Finite Group Databasebeta

← #15786288

Subgroups — #15786288

Order 3328.

2590 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718881C211yesmaximal, characteristic
2C2×#11718881C211yesmaximal, characteristic
3C2×#11718607C211yesmaximal, characteristic, complemented
4C22×#88071C211yesmaximal, characteristic, complemented
5#13113095C212yesmaximal, complemented
6#13113079C212yesmaximal, complemented
7#13113069C212yesmaximal, complemented
8#13113059C211yesmaximal, characteristic, complemented
9#13113059C212yesmaximal, 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×#6101C2212yes—
29#11718881—24no—
30#11718881C418yescomplemented
31C2×#88071—24no—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38C2×#88071C2212yes—
39C2×#88071C2212yes—
40C2×#88071C2212yes—
41#11718607—24no—
42C25×C13C2311yescharacteristic
43C25×C13C2311yescharacteristic
44C22×D4×C13—22no—
45C22×D4×C13—22no—
46C22×D4×C13—22no—
47C22×D4×C13—22no—
48C22×D4×C13C2×C414yes—
49C22×D4×C13D414yes—
50C22×D4×C13Q814yes—
51C23×C4×C13—22no—
52C23×C4×C13—22no—
53C23×C4×C13—22no—
54C23×C4×C13—22no—
55C23×C4×C13—22no—
56C23×C4×C13—24no—
57C23×C4×C13—24no—
58C23×C4×C13—42no—
59C23×C4×C13—42no—
60C23×C4×C13D414yes—
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C23×Dic13—22no—
67C23×Dic13—22no—
68C23×Dic13—22no—
69C23×Dic13—24no—
70C23×Dic13—22no—
71C23×Dic13—22no—
72C23×Dic13—42no—
73C23×Dic13—42no—
74C23×Dic13—42no—
75C23×Dic13C2×C414yescomplemented
76C23×Dic13C2312yes—
77C23×Dic13C2312yes—
78C23×Dic13C2312yes—
79C23×Dic13C2312yes—
80C4×D4×C13—232no—
81C2×C13×C4⋊C4—22no—
82C2×C13×C4⋊C4—22no—
83C2×C13×C4⋊C4—22no—
84C2×C13×C22⋊C4—22no—
85C2×C13×C22⋊C4—22no—
86C2×C13×C22⋊C4—22no—
87C2×C13×C22⋊C4—22no—
88C2×C13×C22⋊C4—22no—
89C2×C13×C22⋊C4D414yes—
90C2×C42×C13—22no—
91C2×C42×C13—22no—
92C2×C42×C13—22no—
93C2×C22⋊Dic13—22no—
94C2×C22⋊Dic13—22no—
95C2×C22⋊Dic13—24no—
96C2×C22⋊Dic13—22no—
97C2×C22⋊Dic13—22no—
98C2×C22⋊Dic13—22no—
99C2×C22⋊Dic13—24no—
100C2×C22⋊Dic13—42no—
101C2×C22⋊Dic13—42no—
102C2×C22⋊Dic13—42no—
103C2×C22⋊Dic13C2×C414yescomplemented
104C2×C22⋊Dic13C2×C418yescomplemented
105C2×#6101—24no—
106C2×#6101—24no—
107C2×#6101—42no—
108#88071—24no—
109#88071—24no—
110#88071—24no—
111#88071—24no—
112#88071—24no—
113#88071—42no—
114#88071—42no—
115#88071—42no—
116#88071C2×C418yescomplemented
117#14016—131nomaximal, Sylow
118C24×C13—22no—
119C24×C13—22no—
120C24×C13—22no—
121C24×C13—22no—
122C24×C13—21no—
123C24×C13—21no—
124C24×C13—22no—
125C24×C13—22no—
126C24×C13—21no—
127C24×C13—21no—
128C24×C13—22no—
129C24×C13—22no—
130C24×C13C22×C412yes—
131C24×C13C22×C412yes—
132C24×C13C2×D412yes—
