Finite Group Databasebeta

← #15784873

Subgroups — #15784873

Order 3328.

1846 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718651C212yesmaximal
2C2×#11718648C211yesmaximal, characteristic
3C2×#11718648C211yesmaximal, characteristic
4C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
5C2×C4×#6103C211yesmaximal, characteristic
6#13113095C212yesmaximal, complemented
7#13113078C212yesmaximal
8#13113068C212yesmaximal, complemented
9#13113066C211yesmaximal, characteristic, complemented
10#13113065C211yesmaximal, characteristic, complemented
11C2×C13×#384C211yesmaximal, characteristic, complemented
12C23×C4×D13C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2212yes—
15C22×C13×C4⋊C4C2212yes—
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C42×C13C2211yescharacteristic
18C22×#6103C2212yes—
19C22×#6103C2212yes—
20C22×#6103C2211yescharacteristic
21C22×#6103C2211yescharacteristic
22C22×C4⋊Dic13C2211yescharacteristic
23C22×C4⋊Dic13C2211yescharacteristic
24C22×C4×Dic13C2212yes—
25C22×C4×Dic13C2211yescharacteristic
26C13×#384—24no—
27C2×#88071C2212yes—
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2211yescharacteristic
35C2×#88071C2211yescharacteristic
36#11718651—28no—
37#11718648—24no—
38#11718648—24no—
39C4⋊C4×Dic13—24no—
40C4×#6103C418yescomplemented
41C24×D13C2311yescharacteristic
42C23×C4×C13C2312yes—
43C23×C4×C13C2312yes—
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2311yescharacteristic
46C23×C4×C13C2311yescharacteristic
47C23×Dic13C2312yes—
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2312yes—
51C23×Dic13C2311yescharacteristic
52C22×C4×D13—22no—
53C22×C4×D13—22no—
54C22×C4×D13—22no—
55C22×C4×D13—22no—
56C22×C4×D13—22no—
57C22×C4×D13—22no—
58C22×C4×D13C2×C414yes—
59C2×C13×C4⋊C4—22no—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—24no—
62C2×C13×C4⋊C4—24no—
63C2×C13×C4⋊C4—22no—
64C2×C13×C4⋊C4—22no—
65C2×C13×C4⋊C4—24no—
66C2×C13×C4⋊C4—24no—
67C2×C13×C4⋊C4—22no—
68C2×C13×C4⋊C4—42no—
69C2×C13×C4⋊C4—42no—
70C2×C13×C4⋊C4D414yes—
71C2×C42×C13—22no—
72C2×C42×C13—22no—
73C2×C42×C13C2×C414yes—
74C2×#6103—22no—
75C2×#6103—22no—
76C2×#6103—24no—
77C2×#6103—24no—
78C2×#6103—24no—
79C2×#6103—24no—
80C2×#6103—42no—
81C2×#6103—42no—
82C2×#6103C2×C414yes—
83C2×#6103C2×C414yes—
84C2×#6103D414yes—
85C2×#6103Q814yes—
86C2×C4⋊Dic13—22no—
87C2×C4⋊Dic13—22no—
88C2×C4⋊Dic13—22no—
89C2×C4⋊Dic13—22no—
90C2×C4⋊Dic13—22no—
91C2×C4⋊Dic13D414yes—
92C2×C4×Dic13—22no—
93C2×C4×Dic13—22no—
94C2×C4×Dic13—24no—
95C2×C4×Dic13—24no—
96C2×C4×Dic13—42no—
97C2×C4×Dic13C2×C414yes—
98#88071—24no—
99#88071—24no—
100#88071—24no—
101#88071—24no—
102#88071—24no—
103#88071—24no—
104#88071—42no—
105#88071C2×C414yes—
106#88071C2×C414yes—
107#13876—131nomaximal, Sylow
108C24×C13C2411yescharacteristic
109C23×D13—21no—
110C23×D13—21no—
111C23×D13—21no—
112C23×D13—21no—
113C23×D13—21no—
114C23×D13—21no—
115C23×D13—21no—
116C23×D13—21no—
117C23×D13—21no—
118C23×D13—21no—
