Finite Group Databasebeta

← C2×#13078762 #15621894

Subgroups — C2×#13078762 #15621894

Order 2816.

2430 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623127C211yesmaximal, characteristic, complemented
2C2×#10623053C211yesmaximal, characteristic, complemented
3#13078762C2116yesmaximal, direct product factor
4C2×#10622616C211yesmaximal, characteristic, complemented
5C2×#10622467C211yesmaximal, characteristic, complemented
6C2×#10622503C211yesmaximal, characteristic, complemented
7C2×#10622375C211yesmaximal, characteristic, complemented
8C2×#10622399C211yesmaximal, characteristic, complemented
9C2×#10622347C211yesmaximal, characteristic, complemented
10C2×#10622650C211yesmaximal, characteristic, complemented
11C2×#10622482C211yesmaximal, characteristic, complemented
12C2×#10622398C211yesmaximal, characteristic, complemented
13C2×#10622502C211yesmaximal, characteristic, complemented
14C2×#10622370C211yesmaximal, characteristic, complemented
15C2×#10622332C211yesmaximal, characteristic, complemented
16C2×C11×#482C211yesmaximal, characteristic, complemented
17C22×#4341—21no—
18C22×#4339C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×C11×#117C2211yescharacteristic
21C2×#66993C2211yescharacteristic
22C2×#66992—21no—
23C2×D4×Dic11C2211yescharacteristic
24C22×#4324C2211yescharacteristic
25C22×#4323C2211yescharacteristic
26C2×#66983C2211yescharacteristic
27C22×C4×Dic11C2211yescharacteristic
28C22×D88C2211yescharacteristic
29C22×#4314C2211yescharacteristic
30#10623127—24no—
31#10623127C2218yescomplemented
32#10623053—24no—
33#10623053C2218yescomplemented
34C2×#66946C2211yescharacteristic
35C2×#66946C2211yescharacteristic
36C2×#66946C2211yescharacteristic
37C2×#66941C2211yescharacteristic
38C2×#66940C2211yescharacteristic
39C2×#66940C2211yescharacteristic
40C2×#66938—21no—
41C2×(C22⋊D11)⋊C4—21no—
42C2×(C22⋊D11)⋊C4—21no—
43C2×(C22⋊D11)⋊C4—21no—
44C2×#66925—21no—
45C2×C42×D11—21no—
46C11×#482C2218yescomplemented
47C2×C11×#107C2211yescharacteristic
48C2×C11×#106C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×C11×#102C2211yescharacteristic
51C2×C11×C22⋊C8C2211yescharacteristic
52C2×C22⋊(C11⋊C8)C2211yescharacteristic
53C2×#66885C2211yescharacteristic
54C2×#66880C2211yescharacteristic
55C2×#66879C2211yescharacteristic
56C2×#66879C2211yescharacteristic
57C2×Dic11⋊C8C2211yescharacteristic
58C2×Dic11⋊C8C2211yescharacteristic
59#10622650C2218yescomplemented
60#10622616C2218yescomplemented
61C2×#66874C2211yescharacteristic
62C2×#66873C2211yescharacteristic
63C2×#66873C2211yescharacteristic
64C2×#66873C2211yescharacteristic
65C2×#66872C2211yescharacteristic
66C2×#66871C2211yescharacteristic
67#10622503C2218yescomplemented
68#10622502C2218yescomplemented
69#10622482C2218yescomplemented
70#10622467C2218yescomplemented
71#10622399C2218yescomplemented
72#10622398C2218yescomplemented
73#10622375C2218yescomplemented
74#10622370C2218yescomplemented
75#10622347C2218yescomplemented
76#10622332C2218yescomplemented
77C22×D4×C11—21no—
