Finite Group Databasebeta

← C2×#13082498 #15662214

Subgroups — C2×#13082498 #15662214

Order 2816.

7022 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082498C2132yesmaximal, direct product factor
2C2×#10623216C214yesmaximal, complemented
3C2×#10623233C214yesmaximal, complemented
4C2×#10623239C214yesmaximal, complemented
5C2×#10623224C214yesmaximal, complemented
6C2×#10623228C211yesmaximal, characteristic, complemented
7C2×#10623049C211yesmaximal, characteristic, complemented
8C2×#10623262C211yesmaximal, characteristic, complemented
9C2×#10623159C212yesmaximal
10C2×#10623219C211yesmaximal, characteristic, complemented
11C2×#10623109C212yesmaximal, complemented
12C2×#10623153C212yesmaximal, complemented
13C2×D11×C4⋊Q8C211yesmaximal, characteristic, complemented
14C2×#10623103C212yesmaximal, complemented
15C2×#10623053C211yesmaximal, characteristic
16C2×C11×#541C211yesmaximal, characteristic, complemented
17C22×Q8×D11C2212yes—
18C22×#4339C2211yescharacteristic
19C11×#541C22116yescomplemented
20C2×C11×C4⋊Q8C2211yescharacteristic
21C2×C11×#126C2214yes—
22C2×C11×#125C2214yes—
23C2×C11×#125C2211yescharacteristic
24C2×C11×C22⋊Q8C2212yes—
25C2×C4×Q8×C11C2212yes—
26C2×C11×#117C2211yescharacteristic
27C2×#66999C2212yes—
28C2×Q8×Dic11C2212yes—
29C2×#66997C2212yes—
30C2×#66977C2212yes—
31C22×C4×Dic11C2211yescharacteristic
32#10623262C22116yescomplemented
33D11×C4⋊Q8C22116yescomplemented
34#10623239C22164yescomplemented
35#10623233C22164yescomplemented
36#10623228C22116yescomplemented
37#10623224C22164yescomplemented
38#10623219C22116yescomplemented
39#10623216C22164yescomplemented
40#10623159C22132yes—
41#10623153C22132yescomplemented
42#10623109C22132yescomplemented
43#10623103C22132yescomplemented
44#10623053C22116yes—
45#10623049C22116yescomplemented
46C2×#66951C2214yes—
47C2×#66951C2214yes—
48C2×#66950C2212yes—
49C2×#66949C2214yes—
50C2×#66949C2214yes—
51C2×#66947C2214yes—
52C2×#66946C2212yes—
53C2×#66945C2214yes—
54C2×#66945C2212yes—
55C2×C4⋊C4×D11C2214yes—
56C2×#66943C2214yes—
57C2×#66942C2214yes—
58C2×#66942C2214yes—
59C2×#66942C2214yes—
60C2×#66942C2214yes—
61C2×#66941C2214yes—
62C2×#66941C2212yes—
63C2×#66941C2214yes—
64C2×#66940C2214yes—
65C2×#66940C2212yes—
66C2×#66940C2214yes—
67C2×#66940C2214yes—
68C2×#66940C2212yes—
69C2×#66938C2214yes—
70C2×#66936C2214yes—
71C2×(C22⋊D11)⋊C4C2212yes—
72C2×(C22⋊D11)⋊C4C2212yes—
73C2×#66932C2214yes—
74C2×#66931C2214yes—
75C2×#66930C2214yes—
76C2×#66925C2214yes—
