Finite Group Databasebeta

← C2×#13128718 #16771360

Subgroups — C2×#13128718 #16771360

Order 3328.

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#13128718C2132yesmaximal, direct product factor
2C2×#11719390C214yesmaximal, complemented
3C2×#11719407C214yesmaximal, complemented
4C2×#11719413C214yesmaximal, complemented
5C2×#11719398C214yesmaximal, complemented
6C2×#11719402C211yesmaximal, characteristic, complemented
7C2×#11719223C211yesmaximal, characteristic, complemented
8C2×#11719436C211yesmaximal, characteristic, complemented
9C2×#11719333C212yesmaximal
10C2×#11719393C211yesmaximal, characteristic, complemented
11C2×#11719283C212yesmaximal, complemented
12C2×#11719327C212yesmaximal, complemented
13C2×D13×C4⋊Q8C211yesmaximal, characteristic, complemented
14C2×#11719277C212yesmaximal, complemented
15C2×#11719227C211yesmaximal, characteristic
16C2×C13×#541C211yesmaximal, characteristic, complemented
17C22×Q8×D13C2212yes—
18C22×#6127C2211yescharacteristic
19C13×#541C22116yescomplemented
20C2×C13×C4⋊Q8C2211yescharacteristic
21C2×C13×#126C2214yes—
22C2×C13×#125C2211yescharacteristic
23C2×C13×#125C2214yes—
24C2×C13×C22⋊Q8C2212yes—
25C2×C4×Q8×C13C2212yes—
26C2×C13×#117C2211yescharacteristic
27C2×#88200C2212yes—
28C2×Q8×Dic13C2212yes—
29C2×#88198C2212yes—
30C2×#88178C2212yes—
31C22×C4×Dic13C2211yescharacteristic
32#11719436C22116yescomplemented
33D13×C4⋊Q8C22116yescomplemented
34#11719413C22164yescomplemented
35#11719407C22164yescomplemented
36#11719402C22116yescomplemented
37#11719398C22164yescomplemented
38#11719393C22116yescomplemented
39#11719390C22164yescomplemented
40#11719333C22132yes—
41#11719327C22132yescomplemented
42#11719283C22132yescomplemented
43#11719277C22132yescomplemented
44#11719227C22116yes—
45#11719223C22116yescomplemented
46C2×#88152C2214yes—
47C2×#88152C2214yes—
48C2×#88151C2212yes—
49C2×#88150C2214yes—
50C2×#88150C2214yes—
51C2×#88148C2214yes—
52C2×#88147C2212yes—
53C2×#88146C2214yes—
54C2×#88146C2212yes—
55C2×C4⋊C4×D13C2214yes—
56C2×#88144C2214yes—
57C2×#88143C2214yes—
58C2×#88143C2214yes—
59C2×#88143C2214yes—
60C2×#88143C2214yes—
61C2×#88142C2214yes—
62C2×#88142C2212yes—
63C2×#88142C2214yes—
64C2×#88141C2212yes—
65C2×#88141C2212yes—
66C2×#88141C2214yes—
67C2×#88141C2214yes—
68C2×#88141C2214yes—
69C2×#88139C2214yes—
70C2×#88137C2214yes—
71C2×#88135C2212yes—
72C2×#88135C2212yes—
73C2×#88133C2214yes—
74C2×#88132C2214yes—
75C2×#88131C2214yes—