133C24×C13C2×D412yes—
134C24×C13C2×D412yes—
135C24×C13C2×D412yes—
136C24×C13C2×Q812yes—
137C24×C13C2×Q812yes—
138C24×C13#4112yes—
139C24×C13#4112yes—
140C24×C13C2411yescharacteristic
141C2×D4×C13—28no—
142C2×D4×C13—28no—
143C2×D4×C13—28no—
144C2×D4×C13—28no—
145C2×D4×C13—28no—
146C2×D4×C13—28no—
147C2×D4×C13C4⋊C4116yescomplemented
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—22no—
155C22×C4×C13—28no—
156C22×C4×C13—28no—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—22no—
164C22×C4×C13—22no—
165C22×C4×C13—22no—
166C22×C4×C13—22no—
167C22×C4×C13—22no—
168C22×C4×C13—22no—
169C22×C4×C13—28no—
170C22×C4×C13—44no—
171C22×C4×C13—48no—
172C22×C4×C13—48no—
173C22×C4×C13—48no—
174C22×C4×C13—48no—
175C22×C4×C13—44no—
176C22×C4×C13—44no—
177C22×C4×C13C22×C412yes—
178C22×C4×C13C2×D412yes—
179C22×C4×C13C2×D412yes—
180C22×C4×C13C2×D412yes—
181C22×C4×C13C2×D412yes—
182C22×C4×C13C2×D412yes—
183C22×C4×C13C2×Q812yes—
184C22×C4×C13#4114yes—
185C22×Dic13—28no—
186C22×Dic13—28no—
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×Dic13—22no—
197C22×Dic13—22no—
198C22×Dic13—22no—
199C22×Dic13—22no—
200C22×Dic13—22no—
201C22×Dic13—22no—
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—48no—
213C22×Dic13—48no—
214C22×Dic13—48no—
215C22×Dic13—44no—
216C22×Dic13—44no—
217C22×Dic13—44no—
218C22×Dic13—48no—
219C22×Dic13—44no—
220C22×Dic13C22×C414yes—
221C22×Dic13C22×C414yes—
222C22×Dic13#4114yes—
223C13×C4⋊C4—28no—
224C13×C22⋊C4—28no—
225C13×C22⋊C4—28no—
226C42×C13—28no—
227C22⋊Dic13—28no—
228C22⋊Dic13—48no—
229C22⋊Dic13—48no—
230C22⋊Dic13—44no—
231#6101—48no—
232C22×C4×D4D1311yescharacteristic
233C2×#386—131no—
234C2×#386—131no—
235C2×#385—131no—
236C22×#95—131no—
237#1442—132no—
238#1439—132no—
239#1436—132no—
240C22⋊#95—131no—
241C22⋊#95—132no—
242C22⋊#95—131no—
243C23×C13—24no—
244C23×C13—24no—
245C23×C13—22no—
246C23×C13—22no—
247C23×C13—24no—
248C23×C13—22no—
249C23×C13—22no—
250C23×C13—24no—
251C23×C13—24no—
252C23×C13—24no—
253C23×C13—24no—
254C23×C13—24no—
255C23×C13—24no—
256C23×C13—24no—
257C23×C13—24no—
258C23×C13—24no—
259C23×C13—22no—
260C23×C13—22no—
261C23×C13—24no—
262C23×C13—24no—
263C23×C13—22no—
264C23×C13—22no—
265C23×C13—22no—
266C23×C13—22no—
267C23×C13—24no—
268C23×C13—24no—
269C23×C13—24no—
270C23×C13—24no—
271C23×C13—41no—
272C23×C13—41no—
273C23×C13—42no—
274C23×C13—41no—
275C23×C13—41no—
276C23×C13—42no—
277C23×C13—42no—
278C23×C13—42no—
279C23×C13—42no—
280C23×C13—42no—
281C23×C13C2×C4⋊C414yes—
282C23×C13C2×C4⋊C414yes—
283C23×C13C4×D414yes—
284C23×C13C4×D414yes—
285C23×C13#12014yes—
286C23×C13C22⋊Q814yes—
287C23×C13C22⋊Q814yes—
288C23×C13#12314yes—
