Finite Group Databasebeta

← #15799668

Subgroups — #15799668

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×#11718653C212yesmaximal, complemented
2C2×#11718600C211yesmaximal, characteristic
3C2×#11718649C211yesmaximal, characteristic
4C2×#11718649C211yesmaximal, characteristic
5C2×#11718634C211yesmaximal, characteristic, complemented
6C2×C4×#6101C211yesmaximal, characteristic, complemented
7#13113080C212yesmaximal, complemented
8#13113080C212yesmaximal, complemented
9#13113078C212yesmaximal, complemented
10#13113065C211yesmaximal, characteristic, complemented
11C2×C13×#389C211yesmaximal, characteristic, complemented
12C23×D52C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2212yes—
15C22×C13×C4⋊C4C2211yescharacteristic
16C22×C42×C13C2211yescharacteristic
17C22×#6103C2212yes—
18C22×#6103C2212yes—
19C22×#6103C2212yes—
20C22×#6103C2212yes—
21C22×#6103C2212yes—
22C22×#6103C2212yes—
23C22×C4⋊Dic13C2211yescharacteristic
24C22×#6101C2211yescharacteristic
25C22×#6101C2212yes—
26C22×#6101C2211yescharacteristic
27C22×C4×Dic13C2211yescharacteristic
28C22×C4×Dic13C2211yescharacteristic
29C13×#389—24no—
30C2×C13×#95C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2211yescharacteristic
34C2×#88071C2211yescharacteristic
35C2×#88071C2212yes—
36#11718653—28no—
37#11718649—24no—
38#11718649—24no—
39#11718634—24no—
40#11718600—24no—
41C4×#6101—24no—
42C24×D13C2312yes—
43C23×C4×C13C2312yes—
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2312yes—
46C23×C4×C13C2311yescharacteristic
47C23×C4×C13C2311yescharacteristic
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2312yes—
51C23×Dic13C2311yescharacteristic
52C23×Dic13C2311yescharacteristic
53C22×D52—22no—
54C22×D52—22no—
55C22×D52—22no—
56C22×D52—22no—
57C22×D52—22no—
58C22×D52—22no—
59C22×D52Q814yes—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—22no—
62C2×C13×C4⋊C4—24no—
63C2×C13×C4⋊C4—22no—
64C2×C13×C4⋊C4—22no—
65C2×C13×C4⋊C4—22no—
66C2×C13×C4⋊C4—24no—
67C2×C13×C4⋊C4—42no—
68C2×C13×C4⋊C4D414yes—
69C2×C42×C13—22no—
70C2×C42×C13—22no—
71C2×C42×C13—22no—
72C2×#6103—24no—
73C2×#6103—24no—
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×C4⋊Dic13—22no—
91C2×C4⋊Dic13—22no—
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—
108C13×#95—24no—
109#88071—22no—
110#88071—22no—
111#88071—24no—
112#88071—24no—
113#88071—42no—
114#15148—131nomaximal, Sylow
115C24×C13C2411yescharacteristic
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×D13—22no—
128C23×D13—22no—
129C23×D13—22no—
130C23×D13C2×Q814yes—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—22no—
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—22no—
141C22×C4×C13—22no—
142C22×C4×C13—22no—
143C22×C4×C13—22no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—22no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—22no—
150C22×C4×C13—22no—
151C22×C4×C13—22no—
152C22×C4×C13—22no—
153C22×C4×C13—22no—
154C22×C4×C13—22no—
155C22×C4×C13—22no—
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—21no—
187C22×Dic13—22no—
188C22×Dic13—21no—
189C22×Dic13—21no—
190C22×Dic13—21no—
191C22×Dic13—21no—
192C22×Dic13—21no—
193C22×Dic13—21no—
194C22×Dic13C2×D412yes—