78C22×D4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C22×C22⋊D11—21no—
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C23×Dic11—21no—
85C23×Dic11D411yescharacteristic
86C23×Dic11D411yescharacteristic
87C2×#4341—28no—
88C2×#4341—48no—
89C2×#4339—22no—
90C2×#4339—24no—
91C2×#4339—24no—
92C2×#4339C2314yes—
93C22×D44C2311yescharacteristic
94C22×D44C2311yescharacteristic
95C22×C4×D11—21no—
96C22×C4×D11—21no—
97C22×C4×D11—21no—
98C22×C4×D11—21no—
99C22×Dic22—21no—
100C22×Dic22C2311yescharacteristic
101C22×C8×C11C2311yescharacteristic
102C22×C8×C11C2311yescharacteristic
103C11×#121—22no—
104C11×#121C2314yes—
105C11×#117—22no—
106C11×#117C2314yes—
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4—21no—
112C2×C42×C11—21no—
113C2×C22⋊Dic11—21no—
114#66993—22no—
115#66993C2314yes—
116#66992—28no—
117D4×Dic11—22no—
118D4×Dic11C2314yes—
119C2×#4324—24no—
120C2×#4324C2314yes—
121C2×#4323—24no—
122C2×#4323C2314yes—
123#66983—22no—
124#66983C2314yes—
125C2×(C2×D11)⋊C4—21no—
126C2×(C2×D11)⋊C4—21no—
127C2×(C2×D11)⋊C4—21no—
128C2×(C2×D11)⋊C4—21no—
129C2×C4⋊Dic11C2311yescharacteristic
130C2×Dic11⋊C4—21no—
131C2×Dic11⋊C4—21no—
132C2×Dic11⋊C4—21no—
133C2×C4×Dic11—21no—
134C2×C4×Dic11—21no—
135C2×C4×Dic11D411yescharacteristic
136C2×C4×Dic11D411yescharacteristic
137C2×C4×Dic11D414yes—
138C2×C4×Dic11C2311yescharacteristic
139C2×C4×Dic11C2311yescharacteristic
140C2×C4×Dic11C2314yes—
141C22×C11⋊C8C2311yescharacteristic
142C22×C11⋊C8C2311yescharacteristic
143C2×D88—24no—
144C2×D88C2314yes—
145C2×#4314—24no—
146C2×#4314C2314yes—
147#66946—22no—
148#66946—22no—
149#66946—22no—
150#66946C2314yes—
151#66946C2314yes—
152#66946C2314yes—
153#66941—22no—
154#66941C2314yes—
155#66940—22no—
156#66940—22no—
157#66940C2314yes—
158#66940C2314yes—
159#66938—28no—
160(C22⋊D11)⋊C4—28no—
161(C22⋊D11)⋊C4—28no—
162(C22⋊D11)⋊C4—28no—
163#66925—28no—
164C42×D11—28no—
165C11×#107C2314yes—
166C11×#106C2314yes—
167C11×#102C2314yes—
168C11×#102C2314yes—
169C11×C22⋊C8C2314yes—
170C22⋊(C11⋊C8)C2314yes—
171#66885C2314yes—
172#66880C2314yes—
173#66879C2314yes—
174#66879C2314yes—
175Dic11⋊C8C2314yes—
176Dic11⋊C8C2314yes—
177#66874C2314yes—
178#66873C2314yes—
179#66873C2314yes—
180#66873C2314yes—
181#66872C2314yes—
182#66871C2314yes—
183C2×#3115—111nomaximal, Sylow
184C24×C11—21no—
185C24×C11C2×D411yescharacteristic
186C23×D11—21no—
187C23×D11—21no—
188C2×D4×C11—24no—
189C2×D4×C11—21no—
190C2×D4×C11—22no—
191C2×D4×C11—22no—
192C2×D4×C11—44no—
193C2×D4×C11C2412yes—
194C22×C4×C11—22no—
195C22×C4×C11—22no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2×D412yes—
201C22×C4×C11C2412yes—
202C22×C4×C11C2411yescharacteristic
203C2×C22⋊D11—28no—
204C2×C22⋊D11—24no—
205C2×C22⋊D11—24no—
206C2×C22⋊D11—24no—
207C2×C22⋊D11—24no—
208C2×C22⋊D11—44no—
209C2×C22⋊D11—44no—
210C2×C22⋊D11—44no—
211C22×Dic11—24no—
212C22×Dic11—24no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—42no—
216C22×Dic11—44no—
217C22×Dic11C2×D414yes—
218C22×Dic11C2×D411yescharacteristic
219C22×Dic11C2×D411yescharacteristic
220C22×Dic11C2×D411yescharacteristic
