Finite Group Databasebeta

← #15799670

Subgroups — #15799670

Order 3328.

1922 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718610C212yesmaximal, complemented
2C2×#11718882C211yesmaximal, characteristic
3C2×#11718882C211yesmaximal, characteristic
4C2×#11718646C211yesmaximal, characteristic, complemented
5C2×#11718589C211yesmaximal, characteristic, complemented
6C2×C4×#6101C211yesmaximal, characteristic, complemented
7#13113081C212yesmaximal, complemented
8#13113079C212yesmaximal, complemented
9#13113079C212yesmaximal, complemented
10#13113065C211yesmaximal, characteristic, complemented
11C2×C13×#390C211yesmaximal, characteristic
12C23×D4×C13C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C22⋊C4C2212yes—
15C22×C13×C22⋊C4C2212yes—
16C22×C42×C13C2211yescharacteristic
17C22×C22⋊Dic13C2212yes—
18C22×C22⋊Dic13C2212yes—
19C22×C22⋊Dic13C2212yes—
20C22×C22⋊Dic13C2212yes—
21C22×C4⋊Dic13C2211yescharacteristic
22C22×C4⋊Dic13C2212yes—
23C22×C4⋊Dic13C2211yescharacteristic
24C22×#6101C2211yescharacteristic
25C22×#6101C2212yes—
26C22×#6101C2211yescharacteristic
27C22×C4×Dic13C2211yescharacteristic
28C22×C4×Dic13C2211yescharacteristic
29C13×#390—24no—
30#11718882—24no—
31#11718882—24no—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2211yescharacteristic
36C2×#88071C2211yescharacteristic
37C2×#88071C2212yes—
38#11718646—24no—
39#11718610—28no—
40C4×#6101—24no—
41#11718589—24no—
42C25×C13C2312yes—
43C22×D4×C13—22no—
44C22×D4×C13—22no—
45C22×D4×C13—22no—
46C22×D4×C13—22no—
47C22×D4×C13—22no—
48C22×D4×C13—22no—
49C22×D4×C13Q814yes—
50C23×C4×C13C2311yescharacteristic
51C23×C4×C13C2312yes—
52C23×C4×C13C2311yescharacteristic
53C23×C4×C13C2311yescharacteristic
54C23×Dic13C2312yes—
55C23×Dic13C2311yescharacteristic
56C23×Dic13C2311yescharacteristic
57C23×Dic13C2312yes—
58C23×Dic13C2311yescharacteristic
59C23×Dic13C2311yescharacteristic
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—22no—
62C2×C13×C4⋊C4D414yes—
63C2×C13×C22⋊C4—24no—
64C2×C13×C22⋊C4—24no—
65C2×C13×C22⋊C4—24no—
66C2×C13×C22⋊C4—24no—
67C2×C13×C22⋊C4—42no—
68C2×C13×C22⋊C4—42no—
69C2×C42×C13—22no—
70C2×C42×C13—22no—
71C2×C42×C13—22no—
72C2×C22⋊Dic13—24no—
73C2×C22⋊Dic13—24no—
74C2×C22⋊Dic13—24no—
75C2×C22⋊Dic13—24no—
76C2×C22⋊Dic13—24no—
77C2×C22⋊Dic13—24no—
78C2×C22⋊Dic13—24no—
79C2×C22⋊Dic13—24no—
80C2×C22⋊Dic13—42no—
81C2×C22⋊Dic13—42no—
82C2×C22⋊Dic13—42no—
83C2×C22⋊Dic13—42no—
84C2×C4⋊Dic13—22no—
85C2×C4⋊Dic13—22no—
86C2×C4⋊Dic13—22no—
87C2×C4⋊Dic13—22no—
88C2×C4⋊Dic13—24no—
89C2×C4⋊Dic13—22no—
90C2×C4⋊Dic13—24no—
91C2×C4⋊Dic13—42no—
92C2×C4⋊Dic13D414yes—
93C2×#6101—22no—
94C2×#6101—22no—
95C2×#6101—22no—
96C2×#6101—22no—
97C2×#6101—22no—
98C2×#6101—24no—
99C2×#6101—24no—
100C2×#6101—42no—
101C2×#6101D414yescomplemented
102C2×C4×Dic13—22no—
103C2×C4×Dic13—22no—
104C2×C4×Dic13—22no—
105C2×C4×Dic13—22no—
106C2×C4×Dic13—22no—
107C2×C4×Dic13D414yes—
108#88071—24no—
