Finite Group Databasebeta

← C2×#13124783 #16730724

Subgroups — C2×#13124783 #16730724

Order 3328.

2326 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13×C22⋊Q8C211yesmaximal, characteristic
2C2×D13×#117C211yesmaximal, characteristic
3#13124783C2116yesmaximal, direct product factor
4C2×#11718545C211yesmaximal, characteristic, complemented
5C2×#11718470C211yesmaximal, characteristic, complemented
6C2×#11718384C211yesmaximal, characteristic, complemented
7C2×#11718657C211yesmaximal, characteristic, complemented
8C2×#11718706C211yesmaximal, characteristic, complemented
9C2×#11718523C211yesmaximal, characteristic, complemented
10C2×#11718466C211yesmaximal, characteristic, complemented
11C2×#11718542C211yesmaximal, characteristic, complemented
12C2×#11718522C211yesmaximal, characteristic, complemented
13C2×#11718463C211yesmaximal, characteristic, complemented
14C2×#11718463C211yesmaximal, characteristic, complemented
15C2×#11718387C211yesmaximal, characteristic
16C2×C13×#485C211yesmaximal, characteristic, complemented
17C22×Q8×D13C2211yescharacteristic
18C23×C4×D13C2211yescharacteristic
19C2×C13×C22⋊Q8C2211yescharacteristic
20C2×C13×#117C2211yescharacteristic
21C2×#88200C2211yescharacteristic
22C2×#88180C2211yescharacteristic
23C2×#88178C2211yescharacteristic
24C22×#6094C2211yescharacteristic
25C22×#6094C2211yescharacteristic
26D13×C22⋊Q8—24no—
27D13×C22⋊Q8C2218yes—
28D13×#117—24no—
29D13×#117C2218yes—
30C2×#88151C2211yescharacteristic
31C2×#88150—21no—
32C2×#88146C2211yescharacteristic
33C2×#88146C2211yescharacteristic
34C2×C4⋊C4×D13—21no—
35C2×C4⋊C4×D13C2211yescharacteristic
36C2×C4⋊C4×D13C2211yescharacteristic
37C2×C4⋊C4×D13C2211yescharacteristic
38C2×C22⋊C4×D13—21no—
39C2×C22⋊C4×D13—21no—
40C2×#88132—21no—
41C2×#88131—21no—
42C2×#88126—21no—
43C2×C42×D13—21no—
44C13×#485C2218yescomplemented
45C2×C13×#107C2211yescharacteristic, complemented
46C2×C13×#106C2211yescharacteristic, complemented
47C2×C13×#103C2211yescharacteristic, complemented
48C2×C13×#103C2211yescharacteristic, complemented
49C2×C13×C22⋊C8C2211yescharacteristic
50C2×#88075C2211yescharacteristic, complemented
51C2×#88075C2211yescharacteristic, complemented
52C2×C22⋊#1055C2211yescharacteristic
53C2×#88060C2211yescharacteristic
54C2×#88060C2211yescharacteristic
55C2×#88058C2211yescharacteristic, complemented
56C2×#88057C2211yescharacteristic, complemented
57C2×#88056C2211yescharacteristic, complemented
58C2×#88056C2211yescharacteristic, complemented
59#11718706C2218yescomplemented
60#11718657C2218yescomplemented
61C2×#88050C2211yescharacteristic, complemented
62C2×#88050C2211yescharacteristic, complemented
63C2×#88048C2211yescharacteristic, complemented
64C2×#88048C2211yescharacteristic, complemented
65C2×#88047C2211yescharacteristic, complemented
