Finite Group Databasebeta

← C2×#13078763 #15621895

Subgroups — C2×#13078763 #15621895

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×#10623079C211yesmaximal, characteristic, complemented
2C2×C4×#4341C211yesmaximal, characteristic, complemented
3#13078763C2116yesmaximal, direct product factor
4C2×#10622479C211yesmaximal, characteristic, complemented
5C2×#10622397C211yesmaximal, characteristic, complemented
6C2×#10622467C211yesmaximal, characteristic, complemented
7C2×#10622372C211yesmaximal, characteristic, complemented
8C2×#10622375C211yesmaximal, characteristic, complemented
9C2×#10622763C211yesmaximal, characteristic, complemented
10C2×#10622394C211yesmaximal, characteristic, complemented
11C2×#10622771C211yesmaximal, characteristic, complemented
12C2×#10622627C211yesmaximal, characteristic, complemented
13C2×#10622323C211yesmaximal, characteristic, complemented
14C2×#10622631C211yesmaximal, characteristic, complemented
15C2×#10622318C211yesmaximal, characteristic, complemented
16C2×C11×#442C211yesmaximal, characteristic, complemented
17C22×#4341C2211yescharacteristic
18C22×#4339—21no—
19C22×C11×D8C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×#66993C2211yescharacteristic
23C2×#66991C2211yescharacteristic
24C2×D4×Dic11C2211yescharacteristic
25C22×#4324C2211yescharacteristic
26C22×#4323C2211yescharacteristic
27C2×C4×C22⋊D11—21no—
28C2×C4×C22⋊D11—21no—
29C22×C4×Dic11—21no—
30C22×#4314C2211yescharacteristic
31#10623079—24no—
32#10623079C2218yescomplemented
33C4×#4341—24no—
34C4×#4341C2218yescomplemented
35C2×#66948C2211yescharacteristic
36C2×#66945C2211yescharacteristic
37C2×#66941C2211yescharacteristic
38C2×#66940C2211yescharacteristic
39C2×#66938—21no—
40C2×#66937—21no—
41C2×(C22⋊D11)⋊C4—21no—
42C2×#66930—21no—
43C2×C4×D44C2211yescharacteristic
44C2×C42×D11C2211yescharacteristic
45C2×C4×Dic22C2211yescharacteristic
46C11×#442C2218yescomplemented
47C2×C11×#106C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×C11×#102C2211yescharacteristic
50C2×C11×#97C2211yescharacteristic
51C2×#66896C2211yescharacteristic
52C2×#66896C2211yescharacteristic
53#10622771C2218yescomplemented
54#10622763C2218yescomplemented
55C2×#66885C2211yescharacteristic
56C2×(C2×D11)⋊C8C2211yescharacteristic
57C2×(C2×D11)⋊C8C2211yescharacteristic
58C2×#66882C2211yescharacteristic
59C2×#66880C2211yescharacteristic
60C2×Dic11⋊C8C2211yescharacteristic
61C2×Dic11⋊C8C2211yescharacteristic
62#10622631C2218yescomplemented
63#10622627C2218yescomplemented
64C2×#66874C2211yescharacteristic
65C2×#66873C2211yescharacteristic
66C2×#66872C2211yescharacteristic
67C2×#66871C2211yescharacteristic
68C2×#66867C2211yescharacteristic
69#10622479C2218yescomplemented
70#10622467C2218yescomplemented
71#10622397C2218yescomplemented
72#10622394C2218yescomplemented
73#10622375C2218yescomplemented
