Finite Group Databasebeta

← C2×#13127049 #16739729

Subgroups — C2×#13127049 #16739729

Order 3328.

2254 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719399C211yesmaximal, characteristic, complemented
2C2×#11719259C211yesmaximal, characteristic
3#13127049C2116yesmaximal, direct product factor
4C2×#11718729C211yesmaximal, characteristic, complemented
5C2×#11718524C211yesmaximal, characteristic, complemented
6C2×#11718549C211yesmaximal, characteristic, complemented
7C2×#11718529C211yesmaximal, characteristic, complemented
8C2×#11718547C211yesmaximal, characteristic, complemented
9C2×#11718506C211yesmaximal, characteristic, complemented
10C2×#11718444C211yesmaximal, characteristic, complemented
11C2×#11718437C211yesmaximal, characteristic, complemented
12C2×C4×#6105C211yesmaximal, characteristic, complemented
13C2×#11718499C211yesmaximal, characteristic, complemented
14C2×#11718432C211yesmaximal, characteristic, complemented
15C2×#11718431C211yesmaximal, characteristic, complemented
16C2×C13×#478C211yesmaximal, characteristic, complemented
17C22×#6129C2211yescharacteristic
18C22×D4×D13C2211yescharacteristic
19C2×C13×#125C2211yescharacteristic, complemented
20C2×C4×D4×C13C2211yescharacteristic
21C22×#6105C2211yescharacteristic
22C2×#88184—21no—
23C22×#6103—21no—
24C22×Dic52C2211yescharacteristic, complemented
25C22×#6095C2211yescharacteristic
26C22×#6094C2211yescharacteristic
27C22×#6094C2211yescharacteristic, complemented
28#11719399—24no—
29#11719399C2218yescomplemented
30#11719259—24no—
31#11719259C2218yes—
32C2×#88152—21no—
33C2×#88151C2211yescharacteristic
34C2×#88151C2211yescharacteristic
35C2×#88151C2211yescharacteristic, complemented
36C2×#88149C2211yescharacteristic
37C2×#88148—21no—
38C2×#88146—21no—
39C2×#88146C2211yescharacteristic
40C2×C4⋊C4×D13C2211yescharacteristic, complemented
41C2×#88144—21no—
42C2×#88140—21no—
43C2×#88136—21no—
44C2×#88129C2211yescharacteristic
45C2×C4×D52C2211yescharacteristic
46C2×C4×Dic26C2211yescharacteristic, complemented
47C13×#478C2218yescomplemented
48C2×C13×#107C2211yescharacteristic, complemented
49C2×C13×#106C2211yescharacteristic, complemented
50C2×C13×C4⋊C8C2211yescharacteristic, complemented
51C2×C13×#102C2211yescharacteristic
52C2×C13×#102C2211yescharacteristic
53C2×#88072C2211yescharacteristic
54C2×#88061C2211yescharacteristic
55C2×#88060C2211yescharacteristic
56C2×#88060C2211yescharacteristic, complemented
57C2×#88056C2211yescharacteristic, complemented
58#11718729C2218yescomplemented
59C4×#6105C2218yescomplemented
60C2×#88050C2211yescharacteristic, complemented
61C2×#88050C2211yescharacteristic, complemented
62C2×#88050C2211yescharacteristic, complemented
63C2×#88049C2211yescharacteristic
64C2×#88049C2211yescharacteristic
65C2×#88048C2211yescharacteristic, complemented
66C2×C4×#1055C2211yescharacteristic, complemented