77C2×#66925C2214yes—
78C2×#66925C2211yescharacteristic
79C2×#66925C2211yescharacteristic
80C2×C42×D11C2211yescharacteristic
81C2×C42×D11C2211yescharacteristic
82C2×#66923C2211yescharacteristic
83C2×#66922C2211yescharacteristic
84C2×C4×Dic22C2214yes—
85C2×C4×Dic22C2214yes—
86C2×C4×Dic22C2212yes—
87C22×Q8×C11C2312yes—
88C23×C4×C11C2311yescharacteristic
89C22×C22⋊D11C2311yescharacteristic
90C22×C22⋊D11C2311yescharacteristic
91C23×Dic11C2312yes—
92C2×Q8×D11—216no—
93C2×Q8×D11C23116yes—
94C2×#4339—28no—
95C2×#4339C2318yes—
96C22×D44C2311yescharacteristic
97C22×C4×D11C2312yes—
98C22×C4×D11C2311yescharacteristic
99C22×C4×D11C2312yes—
100C22×C4×D11C2314yes—
101C22×C4×D11C2311yescharacteristic
102C22×Dic22C2312yes—
103C22×Dic22C2314yes—
104C22×Dic22C2314yes—
105C22×Dic22C2311yescharacteristic
106C11×C4⋊Q8C2318yes—
107C11×#126C23132yes—
108C11×#125C23132yes—
109C11×#125C2318yes—
110C11×C22⋊Q8C23116yes—
111C4×Q8×C11C23116yes—
112C11×#117C2318yes—
113C2×C11×C4⋊C4C2314yes—
114C2×C11×C4⋊C4C2312yes—
115C2×C11×C4⋊C4C2312yes—
116C2×C11×C4⋊C4C2314yes—
117C2×C11×C4⋊C4C2314yes—
118C2×C11×C4⋊C4C2314yes—
119C2×C11×C22⋊C4C2314yes—
120C2×C11×C22⋊C4C2312yes—
121C2×C42×C11C2311yescharacteristic
122C2×C42×C11C2314yes—
123C2×C42×C11C2311yescharacteristic
124C2×C22⋊Dic11C2314yes—
125#66999C23116yes—
126Q8×Dic11C23116yes—
127#66997C23116yes—
128C2×(C2×D11)⋊C4C2312yes—
129C2×(C2×D11)⋊C4C2312yes—
130C2×(C2×D11)⋊C4C2314yes—
131C2×(C2×D11)⋊C4C2314yes—
132C2×(C2×D11)⋊C4C2314yes—
133C2×C4⋊Dic11C2312yes—
134C2×C4⋊Dic11C2314yes—
135C2×C4⋊Dic11C2314yes—
136C2×C4⋊Dic11C2314yes—
137#66977C23116yes—
138C2×Dic11⋊C4C2314yes—
139C2×Dic11⋊C4C2312yes—
140C2×Dic11⋊C4C2314yes—
141C2×Dic11⋊C4C2314yes—
142C2×Dic11⋊C4C2314yes—
143C2×Dic11⋊C4C2314yes—
144C2×Dic11⋊C4C2314yes—
145C2×Dic11⋊C4C2314yes—
146C2×Dic11⋊C4C2312yes—
147C2×Dic11⋊C4C2314yes—
148C2×C4×Dic11C2312yes—
149C2×C4×Dic11C2314yes—
150C2×C4×Dic11C2314yes—
151C2×C4×Dic11C2314yes—
152C2×C4×Dic11C2311yescharacteristic
153C2×C4×Dic11C2312yes—
154C2×C4×Dic11C2311yescharacteristic
155C2×C4×Dic11C2314yes—
156C2×C4×Dic11C2312yes—
157C2×C4×Dic11C2318yes—
158#66951C23132yes—
159#66951C23132yes—
160#66950C23116yes—
161#66949C23132yes—
162#66949C23132yes—
163#66947C23132yes—
164#66946C23116yes—
165#66945C23132yes—
166#66945C23116yes—
167C4⋊C4×D11C23132yes—
168#66943C23132yes—
169#66942C23132yes—
170#66942C23132yes—
171#66942C23132yes—
172#66942C23132yes—
173#66941C23132yes—
174#66941C23116yes—
