Finite Group Databasebeta

← #15799565

Subgroups — #15799565

Order 3328.

1814 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718610C212yesmaximal
2C2×#11718646C211yesmaximal, characteristic, complemented
3C2×#11718634C211yesmaximal, characteristic, complemented
4C2×#11718637C211yesmaximal, characteristic, complemented
5C2×#11718873C211yesmaximal, characteristic
6C2×C4×C22⋊Dic13C211yesmaximal, characteristic
7#13113102C212yesmaximal, complemented
8#13113100C212yesmaximal, complemented
9#13113079C212yesmaximal
10#13113065C211yesmaximal, characteristic, complemented
11C2×C13×#380C211yesmaximal, characteristic
12C24×C4×C13C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C13×C22⋊C4C2212yes—
16C22×C22⋊Dic13C2212yes—
17C22×C22⋊Dic13C2211yescharacteristic
18C22×C22⋊Dic13C2211yescharacteristic
19C22×C4⋊Dic13C2211yescharacteristic
20C22×C4⋊Dic13C2212yes—
21C22×C4⋊Dic13C2211yescharacteristic
22C22×#6101C2212yes—
23C22×#6101C2212yes—
24C22×#6101C2212yes—
25C22×C4×Dic13C2211yescharacteristic
26C22×C4×Dic13C2211yescharacteristic
27C13×#380—24no—
28C2×C13×#95C2212yes—
29#11718873—24no—
30C4×C22⋊Dic13—24no—
31C2×#88071C2211yescharacteristic
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2211yescharacteristic
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38#11718646—24no—
39#11718637—24no—
40#11718634—24no—
41#11718610—28no—
42C25×C13C2311yescharacteristic
43C23×C4×C13—22no—
44C23×C4×C13—22no—
45C23×C4×C13—22no—
46C23×C4×C13—22no—
47C23×C4×C13—22no—
48C23×C4×C13—22no—
49C23×C4×C13Q814yes—
50C23×C4×C13C2312yes—
51C23×C4×C13C2312yes—
52C23×C4×C13C2311yescharacteristic
53C23×C4×C13C2311yescharacteristic
54C23×Dic13C2312yes—
55C23×Dic13C2311yescharacteristic
56C23×Dic13C2312yes—
57C23×Dic13C2311yescharacteristic
58C23×Dic13C2311yescharacteristic
59C23×Dic13C2311yescharacteristic
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—22no—
62C2×C13×C4⋊C4—22no—
63C2×C13×C4⋊C4—22no—
64C2×C13×C4⋊C4—22no—
65C2×C13×C4⋊C4D414yes—
66C2×C13×C22⋊C4—24no—
67C2×C13×C22⋊C4—24no—
68C2×C13×C22⋊C4—42no—
69C2×C22⋊Dic13—22no—
70C2×C22⋊Dic13—22no—
71C2×C22⋊Dic13—22no—
72C2×C22⋊Dic13—22no—
73C2×C22⋊Dic13—24no—
74C2×C22⋊Dic13—24no—
75C2×C22⋊Dic13—42no—
76C2×C22⋊Dic13D414yes—
77C2×C22⋊Dic13Q814yes—
78C2×C4⋊Dic13—22no—
79C2×C4⋊Dic13—22no—
80C2×C4⋊Dic13—22no—
81C2×C4⋊Dic13—22no—
82C2×C4⋊Dic13—24no—
83C2×C4⋊Dic13—22no—
84C2×C4⋊Dic13—24no—
85C2×C4⋊Dic13—42no—
86C2×C4⋊Dic13D414yes—
87C2×#6101—24no—
88C2×#6101—24no—
89C2×#6101—24no—
90C2×#6101—24no—
91C2×#6101—24no—
92C2×#6101—24no—
93C2×#6101—42no—
94C2×#6101—42no—
95C2×#6101—42no—
96C2×C4×Dic13—22no—
97C2×C4×Dic13—22no—
98C2×C4×Dic13—22no—
99C2×C4×Dic13—22no—
100C2×C4×Dic13—22no—
101C2×C4×Dic13D414yes—
102C13×#95—24no—
103#88071—24no—
104#88071—24no—
105#88071—22no—
106#88071—22no—
107#88071—24no—
108#88071—24no—
109#88071—24no—
110#15135—131nomaximal, Sylow