109#88071—24no—
110#88071—22no—
111#88071—22no—
112#88071—24no—
113#88071—42no—
114#15148—131nomaximal, Sylow
115C24×C13—22no—
116C24×C13—22no—
117C24×C13—22no—
118C24×C13—22no—
119C24×C13—22no—
120C24×C13—22no—
121C24×C13—22no—
122C24×C13—22no—
123C24×C13—22no—
124C24×C13—22no—
125C24×C13—22no—
126C24×C13—22no—
127C24×C13—22no—
128C24×C13—22no—
129C24×C13C2×Q814yes—
130C24×C13C2411yescharacteristic
131C2×D4×C13—28no—
132C2×D4×C13—28no—
133C2×D4×C13—28no—
134C2×D4×C13—44no—
135C2×D4×C13—44no—
136C2×D4×C13—44no—
137C2×D4×C13—44no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—22no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—22no—
148C22×C4×C13—22no—
149C22×C4×C13—22no—
150C22×C4×C13—22no—
151C22×C4×C13—21no—
152C22×C4×C13—22no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13C2×D412yes—
157C22×C4×C13C2×D412yes—
158C22×C4×C13C2×D412yes—
159C22×C4×C13C2×D414yes—
160C22×C4×C13C2×D412yes—
161C22×C4×C13C2×Q812yes—
162C22×C4×C13#4112yes—
163C22×C4×C13#4112yes—
164C22×C4×C13#4112yes—
165C22×C4×C13#4112yes—
166C22×Dic13—21no—
167C22×Dic13—21no—
168C22×Dic13—21no—
169C22×Dic13—21no—
170C22×Dic13—21no—
171C22×Dic13—21no—
172C22×Dic13—21no—
173C22×Dic13—22no—
174C22×Dic13—21no—
175C22×Dic13—21no—
176C22×Dic13—21no—
177C22×Dic13—21no—
178C22×Dic13—21no—
179C22×Dic13—21no—
180C22×Dic13—21no—
181C22×Dic13—22no—
182C22×Dic13—22no—
183C22×Dic13—22no—
184C22×Dic13—21no—
185C22×Dic13—22no—
186C22×Dic13—22no—
187C22×Dic13—21no—
188C22×Dic13—21no—
189C22×Dic13—21no—
190C22×Dic13—21no—
191C22×Dic13—21no—
192C22×Dic13—21no—
193C22×Dic13—21no—
194C22×Dic13—22no—
195C22×Dic13—22no—
196C22×Dic13—22no—
197C22×Dic13—22no—
198C22×Dic13—22no—
199C22×Dic13—22no—
200C22×Dic13—22no—
201C22×Dic13C2×D412yes—
202C22×Dic13C2×D414yes—
203C22×Dic13C2×D412yes—
204C22×Dic13C2×D412yes—
205C22×Dic13C2×D412yes—
206C22×Dic13#4112yes—
207C22×Dic13#4112yes—
208C13×C4⋊C4—28no—
209C13×C22⋊C4—48no—
210C13×C22⋊C4—48no—
211C42×C13—44no—
212C22⋊Dic13—48no—
213C22⋊Dic13—48no—
214C22⋊Dic13—48no—
215C22⋊Dic13—48no—
216C4⋊Dic13—28no—
217C4⋊Dic13—48no—
218C4⋊Dic13—44no—
219#6101—28no—
220#6101—28no—
221#6101—48no—
222C4×Dic13—28no—
223C4×Dic13—44no—
224C2×#399—132no—
225C2×#390—131no—
226C2×#390—131no—
227C2×#390D1311yescharacteristic
228C2×#389—131no—
229C2×#389—131no—
230C2×C4×C4⋊C4—131no—
231#1439—132no—
232#1439—132no—
233#1439—132no—
234C4⋊#95—131no—
235C23×C13—24no—
236C23×C13—24no—
237C23×C13—24no—
238C23×C13—24no—
239C23×C13—24no—
240C23×C13—24no—
241C23×C13—24no—
242C23×C13—42no—
243C23×C13—42no—
244C23×C13—42no—
245C23×C13—42no—
246C23×C13—42no—
247C23×C13—42no—
248C23×C13—42no—
249C23×C13—42no—
250C23×C13—42no—
251C23×C13—42no—
252C23×C13—42no—
253C23×C13—42no—
254C23×C13—42no—
255C23×C13—42no—
256C23×C13—42no—
257C23×C13—42no—
258C23×C13—42no—
259C23×C13—42no—
260C23×C13—42no—
261C23×C13—42no—
262C23×C13—42no—
263C23×C13—42no—
264C23×C13—42no—
265C23×C13—42no—