119C23×D13—21no—
120C23×D13—21no—
121C23×D13C22×C412yes—
122C23×D13C2×D412yes—
123C23×D13C2×Q812yes—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—22no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—22no—
140C22×C4×C13—22no—
141C22×C4×C13—22no—
142C22×C4×C13—22no—
143C22×C4×C13—22no—
144C22×C4×C13—22no—
145C22×C4×C13C22×C412yes—
146C22×C4×C13C22×C412yes—
147C22×C4×C13C22×C412yes—
148C22×C4×C13C2×D412yes—
149C22×C4×C13C2×D412yes—
150C22×C4×C13C2×D414yes—
151C22×C4×C13C2×D412yes—
152C22×C4×C13C2×Q812yes—
153C22×C4×C13#4112yes—
154C22×C4×C13#4112yes—
155C22×C4×C13#4112yes—
156C22×C4×C13#4112yes—
157C22×C4×C13#4112yes—
158C22×C4×C13#4112yes—
159C22×Dic13—21no—
160C22×Dic13—21no—
161C22×Dic13—21no—
162C22×Dic13—21no—
163C22×Dic13—21no—
164C22×Dic13—21no—
165C22×Dic13—21no—
166C22×Dic13—22no—
167C22×Dic13—22no—
168C22×Dic13—21no—
169C22×Dic13—22no—
170C22×Dic13—22no—
171C22×Dic13—21no—
172C22×Dic13—21no—
173C22×Dic13—21no—
174C22×Dic13—21no—
175C22×Dic13—21no—
176C22×Dic13—21no—
177C22×Dic13—21no—
178C22×Dic13—22no—
179C22×Dic13—21no—
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×Dic13C22×C412yes—
189C22×Dic13C22×C412yes—
190C22×Dic13C22×C412yes—
191C22×Dic13C2×D414yes—
192C22×Dic13C2×D412yes—
193C22×Dic13C2×Q812yes—
194C2×C4×D13—28no—
195C2×C4×D13—28no—
196C2×C4×D13—28no—
197C2×C4×D13—44no—
198C2×C4×D13—44no—
199C2×C4×D13—44no—
200C2×C4×D13—44no—
201C13×C4⋊C4—28no—
202C13×C4⋊C4—48no—
203C13×C4⋊C4—48no—
204C13×C4⋊C4—44no—
205C42×C13—28no—
206#6103—28no—
207#6103—48no—
208#6103—48no—
209#6103C4⋊C4116yescomplemented
210C4⋊Dic13—28no—
211C4⋊Dic13—44no—
212C4×Dic13—28no—
213C4×Dic13—48no—
214C2×#388—132no—
215C2×#384D1311yescharacteristic, complemented
216C2×#380—131no—
217C2×#380—131no—
218C2×C4×C4⋊C4—131no—
219C2×C4×C22⋊C4—131no—
220#1442—132no—
221#1439—132no—
222#1436—132no—
223C4⋊#95—131no—
224C4⋊#95—131no—
225C23×C13C23×C411yescharacteristic
226C23×C13C22×D411yescharacteristic
227C23×C13C22×D411yescharacteristic
228C23×C13C22×D411yescharacteristic
229C23×C13C22×Q811yescharacteristic
230C23×C13C2×#4111yescharacteristic
231C23×C13C2×#4111yescharacteristic
232C23×C13C2×#4111yescharacteristic
233C23×C13C2×#4111yescharacteristic
234C23×C13C2×#4111yescharacteristic
235C23×C13C2×#4111yescharacteristic
236C23×C13H(5,𝔽2)11yescharacteristic
237C23×C13H(5,𝔽2)11yescharacteristic
238C23×C132−1+411yescharacteristic
239C23×C132−1+411yescharacteristic
240C22×D13—22no—
241C22×D13—22no—
242C22×D13—22no—
243C22×D13—22no—
244C22×D13—22no—
245C22×D13—22no—
246C22×D13—22no—
247C22×D13—22no—
248C22×D13—22no—
249C22×D13—22no—
250C22×D13—22no—
251C22×D13—22no—
252C22×D13—22no—
253C22×D13—22no—
254C22×D13—22no—
255C22×D13—22no—
256C22×D13—22no—
257C22×D13—22no—
258C22×D13—41no—
259C22×D13—41no—
260C22×D13—41no—
261C22×D13—41no—
262C22×D13—41no—
263C22×D13—41no—
264C22×D13—41no—
265C22×D13—41no—
266C22×D13—41no—
267C22×D13—41no—
268C22×D13—41no—
269C22×D13—41no—