66C2×#88047C2211yescharacteristic, complemented
67#11718545C2218yescomplemented
68#11718542C2218yescomplemented
69#11718523C2218yescomplemented
70#11718522C2218yescomplemented
71#11718470C2218yescomplemented
72#11718466C2218yescomplemented
73#11718463C2218yescomplemented
74#11718463C2218yescomplemented
75#11718387C2218yes—
76#11718384C2218yescomplemented
77C24×D13D411yescharacteristic
78C22×Q8×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×Dic13D411yescharacteristic
81C2×Q8×D13—22no—
82C2×Q8×D13—24no—
83C2×Q8×D13—24no—
84C2×Q8×D13C2314yes—
85C22×C4×D13—24no—
86C22×C4×D13—24no—
87C22×C4×D13—21no—
88C22×C4×D13—21no—
89C22×C4×D13—21no—
90C22×C4×D13—21no—
91C22×C4×D13D411yescharacteristic
92C22×C4×D13D411yescharacteristic
93C22×C4×D13D414yes—
94C22×C4×D13C2311yescharacteristic
95C22×C4×D13C2314yes—
96C22×C4×D13C2311yescharacteristic
97C22×Dic26—21no—
98C22×Dic26C2311yescharacteristic
99C22×C8×C13C2311yescharacteristic
100C22×C8×C13C2311yescharacteristic
101C13×C22⋊Q8—22no—
102C13×C22⋊Q8C2314yes—
103C13×#117—22no—
104C13×#117C2314yes—
105C2×C13×C4⋊C4—21no—
106C2×C13×C4⋊C4C2311yescharacteristic
107C2×C13×C4⋊C4C2311yescharacteristic
108C2×C13×C4⋊C4C2311yescharacteristic
109C2×C13×C22⋊C4—21no—
110C2×C13×C22⋊C4—21no—
111C2×C42×C13—21no—
112C2×C22⋊Dic13—21no—
113C2×C22⋊Dic13—21no—
114#88200—22no—
115#88200C2314yes—
116C2×#6103—21no—
117C2×#6103—21no—
118C2×#6103—21no—
119C2×#6103—21no—
120#88180—22no—
121#88180C2314yes—
122C2×C4⋊Dic13—21no—
123C2×C4⋊Dic13C2311yescharacteristic
124C2×C4⋊Dic13C2311yescharacteristic
125C2×C4⋊Dic13C2311yescharacteristic
126#88178—22no—
127#88178C2314yes—
128C2×#6101—21no—
129C2×#6101—21no—
130C2×#6101—21no—
131C2×#6101—21no—
132C2×#6101—21no—
133C2×C4×Dic13—21no—
134C2×C4×Dic13—21no—
135C2×C4×Dic13—21no—
136C22×#1055C2311yescharacteristic
137C22×#1055C2311yescharacteristic
138C2×#6094—24no—
139C2×#6094—24no—
140C2×#6094C2314yes—
141C2×#6094C2314yes—
142#88151—22no—
143#88151C2314yes—
144#88150—28no—
145#88146—22no—
146#88146—22no—
147#88146C2314yes—
148#88146C2314yes—
149C4⋊C4×D13—28no—
150C4⋊C4×D13—22no—
151C4⋊C4×D13—22no—
152C4⋊C4×D13—22no—
153C4⋊C4×D13C2314yes—
154C4⋊C4×D13C2314yes—
155C4⋊C4×D13C2314yes—
156C22⋊C4×D13—28no—
157C22⋊C4×D13—28no—
158#88132—28no—
159#88131—28no—
160#88126—28no—
161C42×D13—28no—
162C13×#107C2314yescomplemented
163C13×#106C2314yescomplemented
164C13×#103C2314yescomplemented
165C13×#103C2314yescomplemented
166C13×C22⋊C8C2314yes—
167#88075C2314yescomplemented
168#88075C2314yescomplemented
169C22⋊#1055C2314yes—
170#88060C2314yes—
171#88060C2314yes—
172#88058C2314yescomplemented
173#88057C2314yescomplemented
174#88056C2314yescomplemented
175#88056C2314yescomplemented
176#88050C2314yescomplemented
177#88050C2314yescomplemented
