Finite Group Databasebeta

← C2×#13124747 #16730684

Subgroups — C2×#13124747 #16730684

Order 3328.

2378 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719533C211yesmaximal, characteristic
2C2×D13×#117C211yesmaximal, characteristic, complemented
3#13124747C2116yesmaximal, direct product factor
4C2×#11718470C211yesmaximal, characteristic, complemented
5C2×#11718438C211yesmaximal, characteristic, complemented
6C2×#11718475C211yesmaximal, characteristic, complemented
7C2×#11718476C211yesmaximal, characteristic, complemented
8C2×#11718440C211yesmaximal, characteristic, complemented
9C2×#11718445C211yesmaximal, characteristic, complemented
10C2×#11718466C211yesmaximal, characteristic, complemented
11C2×#11718435C211yesmaximal, characteristic, complemented
12C2×#11718767C211yesmaximal, characteristic, complemented
13C2×#11718659C211yesmaximal, characteristic, complemented
14C2×#11718894C211yesmaximal, characteristic, complemented
15C22×#88060C211yesmaximal, characteristic, complemented
16C2×C13×#416C211yesmaximal, characteristic, complemented
17C22×C13×#41C2211yescharacteristic
18C23×C4×D13C2211yescharacteristic
19C23×C8×C13C2211yescharacteristic
20C2×C13×#117C2211yescharacteristic
21#11719533—24no—
22#11719533C2218yes—
23C2×#88200C2211yescharacteristic
24C2×#88200C2211yescharacteristic
25C2×#88192C2211yescharacteristic
26C2×#88192C2211yescharacteristic
27C2×#88191—21no—
28C2×#88189—21no—
29C2×C4×C22⋊D13—21no—
30C2×C4×C22⋊D13—21no—
31C2×#88180C2211yescharacteristic
32C2×#88180C2211yescharacteristic
33C23×#1055C2211yescharacteristic
34D13×#117—24no—
35D13×#117C2218yescomplemented
36C2×#88146C2211yescharacteristic
37C2×#88146C2211yescharacteristic
38C2×C4⋊C4×D13C2211yescharacteristic
39C2×C4⋊C4×D13C2211yescharacteristic
40C2×C22⋊C4×D13—21no—
41C2×#88131—21no—
42C2×#88126—21no—
43C2×C42×D13—21no—
44C13×#416C2218yescomplemented
45C2×C13×#103C2211yescharacteristic, complemented
46C2×C13×#103C2211yescharacteristic, complemented
47C2×C13×#102C2211yescharacteristic, complemented
48C2×C13×#102C2211yescharacteristic, complemented
49#11718894C2218yescomplemented
50C2×#88075C2211yescharacteristic, complemented
51C2×#88075C2211yescharacteristic, complemented
52C2×#88072C2211yescharacteristic, complemented
53C2×#88072C2211yescharacteristic, complemented
54C2×#88060C2211yescharacteristic
55C2×#88060C2211yescharacteristic
56C2×#88060C2211yescharacteristic
57C2×#88060C2211yescharacteristic
58C2×#88060C2218yescomplemented
59#11718767C2218yescomplemented
60C2×#88058C2211yescharacteristic, complemented
61C2×#88058C2211yescharacteristic, complemented
62C2×#88057C2211yescharacteristic, complemented
63C2×#88057C2211yescharacteristic, complemented
64#11718659C2218yescomplemented
65C2×#88048C2211yescharacteristic, complemented
66C2×#88048C2211yescharacteristic, complemented
67C2×#88047C2211yescharacteristic, complemented