111C24×C13—21no—
112C24×C13—21no—
113C24×C13—21no—
114C24×C13—21no—
115C24×C13—21no—
116C24×C13—21no—
117C24×C13—21no—
118C24×C13—21no—
119C24×C13—21no—
120C24×C13—21no—
121C24×C13—21no—
122C24×C13—21no—
123C24×C13C2×D412yes—
124C24×C13C2×Q812yes—
125C24×C13C2×Q812yes—
126C24×C13C2411yescharacteristic
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—22no—
130C22×C4×C13—21no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—28no—
140C22×C4×C13—28no—
141C22×C4×C13—28no—
142C22×C4×C13—22no—
143C22×C4×C13—22no—
144C22×C4×C13—22no—
145C22×C4×C13—22no—
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13—22no—
149C22×C4×C13—44no—
150C22×C4×C13—44no—
151C22×C4×C13—44no—
152C22×C4×C13—44no—
153C22×C4×C13C2×D412yes—
154C22×C4×C13C2×D412yes—
155C22×C4×C13C2×D414yes—
156C22×C4×C13C2×D412yes—
157C22×C4×C13C2×Q812yes—
158C22×C4×C13C2×Q812yes—
159C22×C4×C13#4112yes—
160C22×C4×C13#4112yes—
161C22×C4×C13#4112yes—
162C22×Dic13—21no—
163C22×Dic13—21no—
164C22×Dic13—21no—
165C22×Dic13—21no—
166C22×Dic13—21no—
167C22×Dic13—21no—
168C22×Dic13—21no—
169C22×Dic13—21no—
170C22×Dic13—21no—
171C22×Dic13—21no—
172C22×Dic13—21no—
173C22×Dic13—21no—
174C22×Dic13—22no—
175C22×Dic13—21no—
176C22×Dic13—21no—
177C22×Dic13—22no—
178C22×Dic13—22no—
179C22×Dic13—22no—
180C22×Dic13—21no—
181C22×Dic13—21no—
182C22×Dic13—21no—
183C22×Dic13—22no—
184C22×Dic13—21no—
185C22×Dic13—22no—
186C22×Dic13—21no—
187C22×Dic13—21no—
188C22×Dic13—22no—
189C22×Dic13—22no—
190C22×Dic13—22no—
191C22×Dic13—22no—
192C22×Dic13—22no—
193C22×Dic13—22no—
194C22×Dic13—22no—
195C22×Dic13C2×D414yes—
196C22×Dic13C2×D412yes—
197C22×Dic13C2×D412yes—
198C22×Dic13C2×D412yes—
199C22×Dic13C2×D412yes—
200C22×Dic13C2×Q812yes—
201C22×Dic13C2×Q812yes—
202C22×Dic13#4112yes—
203C22×Dic13#4112yes—
204C13×C4⋊C4—28no—
205C13×C4⋊C4—44no—
206C13×C22⋊C4—48no—
207C22⋊Dic13—28no—
208C22⋊Dic13—28no—
209C22⋊Dic13—48no—
210C4⋊Dic13—28no—
211C4⋊Dic13—48no—
212C4⋊Dic13—44no—
213#6101—48no—
214#6101—48no—
215#6101—48no—
216C4×Dic13—28no—
217C4×Dic13—44no—
218C2×#399—132no—
219C2×#389—131no—
220C2×#389—131no—
221C2×#384—131no—
222C2×#380—131no—
223C2×#380D1311yescharacteristic
224C2×C4×C22⋊C4—131no—
225#1445—132no—
226#1444—132no—
227#1439—132no—
228C4⋊#95—131no—
229C23×C13—22no—
230C23×C13—22no—
231C23×C13—22no—
232C23×C13—22no—
233C23×C13—22no—
234C23×C13—22no—
235C23×C13—22no—
236C23×C13—22no—
237C23×C13—22no—
238C23×C13—22no—
239C23×C13—22no—
240C23×C13—22no—
241C23×C13—22no—
242C23×C13—22no—
243C23×C13—22no—
244C23×C13—22no—
245C23×C13—22no—
246C23×C13—22no—
247C23×C13—41no—
248C23×C13—41no—
249C23×C13—41no—
250C23×C13—41no—
251C23×C13—41no—
252C23×C13—41no—
253C23×C13—41no—
254C23×C13—41no—
255C23×C13—41no—
256C23×C13—41no—
257C23×C13—41no—
258C23×C13—41no—
259C23×C13—41no—
260C23×C13—41no—
261C23×C13—41no—
262C23×C13—41no—