289C23×C13C23×C411yescharacteristic
290C23×C13C22×D411yescharacteristic
291C23×C13C22×D411yescharacteristic
292C23×C13C22×D411yescharacteristic
293C23×C13C22×Q811yescharacteristic
294C23×C13C2×#4111yescharacteristic
295C23×C13C2×#4111yescharacteristic
296C23×C13C2×#4112yes—
297C23×C13C2×#4112yes—
298C23×C13H(5,𝔽2)12yes—
299C23×C13H(5,𝔽2)12yes—
300D4×C13—232no—
301C2×C4×C13—22no—
302C2×C4×C13—22no—
303C2×C4×C13—22no—
304C2×C4×C13—22no—
305C2×C4×C13—22no—
306C2×C4×C13—22no—
307C2×C4×C13—22no—
308C2×C4×C13—22no—
309C2×C4×C13—24no—
310C2×C4×C13—24no—
311C2×C4×C13—22no—
312C2×C4×C13—22no—
313C2×C4×C13—22no—
314C2×C4×C13—22no—
315C2×C4×C13—22no—
316C2×C4×C13—24no—
317C2×C4×C13—24no—
318C2×C4×C13—416no—
319C2×C4×C13—416no—
320C2×C4×C13—41no—
321C2×C4×C13—41no—
322C2×C4×C13—41no—
323C2×C4×C13—41no—
324C2×C4×C13—42no—
325C2×C4×C13—42no—
326C2×C4×C13—42no—
327C2×C4×C13—42no—
328C2×C4×C13C2×C4⋊C414yes—
329C2×C4×C13#12314yes—
330C2×Dic13—24no—
331C2×Dic13—24no—
332C2×Dic13—24no—
333C2×Dic13—24no—
334C2×Dic13—24no—
335C2×Dic13—24no—
336C2×Dic13—24no—
337C2×Dic13—24no—
338C2×Dic13—24no—
339C2×Dic13—416no—
340C2×Dic13—416no—
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—
351C2×Dic13—42no—
352C2×Dic13—42no—
353C2×Dic13—42no—
354C2×Dic13—42no—
355C2×Dic13—42no—
356C2×Dic13—42no—
357C2×Dic13—42no—
358C2×Dic13—42no—
359C2×Dic13—42no—
360C23×D4C2×D1311yescharacteristic
361C24×C4—131no—
362C24×C4—131no—
363C24×C4C2×D1311yescharacteristic
364C24×C4C2×D1311yescharacteristic
365C2×C4×D4—24no—
366C2×C4×D4—24no—
367C2×C4×D4—24no—
368C22×C4⋊C4—132no—
369C22×C4⋊C4C2×D1311yescharacteristic
370C22×C22⋊C4—131no—
371C22×C22⋊C4—132no—
372C22×C22⋊C4—131no—
373C22×C22⋊C4—132no—
374C22×C22⋊C4C2×D1311yescharacteristic
375C22×C22⋊C4C2×D1311yescharacteristic
376C22×C42C2×D1311yescharacteristic
377#386—138no—
378#386—264no—
379#385—264no—
380C2×#95—132no—
381C2×#95—132no—
382C2×#95—132no—
383C2×#95—132no—
384C2×#95—132no—
385C2×#95—132no—
386C2×#95—132no—
387C2×#95—132no—
388C2×#95—132no—
389C2×#95—264no—
390C22×C13—24no—
391C22×C13—24no—
392C22×C13—28no—
393C22×C13—28no—
394C22×C13—24no—
395C22×C13—24no—
396C22×C13—28no—
397C22×C13—28no—
398C22×C13—24no—
399C22×C13—24no—
400C22×C13—28no—
401C22×C13—24no—
402C22×C13—42no—
403C22×C13—42no—
404C22×C13—44no—
405C22×C13—42no—
406C22×C13—42no—
407C22×C13—44no—
408C22×C13—44no—
409C22×C13—42no—
410C22×C13—42no—
411C22×C13#38518yes—
412C22×C13C22×C4⋊C411yescharacteristic
413C22×C13C2×C4×D411yescharacteristic
414C22×C13C2×C4×D411yescharacteristic
415C22×C13C4×#4112yes—
416C22×C13#51812yes—
417C22×C13C2×#12011yescharacteristic
418C22×C13C2×C22⋊Q811yescharacteristic