68C2×#88047C2211yescharacteristic, complemented
69#11718476C2218yescomplemented
70#11718475C2218yescomplemented
71#11718470C2218yescomplemented
72#11718466C2218yescomplemented
73#11718445C2218yescomplemented
74#11718440C2218yescomplemented
75#11718438C2218yescomplemented
76#11718435C2218yescomplemented
77C24×D13D411yescharacteristic
78C2×C13×#41—22no—
79C2×C13×#41—24no—
80C2×C13×#41—24no—
81C2×C13×#41C2314yes—
82C22×Q8×C13C2311yescharacteristic
83C22×D4×C13—21no—
84C22×D4×C13C2311yescharacteristic
85C23×C4×C13—21no—
86C23×C4×C13C2311yescharacteristic
87C22×C22⋊D13—21no—
88C22×C22⋊D13—21no—
89C23×Dic13D411yescharacteristic
90C22×C4×D13—24no—
91C22×C4×D13—24no—
92C22×C4×D13—21no—
93C22×C4×D13—21no—
94C22×C4×D13D411yescharacteristic
95C22×C4×D13D411yescharacteristic
96C22×C4×D13D414yes—
97C22×C4×D13C2311yescharacteristic
98C22×C4×D13C2311yescharacteristic
99C22×C4×D13C2314yes—
100C22×C8×C13—24no—
101C22×C8×C13C2311yescharacteristic
102C22×C8×C13C2311yescharacteristic
103C22×C8×C13C2314yes—
104C13×#117—22no—
105C13×#117C2314yes—
106C2×C13×C4⋊C4C2311yescharacteristic
107C2×C13×C4⋊C4C2311yescharacteristic
108C2×C13×C22⋊C4—21no—
109C2×C42×C13—21no—
110C2×C22⋊Dic13—21no—
111C2×C22⋊Dic13—21no—
112C2×C22⋊Dic13—21no—
113C2×C22⋊Dic13—21no—
114#88200—22no—
115#88200—22no—
116#88200C2314yes—
117#88200C2314yes—
118#88192—22no—
119#88192—22no—
120#88192C2314yes—
121#88192C2314yes—
122#88191—28no—
123#88189—28no—
124C4×C22⋊D13—28no—
125C4×C22⋊D13—28no—
126C2×#6103—21no—
127C2×#6103—21no—
128C2×#6103—21no—
129C2×#6103—21no—
130#88180—22no—
131#88180—22no—
132#88180C2314yes—
133#88180C2314yes—
134C2×C4⋊Dic13C2311yescharacteristic
135C2×C4⋊Dic13C2311yescharacteristic
136C2×C4⋊Dic13C2311yescharacteristic
137C2×C4⋊Dic13C2311yescharacteristic
138C2×#6101—21no—
139C2×#6101—21no—
140C2×#6101—21no—
141C2×#6101—21no—
142C2×C4×Dic13—21no—
143C2×C4×Dic13—21no—
144C2×C4×Dic13—21no—
145C2×C4×Dic13—21no—
146C22×#1055—24no—
147C22×#1055C2314yes—
148C22×#1055C2311yescharacteristic
149C22×#1055C2311yescharacteristic
150#88146—22no—
151#88146—22no—
152#88146C2314yes—
153#88146C2314yes—
154C4⋊C4×D13—22no—
155C4⋊C4×D13—22no—
156C4⋊C4×D13C2314yes—
157C4⋊C4×D13C2314yes—
158C22⋊C4×D13—28no—
159#88131—28no—
160#88126—28no—
161C42×D13—28no—
162C13×#103C2314yescomplemented
163C13×#103C2314yescomplemented
164C13×#102C2314yescomplemented
165C13×#102C2314yescomplemented
166#88075C2314yescomplemented
167#88075C2314yescomplemented
168#88072C2314yescomplemented
169#88072C2314yescomplemented
170#88060C2314yes—
171#88060C2314yes—
172#88060C2314yes—
173#88060C2314yes—
174#88058C2314yescomplemented
175#88058C2314yescomplemented
176#88057C2314yescomplemented
177#88057C2314yescomplemented
178#88048C2314yescomplemented
179#88048C2314yescomplemented
180#88047C2314yescomplemented
181#88047C2314yescomplemented