263C23×C13C4⋊Q814yes—
264C23×C13C22×D411yescharacteristic
265C23×C13C22×D411yescharacteristic
266C23×C13C22×D411yescharacteristic
267C23×C13C22×D411yescharacteristic
268C23×C13C22×Q811yescharacteristic
269C23×C13C22×Q811yescharacteristic
270C23×C13C2×#4111yescharacteristic
271C23×C13C2×#4111yescharacteristic
272C23×C13C2×#4111yescharacteristic
273C23×C13C2×#4111yescharacteristic
274C23×C13C2×#4111yescharacteristic
275C23×C13H(5,𝔽2)11yescharacteristic
276C23×C13H(5,𝔽2)11yescharacteristic
277C23×C132−1+411yescharacteristic
278C23×C132−1+411yescharacteristic
279C2×C4×C13—22no—
280C2×C4×C13—22no—
281C2×C4×C13—22no—
282C2×C4×C13—24no—
283C2×C4×C13—24no—
284C2×C4×C13—24no—
285C2×C4×C13—41no—
286C2×C4×C13—41no—
287C2×C4×C13—41no—
288C2×C4×C13—41no—
289C2×C4×C13—42no—
290C2×C4×C13—42no—
291C2×C4×C13—42no—
292C2×C4×C13—42no—
293C2×C4×C13—416no—
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×C13C22⋊Q814yes—
302C2×C4×C13C22⋊Q814yes—
303C2×C4×C13C22⋊Q814yes—
304C2×C4×C13#12314yes—
305C2×C4×C13#12314yes—
306C2×C4×C13#12314yes—
307C2×C4×C13#12714yes—
308C2×Dic13—22no—
309C2×Dic13—22no—
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—22no—
324C2×Dic13—24no—
325C2×Dic13—22no—
326C2×Dic13—24no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—41no—
330C2×Dic13—41no—
331C2×Dic13—42no—
332C2×Dic13—41no—
333C2×Dic13—41no—
334C2×Dic13—42no—
335C2×Dic13—42no—
336C2×Dic13—41no—
337C2×Dic13—41no—
338C2×Dic13—41no—
339C2×Dic13—41no—
340C2×Dic13—42no—
341C2×Dic13—42no—
342C2×Dic13—42no—
343C2×Dic13—42no—
344C2×Dic13—42no—
345C2×Dic13—42no—
346C2×Dic13—42no—
347C2×Dic13—42no—
348C2×Dic13#12114yes—
349C2×Dic13C22⋊Q814yes—
350C24×C4C2×D1311yescharacteristic
351C22×C4⋊C4—131no—
352C22×C4⋊C4—132no—
353C22×C4⋊C4—131no—
354C22×C4⋊C4—132no—
355C22×C4⋊C4—132no—
356C22×C4⋊C4—132no—
357C22×C4⋊C4C2×D1311yescharacteristic
358C22×C4⋊C4C2×D1311yescharacteristic
359C22×C22⋊C4—131no—
360C22×C22⋊C4—131no—
361C22×C22⋊C4—132no—
362C22×C22⋊C4C2×D1312yes—
363C22×C42—131no—
364C22×C42—131no—
365#399—268no—
366#389—264no—
367#389—264no—
368#384—264no—
369#380—24no—
370#380—264no—
371C4×C22⋊C4—264no—
372C2×#95—132no—
373C2×#95—132no—
374C2×#95—132no—
375C2×#95—132no—
376C2×#95—131no—
377C2×#95—132no—
378C2×#95—131no—
379C2×#95C2×D1312yes—
380C22×C13—24no—
381C22×C13—24no—
382C22×C13—24no—
383C22×C13—42no—
384C22×C13—42no—
385C22×C13—42no—
386C22×C13—42no—
387C22×C13—42no—
388C22×C13—42no—
389C22×C13—42no—
390C22×C13—42no—
391C22×C13—42no—
392C22×C13—42no—
393C22×C13—42no—
394C22×C13—42no—
395C22×C13C2×#12111yescharacteristic
396C22×C13C2×C22⋊Q811yescharacteristic
397C22×C13C2×C22⋊Q811yescharacteristic
398C22×C13C2×C22⋊Q811yescharacteristic
399C22×C13C2×C22⋊Q811yescharacteristic
400C22×C13C2×#12311yescharacteristic
401C22×C13C2×#12311yescharacteristic
402C22×C13C2×#12311yescharacteristic
403C22×C13C2×#12711yescharacteristic
