Finite Group Databasebeta

← #15786360

Subgroups — #15786360

Order 3328.

1954 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718600C211yesmaximal, characteristic
2C2×#11718600C211yesmaximal, characteristic
3C2×#11718600C211yesmaximal, characteristic
4C2×#11718651C212yesmaximal, complemented
5C2×C4×C4⋊Dic13C211yesmaximal, characteristic, complemented
6#13113084C212yesmaximal, complemented
7#13113078C212yesmaximal, complemented
8#13113072C212yesmaximal, complemented
9#13113066C211yesmaximal, characteristic, complemented
10#13113066C211yesmaximal, characteristic, complemented
11C2×C4×C13×C4⋊C4C211yesmaximal, characteristic, complemented
12C23×D52C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C42×C13C2211yescharacteristic
16C22×C42×C13C2211yescharacteristic
17C22×C42×C13C2211yescharacteristic
18C22×#6103C2212yes—
19C22×#6103C2212yes—
20C22×#6103C2212yes—
21C22×#6103C2212yes—
22C22×#6103C2212yes—
23C22×#6103C2212yes—
24C22×C4⋊Dic13C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C22×C4×Dic13C2212yes—
28C4×C13×C4⋊C4—24no—
29C2×C13×#95C2211yescharacteristic
30C2×C13×#95C2211yescharacteristic
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36#11718651—28no—
37#11718600—24no—
38#11718600—24no—
39#11718600C418yescomplemented
40C4×C4⋊Dic13—24no—
41C24×D13C2312yes—
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2311yescharacteristic
46C23×C4×C13C2311yescharacteristic
47C23×C4×C13C2311yescharacteristic
48C23×C4×C13C2311yescharacteristic
49C23×Dic13C2312yes—
50C23×Dic13C2312yes—
51C23×Dic13C2312yes—
52C22×D52—22no—
53C22×D52—22no—
54C22×D52—22no—
55C22×D52—22no—
56C22×D52—22no—
57C22×D52—22no—
58C22×D52C2×C414yes—
59C2×C13×C4⋊C4—22no—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—22no—
62C2×C13×C4⋊C4—22no—
63C2×C13×C4⋊C4—22no—
64C2×C13×C4⋊C4D414yescomplemented
65C2×C42×C13—22no—
66C2×C42×C13—22no—
67C2×C42×C13—22no—
68C2×C42×C13—22no—
69C2×C42×C13—22no—
70C2×C42×C13—22no—
71C2×C42×C13—22no—
72C2×C42×C13C2×C414yes—
73C2×C42×C13D414yes—
74C2×#6103—24no—
75C2×#6103—24no—
76C2×#6103—24no—
77C2×#6103—24no—
78C2×#6103—24no—
79C2×#6103—24no—
80C2×#6103—24no—
81C2×#6103—24no—
82C2×#6103—24no—
83C2×#6103—24no—
84C2×#6103—42no—
85C2×#6103—42no—
86C2×#6103—42no—
87C2×#6103—42no—
88C2×#6103—42no—
89C2×#6103—42no—
90C2×#6103C2×C418yes—
91C2×#6103C2×C418yes—
92C2×C4⋊Dic13—22no—
93C2×C4⋊Dic13—22no—
94C2×C4⋊Dic13—22no—
95C2×C4⋊Dic13—22no—
96C2×C4⋊Dic13—22no—
97C2×C4⋊Dic13—22no—
98C2×C4⋊Dic13—22no—
99C2×C4⋊Dic13C2×C414yes—
100C2×C4⋊Dic13D414yes—
101C2×C4×Dic13—24no—
102C2×C4×Dic13—24no—
103C2×C4×Dic13—42no—
104C13×#95—22no—
105C13×#95—22no—
106#88071—24no—
107#88071—24no—
108#88071—24no—
109#88071—42no—
110#88071—42no—
111#14022—131nomaximal, Sylow
112C24×C13C2411yescharacteristic
113C23×D13—22no—
114C23×D13—22no—
115C23×D13—22no—
116C23×D13—22no—
117C23×D13—22no—
118C23×D13—22no—
