Finite Group Databasebeta

← #15784855

Subgroups — #15784855

Order 3328.

1702 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718638C211yesmaximal, characteristic, complemented
2C2×#11718873C211yesmaximal, characteristic
3C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Dic13C211yesmaximal, characteristic
5#13113097C212yesmaximal, complemented
6#13113083C212yesmaximal
7#13113073C212yesmaximal
8#13113065C211yesmaximal, characteristic, complemented
9#13113065C211yesmaximal, characteristic, complemented
10#13113060C212yesmaximal, 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⋊Dic13C2211yescharacteristic
21C22×C4×Dic13C2212yes—
22C22×C4×Dic13C2211yescharacteristic
23C22×C4×Dic13C2211yescharacteristic
24C13×#380—24no—
25C2×C13×#95C2212yes—
26#11718873—24no—
27C4×C22⋊Dic13C418yescomplemented
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2211yescharacteristic
37C2×#88071C2211yescharacteristic
38#11718638—24no—
39C4⋊C4×Dic13—24no—
40C25×C13C2311yescharacteristic
41C23×C4×C13—22no—
42C23×C4×C13—22no—
43C23×C4×C13—22no—
44C23×C4×C13—22no—
45C23×C4×C13—22no—
46C23×C4×C13—22no—
47C23×C4×C13C2×C414yes—
48C23×C4×C13C2312yes—
49C23×C4×C13C2311yescharacteristic
50C23×C4×C13C2312yes—
51C23×C4×C13C2311yescharacteristic
52C23×Dic13C2312yes—
53C23×Dic13C2311yescharacteristic
54C23×Dic13C2311yescharacteristic
55C23×Dic13C2311yescharacteristic
56C23×Dic13C2312yes—
57C23×Dic13C2311yescharacteristic
58C2×C13×C4⋊C4—22no—
59C2×C13×C4⋊C4—22no—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—22no—
62C2×C13×C4⋊C4—22no—
63C2×C13×C4⋊C4D414yes—
64C2×C13×C22⋊C4—24no—
65C2×C13×C22⋊C4—24no—
66C2×C13×C22⋊C4—42no—
67C2×C22⋊Dic13—22no—
68C2×C22⋊Dic13—22no—
69C2×C22⋊Dic13—22no—
70C2×C22⋊Dic13—22no—
71C2×C22⋊Dic13—24no—
72C2×C22⋊Dic13—24no—
73C2×C22⋊Dic13—42no—
74C2×C22⋊Dic13C2×C414yes—
75C2×C22⋊Dic13C2×C414yes—
76C2×C4⋊Dic13—22no—
77C2×C4⋊Dic13—22no—
78C2×C4⋊Dic13—22no—
79C2×C4⋊Dic13—22no—
80C2×C4⋊Dic13—22no—
81C2×C4⋊Dic13D414yes—
82C2×C4×Dic13—22no—
83C2×C4×Dic13—22no—
84C2×C4×Dic13—22no—
85C2×C4×Dic13—22no—
86C2×C4×Dic13—24no—
87C2×C4×Dic13—24no—
88C2×C4×Dic13—42no—
89C2×C4×Dic13C2×C414yes—
90C2×C4×Dic13C2×C414yes—
91C13×#95—24no—
92#88071—24no—
93#88071—24no—
94#88071—24no—
95#88071—24no—
96#88071—24no—
97#88071—42no—
98#88071—42no—
99#88071—42no—
100#88071C2×C414yes—
101#88071C2×C414yes—
102#13875—131nomaximal, Sylow
103C24×C13—21no—
104C24×C13—21no—
105C24×C13—21no—
106C24×C13—21no—
107C24×C13—21no—
108C24×C13—21no—
109C24×C13—21no—
110C24×C13—21no—
111C24×C13—21no—
112C24×C13—21no—
113C24×C13—21no—
114C24×C13—21no—
115C24×C13C22×C412yes—
116C24×C13#4112yes—
117C24×C13#4112yes—
118C24×C13C2411yescharacteristic