67#11718549C2218yescomplemented
68#11718547C2218yescomplemented
69#11718529C2218yescomplemented
70#11718524C2218yescomplemented
71#11718506C2218yescomplemented
72#11718499C2218yescomplemented
73#11718444C2218yescomplemented
74#11718437C2218yescomplemented
75#11718432C2218yescomplemented
76#11718431C2218yescomplemented
77C24×D13—21no—
78C22×D4×C13C2311yescharacteristic
79C23×C4×C13—21no—
80C22×C22⋊D13—21no—
81C22×C22⋊D13—21no—
82C23×Dic13—21no—
83C2×#6129—24no—
84C2×#6129—22no—
85C2×#6129—42no—
86C2×#6129C2314yes—
87C2×D4×D13—24no—
88C2×D4×D13—22no—
89C2×D4×D13—42no—
90C2×D4×D13C2314yes—
91C22×D52—21no—
92C22×D52D411yescharacteristic
93C22×D52C2311yescharacteristic
94C22×C4×D13—21no—
95C22×C4×D13C2311yescharacteristic
96C22×C4×D13C2311yescharacteristic
97C22×Dic26C2311yescharacteristic
98C22×Dic26C2311yescharacteristic
99C22×C8×C13C2311yescharacteristic
100C22×C8×C13C2311yescharacteristic
101C13×#125—22no—
102C13×#125C2314yescomplemented
103C4×D4×C13—22no—
104C4×D4×C13C2314yes—
105C2×C13×C4⋊C4—21no—
106C2×C13×C4⋊C4—21no—
107C2×C13×C4⋊C4C2311yescharacteristic
108C2×C13×C4⋊C4C2311yescharacteristic
109C2×C13×C4⋊C4C2311yescharacteristic
110C2×C13×C22⋊C4—21no—
111C2×C42×C13C2311yescharacteristic
112C2×#6105—24no—
113C2×#6105C2314yes—
114#88184—28no—
115C2×#6103—21no—
116C2×#6103—21no—
117C2×#6103—21no—
118C2×#6103—21no—
119C2×#6103—21no—
120C2×#6103—21no—
121C2×#6103—21no—
122C2×#6103—28no—
123C2×#6103D411yescharacteristic
124C2×#6103D411yescharacteristic
125C2×C4⋊Dic13—21no—
126C2×C4⋊Dic13—21no—
127C2×C4⋊Dic13—21no—
128C2×C4⋊Dic13D411yescharacteristic
129C2×C4⋊Dic13C2311yescharacteristic
130C2×#6101—21no—
131C2×#6101—21no—
132C2×C4×Dic13—21no—
133C2×C4×Dic13—21no—
134C22×#1055C2311yescharacteristic
135C22×#1055C2311yescharacteristic
136C2×Dic52—42no—
137C2×Dic52C2314yescomplemented
138C2×#6095—42no—
139C2×#6095C2314yes—
140C2×#6094—42no—
141C2×#6094—42no—
142C2×#6094C2314yes—
143C2×#6094C2314yescomplemented
144#88152—28no—
145#88151—22no—
146#88151—22no—
147#88151—22no—
148#88151C2314yes—
149#88151C2314yes—
150#88151C2314yescomplemented
151#88149—22no—
152#88149C2314yes—
153#88148—28no—
154#88146—22no—
155#88146—28no—
156#88146C2314yes—
157C4⋊C4×D13—22no—
158C4⋊C4×D13C2314yescomplemented
159#88144—28no—
160#88140—28no—
161#88136—28no—
162#88129—22no—
163#88129C2314yes—
164C4×D52D414yes—
165C4×D52C2314yes—
166C4×Dic26—22no—
167C4×Dic26C2314yescomplemented
168C13×#107C2314yescomplemented
169C13×#106C2314yescomplemented
170C13×C4⋊C8C2314yescomplemented
171C13×#102C2314yes—
172C13×#102C2314yes—
173#88072C2314yes—
174#88061C2314yes—
175#88060C2314yes—
176#88060C2314yescomplemented
177#88056C2314yescomplemented
178#88050C2314yescomplemented
179#88050C2314yescomplemented
180#88050C2314yescomplemented
181#88049C2314yes—
182#88049C2314yes—
183#88048C2314yescomplemented