419C22×C13C2×C22⋊Q811yescharacteristic
420C22×C13C2×#12311yescharacteristic
421C22×C13C2×#12311yescharacteristic
422C22×C13#52511yescharacteristic
423C22×C13#52912yes—
424C22×C13#53411yescharacteristic
425C22×C13#53511yescharacteristic
426C22×C13#53812yes—
427C22×C13#54612yes—
428C22×C13#54612yes—
429C22×C13#54612yes—
430C22×C13#54612yes—
431C22×C13#55312yes—
432C22×C13#55312yes—
433C22×C13#55412yes—
434C22×C13#55412yes—
435C4×C13—24no—
436C4×C13—24no—
437C4×C13—42no—
438C4×C13—42no—
439C4×C13—42no—
440Dic13—44no—
441Dic13—44no—
442Dic13—44no—
443Dic13—82no—
444C25C22×D1311yescharacteristic
445C25C22×D1311yescharacteristic
446C22×D4—22no—
447C22×D4—22no—
448C22×D4—22no—
449C22×D4—22no—
450C22×D4Dic2614yes—
451C22×D4C4×D1314yes—
452C22×D4C22⋊D1314yes—
453C23×C4—22no—
454C23×C4—22no—
455C23×C4—22no—
456C23×C4—24no—
457C23×C4—22no—
458C23×C4—22no—
459C23×C4—24no—
460C23×C4—42no—
461C23×C4—42no—
462C23×C4—132no—
463C23×C4—132no—
464C23×C4—132no—
465C23×C4—134no—
466C23×C4—132no—
467C23×C4—264no—
468C23×C4—262no—
469C23×C4—262no—
470C23×C4—262no—
471C23×C4—262no—
472C23×C4—262no—
473C23×C4—522no—
474C23×C4—522no—
475C23×C4—522no—
476C23×C4C22⋊D1314yes—
477C23×C4C22×D1311yescharacteristic
478C23×C4C22×D1311yescharacteristic
479C23×C4C22×D1311yescharacteristic
480C23×C4C22×D1311yescharacteristic
481C23×C4C22×D1311yescharacteristic
482C4×D4—232no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—264no—
487C2×C4⋊C4—264no—
488C2×C4⋊C4—522no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—134no—
495C2×C22⋊C4—138no—
496C2×C22⋊C4—262no—
497C2×C22⋊C4—262no—
498C2×C22⋊C4—264no—
499C2×C22⋊C4—262no—
500C2×C22⋊C4—262no—
501C2×C22⋊C4—264no—
502C2×C22⋊C4—262no—
503C2×C22⋊C4—522no—
504C2×C22⋊C4—522no—
505C2×C22⋊C4—522no—
506C2×C22⋊C4C22⋊D1314yes—
507C2×C42—22no—
508C2×C42—22no—
509C2×C42—22no—
510#95—138no—
511#95—264no—
512#95—264no—
513#95—264no—
514#95—264no—
515#95—264no—
516#95—522no—
517#95—522no—
518#95—522no—
519C2×C13—28no—
520C2×C13—44no—
521C2×C13C2×#38511yescharacteristic
522C2×C13C4×#12311yescharacteristic
523C2×C13#232111yescharacteristic
524C2×C13#234912yes—
525C2×C13#236412yes—
526C2×C13#240411yescharacteristic
527C2×C13#240511yescharacteristic
528C2×C13#244412yes—
529C2×C13#245012yes—
530C2×C13#248711yescharacteristic
531C2×C13#257911yescharacteristic
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—21no—
537C24—21no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—21no—
543C24—21no—
544C24C2×Dic2612yes—
545C24C2×Dic2612yes—
546C24C2×C4×D1312yes—
547C24C2×C4×D1312yes—
548C24#612712yes—
549C24#612712yes—
550C24C2×C22⋊D1312yes—
551C24C2×C22⋊D1312yes—
