Finite Group Databasebeta

← C2×#13126717 #16739320

Subgroups — C2×#13126717 #16739320

Order 3328.

2146 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719257C211yesmaximal, characteristic
2#13126717C2116yesmaximal, direct product factor
3C2×#11718729C211yesmaximal, characteristic, complemented
4C2×#11718657C211yesmaximal, characteristic, complemented
5C2×#11718628C211yesmaximal, characteristic, complemented
6C2×#11718724C211yesmaximal, characteristic, complemented
7C2×#11718712C211yesmaximal, characteristic, complemented
8C2×#11718709C211yesmaximal, characteristic, complemented
9C2×#11718689C211yesmaximal, characteristic, complemented
10C2×#11718708C211yesmaximal, characteristic, complemented
11C2×#11718711C211yesmaximal, characteristic, complemented
12C2×C4×#6107C211yesmaximal, characteristic, complemented
13C2×D4×#1055C211yesmaximal, characteristic, complemented
14C2×#11718663C211yesmaximal, characteristic, complemented
15C22×#88050C211yesmaximal, characteristic, complemented
16C2×C13×#552C211yesmaximal, characteristic, complemented
17C22×#6127C2211yescharacteristic
18C23×Dic26C2211yescharacteristic
19C13×#552—24no—
20C13×#552C2218yescomplemented
21C2×C13×#126—21no—
22C2×C13×#125—21no—
23C2×C13×#125C2211yescharacteristic
24C2×C13×#123—21no—
25C2×C13×C22⋊Q8C2211yescharacteristic
26C2×C13×C22⋊Q8C2211yescharacteristic
27C2×C4×Q8×C13C2211yescharacteristic
28C2×C4×D4×C13C2211yescharacteristic
29C2×C13×#117—21no—
30C2×C13×#117C2211yescharacteristic
31C22×C13×C4⋊C4C2211yescharacteristic
32C22×#6107C2211yescharacteristic
33C22×#6107C2211yescharacteristic
34C22×#6106C2211yescharacteristic
35C2×#88193—21no—
36C2×#88184C2211yescharacteristic
37C2×#88178C2211yescharacteristic
38C23×#1055C2211yescharacteristic
39C23×#1055C2211yescharacteristic
40#11719257—24no—
41#11719257C2218yes—
42C2×#88150—21no—
43C2×#88139—21no—
44C2×#88135—21no—
45C2×#88129C2211yescharacteristic
46C2×C4×Dic26C2211yescharacteristic
47C2×#88075C2211yescharacteristic
48C2×C22⋊#1055C2211yescharacteristic
49C2×C22⋊#1055C2211yescharacteristic
50#11718729C2218yescomplemented
51#11718724C2218yescomplemented
52#11718712C2218yescomplemented
53#11718711C2218yescomplemented
54#11718709C2218yescomplemented
55#11718708C2218yescomplemented
56C4×#6107C2218yescomplemented
57#11718689C2218yescomplemented
58D4×#1055C2218yescomplemented
59#11718663C2218yescomplemented
60#11718657C2218yescomplemented
61C2×#88050C2211yescharacteristic
62C2×#88050C2211yescharacteristic
63C2×#88050C2211yescharacteristic
64C2×#88050C2211yescharacteristic
65C2×#88050C2211yescharacteristic
66C2×#88050C2211yescharacteristic
67C2×#88050C2218yescomplemented
68#11718628C2218yescomplemented
69C2×#88049C2211yescharacteristic
70C2×#88049C2211yescharacteristic
71C2×#88049C2211yescharacteristic
72C2×#88048C2211yescharacteristic
73C2×#88047C2211yescharacteristic
74C2×#88047C2211yescharacteristic
75C2×C4⋊#1055C2211yescharacteristic
76C2×C4×#1055C2211yescharacteristic