195C22×Dic13C2×D414yes—
196C22×Dic13C2×D412yes—
197C22×Dic13C2×D412yes—
198C22×Dic13C2×D412yes—
199C22×Dic13#4112yes—
200C22×Dic13#4112yes—
201C2×D52—28no—
202C2×D52—28no—
203C2×D52—28no—
204C2×D52—44no—
205C2×D52—44no—
206C2×D52—44no—
207C2×D52—44no—
208C13×C4⋊C4—28no—
209C13×C4⋊C4—48no—
210C13×C4⋊C4—44no—
211C42×C13—44no—
212#6103—48no—
213#6103—48no—
214#6103—48no—
215#6103—48no—
216#6103—48no—
217#6103—48no—
218C4⋊Dic13—28no—
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×#390—131no—
228C2×#389—131no—
229C2×#389D1311yescharacteristic, complemented
230C2×C4×C4⋊C4—131no—
231#1439—132no—
232#1439—132no—
233#1439—132no—
234C4⋊#95—131no—
235C23×C13C22×D411yescharacteristic
236C23×C13C22×D411yescharacteristic
237C23×C13C22×D411yescharacteristic
238C23×C13C22×D411yescharacteristic
239C23×C13C22×Q811yescharacteristic
240C23×C13C2×#4111yescharacteristic
241C23×C13C2×#4111yescharacteristic
242C23×C13C2×#4111yescharacteristic
243C23×C13C2×#4111yescharacteristic
244C23×C13C2×#4111yescharacteristic
245C23×C13C2×#4111yescharacteristic
246C23×C13H(5,𝔽2)11yescharacteristic
247C23×C13H(5,𝔽2)11yescharacteristic
248C23×C13H(5,𝔽2)11yescharacteristic
249C23×C132−1+411yescharacteristic
250C22×D13—24no—
251C22×D13—24no—
252C22×D13—24no—
253C22×D13—24no—
254C22×D13—24no—
255C22×D13—24no—
256C22×D13—24no—
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—
281C22×D13—42no—
282C22×D13—42no—
283C22×D13—42no—
284C22×D13—42no—
285C2×C4×C13—22no—
286C2×C4×C13—24no—
287C2×C4×C13—22no—
288C2×C4×C13—22no—
289C2×C4×C13—24no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13—24no—
293C2×C4×C13—22no—
294C2×C4×C13—41no—
295C2×C4×C13—41no—
296C2×C4×C13—42no—
297C2×C4×C13—41no—
298C2×C4×C13—41no—
299C2×C4×C13—42no—
300C2×C4×C13—41no—
301C2×C4×C13—41no—
302C2×C4×C13—42no—
303C2×C4×C13—41no—
304C2×C4×C13—41no—
305C2×C4×C13—42no—
306C2×C4×C13—42no—
307C2×C4×C13—42no—
308C2×C4×C13—42no—
309C2×C4×C13—42no—
310C2×C4×C13—42no—
311C2×C4×C13—42no—
312C2×C4×C13—42no—
313C2×C4×C13C22⋊Q814yes—
314C2×C4×C13C22⋊Q814yes—
315C2×C4×C13C22⋊Q814yes—
316C2×C4×C13#12314yes—
317C2×C4×C13#12314yes—
318C2×C4×C13#12314yes—
319C2×C4×C13#12714yes—
320C2×Dic13—22no—
321C2×Dic13—22no—
322C2×Dic13—22no—
323C2×Dic13—22no—
324C2×Dic13—22no—
325C2×Dic13—22no—
326C2×Dic13—22no—
327C2×Dic13—22no—
328C2×Dic13—24no—
329C2×Dic13—22no—
330C2×Dic13—22no—
331C2×Dic13—22no—
332C2×Dic13—22no—
333C2×Dic13—24no—
334C2×Dic13—22no—
335C2×Dic13—22no—
336C2×Dic13—24no—
337C2×Dic13—22no—
338C2×Dic13—41no—
339C2×Dic13—41no—
340C2×Dic13—42no—
341C2×Dic13—41no—
342C2×Dic13—41no—
343C2×Dic13—41no—
344C2×Dic13—41no—
345C2×Dic13—42no—
346C2×Dic13—41no—
347C2×Dic13—41no—
348C2×Dic13—41no—
349C2×Dic13—41no—
350C2×Dic13—42no—
351C2×Dic13—41no—
352C2×Dic13—41no—
353C2×Dic13—42no—
354C2×Dic13#12114yes—
355D52—416no—
356C23×D4—131no—
357C22×C4⋊C4—131no—
358C22×C4⋊C4—131no—
359C22×C4⋊C4—131no—
360C22×C4⋊C4—132no—
361C22×C4⋊C4C2×D1311yescharacteristic
362C22×C4⋊C4C2×D1312yes—
363C22×C4⋊C4C2×D1311yescharacteristic
364C22×C22⋊C4—132no—
365C22×C22⋊C4—132no—
366C22×C22⋊C4—132no—
367C22×C22⋊C4—132no—
368C22×C22⋊C4—132no—
369C22×C22⋊C4—132no—
370C22×C42—131no—
371C22×C42—131no—