182C2×#3091—131nomaximal, Sylow
183C24×C13—21no—
184C24×C13C2×D411yescharacteristic
185C23×D13—24no—
186C23×D13—24no—
187C23×D13—42no—
188C23×D13C2×D411yescharacteristic
189C23×D13C2×D414yes—
190C23×D13C2×D411yescharacteristic
191C13×#41—28no—
192C13×#41—28no—
193C13×#41—48no—
194C2×Q8×C13—21no—
195C2×Q8×C13—22no—
196C2×Q8×C13—22no—
197C2×Q8×C13C2412yes—
198C2×D4×C13—24no—
199C2×D4×C13—21no—
200C2×D4×C13—22no—
201C2×D4×C13—22no—
202C2×D4×C13—44no—
203C2×D4×C13C2412yes—
204C22×C4×C13—21no—
205C22×C4×C13—21no—
206C22×C4×C13—21no—
207C22×C4×C13—24no—
208C22×C4×C13—44no—
209C22×C4×C13C2×D412yes—
210C22×C4×C13C2×D411yescharacteristic
211C22×C4×C13#4114yes—
212C22×C4×C13#4114yes—
213C22×C4×C13C2411yescharacteristic
214C22×C4×C13C2412yes—
215C2×C22⋊D13—24no—
216C2×C22⋊D13—24no—
217C2×C22⋊D13—44no—
218C2×C22⋊D13—44no—
219C22×Dic13—24no—
220C22×Dic13—21no—
221C22×Dic13—21no—
222C22×Dic13—21no—
223C22×Dic13—21no—
224C22×Dic13C2×D414yes—
225C22×Dic13C2×D411yescharacteristic
226C22×Dic13C2×D411yescharacteristic
227C2×C4×D13—24no—
228C2×C4×D13—24no—
229C2×C4×D13—216no—
230C2×C4×D13—22no—
231C2×C4×D13—22no—
232C2×C4×D13—28no—
233C2×C4×D13—22no—
234C2×C4×D13—22no—
235C2×C4×D13—28no—
236C2×C4×D13—24no—
237C2×C4×D13—24no—
238C2×C4×D13—44no—
239C2×C4×D13—44no—
240C2×C4×D13C2×D414yes—
241C2×C4×D13C2×D414yes—
242C2×C4×D13C2×D412yes—
243C2×C4×D13C2×D412yes—
244C2×C4×D13C2412yes—
245C2×C4×D13C2412yes—
246C2×C8×C13—22no—
247C2×C8×C13—22no—
248C2×C8×C13—28no—
249C2×C8×C13C2412yes—
250C2×C8×C13C2412yes—
251C13×C4⋊C4—21no—
252C13×C4⋊C4—21no—
253C13×C4⋊C4C2412yes—
254C13×C4⋊C4C2412yes—
255C13×C22⋊C4—24no—
256C42×C13—24no—
257C22⋊Dic13—24no—
258C22⋊Dic13—24no—
259C22⋊Dic13—24no—
260C22⋊Dic13—24no—
261#6103—24no—
262#6103—24no—
263#6103—24no—
264#6103—24no—
265C4⋊Dic13—21no—
266C4⋊Dic13—21no—
267C4⋊Dic13—21no—
268C4⋊Dic13—21no—
269C4⋊Dic13C2412yes—
270C4⋊Dic13C2412yes—
271C4⋊Dic13C2412yes—
272C4⋊Dic13C2412yes—
273#6101—24no—
274#6101—24no—
275#6101—24no—
276#6101—24no—
277C4×Dic13—24no—
278C4×Dic13—24no—
279C4×Dic13—24no—
280C4×Dic13—24no—
281C2×#1055—22no—
282C2×#1055—22no—
283C2×#1055—28no—
284C2×#1055C2412yes—
285C2×#1055C2412yes—
286C2×#525—131no—
287C22×#117—131no—
288#3091—1316no—
289C2×#484—131no—
290C2×#481—131no—
291C2×#485—131no—
292C2×#485—131no—
293C2×#482—131no—
294C2×#482—131no—
295C2×#483—131no—
296C2×#480—131no—
297C2×#427—131no—
298C2×#427—131no—
299C2×#416—131no—
300C2×#416D1311yescharacteristic, complemented
301C22×C22⋊C8—131no—
302C23×C13—22no—
303C23×C13—22no—
304C23×C13—22no—
305C23×C13—42no—
306C23×C13—42no—
307C23×C13—42no—
308C23×C13#12314yes—
309C23×C13C22×D412yes—
310C23×C13C22×D411yescharacteristic
311C22×D13—22no—
312C22×D13—22no—
313C22×D13—28no—
314C22×D13—22no—
315C22×D13—22no—
316C22×D13—22no—
317C22×D13—28no—
318C22×D13—44no—
319C22×D13—416no—
320C22×D13#13514yes—
321C22×D13C22×D412yes—
