Finite Group Databasebeta

← #15786277

Subgroups — #15786277

Order 3328.

2950 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#6101C211yesmaximal, characteristic, complemented
2C2×#11718881C211yesmaximal, characteristic
3C2×#11718881C211yesmaximal, characteristic
4C2×#11718871C212yesmaximal, complemented
5C2×#11718607C211yesmaximal, characteristic, complemented
6#13113099C212yesmaximal, complemented
7#13113079C212yesmaximal, complemented
8#13113069C212yesmaximal, complemented
9#13113059C211yesmaximal, characteristic, complemented
10#13113058C211yesmaximal, characteristic, complemented
11C22×C4×D4×C13C211yesmaximal, characteristic
12C23×D4×C13C2211yescharacteristic
13C24×C4×C13C2211yescharacteristic
14C24×C4×C13C2211yescharacteristic
15C24×Dic13C2211yescharacteristic
16C24×Dic13C2211yescharacteristic
17C2×C4×D4×C13—24no—
18C2×C4×D4×C13—24no—
19C2×C4×D4×C13—24no—
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C42×C13C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C22×C22⋊Dic13C2212yes—
26C22×C22⋊Dic13C2211yescharacteristic
27C22×C22⋊Dic13C2212yes—
28C22×#6101—24no—
29C22×#6101—28no—
30C22×#6101C2212yes—
31C22×#6101C2212yes—
32C22×#6101C2212yes—
33#11718881—24no—
34#11718881C418yescomplemented
35#11718871—28no—
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38C2×#88071C2212yes—
39C2×#88071C2212yes—
40C2×#88071C2212yes—
41C2×#88071C2212yes—
42C2×#88071C2212yes—
43#11718607—24no—
44C25×C13C2311yescharacteristic
45C25×C13C2311yescharacteristic
46C22×D4×C13—22no—
47C22×D4×C13—22no—
48C22×D4×C13—22no—
49C22×D4×C13—22no—
50C22×D4×C13C2×C414yes—
51C22×D4×C13D414yes—
52C22×D4×C13Q814yes—
53C23×C4×C13—22no—
54C23×C4×C13—22no—
55C23×C4×C13—22no—
56C23×C4×C13—24no—
57C23×C4×C13—22no—
58C23×C4×C13—22no—
59C23×C4×C13—24no—
60C23×C4×C13—42no—
61C23×C4×C13—42no—
62C23×C4×C13D414yes—
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C23×C4×C13C2311yescharacteristic
67C23×C4×C13C2311yescharacteristic
68C23×Dic13—22no—
69C23×Dic13—22no—
70C23×Dic13—24no—
71C23×Dic13—24no—
72C23×Dic13—22no—
73C23×Dic13—24no—
74C23×Dic13—22no—
75C23×Dic13—22no—
76C23×Dic13—42no—
77C23×Dic13C2×C414yescomplemented
78C23×Dic13C2312yes—
79C23×Dic13C2312yes—
80C23×Dic13C2312yes—
81C23×Dic13C2312yes—
82C4×D4×C13—232no—
83C2×C13×C4⋊C4—22no—
84C2×C13×C4⋊C4—22no—
85C2×C13×C4⋊C4—22no—
86C2×C13×C22⋊C4—22no—
87C2×C13×C22⋊C4—22no—
88C2×C13×C22⋊C4—22no—
89C2×C13×C22⋊C4—22no—
90C2×C13×C22⋊C4—22no—
91C2×C13×C22⋊C4D414yes—
92C2×C42×C13—22no—
93C2×C42×C13—22no—
94C2×C42×C13—22no—
95C2×C22⋊Dic13—22no—
96C2×C22⋊Dic13—22no—
97C2×C22⋊Dic13—24no—
98C2×C22⋊Dic13—24no—
99C2×C22⋊Dic13—24no—
100C2×C22⋊Dic13—22no—
101C2×C22⋊Dic13—22no—
102C2×C22⋊Dic13—22no—
103C2×C22⋊Dic13—24no—
104C2×C22⋊Dic13—42no—
105C2×C22⋊Dic13C2×C414yescomplemented
106C2×C22⋊Dic13C2×C418yescomplemented
107C2×#6101—232no—
108C2×#6101—24no—
109C2×#6101—24no—
110C2×#6101—24no—
111C2×#6101—24no—
112C2×#6101—24no—