266C23×C13—42no—
267C23×C13—42no—
268C23×C13—42no—
269C23×C13—42no—
270C23×C13C22×D411yescharacteristic
271C23×C13C22×D411yescharacteristic
272C23×C13C22×D411yescharacteristic
273C23×C13C22×D411yescharacteristic
274C23×C13C22×Q811yescharacteristic
275C23×C13C2×#4111yescharacteristic
276C23×C13C2×#4111yescharacteristic
277C23×C13C2×#4111yescharacteristic
278C23×C13C2×#4111yescharacteristic
279C23×C13C2×#4111yescharacteristic
280C23×C13C2×#4111yescharacteristic
281C23×C13H(5,𝔽2)11yescharacteristic
282C23×C13H(5,𝔽2)11yescharacteristic
283C23×C13H(5,𝔽2)11yescharacteristic
284C23×C132−1+411yescharacteristic
285D4×C13—416no—
286C2×C4×C13—22no—
287C2×C4×C13—24no—
288C2×C4×C13—22no—
289C2×C4×C13—22no—
290C2×C4×C13—24no—
291C2×C4×C13—22no—
292C2×C4×C13—22no—
293C2×C4×C13—24no—
294C2×C4×C13—22no—
295C2×C4×C13—41no—
296C2×C4×C13—41no—
297C2×C4×C13—42no—
298C2×C4×C13—41no—
299C2×C4×C13—41no—
300C2×C4×C13—42no—
301C2×C4×C13—41no—
302C2×C4×C13—41no—
303C2×C4×C13—42no—
304C2×C4×C13—41no—
305C2×C4×C13—41no—
306C2×C4×C13—42no—
307C2×C4×C13C22⋊Q814yes—
308C2×C4×C13C22⋊Q814yes—
309C2×C4×C13C22⋊Q814yes—
310C2×C4×C13#12314yes—
311C2×C4×C13#12314yes—
312C2×C4×C13#12314yes—
313C2×C4×C13#12714yes—
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—22no—
324C2×Dic13—22no—
325C2×Dic13—22no—
326C2×Dic13—24no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—22no—
330C2×Dic13—24no—
331C2×Dic13—22no—
332C2×Dic13—41no—
333C2×Dic13—41no—
334C2×Dic13—42no—
335C2×Dic13—41no—
336C2×Dic13—41no—
337C2×Dic13—41no—
338C2×Dic13—41no—
339C2×Dic13—42no—
340C2×Dic13—41no—
341C2×Dic13—41no—
342C2×Dic13—41no—
343C2×Dic13—41no—
344C2×Dic13—42no—
345C2×Dic13—41no—
346C2×Dic13—41no—
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#12114yes—
356C23×D4C2×D1311yescharacteristic
357C22×C4⋊C4—131no—
358C22×C4⋊C4—131no—
359C22×C4⋊C4—131no—
360C22×C4⋊C4—131no—
361C22×C4⋊C4—132no—
362C22×C4⋊C4—132no—
363C22×C4⋊C4C2×D1311yescharacteristic
364C22×C22⋊C4—132no—
365C22×C22⋊C4—132no—
366C22×C22⋊C4—132no—
367C22×C22⋊C4—132no—
368C22×C22⋊C4C2×D1312yes—
369C22×C22⋊C4C2×D1312yes—
370C22×C42—131no—
371C22×C42—131no—
372C22×C42C2×D1311yescharacteristic
373#399—268no—
374#390—24no—
375#390—264no—
376#390—264no—
377#389—264no—
378#389—264no—
379C4×C4⋊C4—264no—
380C2×#95—132no—
381C2×#95—131no—
382C2×#95—131no—
383C2×#95—132no—
384C2×#95—132no—
385C2×#95—132no—
386C22×C13—44no—
387C22×C13—44no—
388C22×C13—44no—
389C22×C13—44no—
390C22×C13—44no—
391C22×C13—44no—
392C22×C13—44no—
393C22×C13—82no—
394C22×C13—82no—
395C22×C13—82no—
396C22×C13—82no—
397C22×C13—82no—
398C22×C13—82no—
399C22×C13—82no—
400C22×C13—82no—
401C22×C13C2×#12111yescharacteristic
402C22×C13C2×C22⋊Q811yescharacteristic
403C22×C13C2×C22⋊Q811yescharacteristic
404C22×C13C2×C22⋊Q811yescharacteristic
405C22×C13C2×#12311yescharacteristic
406C22×C13C2×#12311yescharacteristic
407C22×C13C2×#12311yescharacteristic
408C22×C13#52511yescharacteristic