178#88048C2314yescomplemented
179#88048C2314yescomplemented
180#88047C2314yescomplemented
181#88047C2314yescomplemented
182C2×#3095—131nomaximal, Sylow
183C24×C13C2×D411yescharacteristic
184C23×D13—24no—
185C23×D13—24no—
186C23×D13—42no—
187C23×D13C2×D414yes—
188C23×D13C2×D411yescharacteristic
189C23×D13C2×D411yescharacteristic
190C2×Q8×C13—21no—
191C2×Q8×C13—22no—
192C2×Q8×C13—22no—
193C2×Q8×C13C2412yes—
194C22×C4×C13—22no—
195C22×C4×C13—22no—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13C2×D411yescharacteristic
201C22×C4×C13C2×D412yes—
202C22×C4×C13C2412yes—
203C22×C4×C13C2411yescharacteristic
204C22×Dic13—24no—
205C22×Dic13—21no—
206C22×Dic13—21no—
207C22×Dic13—21no—
208C22×Dic13—21no—
209C22×Dic13C2×D414yes—
210C22×Dic13C2×D411yescharacteristic
211C22×Dic13C2×D411yescharacteristic
212Q8×D13—28no—
213Q8×D13—28no—
214Q8×D13—48no—
215C2×C4×D13—24no—
216C2×C4×D13—22no—
217C2×C4×D13—22no—
218C2×C4×D13—24no—
219C2×C4×D13—216no—
220C2×C4×D13—28no—
221C2×C4×D13—28no—
222C2×C4×D13—24no—
223C2×C4×D13—24no—
224C2×C4×D13—24no—
225C2×C4×D13—24no—
226C2×C4×D13—44no—
227C2×C4×D13—44no—
228C2×C4×D13—44no—
229C2×C4×D13—44no—
230C2×C4×D13C2×D414yes—
231C2×C4×D13C2×D414yes—
232C2×C4×D13C2×D412yes—
233C2×C4×D13C2×D412yes—
234C2×C4×D13#4114yes—
235C2×C4×D13#4114yes—
236C2×C4×D13C2412yes—
237C2×C4×D13C2412yes—
238C2×Dic26—22no—
239C2×Dic26—22no—
240C2×Dic26—21no—
241C2×Dic26—24no—
242C2×Dic26—44no—
243C2×Dic26C2412yes—
244C2×C8×C13—22no—
245C2×C8×C13—22no—
246C2×C8×C13C2412yes—
247C2×C8×C13C2412yes—
248C13×C4⋊C4—21no—
249C13×C4⋊C4—21no—
250C13×C4⋊C4—24no—
251C13×C4⋊C4—21no—
252C13×C4⋊C4C2412yes—
253C13×C4⋊C4C2412yes—
254C13×C4⋊C4C2412yes—
255C13×C22⋊C4—24no—
256C13×C22⋊C4—24no—
257C42×C13—24no—
258C22⋊Dic13—24no—
259C22⋊Dic13—24no—
260#6103—24no—
261#6103—24no—
262#6103—24no—
263#6103—24no—
264C4⋊Dic13—21no—
265C4⋊Dic13—21no—
266C4⋊Dic13—21no—
267C4⋊Dic13—24no—
268C4⋊Dic13C2412yes—
269C4⋊Dic13C2412yes—
270C4⋊Dic13C2412yes—
271#6101—24no—
272#6101—24no—
273#6101—24no—
274#6101—24no—
275#6101—24no—
276C4×Dic13—24no—
277C4×Dic13—24no—
278C4×Dic13—24no—
279C2×#1055—22no—
280C2×#1055—22no—
281C2×#1055C2412yes—
282C2×#1055C2412yes—
283#6094—28no—
284#6094—28no—
285C22×C22⋊Q8—131no—
286C22×#117—131no—
287#3095—1316no—
288C2×#484—131no—
289C2×#484—131no—
290C2×#485—131no—
291C2×#485—131no—
292C2×#485—131no—
293C2×#485D1311yescharacteristic, complemented
294C2×#483—131no—
295C2×#483—131no—
296C2×#428—131no—
297C2×#428—131no—
298C2×#419—131no—
299C2×#419—131no—
300C2×#407—131no—
301C23×C13—22no—
302C23×C13—22no—
303C23×C13—22no—
304C23×C13C22×D412yes—
305C23×C13C22×D411yescharacteristic
306C22×D13—22no—
307C22×D13—22no—
308C22×D13—22no—
309C22×D13—22no—
310C22×D13—28no—
311C22×D13—28no—
312C22×D13—44no—
313C22×D13—416no—
