Finite Group Databasebeta

← C2×#13126827 #16739493

Subgroups — C2×#13126827 #16739493

Order 3328.

2374 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719260C211yesmaximal, characteristic, complemented
2#13126827C2116yesmaximal, direct product factor
3C2×#11718716C211yesmaximal, characteristic, complemented
4C2×#11718705C211yesmaximal, characteristic, complemented
5C2×#11718694C211yesmaximal, characteristic, complemented
6C2×#11718682C211yesmaximal, characteristic, complemented
7C2×#11718710C211yesmaximal, characteristic, complemented
8C2×#11718699C211yesmaximal, characteristic, complemented
9C2×#11718718C211yesmaximal, characteristic, complemented
10C2×#11718899C211yesmaximal, characteristic, complemented
11C2×#11718888C211yesmaximal, characteristic, complemented
12C2×#11718687C211yesmaximal, characteristic, complemented
13C2×#11718672C211yesmaximal, characteristic, complemented
14C2×#11718893C211yesmaximal, characteristic, complemented
15C22×#88075C211yesmaximal, characteristic, complemented
16C2×C13×#548C211yesmaximal, characteristic, complemented
17C22×C13×#41C2211yescharacteristic
18C23×Q8×C13C2211yescharacteristic
19C22×#6129—21no—
20C13×#548—24no—
21C13×#548C2218yescomplemented
22C2×C13×#124—21no—
23C2×C13×#124C2211yescharacteristic
24C2×C13×C22⋊Q8—21no—
25C2×C13×C22⋊Q8C2211yescharacteristic
26C2×C13×#121—21no—
27C2×C13×#121C2211yescharacteristic
28C2×C4×Q8×C13C2211yescharacteristic
29C2×C4×D4×C13—21no—
30C2×C4×D4×C13C2211yescharacteristic
31C22×#6106C2211yescharacteristic
32C22×#6106C2211yescharacteristic
33C22×#6104C2211yescharacteristic
34C2×#88184C2211yescharacteristic
35C2×#88184C2211yescharacteristic
36C22×C4⋊Dic13C2211yescharacteristic
37C22×C4⋊Dic13C2211yescharacteristic
38C22×#6099C2211yescharacteristic
39C23×#1055C2211yescharacteristic
40#11719260—24no—
41#11719260C2218yescomplemented
42C2×#88151—21no—
43C2×#88140—21no—
44C2×#88140—21no—
45C2×C4×D52C2211yescharacteristic
46C2×#88123C2211yescharacteristic
47#11718899C2218yescomplemented
48#11718893C2218yescomplemented
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#11718716C2218yescomplemented
64#11718710C2218yescomplemented
65#11718705C2218yescomplemented
66#11718699C2218yescomplemented
67#11718694C2218yescomplemented
68#11718687C2218yescomplemented
69#11718682C2218yescomplemented
70#11718672C2218yescomplemented
71C2×#88049C2211yescharacteristic
72C2×#88047C2211yescharacteristic
73C2×#88047C2211yescharacteristic
74C2×#88047C2211yescharacteristic
75C2×C4⋊#1055C2211yescharacteristic
76C2×#88043C2211yescharacteristic