119C23×D13—22no—
120C23×D13—22no—
121C23×D13—22no—
122C23×D13—22no—
123C23×D13—22no—
124C23×D13—22no—
125C23×D13—22no—
126C23×D13—22no—
127C23×D13C22×C414yes—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13C22×C412yes—
161C22×C4×C13C22×C412yes—
162C22×C4×C13C22×C412yes—
163C22×C4×C13C2×D412yes—
164C22×C4×C13C2×D412yes—
165C22×C4×C13C2×D412yes—
166C22×C4×C13C2×D412yes—
167C22×C4×C13C2×D412yes—
168C22×C4×C13C2×D412yes—
169C22×C4×C13C2×D412yes—
170C22×C4×C13#4112yes—
171C22×C4×C13#4112yes—
172C22×C4×C13#4112yes—
173C22×C4×C13#4112yes—
174C22×C4×C13#4112yes—
175C22×C4×C13#4112yes—
176C22×C4×C13#4112yes—
177C22×Dic13—22no—
178C22×Dic13—22no—
179C22×Dic13—22no—
180C22×Dic13—22no—
181C22×Dic13—22no—
182C22×Dic13—22no—
183C22×Dic13—22no—
184C22×Dic13—22no—
185C22×Dic13—22no—
186C22×Dic13—22no—
187C22×Dic13—22no—
188C22×Dic13—22no—
189C22×Dic13—22no—
190C22×Dic13—22no—
191C22×Dic13—22no—
192C22×Dic13—22no—
193C22×Dic13—22no—
194C22×Dic13—22no—
195C22×Dic13—22no—
196C22×Dic13C22×C414yes—
197C22×Dic13C2×D414yes—
198C2×D52—28no—
199C2×D52—28no—
200C2×D52—28no—
201C2×D52—44no—
202C2×D52—44no—
203C2×D52—44no—
204C2×D52—44no—
205C13×C4⋊C4—28no—
206C13×C4⋊C4—28no—
207C42×C13—28no—
208C42×C13—28no—
209C42×C13—44no—
210#6103—216no—
211#6103—48no—
212#6103—48no—
213#6103—48no—
214#6103—48no—
215#6103—48no—
216C4⋊Dic13—28no—
217C4⋊Dic13—28no—
218C4⋊Dic13—44no—
219C4×Dic13—48no—
220C2×#390—131no—
221C2×#390—131no—
222C2×#390—131no—
223C2×#388—132no—
224C2×C4×C4⋊C4—131no—
225C2×C4×C4⋊C4D1311yescharacteristic, complemented
226#1440—132no—
227#1439—132no—
228#1437—132no—
229C4⋊#95—131no—
230C4⋊#95—131no—
231C23×C13C23×C411yescharacteristic
232C23×C13C22×D411yescharacteristic
233C23×C13C22×D411yescharacteristic
234C23×C13C22×D411yescharacteristic
235C23×C13C2×#4111yescharacteristic
236C23×C13C2×#4111yescharacteristic
237C23×C13C2×#4111yescharacteristic
238C23×C13C2×#4111yescharacteristic
239C23×C13C2×#4111yescharacteristic
240C23×C13C2×#4111yescharacteristic
241C23×C13C2×#4111yescharacteristic
242C23×C13H(5,𝔽2)11yescharacteristic
243C23×C13H(5,𝔽2)11yescharacteristic
244C23×C13H(5,𝔽2)11yescharacteristic
245C23×C132−1+411yescharacteristic
246C22×D13—24no—
247C22×D13—24no—
248C22×D13—24no—
249C22×D13—24no—
250C22×D13—24no—
251C22×D13—24no—
252C22×D13—24no—
253C22×D13—42no—
254C22×D13—42no—
255C22×D13—42no—
256C22×D13—42no—
257C22×D13—42no—
258C22×D13—42no—
259C22×D13—42no—
260C22×D13—42no—
261C22×D13—42no—
262C22×D13—42no—
263C22×D13—42no—
264C22×D13—42no—
265C22×D13—42no—
266C22×D13—42no—
267C22×D13—42no—
268C22×D13—42no—
269C22×D13—42no—
270C22×D13—42no—
271C22×D13—42no—
272C22×D13—42no—
273C22×D13—42no—
274C22×D13—42no—
275C22×D13—42no—
276C22×D13—42no—
277C22×D13—42no—
278C22×D13—42no—
279C22×D13—42no—
280C22×D13—42no—
281C2×C4×C13—22no—
282C2×C4×C13—22no—
283C2×C4×C13—22no—
284C2×C4×C13—22no—
285C2×C4×C13—22no—