113C2×#6101—24no—
114C2×#6101—24no—
115C2×#6101—42no—
116C2×#6101D418yescomplemented
117#88071—24no—
118#88071—24no—
119#88071—24no—
120#88071—24no—
121#88071—24no—
122#88071—42no—
123#88071C2×C418yescomplemented
124#14015—131nomaximal, Sylow
125C24×C13—22no—
126C24×C13—22no—
127C24×C13—22no—
128C24×C13—22no—
129C24×C13—22no—
130C24×C13—21no—
131C24×C13—21no—
132C24×C13—22no—
133C24×C13—21no—
134C24×C13—21no—
135C24×C13—22no—
136C24×C13—22no—
137C24×C13C22×C412yes—
138C24×C13C22×C412yes—
139C24×C13C2×D412yes—
140C24×C13C2×D412yes—
141C24×C13C2×D412yes—
142C24×C13C2×D412yes—
143C24×C13C2×Q812yes—
144C24×C13C2×Q812yes—
145C24×C13#4112yes—
146C24×C13#4112yes—
147C24×C13C2411yescharacteristic
148C2×D4×C13—28no—
149C2×D4×C13—28no—
150C2×D4×C13—28no—
151C2×D4×C13—28no—
152C2×D4×C13—28no—
153C2×D4×C13—28no—
154C2×D4×C13C4⋊C4116yescomplemented
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—22no—
162C22×C4×C13—28no—
163C22×C4×C13—28no—
164C22×C4×C13—22no—
165C22×C4×C13—22no—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—22no—
173C22×C4×C13—22no—
174C22×C4×C13—22no—
175C22×C4×C13—22no—
176C22×C4×C13—28no—
177C22×C4×C13—44no—
178C22×C4×C13—48no—
179C22×C4×C13—48no—
180C22×C4×C13—48no—
181C22×C4×C13—48no—
182C22×C4×C13—44no—
183C22×C4×C13—44no—
184C22×C4×C13C22×C412yes—
185C22×C4×C13C2×D414yes—
186C22×C4×C13C2×D412yes—
187C22×C4×C13C2×D412yes—
188C22×C4×C13C2×D412yes—
189C22×C4×C13C2×D412yes—
190C22×C4×C13C2×D412yes—
191C22×C4×C13C2×Q812yes—
192C22×Dic13—28no—
193C22×Dic13—216no—
194C22×Dic13—28no—
195C22×Dic13—28no—
196C22×Dic13—22no—
197C22×Dic13—22no—
198C22×Dic13—22no—
199C22×Dic13—22no—
200C22×Dic13—216no—
201C22×Dic13—28no—
202C22×Dic13—22no—
203C22×Dic13—22no—
204C22×Dic13—22no—
205C22×Dic13—22no—
206C22×Dic13—22no—
207C22×Dic13—22no—
208C22×Dic13—22no—
209C22×Dic13—22no—
210C22×Dic13—22no—
211C22×Dic13—22no—
212C22×Dic13—22no—
213C22×Dic13—22no—
214C22×Dic13—22no—
215C22×Dic13—22no—
216C22×Dic13—22no—
217C22×Dic13—22no—
218C22×Dic13—22no—
219C22×Dic13—22no—
220C22×Dic13—22no—
221C22×Dic13—48no—
222C22×Dic13—48no—
223C22×Dic13—44no—
224C22×Dic13—44no—
225C22×Dic13C22×C414yes—
226C22×Dic13C22×C414yes—
227C22×Dic13C2×D414yes—
228C22×Dic13C2×D414yes—
229C22×Dic13#4114yes—
230C13×C4⋊C4—28no—
231C13×C22⋊C4—28no—
232C13×C22⋊C4—28no—
233C42×C13—28no—
234C22⋊Dic13—28no—
235C22⋊Dic13—216no—
236C22⋊Dic13—48no—
237C22⋊Dic13—44no—
238#6101—216no—
239#6101—216no—
240#6101—48no—
241C22×C4×D4D1311yescharacteristic
242C23×C4⋊C4—131no—
243C2×#386—131no—
244C2×#386—131no—
245C2×#385—132no—
246C2×#385—131no—
247#1444—132no—
248#1439—132no—
249#1436—132no—
250C22⋊#95—131no—
251C22⋊#95—131no—
252C23×C13—24no—
253C23×C13—24no—
254C23×C13—22no—
255C23×C13—22no—
256C23×C13—24no—
257C23×C13—22no—
258C23×C13—22no—
259C23×C13—24no—
260C23×C13—24no—
261C23×C13—24no—
262C23×C13—24no—
263C23×C13—24no—
264C23×C13—24no—
265C23×C13—24no—
266C23×C13—24no—
267C23×C13—24no—
268C23×C13—24no—
