Finite Group Databasebeta

← C2×#13126738 #16739342

Subgroups — C2×#13126738 #16739342

Order 3328.

2210 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719270C211yesmaximal, characteristic, complemented
2#13126738C2116yesmaximal, direct product factor
3C2×#11718717C211yesmaximal, characteristic, complemented
4C2×#11718695C211yesmaximal, characteristic, complemented
5C2×#11718706C211yesmaximal, characteristic, complemented
6C2×#11718683C211yesmaximal, characteristic, complemented
7C2×#11718699C211yesmaximal, characteristic, complemented
8C2×#11718709C211yesmaximal, characteristic, complemented
9C2×#11718718C211yesmaximal, characteristic, complemented
10C2×#11718899C211yesmaximal, characteristic, complemented
11C2×#11718888C211yesmaximal, characteristic, complemented
12C2×C4×#6106C211yesmaximal, characteristic, complemented
13C2×D4×#1055C211yesmaximal, characteristic, complemented
14C2×#11718894C211yesmaximal, characteristic, complemented
15C22×#88075C211yesmaximal, characteristic, complemented
16C2×C13×#548C211yesmaximal, characteristic, complemented
17C22×C13×#41C2211yescharacteristic
18C23×Q8×C13C2211yescharacteristic
19C13×#548—24no—
20C13×#548C2218yescomplemented
21C2×C13×#124—21no—
22C2×C13×#124C2211yescharacteristic
23C2×C13×C22⋊Q8—21no—
24C2×C13×C22⋊Q8C2211yescharacteristic
25C2×C13×#121—21no—
26C2×C13×#121C2211yescharacteristic
27C2×C4×Q8×C13C2211yescharacteristic
28C2×C4×D4×C13—21no—
29C2×C4×D4×C13C2211yescharacteristic
30C22×#6106C2211yescharacteristic
31C22×#6106C2211yescharacteristic
32C2×#88193—21no—
33C22×#6104C2211yescharacteristic
34C2×#88184C2211yescharacteristic
35C2×#88184C2211yescharacteristic
36C2×#88180C2211yescharacteristic
37C22×C4⋊Dic13C2211yescharacteristic
38C23×#1055C2211yescharacteristic
39C23×#1055C2211yescharacteristic
40#11719270—24no—
41#11719270C2218yescomplemented
42C2×#88152—21no—
43C2×#88137—21no—
44C2×#88135—21no—
45C2×C4×D52C2211yescharacteristic
46C2×#88124C2211yescharacteristic
47#11718899C2218yescomplemented
48#11718894C2218yescomplemented
49#11718888C2218yescomplemented
50C2×#88075C2211yescharacteristic
51C2×#88075C2211yescharacteristic
52C2×#88075C2211yescharacteristic
53C2×#88075C2211yescharacteristic
54C2×#88075C2211yescharacteristic
55C2×#88075C2211yescharacteristic
56C2×#88075C2218yescomplemented
57C2×#88072C2211yescharacteristic
58C2×#88072C2211yescharacteristic
59C2×#88072C2211yescharacteristic
60C2×C22⋊#1055C2211yescharacteristic
61C2×C22⋊#1055C2211yescharacteristic
62#11718718C2218yescomplemented
63#11718717C2218yescomplemented
64#11718709C2218yescomplemented
65#11718706C2218yescomplemented
66#11718699C2218yescomplemented