74#10622372C2218yescomplemented
75#10622323C2218yescomplemented
76#10622318C2218yescomplemented
77C22×D4×C11C2311yescharacteristic
78C22×D4×C11C2311yescharacteristic
79C23×C4×C11—21no—
80C23×C4×C11—21no—
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C23×Dic11—21no—
86C23×Dic11—21no—
87C2×#4341—24no—
88C2×#4341—22no—
89C2×#4341—24no—
90C2×#4341C2314yes—
91C2×#4339—28no—
92C2×#4339—48no—
93C22×D44—21no—
94C22×D44C2311yescharacteristic
95C22×C4×D11—21no—
96C22×C4×D11D411yescharacteristic
97C22×C4×D11D411yescharacteristic
98C22×C4×D11C2311yescharacteristic
99C22×Dic22—21no—
100C22×Dic22C2311yescharacteristic
101C2×C11×D8—24no—
102C2×C11×D8C2314yes—
103C22×C8×C11C2311yescharacteristic
104C22×C8×C11C2311yescharacteristic
105C4×D4×C11—22no—
106C4×D4×C11—22no—
107C4×D4×C11C2314yes—
108C4×D4×C11C2314yes—
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C42×C11C2311yescharacteristic
114C2×C22⋊Dic11—21no—
115C2×C22⋊Dic11—21no—
116#66993—22no—
117#66993C2314yes—
118#66991—22no—
119#66991C2314yes—
120D4×Dic11—22no—
121D4×Dic11C2314yes—
122C2×#4324—24no—
123C2×#4324C2314yes—
124C2×#4323—24no—
125C2×#4323C2314yes—
126C4×C22⋊D11—28no—
127C4×C22⋊D11—28no—
128C2×(C2×D11)⋊C4—21no—
129C2×(C2×D11)⋊C4—21no—
130C2×(C2×D11)⋊C4—21no—
131C2×C4⋊Dic11C2311yescharacteristic
132C2×C4⋊Dic11C2311yescharacteristic
133C2×Dic11⋊C4—21no—
134C2×Dic11⋊C4—21no—
135C2×Dic11⋊C4—21no—
136C2×C4×Dic11—21no—
137C2×C4×Dic11—21no—
138C2×C4×Dic11—21no—
139C2×C4×Dic11—28no—
140C2×C4×Dic11D411yescharacteristic
141C2×C4×Dic11D411yescharacteristic
142C2×C4×Dic11C2311yescharacteristic
143C22×C11⋊C8C2311yescharacteristic
144C22×C11⋊C8C2311yescharacteristic
145C2×#4314—24no—
146C2×#4314C2314yes—
147#66948—22no—
148#66948C2314yes—
149#66945—22no—
150#66945C2314yes—
151#66941—22no—
152#66941C2314yes—
153#66940—22no—
154#66940C2314yes—
155#66938—28no—
156#66937—28no—
157(C22⋊D11)⋊C4—28no—
158#66930—28no—
159C4×D44—22no—
160C4×D44C2314yes—
161C42×D11D414yes—
162C42×D11C2314yes—
163C4×Dic22—22no—
164C4×Dic22C2314yes—
165C11×#106C2314yes—
166C11×#102C2314yes—
167C11×#102C2314yes—
168C11×#97C2314yes—
169#66896C2314yes—
170#66896C2314yes—
171#66885C2314yes—
172(C2×D11)⋊C8C2314yes—
173(C2×D11)⋊C8C2314yes—
174#66882C2314yes—
175#66880C2314yes—
176Dic11⋊C8C2314yes—
177Dic11⋊C8C2314yes—
178#66874C2314yes—
179#66873C2314yes—
180#66872C2314yes—
181#66871C2314yes—
182#66867C2314yes—
183C2×#3115—111nomaximal, Sylow
184C24×C11—21no—
185C24×C11—21no—
186C23×D11—21no—
187C23×D11C2×D411yescharacteristic
188C2×D4×C11—21no—
189C2×D4×C11—21no—
190C2×D4×C11—22no—
191C2×D4×C11—22no—
192C2×D4×C11—22no—
193C2×D4×C11#4114yescomplemented
194C2×D4×C11C2412yes—
195C2×D4×C11C2412yes—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—24no—
199C22×C4×C11—24no—
200C22×C4×C11—44no—
201C22×C4×C11—44no—
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2×D411yescharacteristic