322C22×D13C22×D412yes—
323Q8×C13—22no—
324Q8×C13—22no—
325Q8×C13—42no—
326D4×C13—22no—
327D4×C13—22no—
328D4×C13—48no—
329D4×C13—42no—
330C2×C4×C13—22no—
331C2×C4×C13—22no—
332C2×C4×C13—22no—
333C2×C4×C13—42no—
334C2×C4×C13—42no—
335C2×C4×C13—42no—
336C2×C4×C13—48no—
337C2×C4×C13#12314yes—
338C2×C4×C13#12318yes—
339C2×C4×C13C22×D412yes—
340C2×C4×C13C22×D411yescharacteristic
341C2×C4×C13C2×#4112yes—
342C2×C4×C13C2×#4114yes—
343C2×C4×C13C2×#4112yes—
344C2×C4×C13C2×#4114yes—
345C2×C4×C13C2511yescharacteristic
346C22⋊D13—48no—
347C22⋊D13—48no—
348C2×Dic13—28no—
349C2×Dic13—22no—
350C2×Dic13—22no—
351C2×Dic13—22no—
352C2×Dic13—22no—
353C2×Dic13—22no—
354C2×Dic13—22no—
355C2×Dic13—42no—
356C2×Dic13—42no—
357C2×Dic13—42no—
358C2×Dic13—42no—
359C2×Dic13C22×D412yes—
360C2×Dic13C22×D412yes—
361C4×D13—28no—
362C4×D13—28no—
363C4×D13—24no—
364C4×D13—24no—
365C4×D13—22no—
366C4×D13—22no—
367C4×D13—22no—
368C4×D13—22no—
369C4×D13—48no—
370C4×D13—48no—
371C8×C13—22no—
372C8×C13—22no—
373#1055—22no—
374#1055—22no—
375C22×#41C2×D1311yescharacteristic
376C24×C4—131no—
377C23×C8—131no—
378C23×C8C2×D1311yescharacteristic
379#525—138no—
380#525—264no—
381C2×#123—261no—
382C2×C22⋊Q8—131no—
383C2×C22⋊Q8—131no—
384C2×#121—131no—
385C2×#121—131no—
386C2×#120—261no—
387C2×C4×D4—261no—
388C2×C4×D4—261no—
389C2×#117—131no—
390C2×#117—131no—
391C2×#117—138no—
392C2×#117—131no—
393C2×#117—131no—
394C2×#117—261no—
395C2×#117—261no—
396C2×#117—264no—
397C2×#117C2×D1311yescharacteristic
398C22×C4⋊C4—131no—
399C22×C4⋊C4—131no—
400C22×C22⋊C4—261no—
401C22×C42—261no—
402#485—138no—
403#485—138no—
404#484—138no—
405#483—138no—
406#482—138no—
407#482—138no—
408#481—138no—
409#480—138no—
410#427—138no—
411#427—138no—
412C2×#107—131no—
413C2×#107—131no—
414C2×#107—131no—
415C2×#107—131no—
416C2×#106—131no—
417C2×#106—131no—
418C2×#106—131no—
419C2×#106—131no—
420#416—138no—
421#416C2×D1318yescomplemented
422C2×#103—131no—
423C2×#103—131no—
424C2×#103C2×D1311yescharacteristic, complemented
425C2×#103C2×D1311yescharacteristic, complemented
426C2×#102—131no—
427C2×#102—131no—
428C2×#102C2×D1311yescharacteristic, complemented
429C2×#102C2×D1311yescharacteristic, complemented
430C2×C22⋊C8—131no—
431C2×C22⋊C8—131no—
432C2×C22⋊C8—131no—
433C2×C22⋊C8—131no—
434C2×C22⋊C8—138no—
435C22×C13—28no—
436C22×C13—22no—
437C22×C13—22no—
438C22×C13—42no—
439C22×C13—42no—
440C22×C13—42no—
441C22×C13—84no—
442C22×C13C2×#12314yes—
443C22×C13C2×#12312yes—
444C22×C13C2×#13512yes—
445C22×C13#57512yes—
446C22×C13C23×D411yescharacteristic
447C2×D13—28no—
448C2×D13—22no—
449C2×D13—22no—
450C2×D13—22no—
451C2×D13—22no—
452C2×D13—22no—
453C2×D13—416no—
454C2×D13—44no—
455C2×D13C2×#13514yes—
456C4×C13—42no—
457C4×C13—42no—
458C4×C13—42no—
459C4×C13C2×#12314yes—
460C4×C13C2×#12312yes—
461C4×C13C22×#4111yescharacteristic
462C4×C13C22×#4111yescharacteristic