286C2×C4×C13—22no—
287C2×C4×C13—22no—
288C2×C4×C13—22no—
289C2×C4×C13—22no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13—22no—
293C2×C4×C13—22no—
294C2×C4×C13—22no—
295C2×C4×C13—22no—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
299C2×C4×C13—22no—
300C2×C4×C13—22no—
301C2×C4×C13—22no—
302C2×C4×C13—22no—
303C2×C4×C13—22no—
304C2×C4×C13—22no—
305C2×C4×C13—41no—
306C2×C4×C13—41no—
307C2×C4×C13—41no—
308C2×C4×C13—41no—
309C2×C4×C13—41no—
310C2×C4×C13—41no—
311C2×C4×C13—41no—
312C2×C4×C13—41no—
313C2×C4×C13—41no—
314C2×C4×C13—41no—
315C2×C4×C13—41no—
316C2×C4×C13—41no—
317C2×C4×C13—41no—
318C2×C4×C13—41no—
319C2×C4×C13—41no—
320C2×C4×C13—41no—
321C2×C4×C13#11714yes—
322C2×C4×C13C4×D414yes—
323C2×C4×C13C4×D414yes—
324C2×C4×C13C4×D414yes—
325C2×C4×C13#12114yes—
326C2×C4×C13#12114yes—
327C2×C4×C13#12314yes—
328C2×C4×C13#12414yes—
329C2×C4×C13#12614yes—
330C2×Dic13—24no—
331C2×Dic13—24no—
332C2×Dic13—24no—
333C2×Dic13—24no—
334C2×Dic13—24no—
335C2×Dic13—24no—
336C2×Dic13—42no—
337C2×Dic13—42no—
338C2×Dic13—42no—
339C2×Dic13—42no—
340C2×Dic13—42no—
341C2×Dic13—42no—
342C2×Dic13—42no—
343C2×Dic13—42no—
344C2×Dic13—42no—
345C2×Dic13—42no—
346C2×Dic13—42no—
347C2×Dic13—42no—
348C2×Dic13—42no—
349C2×Dic13—42no—
350C2×Dic13—42no—
351D52—416no—
352C23×D4—131no—
353C22×C4⋊C4—131no—
354C22×C4⋊C4—131no—
355C22×C4⋊C4—131no—
356C22×C4⋊C4C2×D1311yescharacteristic
357C22×C4⋊C4C2×D1311yescharacteristic
358C22×C22⋊C4—132no—
359C22×C22⋊C4—132no—
360C22×C22⋊C4—132no—
361C22×C22⋊C4—132no—
362C22×C22⋊C4—132no—
363C22×C22⋊C4—132no—
364C22×C42—132no—
365C22×C42C2×D1311yescharacteristic
366C22×C42C2×D1311yescharacteristic
367C22×C42C2×D1311yescharacteristic
368#390—138no—
369#390—264no—
370#390—264no—
371#388—268no—
372C4×C4⋊C4—24no—
373C4×C4⋊C4—264no—
374C2×#95—132no—
375C2×#95—132no—
376C2×#95—132no—
377C2×#95—132no—
378C2×#95—132no—
379C2×#95C2×D1311yescharacteristic
380C2×#95C2×D1311yescharacteristic
381C22×C13C2×#11711yescharacteristic
382C22×C13C2×C4×D411yescharacteristic
383C22×C13C2×C4×D411yescharacteristic
384C22×C13C2×C4×D411yescharacteristic
385C22×C13C4×#4111yescharacteristic
386C22×C13#51811yescharacteristic
387C22×C13#52011yescharacteristic
388C22×C13C2×#12111yescharacteristic
389C22×C13C2×#12111yescharacteristic
390C22×C13C2×#12311yescharacteristic
391C22×C13#52511yescharacteristic
392C22×C13C2×#12411yescharacteristic
393C22×C13C2×#12611yescharacteristic
394C22×C13#52911yescharacteristic
395C22×C13#53211yescharacteristic
396C22×C13#53511yescharacteristic
397C22×C13#53711yescharacteristic
398C22×C13#54011yescharacteristic
399C22×C13#54211yescharacteristic
400C22×C13D4211yescharacteristic
401C22×C13#54611yescharacteristic
402C22×C13#54711yescharacteristic
403C22×C13#54811yescharacteristic
404C22×C13#55011yescharacteristic
405C22×C13#55011yescharacteristic
406C22×C13#55011yescharacteristic