204C22×C4×C11C2411yescharacteristic
205C2×C22⋊D11—28no—
206C2×C22⋊D11—24no—
207C2×C22⋊D11—24no—
208C2×C22⋊D11—24no—
209C2×C22⋊D11—24no—
210C2×C22⋊D11—44no—
211C2×C22⋊D11—44no—
212C2×C22⋊D11—44no—
213C22×Dic11—28no—
214C22×Dic11—24no—
215C22×Dic11—24no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—44no—
220C22×Dic11C2×D411yescharacteristic
221C22×Dic11C2×D411yescharacteristic
222C22×Dic11C2×D411yescharacteristic
223#4341—216no—
224#4341—28no—
225#4341—28no—
226#4339—432no—
227C2×D44—24no—
228C2×D44—21no—
229C2×D44—22no—
230C2×D44—22no—
231C2×D44—44no—
232C2×D44C2412yes—
233C2×C4×D11—24no—
234C2×C4×D11—24no—
235C2×C4×D11—22no—
236C2×C4×D11—22no—
237C2×C4×D11—42no—
238C2×C4×D11—44no—
239C2×C4×D11C2×D412yes—
240C2×C4×D11C2×D414yes—
241C2×C4×D11C2×D414yes—
242C2×C4×D11C2412yes—
243C2×Dic22—24no—
244C2×Dic22—21no—
245C2×Dic22—22no—
246C2×Dic22—44no—
247C2×Dic22#4114yescomplemented
248C2×Dic22C2412yes—
249C11×D8—28no—
250C2×C8×C11—22no—
251C2×C8×C11—22no—
252C2×C8×C11C2412yes—
253C2×C8×C11C2412yes—
254C11×C4⋊C4—21no—
255C11×C4⋊C4—21no—
256C11×C4⋊C4C2412yes—
257C11×C4⋊C4C2412yes—
258C11×C22⋊C4—24no—
259C11×C22⋊C4—24no—
260C42×C11C2×D412yes—
261C42×C11C2412yes—
262C22⋊Dic11—24no—
263C22⋊Dic11—24no—
264#4324—28no—
265#4323—28no—
266(C2×D11)⋊C4—24no—
267(C2×D11)⋊C4—24no—
268(C2×D11)⋊C4—24no—
269C4⋊Dic11—21no—
270C4⋊Dic11—21no—
271C4⋊Dic11C2412yes—
272C4⋊Dic11C2412yes—
273Dic11⋊C4—24no—
274Dic11⋊C4—24no—
275Dic11⋊C4—24no—
276C4×Dic11—24no—
277C4×Dic11—24no—
278C4×Dic11—24no—
279C4×Dic11C2×D412yes—
280C4×Dic11C2×D414yes—
281C4×Dic11C2×D414yes—
282C4×Dic11C2412yes—
283C2×C11⋊C8—22no—
284C2×C11⋊C8—22no—
285C2×C11⋊C8C2412yes—
286C2×C11⋊C8C2412yes—
287#4314—28no—
288C2×#532—111no—
289C2×C4×#41—111no—
290#3115—1116no—
291C2×#482—111no—
292C2×#482—111no—
293C2×#475—111no—
294C2×#474—111no—
295C2×#460—111no—
296C2×#459—111no—
297C2×#449—111no—
298C2×#449—111no—
299C2×#442—111no—
300C2×#442D1111yescharacteristic, complemented
301C2×#440—111no—
302C2×#440—111no—
303C2×#432—111no—
304C23×C11—24no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—42no—
308C23×C11—42no—
309C23×C11—42no—
310C23×C11—42no—
311C23×C11—42no—
312C23×C11C22×D411yescharacteristic
313C22×D11—22no—
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—22no—
317C22×D11—42no—
318C22×D11—42no—
319C22×D11—42no—
320C22×D11C22×D412yes—
321D4×C11—24no—
322D4×C11—22no—
323D4×C11—22no—
324D4×C11—22no—
325D4×C11—42no—
326D4×C11C2×#4114yescomplemented
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—48no—
332C2×C4×C11—48no—
333C2×C4×C11—42no—
334C2×C4×C11—42no—
335C2×C4×C11C22×D412yes—
336C2×C4×C11C22×D412yes—
337C2×C4×C11C22×D411yescharacteristic
338C2×C4×C11C2×#4112yes—
339C2×C4×C11C2×#4112yes—
340C2×C4×C11C2511yescharacteristic
341C22⋊D11—216no—
342C22⋊D11—48no—
343C22⋊D11—48no—