314C22×D13#12314yes—
315C22×D13#13714yes—
316C22×D13C22×D412yes—
317C22×D13C22×D412yes—
318Q8×C13—22no—
319Q8×C13—22no—
320Q8×C13—42no—
321C2×C4×C13—22no—
322C2×C4×C13—24no—
323C2×C4×C13—22no—
324C2×C4×C13—22no—
325C2×C4×C13—22no—
326C2×C4×C13—22no—
327C2×C4×C13—22no—
328C2×C4×C13—22no—
329C2×C4×C13—42no—
330C2×C4×C13—42no—
331C2×C4×C13—42no—
332C2×C4×C13—42no—
333C2×C4×C13C22×D412yes—
334C2×C4×C13C22×D411yescharacteristic
335C2×C4×C13C2×#4112yes—
336C2×C4×C13C2×#4112yes—
337C2×C4×C13C2511yescharacteristic
338C2×Dic13—22no—
339C2×Dic13—28no—
340C2×Dic13—22no—
341C2×Dic13—22no—
342C2×Dic13—22no—
343C2×Dic13—22no—
344C2×Dic13—42no—
345C2×Dic13—42no—
346C2×Dic13—42no—
347C2×Dic13—42no—
348C2×Dic13#12314yes—
349C2×Dic13C22×D412yes—
350C2×Dic13C22×D412yes—
351C4×D13—28no—
352C4×D13—24no—
353C4×D13—22no—
354C4×D13—22no—
355C4×D13—28no—
356C4×D13—48no—
357C4×D13—48no—
358C4×D13—48no—
359C4×D13—48no—
360C4×D13#12318yes—
361C4×D13C2×#4114yes—
362C4×D13C2×#4114yes—
363Dic26—22no—
364Dic26—22no—
365Dic26—42no—
366Dic26—48no—
367C8×C13—22no—
368C8×C13—22no—
369#1055—22no—
370#1055—22no—
371C23×Q8—131no—
372C24×C4—131no—
373C22×M16—131no—
374C22×M16—131no—
375C2×C22⋊Q8—131no—
376C2×C22⋊Q8—131no—
377C2×C22⋊Q8—138no—
378C2×C22⋊Q8—131no—
379C2×C22⋊Q8—261no—
380C2×C22⋊Q8—261no—
381C2×C22⋊Q8—264no—
382C2×C22⋊Q8C2×D1311yescharacteristic
383C2×#117—131no—
384C2×#117—138no—
385C2×#117—131no—
386C2×#117—131no—
387C2×#117—261no—
388C2×#117—261no—
389C2×#117—264no—
390C2×#117C2×D1311yescharacteristic
391C22×C4⋊C4—131no—
392C22×C4⋊C4—131no—
393C22×C4⋊C4—131no—
394C22×C4⋊C4—261no—
395C22×C22⋊C4—261no—
396C22×C22⋊C4—261no—
397C22×C42—261no—
398#485—138no—
399#485—138no—
400#485—138no—
401#485C2×D1318yescomplemented
402#484—138no—
403#484—138no—
404#483—138no—
405#483—138no—
406#428—138no—
407#428—138no—
408C2×#107—131no—
409C2×#107—131no—
410C2×#107—131no—
411C2×#107C2×D1311yescharacteristic, complemented
412C2×#106—131no—
413C2×#106—131no—
414C2×#106—131no—
415C2×#106C2×D1311yescharacteristic, complemented
416#419—138no—
417#419—138no—
418C2×#103—131no—
419C2×#103—131no—
420C2×#103—131no—
421C2×#103—131no—
422C2×#103—131no—
423C2×#103—131no—
424C2×#103C2×D1311yescharacteristic, complemented
425C2×#103C2×D1311yescharacteristic, complemented
426#407—138no—
427C2×C22⋊C8—131no—
428C2×C22⋊C8—131no—
429C2×C22⋊C8—131no—
430C2×C22⋊C8C2×D1311yescharacteristic
431C22×C13—22no—
432C22×C13—22no—
433C22×C13—22no—
434C22×C13—44no—
435C22×C13C2×#12312yes—
436C22×C13C2×#13712yes—
437C22×C13#57512yes—
438C22×C13C23×D411yescharacteristic
439C2×D13—28no—
440C2×D13—28no—
441C2×D13—22no—
442C2×D13—22no—
443C2×D13—22no—
444C2×D13—22no—
445C2×D13—416no—
446C2×D13C2×#12314yes—
447C2×D13C2×#13714yes—
448C4×C13—22no—
449C4×C13—42no—