269C23×C13—22no—
270C23×C13—22no—
271C23×C13—24no—
272C23×C13—22no—
273C23×C13—22no—
274C23×C13—22no—
275C23×C13—22no—
276C23×C13—24no—
277C23×C13—24no—
278C23×C13—24no—
279C23×C13—24no—
280C23×C13—41no—
281C23×C13—41no—
282C23×C13—42no—
283C23×C13—41no—
284C23×C13—41no—
285C23×C13—42no—
286C23×C13—42no—
287C23×C13—42no—
288C23×C13—42no—
289C23×C13—42no—
290C23×C13C2×C4⋊C414yes—
291C23×C13C2×C4⋊C414yescomplemented
292C23×C13C4×D414yes—
293C23×C13C4×D414yes—
294C23×C13#12014yes—
295C23×C13C22⋊Q814yes—
296C23×C13C22⋊Q814yes—
297C23×C13#12314yes—
298C23×C13C23×C411yescharacteristic
299C23×C13C22×D411yescharacteristic
300C23×C13C22×D411yescharacteristic
301C23×C13C22×D411yescharacteristic
302C23×C13C22×D412yes—
303C23×C13C22×Q811yescharacteristic
304C23×C13C2×#4111yescharacteristic
305C23×C13C2×#4111yescharacteristic
306C23×C13C2×#4112yes—
307C23×C13H(5,𝔽2)12yes—
308C23×C132−1+412yes—
309D4×C13—232no—
310C2×C4×C13—22no—
311C2×C4×C13—22no—
312C2×C4×C13—22no—
313C2×C4×C13—22no—
314C2×C4×C13—22no—
315C2×C4×C13—22no—
316C2×C4×C13—22no—
317C2×C4×C13—22no—
318C2×C4×C13—24no—
319C2×C4×C13—24no—
320C2×C4×C13—22no—
321C2×C4×C13—22no—
322C2×C4×C13—22no—
323C2×C4×C13—22no—
324C2×C4×C13—22no—
325C2×C4×C13—24no—
326C2×C4×C13—24no—
327C2×C4×C13—416no—
328C2×C4×C13—416no—
329C2×C4×C13—41no—
330C2×C4×C13—41no—
331C2×C4×C13—41no—
332C2×C4×C13—41no—
333C2×C4×C13—42no—
334C2×C4×C13—42no—
335C2×C4×C13—42no—
336C2×C4×C13—42no—
337C2×C4×C13C2×C4⋊C414yescomplemented
338C2×C4×C13#12014yes—
339C2×Dic13—232no—
340C2×Dic13—24no—
341C2×Dic13—24no—
342C2×Dic13—24no—
343C2×Dic13—24no—
344C2×Dic13—24no—
345C2×Dic13—24no—
346C2×Dic13—24no—
347C2×Dic13—24no—
348C2×Dic13—24no—
349C2×Dic13—24no—
350C2×Dic13—24no—
351C2×Dic13—24no—
352C2×Dic13—416no—
353C2×Dic13—42no—
354C2×Dic13—42no—
355C2×Dic13—42no—
356C2×Dic13—42no—
357C2×Dic13—42no—
358C2×Dic13—42no—
359C2×Dic13—42no—
360C2×Dic13—42no—
361C2×Dic13—42no—
362C2×Dic13—42no—
363C2×Dic13—42no—
364C2×Dic13—42no—
365C2×Dic13—42no—
366C2×Dic13—42no—
367C2×Dic13—42no—
368C2×Dic13C4×D418yescomplemented
369C23×D4C2×D1311yescharacteristic
370C24×C4—131no—
371C24×C4—131no—
372C24×C4C2×D1311yescharacteristic
373C24×C4C2×D1311yescharacteristic
374C2×C4×D4—24no—
375C2×C4×D4—24no—
376C2×C4×D4—24no—
377C22×C4⋊C4—132no—
378C22×C4⋊C4—132no—
379C22×C4⋊C4—132no—
380C22×C4⋊C4—268no—
381C22×C4⋊C4—264no—
382C22×C4⋊C4C2×D1311yescharacteristic
383C22×C22⋊C4—131no—
384C22×C22⋊C4—132no—
385C22×C22⋊C4—131no—
386C22×C22⋊C4—132no—
387C22×C22⋊C4C2×D1311yescharacteristic
388C22×C22⋊C4C2×D1311yescharacteristic
389C22×C42C2×D1311yescharacteristic
390#386—138no—
391#386—264no—
392#385—268no—
393#385—264no—
394C2×#95—132no—
395C2×#95—132no—
396C2×#95—132no—
397C2×#95—132no—
398C2×#95—132no—
399C2×#95—132no—
400C2×#95—132no—
401C22×C13—24no—
402C22×C13—24no—
403C22×C13—28no—
404C22×C13—28no—
405C22×C13—24no—
406C22×C13—24no—
407C22×C13—24no—
408C22×C13—28no—
409C22×C13—28no—