344C22⋊D11—48no—
345C2×Dic11—216no—
346C2×Dic11—24no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—22no—
352C2×Dic11—42no—
353C2×Dic11—42no—
354C2×Dic11—48no—
355C2×Dic11AGL(1,ℤ/8)14yes—
356C2×Dic11C22×D412yes—
357C2×Dic11C22×D412yes—
358C2×Dic11C22×D412yes—
359D44—22no—
360D44—22no—
361D44—48no—
362D44—42no—
363C4×D11—24no—
364C4×D11—22no—
365C4×D11—22no—
366C4×D11—28no—
367C4×D11—44no—
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×D8C2×D1111yescharacteristic
383#532—118no—
384#532—224no—
385C2×C4⋊Q8—111no—
386C2×#127—111no—
387C2×#124—221no—
388C2×#121—111no—
389C2×#121—111no—
390C2×#121—221no—
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—221no—
398C2×C4×D4—221no—
399C2×C4×D4—221no—
400C2×C4×D4C2×D1111yescharacteristic
401C2×C4×D4C2×D1111yescharacteristic
402C2×#117—111no—
403C2×#117—221no—
404C22×C42—111no—
405C22×C42—221no—
406#482—118no—
407#482—118no—
408#475—118no—
409#474—118no—
410#460—118no—
411#459—118no—
412#449—118no—
413#449—118no—
414#442—118no—
415#442C2×D1118yescomplemented
416#440—118no—
417#440—118no—
418#432—118no—
419C2×#107—111no—
420C2×#107—111no—
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⋊C8—111no—
435C2×#97—111no—
436C2×#97C2×D1111yescharacteristic
437C22×C11—24no—
438C22×C11—48no—
439C22×C11—42no—
440C22×C11—42no—
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—22no—
450C2×D11—22no—
451C2×D11—22no—
452C2×D11—44no—
453C2×D11—42no—
454C2×D11—42no—
455C2×D11—42no—
456C2×D11—84no—
457C4×C11—22no—
458C4×C11—22no—
459C4×C11—42no—
460C4×C11—42no—
461C4×C11#52512yes—
462C4×C11C22×#4111yescharacteristic
463C4×C11C22×#4111yescharacteristic
464Dic11—24no—
465Dic11—22no—
466Dic11—22no—
467Dic11—42no—
468Dic11—42no—
469Dic11C2×AGL(1,ℤ/8)14yes—
470C2×#41—114no—
471C2×#41—228no—
472C2×#41—222no—
473C2×#41—224no—
474C2×#41—224no—
475C2×#41—448no—
476C22×Q8—111no—
477C22×Q8—221no—
478C22×D4—111no—
479C22×D4—221no—
480C22×D4—221no—
481C22×D4—221no—
482C22×D4—221no—
483C22×D4—221no—
484C22×D4C22×D1111yescharacteristic
485C22×D4C22×D1111yescharacteristic
486C23×C4—21no—
487C23×C4—21no—
488C23×C4—111no—
489C23×C4—111no—
490C23×C4—111no—
491C23×C4—221no—
492C23×C4—221no—
493C23×C4—221no—
494C2×SD16—114no—
495C2×SD16—114no—
496C2×SD16—224no—
497C2×SD16—224no—
498C2×D8—24no—
499C2×D8—114no—
500C2×D8—224no—
501C2×D8C22×D1114yes—
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—114no—
512#121—114no—
513#121—228no—
514#121—222no—
515#121—222no—
516C4×Q8—114no—
517C4×Q8—114no—
518C4×Q8—222no—
519C4×Q8—222no—
520C4×D4—22no—
521C4×D4—22no—
522C4×D4—114no—
523C4×D4—114no—
524C4×D4—228no—
525C4×D4—222no—
526C4×D4—228no—
527C4×D4—228no—
528C4×D4—222no—
529C4×D4C22×D1114yes—
530C4×D4C22×D1114yes—
531#117—114no—
532#117—228no—
533#117—222no—
534C2×C4⋊C4—111no—
535C2×C4⋊C4—111no—
536C2×C4⋊C4—221no—
537C2×C4⋊C4—221no—