184C4×#1055C2314yescomplemented
185C2×#3323—131nomaximal, Sylow
186C24×C13—21no—
187C23×D13—21no—
188C23×D13—24no—
189C23×D13—44no—
190C23×D13—44no—
191C23×D13—82no—
192C23×D13C2×D411yescharacteristic
193C23×D13C2×D411yescharacteristic
194C2×D4×C13—21no—
195C2×D4×C13—22no—
196C2×D4×C13#4114yes—
197C2×D4×C13C2412yes—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—24no—
202C22×C4×C13—82no—
203C22×C4×C13C2×D411yescharacteristic
204C22×C4×C13C2×D411yescharacteristic
205C22×C4×C13C2411yescharacteristic
206C2×C22⋊D13—24no—
207C2×C22⋊D13—24no—
208C2×C22⋊D13—44no—
209C2×C22⋊D13—44no—
210C22×Dic13—21no—
211C22×Dic13—21no—
212C22×Dic13—21no—
213C22×Dic13—24no—
214C22×Dic13—44no—
215C22×Dic13C2×D411yescharacteristic
216C22×Dic13C2×D411yescharacteristic
217#6129—28no—
218#6129—44no—
219#6129—48no—
220D4×D13—28no—
221D4×D13—44no—
222D4×D13—48no—
223C2×D52—22no—
224C2×D52—22no—
225C2×D52—21no—
226C2×D52—24no—
227C2×D52—42no—
228C2×D52—82no—
229C2×D52C2×D414yes—
230C2×D52C2412yes—
231C2×C4×D13—22no—
232C2×C4×D13—22no—
233C2×C4×D13—22no—
234C2×C4×D13—22no—
235C2×C4×D13—24no—
236C2×C4×D13—44no—
237C2×C4×D13C2×D412yes—
238C2×C4×D13C2×D412yes—
239C2×C4×D13C2412yes—
240C2×C4×D13C2412yes—
241C2×Dic26—22no—
242C2×Dic26—22no—
243C2×Dic26—22no—
244C2×Dic26—22no—
245C2×Dic26—21no—
246C2×Dic26—21no—
247C2×Dic26C2412yes—
248C2×Dic26C2412yes—
249C2×C8×C13—22no—
250C2×C8×C13—22no—
251C2×C8×C13C2412yes—
252C2×C8×C13C2412yes—
253C13×C4⋊C4—24no—
254C13×C4⋊C4—21no—
255C13×C4⋊C4—21no—
256C13×C4⋊C4—24no—
257C13×C4⋊C4—21no—
258C13×C4⋊C4C2412yes—
259C13×C4⋊C4C2412yes—
260C13×C4⋊C4C2412yes—
261C13×C22⋊C4—24no—
262C42×C13C2×D412yes—
263C42×C13C2412yes—
264#6105—28no—
265#6103—24no—
266#6103—24no—
267#6103—24no—
268#6103—24no—
269#6103—24no—
270#6103—24no—
271#6103—24no—
272#6103C2×D414yes—
273#6103C2×D414yes—
274C4⋊Dic13—21no—
275C4⋊Dic13—24no—
276C4⋊Dic13—24no—
277C4⋊Dic13—24no—
278C4⋊Dic13C2×D414yes—
279C4⋊Dic13C2412yes—
280#6101—24no—
281#6101—24no—
282C4×Dic13—24no—
283C4×Dic13—24no—
284C2×#1055—22no—
285C2×#1055—22no—
286C2×#1055C2412yes—
287C2×#1055C2412yes—
288Dic52—44no—
289#6095—44no—
290#6094—44no—
291#6094—44no—
292C2×#552—131no—
293C2×#546—131no—
294#3323—1316no—
295C2×#488—131no—
296C2×#481—131no—
297C2×#485—131no—
298C2×#478D1311yescharacteristic, complemented
299C2×#470—131no—
300C2×#468—131no—
301C2×#464—131no—
302C2×#452—131no—
303C2×#450—131no—
304C2×C4×SD16—131no—
305C2×#436—131no—
306C2×#417—131no—
307C2×#418—131no—
308C23×C13—24no—
309C23×C13—22no—
310C23×C13—42no—
311C23×C13—42no—
312C23×C13C22×D411yescharacteristic
313C22×D13—22no—
314C22×D13—22no—
315C22×D13—22no—
316C22×D13—22no—
317C22×D13—22no—
318C22×D13—22no—
319C22×D13—22no—
320C22×D13—48no—
321C22×D13—48no—
322C22×D13—42no—
323C22×D13—42no—
324C22×D13—42no—
325C22×D13—84no—
326C22×D13—816no—
327C22×D13C22×D412yes—
328C22×D13C22×D412yes—