404C22×C13C2×C4⋊Q811yescharacteristic
405C22×C13#53211yescharacteristic
406C22×C13#53311yescharacteristic
407C22×C13#53311yescharacteristic
408C22×C13#53511yescharacteristic
409C22×C13#53611yescharacteristic
410C22×C13#54211yescharacteristic
411C22×C13#54211yescharacteristic
412C22×C13#54411yescharacteristic
413C22×C13#54411yescharacteristic
414C22×C13D4211yescharacteristic
415C22×C13D4211yescharacteristic
416C22×C13#54711yescharacteristic
417C22×C13#54711yescharacteristic
418C22×C13#54711yescharacteristic
419C22×C13#54711yescharacteristic
420C22×C13D4×Q811yescharacteristic
421C22×C13D4×Q811yescharacteristic
422C22×C13#55011yescharacteristic
423C22×C13#55011yescharacteristic
424C22×C13#55211yescharacteristic
425C22×C13#55211yescharacteristic
426C22×C13#55311yescharacteristic
427C22×C13#55311yescharacteristic
428C22×C13#55411yescharacteristic
429C22×C13#55411yescharacteristic
430C4×C13—42no—
431C4×C13—44no—
432C4×C13—82no—
433C4×C13#39918yescomplemented
434Dic13—24no—
435Dic13—24no—
436Dic13—44no—
437Dic13—42no—
438Dic13—42no—
439Dic13—82no—
440C25C22×D1311yescharacteristic
441C23×C4—22no—
442C23×C4—22no—
443C23×C4—22no—
444C23×C4—22no—
445C23×C4—22no—
446C23×C4—22no—
447C23×C4—131no—
448C23×C4—131no—
449C23×C4—131no—
450C23×C4—132no—
451C23×C4—131no—
452C23×C4—132no—
453C23×C4Dic2614yes—
454C23×C4C22×D1312yes—
455C23×C4C22×D1311yescharacteristic
456C23×C4C22×D1312yes—
457C23×C4C22×D1311yescharacteristic
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—134no—
464C2×C4⋊C4—262no—
465C2×C4⋊C4—262no—
466C2×C4⋊C4—264no—
467C2×C4⋊C4—264no—
468C2×C4⋊C4—264no—
469C2×C4⋊C4—264no—
470C2×C4⋊C4—264no—
471C2×C4⋊C4—264no—
472C2×C4⋊C4—264no—
473C2×C4⋊C4—262no—
474C2×C4⋊C4—262no—
475C2×C4⋊C4—264no—
476C2×C4⋊C4—262no—
477C2×C4⋊C4—522no—
478C2×C4⋊C4—522no—
479C2×C4⋊C4—522no—
480C2×C4⋊C4—522no—
481C2×C4⋊C4C22⋊D1314yes—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—42no—
485C2×C22⋊C4—134no—
486C2×C22⋊C4—134no—
487C2×C22⋊C4—262no—
488C2×C22⋊C4—262no—
489C2×C22⋊C4—262no—
490C2×C22⋊C4—262no—
491C2×C22⋊C4—264no—
492C2×C22⋊C4—264no—
493C2×C22⋊C4—522no—
494C2×C42—134no—
495C2×C42—262no—
496C2×C42—262no—
497C2×C42—262no—
498C2×C42—262no—
499C2×C42—262no—
500#95—24no—
501#95—264no—
502#95—262no—
503#95—262no—
504#95—264no—
505#95—264no—
506#95—264no—
507#95—264no—
508C2×C13—44no—
509C2×C13C2×#39911yescharacteristic
510C2×C13#242211yescharacteristic
511C2×C13#242211yescharacteristic
512C2×C13#242311yescharacteristic
513C2×C13#242311yescharacteristic
514C2×C13#244011yescharacteristic
515C2×C13#244011yescharacteristic
516C2×C13#244111yescharacteristic
517C2×C13#244111yescharacteristic
518C2×C13#248611yescharacteristic
519C2×C13#248711yescharacteristic
520C2×C13#254111yescharacteristic
521C2×C13#254211yescharacteristic
522C2×C13#262811yescharacteristic
523C2×C13#285711yescharacteristic
