Finite Group Databasebeta

← C2×#13126723 #16739326

Subgroups — C2×#13126723 #16739326

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×#11719246C211yesmaximal, characteristic, complemented
2#13126723C2116yesmaximal, direct product factor
3C2×#11718717C211yesmaximal, characteristic, complemented
4C2×#11718706C211yesmaximal, characteristic, complemented
5C2×#11718694C211yesmaximal, characteristic, complemented
6C2×#11718683C211yesmaximal, characteristic, complemented
7C2×#11718712C211yesmaximal, characteristic, complemented
8C2×#11718702C211yesmaximal, characteristic, complemented
9C2×#11718715C211yesmaximal, characteristic, complemented
10C2×#11718900C211yesmaximal, characteristic, complemented
11C2×#11718889C211yesmaximal, characteristic, complemented
12C2×C4×#6107C211yesmaximal, characteristic, complemented
13C2×D4×#1055C211yesmaximal, characteristic, complemented
14C2×#11718894C211yesmaximal, characteristic, complemented
15C22×#88075C211yesmaximal, characteristic, complemented
16C2×C13×#548C211yesmaximal, characteristic
17C22×C13×#41C2211yescharacteristic
18C23×Q8×C13C2211yescharacteristic
19C13×#548—24no—
20C13×#548C2218yes—
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×#6107C2211yescharacteristic
31C22×#6107C2211yescharacteristic
32C2×#88189—21no—
33C22×#6105C2211yescharacteristic
34C2×#88180C2211yescharacteristic
35C22×C4⋊Dic13C2211yescharacteristic
36C2×#88178C2211yescharacteristic
37C2×#88178C2211yescharacteristic
38C23×#1055C2211yescharacteristic
39C23×#1055C2211yescharacteristic
40#11719246—24no—
41#11719246C2218yescomplemented
42C2×#88143—21no—
43C2×#88133—21no—
44C2×#88131—21no—
45C2×#88124C2211yescharacteristic
46C2×C4×Dic26C2211yescharacteristic
47#11718900C2218yescomplemented
48#11718894C2218yescomplemented
49#11718889C2218yescomplemented
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#11718717C2218yescomplemented
63#11718715C2218yescomplemented
64#11718712C2218yescomplemented
65#11718706C2218yescomplemented
66#11718702C2218yescomplemented
67#11718694C2218yescomplemented
68C4×#6107C2218yescomplemented
69#11718683C2218yescomplemented
70D4×#1055C2218yescomplemented
71C2×#88050C2211yescharacteristic
72C2×#88048C2211yescharacteristic
73C2×#88047C2211yescharacteristic
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
96C23×Dic13—21no—
97C22×Dic26C2311yescharacteristic
98C13×#124—28no—
99C13×#124—22no—
100C13×#124C2314yes—
101C13×C22⋊Q8—22no—
102C13×C22⋊Q8—28no—
103C13×C22⋊Q8C2314yes—
104C13×#121—28no—
105C13×#121—22no—
106C13×#121C2314yes—
107C4×Q8×C13—22no—
108C4×Q8×C13C2314yes—
109C4×D4×C13—28no—
110C4×D4×C13D414yes—
111C4×D4×C13C2314yes—
112C2×C13×C4⋊C4—21no—
113C2×C13×C4⋊C4—21no—
114C2×C13×C4⋊C4D411yescharacteristic
115C2×C13×C4⋊C4C2311yescharacteristic
116C2×C13×C22⋊C4—21no—
117C2×C13×C22⋊C4—21no—
118C2×C13×C22⋊C4—21no—
119C2×C13×C22⋊C4—21no—
120C2×C13×C22⋊C4D411yescharacteristic
121C2×C13×C22⋊C4D411yescharacteristic