221C22×Dic11C2×D414yes—
222C22×Dic11C2×D411yescharacteristic
223#4341—432no—
224#4339—216no—
225#4339—28no—
226#4339—28no—
227C2×D44—21no—
228C2×D44—21no—
229C2×D44—22no—
230C2×D44—22no—
231C2×D44—22no—
232C2×D44#4114yescomplemented
233C2×D44C2412yes—
234C2×D44C2412yes—
235C2×C4×D11—28no—
236C2×C4×D11—24no—
237C2×C4×D11—24no—
238C2×C4×D11—24no—
239C2×C4×D11—24no—
240C2×C4×D11—44no—
241C2×C4×D11—44no—
242C2×C4×D11—44no—
243C2×Dic22—24no—
244C2×Dic22—21no—
245C2×Dic22—22no—
246C2×Dic22—44no—
247C2×Dic22#4114yescomplemented
248C2×Dic22C2412yes—
249C2×C8×C11—22no—
250C2×C8×C11—22no—
251C2×C8×C11C2412yes—
252C2×C8×C11C2412yes—
253C11×C4⋊C4—21no—
254C11×C4⋊C4—21no—
255C11×C4⋊C4—21no—
256C11×C4⋊C4C2412yes—
257C11×C4⋊C4C2412yes—
258C11×C4⋊C4C2412yes—
259C11×C22⋊C4—24no—
260C11×C22⋊C4—24no—
261C42×C11—24no—
262C22⋊Dic11—24no—
263#4324—28no—
264#4323—28no—
265(C2×D11)⋊C4—24no—
266(C2×D11)⋊C4—24no—
267(C2×D11)⋊C4—24no—
268(C2×D11)⋊C4—24no—
269C4⋊Dic11—21no—
270C4⋊Dic11C2412yes—
271Dic11⋊C4—24no—
272Dic11⋊C4—24no—
273Dic11⋊C4—24no—
274C4×Dic11—24no—
275C4×Dic11—24no—
276C4×Dic11C2×D414yes—
277C4×Dic11C2×D414yes—
278C4×Dic11C2×D412yes—
279C4×Dic11C2×D412yes—
280C4×Dic11C2412yes—
281C4×Dic11C2412yes—
282C2×C11⋊C8—22no—
283C2×C11⋊C8—22no—
284C2×C11⋊C8C2412yes—
285C2×C11⋊C8C2412yes—
286D88—28no—
287#4314—28no—
288C2×#532—111no—
289C2×C4×#41—111no—
290#3115—1116no—
291C2×#482—111no—
292C2×#482D1111yescharacteristic, complemented
293C2×#475—111no—
294C2×#474—111no—
295C2×#460—111no—
296C2×#459—111no—
297C2×#449—111no—
298C2×#449—111no—
299C2×#442—111no—
300C2×#442—111no—
301C2×#440—111no—
302C2×#440—111no—
303C2×#432—111no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—42no—
309C23×C11—42no—
310C23×C11—42no—
311C23×C11C22×D412yes—
312C23×C11C22×D411yescharacteristic
313C22×D11—24no—
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—42no—
317C22×D11—42no—
318C22×D11—42no—
319C22×D11—42no—
320C22×D11—42no—
321D4×C11—22no—
322D4×C11—22no—
323D4×C11—48no—
324D4×C11—42no—
325C2×C4×C11—22no—
326C2×C4×C11—24no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—42no—
333C2×C4×C11—42no—
334C2×C4×C11—42no—
335C2×C4×C11C22×D412yes—
336C2×C4×C11C22×D411yescharacteristic
337C2×C4×C11C2×#4112yes—
338C2×C4×C11C2×#4112yes—
339C2×C4×C11C2511yescharacteristic
340C22⋊D11—216no—
341C22⋊D11—48no—
342C22⋊D11—48no—
343C22⋊D11—48no—
344C2×Dic11—24no—
345C2×Dic11—22no—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—28no—
350C2×Dic11—22no—
351C2×Dic11—44no—
352C2×Dic11—48no—
353C2×Dic11—42no—
354C2×Dic11AGL(1,ℤ/8)14yes—
355C2×Dic11C22×D412yes—
356C2×Dic11C22×D412yes—
357C2×Dic11C22×D412yes—
358C2×Dic11C22×D412yes—
359D44—24no—
360D44—22no—
361D44—22no—
362D44—22no—
363D44—42no—
364D44C2×#4114yescomplemented
365C4×D11—216no—
366C4×D11—48no—
367C4×D11—48no—
368C4×D11—48no—
369Dic22—24no—
370Dic22—22no—
371Dic22—48no—
372Dic22C2×#4114yescomplemented
373C8×C11—22no—
374C8×C11—22no—
375C11⋊C8—22no—
376C11⋊C8—22no—
377C22×#41—111no—
378C22×#41—221no—
379C22×SD16—111no—