410C22×C13—24no—
411C22×C13—28no—
412C22×C13—24no—
413C22×C13—42no—
414C22×C13—42no—
415C22×C13—44no—
416C22×C13—42no—
417C22×C13—42no—
418C22×C13—42no—
419C22×C13—44no—
420C22×C13—44no—
421C22×C13—42no—
422C22×C13#38518yescomplemented
423C22×C13C22×C4⋊C411yescharacteristic
424C22×C13C2×C4×D411yescharacteristic
425C22×C13C2×C4×D411yescharacteristic
426C22×C13C2×C4×D412yes—
427C22×C13#52012yes—
428C22×C13C2×#12011yescharacteristic
429C22×C13C2×#12011yescharacteristic
430C22×C13C2×C22⋊Q811yescharacteristic
431C22×C13C2×C22⋊Q811yescharacteristic
432C22×C13C2×#12311yescharacteristic
433C22×C13#52512yes—
434C22×C13#52511yescharacteristic
435C22×C13#53411yescharacteristic
436C22×C13#53611yescharacteristic
437C22×C13#53912yes—
438C22×C13D4212yes—
439C22×C13D4212yes—
440C22×C13#54712yes—
441C22×C13#54712yes—
442C22×C13#54812yes—
443C22×C13D4×Q812yes—
444C22×C13#55312yes—
445C22×C13#55412yes—
446C4×C13—24no—
447C4×C13—24no—
448C4×C13—42no—
449C4×C13—42no—
450C4×C13—42no—
451Dic13—28no—
452Dic13—44no—
453Dic13—44no—
454Dic13—82no—
455C25C22×D1311yescharacteristic
456C25C22×D1311yescharacteristic
457C22×D4—22no—
458C22×D4—22no—
459C22×D4—22no—
460C22×D4—22no—
461C22×D4Dic2614yes—
462C22×D4C4×D1314yes—
463C22×D4C22⋊D1314yes—
464C23×C4—22no—
465C23×C4—22no—
466C23×C4—22no—
467C23×C4—24no—
468C23×C4—22no—
469C23×C4—22no—
470C23×C4—24no—
471C23×C4—42no—
472C23×C4—42no—
473C23×C4—132no—
474C23×C4—134no—
475C23×C4—132no—
476C23×C4—132no—
477C23×C4—132no—
478C23×C4—264no—
479C23×C4—264no—
480C23×C4—264no—
481C23×C4—262no—
482C23×C4—262no—
483C23×C4—262no—
484C23×C4—262no—
485C23×C4—262no—
486C23×C4—522no—
487C23×C4C22⋊D1314yes—
488C23×C4C22×D1311yescharacteristic
489C23×C4C22×D1311yescharacteristic
490C23×C4C22×D1311yescharacteristic
491C23×C4C22×D1311yescharacteristic
492C23×C4C22×D1311yescharacteristic
493C4×D4—232no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—138no—
498C2×C4⋊C4—264no—
499C2×C4⋊C4—264no—
500C2×C4⋊C4—2632no—
501C2×C4⋊C4—264no—
502C2×C4⋊C4—264no—
503C2×C4⋊C4—264no—
504C2×C4⋊C4—264no—
505C2×C4⋊C4—264no—
506C2×C4⋊C4—522no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—138no—
513C2×C22⋊C4—134no—
514C2×C22⋊C4—264no—
515C2×C22⋊C4—264no—
516C2×C22⋊C4—262no—
517C2×C22⋊C4—262no—
518C2×C22⋊C4—264no—
519C2×C22⋊C4—262no—
520C2×C22⋊C4—262no—
521C2×C22⋊C4—264no—
522C2×C22⋊C4—262no—
523C2×C22⋊C4—522no—
524C2×C22⋊C4C22⋊D1314yes—
525C2×C42—22no—
526C2×C42—22no—
527C2×C42—22no—
528#95—138no—
529#95—264no—
530#95—264no—
531#95—264no—
532#95—264no—
533#95—264no—
534#95—522no—
535C2×C13—28no—
536C2×C13—44no—
537C2×C13C2×#38511yescharacteristic
538C2×C13C4×#12011yescharacteristic
539C2×C13#232211yescharacteristic
540C2×C13D4×C4⋊C412yes—
541C2×C13#236112yes—
542C2×C13#240311yescharacteristic
543C2×C13#240611yescharacteristic
544C2×C13#240911yescharacteristic
545C2×C13#244312yes—
546C2×C13#244912yes—
547C2×C13#257911yescharacteristic