329D4×C13—24no—
330D4×C13—22no—
331D4×C13C2×#4114yes—
332C2×C4×C13—22no—
333C2×C4×C13—22no—
334C2×C4×C13—22no—
335C2×C4×C13—22no—
336C2×C4×C13—22no—
337C2×C4×C13—42no—
338C2×C4×C13—42no—
339C2×C4×C13—42no—
340C2×C4×C13—84no—
341C2×C4×C13C22×D412yes—
342C2×C4×C13C22×D412yes—
343C2×C4×C13C22×D411yescharacteristic
344C2×C4×C13C2×#4112yes—
345C2×C4×C13H(5,𝔽2)12yes—
346C2×C4×C13C2511yescharacteristic
347C22⋊D13—48no—
348C22⋊D13—48no—
349C2×Dic13—22no—
350C2×Dic13—22no—
351C2×Dic13—22no—
352C2×Dic13—22no—
353C2×Dic13—22no—
354C2×Dic13—48no—
355C2×Dic13—42no—
356C2×Dic13—42no—
357C2×Dic13—42no—
358C2×Dic13C22×D412yes—
359C2×Dic13C22×D412yes—
360D52—22no—
361D52—22no—
362D52—44no—
363D52—42no—
364D52—84no—
365C4×D13—24no—
366C4×D13—24no—
367C4×D13—22no—
368C4×D13—22no—
369C4×D13—22no—
370C4×D13—22no—
371C4×D13—48no—
372Dic26—22no—
373Dic26—22no—
374Dic26—22no—
375Dic26—22no—
376Dic26—42no—
377Dic26—42no—
378C8×C13—22no—
379C8×C13—22no—
380#1055—22no—
381#1055—22no—
382C22×#41—131no—
383C23×D4—131no—
384C22×Q16—131no—
385C22×SD16—131no—
386C22×SD16—131no—
387C22×M16—131no—
388C22×M16—131no—
389#552—138no—
390#552—264no—
391#546—138no—
392#546—264no—
393C2×#126—261no—
394C2×#125—261no—
395C2×#125C2×D1311yescharacteristic, complemented
396C2×#124—131no—
397C2×#123—261no—
398C2×#123—261no—
399C2×C22⋊Q8—131no—
400C2×C22⋊Q8—131no—
401C2×C22⋊Q8—131no—
402C2×#121—131no—
403C2×#121—261no—
404C2×#120—261no—
405C2×C4×Q8—131no—
406C2×C4×D4—131no—
407C2×C4×D4C2×D1311yescharacteristic
408C2×#117—131no—
409C2×#117—261no—
410C22×C4⋊C4—131no—
411C22×C22⋊C4—261no—
412#488—138no—
413#485—138no—
414#481—138no—
415#478C2×D1318yescomplemented
416#470—138no—
417#468—138no—
418#464—138no—
419#452—138no—
420#450—138no—
421C4×SD16—138no—
422#436—138no—
423C2×#107C2×D1311yescharacteristic, complemented
424C2×#106—131no—
425C2×#106C2×D1311yescharacteristic, complemented
426C2×C4⋊C8C2×D1311yescharacteristic, complemented
427#418—138no—
428#417—138no—
429C2×#103—131no—
430C2×#103—131no—
431C2×#103—131no—
432C2×#103—131no—
433C2×#102—131no—
434C2×#102—131no—
435C2×#102—131no—
436C2×#102—131no—
437C2×#102C2×D1311yescharacteristic
438C2×#102C2×D1311yescharacteristic
439C2×C22⋊C8—131no—
440C2×C22⋊C8—131no—
441C2×C4×C8—131no—
442C22×C13—24no—
443C22×C13—48no—
444C22×C13—42no—
445C22×C13—42no—
446C22×C13#54612yes—
447C22×C13#57512yes—
448C22×C13#57712yes—
449C22×C13C23×D411yescharacteristic
450C2×D13—22no—
451C2×D13—22no—
452C2×D13—22no—
453C2×D13—22no—
454C2×D13—22no—
455C2×D13—22no—
456C2×D13—44no—
457C2×D13—44no—
458C2×D13—42no—
459C2×D13—42no—
460C2×D13—42no—
461C2×D13—816no—
462C2×D13—84no—
463C4×C13—22no—
464C4×C13—22no—
465C4×C13—42no—
466C4×C13—42no—
467C4×C13—42no—
468C4×C13#54612yes—
469C4×C13C22×#4111yescharacteristic
470C4×C13C2×H(5,𝔽2)11yescharacteristic
471Dic13—22no—
472Dic13—22no—