67#11718695C2218yescomplemented
68C4×#6106C2218yescomplemented
69#11718683C2218yescomplemented
70D4×#1055C2218yescomplemented
71C2×#88049C2211yescharacteristic
72C2×#88048C2211yescharacteristic
73C2×#88048C2211yescharacteristic
74C2×#88047C2211yescharacteristic
75C2×C4⋊#1055C2211yescharacteristic
76C2×C4×#1055C2211yescharacteristic
77C2×C13×#41—22no—
78C2×C13×#41—24no—
79C2×C13×#41—42no—
80C2×C13×#41C2314yes—
81C22×Q8×C13—21no—
82C22×Q8×C13—22no—
83C22×Q8×C13—24no—
84C22×Q8×C13—42no—
85C22×Q8×C13C2311yescharacteristic
86C22×Q8×C13C2314yes—
87C22×Q8×C13C2311yescharacteristic
88C22×D4×C13—21no—
89C22×D4×C13—21no—
90C22×D4×C13D411yescharacteristic
91C22×D4×C13C2311yescharacteristic
92C23×C4×C13—21no—
93C23×C4×C13—21no—
94C23×C4×C13C2311yescharacteristic
95C23×C4×C13C2311yescharacteristic
96C22×C22⋊D13—21no—
97C22×C22⋊D13—21no—
98C23×Dic13—21no—
99C22×D52C2311yescharacteristic
100C22×C4×D13—21no—
101C13×#124—28no—
102C13×#124—22no—
103C13×#124C2314yes—
104C13×C22⋊Q8—22no—
105C13×C22⋊Q8—28no—
106C13×C22⋊Q8C2314yes—
107C13×#121—28no—
108C13×#121—22no—
109C13×#121C2314yes—
110C4×Q8×C13—22no—
111C4×Q8×C13C2314yes—
112C4×D4×C13—28no—
113C4×D4×C13D414yes—
114C4×D4×C13C2314yes—
115C2×C13×C4⋊C4—21no—
116C2×C13×C4⋊C4—21no—
117C2×C13×C4⋊C4D411yescharacteristic
118C2×C13×C4⋊C4C2311yescharacteristic
119C2×C13×C22⋊C4—21no—
120C2×C13×C22⋊C4—21no—
121C2×C13×C22⋊C4—21no—
122C2×C13×C22⋊C4—21no—
123C2×C13×C22⋊C4D411yescharacteristic
124C2×C13×C22⋊C4D411yescharacteristic
125C2×C42×C13—21no—
126C2×C42×C13C2311yescharacteristic
127C2×C22⋊Dic13—21no—
128C2×#6106—24no—
129C2×#6106—42no—
130C2×#6106C2314yes—
131C2×#6106C2314yes—
132#88193—28no—
133C2×#6104—42no—
134C2×#6104C2314yes—
135#88184—22no—
136#88184—22no—
137#88184C2314yes—
138#88184C2314yes—
139C2×#6103—21no—
140C2×#6103—21no—
141C2×#6103—21no—
142#88180—22no—
143#88180C2314yes—
144C2×C4⋊Dic13—21no—
145C2×C4⋊Dic13—22no—
146C2×C4⋊Dic13C2311yescharacteristic
147C2×C4⋊Dic13C2311yescharacteristic
148C2×C4⋊Dic13C2311yescharacteristic
149C2×C4⋊Dic13C2314yes—
150C2×#6101—21no—
151C2×#6101—21no—
152C2×C4×Dic13—21no—
153C22×#1055—42no—
154C22×#1055—42no—
155C22×#1055C2311yescharacteristic
156C22×#1055C2311yescharacteristic
157C22×#1055C2311yescharacteristic
158C22×#1055C2311yescharacteristic
159C22×#1055C2314yes—
160C22×#1055C2314yes—
161#88152—28no—
162#88137—28no—
163#88135—28no—
164C4×D52—22no—
165C4×D52C2314yes—
166#88124—22no—
167#88124C2314yes—
168#88075C2314yes—
169#88075C2314yes—
170#88075C2314yes—
171#88075C2314yes—
172#88075C2314yes—
173#88075C2314yes—
174#88072C2314yes—
175#88072C2314yes—
176#88072C2314yes—
177C22⋊#1055C2314yes—