175#66941C23132yes—
176#66940C23132yes—
177#66940C23132yes—
178#66940C23116yes—
179#66940C23116yes—
180#66940C23132yes—
181#66938C23132yes—
182#66936C23132yes—
183(C22⋊D11)⋊C4C23116yes—
184(C22⋊D11)⋊C4C23116yes—
185#66932C23132yes—
186#66931C23132yes—
187#66930C23132yes—
188#66925C23132yes—
189#66925C23132yes—
190#66925C2318yes—
191#66925C2318yes—
192C42×D11C2318yes—
193C42×D11C2318yes—
194#66923C2318yes—
195#66922C2318yes—
196C4×Dic22C23132yes—
197C4×Dic22C23132yes—
198C4×Dic22C23116yes—
199C2×#3509—111nomaximal, Sylow
200C24×C11C2411yescharacteristic
201C23×D11C2411yescharacteristic
202C23×D11C2411yescharacteristic
203C2×Q8×C11—28no—
204C2×Q8×C11C2418yes—
205C22×C4×C11—24no—
206C22×C4×C11C2412yes—
207C22×C4×C11C2411yescharacteristic
208C22×C4×C11C2414yes—
209C22×C4×C11C2414yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2414yes—
212C22×C4×C11C2411yescharacteristic
213C2×C22⋊D11—24no—
214C2×C22⋊D11—24no—
215C2×C22⋊D11C2414yes—
216C2×C22⋊D11C2414yes—
217C22×Dic11—28no—
218C22×Dic11C2418yes—
219C22×Dic11C2412yes—
220C22×Dic11C2414yes—
221C22×Dic11C2411yescharacteristic
222C22×Dic11C2414yes—
223C22×Dic11C2411yescharacteristic
224C22×Dic11C2412yes—
225Q8×D11—264no—
226#4339—232no—
227C2×D44—24no—
228C2×D44C2414yes—
229C2×C4×D11—28no—
230C2×C4×D11—28no—
231C2×C4×D11—216no—
232C2×C4×D11—24no—
233C2×C4×D11#4118yes—
234C2×C4×D11C2418yes—
235C2×C4×D11C2414yes—
236C2×C4×D11C2418yes—
237C2×C4×D11C24116yes—
238C2×C4×D11C2414yes—
239C2×Dic22—24no—
240C2×Dic22—216no—
241C2×Dic22—216no—
242C2×Dic22—28no—
243C2×Dic22C2418yes—
244C2×Dic22C24116yes—
245C2×Dic22C24116yes—
246C2×Dic22C2414yes—
247C11×C4⋊C4C24116yes—
248C11×C4⋊C4C2418yes—
249C11×C4⋊C4C2418yes—
250C11×C4⋊C4C24116yes—
251C11×C4⋊C4C24116yes—
252C11×C4⋊C4C24116yes—
253C11×C22⋊C4C24116yes—
254C11×C22⋊C4C2418yes—
255C42×C11C2414yes—
256C42×C11C24116yes—
257C42×C11C2414yes—
258C22⋊Dic11C24116yes—
259(C2×D11)⋊C4C2418yes—
260(C2×D11)⋊C4C2418yes—
261(C2×D11)⋊C4C24116yes—
262(C2×D11)⋊C4C24116yes—
263(C2×D11)⋊C4C24116yes—
264C4⋊Dic11C2418yes—
265C4⋊Dic11C24116yes—
266C4⋊Dic11C24116yes—
267C4⋊Dic11C24116yes—
268Dic11⋊C4C24116yes—
269Dic11⋊C4C2418yes—
270Dic11⋊C4C24116yes—
271Dic11⋊C4C24116yes—
272Dic11⋊C4C24116yes—
273Dic11⋊C4C24116yes—
274Dic11⋊C4C24116yes—
275Dic11⋊C4C24116yes—
276Dic11⋊C4C2418yes—
277Dic11⋊C4C24116yes—
278C4×Dic11C2418yes—
279C4×Dic11C24116yes—
280C4×Dic11C24116yes—
281C4×Dic11C24116yes—
282C4×Dic11C2414yes—
283C4×Dic11C2418yes—