524C24—21no—
525C24—21no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24—21no—
530C24—21no—
531C24—21no—
532C24—21no—
533C24—21no—
534C24—21no—
535C24—21no—
536C24C2×Dic2612yes—
537C24D4×D1312yes—
538C24Q8×D1312yes—
539C24C23×D1311yescharacteristic
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—28no—
553C22×C4—28no—
554C22×C4—28no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—132no—
567C22×C4—132no—
568C22×C4—132no—
569C22×C4—132no—
570C22×C4—132no—
571C22×C4—132no—
572C22×C4—134no—
573C22×C4—132no—
574C22×C4—132no—
575C22×C4—261no—
576C22×C4—261no—
577C22×C4—261no—
578C22×C4—261no—
579C22×C4—261no—
580C22×C4—261no—
581C22×C4—261no—
582C22×C4—261no—
583C22×C4—262no—
584C22×C4—261no—
585C22×C4—261no—
586C22×C4—261no—
587C22×C4—262no—
588C22×C4—261no—
589C22×C4—262no—
590C22×C4—261no—
591C22×C4—261no—
592C22×C4—262no—
593C22×C4—262no—
594C22×C4—261no—
595C22×C4—261no—
596C22×C4—262no—
597C22×C4—261no—
598C22×C4—261no—
599C22×C4—261no—
600C22×C4—261no—
601C22×C4—262no—
602C22×C4—262no—
603C22×C4—262no—
604C22×C4—262no—
605C22×C4—262no—
606C22×C4—262no—
607C22×C4—262no—
608C22×C4C2×Dic2612yes—
609C22×C4C2×Dic2612yes—
610C22×C4#612712yes—
611C22×C4D4×D1312yes—
612C22×C4D4×D1312yes—
613C22×C4#612912yes—
614C22×C4#612912yes—
615C22×C4C2×C22⋊D1314yes—
616C22×C4C2×C22⋊D1312yes—
617C4⋊C4—28no—
618C4⋊C4—44no—
619C4⋊C4—268no—
620C4⋊C4—528no—
621C4⋊C4—528no—
622C4⋊C4—528no—
623C4⋊C4—528no—
624C4⋊C4—524no—
625C22⋊C4—48no—
626C22⋊C4—268no—
627C22⋊C4—268no—
628C22⋊C4—528no—
629C42—268no—
630C42—524no—
631C13#1513511yescharacteristic, complemented, Sylow
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23#8814214yes—
667C23C22×Dic2611yescharacteristic
668C23C2×#612711yescharacteristic
669C23C2×D4×D1311yescharacteristic
670C23C2×D4×D1311yescharacteristic
671C23C2×D4×D1311yescharacteristic
672C23C2×#612911yescharacteristic
673C23C2×#612911yescharacteristic
674C23#8825111yescharacteristic
675C23C2×Q8×D1311yescharacteristic
676C23#8825411yescharacteristic
677C23#41×D1311yescharacteristic
678C23#41×D1311yescharacteristic
679C23#8825611yescharacteristic
680C23#8825711yescharacteristic
681C23C22×C22⋊D1311yescharacteristic
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—416no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—134no—
705C2×C4—134no—
706C2×C4—262no—
707C2×C4—262no—
708C2×C4—262no—
709C2×C4—262no—
710C2×C4—262no—
711C2×C4—262no—
712C2×C4—262no—
713C2×C4—262no—
714C2×C4—262no—
715C2×C4—262no—
716C2×C4—262no—
717C2×C4—262no—
718C2×C4—264no—
719C2×C4—262no—
720C2×C4—262no—
721C2×C4—262no—
722C2×C4—264no—
723C2×C4—262no—
724C2×C4—262no—
725C2×C4—264no—
726C2×C4—262no—
727C2×C4—522no—
728C2×C4—522no—
729C2×C4—521no—
730C2×C4—521no—
731C2×C4—521no—
732C2×C4—521no—
733C2×C4—522no—
734C2×C4—521no—
735C2×C4—521no—
736C2×C4—521no—
737C2×C4—521no—
738C2×C4—522no—