552C24C2×C22⋊D1312yes—
553C24C2×C22⋊D1312yes—
554C24C23×D1311yescharacteristic
555C2×D4—28no—
556C2×D4—28no—
557C2×D4—28no—
558C2×D4—28no—
559C2×D4—28no—
560C2×D4—28no—
561C2×D4#6101116yescomplemented
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—28no—
570C22×C4—28no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—28no—
584C22×C4—44no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—134no—
592C22×C4—134no—
593C22×C4—134no—
594C22×C4—268no—
595C22×C4—268no—
596C22×C4—262no—
597C22×C4—262no—
598C22×C4—262no—
599C22×C4—262no—
600C22×C4—262no—
601C22×C4—262no—
602C22×C4—262no—
603C22×C4—262no—
604C22×C4—262no—
605C22×C4—262no—
606C22×C4—262no—
607C22×C4—262no—
608C22×C4—262no—
609C22×C4—262no—
610C22×C4—262no—
611C22×C4—262no—
612C22×C4—262no—
613C22×C4—262no—
614C22×C4—262no—
615C22×C4—262no—
616C22×C4—262no—
617C22×C4—262no—
618C22×C4—262no—
619C22×C4—262no—
620C22×C4—262no—
621C22×C4—528no—
622C22×C4—528no—
623C22×C4—528no—
624C22×C4—524no—
625C22×C4—528no—
626C22×C4—524no—
627C22×C4—524no—
628C22×C4—524no—
629C22×C4C2×Dic2612yes—
630C22×C4C2×C4×D1312yes—
631C22×C4#612914yes—
632C22×C4C2×C22⋊D1312yes—
633C22×C4C2×C22⋊D1312yes—
634C22×C4C2×C22⋊D1312yes—
635C22×C4C2×C22⋊D1312yes—
636C22×C4C2×C22⋊D1312yes—
637C4⋊C4—28no—
638C4⋊C4—528no—
639C22⋊C4—28no—
640C22⋊C4—28no—
641C22⋊C4—268no—
642C22⋊C4—528no—
643C22⋊C4—528no—
644C22⋊C4—524no—
645C42—28no—
646C13#1401611yescharacteristic, complemented, Sylow
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—22no—
652C23—24no—
653C23—24no—
654C23—22no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—22no—
660C23—24no—
661C23—24no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—22no—
675C23—42no—
676C23—42no—
677C23—41no—
678C23—41no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—41no—
683C23—42no—
684C23—41no—
685C23C2×#610114yes—
686C23C2×#610114yes—
687C23#8817814yes—
688C23#8817814yes—
689C23C4×C22⋊D1314yes—
690C23C4×C22⋊D1314yes—
691C23#8818314yes—
692C23#8820714yes—
693C23C22×Dic2611yescharacteristic
694C23C22×C4×D1311yescharacteristic
695C23C2×#612711yescharacteristic
696C23C2×#612711yescharacteristic
697C23C2×#612912yes—
698C23#8825112yes—
699C23#41×D1312yes—
700C23#8825612yes—
701C23C22×C22⋊D1311yescharacteristic
702C23C22×C22⋊D1311yescharacteristic
703C23C22×C22⋊D1311yescharacteristic
704D4—232no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—416no—
723C2×C4—416no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—264no—
733C2×C4—264no—
734C2×C4—264no—
735C2×C4—264no—
736C2×C4—264no—
737C2×C4—264no—
738C2×C4—264no—
739C2×C4—264no—
740C2×C4—264no—
741C2×C4—5216no—
742C2×C4—5216no—