270C22×D13—41no—
271C22×D13—41no—
272C22×D13—41no—
273C22×D13—41no—
274C22×D13C2×C4⋊C414yes—
275C2×C4×C13—22no—
276C2×C4×C13—22no—
277C2×C4×C13—22no—
278C2×C4×C13—22no—
279C2×C4×C13—22no—
280C2×C4×C13—22no—
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—24no—
288C2×C4×C13—24no—
289C2×C4×C13—24no—
290C2×C4×C13—42no—
291C2×C4×C13—42no—
292C2×C4×C13—42no—
293C2×C4×C13—42no—
294C2×C4×C13—42no—
295C2×C4×C13—42no—
296C2×C4×C13—42no—
297C2×C4×C13—42no—
298C2×C4×C13—42no—
299C2×C4×C13—42no—
300C2×C4×C13—42no—
301C2×C4×C13C2×C4⋊C414yes—
302C2×C4×C13#11714yes—
303C2×C4×C13#11714yes—
304C2×C4×C13C4×D414yes—
305C2×C4×C13C4×D414yes—
306C2×C4×C13#12114yes—
307C2×C4×C13#12314yes—
308C2×C4×C13#12414yes—
309C2×C4×C13#12614yes—
310C2×Dic13—22no—
311C2×Dic13—22no—
312C2×Dic13—22no—
313C2×Dic13—22no—
314C2×Dic13—22no—
315C2×Dic13—22no—
316C2×Dic13—22no—
317C2×Dic13—22no—
318C2×Dic13—22no—
319C2×Dic13—22no—
320C2×Dic13—22no—
321C2×Dic13—22no—
322C2×Dic13—24no—
323C2×Dic13—24no—
324C2×Dic13—24no—
325C2×Dic13—41no—
326C2×Dic13—41no—
327C2×Dic13—41no—
328C2×Dic13—41no—
329C2×Dic13—42no—
330C2×Dic13—42no—
331C2×Dic13—41no—
332C2×Dic13—42no—
333C2×Dic13—41no—
334C2×Dic13—42no—
335C2×Dic13—41no—
336C2×Dic13—41no—
337C2×Dic13—42no—
338C2×Dic13—42no—
339C2×Dic13—42no—
340C2×Dic13—42no—
341C2×Dic13—42no—
342C2×Dic13—42no—
343C2×Dic13—42no—
344C2×Dic13C2×C4⋊C414yes—
345C4×D13—416no—
346C24×C4—131no—
347C22×C4⋊C4—131no—
348C22×C4⋊C4—131no—
349C22×C4⋊C4C2×D1311yescharacteristic
350C22×C4⋊C4C2×D1312yes—
351C22×C4⋊C4C2×D1312yes—
352C22×C4⋊C4C2×D1311yescharacteristic
353C22×C22⋊C4—131no—
354C22×C22⋊C4—131no—
355C22×C22⋊C4—132no—
356C22×C22⋊C4—132no—
357C22×C42—131no—
358C22×C42—132no—
359C22×C42C2×D1311yescharacteristic
360#388—268no—
361#384—24no—
362#380—264no—
363#380—264no—
364C4×C4⋊C4—264no—
365C4×C22⋊C4—138no—
366C2×#95—131no—
367C2×#95—131no—
368C2×#95—132no—
369C2×#95—132no—
370C2×#95—132no—
371C2×#95—132no—
372C2×#95—132no—
373C2×#95—132no—
374C2×#95—132no—
375C22×C13C22×C4⋊C411yescharacteristic
376C22×C13C2×#11711yescharacteristic
377C22×C13C2×#11711yescharacteristic
378C22×C13C2×C4×D411yescharacteristic
379C22×C13C2×C4×D411yescharacteristic
380C22×C13#52011yescharacteristic
381C22×C13#52011yescharacteristic
382C22×C13C2×#12111yescharacteristic
383C22×C13C2×#12311yescharacteristic
384C22×C13C2×#12411yescharacteristic
385C22×C13C2×#12611yescharacteristic
386C22×C13#53211yescharacteristic
387C22×C13#53211yescharacteristic
388C22×C13#53311yescharacteristic
389C22×C13#53311yescharacteristic
390C22×C13#54011yescharacteristic
391C22×C13#54111yescharacteristic
392C22×C13#54211yescharacteristic
393C22×C13#54211yescharacteristic
394C22×C13D4211yescharacteristic
395C22×C13D4211yescharacteristic
396C22×C13#54611yescharacteristic
397C22×C13#54711yescharacteristic
398C22×C13#54711yescharacteristic
399C22×C13#54711yescharacteristic
400C22×C13#54811yescharacteristic
401C22×C13D4×Q811yescharacteristic