739C2×C4—522no—
740C2×C4—522no—
741C2×C4—522no—
742C2×C4—522no—
743C2×C4—522no—
744C2×C4—522no—
745C2×C4—522no—
746C2×C4#8813214yes—
747C2×C4#8813214yes—
748C2×C4#8813714yes—
749C2×C4#8813714yes—
750C2×C4#8817814yes—
751C2×C4#8818914yes—
752C2×C4#8819414yes—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22C2×#8813211yescharacteristic
769C22C2×#8813211yescharacteristic
770C22C2×#8813711yescharacteristic
771C22C2×#8813711yescharacteristic
772C22C2×#8814211yescharacteristic
773C22#1171920511yescharacteristic
774C22#1171921211yescharacteristic
775C22#1171921611yescharacteristic
776C22#1171922211yescharacteristic
777C22#1171922411yescharacteristic
778C22#1171923411yescharacteristic
779C22#1171923511yescharacteristic
780C22#1171930111yescharacteristic
781C22#1171930411yescharacteristic
782C22#1171930811yescharacteristic
783C22D13×#12111yescharacteristic
784C22#1171931211yescharacteristic
785C22#1171931411yescharacteristic
786C22#1171931611yescharacteristic
787C22#1171931911yescharacteristic
788C22#1171932711yescharacteristic
789C22D13×C22⋊Q811yescharacteristic
790C22#1171933311yescharacteristic
791C22#1171933611yescharacteristic
792C22#1171933711yescharacteristic
793C22#1171934011yescharacteristic
794C22#1171934411yescharacteristic
795C22#1171934811yescharacteristic
796C22C2×#8817811yescharacteristic
797C22C2×#8818911yescharacteristic
798C22D4×C22⋊D1311yescharacteristic
799C22C2×#8819411yescharacteristic
800C22Q8×C22⋊D1311yescharacteristic
801C22#1171952911yescharacteristic
802C22#1171953911yescharacteristic
803C4—42no—
804C4—44no—
805C4—82no—
806C4—264no—
807C4—264no—
808C4—522no—
809C4—522no—
810C4—524no—
811C4—1042no—
812C4#1171861018yescomplemented
813C2—44no—
814C2C2×#1171861011yescharacteristic
815C2#1311834611yescharacteristic
816C2#1311835211yescharacteristic
817C2#1311835711yescharacteristic
818C2#1311836311yescharacteristic
819C2#1311853211yescharacteristic
820C2#1311853911yescharacteristic
821C2#1311854311yescharacteristic
822C2#1311855011yescharacteristic
823C2#1311914011yescharacteristic
824C2#1311914911yescharacteristic
825C2#1311977911yescharacteristic
826C2#1311978611yescharacteristic
827C2#1312066111yescharacteristic
828C2#1312318611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutator, socle, cosocleC24×C13C24
FittingC2×C13×#380C2
prime radicalC25×C13C23
hypercenterC2×#380D13
hypocenterC13#15135
LCSG ▷ C24×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×#11718646C2semidirect
3. C2×#11718634C2semidirect
4. C2×#11718637C2semidirect
7. #13113102C2semidirect
8. #13113100C2semidirect
10. #13113065C2semidirect
433. C4×C13#399semidirect
631. C13#15135semidirect
812. 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×#117186462
C2×#117186342
C2×#117186372
C2×#117188732
C2×C4×C22⋊Dic132
#131131022
#131131002
#131130792
#131130652
C2×C13×#3802
#1513513