372C22×C42C2×D1311yescharacteristic
373#399—268no—
374#390—264no—
375#390—264no—
376#390—264no—
377#389—24no—
378#389—264no—
379C4×C4⋊C4—264no—
380C2×#95—132no—
381C2×#95—131no—
382C2×#95—131no—
383C2×#95—132no—
384C2×#95—132no—
385C2×#95C2×D1312yes—
386C22×C13C2×#12111yescharacteristic
387C22×C13C2×C22⋊Q811yescharacteristic
388C22×C13C2×C22⋊Q811yescharacteristic
389C22×C13C2×C22⋊Q811yescharacteristic
390C22×C13C2×#12311yescharacteristic
391C22×C13C2×#12311yescharacteristic
392C22×C13C2×#12311yescharacteristic
393C22×C13#52511yescharacteristic
394C22×C13#52911yescharacteristic
395C22×C13#52911yescharacteristic
396C22×C13C2×#12711yescharacteristic
397C22×C13#53211yescharacteristic
398C22×C13#53211yescharacteristic
399C22×C13#53511yescharacteristic
400C22×C13#53711yescharacteristic
401C22×C13#54011yescharacteristic
402C22×C13#54011yescharacteristic
403C22×C13#54211yescharacteristic
404C22×C13#54211yescharacteristic
405C22×C13D4211yescharacteristic
406C22×C13D4211yescharacteristic
407C22×C13#54611yescharacteristic
408C22×C13#54611yescharacteristic
409C22×C13#54811yescharacteristic
410C22×C13#54811yescharacteristic
411C22×C13D4×Q811yescharacteristic
412C22×C13#55011yescharacteristic
413C22×C13#55011yescharacteristic
414C22×C13#55011yescharacteristic
415C22×C13#55411yescharacteristic
416C22×C13#55411yescharacteristic
417C22×C13#55411yescharacteristic
418C22×C13#55611yescharacteristic
419C22×C13#55911yescharacteristic
420C22×C13#55911yescharacteristic
421C2×D13—44no—
422C2×D13—44no—
423C2×D13—44no—
424C2×D13—44no—
425C2×D13—44no—
426C2×D13—44no—
427C2×D13—44no—
428C2×D13—82no—
429C2×D13—82no—
430C2×D13—82no—
431C2×D13—82no—
432C2×D13—82no—
433C2×D13—82no—
434C2×D13—82no—
435C2×D13—82no—
436C4×C13—44no—
437C4×C13—42no—
438C4×C13—42no—
439C4×C13—82no—
440C4×C13#39918yescomplemented
441Dic13—24no—
442Dic13—42no—
443Dic13—44no—
444Dic13—42no—
445Dic13—42no—
446C25—132no—
447C22×D4—134no—
448C22×D4—262no—
449C22×D4—262no—
450C22×D4—262no—
451C22×D4—262no—
452C22×D4—262no—
453C22×D4—262no—
454C23×C4—131no—
455C23×C4—131no—
456C23×C4—132no—
457C23×C4—131no—
458C23×C4—131no—
459C23×C4C22×D1312yes—
460C23×C4C22×D1311yescharacteristic
461C23×C4C22×D1311yescharacteristic
462C23×C4C22×D1312yes—
463C23×C4C22×D1311yescharacteristic
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—24no—
469C2×C4⋊C4—24no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—42no—
472C2×C4⋊C4—134no—
473C2×C4⋊C4—134no—
474C2×C4⋊C4—262no—
475C2×C4⋊C4—262no—
476C2×C4⋊C4—262no—
477C2×C4⋊C4—262no—
478C2×C4⋊C4—262no—
479C2×C4⋊C4—262no—
480C2×C4⋊C4—262no—
481C2×C4⋊C4—264no—
482C2×C4⋊C4—264no—
483C2×C4⋊C4—522no—
484C2×C4⋊C4C22⋊D1314yes—
485C2×C22⋊C4—264no—
486C2×C22⋊C4—264no—
487C2×C22⋊C4—264no—
488C2×C22⋊C4—264no—
489C2×C22⋊C4—264no—
490C2×C22⋊C4—264no—
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—522no—
498C2×C22⋊C4—522no—
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—24no—
513#95—262no—
514#95—262no—
515#95—264no—
516#95—264no—
517#95—522no—
518C2×C13C2×#39911yescharacteristic
519C2×C13#244511yescharacteristic
520C2×C13#244511yescharacteristic
521C2×C13#244811yescharacteristic
522C2×C13#244811yescharacteristic