119C22×C4×C13—21no—
120C22×C4×C13—21no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—22no—
130C22×C4×C13—22no—
131C22×C4×C13—28no—
132C22×C4×C13—28no—
133C22×C4×C13—28no—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—22no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—22no—
140C22×C4×C13—22no—
141C22×C4×C13—44no—
142C22×C4×C13—44no—
143C22×C4×C13—44no—
144C22×C4×C13—44no—
145C22×C4×C13C22×C412yes—
146C22×C4×C13C22×C412yes—
147C22×C4×C13C2×D412yes—
148C22×C4×C13C2×D414yes—
149C22×C4×C13C2×D412yes—
150C22×C4×C13#4112yes—
151C22×C4×C13#4112yes—
152C22×C4×C13#4112yes—
153C22×C4×C13#4112yes—
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—21no—
157C22×Dic13—21no—
158C22×Dic13—21no—
159C22×Dic13—21no—
160C22×Dic13—21no—
161C22×Dic13—22no—
162C22×Dic13—21no—
163C22×Dic13—21no—
164C22×Dic13—21no—
165C22×Dic13—22no—
166C22×Dic13—22no—
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—22no—
178C22×Dic13—21no—
179C22×Dic13—21no—
180C22×Dic13—21no—
181C22×Dic13—22no—
182C22×Dic13—22no—
183C22×Dic13—22no—
184C22×Dic13—22no—
185C22×Dic13—22no—
186C22×Dic13—22no—
187C22×Dic13—22no—
188C22×Dic13—22no—
189C22×Dic13C22×C412yes—
190C22×Dic13C22×C412yes—
191C22×Dic13C22×C412yes—
192C22×Dic13C22×C412yes—
193C22×Dic13C2×D414yes—
194C22×Dic13#4112yes—
195C22×Dic13#4112yes—
196C13×C4⋊C4—28no—
197C13×C4⋊C4—44no—
198C13×C22⋊C4—48no—
199C22⋊Dic13—28no—
200C22⋊Dic13—28no—
201C22⋊Dic13—48no—
202C4⋊Dic13—28no—
203C4⋊Dic13—44no—
204C4×Dic13—28no—
205C4×Dic13—28no—
206C4×Dic13—48no—
207C2×#382—131no—
208C2×#380—131no—
209C2×#380D1311yescharacteristic
210C2×C4×C4⋊C4—131no—
211C2×C4×C22⋊C4—131no—
212#1443—132no—
213#1440—132no—
214#1437—132no—
215C4⋊#95—131no—
216C4⋊#95—131no—
217#1434—132no—
218C23×C13—22no—
219C23×C13—22no—
220C23×C13—22no—
221C23×C13—22no—
222C23×C13—22no—
223C23×C13—22no—
224C23×C13—22no—
225C23×C13—22no—
226C23×C13—22no—
227C23×C13—22no—
228C23×C13—22no—
229C23×C13—22no—
230C23×C13—22no—
231C23×C13—22no—
232C23×C13—22no—
233C23×C13—22no—
234C23×C13—22no—
235C23×C13—22no—
236C23×C13—41no—
237C23×C13—41no—
238C23×C13—41no—
239C23×C13—41no—
240C23×C13—41no—
241C23×C13—41no—
242C23×C13—41no—
243C23×C13—41no—
244C23×C13—41no—
245C23×C13—41no—
246C23×C13—41no—
247C23×C13—41no—
248C23×C13—41no—
249C23×C13—41no—
250C23×C13—41no—
251C23×C13—41no—
252C23×C13#11714yes—
253C23×C13C23×C411yescharacteristic
254C23×C13C22×D411yescharacteristic
255C23×C13C22×D411yescharacteristic
256C23×C13C2×#4111yescharacteristic
257C23×C13C2×#4111yescharacteristic
258C23×C13C2×#4111yescharacteristic
259C23×C13C2×#4111yescharacteristic
260C23×C13C2×#4111yescharacteristic
261C23×C13C2×#4111yescharacteristic
262C23×C13C2×#4111yescharacteristic