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—
99C23×Dic13—21no—
100C2×#6129—28no—
101C2×#6129—48no—
102C22×D52C2311yescharacteristic
103C22×C4×D13—21no—
104C22×Dic26—21no—
105C13×#124—28no—
106C13×#124—22no—
107C13×#124C2314yes—
108C13×C22⋊Q8—22no—
109C13×C22⋊Q8—28no—
110C13×C22⋊Q8C2314yes—
111C13×#121—28no—
112C13×#121—22no—
113C13×#121C2314yes—
114C4×Q8×C13—22no—
115C4×Q8×C13C2314yes—
116C4×D4×C13—28no—
117C4×D4×C13D414yes—
118C4×D4×C13C2314yes—
119C2×C13×C4⋊C4—21no—
120C2×C13×C4⋊C4—21no—
121C2×C13×C4⋊C4D411yescharacteristic
122C2×C13×C4⋊C4C2311yescharacteristic
123C2×C13×C22⋊C4—21no—
124C2×C13×C22⋊C4—21no—
125C2×C13×C22⋊C4—21no—
126C2×C13×C22⋊C4—21no—
127C2×C13×C22⋊C4D411yescharacteristic
128C2×C13×C22⋊C4D411yescharacteristic
129C2×C42×C13—21no—
130C2×C42×C13C2311yescharacteristic
131C2×#6106—24no—
132C2×#6106—42no—
133C2×#6106C2314yes—
134C2×#6106C2314yes—
135C2×#6104—42no—
136C2×#6104C2314yes—
137#88184—22no—
138#88184—22no—
139#88184C2314yes—
140#88184C2314yes—
141C2×#6103—21no—
142C2×#6103—21no—
143C2×#6103—21no—
144C2×C4⋊Dic13—21no—
145C2×C4⋊Dic13—21no—
146C2×C4⋊Dic13—21no—
147C2×C4⋊Dic13—22no—
148C2×C4⋊Dic13—22no—
149C2×C4⋊Dic13C2311yescharacteristic
150C2×C4⋊Dic13C2311yescharacteristic
151C2×C4⋊Dic13C2311yescharacteristic
152C2×C4⋊Dic13C2314yes—
153C2×C4⋊Dic13C2314yes—
154C2×#6099—42no—
155C2×#6099C2314yes—
156C22×#1055—42no—
157C22×#1055C2311yescharacteristic
158C22×#1055C2311yescharacteristic
159C22×#1055C2311yescharacteristic
160C22×#1055C2311yescharacteristic
161C22×#1055C2314yes—
162#88151—28no—
163#88140—28no—
164#88140—28no—
165C4×D52—22no—
166C4×D52C2314yes—
167#88123—22no—
168#88123C2314yes—
169#88075C2314yes—
170#88075C2314yes—
171#88075C2314yes—
172#88075C2314yes—
173#88075C2314yes—
174#88075C2314yes—
175#88072C2314yes—
176#88072C2314yes—
177#88072C2314yes—
178C22⋊#1055C2314yes—
179C22⋊#1055C2314yes—
180#88049C2314yes—
181#88047C2314yes—
182#88047C2314yes—
183#88047C2314yes—
184C4⋊#1055C2314yes—
185#88043C2314yes—
186C2×#3308—131nomaximal, Sylow
187C24×C13—21no—
188C24×C13C2×D411yescharacteristic
189C24×C13C2×D411yescharacteristic
190C23×D13—21no—
191C13×#41—28no—
192C13×#41—44no—
193C13×#41—48no—
194C2×Q8×C13—21no—
195C2×Q8×C13—24no—
196C2×Q8×C13—21no—
197C2×Q8×C13—22no—
198C2×Q8×C13—28no—
199C2×Q8×C13—22no—
200C2×Q8×C13—22no—
201C2×Q8×C13—44no—
202C2×Q8×C13—44no—
203C2×Q8×C13—48no—
204C2×Q8×C13#4114yescomplemented
205C2×Q8×C13C2412yes—
206C2×Q8×C13C2412yes—
207C2×D4×C13—24no—
208C2×D4×C13—24no—
209C2×D4×C13—24no—
210C2×D4×C13—21no—
211C2×D4×C13—22no—
212C2×D4×C13—22no—
213C2×D4×C13—44no—