402C22×C13D4×Q811yescharacteristic
403C22×C13#55011yescharacteristic
404C22×C13#55211yescharacteristic
405C22×C13#55311yescharacteristic
406C22×C13#55411yescharacteristic
407C22×C13#55411yescharacteristic
408C22×C13#55511yescharacteristic
409C22×C13#55611yescharacteristic
410C2×D13—24no—
411C2×D13—24no—
412C2×D13—24no—
413C2×D13—42no—
414C2×D13—42no—
415C2×D13—42no—
416C2×D13—42no—
417C2×D13—42no—
418C2×D13—42no—
419C2×D13—42no—
420C2×D13—42no—
421C2×D13—42no—
422C2×D13—42no—
423C2×D13—42no—
424C2×D13—42no—
425C4×C13—24no—
426C4×C13—24no—
427C4×C13—44no—
428C4×C13—82no—
429C4×C13#38818yescomplemented
430Dic13—24no—
431Dic13—42no—
432Dic13—44no—
433Dic13—42no—
434Dic13—82no—
435C25—131no—
436C23×C4—131no—
437C23×C4—132no—
438C23×C4—131no—
439C23×C4—131no—
440C23×C4—134no—
441C23×C4—132no—
442C23×C4—262no—
443C23×C4—262no—
444C23×C4—262no—
445C23×C4—262no—
446C23×C4—262no—
447C23×C4—262no—
448C23×C4C22×D1312yes—
449C23×C4C22×D1312yes—
450C23×C4C22×D1311yescharacteristic
451C23×C4C22×D1311yescharacteristic
452C23×C4C22×D1311yescharacteristic
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—24no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—24no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4—134no—
465C2×C4⋊C4—262no—
466C2×C4⋊C4—262no—
467C2×C4⋊C4—262no—
468C2×C4⋊C4—262no—
469C2×C4⋊C4—262no—
470C2×C4⋊C4C22⋊D1314yes—
471C2×C22⋊C4—134no—
472C2×C22⋊C4—134no—
473C2×C22⋊C4—134no—
474C2×C22⋊C4—134no—
475C2×C22⋊C4—262no—
476C2×C22⋊C4—262no—
477C2×C22⋊C4—264no—
478C2×C22⋊C4—264no—
479C2×C22⋊C4—264no—
480C2×C22⋊C4—264no—
481C2×C22⋊C4—522no—
482C2×C22⋊C4—522no—
483C2×C42—22no—
484C2×C42—22no—
485C2×C42—134no—
486C2×C42—262no—
487C2×C42—262no—
488C2×C42—264no—
489C2×C42—264no—
490C2×C42—522no—
491C2×C42C4×D1314yes—
492#95—134no—
493#95—134no—
494#95—264no—
495#95—264no—
496#95—264no—
497#95—264no—
498#95—264no—
499#95—264no—
500#95—522no—
501C2×C13#228511yescharacteristic
502C2×C13C2×#38811yescharacteristic
503C2×C13#231411yescharacteristic
504C2×C13D4×C4⋊C411yescharacteristic
505C2×C13D4×C4⋊C411yescharacteristic
506C2×C13#235211yescharacteristic
507C2×C13#235411yescharacteristic
508C2×C13#242211yescharacteristic
509C2×C13#242311yescharacteristic
510C2×C13#242811yescharacteristic
511C2×C13#242911yescharacteristic
512C2×C13#249111yescharacteristic
513C2×C13#249211yescharacteristic
514C2×C13#249611yescharacteristic
515C2×C13#249711yescharacteristic
516D13—44no—
517C24—132no—
518C24—132no—
519C24—132no—
520C24—261no—
521C24—261no—
522C24—261no—
523C24—261no—
524C24—261no—
525C24—261no—
526C24—261no—
527C24—261no—
528C24—261no—
529C24—261no—
530C24—261no—
531C24—261no—
532C24C23×D1311yescharacteristic
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—132no—
555C22×C4—132no—
556C22×C4—132no—
557C22×C4—132no—
558C22×C4—132no—
559C22×C4—134no—
560C22×C4—261no—
561C22×C4—261no—
562C22×C4—261no—
563C22×C4—261no—
564C22×C4—262no—
565C22×C4—261no—