178C22⋊#1055C2314yes—
179#88049C2314yes—
180#88048C2314yes—
181#88048C2314yes—
182#88047C2314yes—
183C4⋊#1055C2314yes—
184C4×#1055C2314yes—
185C2×#3301—131nomaximal, Sylow
186C24×C13—21no—
187C24×C13C2×D411yescharacteristic
188C24×C13C2×D411yescharacteristic
189C23×D13—21no—
190C13×#41—28no—
191C13×#41—44no—
192C13×#41—48no—
193C2×Q8×C13—21no—
194C2×Q8×C13—24no—
195C2×Q8×C13—21no—
196C2×Q8×C13—22no—
197C2×Q8×C13—28no—
198C2×Q8×C13—22no—
199C2×Q8×C13—22no—
200C2×Q8×C13—44no—
201C2×Q8×C13—44no—
202C2×Q8×C13—48no—
203C2×Q8×C13#4114yes—
204C2×Q8×C13C2412yes—
205C2×Q8×C13C2412yes—
206C2×D4×C13—24no—
207C2×D4×C13—24no—
208C2×D4×C13—24no—
209C2×D4×C13—21no—
210C2×D4×C13—22no—
211C2×D4×C13—22no—
212C2×D4×C13—44no—
213C2×D4×C13—44no—
214C2×D4×C13C2×D414yes—
215C2×D4×C13C2412yes—
216C22×C4×C13—21no—
217C22×C4×C13—22no—
218C22×C4×C13—22no—
219C22×C4×C13—22no—
220C22×C4×C13—22no—
221C22×C4×C13—21no—
222C22×C4×C13—21no—
223C22×C4×C13—24no—
224C22×C4×C13—24no—
225C22×C4×C13—44no—
226C22×C4×C13—44no—
227C22×C4×C13C2×D411yescharacteristic
228C22×C4×C13C2×D411yescharacteristic
229C22×C4×C13C2×D411yescharacteristic
230C22×C4×C13C2×D411yescharacteristic
231C22×C4×C13C2×D412yes—
232C22×C4×C13C2×D412yes—
233C22×C4×C13C2412yes—
234C22×C4×C13C2412yes—
235C22×C4×C13C2411yescharacteristic
236C2×C22⋊D13—24no—
237C2×C22⋊D13—24no—
238C2×C22⋊D13—44no—
239C2×C22⋊D13—82no—
240C22×Dic13—21no—
241C22×Dic13—21no—
242C22×Dic13—21no—
243C22×Dic13—24no—
244C22×Dic13—82no—
245C2×D52—22no—
246C2×D52—22no—
247C2×D52—21no—
248C2×D52C2412yes—
249C2×C4×D13—24no—
250C2×C4×D13—82no—
251C13×C4⋊C4—24no—
252C13×C4⋊C4—24no—
253C13×C4⋊C4—21no—
254C13×C4⋊C4C2×D414yes—
255C13×C4⋊C4C2412yes—
256C13×C22⋊C4—24no—
257C13×C22⋊C4—24no—
258C13×C22⋊C4—24no—
259C13×C22⋊C4—24no—
260C13×C22⋊C4C2×D414yes—
261C13×C22⋊C4C2×D414yes—
262C42×C13—24no—
263C42×C13C2×D412yes—
264C42×C13C2412yes—
265C22⋊Dic13—24no—
266#6106—28no—
267#6106—44no—
268#6104—44no—
269#6103—24no—
270#6103—24no—
271#6103—24no—
272C4⋊Dic13—21no—
273C4⋊Dic13—21no—
274C4⋊Dic13—21no—
275C4⋊Dic13—24no—
276C4⋊Dic13C2412yes—
277C4⋊Dic13C2412yes—
278C4⋊Dic13C2412yes—
279#6101—24no—
280#6101—24no—
281C4×Dic13—24no—
282C2×#1055—22no—
283C2×#1055—22no—
284C2×#1055—22no—
285C2×#1055—22no—
286C2×#1055—44no—
287C2×#1055—44no—
288C2×#1055C2412yes—
289C2×#1055C2412yes—
290C2×#1055C2412yes—
291C2×#1055C2412yes—
292C2×#553—131no—
293C2×#548D1311yescharacteristic, complemented
294#3301—1316no—
295C2×#488—131no—
296C2×#481—131no—
297C2×#485—131no—
298C2×#479—131no—
299C2×#466—131no—
300C2×#465—131no—
301C2×#463—131no—
302C2×#449—131no—
303C2×#448—131no—
304C2×C4×SD16—131no—