407C22×C13#55311yescharacteristic
408C22×C13#55311yescharacteristic
409C22×C13#55511yescharacteristic
410C22×C13#55611yescharacteristic
411C22×C13#55611yescharacteristic
412C22×C13#55911yescharacteristic
413C22×C13#55911yescharacteristic
414C22×C13#55911yescharacteristic
415C22×C13#55911yescharacteristic
416C2×D13—44no—
417C2×D13—44no—
418C2×D13—44no—
419C2×D13—44no—
420C2×D13—44no—
421C2×D13—44no—
422C2×D13—44no—
423C2×D13—82no—
424C2×D13—82no—
425C2×D13—82no—
426C2×D13—82no—
427C2×D13—82no—
428C2×D13—82no—
429C2×D13—82no—
430C2×D13—82no—
431C4×C13—24no—
432C4×C13—24no—
433C4×C13—42no—
434C4×C13—42no—
435C4×C13—42no—
436C4×C13—42no—
437C4×C13#38818yescomplemented
438Dic13—44no—
439Dic13—44no—
440Dic13—82no—
441C25—132no—
442C22×D4—134no—
443C22×D4—262no—
444C22×D4—262no—
445C22×D4—262no—
446C22×D4—262no—
447C22×D4—262no—
448C22×D4—262no—
449C23×C4—132no—
450C23×C4—132no—
451C23×C4—132no—
452C23×C4C22×D1311yescharacteristic
453C23×C4C22×D1311yescharacteristic
454C23×C4C22×D1311yescharacteristic
455C23×C4C22×D1311yescharacteristic
456C23×C4C22×D1311yescharacteristic
457C23×C4C22×D1311yescharacteristic
458C23×C4C22×D1311yescharacteristic
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—134no—
465C2×C4⋊C4—134no—
466C2×C4⋊C4—262no—
467C2×C4⋊C4—262no—
468C2×C4⋊C4—262no—
469C2×C4⋊C4—262no—
470C2×C4⋊C4—262no—
471C2×C4⋊C4—262no—
472C2×C4⋊C4—262no—
473C2×C4⋊C4D5214yescomplemented
474C2×C22⋊C4—138no—
475C2×C22⋊C4—138no—
476C2×C22⋊C4—264no—
477C2×C22⋊C4—264no—
478C2×C22⋊C4—264no—
479C2×C22⋊C4—264no—
480C2×C22⋊C4—264no—
481C2×C22⋊C4—264no—
482C2×C22⋊C4—264no—
483C2×C22⋊C4—264no—
484C2×C22⋊C4—264no—
485C2×C22⋊C4—264no—
486C2×C22⋊C4—522no—
487C2×C22⋊C4—522no—
488C2×C22⋊C4—522no—
489C2×C22⋊C4—522no—
490C2×C22⋊C4—522no—
491C2×C22⋊C4—522no—
492C2×C42—22no—
493C2×C42—22no—
494C2×C42—22no—
495C2×C42—22no—
496C2×C42—22no—
497C2×C42—22no—
498C2×C42—22no—
499C2×C42—264no—
500C2×C42—264no—
501C2×C42—522no—
502C2×C42C4×D1314yes—
503C2×C42C22⋊D1314yes—
504#95—22no—
505#95—22no—
506#95—264no—
507#95—264no—
508#95—264no—
509#95—522no—
510#95—522no—
511C2×C13C2×#38811yescharacteristic
512C2×C13C4×#12111yescharacteristic
513C2×C13#232411yescharacteristic
514C2×C13#235411yescharacteristic
515C2×C13#235711yescharacteristic
516C2×C13#236611yescharacteristic
517C2×C13#236711yescharacteristic
518C2×C13#241411yescharacteristic
519C2×C13#241611yescharacteristic
520C2×C13#244511yescharacteristic
521C2×C13#244811yescharacteristic
522C2×C13#251211yescharacteristic
523C2×C13#251311yescharacteristic
524C2×C13#254811yescharacteristic
525C2×C13#259211yescharacteristic
526D13—84no—
527C24—134no—
528C24—262no—
529C24—262no—
530C24—262no—
531C24—262no—
532C24—262no—
533C24—262no—
534C24—262no—
535C24—262no—
536C24—262no—
537C24—262no—
538C24—262no—
539C24—262no—
540C24—262no—
541C24—262no—
542C24C23×D1311yescharacteristic