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—21no—
553C24—21no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—21no—
559C24—21no—
560C24C2×Dic2612yes—
561C24C2×Dic2612yes—
562C24C2×C4×D1312yes—
563C24C2×C4×D1312yes—
564C24#612712yes—
565C24#612712yes—
566C24C2×C22⋊D1312yes—
567C24C2×C22⋊D1312yes—
568C24C2×C22⋊D1312yes—
569C24C2×C22⋊D1312yes—
570C24C23×D1311yescharacteristic
571C2×D4—28no—
572C2×D4—28no—
573C2×D4—28no—
574C2×D4—28no—
575C2×D4—28no—
576C2×D4—28no—
577C2×D4#6101116yescomplemented
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—28no—
586C22×C4—28no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—28no—
600C22×C4—44no—
601C22×C4—48no—
602C22×C4—48no—
603C22×C4—48no—
604C22×C4—48no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—134no—
608C22×C4—134no—
609C22×C4—134no—
610C22×C4—134no—
611C22×C4—134no—
612C22×C4—2616no—
613C22×C4—268no—
614C22×C4—2616no—
615C22×C4—268no—
616C22×C4—268no—
617C22×C4—262no—
618C22×C4—262no—
619C22×C4—262no—
620C22×C4—262no—
621C22×C4—268no—
622C22×C4—262no—
623C22×C4—262no—
624C22×C4—262no—
625C22×C4—262no—
626C22×C4—262no—
627C22×C4—262no—
628C22×C4—262no—
629C22×C4—262no—
630C22×C4—262no—
631C22×C4—262no—
632C22×C4—262no—
633C22×C4—262no—
634C22×C4—262no—
635C22×C4—262no—
636C22×C4—262no—
637C22×C4—262no—
638C22×C4—262no—
639C22×C4—262no—
640C22×C4—262no—
641C22×C4—528no—
642C22×C4—528no—
643C22×C4—524no—
644C22×C4—524no—
645C22×C4C2×Dic2612yes—
646C22×C4C2×C4×D1312yes—
647C22×C4D4×D1314yes—
648C22×C4C2×C22⋊D1312yes—
649C22×C4C2×C22⋊D1312yes—
650C22×C4C2×C22⋊D1312yes—
651C22×C4C2×C22⋊D1312yes—
652C22×C4C2×C22⋊D1312yes—
653C4⋊C4—28no—
654C4⋊C4—2616no—
655C4⋊C4—2616no—
656C4⋊C4—528no—
657C22⋊C4—28no—
658C22⋊C4—28no—
659C22⋊C4—2616no—
660C22⋊C4—268no—
661C22⋊C4—528no—
662C22⋊C4—524no—
663C42—28no—
664C13#1401511yescharacteristic, complemented, Sylow
665C23—24no—
666C23—24no—
667C23—24no—
668C23—22no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—22no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—22no—
693C23—42no—
694C23—41no—
695C23—42no—
696C23—42no—
697C23—41no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—41no—
702C23—41no—
703C23C2×#610114yes—
704C23C2×#610114yescomplemented
705C23#8817814yes—
706C23#8817814yes—
707C23C4×C22⋊D1314yes—
708C23C4×C22⋊D1314yes—
709C23#8818314yes—
710C23#8820714yes—
711C23C22×Dic2611yescharacteristic
712C23C22×C4×D1311yescharacteristic
713C23C2×#612711yescharacteristic
714C23C2×#612711yescharacteristic
715C23C2×D4×D1312yes—
716C23#8825112yes—
717C23#41×D1312yes—
718C23#8825712yes—
719C23C22×C22⋊D1311yescharacteristic
720C23C22×C22⋊D1311yescharacteristic
721C23C22×C22⋊D1311yescharacteristic
722D4—232no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—416no—
741C2×C4—416no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—138no—
751C2×C4—2632no—
752C2×C4—264no—
753C2×C4—264no—
754C2×C4—264no—
755C2×C4—264no—
756C2×C4—264no—
757C2×C4—264no—