463Dic13—22no—
464Dic13—22no—
465Dic13—42no—
466Dic13—42no—
467Dic13—42no—
468Dic13—42no—
469C25—131no—
470C2×#41—22no—
471C2×#41—24no—
472C2×#41—24no—
473C2×#41C22×D1314yes—
474C22×Q8C22×D1311yescharacteristic
475C22×D4—21no—
476C22×D4—261no—
477C22×D4—261no—
478C22×D4C22×D1311yescharacteristic
479C23×C4—21no—
480C23×C4—131no—
481C23×C4—134no—
482C23×C4—131no—
483C23×C4—131no—
484C23×C4—131no—
485C23×C4—131no—
486C23×C4—134no—
487C23×C4—261no—
488C23×C4—261no—
489C23×C4—264no—
490C23×C4—264no—
491C23×C4C22×D1311yescharacteristic
492C22×C8—24no—
493C22×C8—131no—
494C22×C8—131no—
495C22×C8—134no—
496C22×C8—264no—
497C22×C8C22×D1311yescharacteristic
498C22×C8C22×D1311yescharacteristic
499C22×C8C22×D1314yes—
500#123—268no—
501C22⋊Q8—134no—
502C22⋊Q8—134no—
503C22⋊Q8—262no—
504C22⋊Q8—262no—
505#121—134no—
506#121—134no—
507#121—262no—
508#121—262no—
509#120—268no—
510C4×D4—268no—
511C4×D4—268no—
512#117—22no—
513#117—134no—
514#117—134no—
515#117—134no—
516#117—134no—
517#117—268no—
518#117—268no—
519#117—262no—
520#117—262no—
521#117—262no—
522#117—262no—
523#117C22×D1314yes—
524C2×C4⋊C4—131no—
525C2×C4⋊C4—131no—
526C2×C4⋊C4—131no—
527C2×C4⋊C4—131no—
528C2×C4⋊C4—134no—
529C2×C4⋊C4—134no—
530C2×C4⋊C4—262no—
531C2×C4⋊C4—262no—
532C2×C4⋊C4—261no—
533C2×C4⋊C4—261no—
534C2×C4⋊C4—261no—
535C2×C4⋊C4—261no—
536C2×C4⋊C4C22×D1311yescharacteristic
537C2×C4⋊C4C22×D1311yescharacteristic
538C2×C22⋊C4—21no—
539C2×C22⋊C4—268no—
540C2×C22⋊C4—261no—
541C2×C22⋊C4—261no—
542C2×C22⋊C4—261no—
543C2×C22⋊C4—261no—
544C2×C22⋊C4—261no—
545C2×C22⋊C4—261no—
546C2×C22⋊C4—261no—
547C2×C22⋊C4—261no—
548C2×C42—21no—
549C2×C42—268no—
550C2×C42—261no—
551C2×C42—261no—
552C2×C42—261no—
553C2×C42—261no—
554#107—134no—
555#107—134no—
556#107—134no—
557#107—134no—
558#106—134no—
559#106—134no—
560#106—134no—
561#106—134no—
562#103—134no—
563#103—134no—
564#103C22×D1314yescomplemented
565#103C22×D1314yescomplemented
566#102—134no—
567#102—134no—
568#102C22×D1314yescomplemented
569#102C22×D1314yescomplemented
570C22⋊C8—134no—
571C22⋊C8—134no—
572C22⋊C8—134no—
573C22⋊C8—134no—
574C2×C13—24no—
575C2×C13—82no—
576C2×C13#309114yescomplemented
577C2×C13C22×#12311yescharacteristic
578C2×C13C22×#13511yescharacteristic
579C2×C13C2×#57511yescharacteristic
580D13—24no—
581D13—42no—
582C24—21no—
583C24—131no—
584C24—131no—
585C24—134no—
586C24—264no—
587C24—264no—
588C24—522no—
589C24D4×D1311yescharacteristic
590#41—28no—
591#41—28no—
592#41—48no—
593C2×Q8—21no—
594C2×Q8—22no—
595C2×Q8—22no—
596C2×Q8C23×D1312yes—
597C2×D4—24no—
598C2×D4—22no—
599C2×D4—21no—
600C2×D4—22no—
601C2×D4—44no—
602C2×D4—264no—
603C2×D4—264no—
604C2×D4—524no—
605C2×D4—524no—
606C2×D4C23×D1312yes—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—24no—
611C22×C4—44no—
612C22×C4—131no—
613C22×C4—131no—
614C22×C4—134no—
615C22×C4—134no—
616C22×C4—132no—
617C22×C4—134no—