409C22×C13#52911yescharacteristic
410C22×C13#52911yescharacteristic
411C22×C13C2×#12711yescharacteristic
412C22×C13#53211yescharacteristic
413C22×C13#53211yescharacteristic
414C22×C13#53511yescharacteristic
415C22×C13#53711yescharacteristic
416C22×C13#54011yescharacteristic
417C22×C13#54011yescharacteristic
418C22×C13#54211yescharacteristic
419C22×C13#54211yescharacteristic
420C22×C13D4211yescharacteristic
421C22×C13D4211yescharacteristic
422C22×C13#54611yescharacteristic
423C22×C13#54611yescharacteristic
424C22×C13#54811yescharacteristic
425C22×C13#54811yescharacteristic
426C22×C13D4×Q811yescharacteristic
427C22×C13#55011yescharacteristic
428C22×C13#55011yescharacteristic
429C22×C13#55011yescharacteristic
430C22×C13#55411yescharacteristic
431C22×C13#55411yescharacteristic
432C22×C13#55411yescharacteristic
433C22×C13#55611yescharacteristic
434C22×C13#55911yescharacteristic
435C22×C13#55911yescharacteristic
436C4×C13—44no—
437C4×C13—42no—
438C4×C13—42no—
439C4×C13#39918yescomplemented
440Dic13—24no—
441Dic13—42no—
442Dic13—44no—
443Dic13—42no—
444Dic13—42no—
445Dic13—82no—
446C25C22×D1312yes—
447C22×D4—22no—
448C22×D4—22no—
449C22×D4—22no—
450C22×D4—22no—
451C22×D4—22no—
452C22×D4—22no—
453C22×D4Dic2614yes—
454C23×C4—131no—
455C23×C4—131no—
456C23×C4—132no—
457C23×C4—131no—
458C23×C4—131no—
459C23×C4—132no—
460C23×C4C22×D1311yescharacteristic
461C23×C4C22×D1311yescharacteristic
462C23×C4C22×D1312yes—
463C23×C4C22×D1311yescharacteristic
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—134no—
467C2×C4⋊C4—134no—
468C2×C4⋊C4—262no—
469C2×C4⋊C4—262no—
470C2×C4⋊C4—262no—
471C2×C4⋊C4—262no—
472C2×C4⋊C4—262no—
473C2×C4⋊C4—262no—
474C2×C4⋊C4—262no—
475C2×C4⋊C4—264no—
476C2×C4⋊C4—264no—
477C2×C4⋊C4—264no—
478C2×C4⋊C4—262no—
479C2×C4⋊C4—262no—
480C2×C4⋊C4—264no—
481C2×C4⋊C4—262no—
482C2×C4⋊C4—522no—
483C2×C4⋊C4—522no—
484C2×C4⋊C4C22⋊D1314yes—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—42no—
490C2×C22⋊C4—42no—
491C2×C22⋊C4—264no—
492C2×C22⋊C4—264no—
493C2×C22⋊C4—264no—
494C2×C22⋊C4—264no—
495C2×C22⋊C4—264no—
496C2×C22⋊C4—264no—
497C2×C22⋊C4—264no—
498C2×C22⋊C4—264no—
499C2×C22⋊C4—522no—
500C2×C22⋊C4—522no—
501C2×C22⋊C4—522no—
502C2×C22⋊C4—522no—
503C2×C42—22no—
504C2×C42—22no—
505C2×C42—22no—
506C2×C42—134no—
507C2×C42—262no—
508C2×C42—262no—
509C2×C42—262no—
510C2×C42—262no—
511C2×C42—262no—
512#95—262no—
513#95—262no—
514#95—264no—
515#95—264no—
516#95—264no—
517#95—522no—
518C2×C13—84no—
519C2×C13C2×#39911yescharacteristic
520C2×C13#244511yescharacteristic
521C2×C13#244511yescharacteristic
522C2×C13#244811yescharacteristic
523C2×C13#244811yescharacteristic
524C2×C13#245211yescharacteristic
525C2×C13#245211yescharacteristic
526C2×C13#245411yescharacteristic
527C2×C13#245411yescharacteristic
528C2×C13#253811yescharacteristic
529C2×C13#254011yescharacteristic
530C2×C13#254111yescharacteristic
531C2×C13#258011yescharacteristic