380C22×SD16—111no—
381C22×D8—111no—
382C22×D8—111no—
383#532—118no—
384#532—224no—
385C2×C4⋊Q8—111no—
386C2×#127—111no—
387C2×#124—221no—
388C2×#121—111no—
389C2×#121—221no—
390C2×#121C2×D1111yescharacteristic
391C4×#41—118no—
392C4×#41—224no—
393C2×C4×Q8—111no—
394C2×C4×Q8—111no—
395C2×C4×D4—111no—
396C2×C4×D4—111no—
397C2×C4×D4—111no—
398C2×C4×D4—111no—
399C2×C4×D4—221no—
400C2×C4×D4—221no—
401C2×C4×D4—221no—
402C2×#117—221no—
403C2×#117C2×D1111yescharacteristic
404C22×C42—111no—
405C22×C42—221no—
406#482—118no—
407#482C2×D1118yescomplemented
408#475—118no—
409#474—118no—
410#460—118no—
411#459—118no—
412#449—118no—
413#449—118no—
414#442—118no—
415#442—118no—
416#440—118no—
417#440—118no—
418#432—118no—
419C2×#107—111no—
420C2×#107C2×D1111yescharacteristic
421C2×#106—111no—
422C2×#106C2×D1111yescharacteristic
423C2×C4⋊C8—111no—
424C2×C4⋊C8—111no—
425C2×#103—111no—
426C2×#103—111no—
427C2×#102—111no—
428C2×#102—111no—
429C2×#102—111no—
430C2×#102—111no—
431C2×#102C2×D1111yescharacteristic
432C2×#102C2×D1111yescharacteristic
433C2×C22⋊C8—111no—
434C2×C22⋊C8C2×D1111yescharacteristic
435C2×#97—111no—
436C2×#97—111no—
437C22×C11—22no—
438C22×C11—22no—
439C22×C11—22no—
440C22×C11—44no—
441C22×C11—42no—
442C22×C11—42no—
443C22×C11—42no—
444C22×C11—84no—
445C22×C11#52512yes—
446C22×C11C2×AGL(1,ℤ/8)12yes—
447C22×C11#57512yes—
448C22×C11C23×D411yescharacteristic
449C2×D11—24no—
450C2×D11—48no—
451C2×D11—42no—
452C2×D11—42no—
453C2×D11—42no—
454C2×D11—42no—
455C2×D11—42no—
456C2×D11—84no—
457C4×C11—22no—
458C4×C11—42no—
459C4×C11—42no—
460C4×C11—42no—
461C4×C11#52512yes—
462C4×C11C22×#4111yescharacteristic
463C4×C11C22×#4111yescharacteristic
464Dic11—24no—
465Dic11—22no—
466Dic11—22no—
467Dic11—22no—
468Dic11—42no—
469Dic11C2×AGL(1,ℤ/8)14yes—
470C2×#41—114no—
471C2×#41—224no—
472C2×#41—224no—
473C2×#41—228no—
474C2×#41—222no—
475C2×#41—448no—
476C22×Q8—111no—
477C22×Q8—221no—
478C22×D4—21no—
479C22×D4—111no—
480C22×D4—111no—
481C22×D4—221no—
482C22×D4—221no—
483C22×D4—221no—
484C22×D4—221no—
485C22×D4C22×D1111yescharacteristic
486C23×C4—111no—
487C23×C4—111no—
488C23×C4—221no—
489C23×C4—221no—
490C23×C4—221no—
491C23×C4—221no—
492C23×C4—221no—
493C23×C4C22×D1111yescharacteristic
494C2×SD16—114no—
495C2×SD16—114no—
496C2×SD16—224no—
497C2×SD16—224no—
498C2×D8—114no—
499C2×D8—114no—
500C2×D8—224no—
501C2×D8—224no—
502C22×C8—111no—
503C22×C8—111no—
504C22×C8C22×D1111yescharacteristic
505C22×C8C22×D1111yescharacteristic
506C4⋊Q8—114no—
507C4⋊Q8—222no—
508#127—114no—
509#127—222no—
510#124—228no—
511#121—22no—
512#121—114no—
513#121—228no—
514#121—222no—
515#121C22×D1114yes—
516C4×Q8—114no—
517C4×Q8—114no—
518C4×Q8—222no—
519C4×Q8—222no—
520C4×D4—114no—
521C4×D4—114no—
522C4×D4—114no—
523C4×D4—114no—
524C4×D4—228no—
525C4×D4—222no—
526C4×D4—222no—
527C4×D4—222no—
528C4×D4—222no—
529C4×D4—228no—
530C4×D4—228no—
531#117—22no—
532#117—228no—
533#117C22×D1114yes—
534C2×C4⋊C4—111no—
535C2×C4⋊C4—221no—
536C2×C4⋊C4—221no—
537C2×C4⋊C4—221no—
538C2×C4⋊C4C22×D1111yescharacteristic