543C2×D4—268no—
544C2×D4—268no—
545C2×D4—268no—
546C2×D4—524no—
547C2×D4—524no—
548C2×D4—524no—
549C2×D4—524no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—134no—
583C22×C4—134no—
584C22×C4—262no—
585C22×C4—262no—
586C22×C4—262no—
587C22×C4—262no—
588C22×C4—262no—
589C22×C4—262no—
590C22×C4—262no—
591C22×C4—262no—
592C22×C4—262no—
593C22×C4—262no—
594C22×C4—262no—
595C22×C4—262no—
596C22×C4—262no—
597C22×C4—262no—
598C22×C4—262no—
599C22×C4—262no—
600C22×C4—262no—
601C22×C4—262no—
602C22×C4—262no—
603C22×C4C2×C4×D1312yes—
604C22×C4C2×C4×D1312yes—
605C22×C4C2×C4×D1312yes—
606C22×C4C2×D5212yes—
607C22×C4C2×D5212yes—
608C22×C4C2×D5212yes—
609C22×C4#612712yes—
610C22×C4#612712yes—
611C22×C4#612712yes—
612C22×C4#612712yes—
613C22×C4D4×D1312yes—
614C22×C4#612912yes—
615C22×C4#613112yes—
616C22×C4#613112yes—
617C22×C4C2×C22⋊D1312yes—
618C22×C4C2×C22⋊D1312yes—
619C22×C4C2×C22⋊D1312yes—
620C4⋊C4—28no—
621C4⋊C4—28no—
622C4⋊C4—268no—
623C4⋊C4—268no—
624C4⋊C4—524no—
625C22⋊C4—2616no—
626C22⋊C4—528no—
627C22⋊C4—528no—
628C22⋊C4—528no—
629C22⋊C4—528no—
630C22⋊C4—528no—
631C42—28no—
632C42—28no—
633C42—44no—
634C42—528no—
635C13#1402211yescharacteristic, complemented, Sylow
636C23—264no—
637C23—264no—
638C23—264no—
639C23—264no—
640C23—264no—
641C23—264no—
642C23—264no—
643C23—522no—
644C23—522no—
645C23—522no—
646C23—522no—
647C23—522no—
648C23—522no—
649C23—522no—
650C23—522no—
651C23—522no—
652C23—522no—
653C23—522no—
654C23—522no—
655C23—522no—
656C23—522no—
657C23—522no—
658C23—522no—
659C23—522no—
660C23—522no—
661C23—522no—
662C23—522no—
663C23—522no—
664C23—522no—
665C23—522no—
666C23—522no—
667C23—522no—
668C23—522no—
669C23—522no—
670C23—522no—
671C23C22×C4×D1311yescharacteristic
672C23C22×D5211yescharacteristic
673C23C2×#612711yescharacteristic
674C23C2×#612711yescharacteristic
675C23C2×#612711yescharacteristic
676C23C2×#612711yescharacteristic
677C23C2×D4×D1311yescharacteristic
678C23C2×#612911yescharacteristic
679C23C2×#613111yescharacteristic
680C23C2×#613111yescharacteristic
681C23#8825611yescharacteristic
682C23#8825611yescharacteristic
683C23#8825611yescharacteristic
684C23#8825711yescharacteristic
685C23C22×C22⋊D1311yescharacteristic
686D4—5216no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—264no—
728C2×C4—264no—
729C2×C4—264no—
730C2×C4—264no—
731C2×C4—264no—
732C2×C4—264no—
733C2×C4—522no—
734C2×C4—522no—
735C2×C4—522no—
736C2×C4—522no—
737C2×C4—522no—
738C2×C4—522no—
739C2×C4—522no—
740C2×C4—522no—
741C2×C4—522no—
742C2×C4—522no—
743C2×C4—522no—
744C2×C4—522no—
745C2×C4—522no—
746C2×C4—522no—
747C2×C4—522no—
748C2×C4C4×D5214yes—
749C2×C4#8814614yes—
750C2×C4#8814714yes—
751C2×C4#8814814yes—
752C2×C4#8815214yes—
753C2×C4C4×C22⋊D1314yes—
754C2×C4#8818414yes—
755C2×C4#8819314yes—
756C2×C4#8820114yes—
757C22—524no—
758C22—524no—
759C22—524no—
760C22—524no—
761C22—524no—