532C2×C13#262411yescharacteristic
533C2×C13#285411yescharacteristic
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24C2×Dic2614yes—
549C24C23×D1311yescharacteristic
550C2×D4—28no—
551C2×D4—28no—
552C2×D4—28no—
553C2×D4—44no—
554C2×D4—44no—
555C2×D4—44no—
556C2×D4—44no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—132no—
576C22×C4—132no—
577C22×C4—132no—
578C22×C4—132no—
579C22×C4—134no—
580C22×C4—132no—
581C22×C4—132no—
582C22×C4—261no—
583C22×C4—261no—
584C22×C4—261no—
585C22×C4—261no—
586C22×C4—261no—
587C22×C4—262no—
588C22×C4—261no—
589C22×C4—261no—
590C22×C4—262no—
591C22×C4—261no—
592C22×C4—261no—
593C22×C4—261no—
594C22×C4—262no—
595C22×C4—261no—
596C22×C4—261no—
597C22×C4—262no—
598C22×C4—261no—
599C22×C4—261no—
600C22×C4—261no—
601C22×C4—262no—
602C22×C4—261no—
603C22×C4—261no—
604C22×C4—261no—
605C22×C4—262no—
606C22×C4—261no—
607C22×C4—261no—
608C22×C4—261no—
609C22×C4—261no—
610C22×C4—262no—
611C22×C4—262no—
612C22×C4—262no—
613C22×C4—262no—
614C22×C4—262no—
615C22×C4—262no—
616C22×C4—262no—
617C22×C4C2×Dic2612yes—
618C22×C4#612712yes—
619C22×C4D4×D1312yes—
620C22×C4D4×D1312yes—
621C22×C4D4×D1312yes—
622C22×C4#612912yes—
623C22×C4#612912yes—
624C22×C4#612912yes—
625C22×C4C2×C22⋊D1314yes—
626C22×C4C2×C22⋊D1312yes—
627C4⋊C4—28no—
628C4⋊C4—268no—
629C4⋊C4—268no—
630C4⋊C4—268no—
631C4⋊C4—528no—
632C4⋊C4—528no—
633C4⋊C4—524no—
634C22⋊C4—48no—
635C22⋊C4—48no—
636C22⋊C4—528no—
637C22⋊C4—528no—
638C22⋊C4—528no—
639C22⋊C4—528no—
640C42—44no—
641C42—268no—
642C42—524no—
643C13#1514811yescharacteristic, complemented, Sylow
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23C22×Dic2611yescharacteristic
680C23C2×#612711yescharacteristic
681C23C2×D4×D1311yescharacteristic
682C23C2×D4×D1311yescharacteristic
683C23C2×D4×D1311yescharacteristic
684C23C2×#612911yescharacteristic
685C23C2×#612911yescharacteristic
686C23C2×#612911yescharacteristic
687C23#8825111yescharacteristic
688C23#8825111yescharacteristic
689C23#41×D1311yescharacteristic
690C23#41×D1311yescharacteristic
691C23#8825611yescharacteristic
692C23#8825711yescharacteristic
693C23C22×C22⋊D1311yescharacteristic
694D4—416no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—42no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—134no—
717C2×C4—262no—
718C2×C4—262no—
719C2×C4—262no—
720C2×C4—262no—
721C2×C4—262no—
722C2×C4—262no—
723C2×C4—262no—
724C2×C4—264no—
725C2×C4—262no—
726C2×C4—262no—
727C2×C4—262no—
728C2×C4—262no—
729C2×C4—262no—
730C2×C4—262no—
731C2×C4—262no—
732C2×C4—264no—
733C2×C4—262no—
734C2×C4—264no—
735C2×C4—521no—
736C2×C4—521no—
737C2×C4—521no—
738C2×C4—522no—
739C2×C4—521no—
740C2×C4—521no—
741C2×C4—521no—
742C2×C4—522no—
743C2×C4—521no—
744C2×C4—521no—
745C2×C4—521no—
746C2×C4—521no—
747C2×C4—521no—
748C2×C4—522no—
749C2×C4—521no—
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#8813214yes—
759C2×C4#8813214yes—
760C2×C4#8813714yes—