450C4×C13—42no—
451C4×C13—42no—
452C4×C13—42no—
453C4×C13C2×#12312yes—
454C4×C13C22×#4111yescharacteristic
455C4×C13C22×#4111yescharacteristic
456Dic13—22no—
457Dic13—42no—
458Dic13—42no—
459Dic13—42no—
460Dic13—42no—
461Dic13C2×#12314yes—
462C25—131no—
463C22×Q8—134no—
464C22×Q8—131no—
465C22×Q8—261no—
466C22×Q8—262no—
467C22×Q8—264no—
468C22×Q8—264no—
469C22×Q8C22×D1311yescharacteristic
470C23×C4—131no—
471C23×C4—131no—
472C23×C4—131no—
473C23×C4—134no—
474C23×C4—131no—
475C23×C4—131no—
476C23×C4—134no—
477C23×C4—264no—
478C23×C4—264no—
479C23×C4—261no—
480C23×C4—261no—
481C23×C4—261no—
482C23×C4—261no—
483C23×C4C22×D1311yescharacteristic
484C2×M16—134no—
485C2×M16—134no—
486C2×M16—264no—
487C2×M16—264no—
488C22×C8—131no—
489C22×C8—131no—
490C22×C8C22×D1311yescharacteristic
491C22×C8C22×D1311yescharacteristic
492C22⋊Q8—22no—
493C22⋊Q8—134no—
494C22⋊Q8—134no—
495C22⋊Q8—134no—
496C22⋊Q8—268no—
497C22⋊Q8—268no—
498C22⋊Q8—262no—
499C22⋊Q8—262no—
500C22⋊Q8—262no—
501C22⋊Q8C22×D1314yes—
502#117—22no—
503#117—134no—
504#117—134no—
505#117—134no—
506#117—268no—
507#117—268no—
508#117—262no—
509#117—262no—
510#117—262no—
511#117C22×D1314yes—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—131no—
514C2×C4⋊C4—131no—
515C2×C4⋊C4—131no—
516C2×C4⋊C4—134no—
517C2×C4⋊C4—134no—
518C2×C4⋊C4—134no—
519C2×C4⋊C4—262no—
520C2×C4⋊C4—262no—
521C2×C4⋊C4—262no—
522C2×C4⋊C4—268no—
523C2×C4⋊C4—261no—
524C2×C4⋊C4—261no—
525C2×C4⋊C4—261no—
526C2×C4⋊C4—261no—
527C2×C4⋊C4—261no—
528C2×C4⋊C4—261no—
529C2×C4⋊C4C22×D1311yescharacteristic
530C2×C4⋊C4C22×D1311yescharacteristic
531C2×C4⋊C4C22×D1311yescharacteristic
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—268no—
535C2×C22⋊C4—268no—
536C2×C22⋊C4—261no—
537C2×C22⋊C4—261no—
538C2×C22⋊C4—261no—
539C2×C22⋊C4—261no—
540C2×C22⋊C4—261no—
541C2×C22⋊C4—261no—
542C2×C42—21no—
543C2×C42—268no—
544C2×C42—261no—
545C2×C42—261no—
546C2×C42—261no—
547#107—134no—
548#107—134no—
549#107—134no—
550#107C22×D1314yescomplemented
551#106—134no—
552#106—134no—
553#106—134no—
554#106C22×D1314yescomplemented
555#103—134no—
556#103—134no—
557#103—134no—
558#103—134no—
559#103—134no—
560#103—134no—
561#103C22×D1314yescomplemented
562#103C22×D1314yescomplemented
563C22⋊C8—134no—
564C22⋊C8—134no—
565C22⋊C8—134no—
566C22⋊C8C22×D1314yes—
567C2×C13—42no—
568C2×C13#309514yescomplemented
569C2×C13C22×#12311yescharacteristic
570C2×C13C22×#13711yescharacteristic
571C2×C13C2×#57511yescharacteristic
572D13—24no—
573D13—24no—
574C24—131no—
575C24—131no—
576C24—134no—
577C24—264no—
578C24—264no—
579C24—522no—
580C24D4×D1311yescharacteristic
581C2×Q8—21no—
582C2×Q8—22no—
583C2×Q8—22no—
584C2×Q8—132no—
585C2×Q8—264no—
586C2×Q8—268no—
587C2×Q8—268no—
588C2×Q8—261no—
589C2×Q8—262no—
590C2×Q8—262no—
591C2×Q8—524no—