538C2×C4⋊C4—221no—
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—111no—
549C2×C42—111no—
550C2×C42—111no—
551C2×C42—114no—
552C2×C42—114no—
553C2×C42—228no—
554C2×C42—221no—
555C2×C42—221no—
556C2×C42—221no—
557C2×C42C22×D1111yescharacteristic
558#107—114no—
559#107—114no—
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⋊C8—114no—
574#97—114no—
575#97C22×D1114yes—
576C2×C11—44no—
577C2×C11—82no—
578C2×C11#311514yescomplemented
579C2×C11C2×#52511yescharacteristic
580C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
581C2×C11C2×#57511yescharacteristic
582D11—42no—
583D11—82no—
584C24—21no—
585C24—21no—
586C24—111no—
587C24—221no—
588#41—228no—
589#41—2216no—
590#41—228no—
591#41—4432no—
592C2×Q8—114no—
593C2×Q8—112no—
594C2×Q8—224no—
595C2×Q8—222no—
596C2×Q8—221no—
597C2×Q8—444no—
598C2×D4—22no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—112no—
604C2×D4—224no—
605C2×D4—224no—
606C2×D4—224no—
607C2×D4—224no—
608C2×D4—228no—
609C2×D4—224no—
610C2×D4—222no—
611C2×D4—221no—
612C2×D4—222no—
613C2×D4—444no—
614C2×D4—444no—
615C2×D4—444no—
616C2×D4—444no—
617C2×D4#433914yescomplemented
618C2×D4C23×D1112yes—
619C2×D4C23×D1112yes—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—24no—
623C22×C4—24no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4—111no—
627C22×C4—111no—
628C22×C4—111no—
629C22×C4—112no—
630C22×C4—114no—
631C22×C4—112no—
632C22×C4—114no—
633C22×C4—224no—
634C22×C4—224no—
635C22×C4—224no—
636C22×C4—228no—
637C22×C4—221no—
638C22×C4—222no—
639C22×C4—222no—
640C22×C4—221no—
641C22×C4—221no—
642C22×C4—224no—
643C22×C4—442no—
644C22×C4—444no—
645C22×C4—444no—
646C22×C4D4×D1111yescharacteristic
647C22×C4D4×D1111yescharacteristic
648C22×C4C23×D1111yescharacteristic
649SD16—228no—
650SD16—228no—
651D8—28no—
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—112no—
664C4⋊C4—112no—
665C4⋊C4—224no—
666C4⋊C4—224no—
667C4⋊C4—221no—
668C4⋊C4—221no—
669C4⋊C4—224no—
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—114no—
680C42—114no—
681C42—112no—
682C42—112no—
683C42—224no—
684C42—224no—
685C42—224no—
686C42D4×D1112yes—
687C42C23×D1112yes—
688C11C2×#311511yescharacteristic, complemented, Sylow
689C23—24no—
690C23—22no—
691C23—22no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—112no—
698C23—222no—
699C23—222no—
700C23—222no—
701C23—222no—
702C23—442no—
703C23—442no—
704C23—442no—
705C23C2×D4×D1111yescharacteristic
706Q8—114no—
707Q8—224no—
708Q8—222no—
709Q8—448no—
710D4—24no—
711D4—22no—
712D4—22no—
713D4—22no—
714D4—42no—
715D4—2216no—
716D4—222no—
717D4—222no—
718D4—448no—
719D4—448no—
720D4—448no—
721D4—448no—
722D4—442no—
723D4C2×#433914yescomplemented
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—48no—
729C2×C4—48no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—114no—
733C2×C4—112no—
734C2×C4—112no—
735C2×C4—112no—