76C2×#88126C2211yescharacteristic
77C2×#88126C2211yescharacteristic
78C2×#88126C2214yes—
79C2×#88126C2214yes—
80C2×C42×D13C2211yescharacteristic
81C2×C42×D13C2211yescharacteristic
82C2×#88124C2211yescharacteristic
83C2×#88123C2211yescharacteristic
84C2×C4×Dic26C2212yes—
85C2×C4×Dic26C2214yes—
86C2×C4×Dic26C2214yes—
87C22×Q8×C13C2312yes—
88C23×C4×C13C2311yescharacteristic
89C22×C22⋊D13C2311yescharacteristic
90C22×C22⋊D13C2311yescharacteristic
91C23×Dic13C2312yes—
92C2×Q8×D13—216no—
93C2×Q8×D13C23116yes—
94C2×#6127—28no—
95C2×#6127C2318yes—
96C22×D52C2311yescharacteristic
97C22×C4×D13C2312yes—
98C22×C4×D13C2311yescharacteristic
99C22×C4×D13C2312yes—
100C22×C4×D13C2314yes—
101C22×C4×D13C2311yescharacteristic
102C22×Dic26C2312yes—
103C22×Dic26C2314yes—
104C22×Dic26C2314yes—
105C22×Dic26C2311yescharacteristic
106C13×C4⋊Q8C2318yes—
107C13×#126C23132yes—
108C13×#125C23132yes—
109C13×#125C2318yes—
110C13×C22⋊Q8C23116yes—
111C4×Q8×C13C23116yes—
112C13×#117C2318yes—
113C2×C13×C4⋊C4C2314yes—
114C2×C13×C4⋊C4C2312yes—
115C2×C13×C4⋊C4C2312yes—
116C2×C13×C4⋊C4C2314yes—
117C2×C13×C4⋊C4C2314yes—
118C2×C13×C4⋊C4C2314yes—
119C2×C13×C22⋊C4C2314yes—
120C2×C13×C22⋊C4C2312yes—
121C2×C42×C13C2311yescharacteristic
122C2×C42×C13C2314yes—
123C2×C42×C13C2311yescharacteristic
124C2×C22⋊Dic13C2314yes—
125#88200C23116yes—
126Q8×Dic13C23116yes—
127#88198C23116yes—
128C2×#6103C2312yes—
129C2×#6103C2312yes—
130C2×#6103C2314yes—
131C2×#6103C2314yes—
132C2×#6103C2314yes—
133C2×C4⋊Dic13C2312yes—
134C2×C4⋊Dic13C2314yes—
135C2×C4⋊Dic13C2314yes—
136C2×C4⋊Dic13C2314yes—
137#88178C23116yes—
138C2×#6101C2314yes—
139C2×#6101C2312yes—
140C2×#6101C2314yes—
141C2×#6101C2314yes—
142C2×#6101C2314yes—
143C2×#6101C2314yes—
144C2×#6101C2314yes—
145C2×#6101C2314yes—
146C2×#6101C2312yes—
147C2×#6101C2314yes—
148C2×C4×Dic13C2312yes—
149C2×C4×Dic13C2314yes—
150C2×C4×Dic13C2314yes—
151C2×C4×Dic13C2314yes—
152C2×C4×Dic13C2311yescharacteristic
153C2×C4×Dic13C2312yes—
154C2×C4×Dic13C2311yescharacteristic
155C2×C4×Dic13C2314yes—
156C2×C4×Dic13C2312yes—
157C2×C4×Dic13C2318yes—
158#88152C23132yes—
159#88152C23132yes—
160#88151C23116yes—
161#88150C23132yes—
162#88150C23132yes—
163#88148C23132yes—
164#88147C23116yes—
165#88146C23116yes—
166#88146C23132yes—
167C4⋊C4×D13C23132yes—
168#88144C23132yes—
169#88143C23132yes—
170#88143C23132yes—
171#88143C23132yes—
172#88143C23132yes—
173#88142C23132yes—
174#88142C23116yes—
175#88142C23132yes—