592C2×Q8—528no—
593C2×Q8C23×D1312yes—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—131no—
601C22×C4—132no—
602C22×C4—134no—
603C22×C4—134no—
604C22×C4—132no—
605C22×C4—134no—
606C22×C4—131no—
607C22×C4—134no—
608C22×C4—134no—
609C22×C4—132no—
610C22×C4—132no—
611C22×C4—264no—
612C22×C4—2616no—
613C22×C4—268no—
614C22×C4—268no—
615C22×C4—264no—
616C22×C4—264no—
617C22×C4—264no—
618C22×C4—264no—
619C22×C4—264no—
620C22×C4—264no—
621C22×C4—262no—
622C22×C4—262no—
623C22×C4—261no—
624C22×C4—261no—
625C22×C4—261no—
626C22×C4—261no—
627C22×C4—524no—
628C22×C4—524no—
629C22×C4—524no—
630C22×C4—524no—
631C22×C4D4×D1312yes—
632C22×C4D4×D1311yescharacteristic
633C22×C4C23×D1312yes—
634C22×C4C23×D1311yescharacteristic
635M16—268no—
636M16—268no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—132no—
640C2×C8—132no—
641C2×C8—262no—
642C2×C8—262no—
643C2×C8C23×D1312yes—
644C2×C8C23×D1312yes—
645C4⋊C4—24no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—132no—
650C4⋊C4—132no—
651C4⋊C4—132no—
652C4⋊C4—264no—
653C4⋊C4—264no—
654C4⋊C4—264no—
655C4⋊C4—264no—
656C4⋊C4—264no—
657C4⋊C4—261no—
658C4⋊C4—261no—
659C4⋊C4—261no—
660C4⋊C4—264no—
661C4⋊C4C23×D1312yes—
662C4⋊C4C23×D1312yes—
663C4⋊C4C23×D1312yes—
664C22⋊C4—24no—
665C22⋊C4—24no—
666C22⋊C4—264no—
667C22⋊C4—264no—
668C22⋊C4—264no—
669C22⋊C4—264no—
670C22⋊C4—264no—
671C22⋊C4—264no—
672C42—24no—
673C42—264no—
674C42—264no—
675C42—264no—
676C13C2×#309511yescharacteristic, complemented, Sylow
677C23—22no—
678C23—22no—
679C23—22no—
680C23—134no—
681C23—134no—
682C23—132no—
683C23—132no—
684C23—268no—
685C23—268no—
686C23—262no—
687C23—262no—
688C23—262no—
689C23—262no—
690C23—524no—
691C23—5216no—
692C23C2×D4×D1312yes—
693C23C2×D4×D1311yescharacteristic
694Q8—22no—
695Q8—22no—
696Q8—42no—
697Q8—262no—
698Q8—262no—
699Q8—528no—
700Q8—522no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—134no—
714C2×C4—132no—
715C2×C4—138no—
716C2×C4—134no—
717C2×C4—134no—
718C2×C4—132no—
719C2×C4—268no—
720C2×C4—268no—
721C2×C4—268no—
722C2×C4—262no—
723C2×C4—264no—
724C2×C4—262no—
725C2×C4—262no—
726C2×C4—262no—
727C2×C4—262no—
728C2×C4—262no—
729C2×C4—262no—
730C2×C4—528no—
731C2×C4—528no—
732C2×C4—528no—
733C2×C4—528no—
734C2×C4—522no—
735C2×C4—522no—
736C2×C4—522no—
737C2×C4—522no—
738C2×C4C2×D4×D1312yes—
739C2×C4C2×D4×D1311yescharacteristic
740C2×C4#41×D1312yes—
741C2×C4#41×D1312yes—
742C2×C4C24×D1311yescharacteristic
743C8—22no—
744C8—22no—
745C8—262no—
746C8—262no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—44no—
751C22—134no—
752C22—134no—
753C22—262no—
754C22—262no—
755C22—262no—
756C22—262no—
757C22—268no—
758C22—268no—
759C22—5216no—
760C22D13×#12312yes—
761C22#1171947312yes—
762C22D13×#13712yes—
763C22C22×D4×D1311yescharacteristic
764C4—22no—