263C23×C13C2×#4111yescharacteristic
264C23×C13H(5,𝔽2)11yescharacteristic
265C23×C13H(5,𝔽2)11yescharacteristic
266C23×C132−1+411yescharacteristic
267C23×C132−1+411yescharacteristic
268C2×C4×C13—22no—
269C2×C4×C13—22no—
270C2×C4×C13—22no—
271C2×C4×C13—24no—
272C2×C4×C13—24no—
273C2×C4×C13—24no—
274C2×C4×C13—41no—
275C2×C4×C13—41no—
276C2×C4×C13—41no—
277C2×C4×C13—41no—
278C2×C4×C13—42no—
279C2×C4×C13—42no—
280C2×C4×C13—42no—
281C2×C4×C13—42no—
282C2×C4×C13—416no—
283C2×C4×C13—42no—
284C2×C4×C13—42no—
285C2×C4×C13—42no—
286C2×C4×C13—42no—
287C2×C4×C13—42no—
288C2×C4×C13—42no—
289C2×C4×C13—42no—
290C2×C4×C13#11714yes—
291C2×C4×C13C4×D414yes—
292C2×C4×C13C4×D414yes—
293C2×C4×C13#12114yes—
294C2×C4×C13#12314yes—
295C2×C4×C13#12414yes—
296C2×C4×C13#12614yes—
297C2×Dic13—22no—
298C2×Dic13—22no—
299C2×Dic13—22no—
300C2×Dic13—22no—
301C2×Dic13—22no—
302C2×Dic13—22no—
303C2×Dic13—22no—
304C2×Dic13—22no—
305C2×Dic13—22no—
306C2×Dic13—22no—
307C2×Dic13—22no—
308C2×Dic13—22no—
309C2×Dic13—22no—
310C2×Dic13—22no—
311C2×Dic13—22no—
312C2×Dic13—24no—
313C2×Dic13—24no—
314C2×Dic13—24no—
315C2×Dic13—42no—
316C2×Dic13—42no—
317C2×Dic13—42no—
318C2×Dic13—41no—
319C2×Dic13—41no—
320C2×Dic13—41no—
321C2×Dic13—41no—
322C2×Dic13—41no—
323C2×Dic13—42no—
324C2×Dic13—41no—
325C2×Dic13—41no—
326C2×Dic13—41no—
327C2×Dic13—41no—
328C2×Dic13—41no—
329C2×Dic13—41no—
330C2×Dic13—41no—
331C2×Dic13—42no—
332C2×Dic13—42no—
333C2×Dic13—42no—
334C2×Dic13—42no—
335C2×Dic13—42no—
336C2×Dic13—42no—
337C2×Dic13—42no—
338C2×Dic13#11714yes—
339C24×C4C2×D1311yescharacteristic
340C22×C4⋊C4—131no—
341C22×C4⋊C4—131no—
342C22×C4⋊C4C2×D1311yescharacteristic
343C22×C4⋊C4C2×D1311yescharacteristic
344C22×C22⋊C4—131no—
345C22×C22⋊C4—131no—
346C22×C22⋊C4—132no—
347C22×C22⋊C4C2×D1312yes—
348C22×C42—131no—
349C22×C42—131no—
350C22×C42—132no—
351#382—264no—
352#380—24no—
353#380—264no—
354C4×C4⋊C4—264no—
355C4×C22⋊C4—138no—
356C2×#95—131no—
357C2×#95—131no—
358C2×#95—132no—
359C2×#95—132no—
360C2×#95—132no—
361C2×#95—132no—
362C2×#95—132no—
363C2×#95—132no—
364C2×#95—132no—
365C2×#95—132no—
366C2×#95C2×D1312yes—
367C22×C13—24no—
368C22×C13—24no—
369C22×C13—24no—
370C22×C13—42no—
371C22×C13—42no—
372C22×C13—42no—
373C22×C13—42no—
374C22×C13—42no—
375C22×C13—42no—
376C22×C13—42no—
377C22×C13—42no—
378C22×C13—42no—
379C22×C13—42no—
380C22×C13—42no—
381C22×C13—42no—
382C22×C13C2×#11711yescharacteristic
383C22×C13C2×#11711yescharacteristic
384C22×C13C2×#11711yescharacteristic
385C22×C13C2×C4×D411yescharacteristic
386C22×C13C2×C4×D411yescharacteristic
387C22×C13#52011yescharacteristic
388C22×C13#52011yescharacteristic
389C22×C13C2×#12111yescharacteristic