176#88141C23116yes—
177#88141C23116yes—
178#88141C23132yes—
179#88141C23132yes—
180#88141C23132yes—
181#88139C23132yes—
182#88137C23132yes—
183#88135C23116yes—
184#88135C23116yes—
185#88133C23132yes—
186#88132C23132yes—
187#88131C23132yes—
188#88126C2318yes—
189#88126C2318yes—
190#88126C23132yes—
191#88126C23132yes—
192C42×D13C2318yes—
193C42×D13C2318yes—
194#88124C2318yes—
195#88123C2318yes—
196C4×Dic26C23116yes—
197C4×Dic26C23132yes—
198C4×Dic26C23132yes—
199C2×#3509—131nomaximal, Sylow
200C24×C13C2411yescharacteristic
201C23×D13C2411yescharacteristic
202C23×D13C2411yescharacteristic
203C2×Q8×C13—28no—
204C2×Q8×C13C2418yes—
205C22×C4×C13—24no—
206C22×C4×C13C2412yes—
207C22×C4×C13C2411yescharacteristic
208C22×C4×C13C2414yes—
209C22×C4×C13C2414yes—
210C22×C4×C13C2412yes—
211C22×C4×C13C2414yes—
212C22×C4×C13C2411yescharacteristic
213C2×C22⋊D13—24no—
214C2×C22⋊D13—24no—
215C2×C22⋊D13C2414yes—
216C2×C22⋊D13C2414yes—
217C22×Dic13—28no—
218C22×Dic13C2418yes—
219C22×Dic13C2412yes—
220C22×Dic13C2414yes—
221C22×Dic13C2411yescharacteristic
222C22×Dic13C2414yes—
223C22×Dic13C2411yescharacteristic
224C22×Dic13C2412yes—
225Q8×D13—264no—
226#6127—232no—
227C2×D52—24no—
228C2×D52C2414yes—
229C2×C4×D13—216no—
230C2×C4×D13—24no—
231C2×C4×D13—28no—
232C2×C4×D13—28no—
233C2×C4×D13#4118yes—
234C2×C4×D13C2418yes—
235C2×C4×D13C2414yes—
236C2×C4×D13C2418yes—
237C2×C4×D13C24116yes—
238C2×C4×D13C2414yes—
239C2×Dic26—28no—
240C2×Dic26—24no—
241C2×Dic26—216no—
242C2×Dic26—216no—
243C2×Dic26C2418yes—
244C2×Dic26C24116yes—
245C2×Dic26C24116yes—
246C2×Dic26C2414yes—
247C13×C4⋊C4C24116yes—
248C13×C4⋊C4C2418yes—
249C13×C4⋊C4C2418yes—
250C13×C4⋊C4C24116yes—
251C13×C4⋊C4C24116yes—
252C13×C4⋊C4C24116yes—
253C13×C22⋊C4C24116yes—
254C13×C22⋊C4C2418yes—
255C42×C13C2414yes—
256C42×C13C24116yes—
257C42×C13C2414yes—
258C22⋊Dic13C24116yes—
259#6103C2418yes—
260#6103C2418yes—
261#6103C24116yes—
262#6103C24116yes—
263#6103C24116yes—
264C4⋊Dic13C2418yes—
265C4⋊Dic13C24116yes—
266C4⋊Dic13C24116yes—
267C4⋊Dic13C24116yes—
268#6101C24116yes—
269#6101C2418yes—
270#6101C24116yes—
271#6101C24116yes—
272#6101C24116yes—
273#6101C24116yes—
274#6101C24116yes—
275#6101C24116yes—
276#6101C2418yes—
277#6101C24116yes—
278C4×Dic13C2418yes—
279C4×Dic13C24116yes—
280C4×Dic13C24116yes—
281C4×Dic13C24116yes—
282C4×Dic13C2414yes—
283C4×Dic13C2418yes—
284C4×Dic13C2414yes—
285C4×Dic13C24116yes—
286C4×Dic13C2418yes—
287#3509—1332no—