539C2×C4⋊C4C22×D1111yescharacteristic
540C2×C4⋊C4C22×D1111yescharacteristic
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—221no—
544C2×C22⋊C4—221no—
545C2×C22⋊C4—221no—
546C2×C22⋊C4—221no—
547C2×C22⋊C4—221no—
548C2×C42—21no—
549C2×C42—111no—
550C2×C42—114no—
551C2×C42—111no—
552C2×C42—111no—
553C2×C42—111no—
554C2×C42—114no—
555C2×C42—228no—
556C2×C42—221no—
557C2×C42—221no—
558#107—114no—
559#107C22×D1114yes—
560#106—114no—
561#106C22×D1114yes—
562C4⋊C8—114no—
563C4⋊C8—114no—
564#103—114no—
565#103—114no—
566#102—114no—
567#102—114no—
568#102—114no—
569#102—114no—
570#102C22×D1114yes—
571#102C22×D1114yes—
572C22⋊C8—114no—
573C22⋊C8C22×D1114yes—
574#97—114no—
575#97—114no—
576C2×C11—42no—
577C2×C11—82no—
578C2×C11#311514yescomplemented
579C2×C11C2×#52511yescharacteristic
580C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
581C2×C11C2×#57511yescharacteristic
582D11—44no—
583D11—82no—
584C24—21no—
585C24—221no—
586C24—221no—
587C24D4×D1111yescharacteristic
588#41—228no—
589#41—228no—
590#41—2216no—
591#41—4432no—
592C2×Q8—114no—
593C2×Q8—112no—
594C2×Q8—224no—
595C2×Q8—221no—
596C2×Q8—222no—
597C2×Q8—444no—
598C2×D4—24no—
599C2×D4—21no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—44no—
603C2×D4—114no—
604C2×D4—112no—
605C2×D4—112no—
606C2×D4—224no—
607C2×D4—224no—
608C2×D4—228no—
609C2×D4—224no—
610C2×D4—224no—
611C2×D4—221no—
612C2×D4—221no—
613C2×D4—222no—
614C2×D4—222no—
615C2×D4—222no—
616C2×D4—444no—
617C2×D4—444no—
618C2×D4—444no—
619C2×D4C23×D1112yes—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—111no—
626C22×C4—114no—
627C22×C4—111no—
628C22×C4—111no—
629C22×C4—111no—
630C22×C4—114no—
631C22×C4—224no—
632C22×C4—224no—
633C22×C4—224no—
634C22×C4—228no—
635C22×C4—224no—
636C22×C4—224no—
637C22×C4—221no—
638C22×C4—224no—
639C22×C4—221no—
640C22×C4—444no—
641C22×C4—444no—
642C22×C4—444no—
643C22×C4—442no—
644C22×C4—444no—
645C22×C4D4×D1112yes—
646C22×C4D4×D1111yescharacteristic
647C22×C4C23×D1112yes—
648C22×C4C23×D1111yescharacteristic
649SD16—228no—
650SD16—228no—
651D8—228no—
652D8—228no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—112no—
656C2×C8—112no—
657C2×C8—222no—
658C2×C8—222no—
659C2×C8C23×D1112yes—
660C2×C8C23×D1112yes—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—112no—
665C4⋊C4—224no—
666C4⋊C4—224no—
667C4⋊C4—224no—
668C4⋊C4—221no—
669C4⋊C4C23×D1112yes—
670C4⋊C4C23×D1112yes—
671C4⋊C4C23×D1112yes—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—224no—
675C22⋊C4—224no—
676C22⋊C4—224no—
677C22⋊C4—224no—
678C22⋊C4—224no—
679C42—24no—
680C42—114no—
681C42—114no—
682C42—112no—
683C42—112no—
684C42—112no—
685C42—112no—
686C42—224no—
687C42—224no—
688C11C2×#311511yescharacteristic, complemented, Sylow
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—224no—
697C23—222no—
698C23—222no—
699C23—442no—
700C23—442no—
701C23—442no—
702C23—442no—
703C23—442no—
704C23C2×D4×D1112yes—
705C23C2×D4×D1111yescharacteristic
706Q8—114no—
707Q8—224no—
708Q8—222no—
709Q8—448no—
710D4—22no—