122C2×C42×C13—21no—
123C2×C42×C13C2311yescharacteristic
124C2×C22⋊Dic13—21no—
125C2×C22⋊Dic13—21no—
126C2×C22⋊Dic13—21no—
127C2×#6107—24no—
128C2×#6107—42no—
129C2×#6107C2314yes—
130C2×#6107C2314yes—
131#88189—28no—
132C2×#6105—42no—
133C2×#6105C2314yes—
134#88180—22no—
135#88180C2314yes—
136C2×C4⋊Dic13—21no—
137C2×C4⋊Dic13—22no—
138C2×C4⋊Dic13C2311yescharacteristic
139C2×C4⋊Dic13C2311yescharacteristic
140C2×C4⋊Dic13C2311yescharacteristic
141C2×C4⋊Dic13C2314yes—
142#88178—22no—
143#88178—22no—
144#88178C2314yes—
145#88178C2314yes—
146C2×#6101—21no—
147C2×#6101—21no—
148C2×#6101—21no—
149C2×#6101—21no—
150C2×#6101—21no—
151C2×C4×Dic13—21no—
152C2×C4×Dic13—21no—
153C22×#1055—42no—
154C22×#1055—42no—
155C22×#1055C2311yescharacteristic
156C22×#1055C2311yescharacteristic
157C22×#1055C2311yescharacteristic
158C22×#1055C2311yescharacteristic
159C22×#1055C2314yes—
160C22×#1055C2314yes—
161#88143—28no—
162#88133—28no—
163#88131—28no—
164#88124—22no—
165#88124C2314yes—
166C4×Dic26—22no—
167C4×Dic26C2314yes—
168#88075C2314yes—
169#88075C2314yes—
170#88075C2314yes—
171#88075C2314yes—
172#88075C2314yes—
173#88075C2314yes—
174#88072C2314yes—
175#88072C2314yes—
176#88072C2314yes—
177C22⋊#1055C2314yes—
178C22⋊#1055C2314yes—
179#88050C2314yes—
180#88048C2314yes—
181#88047C2314yes—
182#88047C2314yes—
183C4⋊#1055C2314yes—
184C4×#1055C2314yes—
185C2×#3300—131nomaximal, Sylow
186C24×C13—21no—
187C24×C13C2×D411yescharacteristic
188C24×C13C2×D411yescharacteristic
189C13×#41—28no—
190C13×#41—44no—
191C13×#41—48no—
192C2×Q8×C13—21no—
193C2×Q8×C13—24no—
194C2×Q8×C13—21no—
195C2×Q8×C13—22no—
196C2×Q8×C13—28no—
197C2×Q8×C13—22no—
198C2×Q8×C13—22no—
199C2×Q8×C13—44no—
200C2×Q8×C13—44no—
201C2×Q8×C13—48no—
202C2×Q8×C13#4114yes—
203C2×Q8×C13C2412yes—
204C2×Q8×C13C2412yes—
205C2×D4×C13—24no—
206C2×D4×C13—24no—
207C2×D4×C13—24no—
208C2×D4×C13—21no—
209C2×D4×C13—22no—
210C2×D4×C13—22no—
211C2×D4×C13—44no—
212C2×D4×C13—44no—
213C2×D4×C13C2×D414yes—
214C2×D4×C13C2412yes—
215C22×C4×C13—21no—
216C22×C4×C13—22no—
217C22×C4×C13—22no—
218C22×C4×C13—22no—
219C22×C4×C13—22no—
220C22×C4×C13—21no—
221C22×C4×C13—21no—
222C22×C4×C13—24no—
223C22×C4×C13—24no—
224C22×C4×C13—44no—
225C22×C4×C13—44no—
226C22×C4×C13C2×D411yescharacteristic
227C22×C4×C13C2×D411yescharacteristic
228C22×C4×C13C2×D411yescharacteristic
229C22×C4×C13C2×D411yescharacteristic
230C22×C4×C13C2×D412yes—
231C22×C4×C13C2×D412yes—
232C22×C4×C13C2412yes—
233C22×C4×C13C2412yes—
234C22×C4×C13C2411yescharacteristic
235C22×Dic13—24no—
236C22×Dic13—21no—
237C22×Dic13—21no—
238C22×Dic13—21no—
239C22×Dic13—21no—
240C22×Dic13—44no—
241C2×Dic26—22no—
242C2×Dic26—22no—
243C2×Dic26—21no—
244C2×Dic26C2412yes—
245C13×C4⋊C4—24no—
246C13×C4⋊C4—24no—
247C13×C4⋊C4—21no—
248C13×C4⋊C4C2×D414yes—
249C13×C4⋊C4C2412yes—
250C13×C22⋊C4—24no—
251C13×C22⋊C4—24no—
252C13×C22⋊C4—24no—
253C13×C22⋊C4—24no—
254C13×C22⋊C4C2×D414yes—