288C2×#557—134no—
289C2×#556—134no—
290C2×#552—134no—
291C2×#552—134no—
292C2×#541—131no—
293C2×#541—131no—
294C2×#541—131no—
295C2×#541D1311yescharacteristic, complemented
296C2×#536—132no—
297C2×#533—131no—
298C2×#533—132no—
299C2×#533—132no—
300C22×C4⋊Q8—131no—
301C2×#519—132no—
302C2×C4×#41—131no—
303C23×C13—22no—
304C23×C13—24no—
305C23×C13C2512yes—
306C23×C13C2511yescharacteristic
307C22×D13—24no—
308C22×D13—22no—
309C22×D13—24no—
310C22×D13C2×#4114yes—
311C22×D13C2512yes—
312C22×D13C2512yes—
313Q8×C13—216no—
314C2×C4×C13—28no—
315C2×C4×C13—22no—
316C2×C4×C13—28no—
317C2×C4×C13—24no—
318C2×C4×C13—24no—
319C2×C4×C13—28no—
320C2×C4×C13C2×#4114yes—
321C2×C4×C13C2514yes—
322C2×C4×C13C2512yes—
323C2×C4×C13C2518yes—
324C2×C4×C13C2514yes—
325C2×C4×C13C2518yes—
326C2×C4×C13C2512yes—
327C22⋊D13—28no—
328C22⋊D13—28no—
329C2×Dic13—28no—
330C2×Dic13—22no—
331C2×Dic13—28no—
332C2×Dic13—24no—
333C2×Dic13—216no—
334C2×Dic13C2×#4114yes—
335C2×Dic132−1+418yes—
336C2×Dic13C2514yes—
337C2×Dic13C2518yes—
338C2×Dic13C2512yes—
339C2×Dic13C2518yes—
340C2×Dic13C2512yes—
341C2×Dic13C2514yes—
342D52—28no—
343C4×D13—232no—
344C4×D13—28no—
345C4×D13—216no—
346C4×D13—216no—
347C4×D13C2×#41116yes—
348Dic26—216no—
349Dic26—28no—
350Dic26—232no—
351Dic26—232no—
352C22×#41—131no—
353C23×Q8—132no—
354#557—1364no—
355#556—1364no—
356#552—1364no—
357#552—1364no—
358#541—1316no—
359#541—1316no—
360#541—1316no—
361#541C2×D13116yescomplemented
362#536—1332no—
363#533—1316no—
364#533—1332no—
365#533—1332no—
366C2×C4⋊Q8—132no—
367C2×C4⋊Q8—1316no—
368C2×C4⋊Q8—134no—
369C2×C4⋊Q8—132no—
370C2×C4⋊Q8—134no—
371C2×C4⋊Q8—131no—
372C2×C4⋊Q8C2×D1311yescharacteristic
373C2×#126—134no—
374C2×#126—134no—
375C2×#126—134no—
376C2×#126C2×D1314yes—
377C2×#125—134no—
378C2×#125—134no—
379C2×#125—134no—
380C2×#125—134no—
381C2×#125—134no—
382C2×#125—131no—
383C2×#125C2×D1311yescharacteristic
384C2×#125C2×D1314yes—
385C2×#124—134no—
386C2×#123—134no—
387C2×#123—134no—
388C2×C22⋊Q8—132no—
389C2×C22⋊Q8—132no—
390C2×C22⋊Q8—134no—
391C2×C22⋊Q8—134no—
392C2×C22⋊Q8—132no—
393C2×C22⋊Q8—134no—
394C2×C22⋊Q8C2×D1312yes—
395#519—1332no—
396C4×#41—1316no—
397C2×C4×Q8—132no—
398C2×C4×Q8—132no—
399C2×C4×Q8—132no—
400C2×C4×Q8—134no—
401C2×C4×Q8—134no—
402C2×C4×Q8—134no—
403C2×C4×Q8—132no—
404C2×C4×Q8—134no—
405C2×C4×Q8—134no—
406C2×C4×Q8C2×D1312yes—
407C2×C4×D4—132no—
408C2×C4×D4—132no—
409C2×C4×D4—132no—
410C2×#117—132no—
411C2×#117—134no—