214C2×D4×C13—44no—
215C2×D4×C13C2×D414yes—
216C2×D4×C13C2412yes—
217C22×C4×C13—21no—
218C22×C4×C13—22no—
219C22×C4×C13—22no—
220C22×C4×C13—22no—
221C22×C4×C13—22no—
222C22×C4×C13—21no—
223C22×C4×C13—21no—
224C22×C4×C13—24no—
225C22×C4×C13—24no—
226C22×C4×C13—44no—
227C22×C4×C13—44no—
228C22×C4×C13C2×D411yescharacteristic
229C22×C4×C13C2×D411yescharacteristic
230C22×C4×C13C2×D411yescharacteristic
231C22×C4×C13C2×D412yes—
232C22×C4×C13C2×D412yes—
233C22×C4×C13C2×D411yescharacteristic
234C22×C4×C13C2412yes—
235C22×C4×C13C2412yes—
236C22×C4×C13C2411yescharacteristic
237C2×C22⋊D13—24no—
238C2×C22⋊D13—24no—
239C2×C22⋊D13—44no—
240C2×C22⋊D13—44no—
241C22×Dic13—24no—
242C22×Dic13—24no—
243C22×Dic13—21no—
244C22×Dic13—21no—
245C22×Dic13—21no—
246C22×Dic13—44no—
247C22×Dic13—44no—
248#6129—432no—
249C2×D52—22no—
250C2×D52—22no—
251C2×D52—21no—
252C2×D52C2412yes—
253C2×C4×D13—24no—
254C2×C4×D13—44no—
255C2×Dic26—24no—
256C2×Dic26—44no—
257C13×C4⋊C4—24no—
258C13×C4⋊C4—24no—
259C13×C4⋊C4—21no—
260C13×C4⋊C4C2×D414yes—
261C13×C4⋊C4C2412yes—
262C13×C22⋊C4—24no—
263C13×C22⋊C4—24no—
264C13×C22⋊C4—24no—
265C13×C22⋊C4—24no—
266C13×C22⋊C4C2×D414yes—
267C13×C22⋊C4C2×D414yes—
268C42×C13—24no—
269C42×C13C2×D412yes—
270C42×C13C2412yes—
271#6106—28no—
272#6106—44no—
273#6104—44no—
274#6103—24no—
275#6103—24no—
276#6103—24no—
277C4⋊Dic13—21no—
278C4⋊Dic13—21no—
279C4⋊Dic13—24no—
280C4⋊Dic13—21no—
281C4⋊Dic13—24no—
282C4⋊Dic13—24no—
283C4⋊Dic13C2412yes—
284C4⋊Dic13C2412yes—
285C4⋊Dic13C2412yes—
286#6099—44no—
287C2×#1055—22no—
288C2×#1055—22no—
289C2×#1055—22no—
290C2×#1055—22no—
291C2×#1055—44no—
292C2×#1055C2412yes—
293C2×#1055C2412yes—
294C2×#1055C2412yes—
295C2×#1055C2412yes—
296C2×#548D1311yescharacteristic, complemented
297C2×#547—131no—
298#3308—1316no—
299C2×#489—131no—
300C2×#484—131no—
301C2×#480—131no—
302C2×#477—131no—
303C2×#468—131no—
304C2×#466—131no—
305C2×#463—131no—
306C2×#449—131no—
307C2×#448—131no—
308C2×#440—131no—
309C2×#435—131no—
310C2×#417—131no—
311C22×#103—131no—
312C23×C13—22no—
313C23×C13—22no—
314C23×C13—22no—
315C23×C13—22no—
316C23×C13—22no—
317C23×C13—22no—
318C23×C13—42no—
319C23×C13—42no—
320C23×C13—42no—
321C23×C13AGL(1,ℤ/8)14yes—
322C23×C13C22×D412yes—
323C23×C13C22×D412yes—
324C23×C13C22×D411yescharacteristic
325C22×D13—22no—
326C22×D13—42no—
327C22×D13—42no—
328C22×D13—42no—
329Q8×C13—24no—
330Q8×C13—22no—
331Q8×C13—22no—
332Q8×C13—22no—
333Q8×C13—48no—
334Q8×C13—42no—
335Q8×C13C2×#4114yescomplemented
336D4×C13—28no—
337D4×C13—22no—
338D4×C13—22no—
339D4×C13—48no—
340D4×C13—48no—
341D4×C13—42no—
342C2×C4×C13—22no—