762C22—524no—
763C22—524no—
764C22—1042no—
765C22—1042no—
766C22—1042no—
767C22—1042no—
768C22—1042no—
769C22—1042no—
770C22—1042no—
771C22—1042no—
772C22C2×C4×D5211yescharacteristic
773C22C4×#612711yescharacteristic
774C22#1171918211yescharacteristic
775C22#1171918411yescharacteristic
776C22C2×#8814611yescharacteristic
777C22C2×#8814711yescharacteristic
778C22C2×#8814811yescharacteristic
779C22C2×#8815211yescharacteristic
780C22#1171922611yescharacteristic
781C22#1171922811yescharacteristic
782C22#1171923911yescharacteristic
783C22#1171924011yescharacteristic
784C22D4×D5211yescharacteristic
785C22#1171925511yescharacteristic
786C22#1171925711yescharacteristic
787C22#1171925811yescharacteristic
788C22#1171926011yescharacteristic
789C22#1171926811yescharacteristic
790C22#1171927011yescharacteristic
791C22#1171927011yescharacteristic
792C22#1171928211yescharacteristic
793C22#1171928211yescharacteristic
794C22#1171928911yescharacteristic
795C22#1171928911yescharacteristic
796C22#1171929011yescharacteristic
797C22#1171929011yescharacteristic
798C22#1171929011yescharacteristic
799C22#1171929011yescharacteristic
800C22C2×C4×C22⋊D1311yescharacteristic
801C22C2×#8818411yescharacteristic
802C22#1171949611yescharacteristic
803C22C2×#8819311yescharacteristic
804C22C2×#8820111yescharacteristic
805C22#1171953511yescharacteristic
806C22#1171953811yescharacteristic
807C4—24no—
808C4—24no—
809C4—42no—
810C4—42no—
811C4—42no—
812C4—42no—
813C4—524no—
814C4—524no—
815C4—1042no—
816C4#1171865118yescomplemented
817C2—1044no—
818C2C2×#1171865111yescharacteristic
819C2C4×#8818411yescharacteristic
820C2#1311752911yescharacteristic
821C2#1311778311yescharacteristic
822C2#1311780711yescharacteristic
823C2#1311790011yescharacteristic
824C2#1311790511yescharacteristic
825C2#1311825411yescharacteristic
826C2#1311827611yescharacteristic
827C2#1311860111yescharacteristic
828C2#1311863411yescharacteristic
829C2#1311942211yescharacteristic
830C2#1311943311yescharacteristic
831C2#1311983511yescharacteristic
832C2#1312032411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C4×C13×C4⋊C4C2
socle, cosocleC24×C13C24
prime radicalC23×D52C22
hypercenterC2×C4×C4⋊C4D13
hypocenterC13#14022
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×#11718651C2semidirect
5. C2×C4×C4⋊Dic13C2semidirect
6. #13113084C2semidirect
7. #13113078C2semidirect
8. #13113072C2semidirect
9. #13113066C2semidirect
10. #13113066C2semidirect
11. C2×C4×C13×C4⋊C4C2semidirect
39. #11718600C4semidirect
64. C2×C13×C4⋊C4D4semidirect
225. C2×C4×C4⋊C4D13semidirect
437. C4×C13#388semidirect
473. C2×C4⋊C4D52semidirect
635. C13#14022semidirect
816. C4#11718651semidirect

Maximal subgroups

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

subgroupindex
C2×#117186002
C2×#117186512
C2×C4×C4⋊Dic132
#131130842
#131130782
#131130722
#131130662
C2×C4×C13×C4⋊C42
#1402213