390C22×C13C2×#12311yescharacteristic
391C22×C13C2×#12411yescharacteristic
392C22×C13C2×#12611yescharacteristic
393C22×C13#52911yescharacteristic
394C22×C13#52911yescharacteristic
395C22×C13#52911yescharacteristic
396C22×C13#52911yescharacteristic
397C22×C13#54011yescharacteristic
398C22×C13#54111yescharacteristic
399C22×C13#54211yescharacteristic
400C22×C13#54211yescharacteristic
401C22×C13#54611yescharacteristic
402C22×C13#54611yescharacteristic
403C22×C13#54611yescharacteristic
404C22×C13#54711yescharacteristic
405C22×C13#54811yescharacteristic
406C22×C13#54811yescharacteristic
407C22×C13#54811yescharacteristic
408C22×C13#55011yescharacteristic
409C22×C13#55211yescharacteristic
410C22×C13#55211yescharacteristic
411C22×C13#55211yescharacteristic
412C22×C13#55311yescharacteristic
413C22×C13#55311yescharacteristic
414C22×C13#55311yescharacteristic
415C22×C13#55511yescharacteristic
416C22×C13#55611yescharacteristic
417C4×C13—44no—
418C4×C13—42no—
419C4×C13—82no—
420C4×C13#38818yes—
421Dic13—24no—
422Dic13—42no—
423Dic13—42no—
424Dic13—42no—
425Dic13—44no—
426Dic13—82no—
427C25C22×D1311yescharacteristic
428C23×C4—22no—
429C23×C4—22no—
430C23×C4—22no—
431C23×C4—22no—
432C23×C4—22no—
433C23×C4—22no—
434C23×C4—131no—
435C23×C4—132no—
436C23×C4—131no—
437C23×C4—131no—
438C23×C4—131no—
439C23×C4—132no—
440C23×C4C4×D1314yes—
441C23×C4C22×D1312yes—
442C23×C4C22×D1311yescharacteristic
443C23×C4C22×D1312yes—
444C23×C4C22×D1311yescharacteristic
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—134no—
451C2×C4⋊C4—262no—
452C2×C4⋊C4—262no—
453C2×C4⋊C4—262no—
454C2×C4⋊C4—262no—
455C2×C4⋊C4—262no—
456C2×C4⋊C4C22⋊D1314yes—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—42no—
460C2×C22⋊C4—134no—
461C2×C22⋊C4—134no—
462C2×C22⋊C4—262no—
463C2×C22⋊C4—262no—
464C2×C22⋊C4—262no—
465C2×C22⋊C4—262no—
466C2×C22⋊C4—264no—
467C2×C22⋊C4—264no—
468C2×C22⋊C4—522no—
469C2×C42—134no—
470C2×C42—134no—
471C2×C42—262no—
472C2×C42—262no—
473C2×C42—262no—
474C2×C42—262no—
475C2×C42—264no—
476C2×C42—264no—
477C2×C42—522no—
478#95—24no—
479#95—134no—
480#95—134no—
481#95—264no—
482#95—264no—
483#95—264no—
484#95—264no—
485#95—264no—
486#95—522no—
487#95—522no—
488#95—522no—
489C2×C13—44no—
490C2×C13#228311yescharacteristic
491C2×C13C2×#38811yescharacteristic
492C2×C13#231411yescharacteristic
493C2×C13#235211yescharacteristic
494C2×C13#235211yescharacteristic
495C2×C13#235211yescharacteristic
496C2×C13#235411yescharacteristic
497C2×C13#242011yescharacteristic
498C2×C13#242111yescharacteristic
499C2×C13#242611yescharacteristic
500C2×C13#242711yescharacteristic
501C2×C13#248911yescharacteristic
502C2×C13#249011yescharacteristic
503C2×C13#249411yescharacteristic