566C22×C4—261no—
567C22×C4—261no—
568C22×C4—262no—
569C22×C4—261no—
570C22×C4—261no—
571C22×C4—261no—
572C22×C4—262no—
573C22×C4—262no—
574C22×C4—261no—
575C22×C4—261no—
576C22×C4—262no—
577C22×C4—261no—
578C22×C4—261no—
579C22×C4—262no—
580C22×C4—261no—
581C22×C4—261no—
582C22×C4—268no—
583C22×C4—268no—
584C22×C4—268no—
585C22×C4—262no—
586C22×C4—262no—
587C22×C4—262no—
588C22×C4—262no—
589C22×C4—262no—
590C22×C4—262no—
591C22×C4—262no—
592C22×C4—524no—
593C22×C4—524no—
594C22×C4—524no—
595C22×C4—524no—
596C22×C4C2×C4×D1312yes—
597C22×C4C2×C4×D1312yes—
598C22×C4C2×C4×D1312yes—
599C22×C4#612712yes—
600C22×C4D4×D1312yes—
601C22×C4D4×D1312yes—
602C22×C4#612912yes—
603C22×C4#612912yes—
604C22×C4Q8×D1312yes—
605C22×C4#613112yes—
606C22×C4#613112yes—
607C22×C4#613112yes—
608C22×C4C2×C22⋊D1314yes—
609C22×C4C2×C22⋊D1312yes—
610C4⋊C4—28no—
611C4⋊C4—48no—
612C4⋊C4—48no—
613C4⋊C4—44no—
614C4⋊C4—268no—
615C4⋊C4—524no—
616C22⋊C4—1316no—
617C22⋊C4—268no—
618C22⋊C4—528no—
619C22⋊C4—528no—
620C42—28no—
621C42—268no—
622C42—528no—
623C13#1387611yescharacteristic, complemented, Sylow
624C23—134no—
625C23—262no—
626C23—262no—
627C23—262no—
628C23—262no—
629C23—262no—
630C23—262no—
631C23—262no—
632C23—262no—
633C23—262no—
634C23—262no—
635C23—262no—
636C23—262no—
637C23—262no—
638C23—262no—
639C23—262no—
640C23—262no—
641C23—262no—
642C23—262no—
643C23—521no—
644C23—521no—
645C23—521no—
646C23—521no—
647C23—521no—
648C23—521no—
649C23—521no—
650C23—521no—
651C23—521no—
652C23—521no—
653C23—521no—
654C23—521no—
655C23—521no—
656C23—521no—
657C23—521no—
658C23—521no—
659C23C22×C4×D1311yescharacteristic
660C23C2×#612711yescharacteristic
661C23C2×D4×D1311yescharacteristic
662C23C2×D4×D1311yescharacteristic
663C23C2×#612911yescharacteristic
664C23C2×#612911yescharacteristic
665C23#8825111yescharacteristic
666C23#8825111yescharacteristic
667C23C2×Q8×D1311yescharacteristic
668C23C2×#613111yescharacteristic
669C23C2×#613111yescharacteristic
670C23C2×#613111yescharacteristic
671C23#8825411yescharacteristic
672C23#8825411yescharacteristic
673C23C22×C22⋊D1311yescharacteristic
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—134no—
701C2×C4—262no—
702C2×C4—262no—
703C2×C4—262no—
704C2×C4—262no—
705C2×C4—262no—
706C2×C4—262no—
707C2×C4—264no—
708C2×C4—262no—
709C2×C4—262no—
710C2×C4—262no—
711C2×C4—262no—
712C2×C4—262no—
713C2×C4—264no—
714C2×C4—262no—
715C2×C4—264no—
716C2×C4—522no—
717C2×C4—521no—
718C2×C4—521no—
719C2×C4—522no—
720C2×C4—521no—
721C2×C4—521no—
722C2×C4—522no—
723C2×C4—521no—
724C2×C4—522no—
725C2×C4—521no—
726C2×C4—521no—
727C2×C4—521no—
728C2×C4—5216no—
729C2×C4—522no—
730C2×C4—522no—
731C2×C4—522no—
732C2×C4—522no—
733C2×C4—522no—
734C2×C4—522no—
735C2×C4—522no—
736C2×C4C4⋊C4×D1314yes—
737C2×C4#8814614yes—
738C2×C4#8814614yes—
739C2×C4#8814714yes—
740C2×C4#8814814yes—
741C2×C4#8815214yes—
742C2×C4C4×C22⋊D1314yes—
743C2×C4#8819314yes—
744C2×C4#8820114yes—
745C22—264no—