284C4×Dic11C2414yes—
285C4×Dic11C24116yes—
286C4×Dic11C2418yes—
287#3509—1132no—
288C2×#557—114no—
289C2×#556—114no—
290C2×#552—114no—
291C2×#552—114no—
292C2×#541—111no—
293C2×#541—111no—
294C2×#541—111no—
295C2×#541D1111yescharacteristic, complemented
296C2×#536—112no—
297C2×#533—111no—
298C2×#533—112no—
299C2×#533—112no—
300C22×C4⋊Q8—111no—
301C2×#519—112no—
302C2×C4×#41—111no—
303C23×C11—22no—
304C23×C11—24no—
305C23×C11C2512yes—
306C23×C11C2511yescharacteristic
307C22×D11—24no—
308C22×D11—22no—
309C22×D11—24no—
310C22×D11C2×#4114yes—
311C22×D11C2512yes—
312C22×D11C2512yes—
313Q8×C11—216no—
314C2×C4×C11—28no—
315C2×C4×C11—22no—
316C2×C4×C11—28no—
317C2×C4×C11—24no—
318C2×C4×C11—24no—
319C2×C4×C11—28no—
320C2×C4×C11C2×#4114yes—
321C2×C4×C11C2514yes—
322C2×C4×C11C2512yes—
323C2×C4×C11C2518yes—
324C2×C4×C11C2514yes—
325C2×C4×C11C2518yes—
326C2×C4×C11C2512yes—
327C22⋊D11—28no—
328C22⋊D11—28no—
329C2×Dic11—28no—
330C2×Dic11—22no—
331C2×Dic11—28no—
332C2×Dic11—24no—
333C2×Dic11—216no—
334C2×Dic11C2×#4114yes—
335C2×Dic112−1+418yes—
336C2×Dic11C2514yes—
337C2×Dic11C2518yes—
338C2×Dic11C2512yes—
339C2×Dic11C2518yes—
340C2×Dic11C2512yes—
341C2×Dic11C2514yes—
342D44—28no—
343C4×D11—232no—
344C4×D11—28no—
345C4×D11—216no—
346C4×D11—216no—
347C4×D11C2×#41116yes—
348Dic22—216no—
349Dic22—28no—
350Dic22—232no—
351Dic22—232no—
352C22×#41—111no—
353C23×Q8—112no—
354#557—1164no—
355#556—1164no—
356#552—1164no—
357#552—1164no—
358#541—1116no—
359#541—1116no—
360#541—1116no—
361#541C2×D11116yescomplemented
362#536—1132no—
363#533—1116no—
364#533—1132no—
365#533—1132no—
366C2×C4⋊Q8—112no—
367C2×C4⋊Q8—1116no—
368C2×C4⋊Q8—114no—
369C2×C4⋊Q8—112no—
370C2×C4⋊Q8—114no—
371C2×C4⋊Q8—111no—
372C2×C4⋊Q8C2×D1111yescharacteristic
373C2×#126—114no—
374C2×#126—114no—
375C2×#126—114no—
376C2×#126C2×D1114yes—
377C2×#125—114no—
378C2×#125—114no—
379C2×#125—114no—
380C2×#125—114no—
381C2×#125—114no—
382C2×#125—111no—
383C2×#125C2×D1111yescharacteristic
384C2×#125C2×D1114yes—
385C2×#124—114no—
386C2×#123—114no—
387C2×#123—114no—
388C2×C22⋊Q8—112no—
389C2×C22⋊Q8—112no—
390C2×C22⋊Q8—114no—
391C2×C22⋊Q8—114no—
392C2×C22⋊Q8—112no—
393C2×C22⋊Q8—114no—
394C2×C22⋊Q8C2×D1112yes—
395#519—1132no—
396C4×#41—1116no—
397C2×C4×Q8—112no—
398C2×C4×Q8—112no—
399C2×C4×Q8—112no—
400C2×C4×Q8—114no—
401C2×C4×Q8—114no—
402C2×C4×Q8—114no—
403C2×C4×Q8—112no—
404C2×C4×Q8—114no—
405C2×C4×Q8—114no—
406C2×C4×Q8C2×D1112yes—
407C2×C4×D4—112no—
408C2×C4×D4—112no—