504C2×C13#249511yescharacteristic
505C24—21no—
506C24—21no—
507C24—21no—
508C24—21no—
509C24—21no—
510C24—21no—
511C24—21no—
512C24—21no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—21no—
517C24C2×C4×D1312yes—
518C24#612912yes—
519C24#613112yes—
520C24C23×D1311yescharacteristic
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—28no—
534C22×C4—28no—
535C22×C4—28no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—132no—
548C22×C4—132no—
549C22×C4—132no—
550C22×C4—132no—
551C22×C4—132no—
552C22×C4—132no—
553C22×C4—134no—
554C22×C4—261no—
555C22×C4—261no—
556C22×C4—261no—
557C22×C4—261no—
558C22×C4—261no—
559C22×C4—261no—
560C22×C4—261no—
561C22×C4—261no—
562C22×C4—261no—
563C22×C4—261no—
564C22×C4—261no—
565C22×C4—262no—
566C22×C4—261no—
567C22×C4—261no—
568C22×C4—261no—
569C22×C4—261no—
570C22×C4—262no—
571C22×C4—261no—
572C22×C4—261no—
573C22×C4—262no—
574C22×C4—262no—
575C22×C4—261no—
576C22×C4—261no—
577C22×C4—261no—
578C22×C4—262no—
579C22×C4—261no—
580C22×C4—261no—
581C22×C4—262no—
582C22×C4—262no—
583C22×C4—262no—
584C22×C4—262no—
585C22×C4—262no—
586C22×C4—262no—
587C22×C4—262no—
588C22×C4—262no—
589C22×C4C2×C4×D1312yes—
590C22×C4C2×C4×D1312yes—
591C22×C4#612712yes—
592C22×C4D4×D1312yes—
593C22×C4#612912yes—
594C22×C4#612912yes—
595C22×C4#612912yes—
596C22×C4C2×C22⋊D1314yes—
597C22×C4C2×C22⋊D1312yes—
598C4⋊C4—28no—
599C4⋊C4—44no—
600C4⋊C4—268no—
601C4⋊C4—524no—
602C22⋊C4—48no—
603C22⋊C4—268no—
604C22⋊C4—268no—
605C22⋊C4—528no—
606C42—268no—
607C42—268no—
608C42—528no—
609C13#1387511yescharacteristic, complemented, Sylow
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23#8814614yes—
645C23C22×C4×D1311yescharacteristic
646C23C2×#612711yescharacteristic
647C23C2×D4×D1311yescharacteristic
648C23C2×#612911yescharacteristic
649C23C2×#612911yescharacteristic
650C23C2×#612911yescharacteristic
651C23C2×#612911yescharacteristic
652C23#8825111yescharacteristic
653C23C2×#613111yescharacteristic
654C23#8825411yescharacteristic
655C23#41×D1311yescharacteristic
656C23#41×D1311yescharacteristic
657C23#8825611yescharacteristic
658C23#8825711yescharacteristic
659C23C22×C22⋊D1311yescharacteristic
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—416no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—134no—
683C2×C4—262no—
684C2×C4—262no—
685C2×C4—262no—
686C2×C4—262no—
687C2×C4—262no—
688C2×C4—262no—
689C2×C4—262no—
690C2×C4—262no—
691C2×C4—262no—
692C2×C4—262no—
693C2×C4—262no—
694C2×C4—262no—
695C2×C4—262no—
696C2×C4—262no—
697C2×C4—262no—
698C2×C4—264no—
699C2×C4—264no—
700C2×C4—264no—
701C2×C4—521no—
702C2×C4—521no—
703C2×C4—521no—
704C2×C4—521no—
705C2×C4—522no—
706C2×C4—522no—
707C2×C4—521no—