473Dic13—42no—
474Dic13—42no—
475Dic13—42no—
476C25—261no—
477C2×#41—134no—
478C2×#41—262no—
479C2×#41—264no—
480C2×#41—522no—
481C22×Q8—131no—
482C22×Q8—131no—
483C22×D4—134no—
484C22×D4—131no—
485C22×D4—131no—
486C22×D4—261no—
487C22×D4—262no—
488C22×D4—261no—
489C22×D4—264no—
490C22×D4—261no—
491C22×D4—522no—
492C22×D4C22×D1311yescharacteristic
493C23×C4—21no—
494C23×C4—131no—
495C23×C4—131no—
496C23×C4—261no—
497C23×C4—261no—
498C2×Q16—134no—
499C2×Q16—522no—
500C2×SD16—134no—
501C2×SD16—134no—
502C2×SD16—264no—
503C2×SD16—522no—
504C2×M16—134no—
505C2×M16—134no—
506C2×M16—522no—
507C2×M16—522no—
508C22×C8—131no—
509C22×C8—131no—
510C22×C8C22×D1311yescharacteristic
511C22×C8C22×D1311yescharacteristic
512#126—268no—
513#125—22no—
514#125—268no—
515#125C22×D1314yescomplemented
516#124—134no—
517#124—262no—
518#123—268no—
519#123—268no—
520C22⋊Q8—134no—
521C22⋊Q8—134no—
522C22⋊Q8—134no—
523C22⋊Q8—262no—
524C22⋊Q8—262no—
525C22⋊Q8—262no—
526#121—134no—
527#121—268no—
528#121—262no—
529#120—268no—
530C4×Q8—134no—
531C4×Q8—262no—
532C4×D4—22no—
533C4×D4—134no—
534C4×D4—134no—
535C4×D4C22×D1314yes—
536#117—134no—
537#117—268no—
538#117—262no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—131no—
542C2×C4⋊C4—131no—
543C2×C4⋊C4—134no—
544C2×C4⋊C4—262no—
545C2×C4⋊C4—261no—
546C2×C4⋊C4—261no—
547C2×C4⋊C4—261no—
548C2×C4⋊C4—261no—
549C2×C4⋊C4—261no—
550C2×C4⋊C4C22×D1311yescharacteristic
551C2×C4⋊C4C22×D1311yescharacteristic
552C2×C4⋊C4C22×D1311yescharacteristic
553C2×C22⋊C4—21no—
554C2×C22⋊C4—131no—
555C2×C22⋊C4—131no—
556C2×C22⋊C4—268no—
557C2×C22⋊C4—261no—
558C2×C22⋊C4—261no—
559C2×C22⋊C4—261no—
560C2×C22⋊C4—261no—
561C2×C22⋊C4—261no—
562C2×C22⋊C4—261no—
563C2×C22⋊C4—261no—
564C2×C42—261no—
565C2×C42—261no—
566C2×C42C22×D1311yescharacteristic
567#107C22×D1314yescomplemented
568#106—134no—
569#106C22×D1314yescomplemented
570C4⋊C8C22×D1314yescomplemented
571#103—134no—
572#103—134no—
573#103—134no—
574#103—134no—
575#102—134no—
576#102—134no—
577#102—134no—
578#102—134no—
579#102C22×D1314yes—
580#102C22×D1314yes—
581C22⋊C8—134no—
582C22⋊C8—134no—
583C4×C8—134no—
584C2×C13—44no—
585C2×C13#332314yescomplemented
586C2×C13C2×#54611yescharacteristic
587C2×C13C2×#57511yescharacteristic
588C2×C13C2×#57711yescharacteristic
589D13—42no—
590D13—42no—
591D13—82no—
592C24—21no—
593C24—131no—
594C24—131no—
595C24—264no—
596C24—261no—
597C24—524no—
598C24—524no—
599C24—1042no—
600#41—268no—
601#41—524no—
602#41—528no—
603C2×Q8—132no—
604C2×Q8—132no—
605C2×Q8—261no—
606C2×Q8—261no—
607C2×Q8—262no—
608C2×Q8—262no—
609C2×Q8—262no—
610C2×Q8—262no—
611C2×D4—21no—
612C2×D4—22no—
613C2×D4—134no—
614C2×D4—132no—
615C2×D4—264no—
616C2×D4—264no—
617C2×D4—268no—
618C2×D4—264no—
619C2×D4—261no—
620C2×D4—262no—
621C2×D4—262no—
622C2×D4—522no—
623C2×D4—524no—
624C2×D4—528no—
625C2×D4—524no—
626C2×D4—524no—