305C2×C8×D4—131no—
306C2×#416—131no—
307C22×#103—131no—
308C23×C13—22no—
309C23×C13—22no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13—22no—
313C23×C13—22no—
314C23×C13—42no—
315C23×C13—42no—
316C23×C13—42no—
317C23×C13#13514yes—
318C23×C13C22×D412yes—
319C23×C13C22×D412yes—
320C23×C13C22×D411yescharacteristic
321C22×D13—22no—
322C22×D13—42no—
323C22×D13—42no—
324C22×D13—42no—
325Q8×C13—24no—
326Q8×C13—22no—
327Q8×C13—22no—
328Q8×C13—22no—
329Q8×C13—48no—
330Q8×C13—42no—
331Q8×C13C2×#4114yes—
332D4×C13—28no—
333D4×C13—22no—
334D4×C13—22no—
335D4×C13—48no—
336D4×C13—48no—
337D4×C13—42no—
338C2×C4×C13—22no—
339C2×C4×C13—22no—
340C2×C4×C13—24no—
341C2×C4×C13—22no—
342C2×C4×C13—22no—
343C2×C4×C13—22no—
344C2×C4×C13—24no—
345C2×C4×C13—24no—
346C2×C4×C13—22no—
347C2×C4×C13—22no—
348C2×C4×C13—22no—
349C2×C4×C13—22no—
350C2×C4×C13—22no—
351C2×C4×C13—22no—
352C2×C4×C13—48no—
353C2×C4×C13—48no—
354C2×C4×C13—42no—
355C2×C4×C13—42no—
356C2×C4×C13C22×D412yes—
357C2×C4×C13C22×D412yes—
358C2×C4×C13C22×D412yes—
359C2×C4×C13C22×D412yes—
360C2×C4×C13C22×D411yescharacteristic
361C2×C4×C13C2×#4112yes—
362C2×C4×C13H(5,𝔽2)12yes—
363C2×C4×C13C2511yescharacteristic
364C22⋊D13—48no—
365C22⋊D13—84no—
366C2×Dic13—22no—
367C2×Dic13—22no—
368C2×Dic13—22no—
369C2×Dic13—42no—
370C2×Dic13—42no—
371C2×Dic13—42no—
372C2×Dic13—84no—
373D52—22no—
374D52—22no—
375D52—42no—
376C4×D13—84no—
377#1055—22no—
378#1055—22no—
379#1055—22no—
380#1055—22no—
381C22×#41C2×D1311yescharacteristic
382C23×Q8C2×D1311yescharacteristic
383C22×SD16—131no—
384C22×SD16—131no—
385C22×D8—131no—
386C23×C8—131no—
387C23×C8—131no—
388#553—138no—
389#553—264no—
390#548—24no—
391#548C2×D1318yescomplemented
392C2×#126—261no—
393C2×#125—131no—
394C2×#124—21no—
395C2×#124C2×D1311yescharacteristic
396C2×#123—261no—
397C2×C22⋊Q8—21no—
398C2×C22⋊Q8C2×D1311yescharacteristic
399C2×#121—21no—
400C2×#121—131no—
401C2×#121—131no—
402C2×#121—261no—
403C2×#121C2×D1311yescharacteristic
404C2×C4×Q8C2×D1311yescharacteristic
405C2×C4×D4—21no—
406C2×C4×D4—131no—
407C2×C4×D4—261no—
408C2×C4×D4C2×D1311yescharacteristic
409C2×#117—131no—
410C22×C4⋊C4—131no—
411#488—138no—
412#485—138no—
413#481—138no—
414#479—138no—
415#466—138no—
416#465—138no—
417#463—138no—
418#449—138no—
419#448—138no—
420C4×SD16—138no—
421C8×D4—138no—
422C2×#107—131no—
423C2×#106—131no—
424C2×#106—131no—
425C2×C4⋊C8—131no—
426#416—138no—
427C2×#103—131no—
428C2×#103—131no—
429C2×#103—131no—
430C2×#103—131no—
431C2×#103—131no—
432C2×#103—131no—
433C2×#103—138no—
434C2×#102—131no—
435C2×#102—131no—
436C2×#102—131no—
437C2×#102—131no—
438C2×C22⋊C8—131no—
439C2×C22⋊C8—131no—