343C2×C4×C13—22no—
344C2×C4×C13—24no—
345C2×C4×C13—22no—
346C2×C4×C13—22no—
347C2×C4×C13—22no—
348C2×C4×C13—24no—
349C2×C4×C13—24no—
350C2×C4×C13—22no—
351C2×C4×C13—22no—
352C2×C4×C13—22no—
353C2×C4×C13—22no—
354C2×C4×C13—22no—
355C2×C4×C13—22no—
356C2×C4×C13—48no—
357C2×C4×C13—48no—
358C2×C4×C13—42no—
359C2×C4×C13—42no—
360C2×C4×C13C22×D412yes—
361C2×C4×C13C22×D412yes—
362C2×C4×C13C22×D412yes—
363C2×C4×C13C22×D412yes—
364C2×C4×C13C22×D411yescharacteristic
365C2×C4×C13C2×#4112yes—
366C2×C4×C13H(5,𝔽2)12yes—
367C2×C4×C13C2511yescharacteristic
368C22⋊D13—48no—
369C22⋊D13—48no—
370C2×Dic13—22no—
371C2×Dic13—22no—
372C2×Dic13—22no—
373C2×Dic13—48no—
374C2×Dic13—42no—
375C2×Dic13—42no—
376C2×Dic13—42no—
377C2×Dic13—48no—
378D52—22no—
379D52—22no—
380D52—42no—
381C4×D13—48no—
382Dic26—48no—
383#1055—22no—
384#1055—22no—
385#1055—22no—
386#1055—22no—
387C22×#41—261no—
388C22×#41C2×D1311yescharacteristic
389C23×Q8C2×D1311yescharacteristic
390C22×SD16—131no—
391C22×SD16—131no—
392C22×D8—131no—
393C22×M16—131no—
394C23×C8—131no—
395#548—24no—
396#548C2×D1318yescomplemented
397#547—138no—
398#547—264no—
399C2×C4⋊Q8—131no—
400C2×#124—21no—
401C2×#124C2×D1311yescharacteristic
402C2×#123—261no—
403C2×#123—261no—
404C2×C22⋊Q8—21no—
405C2×C22⋊Q8—261no—
406C2×C22⋊Q8C2×D1311yescharacteristic
407C2×#121—21no—
408C2×#121—131no—
409C2×#121—131no—
410C2×#121C2×D1311yescharacteristic
411C2×C4×Q8C2×D1311yescharacteristic
412C2×C4×D4—21no—
413C2×C4×D4—131no—
414C2×C4×D4C2×D1311yescharacteristic
415C22×C4⋊C4—131no—
416C22×C4⋊C4—131no—
417#489—138no—
418#484—138no—
419#480—138no—
420#477—138no—
421#468—138no—
422#466—138no—
423#463—138no—
424#449—138no—
425#448—138no—
426#440—138no—
427#435—138no—
428C2×#107—131no—
429C2×#107—131no—
430C2×#107—131no—
431C2×C4⋊C8—131no—
432#417—138no—
433C2×#103—131no—
434C2×#103—131no—
435C2×#103—131no—
436C2×#103—131no—
437C2×#103—131no—
438C2×#103—131no—
439C2×#103—138no—
440C2×#102—131no—
441C2×#102—131no—
442C2×#102—131no—
443C2×#102—131no—
444C2×C22⋊C8—131no—
445C2×C22⋊C8—131no—
446C2×#97—131no—
447C22×C13—22no—
448C22×C13—28no—
449C22×C13—22no—
450C22×C13—22no—
451C22×C13—22no—
452C22×C13—22no—
453C22×C13—44no—
454C22×C13—42no—
455C22×C13—42no—
456C22×C13—42no—
457C22×C13—84no—
458C22×C13#54612yes—
459C22×C13C2×AGL(1,ℤ/8)14yes—
460C22×C13C2×AGL(1,ℤ/8)12yes—
461C22×C13#57812yes—
462C22×C13C23×D411yescharacteristic
463C2×D13—42no—
464C2×D13—42no—
465C2×D13—42no—
466C2×D13—84no—
467C4×C13—22no—
468C4×C13—22no—
469C4×C13—24no—
470C4×C13—22no—
471C4×C13—22no—
472C4×C13—42no—
473C4×C13—42no—