409C2×C4×D4—112no—
410C2×#117—112no—
411C2×#117—114no—
412C2×#117—114no—
413C2×#117—111no—
414C2×#117—111no—
415C2×#117—114no—
416C2×#117—114no—
417C2×#117C2×D1111yescharacteristic
418C22×C4⋊C4—114no—
419C22×C42—111no—
420C22×C42—111no—
421C22×C42—111no—
422C22×C11—22no—
423C22×C11—24no—
424C22×C11—44no—
425C22×C11C22×#4112yes—
426C22×C11C2×2−1+414yes—
427C22×C11C2611yescharacteristic
428C2×D11—24no—
429C2×D11—28no—
430C2×D11—22no—
431C2×D11—24no—
432C2×D11—44no—
433C2×D11C22×#4114yes—
434C4×C11—22no—
435C4×C11—28no—
436C4×C11—28no—
437C4×C11—24no—
438C4×C11—24no—
439C4×C11C22×#4114yes—
440Dic11—28no—
441Dic11—22no—
442Dic11—28no—
443Dic11—24no—
444Dic11C22×#4114yes—
445Dic11C2×2−1+418yes—
446C2×#41—118no—
447C2×#41—228no—
448C22×Q8—1116no—
449C22×Q8—114no—
450C22×Q8—112no—
451C22×Q8—114no—
452C22×Q8—111no—
453C22×Q8—2216no—
454C22×Q8C22×D1112yes—
455C22×D4—111no—
456C22×D4—111no—
457C22×D4—111no—
458C23×C4—111no—
459C23×C4—112no—
460C23×C4—114no—
461C23×C4—112no—
462C23×C4—112no—
463C23×C4—111no—
464C23×C4C22×D1111yescharacteristic
465C4⋊Q8—1116no—
466C4⋊Q8—1132no—
467C4⋊Q8—1116no—
468C4⋊Q8—1132no—
469C4⋊Q8—118no—
470C4⋊Q8C22×D1118yes—
471#126—1132no—
472#126—1132no—
473#126—1132no—
474#126C22×D11132yes—
475#125—1132no—
476#125—1132no—
477#125—1132no—
478#125—1132no—
479#125—1132no—
480#125—118no—
481#125C22×D1118yes—
482#125C22×D11132yes—
483#124—1132no—
484#123—1132no—
485#123—1132no—
486C22⋊Q8—1116no—
487C22⋊Q8—1116no—
488C22⋊Q8—1116no—
489C22⋊Q8—1132no—
490C22⋊Q8—1132no—
491C22⋊Q8—1132no—
492C22⋊Q8C22×D11116yes—
493C4×Q8—1116no—
494C4×Q8—1116no—
495C4×Q8—1116no—
496C4×Q8—1132no—
497C4×Q8—1132no—
498C4×Q8—1132no—
499C4×Q8—1116no—
500C4×Q8—1132no—
501C4×Q8—1132no—
502C4×Q8C22×D11116yes—
503C4×D4—1116no—
504C4×D4—1116no—
505C4×D4—1116no—
506#117—1116no—
507#117—1132no—
508#117—1132no—
509#117—118no—
510#117—118no—
511#117—1132no—
512#117—1132no—
513#117C22×D1118yes—
514C2×C4⋊C4—114no—
515C2×C4⋊C4—114no—
516C2×C4⋊C4—114no—
517C2×C4⋊C4—114no—
518C2×C4⋊C4—112no—
519C2×C4⋊C4—112no—
520C2×C4⋊C4—112no—
521C2×C4⋊C4—114no—
522C2×C4⋊C4—114no—
523C2×C4⋊C4—114no—
524C2×C4⋊C4—114no—
525C2×C4⋊C4—114no—
526C2×C4⋊C4—114no—
527C2×C4⋊C4—114no—
528C2×C4⋊C4—1132no—
529C2×C4⋊C4C22×D1114yes—
530C2×C4⋊C4C22×D1112yes—
531C2×C4⋊C4C22×D1114yes—
532C2×C4⋊C4C22×D1112yes—
533C2×C4⋊C4C22×D1114yes—
534C2×C4⋊C4C22×D1114yes—
535C2×C22⋊C4—114no—
536C2×C22⋊C4—112no—
537C2×C22⋊C4—114no—
538C2×C22⋊C4—112no—
539C2×C22⋊C4—114no—