255C13×C22⋊C4C2×D414yes—
256C42×C13—24no—
257C42×C13C2×D412yes—
258C42×C13C2412yes—
259C22⋊Dic13—24no—
260C22⋊Dic13—24no—
261C22⋊Dic13—24no—
262#6107—28no—
263#6107—44no—
264#6105—44no—
265C4⋊Dic13—21no—
266C4⋊Dic13—21no—
267C4⋊Dic13—21no—
268C4⋊Dic13—24no—
269C4⋊Dic13C2412yes—
270C4⋊Dic13C2412yes—
271C4⋊Dic13C2412yes—
272#6101—24no—
273#6101—24no—
274#6101—24no—
275#6101—24no—
276#6101—24no—
277C4×Dic13—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×#552—131no—
290C2×#548D1311yescharacteristic
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—22no—
311C23×C13—42no—
312C23×C13—42no—
313C23×C13—42no—
314C23×C13#13514yes—
315C23×C13C22×D412yes—
316C23×C13C22×D412yes—
317C23×C13C22×D411yescharacteristic
318Q8×C13—24no—
319Q8×C13—22no—
320Q8×C13—22no—
321Q8×C13—22no—
322Q8×C13—48no—
323Q8×C13—42no—
324Q8×C13C2×#4114yes—
325D4×C13—28no—
326D4×C13—22no—
327D4×C13—22no—
328D4×C13—48no—
329D4×C13—48no—
330D4×C13—42no—
331C2×C4×C13—22no—
332C2×C4×C13—22no—
333C2×C4×C13—24no—
334C2×C4×C13—22no—
335C2×C4×C13—22no—
336C2×C4×C13—22no—
337C2×C4×C13—24no—
338C2×C4×C13—24no—
339C2×C4×C13—22no—
340C2×C4×C13—22no—
341C2×C4×C13—22no—
342C2×C4×C13—22no—
343C2×C4×C13—22no—
344C2×C4×C13—22no—
345C2×C4×C13—48no—
346C2×C4×C13—48no—
347C2×C4×C13—42no—
348C2×C4×C13—42no—
349C2×C4×C13C22×D412yes—
350C2×C4×C13C22×D412yes—
351C2×C4×C13C22×D412yes—
352C2×C4×C13C22×D412yes—
353C2×C4×C13C22×D411yescharacteristic
354C2×C4×C13C2×#4112yes—
355C2×C4×C13H(5,𝔽2)12yes—
356C2×C4×C13C2511yescharacteristic
357C2×Dic13—22no—
358C2×Dic13—22no—
359C2×Dic13—22no—
360C2×Dic13—22no—
361C2×Dic13—42no—
362C2×Dic13—48no—
363C2×Dic13—42no—
364C2×Dic13—42no—
365C2×Dic13—42no—
366Dic26—22no—
367Dic26—22no—
368Dic26—42no—
369#1055—22no—
370#1055—22no—
371#1055—22no—
372#1055—22no—
373C22×#41C2×D1311yescharacteristic
374C23×Q8C2×D1311yescharacteristic
375C22×Q16—131no—
376C22×Q16—131no—
377C22×SD16—131no—
378C23×C8—131no—
379C23×C8—131no—
380#552—138no—
381#552—264no—
382#548—24no—
383#548C2×D1318yes—
384C2×#126—261no—
385C2×#125—131no—
386C2×#125—261no—
387C2×#124—21no—
388C2×#124C2×D1311yescharacteristic
389C2×#123—261no—
390C2×C22⋊Q8—21no—
391C2×C22⋊Q8—131no—
392C2×C22⋊Q8—131no—
393C2×C22⋊Q8C2×D1311yescharacteristic
394C2×#121—21no—
395C2×#121C2×D1311yescharacteristic
396C2×C4×Q8—131no—
397C2×C4×Q8C2×D1311yescharacteristic
398C2×C4×D4—21no—
399C2×C4×D4C2×D1311yescharacteristic
400C2×#117—131no—
401C2×#117—261no—
402C22×C4⋊C4—131no—
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—138no—
426C2×#103—131no—
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—42no—
441C22×C13—42no—
442C22×C13—42no—
443C22×C13—84no—
444C22×C13#54612yes—
445C22×C13C2×#13514yes—
446C22×C13C2×#13512yes—
447C22×C13#57812yes—
448C22×C13C23×D411yescharacteristic
449C4×C13—22no—
450C4×C13—22no—
451C4×C13—24no—
452C4×C13—22no—
453C4×C13—22no—
454C4×C13—42no—
455C4×C13—42no—
456C4×C13#54612yes—