758C2×C4—264no—
759C2×C4—264no—
760C2×C4—264no—
761C2×C4—264no—
762C2×C4—264no—
763C2×C4—264no—
764C2×C4—5216no—
765C2×C4—522no—
766C2×C4—522no—
767C2×C4—522no—
768C2×C4—522no—
769C2×C4—522no—
770C2×C4—522no—
771C2×C4—522no—
772C2×C4—522no—
773C2×C4—522no—
774C2×C4—522no—
775C2×C4—522no—
776C2×C4—522no—
777C2×C4—522no—
778C2×C4—522no—
779C2×C4—522no—
780C2×C4C2×#610114yescomplemented
781C2×C4#8819114yes—
782C22—28no—
783C22—24no—
784C22—28no—
785C22—24no—
786C22—28no—
787C22—28no—
788C22—24no—
789C22—24no—
790C22—24no—
791C22—24no—
792C22—28no—
793C22—24no—
794C22—42no—
795C22—44no—
796C22—42no—
797C22—44no—
798C22—44no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22#1171887118yescomplemented
804C22D4×Dic2612yes—
805C22#1171924412yes—
806C22#1171924512yes—
807C22C4×D4×D1312yes—
808C22#1171925112yes—
809C22#1171925212yes—
810C22#1171925712yes—
811C22#1171926912yes—
812C22C22×#610111yescharacteristic
813C22C2×#8817811yescharacteristic
814C22C2×#8817811yescharacteristic
815C22C2×C4×C22⋊D1311yescharacteristic
816C22C2×C4×C22⋊D1311yescharacteristic
817C22C2×#8818311yescharacteristic
818C22C2×#8819111yescharacteristic
819C22D4×C22⋊D1312yes—
820C22D4×C22⋊D1312yes—
821C22#1171950911yescharacteristic
822C22#1171952912yes—
823C22#1171952912yes—
824C22#1171953011yescharacteristic
825C22#1171953311yescharacteristic
826C22C2×#8820711yescharacteristic
827C4—24no—
828C4—24no—
829C4—42no—
830C4—42no—
831C4—42no—
832C4—268no—
833C4—524no—
834C4—524no—
835C4—1042no—
836C2—28no—
837C2—44no—
838C2C2×#1171887111yescharacteristic
839C2C4×#8819111yescharacteristic
840C2#1311750111yescharacteristic
841C2D4×#610112yes—
842C2#1311785312yes—
843C2#1311814611yescharacteristic
844C2#1311816711yescharacteristic
845C2#1311820111yescharacteristic
846C2#1311856512yes—
847C2#1311863912yes—
848C2#1312017911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC22×C4×D4×C13C2
socle, cosocleC24×C13C24
prime radicalC23×D4×C13C22
hypercenterC22×C4×D4D13
hypocenterC13#14015
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C23×#6101C2semidirect
4. C2×#11718871C2semidirect
5. C2×#11718607C2semidirect
6. #13113099C2semidirect
7. #13113079C2semidirect
8. #13113069C2semidirect
9. #13113059C2semidirect
10. #13113058C2semidirect
34. #11718881C4semidirect
77. C23×Dic13C2×C4semidirect
105. C2×C22⋊Dic13C2×C4semidirect
106. C2×C22⋊Dic13C2×C4semidirect
116. C2×#6101D4semidirect
123. #88071C2×C4semidirect
154. C2×D4×C13C4⋊C4semidirect
291. C23×C13C2×C4⋊C4semidirect
337. C2×C4×C13C2×C4⋊C4semidirect
368. C2×Dic13C4×D4semidirect
422. C22×C13#385semidirect
577. C2×D4#6101semidirect
664. C13#14015semidirect
704. C23C2×#6101semidirect
780. C2×C4C2×#6101semidirect
803. C22#11718871semidirect

Maximal subgroups

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

subgroupindex
C23×#61012
C2×#117188812
C2×#117188712
C2×#117186072
#131130992
#131130792
#131130692
#131130592
#131130582
C22×C4×D4×C132
#1401513