746C22—264no—
747C22—264no—
748C22—522no—
749C22—522no—
750C22—522no—
751C22—522no—
752C22—522no—
753C22—522no—
754C22—522no—
755C22—522no—
756C22—522no—
757C22—522no—
758C22—522no—
759C22—522no—
760C22C2×C4⋊C4×D1311yescharacteristic
761C22C2×#8814611yescharacteristic
762C22C2×#8814611yescharacteristic
763C22C2×#8814711yescharacteristic
764C22#1171920911yescharacteristic
765C22#1171920911yescharacteristic
766C22C2×#8814811yescharacteristic
767C22#1171921211yescharacteristic
768C22#1171921611yescharacteristic
769C22C2×#8815211yescharacteristic
770C22#1171921811yescharacteristic
771C22#1171921911yescharacteristic
772C22#1171942111yescharacteristic
773C22#1171942211yescharacteristic
774C22#1171942311yescharacteristic
775C22#1171942411yescharacteristic
776C22#1171943011yescharacteristic
777C22#1171943111yescharacteristic
778C22#1171943111yescharacteristic
779C22#1171943211yescharacteristic
780C22#1171943311yescharacteristic
781C22#1171943311yescharacteristic
782C22#1171943511yescharacteristic
783C22#1171943611yescharacteristic
784C22#1171943711yescharacteristic
785C22#1171943811yescharacteristic
786C22#1171943811yescharacteristic
787C22#1171943911yescharacteristic
788C22C2×C4×C22⋊D1311yescharacteristic
789C22D4×C22⋊D1311yescharacteristic
790C22C2×#8819311yescharacteristic
791C22#1171951111yescharacteristic
792C22C2×#8820111yescharacteristic
793C22Q8×C22⋊D1311yescharacteristic
794C22#1171952211yescharacteristic
795C4—24no—
796C4—24no—
797C4—44no—
798C4—82no—
799C4—264no—
800C4—522no—
801C4—522no—
802C4—524no—
803C4—1042no—
804C4#1171865118yescomplemented
805C2—524no—
806C2#1311724111yescharacteristic
807C2C2×#1171865111yescharacteristic
808C2#1311744411yescharacteristic
809C2C4⋊C4×C22⋊D1311yescharacteristic
810C2#1311773611yescharacteristic
811C2#1311776111yescharacteristic
812C2#1311778711yescharacteristic
813C2#1311835311yescharacteristic
814C2#1311836411yescharacteristic
815C2#1311842711yescharacteristic
816C2#1311843811yescharacteristic
817C2#1311920211yescharacteristic
818C2#1311921311yescharacteristic
819C2#1311926111yescharacteristic
820C2#1311927211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#384C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×#384D13
hypocenterC13#13876
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#384

Complements

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

NH ≅ G/Ntype
4. C2×C4⋊C4×Dic13C2semidirect
6. #13113095C2semidirect
8. #13113068C2semidirect
9. #13113066C2semidirect
10. #13113065C2semidirect
11. C2×C13×#384C2semidirect
40. C4×#6103C4semidirect
209. #6103C4⋊C4semidirect
215. C2×#384D13semidirect
429. C4×C13#388semidirect
623. C13#13876semidirect
804. C4#11718651semidirect

Maximal subgroups

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

subgroupindex
C2×#117186512
C2×#117186482
C2×C4⋊C4×Dic132
C2×C4×#61032
#131130952
#131130782
#131130682
#131130662
#131130652
C2×C13×#3842
#1387613