474C4×C13#54612yes—
475C4×C13C22×#4111yescharacteristic
476C4×C13C2×H(5,𝔽2)11yescharacteristic
477Dic13—42no—
478Dic13—42no—
479Dic13—42no—
480C2×#41—22no—
481C2×#41—24no—
482C2×#41—42no—
483C2×#41—268no—
484C2×#41—528no—
485C2×#41C22×D1314yes—
486C22×Q8—21no—
487C22×Q8—22no—
488C22×Q8—24no—
489C22×Q8—42no—
490C22×Q8—261no—
491C22×Q8C22×D1311yescharacteristic
492C22×Q8C22×D1314yes—
493C22×Q8C22×D1311yescharacteristic
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—131no—
497C22×D4—261no—
498C22×D4—261no—
499C22×D4C22⋊D1311yescharacteristic
500C22×D4C22×D1311yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—261no—
504C23×C4—261no—
505C23×C4—261no—
506C23×C4C22×D1311yescharacteristic
507C23×C4C22×D1311yescharacteristic
508C2×SD16—134no—
509C2×SD16—134no—
510C2×SD16—264no—
511C2×SD16—522no—
512C2×D8—134no—
513C2×D8—522no—
514C2×M16—134no—
515C2×M16—522no—
516C22×C8—131no—
517C22×C8—131no—
518C22×C8—131no—
519C22×C8—131no—
520C22×C8—134no—
521C22×C8—522no—
522C4⋊Q8—134no—
523C4⋊Q8—262no—
524#124—28no—
525#124—22no—
526#124C22×D1314yes—
527#123—268no—
528#123—268no—
529C22⋊Q8—22no—
530C22⋊Q8—28no—
531C22⋊Q8—268no—
532C22⋊Q8C22×D1314yes—
533#121—28no—
534#121—22no—
535#121—134no—
536#121—134no—
537#121—262no—
538#121—262no—
539#121C22×D1314yes—
540C4×Q8—22no—
541C4×Q8C22×D1314yes—
542C4×D4—28no—
543C4×D4—134no—
544C4×D4—262no—
545C4×D4C22⋊D1314yes—
546C4×D4C22×D1314yes—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—131no—
550C2×C4⋊C4—131no—
551C2×C4⋊C4—131no—
552C2×C4⋊C4—134no—
553C2×C4⋊C4—134no—
554C2×C4⋊C4—261no—
555C2×C4⋊C4—261no—
556C2×C4⋊C4—262no—
557C2×C4⋊C4—262no—
558C2×C4⋊C4—261no—
559C2×C4⋊C4C22⋊D1311yescharacteristic
560C2×C4⋊C4C22×D1311yescharacteristic
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—261no—
566C2×C22⋊C4—261no—
567C2×C22⋊C4—261no—
568C2×C22⋊C4C22⋊D1311yescharacteristic
569C2×C22⋊C4C22⋊D1311yescharacteristic
570C2×C42—21no—
571C2×C42C22×D1311yescharacteristic
572#107—134no—
573#107—134no—
574#107—134no—
575C4⋊C8—134no—
576#103—134no—
577#103—134no—
578#103—134no—
579#103—134no—
580#103—134no—
581#103—134no—
582#102—134no—
583#102—134no—
584#102—134no—
585#102—134no—
586C22⋊C8—134no—
587C22⋊C8—134no—
588#97—134no—
589C2×C13—24no—
590C2×C13—42no—
591C2×C13—82no—
592C2×C13#330814yescomplemented
593C2×C13C2×#54611yescharacteristic
594C2×C13C22×AGL(1,ℤ/8)11yescharacteristic
595C2×C13C2×#57811yescharacteristic
596D13—82no—
597C24—21no—
598C24—261no—
599C24C2×C22⋊D1311yescharacteristic
600C24C2×C22⋊D1311yescharacteristic
601#41—28no—
602#41—44no—
603#41—48no—
604#41—5232no—
605C2×Q8—22no—