540C2×C22⋊C4—114no—
541C2×C22⋊C4C22×D1114yes—
542C2×C22⋊C4C22×D1112yes—
543C2×C42—111no—
544C2×C42—114no—
545C2×C42—114no—
546C2×C42—114no—
547C2×C42—114no—
548C2×C42—112no—
549C2×C42—112no—
550C2×C42—112no—
551C2×C42—118no—
552C2×C42—111no—
553C2×C42—118no—
554C2×C42—118no—
555C2×C42C22×D1114yes—
556C2×C42C22×D1111yescharacteristic
557C2×C42C22×D1111yescharacteristic
558C2×C11—42no—
559C2×C11#350914yescomplemented
560C2×C11C23×#4111yescharacteristic
561C2×C11C22×2−1+412yes—
562D11—24no—
563D11—42no—
564C24—111no—
565C24—111no—
566C24C23×D1111yescharacteristic
567#41—2232no—
568C2×Q8—28no—
569C2×Q8—1116no—
570C2×Q8—118no—
571C2×Q8—1116no—
572C2×Q8—114no—
573C2×Q8—2216no—
574C2×Q8—224no—
575C2×Q8—2216no—
576C2×Q8—2264no—
577C2×Q8—228no—
578C2×Q8C23×D1118yes—
579C2×D4—114no—
580C2×D4—114no—
581C2×D4—114no—
582C2×D4—224no—
583C2×D4—224no—
584C2×D4—224no—
585C22×C4—24no—
586C22×C4—111no—
587C22×C4—112no—
588C22×C4—118no—
589C22×C4—114no—
590C22×C4—118no—
591C22×C4—112no—
592C22×C4—114no—
593C22×C4—114no—
594C22×C4—111no—
595C22×C4—118no—
596C22×C4—118no—
597C22×C4—114no—
598C22×C4—1116no—
599C22×C4—228no—
600C22×C4—228no—
601C22×C4—2216no—
602C22×C4—228no—
603C22×C4—224no—
604C22×C4C23×D1114yes—
605C22×C4C23×D1112yes—
606C22×C4C23×D1114yes—
607C22×C4C23×D1111yescharacteristic
608C22×C4C23×D1112yes—
609C22×C4C23×D1114yes—
610C22×C4C23×D1111yescharacteristic
611C4⋊C4—1116no—
612C4⋊C4—1116no—
613C4⋊C4—1116no—
614C4⋊C4—1116no—
615C4⋊C4—118no—
616C4⋊C4—118no—
617C4⋊C4—118no—
618C4⋊C4—1116no—
619C4⋊C4—1116no—
620C4⋊C4—1116no—
621C4⋊C4—1116no—
622C4⋊C4—1116no—
623C4⋊C4—1116no—
624C4⋊C4—1116no—
625C4⋊C4C23×D11116yes—
626C4⋊C4C23×D1118yes—
627C4⋊C4C23×D11116yes—
628C4⋊C4C23×D1118yes—
629C4⋊C4C23×D11116yes—
630C4⋊C4C23×D11116yes—
631C22⋊C4—1116no—
632C22⋊C4—118no—
633C22⋊C4—1116no—
634C22⋊C4—118no—
635C22⋊C4—1116no—
636C22⋊C4—1116no—
637C22⋊C4C23×D11116yes—
638C22⋊C4C23×D1118yes—
639C42—114no—
640C42—114no—
641C42—118no—
642C42—118no—
643C42—118no—
644C42—1116no—
645C42—1116no—
646C42—1116no—
647C42—1116no—
648C42C23×D1114yes—
649C42C23×D1114yes—
650C42C23×D11116yes—
651C11C2×#350911yescharacteristic, complemented, Sylow
652C23—22no—
653C23—24no—
654C23—114no—
655C23—112no—
656C23—112no—
657C23—224no—
658C23—222no—
659C23—224no—
660C23C24×D1112yes—
661C23C24×D1111yescharacteristic
662Q8—216no—
663Q8—2232no—
664Q8—228no—
665Q8—2232no—
666Q8—2216no—
667D4—228no—
668D4—228no—
669D4—228no—
670C2×C4—22no—