440C2×C4×C8—131no—
441C22×C13—22no—
442C22×C13—28no—
443C22×C13—22no—
444C22×C13—22no—
445C22×C13—22no—
446C22×C13—22no—
447C22×C13—44no—
448C22×C13—42no—
449C22×C13—42no—
450C22×C13—42no—
451C22×C13—84no—
452C22×C13#54612yes—
453C22×C13C2×#13514yes—
454C22×C13C2×#13512yes—
455C22×C13#57712yes—
456C22×C13C23×D411yescharacteristic
457C2×D13—42no—
458C2×D13—42no—
459C2×D13—42no—
460C2×D13—84no—
461C4×C13—22no—
462C4×C13—22no—
463C4×C13—24no—
464C4×C13—22no—
465C4×C13—22no—
466C4×C13—42no—
467C4×C13—42no—
468C4×C13#54612yes—
469C4×C13C22×#4111yescharacteristic
470C4×C13C2×H(5,𝔽2)11yescharacteristic
471Dic13—42no—
472Dic13—42no—
473Dic13—42no—
474C2×#41—22no—
475C2×#41—24no—
476C2×#41—42no—
477C2×#41C22×D1314yes—
478C22×Q8—21no—
479C22×Q8—22no—
480C22×Q8—24no—
481C22×Q8—42no—
482C22×Q8C22×D1311yescharacteristic
483C22×Q8C22×D1314yes—
484C22×Q8C22×D1311yescharacteristic
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—131no—
488C22×D4—261no—
489C22×D4—261no—
490C22×D4C22⋊D1311yescharacteristic
491C22×D4C22×D1311yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—261no—
495C23×C4—261no—
496C23×C4C22×D1311yescharacteristic
497C23×C4C22×D1311yescharacteristic
498C2×SD16—134no—
499C2×SD16—134no—
500C2×SD16—264no—
501C2×SD16—522no—
502C2×D8—134no—
503C2×D8—522no—
504C22×C8—131no—
505C22×C8—131no—
506C22×C8—131no—
507C22×C8—131no—
508C22×C8—134no—
509C22×C8—134no—
510C22×C8—522no—
511C22×C8—522no—
512#126—268no—
513#125—134no—
514#125—262no—
515#124—28no—
516#124—22no—
517#124C22×D1314yes—
518#123—268no—
519C22⋊Q8—22no—
520C22⋊Q8—28no—
521C22⋊Q8C22×D1314yes—
522#121—28no—
523#121—22no—
524#121—134no—
525#121—134no—
526#121—268no—
527#121—262no—
528#121—262no—
529#121C22×D1314yes—
530C4×Q8—22no—
531C4×Q8C22×D1314yes—
532C4×D4—28no—
533C4×D4—134no—
534C4×D4—268no—
535C4×D4—262no—
536C4×D4C22⋊D1314yes—
537C4×D4C22×D1314yes—
538#117—134no—
539#117—262no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—131no—
543C2×C4⋊C4—131no—
544C2×C4⋊C4—134no—
545C2×C4⋊C4—131no—
546C2×C4⋊C4—261no—
547C2×C4⋊C4—262no—
548C2×C4⋊C4—261no—
549C2×C4⋊C4—261no—
550C2×C4⋊C4C22⋊D1311yescharacteristic
551C2×C4⋊C4C22×D1311yescharacteristic
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—261no—
557C2×C22⋊C4—261no—
558C2×C22⋊C4—261no—
559C2×C22⋊C4—261no—
560C2×C22⋊C4C22⋊D1311yescharacteristic
561C2×C22⋊C4C22⋊D1311yescharacteristic
562C2×C42—21no—
563C2×C42—261no—
564C2×C42C22×D1311yescharacteristic
565#107—134no—
566#106—134no—
567#106—134no—
568C4⋊C8—134no—
569#103—134no—
570#103—134no—
571#103—134no—
572#103—134no—
573#103—134no—
574#103—134no—
575#102—134no—
576#102—134no—
577#102—134no—
578#102—134no—