765C4—42no—
766C4—42no—
767C4—42no—
768C4—42no—
769C4—134no—
770C4—262no—
771C4—522no—
772C4—522no—
773C4—522no—
774C4—522no—
775C4D13×#12312yes—
776C4C2×#41×D1311yescharacteristic
777C4C2×#41×D1311yescharacteristic
778C2—42no—
779C2—264no—
780C2—264no—
781C2#1312478314yesdirect product factor
782C2C2×D13×#12311yescharacteristic
783C2C2×D13×#13711yescharacteristic
784C2C2×#1171947311yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#485C2
socleC23×C13C22×D4
prime radicalC24×D13D4
hypercenterC2×#485D13
hypocenterC13C2×#3095
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
3. #13124783C2direct (N × H)
4. C2×#11718545C2semidirect
5. C2×#11718470C2semidirect
6. C2×#11718384C2semidirect
7. C2×#11718657C2semidirect
8. C2×#11718706C2semidirect
9. C2×#11718523C2semidirect
10. C2×#11718466C2semidirect
11. C2×#11718542C2semidirect
12. C2×#11718522C2semidirect
13. C2×#11718463C2semidirect
14. C2×#11718463C2semidirect
16. C2×C13×#485C2semidirect
44. C13×#485C22semidirect
45. C2×C13×#107C22semidirect
46. C2×C13×#106C22semidirect
47. C2×C13×#103C22semidirect
48. C2×C13×#103C22semidirect
50. C2×#88075C22semidirect
51. C2×#88075C22semidirect
55. C2×#88058C22semidirect
56. C2×#88057C22semidirect
57. C2×#88056C22semidirect
58. C2×#88056C22semidirect
59. #11718706C22semidirect
60. #11718657C22semidirect
61. C2×#88050C22semidirect
62. C2×#88050C22semidirect
63. C2×#88048C22semidirect
64. C2×#88048C22semidirect
65. C2×#88047C22semidirect
66. C2×#88047C22semidirect
67. #11718545C22semidirect
68. #11718542C22semidirect
69. #11718523C22semidirect
70. #11718522C22semidirect
71. #11718470C22semidirect
72. #11718466C22semidirect
73. #11718463C22semidirect
74. #11718463C22semidirect
76. #11718384C22semidirect
162. C13×#107C23semidirect
163. C13×#106C23semidirect
164. C13×#103C23semidirect
165. C13×#103C23semidirect
167. #88075C23semidirect
168. #88075C23semidirect
172. #88058C23semidirect
173. #88057C23semidirect
174. #88056C23semidirect
175. #88056C23semidirect
176. #88050C23semidirect
177. #88050C23semidirect
178. #88048C23semidirect
179. #88048C23semidirect
180. #88047C23semidirect
181. #88047C23semidirect
293. C2×#485D13semidirect
401. #485C2×D13semidirect
411. C2×#107C2×D13semidirect
415. C2×#106C2×D13semidirect
424. C2×#103C2×D13semidirect
425. C2×#103C2×D13semidirect
550. #107C22×D13semidirect
554. #106C22×D13semidirect
561. #103C22×D13semidirect
562. #103C22×D13semidirect
568. C2×C13#3095semidirect
676. C13C2×#3095semidirect
781. C2#13124783direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D13×C22⋊Q82
C2×D13×#1172
#131247832
C2×#117185452
C2×#117184702
C2×#117183842
C2×#117186572
C2×#117187062
C2×#117185232
C2×#117184662
C2×#117185422
C2×#117185222
C2×#117184632
C2×#117183872
C2×C13×#4852
C2×#309513