77C22×Q8×C13C2311yescharacteristic
78C22×D4×C13D411yescharacteristic
79C23×C4×C13—21no—
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C22×C22⋊D13—21no—
83C22×C22⋊D13—21no—
84C23×Dic13—21no—
85C2×#6127—22no—
86C2×#6127—24no—
87C2×#6127—42no—
88C2×#6127C2314yes—
89C22×D52C2311yescharacteristic
90C22×C4×D13—21no—
91C22×Dic26—24no—
92C22×Dic26—21no—
93C22×Dic26—22no—
94C22×Dic26—42no—
95C22×Dic26C2311yescharacteristic
96C22×Dic26C2314yes—
97C22×Dic26C2311yescharacteristic
98C13×#126—28no—
99C13×#125—28no—
100C13×#125—22no—
101C13×#125C2314yes—
102C13×#123—28no—
103C13×C22⋊Q8—22no—
104C13×C22⋊Q8—22no—
105C13×C22⋊Q8C2314yes—
106C13×C22⋊Q8C2314yes—
107C4×Q8×C13—22no—
108C4×Q8×C13C2314yes—
109C4×D4×C13D414yes—
110C4×D4×C13C2314yes—
111C13×#117—22no—
112C13×#117—28no—
113C13×#117C2314yes—
114C2×C13×C4⋊C4—21no—
115C2×C13×C4⋊C4—22no—
116C2×C13×C4⋊C4—21no—
117C2×C13×C4⋊C4—21no—
118C2×C13×C4⋊C4—21no—
119C2×C13×C4⋊C4—21no—
120C2×C13×C4⋊C4—21no—
121C2×C13×C4⋊C4D411yescharacteristic
122C2×C13×C4⋊C4C2311yescharacteristic
123C2×C13×C4⋊C4C2311yescharacteristic
124C2×C13×C4⋊C4C2314yes—
125C2×C13×C4⋊C4C2311yescharacteristic
126C2×C13×C22⋊C4—21no—
127C2×C13×C22⋊C4—21no—
128C2×C13×C22⋊C4—21no—
129C2×C13×C22⋊C4D411yescharacteristic
130C2×C13×C22⋊C4D411yescharacteristic
131C2×C42×C13—21no—
132C2×C42×C13—21no—
133C2×C42×C13C2311yescharacteristic
134C2×C22⋊Dic13—21no—
135C2×#6107—24no—
136C2×#6107—42no—
137C2×#6107C2314yes—
138C2×#6107C2314yes—
139C2×#6106—42no—
140C2×#6106C2314yes—
141#88193—28no—
142#88184—22no—
143#88184C2314yes—
144C2×#6103—21no—
145C2×#6103—21no—
146C2×#6103—21no—
147C2×C4⋊Dic13C2311yescharacteristic
148#88178—22no—
149#88178C2314yes—
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#88150—28no—
162#88139—28no—
163#88135—28no—
164#88129—22no—
165#88129C2314yes—
166C4×Dic26—22no—
167C4×Dic26C2314yes—
168#88075C2314yes—
169C22⋊#1055C2314yes—
170C22⋊#1055C2314yes—
171#88050C2314yes—
172#88050C2314yes—
173#88050C2314yes—
174#88050C2314yes—
175#88050C2314yes—
176#88050C2314yes—
177#88049C2314yes—
178#88049C2314yes—
179#88049C2314yes—
180#88048C2314yes—
181#88047C2314yes—
182#88047C2314yes—
183C4⋊#1055C2314yes—
184C4×#1055C2314yes—
185C2×#3300—131nomaximal, Sylow
186C24×C13C2×D411yescharacteristic
187C24×C13C2×D411yescharacteristic
188C23×D13—21no—
189C2×Q8×C13—21no—
190C2×Q8×C13—22no—
191C2×Q8×C13—22no—
192C2×Q8×C13C2412yes—
193C2×D4×C13—24no—
194C2×D4×C13C2×D414yes—
195C22×C4×C13—22no—
196C22×C4×C13—22no—
197C22×C4×C13—22no—
198C22×C4×C13—22no—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13—24no—
204C22×C4×C13—44no—
205C22×C4×C13C2×D411yescharacteristic
206C22×C4×C13C2×D411yescharacteristic
207C22×C4×C13C2×D411yescharacteristic
208C22×C4×C13C2×D412yes—
209C22×C4×C13C2×D411yescharacteristic
210C22×C4×C13C2×D412yes—
211C22×C4×C13C2412yes—
212C22×C4×C13C2412yes—
213C22×C4×C13C2411yescharacteristic
214C2×C22⋊D13—24no—
215C2×C22⋊D13—24no—
216C2×C22⋊D13—44no—
217C2×C22⋊D13—44no—
218C22×Dic13—21no—