618C22×C4—132no—
619C22×C4—132no—
620C22×C4—132no—
621C22×C4—264no—
622C22×C4—264no—
623C22×C4—264no—
624C22×C4—264no—
625C22×C4—264no—
626C22×C4—2616no—
627C22×C4—262no—
628C22×C4—262no—
629C22×C4—268no—
630C22×C4—262no—
631C22×C4—262no—
632C22×C4—268no—
633C22×C4—261no—
634C22×C4—261no—
635C22×C4—261no—
636C22×C4—261no—
637C22×C4—524no—
638C22×C4—524no—
639C22×C4#612714yes—
640C22×C4D4×D1312yes—
641C22×C4D4×D1311yescharacteristic
642C22×C4#612914yes—
643C22×C4C23×D1311yescharacteristic
644C22×C4C23×D1312yes—
645C2×C8—22no—
646C2×C8—22no—
647C2×C8—28no—
648C2×C8—132no—
649C2×C8—132no—
650C2×C8—262no—
651C2×C8—262no—
652C2×C8—268no—
653C2×C8C23×D1312yes—
654C2×C8C23×D1312yes—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—132no—
658C4⋊C4—132no—
659C4⋊C4—132no—
660C4⋊C4—132no—
661C4⋊C4—264no—
662C4⋊C4—264no—
663C4⋊C4—264no—
664C4⋊C4—264no—
665C4⋊C4—261no—
666C4⋊C4—261no—
667C4⋊C4—261no—
668C4⋊C4—261no—
669C4⋊C4C23×D1312yes—
670C4⋊C4C23×D1312yes—
671C22⋊C4—24no—
672C22⋊C4—264no—
673C22⋊C4—264no—
674C22⋊C4—264no—
675C22⋊C4—264no—
676C22⋊C4—264no—
677C22⋊C4—264no—
678C22⋊C4—264no—
679C22⋊C4—264no—
680C42—24no—
681C42—264no—
682C42—264no—
683C42—264no—
684C42—264no—
685C13C2×#309111yescharacteristic, complemented, Sylow
686C23—22no—
687C23—22no—
688C23—22no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—134no—
693C23—132no—
694C23—132no—
695C23—268no—
696C23—262no—
697C23—262no—
698C23—268no—
699C23—262no—
700C23—262no—
701C23—262no—
702C23—524no—
703C23—5216no—
704C23#8813714yes—
705C23C2×D4×D1312yes—
706C23C2×D4×D1311yescharacteristic
707Q8—22no—
708Q8—22no—
709Q8—42no—
710D4—22no—
711D4—22no—
712D4—48no—
713D4—42no—
714D4—528no—
715D4—528no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—48no—
723C2×C4—132no—
724C2×C4—132no—
725C2×C4—268no—
726C2×C4—262no—
727C2×C4—262no—
728C2×C4—268no—
729C2×C4—268no—
730C2×C4—264no—
731C2×C4—264no—
732C2×C4—262no—
733C2×C4—262no—
734C2×C4—262no—
735C2×C4—262no—
736C2×C4—262no—
737C2×C4—262no—
738C2×C4—262no—
739C2×C4—262no—
740C2×C4—528no—
741C2×C4—528no—
742C2×C4—522no—
743C2×C4—522no—
744C2×C4—522no—
745C2×C4—522no—
746C2×C4#8813714yes—
747C2×C4#8813718yes—
748C2×C4C2×#612712yes—
749C2×C4C2×#612714yes—
750C2×C4C2×D4×D1312yes—
751C2×C4C2×D4×D1311yescharacteristic
752C2×C4C2×#612912yes—
753C2×C4C2×#612914yes—
754C2×C4C24×D1311yescharacteristic
755C8—22no—
756C8—22no—
757C8—262no—
758C8—262no—
759C22—22no—
760C22—22no—
761C22—28no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—84no—
766C22—134no—
767C22—262no—
768C22—262no—
769C22—268no—
770C22—262no—
771C22—262no—
772C22—262no—
773C22—5216no—
774C22—524no—
775C22C2×#8813714yes—
776C22C2×#8813712yes—
777C22D13×#13512yes—
778C22#1171947312yes—
779C22C22×D4×D1311yescharacteristic
780C4—42no—
781C4—42no—
782C4—42no—
783C4—262no—
784C4—262no—
785C4—522no—
786C4—522no—