606C2×Q8—21no—
607C2×Q8—24no—
608C2×Q8—21no—
609C2×Q8—28no—
610C2×Q8—22no—
611C2×Q8—22no—
612C2×Q8—44no—
613C2×Q8—44no—
614C2×Q8—48no—
615C2×Q8—264no—
616C2×Q8—524no—
617C2×Q8#612914yescomplemented
618C2×Q8C23×D1312yes—
619C2×Q8C23×D1312yes—
620C2×D4—24no—
621C2×D4—24no—
622C2×D4—24no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—21no—
626C2×D4—44no—
627C2×D4—44no—
628C2×D4—132no—
629C2×D4—264no—
630C2×D4—264no—
631C2×D4—262no—
632C2×D4—262no—
633C2×D4—261no—
634C2×D4—524no—
635C2×D4—524no—
636C2×D4C2×C22⋊D1314yes—
637C2×D4C23×D1312yes—
638C22×C4—21no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—24no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—24no—
647C22×C4—44no—
648C22×C4—44no—
649C22×C4—264no—
650C22×C4—264no—
651C22×C4—261no—
652C22×C4—261no—
653C22×C4—261no—
654C22×C4—264no—
655C22×C4—524no—
656C22×C4—524no—
657C22×C4—524no—
658C22×C4C2×C22⋊D1312yes—
659C22×C4C2×C22⋊D1312yes—
660C22×C4C2×C22⋊D1311yescharacteristic
661C22×C4C2×C22⋊D1311yescharacteristic
662C22×C4C2×C22⋊D1311yescharacteristic
663C22×C4C2×C22⋊D1311yescharacteristic
664C22×C4C23×D1312yes—
665C22×C4C23×D1312yes—
666C22×C4C23×D1311yescharacteristic
667SD16—268no—
668SD16—524no—
669D8—524no—
670M16—524no—
671C2×C8—132no—
672C2×C8—132no—
673C2×C8—132no—
674C2×C8—132no—
675C2×C8—262no—
676C2×C8—262no—
677C2×C8—262no—
678C2×C8—262no—
679C2×C8—524no—
680C4⋊C4—24no—
681C4⋊C4—24no—
682C4⋊C4—21no—
683C4⋊C4—132no—
684C4⋊C4—132no—
685C4⋊C4—132no—
686C4⋊C4—261no—
687C4⋊C4—261no—
688C4⋊C4—261no—
689C4⋊C4—264no—
690C4⋊C4—264no—
691C4⋊C4—264no—
692C4⋊C4C2×C22⋊D1314yes—
693C4⋊C4C23×D1312yes—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—264no—
699C22⋊C4—264no—
700C22⋊C4—264no—
701C22⋊C4C2×C22⋊D1314yes—
702C22⋊C4C2×C22⋊D1314yes—
703C42—24no—
704C42C2×C22⋊D1312yes—
705C42C23×D1312yes—
706C13C2×#330811yescharacteristic, complemented, Sylow
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—262no—
717C23—522no—
718C23—522no—
719C23—522no—
720C23#8820314yes—
721C23C22×C22⋊D1312yes—
722C23C22×C22⋊D1312yes—
723C23C22×C22⋊D1311yescharacteristic
724Q8—24no—
725Q8—22no—
726Q8—22no—
727Q8—22no—
728Q8—48no—
729Q8—42no—
730Q8—528no—
731Q8C2×#612914yescomplemented
732D4—28no—
733D4—22no—
734D4—22no—
735D4—48no—
736D4—48no—
737D4—42no—
738D4—262no—
739D4—262no—
740D4—528no—
741D4—528no—
742D4—522no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—48no—
758C2×C4—48no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—262no—
762C2×C4—262no—
763C2×C4—262no—
764C2×C4—528no—
765C2×C4—528no—
766C2×C4—522no—
767C2×C4—522no—
768C2×C4—522no—