579C22⋊C8—134no—
580C22⋊C8—134no—
581C4×C8—134no—
582C2×C13—24no—
583C2×C13—42no—
584C2×C13—82no—
585C2×C13#330114yescomplemented
586C2×C13C2×#54611yescharacteristic
587C2×C13C22×#13511yescharacteristic
588C2×C13C2×#57711yescharacteristic
589D13—82no—
590C24—21no—
591C24—261no—
592C24C2×C22⋊D1311yescharacteristic
593C24C2×C22⋊D1311yescharacteristic
594#41—28no—
595#41—44no—
596#41—48no—
597C2×Q8—22no—
598C2×Q8—21no—
599C2×Q8—24no—
600C2×Q8—21no—
601C2×Q8—28no—
602C2×Q8—22no—
603C2×Q8—22no—
604C2×Q8—44no—
605C2×Q8—44no—
606C2×Q8—48no—
607C2×Q8#612914yes—
608C2×Q8C23×D1312yes—
609C2×Q8C23×D1312yes—
610C2×D4—24no—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—21no—
616C2×D4—44no—
617C2×D4—44no—
618C2×D4—132no—
619C2×D4—264no—
620C2×D4—264no—
621C2×D4—262no—
622C2×D4—262no—
623C2×D4—261no—
624C2×D4—524no—
625C2×D4—1042no—
626C2×D4C2×C22⋊D1314yes—
627C2×D4C23×D1312yes—
628C22×C4—21no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—24no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—24no—
637C22×C4—44no—
638C22×C4—44no—
639C22×C4—261no—
640C22×C4—261no—
641C22×C4—261no—
642C22×C4—264no—
643C22×C4—264no—
644C22×C4—1042no—
645C22×C4—1042no—
646C22×C4C2×C22⋊D1312yes—
647C22×C4C2×C22⋊D1312yes—
648C22×C4C2×C22⋊D1311yescharacteristic
649C22×C4C2×C22⋊D1311yescharacteristic
650C22×C4C2×C22⋊D1311yescharacteristic
651C22×C4C2×C22⋊D1311yescharacteristic
652C22×C4C23×D1312yes—
653C22×C4C23×D1312yes—
654C22×C4C23×D1311yescharacteristic
655SD16—268no—
656SD16—524no—
657D8—524no—
658C2×C8—132no—
659C2×C8—132no—
660C2×C8—132no—
661C2×C8—132no—
662C2×C8—262no—
663C2×C8—262no—
664C2×C8—262no—
665C2×C8—262no—
666C2×C8—524no—
667C2×C8—524no—
668C4⋊C4—24no—
669C4⋊C4—24no—
670C4⋊C4—21no—
671C4⋊C4—132no—
672C4⋊C4—132no—
673C4⋊C4—132no—
674C4⋊C4—261no—
675C4⋊C4—261no—
676C4⋊C4—264no—
677C4⋊C4—261no—
678C4⋊C4—264no—
679C4⋊C4—264no—
680C4⋊C4C2×C22⋊D1314yes—
681C4⋊C4C23×D1312yes—
682C22⋊C4—24no—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—264no—
687C22⋊C4—264no—
688C22⋊C4—264no—
689C22⋊C4—264no—
690C22⋊C4C2×C22⋊D1314yes—
691C22⋊C4C2×C22⋊D1314yes—
692C42—24no—
693C42—264no—
694C42C2×C22⋊D1312yes—
695C42C23×D1312yes—
696C13C2×#330111yescharacteristic, complemented, Sylow
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—262no—
707C23—522no—
708C23—522no—
709C23—522no—
710C23#8820414yes—
711C23C22×C22⋊D1312yes—
712C23C22×C22⋊D1312yes—
713C23C22×C22⋊D1311yescharacteristic
714Q8—24no—
715Q8—22no—
716Q8—22no—
717Q8—22no—
718Q8—48no—
719Q8—42no—
720Q8C2×#612914yes—
721D4—28no—
722D4—22no—
723D4—22no—
724D4—48no—
725D4—48no—
726D4—42no—
727D4—262no—
728D4—262no—
729D4—528no—