627C2×D4—1042no—
628C2×D4#613114yes—
629C2×D4C23×D1312yes—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—24no—
634C22×C4—82no—
635C22×C4—131no—
636C22×C4—131no—
637C22×C4—132no—
638C22×C4—132no—
639C22×C4—132no—
640C22×C4—132no—
641C22×C4—264no—
642C22×C4—264no—
643C22×C4—262no—
644C22×C4—262no—
645C22×C4—262no—
646C22×C4—262no—
647C22×C4—261no—
648C22×C4—261no—
649C22×C4—261no—
650C22×C4—524no—
651C22×C4—524no—
652C22×C4D4×D1311yescharacteristic
653C22×C4D4×D1311yescharacteristic
654C22×C4C23×D1311yescharacteristic
655Q16—524no—
656SD16—268no—
657SD16—524no—
658M16—524no—
659M16—524no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—132no—
663C2×C8—132no—
664C2×C8—262no—
665C2×C8—262no—
666C2×C8C23×D1312yes—
667C2×C8C23×D1312yes—
668C4⋊C4—24no—
669C4⋊C4—24no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—134no—
674C4⋊C4—132no—
675C4⋊C4—264no—
676C4⋊C4—264no—
677C4⋊C4—264no—
678C4⋊C4—264no—
679C4⋊C4—261no—
680C4⋊C4—264no—
681C4⋊C4C23×D1312yes—
682C4⋊C4C23×D1312yes—
683C4⋊C4C23×D1312yes—
684C22⋊C4—24no—
685C22⋊C4—134no—
686C22⋊C4—134no—
687C22⋊C4—264no—
688C22⋊C4—264no—
689C22⋊C4—264no—
690C22⋊C4—264no—
691C22⋊C4—264no—
692C22⋊C4—264no—
693C22⋊C4—264no—
694C42—264no—
695C42—264no—
696C42D4×D1312yes—
697C42C23×D1312yes—
698C13C2×#332311yescharacteristic, complemented, Sylow
699C23—24no—
700C23—22no—
701C23—42no—
702C23—42no—
703C23—132no—
704C23—132no—
705C23—262no—
706C23—262no—
707C23—262no—
708C23—262no—
709C23—262no—
710C23—262no—
711C23—262no—
712C23—528no—
713C23—528no—
714C23—522no—
715C23—522no—
716C23—522no—
717C23—1044no—
718C23—10416no—
719C23C2×D4×D1311yescharacteristic
720Q8—262no—
721Q8—262no—
722Q8—262no—
723Q8—262no—
724Q8—522no—
725Q8—522no—
726D4—24no—
727D4—22no—
728D4—262no—
729D4—262no—
730D4—524no—
731D4—528no—
732D4—528no—
733D4—522no—
734D4—1044no—
735D4C2×#613114yes—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—84no—
745C2×C4—132no—
746C2×C4—132no—
747C2×C4—262no—
748C2×C4—262no—
749C2×C4—264no—
750C2×C4—264no—
751C2×C4—262no—
752C2×C4—262no—
753C2×C4—262no—
754C2×C4—262no—
755C2×C4—262no—
756C2×C4—262no—
757C2×C4—262no—
758C2×C4—528no—
759C2×C4—528no—
760C2×C4—522no—
761C2×C4—522no—
762C2×C4—522no—
763C2×C4C2×D4×D1312yes—
764C2×C4C2×D4×D1312yes—
765C2×C4C2×D4×D1311yescharacteristic
766C2×C4C2×#613112yes—
767C2×C4#8825612yes—
768C2×C4C24×D1311yescharacteristic
769C8—22no—
770C8—22no—
771C8—262no—
772C8—262no—
773C22—24no—
774C22—42no—
775C22—42no—
776C22—48no—
777C22—262no—
778C22—262no—
779C22—262no—
780C22—262no—
781C22—262no—
782C22—262no—
783C22—524no—
784C22—524no—
785C22—522no—
786C22—522no—
787C22—522no—
788C22—10416no—
789C22—1044no—
790C22#1171933512yes—
791C22#1171947312yes—
792C22#1171948012yes—
793C22C22×D4×D1311yescharacteristic
794C4—22no—
795C4—22no—
796C4—42no—
797C4—42no—
798C4—42no—
799C4—262no—