736C2×C4—228no—
737C2×C4—2216no—
738C2×C4—222no—
739C2×C4—222no—
740C2×C4—224no—
741C2×C4—222no—
742C2×C4—224no—
743C2×C4—222no—
744C2×C4—222no—
745C2×C4—222no—
746C2×C4—222no—
747C2×C4—444no—
748C2×C4—448no—
749C2×C4—448no—
750C2×C4—442no—
751C2×C4—442no—
752C2×C4C2×#433912yes—
753C2×C4C2×D4×D1112yes—
754C2×C4C2×D4×D1112yes—
755C2×C4C2×D4×D1111yescharacteristic
756C2×C4#41×D1112yes—
757C2×C4C24×D1111yescharacteristic
758C8—22no—
759C8—22no—
760C8—222no—
761C8—222no—
762C22—24no—
763C22—42no—
764C22—42no—
765C22—48no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—84no—
770C22—222no—
771C22—222no—
772C22—222no—
773C22—444no—
774C22—442no—
775C22—442no—
776C22—442no—
777C22—884no—
778C22#1062307812yes—
779C22D11×AGL(1,ℤ/8)12yes—
780C22#1062330412yes—
781C22C22×D4×D1111yescharacteristic
782C4—22no—
783C4—22no—
784C4—42no—
785C4—42no—
786C4—114no—
787C4—222no—
788C4—224no—
789C4—222no—
790C4—442no—
791C4—442no—
792C4#1062307812yes—
793C4C22×#433911yescharacteristic
794C4C2×#41×D1111yescharacteristic
795C2—44no—
796C2—82no—
797C2—442no—
798C2—882no—
799C2#1307876314yesdirect product factor
800C2C2×#1062307811yescharacteristic
801C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
802C2C2×#1062330411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#442C2
socleC23×C11C22×D4
hypercenterC2×#442D11
hypocenterC11C2×#3115
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#10623079C2semidirect
2. C2×C4×#4341C2semidirect
3. #13078763C2direct (N × H)
4. C2×#10622479C2semidirect
5. C2×#10622397C2semidirect
6. C2×#10622467C2semidirect
7. C2×#10622372C2semidirect
8. C2×#10622375C2semidirect
9. C2×#10622763C2semidirect
10. C2×#10622394C2semidirect
11. C2×#10622771C2semidirect
12. C2×#10622627C2semidirect
13. C2×#10622323C2semidirect
14. C2×#10622631C2semidirect
15. C2×#10622318C2semidirect
16. C2×C11×#442C2semidirect
32. #10623079C22semidirect
34. C4×#4341C22semidirect
46. C11×#442C22semidirect
53. #10622771C22semidirect
54. #10622763C22semidirect
62. #10622631C22semidirect
63. #10622627C22semidirect
69. #10622479C22semidirect
70. #10622467C22semidirect
71. #10622397C22semidirect
72. #10622394C22semidirect
73. #10622375C22semidirect
74. #10622372C22semidirect
75. #10622323C22semidirect
76. #10622318C22semidirect
193. C2×D4×C11#41semidirect
247. C2×Dic22#41semidirect
300. C2×#442D11semidirect
326. D4×C11C2×#41semidirect
372. Dic22C2×#41semidirect
415. #442C2×D11semidirect
578. C2×C11#3115semidirect
617. C2×D4#4339semidirect
688. C11C2×#3115semidirect
723. D4C2×#4339semidirect
799. C2#13078763direct (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×C4×#43412
#130787632
C2×#106224792
C2×#106223972
C2×#106224672
C2×#106223722
C2×#106223752
C2×#106227632
C2×#106223942
C2×#106227712
C2×#106226272
C2×#106223232
C2×#106226312
C2×#106223182
C2×C11×#4422
C2×#311511