412C2×#117—134no—
413C2×#117—131no—
414C2×#117—131no—
415C2×#117—134no—
416C2×#117—134no—
417C2×#117C2×D1311yescharacteristic
418C22×C4⋊C4—134no—
419C22×C42—131no—
420C22×C42—131no—
421C22×C42—131no—
422C22×C13—22no—
423C22×C13—24no—
424C22×C13—44no—
425C22×C13C22×#4112yes—
426C22×C13C2×2−1+414yes—
427C22×C13C2611yescharacteristic
428C2×D13—24no—
429C2×D13—28no—
430C2×D13—22no—
431C2×D13—24no—
432C2×D13—44no—
433C2×D13C22×#4114yes—
434C4×C13—28no—
435C4×C13—22no—
436C4×C13—28no—
437C4×C13—24no—
438C4×C13—24no—
439C4×C13C22×#4114yes—
440Dic13—28no—
441Dic13—22no—
442Dic13—28no—
443Dic13—24no—
444Dic13C22×#4114yes—
445Dic13C2×2−1+418yes—
446C2×#41—138no—
447C2×#41—268no—
448C22×Q8—1316no—
449C22×Q8—134no—
450C22×Q8—132no—
451C22×Q8—134no—
452C22×Q8—131no—
453C22×Q8—2616no—
454C22×Q8C22×D1312yes—
455C22×D4—131no—
456C22×D4—131no—
457C22×D4—131no—
458C23×C4—131no—
459C23×C4—132no—
460C23×C4—134no—
461C23×C4—132no—
462C23×C4—132no—
463C23×C4—131no—
464C23×C4C22×D1311yescharacteristic
465C4⋊Q8—1316no—
466C4⋊Q8—1332no—
467C4⋊Q8—1316no—
468C4⋊Q8—1332no—
469C4⋊Q8—138no—
470C4⋊Q8C22×D1318yes—
471#126—1332no—
472#126—1332no—
473#126—1332no—
474#126C22×D13132yes—
475#125—1332no—
476#125—1332no—
477#125—1332no—
478#125—1332no—
479#125—1332no—
480#125—138no—
481#125C22×D1318yes—
482#125C22×D13132yes—
483#124—1332no—
484#123—1332no—
485#123—1332no—
486C22⋊Q8—1316no—
487C22⋊Q8—1316no—
488C22⋊Q8—1316no—
489C22⋊Q8—1332no—
490C22⋊Q8—1332no—
491C22⋊Q8—1332no—
492C22⋊Q8C22×D13116yes—
493C4×Q8—1316no—
494C4×Q8—1316no—
495C4×Q8—1316no—
496C4×Q8—1332no—
497C4×Q8—1332no—
498C4×Q8—1332no—
499C4×Q8—1316no—
500C4×Q8—1332no—
501C4×Q8—1332no—
502C4×Q8C22×D13116yes—
503C4×D4—1316no—
504C4×D4—1316no—
505C4×D4—1316no—
506#117—1316no—
507#117—1332no—
508#117—1332no—
509#117—138no—
510#117—138no—
511#117—1332no—
512#117—1332no—
513#117C22×D1318yes—
514C2×C4⋊C4—134no—
515C2×C4⋊C4—134no—
516C2×C4⋊C4—134no—
517C2×C4⋊C4—134no—
518C2×C4⋊C4—132no—
519C2×C4⋊C4—132no—
520C2×C4⋊C4—132no—
521C2×C4⋊C4—134no—
522C2×C4⋊C4—134no—
523C2×C4⋊C4—134no—
524C2×C4⋊C4—134no—
525C2×C4⋊C4—134no—
526C2×C4⋊C4—134no—
527C2×C4⋊C4—134no—
528C2×C4⋊C4—1332no—
529C2×C4⋊C4C22×D1314yes—
530C2×C4⋊C4C22×D1312yes—
531C2×C4⋊C4C22×D1314yes—
532C2×C4⋊C4C22×D1312yes—
533C2×C4⋊C4C22×D1314yes—
534C2×C4⋊C4C22×D1314yes—
535C2×C22⋊C4—134no—
536C2×C22⋊C4—132no—
537C2×C22⋊C4—134no—
538C2×C22⋊C4—132no—
539C2×C22⋊C4—134no—
540C2×C22⋊C4—134no—
541C2×C22⋊C4C22×D1314yes—