730D4—522no—
731D4—1044no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—48no—
747C2×C4—48no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—262no—
751C2×C4—262no—
752C2×C4—262no—
753C2×C4—522no—
754C2×C4—522no—
755C2×C4—522no—
756C2×C4—1044no—
757C2×C4—1044no—
758C2×C4C2×#612912yes—
759C2×C4#8825112yes—
760C2×C4C22×C22⋊D1312yes—
761C2×C4C22×C22⋊D1312yes—
762C2×C4C22×C22⋊D1312yes—
763C2×C4C22×C22⋊D1312yes—
764C2×C4C22×C22⋊D1311yescharacteristic
765C2×C4C24×D1311yescharacteristic
766C8—262no—
767C8—262no—
768C8—262no—
769C8—262no—
770C22—28no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—84no—
781C22—522no—
782C22—522no—
783C22—522no—
784C22—1044no—
785C22#1171951112yes—
786C22C2×#8820414yes—
787C22C2×#8820412yes—
788C22#1171954212yes—
789C22C23×C22⋊D1311yescharacteristic
790C4—22no—
791C4—22no—
792C4—22no—
793C4—24no—
794C4—22no—
795C4—42no—
796C4—42no—
797C4—522no—
798C4—522no—
799C4—522no—
800C4#1171951112yes—
801C4C22×#612911yescharacteristic
802C4C2×#8825111yescharacteristic
803C2—24no—
804C2—42no—
805C2—82no—
806C2—1042no—
807C2#1312673814yesdirect product factor
808C2C2×#1171951111yescharacteristic
809C2C22×#8820411yescharacteristic
810C2C2×#1171954211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#548C2
socleC23×C13C22×D4
hypercenterC2×#548D13
hypocenterC13C2×#3301
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×#11719270C2semidirect
2. #13126738C2direct (N × H)
3. C2×#11718717C2semidirect
4. C2×#11718695C2semidirect
5. C2×#11718706C2semidirect
6. C2×#11718683C2semidirect
7. C2×#11718699C2semidirect
8. C2×#11718709C2semidirect
9. C2×#11718718C2semidirect
10. C2×#11718899C2semidirect
11. C2×#11718888C2semidirect
12. C2×C4×#6106C2semidirect
13. C2×D4×#1055C2semidirect
14. C2×#11718894C2semidirect
15. C22×#88075C2semidirect
16. C2×C13×#548C2semidirect
20. C13×#548C22semidirect
41. #11719270C22semidirect
47. #11718899C22semidirect
48. #11718894C22semidirect
49. #11718888C22semidirect
56. C2×#88075C22semidirect
62. #11718718C22semidirect
63. #11718717C22semidirect
64. #11718709C22semidirect
65. #11718706C22semidirect
66. #11718699C22semidirect
67. #11718695C22semidirect
68. C4×#6106C22semidirect
69. #11718683C22semidirect
70. D4×#1055C22semidirect
293. C2×#548D13semidirect
391. #548C2×D13semidirect
585. C2×C13#3301semidirect
696. C13C2×#3301semidirect
807. C2#13126738direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192702
#131267382
C2×#117187172
C2×#117186952
C2×#117187062
C2×#117186832
C2×#117186992
C2×#117187092
C2×#117187182
C2×#117188992
C2×#117188882
C2×C4×#61062
C2×D4×#10552
C2×#117188942
C22×#880752
C2×C13×#5482
C2×#330113