219C22×Dic13—24no—
220C22×Dic13—21no—
221C22×Dic13—21no—
222C22×Dic13—44no—
223#6127—28no—
224#6127—44no—
225#6127—48no—
226C2×D52—22no—
227C2×D52—22no—
228C2×D52—21no—
229C2×D52C2412yes—
230C2×C4×D13—24no—
231C2×C4×D13—44no—
232C2×Dic26—21no—
233C2×Dic26—22no—
234C2×Dic26—22no—
235C2×Dic26—22no—
236C2×Dic26—28no—
237C2×Dic26—21no—
238C2×Dic26—24no—
239C2×Dic26—44no—
240C2×Dic26—48no—
241C2×Dic26—44no—
242C2×Dic26#4114yes—
243C2×Dic26C2412yes—
244C2×Dic26C2412yes—
245C13×C4⋊C4—21no—
246C13×C4⋊C4—21no—
247C13×C4⋊C4—24no—
248C13×C4⋊C4—24no—
249C13×C4⋊C4—24no—
250C13×C4⋊C4—24no—
251C13×C4⋊C4—24no—
252C13×C4⋊C4—24no—
253C13×C4⋊C4—21no—
254C13×C4⋊C4C2×D414yes—
255C13×C4⋊C4C2412yes—
256C13×C4⋊C4C2412yes—
257C13×C4⋊C4C2412yes—
258C13×C22⋊C4—24no—
259C13×C22⋊C4—24no—
260C13×C22⋊C4—24no—
261C13×C22⋊C4C2×D414yes—
262C13×C22⋊C4C2×D414yes—
263C42×C13—24no—
264C42×C13—24no—
265C42×C13C2×D412yes—
266C42×C13C2412yes—
267C22⋊Dic13—24no—
268#6107—28no—
269#6107—44no—
270#6106—44no—
271#6103—24no—
272#6103—24no—
273#6103—24no—
274C4⋊Dic13—21no—
275C4⋊Dic13C2412yes—
276#6101—24no—
277#6101—24no—
278C4×Dic13—24no—
279C2×#1055—22no—
280C2×#1055—22no—
281C2×#1055—22no—
282C2×#1055—22no—
283C2×#1055—44no—
284C2×#1055—44no—
285C2×#1055C2412yes—
286C2×#1055C2412yes—
287C2×#1055C2412yes—
288C2×#1055C2412yes—
289C2×#552D1311yescharacteristic, complemented
290C2×#548—131no—
291#3300—1316no—
292C2×#488—131no—
293C2×#485—131no—
294C2×#480—131no—
295C2×#479—131no—
296C2×#467—131no—
297C2×#465—131no—
298C2×#464—131no—
299C2×#452—131no—
300C2×#451—131no—
301C2×C4×Q16—131no—
302C2×C8×D4—131no—
303C2×#416—131no—
304C22×#103—131no—
305C23×C13—22no—
306C23×C13—22no—
307C23×C13—22no—
308C23×C13—22no—
309C23×C13—22no—
310C23×C13#13514yes—
311C23×C13C22×D412yes—
312C23×C13C22×D412yes—
313C23×C13C22×D411yescharacteristic
314C22×D13—22no—
315C22×D13—42no—
316C22×D13—42no—
317C22×D13—42no—
318Q8×C13—22no—
319Q8×C13—22no—
320Q8×C13—42no—
321D4×C13—28no—
322C2×C4×C13—22no—
323C2×C4×C13—22no—
324C2×C4×C13—22no—
325C2×C4×C13—22no—
326C2×C4×C13—24no—
327C2×C4×C13—24no—
328C2×C4×C13—22no—
329C2×C4×C13—22no—
330C2×C4×C13—22no—
331C2×C4×C13—22no—
332C2×C4×C13—22no—
333C2×C4×C13—22no—
334C2×C4×C13—22no—
335C2×C4×C13—22no—
336C2×C4×C13—42no—
337C2×C4×C13—48no—
338C2×C4×C13—42no—
339C2×C4×C13—42no—
340C2×C4×C13—42no—
341C2×C4×C13C22×D412yes—
342C2×C4×C13C22×D412yes—
343C2×C4×C13C22×D412yes—
344C2×C4×C13C22×D412yes—
345C2×C4×C13C22×D411yescharacteristic
346C2×C4×C13C2×#4112yes—
347C2×C4×C13H(5,𝔽2)12yes—
348C2×C4×C13C2511yescharacteristic
349C22⋊D13—48no—
350C22⋊D13—48no—
351C2×Dic13—24no—
352C2×Dic13—22no—
353C2×Dic13—22no—
354C2×Dic13—22no—
355C2×Dic13—48no—
356C2×Dic13—42no—
357C2×Dic13—42no—
358D52—22no—
359D52—22no—
360D52—42no—
361C4×D13—48no—
362Dic26—24no—
363Dic26—22no—
364Dic26—22no—
365Dic26—22no—
366Dic26—48no—
367Dic26—42no—
368Dic26C2×#4114yes—
369#1055—22no—
370#1055—22no—
371#1055—22no—
372#1055—22no—
373C22×#41—131no—
374C23×Q8—131no—