743C2×C4—522no—
744C2×C4—522no—
745C2×C4—522no—
746C2×C4—522no—
747C2×C4—522no—
748C2×C4—522no—
749C2×C4—522no—
750C2×C4—522no—
751C2×C4—522no—
752C2×C4—522no—
753C2×C4—522no—
754C2×C4—522no—
755C2×C4—522no—
756C2×C4—522no—
757C2×C4—522no—
758C2×C4—522no—
759C2×C4—522no—
760C2×C4—522no—
761C2×C4—522no—
762C2×C4C2×#610114yes—
763C2×C4#8818914yes—
764C22—28no—
765C22—24no—
766C22—28no—
767C22—24no—
768C22—24no—
769C22—24no—
770C22—28no—
771C22—28no—
772C22—24no—
773C22—24no—
774C22—28no—
775C22—24no—
776C22—42no—
777C22—44no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—44no—
782C22—44no—
783C22—42no—
784C22—42no—
785C22#1171887118yes—
786C22C4×#612912yes—
787C22#1171924312yes—
788C22#1171924412yes—
789C22#1171924512yes—
790C22#1171924812yes—
791C22#1171925012yes—
792C22#1171926512yes—
793C22#1171927012yes—
794C22C22×#610111yescharacteristic
795C22C2×#8817811yescharacteristic
796C22C2×#8817811yescharacteristic
797C22C2×C4×C22⋊D1311yescharacteristic
798C22C2×C4×C22⋊D1311yescharacteristic
799C22C2×#8818311yescharacteristic
800C22C2×#8818911yescharacteristic
801C22#1171950911yescharacteristic
802C22#1171951112yes—
803C22#1171951112yes—
804C22#1171953311yescharacteristic
805C22#1171953412yes—
806C22#1171953412yes—
807C22#1171953511yescharacteristic
808C22C2×#8820711yescharacteristic
809C4—24no—
810C4—24no—
811C4—42no—
812C4—42no—
813C4—42no—
814C4—524no—
815C4—524no—
816C4—524no—
817C4—1042no—
818C2—28no—
819C2—44no—
820C2C2×#1171887111yescharacteristic
821C2C4×#8818911yescharacteristic
822C2#1311749011yescharacteristic
823C2#1311774112yes—
824C2#1311788112yes—
825C2#1311815111yescharacteristic
826C2#1311815911yescharacteristic
827C2#1311858012yes—
828C2#1311865412yes—
829C2#1311915311yescharacteristic
830C2#1312017911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC22×C4×D4×C13C2
socle, cosocleC24×C13C24
prime radicalC23×D4×C13C22
hypercenterC22×C4×D4D13
hypocenterC13#14016
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
3. C2×#11718607C2semidirect
4. C22×#88071C2semidirect
5. #13113095C2semidirect
6. #13113079C2semidirect
7. #13113069C2semidirect
8. #13113059C2semidirect
9. #13113059C2semidirect
10. #13113058C2semidirect
30. #11718881C4semidirect
75. C23×Dic13C2×C4semidirect
103. C2×C22⋊Dic13C2×C4semidirect
104. C2×C22⋊Dic13C2×C4semidirect
116. #88071C2×C4semidirect
147. C2×D4×C13C4⋊C4semidirect
561. C2×D4#6101semidirect
646. C13#14016semidirect

Maximal subgroups

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

subgroupindex
C2×#117188812
C2×#117186072
C22×#880712
#131130952
#131130792
#131130692
#131130592
#131130582
C22×C4×D4×C132
#1401613