761C2×C4#8813714yes—
762C2×C4#8817814yes—
763C2×C4#8818914yes—
764C2×C4#8819414yes—
765C22—44no—
766C22—44no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22—44no—
771C22—44no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22—82no—
780C22C2×#8813211yescharacteristic
781C22C2×#8813211yescharacteristic
782C22C2×#8813711yescharacteristic
783C22C2×#8813711yescharacteristic
784C22D4×Dic2611yescharacteristic
785C22#1171924411yescharacteristic
786C22#1171924411yescharacteristic
787C22#1171924811yescharacteristic
788C22#1171925311yescharacteristic
789C22#1171926211yescharacteristic
790C22#1171926611yescharacteristic
791C22#1171926711yescharacteristic
792C22#1171930311yescharacteristic
793C22#1171930411yescharacteristic
794C22D13×#12111yescharacteristic
795C22#1171931111yescharacteristic
796C22#1171931211yescharacteristic
797C22#1171931311yescharacteristic
798C22#1171931411yescharacteristic
799C22#1171931711yescharacteristic
800C22#1171937611yescharacteristic
801C22#1171938511yescharacteristic
802C22#1171938611yescharacteristic
803C22#1171938711yescharacteristic
804C22#1171941811yescharacteristic
805C22#1171942111yescharacteristic
806C22#1171942311yescharacteristic
807C22#1171942411yescharacteristic
808C22C2×#8817811yescharacteristic
809C22C2×#8818911yescharacteristic
810C22D4×C22⋊D1311yescharacteristic
811C22C2×#8819411yescharacteristic
812C22#1171951111yescharacteristic
813C22#1171953611yescharacteristic
814C22#1171953911yescharacteristic
815C4—42no—
816C4—42no—
817C4—44no—
818C4—264no—
819C4—522no—
820C4—522no—
821C4—522no—
822C4—524no—
823C4—1042no—
824C4#1171861018yescomplemented
825C2—84no—
826C2C2×#1171861011yescharacteristic
827C2#1311859711yescharacteristic
828C2#1311860211yescharacteristic
829C2#1311863011yescharacteristic
830C2#1311863511yescharacteristic
831C2#1311868011yescharacteristic
832C2#1311868811yescharacteristic
833C2#1311870211yescharacteristic
834C2#1311871011yescharacteristic
835C2#1311975611yescharacteristic
836C2#1311977211yescharacteristic
837C2#1311977911yescharacteristic
838C2#1312019211yescharacteristic
839C2#1312062811yescharacteristic
840C2#1312316611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutator, socle, cosocleC24×C13C24
FittingC2×C13×#390C2
prime radicalC23×D4×C13C22
hypercenterC2×#390D13
hypocenterC13#15148
LCSG ▷ C24×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C2×#11718610C2semidirect
4. C2×#11718646C2semidirect
5. C2×#11718589C2semidirect
6. C2×C4×#6101C2semidirect
7. #13113081C2semidirect
8. #13113079C2semidirect
9. #13113079C2semidirect
10. #13113065C2semidirect
101. C2×#6101D4semidirect
439. C4×C13#399semidirect
643. C13#15148semidirect
824. C4#11718610semidirect

Maximal subgroups

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

subgroupindex
C2×#117186102
C2×#117188822
C2×#117186462
C2×#117185892
C2×C4×#61012
#131130812
#131130792
#131130652
C2×C13×#3902
#1514813