375C22×Q16—131no—
376C22×Q16—131no—
377C22×SD16—131no—
378C23×C8—131no—
379C23×C8—131no—
380#552—24no—
381#552C2×D1318yescomplemented
382#548—138no—
383#548—264no—
384C2×#126—21no—
385C2×#125—21no—
386C2×#125C2×D1311yescharacteristic
387C2×#124—131no—
388C2×#124—261no—
389C2×#123—21no—
390C2×C22⋊Q8—131no—
391C2×C22⋊Q8—261no—
392C2×C22⋊Q8C2×D1311yescharacteristic
393C2×C22⋊Q8C2×D1311yescharacteristic
394C2×#121—131no—
395C2×#121—261no—
396C2×C4×Q8—131no—
397C2×C4×Q8C2×D1311yescharacteristic
398C2×C4×D4—261no—
399C2×C4×D4C2×D1311yescharacteristic
400C2×#117—21no—
401C2×#117C2×D1311yescharacteristic
402C22×C4⋊C4C2×D1311yescharacteristic
403#488—138no—
404#485—138no—
405#480—138no—
406#479—138no—
407#467—138no—
408#465—138no—
409#464—138no—
410#452—138no—
411#451—138no—
412C4×Q16—138no—
413C8×D4—138no—
414C2×#107—131no—
415C2×#107—131no—
416C2×#106—131no—
417C2×C4⋊C8—131no—
418#416—138no—
419C2×#103—131no—
420C2×#103—131no—
421C2×#103—131no—
422C2×#103—131no—
423C2×#103—131no—
424C2×#103—131no—
425C2×#103—131no—
426C2×#103—138no—
427C2×#102—131no—
428C2×#102—131no—
429C2×#102—131no—
430C2×C22⋊C8—131no—
431C2×C22⋊C8—131no—
432C2×C4×C8—131no—
433C22×C13—22no—
434C22×C13—28no—
435C22×C13—22no—
436C22×C13—22no—
437C22×C13—22no—
438C22×C13—22no—
439C22×C13—44no—
440C22×C13#54612yes—
441C22×C13C2×#13514yes—
442C22×C13C2×#13512yes—
443C22×C13#57812yes—
444C22×C13C23×D411yescharacteristic
445C2×D13—42no—
446C2×D13—42no—
447C2×D13—42no—
448C2×D13—84no—
449C4×C13—22no—
450C4×C13—22no—
451C4×C13—22no—
452C4×C13—22no—
453C4×C13—42no—
454C4×C13—42no—
455C4×C13—42no—
456C4×C13—42no—
457C4×C13#54612yes—
458C4×C13C22×#4111yescharacteristic
459C4×C13C2×H(5,𝔽2)11yescharacteristic
460Dic13—24no—
461Dic13—42no—
462Dic13—42no—
463C2×#41—134no—
464C2×#41—264no—
465C2×#41—262no—
466C2×#41—522no—
467C22×Q8—131no—
468C22×Q8—131no—
469C22×Q8—134no—
470C22×Q8—264no—
471C22×Q8—261no—
472C22×Q8—262no—
473C22×Q8—522no—
474C22×Q8C22×D1311yescharacteristic
475C22×D4—131no—
476C22×D4—261no—
477C22×D4—261no—
478C22×D4C22⋊D1311yescharacteristic
479C23×C4—21no—
480C23×C4—261no—
481C23×C4—261no—
482C23×C4C22×D1311yescharacteristic
483C23×C4C22×D1311yescharacteristic
484C2×Q16—134no—
485C2×Q16—134no—
486C2×Q16—264no—
487C2×Q16—522no—
488C2×SD16—134no—
489C2×SD16—522no—
490C22×C8—131no—
491C22×C8—131no—
492C22×C8—131no—
493C22×C8—131no—
494C22×C8—134no—
495C22×C8—134no—
496C22×C8—522no—
497C22×C8—522no—
498#126—28no—
499#125—28no—
500#125—22no—
501#125C22×D1314yes—
502#124—134no—
503#124—268no—
504#124—262no—
505#123—28no—
506C22⋊Q8—22no—
507C22⋊Q8—22no—
508C22⋊Q8—134no—
509C22⋊Q8—262no—
510C22⋊Q8—268no—
511C22⋊Q8C22×D1314yes—
512C22⋊Q8C22×D1314yes—
513#121—134no—
514#121—268no—
515#121—262no—
516C4×Q8—22no—
517C4×Q8—134no—
518C4×Q8—262no—
519C4×Q8C22×D1314yes—
520C4×D4—268no—
521C4×D4C22⋊D1314yes—
522C4×D4C22×D1314yes—
523#117—22no—
524#117—28no—
525#117C22×D1314yes—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—22no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—131no—