523C2×C13#245211yescharacteristic
524C2×C13#245211yescharacteristic
525C2×C13#245411yescharacteristic
526C2×C13#245411yescharacteristic
527C2×C13#253811yescharacteristic
528C2×C13#254011yescharacteristic
529C2×C13#254111yescharacteristic
530C2×C13#258011yescharacteristic
531C2×C13#262411yescharacteristic
532C2×C13#285411yescharacteristic
533D13—84no—
534C24—134no—
535C24—262no—
536C24—262no—
537C24—262no—
538C24—262no—
539C24—262no—
540C24—262no—
541C24—262no—
542C24—262no—
543C24—262no—
544C24—262no—
545C24—262no—
546C24—262no—
547C24—262no—
548C24—262no—
549C24C23×D1311yescharacteristic
550C2×D4—268no—
551C2×D4—268no—
552C2×D4—268no—
553C2×D4—524no—
554C2×D4—524no—
555C2×D4—524no—
556C2×D4—524no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—132no—
583C22×C4—132no—
584C22×C4—132no—
585C22×C4—132no—
586C22×C4—134no—
587C22×C4—132no—
588C22×C4—132no—
589C22×C4—261no—
590C22×C4—261no—
591C22×C4—261no—
592C22×C4—261no—
593C22×C4—261no—
594C22×C4—262no—
595C22×C4—261no—
596C22×C4—261no—
597C22×C4—261no—
598C22×C4—262no—
599C22×C4—261no—
600C22×C4—261no—
601C22×C4—261no—
602C22×C4—261no—
603C22×C4—262no—
604C22×C4—262no—
605C22×C4—261no—
606C22×C4—261no—
607C22×C4—261no—
608C22×C4—261no—
609C22×C4—261no—
610C22×C4—262no—
611C22×C4—261no—
612C22×C4—261no—
613C22×C4—262no—
614C22×C4—261no—
615C22×C4—261no—
616C22×C4—261no—
617C22×C4#612712yes—
618C22×C4#612712yes—
619C22×C4D4×D1312yes—
620C22×C4D4×D1312yes—
621C22×C4D4×D1312yes—
622C22×C4Q8×D1312yes—
623C22×C4#613112yes—
624C22×C4#613112yes—
625C22×C4C2×C22⋊D1314yes—
626C22×C4C2×C22⋊D1312yes—
627C4⋊C4—28no—
628C4⋊C4—48no—
629C4⋊C4—44no—
630C4⋊C4—268no—
631C4⋊C4—268no—
632C4⋊C4—268no—
633C4⋊C4—528no—
634C22⋊C4—528no—
635C22⋊C4—528no—
636C22⋊C4—528no—
637C22⋊C4—528no—
638C22⋊C4—528no—
639C22⋊C4—528no—
640C42—44no—
641C42—268no—
642C42—524no—
643C13#1514811yescharacteristic, complemented, Sylow
644C23—264no—
645C23—264no—
646C23—264no—
647C23—264no—
648C23—264no—
649C23—264no—
650C23—264no—
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—
671C23—522no—
672C23—522no—
673C23—522no—
674C23—522no—
675C23—522no—
676C23—522no—
677C23—522no—
678C23—522no—
679C23C2×#612711yescharacteristic
680C23C2×#612711yescharacteristic
681C23C2×D4×D1311yescharacteristic
682C23C2×D4×D1311yescharacteristic
683C23C2×D4×D1311yescharacteristic
684C23#8825111yescharacteristic
685C23C2×Q8×D1311yescharacteristic
686C23C2×#613111yescharacteristic
687C23C2×#613111yescharacteristic
688C23#8825411yescharacteristic
689C23#41×D1311yescharacteristic
690C23#41×D1311yescharacteristic
691C23#8825611yescharacteristic
692C23#8825611yescharacteristic
693C23C22×C22⋊D1311yescharacteristic
694D4—5216no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—134no—
724C2×C4—262no—
725C2×C4—262no—
726C2×C4—262no—
727C2×C4—262no—
728C2×C4—262no—
729C2×C4—262no—
730C2×C4—262no—
731C2×C4—264no—
732C2×C4—262no—
733C2×C4—262no—
734C2×C4—262no—
735C2×C4—262no—
736C2×C4—264no—
737C2×C4—262no—
738C2×C4—262no—
739C2×C4—262no—
740C2×C4—264no—
741C2×C4—262no—
742C2×C4—522no—
743C2×C4—521no—
744C2×C4—521no—
745C2×C4—521no—
746C2×C4—522no—
747C2×C4—521no—
748C2×C4—521no—
749C2×C4—521no—
750C2×C4—521no—