457C4×C13C22×#4111yescharacteristic
458C4×C13C2×H(5,𝔽2)11yescharacteristic
459Dic13—42no—
460Dic13—42no—
461Dic13—42no—
462Dic13—42no—
463C2×#41—22no—
464C2×#41—24no—
465C2×#41—42no—
466C2×#41C22×D1314yes—
467C22×Q8—21no—
468C22×Q8—22no—
469C22×Q8—24no—
470C22×Q8—42no—
471C22×Q8—131no—
472C22×Q8C22×D1311yescharacteristic
473C22×Q8C22×D1314yes—
474C22×Q8C22×D1311yescharacteristic
475C22×D4—21no—
476C22×D4—21no—
477C22×D4C22⋊D1311yescharacteristic
478C22×D4C22×D1311yescharacteristic
479C23×C4—21no—
480C23×C4—21no—
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—268no—
499#125—134no—
500#125—268no—
501#125—262no—
502#124—28no—
503#124—22no—
504#124C22×D1314yes—
505#123—268no—
506C22⋊Q8—22no—
507C22⋊Q8—28no—
508C22⋊Q8—134no—
509C22⋊Q8—134no—
510C22⋊Q8—262no—
511C22⋊Q8—262no—
512C22⋊Q8C22×D1314yes—
513#121—28no—
514#121—22no—
515#121C22×D1314yes—
516C4×Q8—22no—
517C4×Q8—134no—
518C4×Q8—262no—
519C4×Q8C22×D1314yes—
520C4×D4—28no—
521C4×D4C22⋊D1314yes—
522C4×D4C22×D1314yes—
523#117—134no—
524#117—262no—
525#117—268no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—131no—
529C2×C4⋊C4—131no—
530C2×C4⋊C4—134no—
531C2×C4⋊C4—131no—
532C2×C4⋊C4—261no—
533C2×C4⋊C4—262no—
534C2×C4⋊C4—261no—
535C2×C4⋊C4—261no—
536C2×C4⋊C4—261no—
537C2×C4⋊C4—261no—
538C2×C4⋊C4—261no—
539C2×C4⋊C4C22⋊D1311yescharacteristic
540C2×C4⋊C4C22×D1311yescharacteristic
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
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—261no—
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—82no—
574C2×C13#330014yescomplemented
575C2×C13C2×#54611yescharacteristic
576C2×C13C22×#13511yescharacteristic
577C2×C13C2×#57811yescharacteristic
578C24—21no—
579C24C2×C22⋊D1311yescharacteristic
580C24C2×C22⋊D1311yescharacteristic
581#41—28no—
582#41—44no—
583#41—48no—
584C2×Q8—22no—
585C2×Q8—21no—
586C2×Q8—24no—
587C2×Q8—21no—
588C2×Q8—28no—
589C2×Q8—22no—
590C2×Q8—22no—
591C2×Q8—44no—
592C2×Q8—44no—
593C2×Q8—48no—
594C2×Q8—132no—
595C2×Q8—261no—
596C2×Q8—262no—
597C2×Q8—262no—
598C2×Q8#612914yes—
599C2×Q8C23×D1312yes—
600C2×Q8C23×D1312yes—
601C2×D4—24no—
602C2×D4—24no—
603C2×D4—24no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—21no—
607C2×D4—44no—
608C2×D4—44no—
609C2×D4C2×C22⋊D1314yes—
610C2×D4C23×D1312yes—
611C22×C4—21no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—24no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—24no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—264no—
623C22×C4—261no—
624C22×C4—261no—
625C22×C4—261no—
626C22×C4—261no—
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—24no—
651C4⋊C4—24no—
652C4⋊C4—21no—
653C4⋊C4—132no—
654C4⋊C4—132no—
655C4⋊C4—132no—
656C4⋊C4—261no—
657C4⋊C4—261no—
658C4⋊C4—264no—
659C4⋊C4—261no—
660C4⋊C4—264no—
661C4⋊C4—264no—
662C4⋊C4—264no—
663C4⋊C4—264no—
664C4⋊C4—264no—
665C4⋊C4C2×C22⋊D1314yes—
666C4⋊C4C23×D1312yes—
667C22⋊C4—24no—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—24no—