542C2×C22⋊C4C22×D1312yes—
543C2×C42—131no—
544C2×C42—134no—
545C2×C42—134no—
546C2×C42—134no—
547C2×C42—134no—
548C2×C42—132no—
549C2×C42—132no—
550C2×C42—132no—
551C2×C42—138no—
552C2×C42—131no—
553C2×C42—138no—
554C2×C42—138no—
555C2×C42C22×D1314yes—
556C2×C42C22×D1311yescharacteristic
557C2×C42C22×D1311yescharacteristic
558C2×C13—42no—
559C2×C13#350914yescomplemented
560C2×C13C23×#4111yescharacteristic
561C2×C13C22×2−1+412yes—
562D13—24no—
563D13—42no—
564C24—131no—
565C24—131no—
566C24C23×D1311yescharacteristic
567#41—2632no—
568C2×Q8—28no—
569C2×Q8—1316no—
570C2×Q8—138no—
571C2×Q8—1316no—
572C2×Q8—134no—
573C2×Q8—2616no—
574C2×Q8—264no—
575C2×Q8—2616no—
576C2×Q8—2664no—
577C2×Q8—268no—
578C2×Q8C23×D1318yes—
579C2×D4—134no—
580C2×D4—134no—
581C2×D4—134no—
582C2×D4—264no—
583C2×D4—264no—
584C2×D4—264no—
585C22×C4—24no—
586C22×C4—131no—
587C22×C4—132no—
588C22×C4—138no—
589C22×C4—134no—
590C22×C4—138no—
591C22×C4—132no—
592C22×C4—134no—
593C22×C4—134no—
594C22×C4—131no—
595C22×C4—138no—
596C22×C4—138no—
597C22×C4—134no—
598C22×C4—1316no—
599C22×C4—268no—
600C22×C4—268no—
601C22×C4—2616no—
602C22×C4—268no—
603C22×C4—264no—
604C22×C4C23×D1314yes—
605C22×C4C23×D1312yes—
606C22×C4C23×D1314yes—
607C22×C4C23×D1311yescharacteristic
608C22×C4C23×D1312yes—
609C22×C4C23×D1314yes—
610C22×C4C23×D1311yescharacteristic
611C4⋊C4—1316no—
612C4⋊C4—1316no—
613C4⋊C4—1316no—
614C4⋊C4—1316no—
615C4⋊C4—138no—
616C4⋊C4—138no—
617C4⋊C4—138no—
618C4⋊C4—1316no—
619C4⋊C4—1316no—
620C4⋊C4—1316no—
621C4⋊C4—1316no—
622C4⋊C4—1316no—
623C4⋊C4—1316no—
624C4⋊C4—1316no—
625C4⋊C4C23×D13116yes—
626C4⋊C4C23×D1318yes—
627C4⋊C4C23×D13116yes—
628C4⋊C4C23×D1318yes—
629C4⋊C4C23×D13116yes—
630C4⋊C4C23×D13116yes—
631C22⋊C4—1316no—
632C22⋊C4—138no—
633C22⋊C4—1316no—
634C22⋊C4—138no—
635C22⋊C4—1316no—
636C22⋊C4—1316no—
637C22⋊C4C23×D13116yes—
638C22⋊C4C23×D1318yes—
639C42—134no—
640C42—134no—
641C42—138no—
642C42—138no—
643C42—138no—
644C42—1316no—
645C42—1316no—
646C42—1316no—
647C42—1316no—
648C42C23×D1314yes—
649C42C23×D1314yes—
650C42C23×D13116yes—
651C13C2×#350911yescharacteristic, complemented, Sylow
652C23—22no—
653C23—24no—
654C23—134no—
655C23—132no—
656C23—132no—
657C23—264no—
658C23—262no—
659C23—264no—
660C23C24×D1312yes—
661C23C24×D1311yescharacteristic
662Q8—216no—
663Q8—2632no—
664Q8—2632no—
665Q8—268no—
666Q8—2616no—
667D4—268no—
668D4—268no—
669D4—268no—
670C2×C4—22no—