769C2×C4—528no—
770C2×C4C2×#612912yes—
771C2×C4#8825112yes—
772C2×C4C22×C22⋊D1312yes—
773C2×C4C22×C22⋊D1312yes—
774C2×C4C22×C22⋊D1312yes—
775C2×C4C22×C22⋊D1312yes—
776C2×C4C22×C22⋊D1311yescharacteristic
777C2×C4C24×D1311yescharacteristic
778C8—262no—
779C8—262no—
780C8—262no—
781C8—262no—
782C22—22no—
783C22—22no—
784C22—28no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—44no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—84no—
793C22—522no—
794C22—522no—
795C22—522no—
796C22—1044no—
797C22#1171951112yes—
798C22C2×#8820314yes—
799C22C2×#8820312yes—
800C22#1171954312yes—
801C22C23×C22⋊D1311yescharacteristic
802C4—22no—
803C4—22no—
804C4—24no—
805C4—22no—
806C4—22no—
807C4—42no—
808C4—42no—
809C4—522no—
810C4—522no—
811C4—522no—
812C4#1171951112yes—
813C4C22×#612911yescharacteristic
814C4C2×#8825111yescharacteristic
815C2—24no—
816C2—42no—
817C2—82no—
818C2—1042no—
819C2#1312682714yesdirect product factor
820C2C2×#1171951111yescharacteristic
821C2C22×#8820311yescharacteristic
822C2C2×#1171954311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#548C2
socleC23×C13C22×D4
hypercenterC2×#548D13
hypocenterC13C2×#3308
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×#11719260C2semidirect
2. #13126827C2direct (N × H)
3. C2×#11718716C2semidirect
4. C2×#11718705C2semidirect
5. C2×#11718694C2semidirect
6. C2×#11718682C2semidirect
7. C2×#11718710C2semidirect
8. C2×#11718699C2semidirect
9. C2×#11718718C2semidirect
10. C2×#11718899C2semidirect
11. C2×#11718888C2semidirect
12. C2×#11718687C2semidirect
13. C2×#11718672C2semidirect
14. C2×#11718893C2semidirect
15. C22×#88075C2semidirect
16. C2×C13×#548C2semidirect
21. C13×#548C22semidirect
41. #11719260C22semidirect
47. #11718899C22semidirect
48. #11718893C22semidirect
49. #11718888C22semidirect
56. C2×#88075C22semidirect
62. #11718718C22semidirect
63. #11718716C22semidirect
64. #11718710C22semidirect
65. #11718705C22semidirect
66. #11718699C22semidirect
67. #11718694C22semidirect
68. #11718687C22semidirect
69. #11718682C22semidirect
70. #11718672C22semidirect
204. C2×Q8×C13#41semidirect
296. C2×#548D13semidirect
335. Q8×C13C2×#41semidirect
396. #548C2×D13semidirect
592. C2×C13#3308semidirect
617. C2×Q8#6129semidirect
706. C13C2×#3308semidirect
731. Q8C2×#6129semidirect
819. C2#13126827direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192602
#131268272
C2×#117187162
C2×#117187052
C2×#117186942
C2×#117186822
C2×#117187102
C2×#117186992
C2×#117187182
C2×#117188992
C2×#117188882
C2×#117186872
C2×#117186722
C2×#117188932
C22×#880752
C2×C13×#5482
C2×#330813