800C4—262no—
801C4—522no—
802C4—522no—
803C4—522no—
804C4#1171933512yes—
805C4C22×#613111yescharacteristic
806C4C2×#8825611yescharacteristic
807C2—44no—
808C2—522no—
809C2—522no—
810C2—1042no—
811C2#1312704914yesdirect product factor
812C2C2×#1171933511yescharacteristic
813C2C2×#1171947311yescharacteristic
814C2C2×#1171948011yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#478C2
socleC23×C13C22×D4
prime radicalC2×#11719259C2
hypercenterC2×#478D13
hypocenterC13C2×#3323
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#11719399C2semidirect
3. #13127049C2direct (N × H)
4. C2×#11718729C2semidirect
5. C2×#11718524C2semidirect
6. C2×#11718549C2semidirect
7. C2×#11718529C2semidirect
8. C2×#11718547C2semidirect
9. C2×#11718506C2semidirect
10. C2×#11718444C2semidirect
11. C2×#11718437C2semidirect
12. C2×C4×#6105C2semidirect
13. C2×#11718499C2semidirect
14. C2×#11718432C2semidirect
15. C2×#11718431C2semidirect
16. C2×C13×#478C2semidirect
19. C2×C13×#125C22semidirect
24. C22×Dic52C22semidirect
27. C22×#6094C22semidirect
29. #11719399C22semidirect
35. C2×#88151C22semidirect
40. C2×C4⋊C4×D13C22semidirect
46. C2×C4×Dic26C22semidirect
47. C13×#478C22semidirect
48. C2×C13×#107C22semidirect
49. C2×C13×#106C22semidirect
50. C2×C13×C4⋊C8C22semidirect
56. C2×#88060C22semidirect
57. C2×#88056C22semidirect
58. #11718729C22semidirect
59. C4×#6105C22semidirect
60. C2×#88050C22semidirect
61. C2×#88050C22semidirect
62. C2×#88050C22semidirect
65. C2×#88048C22semidirect
66. C2×C4×#1055C22semidirect
67. #11718549C22semidirect
68. #11718547C22semidirect
69. #11718529C22semidirect
70. #11718524C22semidirect
71. #11718506C22semidirect
72. #11718499C22semidirect
73. #11718444C22semidirect
74. #11718437C22semidirect
75. #11718432C22semidirect
76. #11718431C22semidirect
102. C13×#125C23semidirect
137. C2×Dic52C23semidirect
143. C2×#6094C23semidirect
150. #88151C23semidirect
158. C4⋊C4×D13C23semidirect
167. C4×Dic26C23semidirect
168. C13×#107C23semidirect
169. C13×#106C23semidirect
170. C13×C4⋊C8C23semidirect
176. #88060C23semidirect
177. #88056C23semidirect
178. #88050C23semidirect
179. #88050C23semidirect
180. #88050C23semidirect
183. #88048C23semidirect
184. C4×#1055C23semidirect
298. C2×#478D13semidirect
395. C2×#125C2×D13semidirect
415. #478C2×D13semidirect
423. C2×#107C2×D13semidirect
425. C2×#106C2×D13semidirect
426. C2×C4⋊C8C2×D13semidirect
515. #125C22×D13semidirect
567. #107C22×D13semidirect
569. #106C22×D13semidirect
570. C4⋊C8C22×D13semidirect
585. C2×C13#3323semidirect
698. C13C2×#3323semidirect
811. C2#13127049direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117193992
C2×#117192592
#131270492
C2×#117187292
C2×#117185242
C2×#117185492
C2×#117185292
C2×#117185472
C2×#117185062
C2×#117184442
C2×#117184372
C2×C4×#61052
C2×#117184992
C2×#117184322
C2×#117184312
C2×C13×#4782
C2×#332313