671C2×C4—28no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—28no—
675C2×C4—28no—
676C2×C4—134no—
677C2×C4—138no—
678C2×C4—132no—
679C2×C4—134no—
680C2×C4—1316no—
681C2×C4—134no—
682C2×C4—138no—
683C2×C4—138no—
684C2×C4—132no—
685C2×C4—2616no—
686C2×C4—2616no—
687C2×C4—2632no—
688C2×C4—2616no—
689C2×C4—262no—
690C2×C4—268no—
691C2×C4—264no—
692C2×C4—268no—
693C2×C4—268no—
694C2×C4#41×D1314yes—
695C2×C4C24×D1314yes—
696C2×C4C24×D1318yes—
697C2×C4C24×D1312yes—
698C2×C4C24×D1314yes—
699C2×C4C24×D1318yes—
700C2×C4C24×D1312yes—
701C22—22no—
702C22—24no—
703C22—44no—
704C22—134no—
705C22—268no—
706C22—264no—
707C22—262no—
708C22—264no—
709C22—524no—
710C22C2×#41×D1312yes—
711C22D13×2−1+414yes—
712C22C25×D1311yescharacteristic
713C4—22no—
714C4—28no—
715C4—24no—
716C4—24no—
717C4—28no—
718C4—134no—
719C4—138no—
720C4—262no—
721C4—268no—
722C4—264no—
723C4—268no—
724C4C2×#41×D1314yes—
725C2—42no—
726C2—264no—
727C2—522no—
728C2#1312871814yesdirect product factor
729C2C22×#41×D1311yescharacteristic
730C2C2×D13×2−1+412yes—
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#541C2
socleC23×C13C25
prime radicalC22×#6127C22
hypercenterC2×#541D13
hypocenterC13C2×#3509
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
1. #13128718C2direct (N × H)
2. C2×#11719390C2semidirect
3. C2×#11719407C2semidirect
4. C2×#11719413C2semidirect
5. C2×#11719398C2semidirect
6. C2×#11719402C2semidirect
7. C2×#11719223C2semidirect
8. C2×#11719436C2semidirect
10. C2×#11719393C2semidirect
11. C2×#11719283C2semidirect
12. C2×#11719327C2semidirect
13. C2×D13×C4⋊Q8C2semidirect
14. C2×#11719277C2semidirect
16. C2×C13×#541C2semidirect
19. C13×#541C22semidirect
32. #11719436C22semidirect
33. D13×C4⋊Q8C22semidirect
34. #11719413C22semidirect
35. #11719407C22semidirect
36. #11719402C22semidirect
37. #11719398C22semidirect
38. #11719393C22semidirect
39. #11719390C22semidirect
41. #11719327C22semidirect
42. #11719283C22semidirect
43. #11719277C22semidirect
45. #11719223C22semidirect
295. C2×#541D13semidirect
361. #541C2×D13semidirect
559. C2×C13#3509semidirect
651. C13C2×#3509semidirect
728. C2#13128718direct (N × H)

Maximal subgroups

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

subgroupindex
#131287182
C2×#117193902
C2×#117194072
C2×#117194132
C2×#117193982
C2×#117194022
C2×#117192232
C2×#117194362
C2×#117193332
C2×#117193932
C2×#117192832
C2×#117193272
C2×D13×C4⋊Q82
C2×#117192772
C2×#117192272
C2×C13×#5412
C2×#350913