534C2×C4⋊C4—261no—
535C2×C4⋊C4—261no—
536C2×C4⋊C4C22⋊D1311yescharacteristic
537C2×C4⋊C4C22×D1311yescharacteristic
538C2×C4⋊C4C22×D1311yescharacteristic
539C2×C4⋊C4C22×D1314yes—
540C2×C4⋊C4C22×D1311yescharacteristic
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—261no—
545C2×C22⋊C4—261no—
546C2×C22⋊C4—261no—
547C2×C22⋊C4—261no—
548C2×C22⋊C4C22⋊D1311yescharacteristic
549C2×C22⋊C4C22⋊D1311yescharacteristic
550C2×C42—21no—
551C2×C42—21no—
552C2×C42—261no—
553C2×C42C22×D1311yescharacteristic
554#107—134no—
555#107—134no—
556#106—134no—
557C4⋊C8—134no—
558#103—134no—
559#103—134no—
560#103—134no—
561#103—134no—
562#103—134no—
563#103—134no—
564#103—134no—
565#102—134no—
566#102—134no—
567#102—134no—
568C22⋊C8—134no—
569C22⋊C8—134no—
570C4×C8—134no—
571C2×C13—24no—
572C2×C13—42no—
573C2×C13#330014yescomplemented
574C2×C13C2×#54611yescharacteristic
575C2×C13C22×#13511yescharacteristic
576C2×C13C2×#57811yescharacteristic
577D13—82no—
578C24—261no—
579C24C2×C22⋊D1311yescharacteristic
580C24C2×C22⋊D1311yescharacteristic
581#41—268no—
582#41—524no—
583#41—528no—
584C2×Q8—21no—
585C2×Q8—22no—
586C2×Q8—22no—
587C2×Q8—134no—
588C2×Q8—132no—
589C2×Q8—132no—
590C2×Q8—268no—
591C2×Q8—262no—
592C2×Q8—261no—
593C2×Q8—264no—
594C2×Q8—261no—
595C2×Q8—262no—
596C2×Q8—262no—
597C2×Q8—524no—
598C2×Q8—524no—
599C2×Q8—528no—
600C2×Q8C23×D1312yes—
601C2×D4—24no—
602C2×D4—132no—
603C2×D4—264no—
604C2×D4—264no—
605C2×D4—262no—
606C2×D4—262no—
607C2×D4—261no—
608C2×D4—524no—
609C2×D4—524no—
610C2×D4C2×C22⋊D1314yes—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—24no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—44no—
621C22×C4—261no—
622C22×C4—264no—
623C22×C4—261no—
624C22×C4—261no—
625C22×C4—264no—
626C22×C4—524no—
627C22×C4—524no—
628C22×C4C2×C22⋊D1312yes—
629C22×C4C2×C22⋊D1312yes—
630C22×C4C2×C22⋊D1311yescharacteristic
631C22×C4C2×C22⋊D1311yescharacteristic
632C22×C4C2×C22⋊D1311yescharacteristic
633C22×C4C2×C22⋊D1311yescharacteristic
634C22×C4C23×D1312yes—
635C22×C4C23×D1312yes—
636C22×C4C23×D1311yescharacteristic
637Q16—268no—
638Q16—524no—
639SD16—524no—
640C2×C8—132no—
641C2×C8—132no—
642C2×C8—132no—
643C2×C8—132no—
644C2×C8—262no—
645C2×C8—262no—
646C2×C8—262no—
647C2×C8—262no—
648C2×C8—524no—
649C2×C8—524no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—24no—
653C4⋊C4—24no—
654C4⋊C4—24no—
655C4⋊C4—24no—
656C4⋊C4—24no—
657C4⋊C4—24no—
658C4⋊C4—21no—
659C4⋊C4—132no—
660C4⋊C4—261no—
661C4⋊C4—264no—
662C4⋊C4—264no—
663C4⋊C4C2×C22⋊D1314yes—
664C4⋊C4C23×D1312yes—
665C4⋊C4C23×D1312yes—
666C4⋊C4C23×D1312yes—
667C22⋊C4—24no—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—264no—
671C22⋊C4—264no—
672C22⋊C4—264no—
673C22⋊C4—264no—
674C22⋊C4C2×C22⋊D1314yes—
675C22⋊C4C2×C22⋊D1314yes—
676C42—24no—
677C42—24no—
678C42—264no—
679C42C2×C22⋊D1312yes—
680C42C23×D1312yes—
681C13C2×#330011yescharacteristic, complemented, Sylow