671C2×C4—28no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—28no—
675C2×C4—28no—
676C2×C4—114no—
677C2×C4—118no—
678C2×C4—112no—
679C2×C4—114no—
680C2×C4—1116no—
681C2×C4—114no—
682C2×C4—118no—
683C2×C4—118no—
684C2×C4—112no—
685C2×C4—2216no—
686C2×C4—2216no—
687C2×C4—2232no—
688C2×C4—2216no—
689C2×C4—222no—
690C2×C4—228no—
691C2×C4—224no—
692C2×C4—228no—
693C2×C4—228no—
694C2×C4#41×D1114yes—
695C2×C4C24×D1114yes—
696C2×C4C24×D1118yes—
697C2×C4C24×D1112yes—
698C2×C4C24×D1114yes—
699C2×C4C24×D1118yes—
700C2×C4C24×D1112yes—
701C22—22no—
702C22—24no—
703C22—44no—
704C22—114no—
705C22—224no—
706C22—228no—
707C22—222no—
708C22—224no—
709C22—444no—
710C22C2×#41×D1112yes—
711C22D11×2−1+414yes—
712C22C25×D1111yescharacteristic
713C4—22no—
714C4—28no—
715C4—24no—
716C4—24no—
717C4—28no—
718C4—114no—
719C4—118no—
720C4—222no—
721C4—228no—
722C4—224no—
723C4—228no—
724C4C2×#41×D1114yes—
725C2—42no—
726C2—224no—
727C2—442no—
728C2#1308249814yesdirect product factor
729C2C22×#41×D1111yescharacteristic
730C2C2×D11×2−1+412yes—
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#541C2
socleC23×C11C25
prime radicalC22×#4339C22
hypercenterC2×#541D11
hypocenterC11C2×#3509
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
1. #13082498C2direct (N × H)
2. C2×#10623216C2semidirect
3. C2×#10623233C2semidirect
4. C2×#10623239C2semidirect
5. C2×#10623224C2semidirect
6. C2×#10623228C2semidirect
7. C2×#10623049C2semidirect
8. C2×#10623262C2semidirect
10. C2×#10623219C2semidirect
11. C2×#10623109C2semidirect
12. C2×#10623153C2semidirect
13. C2×D11×C4⋊Q8C2semidirect
14. C2×#10623103C2semidirect
16. C2×C11×#541C2semidirect
19. C11×#541C22semidirect
32. #10623262C22semidirect
33. D11×C4⋊Q8C22semidirect
34. #10623239C22semidirect
35. #10623233C22semidirect
36. #10623228C22semidirect
37. #10623224C22semidirect
38. #10623219C22semidirect
39. #10623216C22semidirect
41. #10623153C22semidirect
42. #10623109C22semidirect
43. #10623103C22semidirect
45. #10623049C22semidirect
295. C2×#541D11semidirect
361. #541C2×D11semidirect
559. C2×C11#3509semidirect
651. C11C2×#3509semidirect
728. C2#13082498direct (N × H)

Maximal subgroups

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

subgroupindex
#130824982
C2×#106232162
C2×#106232332
C2×#106232392
C2×#106232242
C2×#106232282
C2×#106230492
C2×#106232622
C2×#106231592
C2×#106232192
C2×#106231092
C2×#106231532
C2×D11×C4⋊Q82
C2×#106231032
C2×#106230532
C2×C11×#5412
C2×#350911