751C2×C4—522no—
752C2×C4—521no—
753C2×C4—521no—
754C2×C4—521no—
755C2×C4—521no—
756C2×C4—521no—
757C2×C4—522no—
758C2×C4#8814814yes—
759C2×C4#8814814yes—
760C2×C4#8815014yes—
761C2×C4#8815014yes—
762C2×C4#8818314yes—
763C2×C4#8819414yes—
764C2×C4#8820014yes—
765C22—524no—
766C22—524no—
767C22—524no—
768C22—524no—
769C22—524no—
770C22—524no—
771C22—524no—
772C22—1042no—
773C22—1042no—
774C22—1042no—
775C22—1042no—
776C22—1042no—
777C22—1042no—
778C22—1042no—
779C22—1042no—
780C22C2×#8814811yescharacteristic
781C22C2×#8814811yescharacteristic
782C22C2×#8815011yescharacteristic
783C22C2×#8815011yescharacteristic
784C22#1171925311yescharacteristic
785C22#1171925811yescharacteristic
786C22#1171926411yescharacteristic
787C22#1171926711yescharacteristic
788C22#1171927311yescharacteristic
789C22#1171928511yescharacteristic
790C22#1171928711yescharacteristic
791C22#1171929011yescharacteristic
792C22#1171930411yescharacteristic
793C22D13×#12111yescharacteristic
794C22#1171931211yescharacteristic
795C22#1171931411yescharacteristic
796C22#1171933211yescharacteristic
797C22#1171933411yescharacteristic
798C22#1171933511yescharacteristic
799C22#1171933811yescharacteristic
800C22#1171939511yescharacteristic
801C22#1171939511yescharacteristic
802C22#1171939611yescharacteristic
803C22#1171940311yescharacteristic
804C22#1171943011yescharacteristic
805C22#1171943211yescharacteristic
806C22#1171943511yescharacteristic
807C22#1171943811yescharacteristic
808C22C2×#8818311yescharacteristic
809C22D4×C22⋊D1311yescharacteristic
810C22C2×#8819411yescharacteristic
811C22C2×#8820011yescharacteristic
812C22#1171952211yescharacteristic
813C22#1171953411yescharacteristic
814C22#1171953911yescharacteristic
815C4—42no—
816C4—42no—
817C4—44no—
818C4—82no—
819C4—264no—
820C4—522no—
821C4—522no—
822C4—522no—
823C4—524no—
824C4#1171865318yescomplemented
825C2—1044no—
826C2C2×#1171865311yescharacteristic
827C2#1311859511yescharacteristic
828C2#1311860311yescharacteristic
829C2#1311862811yescharacteristic
830C2#1311863611yescharacteristic
831C2#1311868211yescharacteristic
832C2#1311868711yescharacteristic
833C2#1311870411yescharacteristic
834C2#1311870911yescharacteristic
835C2#1311975711yescharacteristic
836C2#1311977411yescharacteristic
837C2#1311977911yescharacteristic
838C2#1312019611yescharacteristic
839C2#1312063011yescharacteristic
840C2#1312316911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutator, socle, cosocleC24×C13C24
FittingC2×C13×#389C2
prime radicalC23×D52C22
hypercenterC2×#389D13
hypocenterC13#15148
LCSG ▷ C24×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C2×#11718653C2semidirect
5. C2×#11718634C2semidirect
6. C2×C4×#6101C2semidirect
7. #13113080C2semidirect
8. #13113080C2semidirect
9. #13113078C2semidirect
10. #13113065C2semidirect
11. C2×C13×#389C2semidirect
101. C2×#6101D4semidirect
229. C2×#389D13semidirect
440. C4×C13#399semidirect
643. C13#15148semidirect
824. C4#11718653semidirect

Maximal subgroups

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

subgroupindex
C2×#117186532
C2×#117186002
C2×#117186492
C2×#117186342
C2×C4×#61012
#131130802
#131130782
#131130652
C2×C13×#3892
#1514813