711D4—22no—
712D4—48no—
713D4—42no—
714D4—114no—
715D4—2216no—
716D4—224no—
717D4—222no—
718D4—222no—
719D4—222no—
720D4—448no—
721D4—448no—
722D4—448no—
723D4—442no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—114no—
735C2×C4—112no—
736C2×C4—112no—
737C2×C4—112no—
738C2×C4—112no—
739C2×C4—2216no—
740C2×C4—228no—
741C2×C4—222no—
742C2×C4—222no—
743C2×C4—222no—
744C2×C4—224no—
745C2×C4—222no—
746C2×C4—222no—
747C2×C4—448no—
748C2×C4—448no—
749C2×C4—448no—
750C2×C4—444no—
751C2×C4—448no—
752C2×C4—442no—
753C2×C4C2×D4×D1112yes—
754C2×C4C2×D4×D1111yescharacteristic
755C2×C4#41×D1112yes—
756C2×C4#41×D1112yes—
757C2×C4C24×D1111yescharacteristic
758C8—22no—
759C8—22no—
760C8—222no—
761C8—222no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—44no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—84no—
770C22—224no—
771C22—442no—
772C22—442no—
773C22—448no—
774C22—442no—
775C22—442no—
776C22—442no—
777C22—884no—
778C22#1062318712yes—
779C22#1062329912yes—
780C22D11×AGL(1,ℤ/8)12yes—
781C22C22×D4×D1111yescharacteristic
782C4—22no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—114no—
787C4—222no—
788C4—222no—
789C4—222no—
790C4—224no—
791C4—442no—
792C4#1062318712yes—
793C4C2×#41×D1111yescharacteristic
794C4C2×#41×D1111yescharacteristic
795C2—42no—
796C2—82no—
797C2—444no—
798C2—882no—
799C2#1307876214yesdirect product factor
800C2C2×#1062318711yescharacteristic
801C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
802C2C2×#1062329911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#482C2
socleC23×C11C22×D4
hypercenterC2×#482D11
hypocenterC11C2×#3115
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#10623127C2semidirect
2. C2×#10623053C2semidirect
3. #13078762C2direct (N × H)
4. C2×#10622616C2semidirect
5. C2×#10622467C2semidirect
6. C2×#10622503C2semidirect
7. C2×#10622375C2semidirect
8. C2×#10622399C2semidirect
9. C2×#10622347C2semidirect
10. C2×#10622650C2semidirect
11. C2×#10622482C2semidirect
12. C2×#10622398C2semidirect
13. C2×#10622502C2semidirect
14. C2×#10622370C2semidirect
15. C2×#10622332C2semidirect
16. C2×C11×#482C2semidirect
31. #10623127C22semidirect
33. #10623053C22semidirect
46. C11×#482C22semidirect
59. #10622650C22semidirect
60. #10622616C22semidirect
67. #10622503C22semidirect
68. #10622502C22semidirect
69. #10622482C22semidirect
70. #10622467C22semidirect
71. #10622399C22semidirect
72. #10622398C22semidirect
73. #10622375C22semidirect
74. #10622370C22semidirect
75. #10622347C22semidirect
76. #10622332C22semidirect
232. C2×D44#41semidirect
247. C2×Dic22#41semidirect
292. C2×#482D11semidirect
364. D44C2×#41semidirect
372. Dic22C2×#41semidirect
407. #482C2×D11semidirect
578. C2×C11#3115semidirect
688. C11C2×#3115semidirect
799. C2#13078762direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231272
C2×#106230532
#130787622
C2×#106226162
C2×#106224672
C2×#106225032
C2×#106223752
C2×#106223992
C2×#106223472
C2×#106226502
C2×#106224822
C2×#106223982
C2×#106225022
C2×#106223702
C2×#106223322
C2×C11×#4822
C2×#311511