671C22⋊C4—264no—
672C22⋊C4—264no—
673C22⋊C4—264no—
674C22⋊C4C2×C22⋊D1314yes—
675C22⋊C4C2×C22⋊D1314yes—
676C42—24no—
677C42—264no—
678C42—264no—
679C42C2×C22⋊D1312yes—
680C42C23×D1312yes—
681C13C2×#330011yescharacteristic, complemented, Sylow
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23#8820414yes—
692C23C22×C22⋊D1312yes—
693C23C22×C22⋊D1312yes—
694C23C22×C22⋊D1311yescharacteristic
695Q8—24no—
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—48no—
700Q8—42no—
701Q8—262no—
702Q8—262no—
703Q8—522no—
704Q8C2×#612914yes—
705D4—28no—
706D4—22no—
707D4—22no—
708D4—48no—
709D4—48no—
710D4—42no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—48no—
726C2×C4—48no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—262no—
730C2×C4—262no—
731C2×C4—262no—
732C2×C4—262no—
733C2×C4—522no—
734C2×C4—528no—
735C2×C4—522no—
736C2×C4—522no—
737C2×C4—522no—
738C2×C4C2×#612912yes—
739C2×C4#8825112yes—
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—42no—
758C22—42no—
759C22—42no—
760C22—84no—
761C22#1171951112yes—
762C22C2×#8820414yes—
763C22C2×#8820412yes—
764C22#1171954312yes—
765C22C23×C22⋊D1311yescharacteristic
766C4—22no—
767C4—22no—
768C4—22no—
769C4—24no—
770C4—22no—
771C4—42no—
772C4—42no—
773C4—522no—
774C4—522no—
775C4—522no—
776C4—522no—
777C4#1171951112yes—
778C4C22×#612911yescharacteristic
779C4C2×#8825111yescharacteristic
780C2—24no—
781C2—42no—
782C2—82no—
783C2#1312672314yesdirect product factor
784C2C2×#1171951111yescharacteristic
785C2C22×#8820411yescharacteristic
786C2C2×#1171954311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
Fitting, prime radicalC2×C13×#548C2
socleC23×C13C22×D4
hypercenterC2×#548D13
hypocenterC13C2×#3300
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×#11719246C2semidirect
2. #13126723C2direct (N × H)
3. C2×#11718717C2semidirect
4. C2×#11718706C2semidirect
5. C2×#11718694C2semidirect
6. C2×#11718683C2semidirect
7. C2×#11718712C2semidirect
8. C2×#11718702C2semidirect
9. C2×#11718715C2semidirect
10. C2×#11718900C2semidirect
11. C2×#11718889C2semidirect
12. C2×C4×#6107C2semidirect
13. C2×D4×#1055C2semidirect
14. C2×#11718894C2semidirect
15. C22×#88075C2semidirect
41. #11719246C22semidirect
47. #11718900C22semidirect
48. #11718894C22semidirect
49. #11718889C22semidirect
56. C2×#88075C22semidirect
62. #11718717C22semidirect
63. #11718715C22semidirect
64. #11718712C22semidirect
65. #11718706C22semidirect
66. #11718702C22semidirect
67. #11718694C22semidirect
68. C4×#6107C22semidirect
69. #11718683C22semidirect
70. D4×#1055C22semidirect
574. C2×C13#3300semidirect
681. C13C2×#3300semidirect
783. C2#13126723direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117192462
#131267232
C2×#117187172
C2×#117187062
C2×#117186942
C2×#117186832
C2×#117187122
C2×#117187022
C2×#117187152
C2×#117189002
C2×#117188892
C2×C4×#61072
C2×D4×#10552
C2×#117188942
C22×#880752
C2×C13×#5482
C2×#330013