787C4—522no—
788C4—522no—
789C4C2×#8813714yes—
790C4C2×#8813712yes—
791C4C22×#612711yescharacteristic
792C4C22×#612911yescharacteristic
793C2—24no—
794C2—82no—
795C2—264no—
796C2—522no—
797C2#1312474714yesdirect product factor
798C2C22×#8813711yescharacteristic
799C2C2×D13×#13511yescharacteristic
800C2C2×#1171947311yescharacteristic
subgroupG/H
centerC22×C4D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#416C2
socleC23×C13C22×D4
prime radicalC2×#11719533C2
hypercenterC2×#416D13
hypocenterC13C2×#3091
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
2. C2×D13×#117C2semidirect
3. #13124747C2direct (N × H)
4. C2×#11718470C2semidirect
5. C2×#11718438C2semidirect
6. C2×#11718475C2semidirect
7. C2×#11718476C2semidirect
8. C2×#11718440C2semidirect
9. C2×#11718445C2semidirect
10. C2×#11718466C2semidirect
11. C2×#11718435C2semidirect
12. C2×#11718767C2semidirect
13. C2×#11718659C2semidirect
14. C2×#11718894C2semidirect
15. C22×#88060C2semidirect
16. C2×C13×#416C2semidirect
35. D13×#117C22semidirect
44. C13×#416C22semidirect
45. C2×C13×#103C22semidirect
46. C2×C13×#103C22semidirect
47. C2×C13×#102C22semidirect
48. C2×C13×#102C22semidirect
49. #11718894C22semidirect
50. C2×#88075C22semidirect
51. C2×#88075C22semidirect
52. C2×#88072C22semidirect
53. C2×#88072C22semidirect
58. C2×#88060C22semidirect
59. #11718767C22semidirect
60. C2×#88058C22semidirect
61. C2×#88058C22semidirect
62. C2×#88057C22semidirect
63. C2×#88057C22semidirect
64. #11718659C22semidirect
65. C2×#88048C22semidirect
66. C2×#88048C22semidirect
67. C2×#88047C22semidirect
68. C2×#88047C22semidirect
69. #11718476C22semidirect
70. #11718475C22semidirect
71. #11718470C22semidirect
72. #11718466C22semidirect
73. #11718445C22semidirect
74. #11718440C22semidirect
75. #11718438C22semidirect
76. #11718435C22semidirect
162. C13×#103C23semidirect
163. C13×#103C23semidirect
164. C13×#102C23semidirect
165. C13×#102C23semidirect
166. #88075C23semidirect
167. #88075C23semidirect
168. #88072C23semidirect
169. #88072C23semidirect
174. #88058C23semidirect
175. #88058C23semidirect
176. #88057C23semidirect
177. #88057C23semidirect
178. #88048C23semidirect
179. #88048C23semidirect
180. #88047C23semidirect
181. #88047C23semidirect
300. C2×#416D13semidirect
421. #416C2×D13semidirect
424. C2×#103C2×D13semidirect
425. C2×#103C2×D13semidirect
428. C2×#102C2×D13semidirect
429. C2×#102C2×D13semidirect
564. #103C22×D13semidirect
565. #103C22×D13semidirect
568. #102C22×D13semidirect
569. #102C22×D13semidirect
576. C2×C13#3091semidirect
685. C13C2×#3091semidirect
797. C2#13124747direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117195332
C2×D13×#1172
#131247472
C2×#117184702
C2×#117184382
C2×#117184752
C2×#117184762
C2×#117184402
C2×#117184452
C2×#117184662
C2×#117184352
C2×#117187672
C2×#117186592
C2×#117188942
C22×#880602
C2×C13×#4162
C2×#309113