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—262no—
688C23—522no—
689C23—522no—
690C23—522no—
691C23#8820414yes—
692C23C22×C22⋊D1312yes—
693C23C22×C22⋊D1312yes—
694C23C22×C22⋊D1311yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—42no—
698Q8—134no—
699Q8—264no—
700Q8—262no—
701Q8—262no—
702Q8—262no—
703Q8—528no—
704Q8—522no—
705D4—28no—
706D4—262no—
707D4—262no—
708D4—528no—
709D4—528no—
710D4—522no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—48no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—264no—
731C2×C4—262no—
732C2×C4—262no—
733C2×C4—262no—
734C2×C4—528no—
735C2×C4—528no—
736C2×C4—522no—
737C2×C4—522no—
738C2×C4#41×D1312yes—
739C2×C4#8825612yes—
740C2×C4C22×C22⋊D1312yes—
741C2×C4C22×C22⋊D1312yes—
742C2×C4C22×C22⋊D1312yes—
743C2×C4C22×C22⋊D1312yes—
744C2×C4C22×C22⋊D1311yescharacteristic
745C2×C4C24×D1311yescharacteristic
746C8—262no—
747C8—262no—
748C8—262no—
749C8—262no—
750C22—28no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—44no—
757C22—522no—
758C22—522no—
759C22—522no—
760C22—1044no—
761C22C2×#8820414yes—
762C22C2×#8820412yes—
763C22#1171953412yes—
764C22#1171954312yes—
765C22C23×C22⋊D1311yescharacteristic
766C4—22no—
767C4—22no—
768C4—22no—
769C4—22no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—42no—
774C4—264no—
775C4—522no—
776C4—522no—
777C4#1171953412yes—
778C4C2×#41×D1311yescharacteristic
779C4C2×#8825611yescharacteristic
780C2—24no—
781C2—42no—
782C2—1042no—
783C2#1312671714yesdirect product factor
784C2C2×#1171953411yescharacteristic
785C2C22×#8820411yescharacteristic
786C2C2×#1171954311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#552C2
socleC23×C13C22×D4
prime radicalC2×#11719257C2
hypercenterC2×#552D13
hypocenterC13C2×#3300
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. #13126717C2direct (N × H)
3. C2×#11718729C2semidirect
4. C2×#11718657C2semidirect
5. C2×#11718628C2semidirect
6. C2×#11718724C2semidirect
7. C2×#11718712C2semidirect
8. C2×#11718709C2semidirect
9. C2×#11718689C2semidirect
10. C2×#11718708C2semidirect
11. C2×#11718711C2semidirect
12. C2×C4×#6107C2semidirect
13. C2×D4×#1055C2semidirect
14. C2×#11718663C2semidirect
15. C22×#88050C2semidirect
16. C2×C13×#552C2semidirect
20. C13×#552C22semidirect
50. #11718729C22semidirect
51. #11718724C22semidirect
52. #11718712C22semidirect
53. #11718711C22semidirect
54. #11718709C22semidirect
55. #11718708C22semidirect
56. C4×#6107C22semidirect
57. #11718689C22semidirect
58. D4×#1055C22semidirect
59. #11718663C22semidirect
60. #11718657C22semidirect
67. C2×#88050C22semidirect
68. #11718628C22semidirect
289. C2×#552D13semidirect
381. #552C2×D13semidirect
573. C2×C13#3300semidirect
681. C13C2×#3300semidirect
783. C2#13126717direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192572
#131267172
C2×#117187292
C2×#117186572
C2×#117186282
C2×#117187242
C2×#117187122
C2×#117187092
C2×#117186892
C2×#117187082
C2×#117187112
C2×C4×#61072
C2×D4×#10552
C2×#117186632
C22×#880502
C2×C13×#5522
C2×#330013