C2×#1062328811yescharacteristic
818C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#447C2
socleC23×C11C22×D4
hypercenterC2×#447D11
hypocenterC11C2×#3122
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#447

Complements

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

NH ≅ G/Ntype
1. C2×#10623150C2semidirect
2. C2×#10623329C2semidirect
3. #13078853C2direct (N × H)
4. C2×#10622350C2semidirect
5. C2×#10622648C2semidirect
6. C2×#10622376C2semidirect
7. C2×#10622379C2semidirect
8. C2×#10622763C2semidirect
9. C2×#10622763C2semidirect
10. C2×#10622830C2semidirect
11. C2×#10622765C2semidirect
12. C2×#10622398C2semidirect
13. C2×D8×Dic11C2semidirect
14. C2×#10622369C2semidirect
15. C2×#10622333C2semidirect
16. C2×C11×#447C2semidirect
23. C2×#66993C22semidirect
27. #10623329C22semidirect
34. C2×D4×Dic11C22semidirect
41. #10623150C22semidirect
42. C2×#66946C22semidirect
43. C2×#66943C22semidirect
46. C11×#447C22semidirect
50. #10622830C22semidirect
53. C2×#66896C22semidirect
54. C2×#66896C22semidirect
56. #10622765C22semidirect
57. #10622763C22semidirect
58. #10622763C22semidirect
59. D8×Dic11C22semidirect
60. C2×#66885C22semidirect
61. C2×#66885C22semidirect
62. C2×#66882C22semidirect
63. C2×#66881C22semidirect
64. C2×#66879C22semidirect
65. C2×Dic11⋊C8C22semidirect
66. C2×Dic11⋊C8C22semidirect
67. C2×C8×Dic11C22semidirect
68. #10622648C22semidirect
69. C2×#66872C22semidirect
70. C2×#66871C22semidirect
71. #10622398C22semidirect
72. #10622379C22semidirect
73. #10622376C22semidirect
74. #10622369C22semidirect
75. #10622350C22semidirect
76. #10622333C22semidirect
119. #66993C23semidirect
133. D4×Dic11C23semidirect
159. #66946C23semidirect
161. #66943C23semidirect
169. #66896C23semidirect
170. #66896C23semidirect
172. #66885C23semidirect
173. #66885C23semidirect
174. #66882C23semidirect
175. #66881C23semidirect
176. #66879C23semidirect
177. Dic11⋊C8C23semidirect
178. Dic11⋊C8C23semidirect
179. C8×Dic11C23semidirect
180. #66872C23semidirect
181. #66871C23semidirect
297. C2×#447D11semidirect
416. #447C2×D11semidirect
586. C2×C11#3122semidirect
695. C11C2×#3122semidirect
815. C2#13078853direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231502
C2×#106233292
#130788532
C2×#106223502
C2×#106226482
C2×#106223762
C2×#106223792
C2×#106227632
C2×#106228302
C2×#106227652
C2×#106223982
C2×D8×Dic112
C2×#106223692
C2×#106223332
C2×C11×#4472
C2×#312211