708C2×C4—521no—
709C2×C4—521no—
710C2×C4—521no—
711C2×C4—522no—
712C2×C4—521no—
713C2×C4—521no—
714C2×C4—521no—
715C2×C4—521no—
716C2×C4—522no—
717C2×C4—522no—
718C2×C4—522no—
719C2×C4—522no—
720C2×C4—522no—
721C2×C4—522no—
722C2×C4—522no—
723C2×C4—522no—
724C2×C4#8813114yes—
725C2×C4#8813314yes—
726C2×C4#8813514yes—
727C2×C4#8813914yes—
728C2×C4C4×C22⋊D1314yes—
729C2×C4#8818914yes—
730C2×C4#8819214yes—
731C22—24no—
732C22—24no—
733C22—24no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22C2×#8813111yescharacteristic
747C22C2×#8813311yescharacteristic
748C22C2×#8813511yescharacteristic
749C22C2×#8813911yescharacteristic
750C22C2×#8814611yescharacteristic
751C22#1171920911yescharacteristic
752C22#1171921811yescharacteristic
753C22#1171921911yescharacteristic
754C22D13×#11711yescharacteristic
755C22#1171922811yescharacteristic
756C22#1171923411yescharacteristic
757C22#1171923511yescharacteristic
758C22#1171930311yescharacteristic
759C22#1171930411yescharacteristic
760C22#1171930511yescharacteristic
761C22#1171930511yescharacteristic
762C22#1171930811yescharacteristic
763C22#1171932111yescharacteristic
764C22#1171932311yescharacteristic
765C22#1171932411yescharacteristic
766C22#1171932911yescharacteristic
767C22#1171932911yescharacteristic
768C22#1171933011yescharacteristic
769C22#1171933511yescharacteristic
770C22#1171933611yescharacteristic
771C22#1171934611yescharacteristic
772C22#1171934711yescharacteristic
773C22#1171934811yescharacteristic
774C22C2×C4×C22⋊D1311yescharacteristic
775C22C2×#8818911yescharacteristic
776C22C2×#8819211yescharacteristic
777C22#1171951111yescharacteristic
778C22#1171952211yescharacteristic
779C22#1171953411yescharacteristic
780C22#1171953611yescharacteristic
781C4—42no—
782C4—44no—
783C4—82no—
784C4—264no—
785C4—522no—
786C4—522no—
787C4—522no—
788C4—524no—
789C4—1042no—
790C4#1171860518yes—
791C2—44no—
792C2#1311723111yescharacteristic
793C2C2×#1171860511yescharacteristic
794C2#1311744311yescharacteristic
795C2#1311776111yescharacteristic
796C2#1311776611yescharacteristic
797C2#1311776711yescharacteristic
798C2#1311778011yescharacteristic
799C2#1311832411yescharacteristic
800C2#1311833511yescharacteristic
801C2#1311839811yescharacteristic
802C2#1311840911yescharacteristic
803C2#1311917311yescharacteristic
804C2#1311918411yescharacteristic
805C2#1311923211yescharacteristic
806C2#1311924311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#380C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×#380D13
hypocenterC13#13875
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C2×#11718638C2semidirect
3. C2×C4⋊C4×Dic13C2semidirect
5. #13113097C2semidirect
8. #13113065C2semidirect
9. #13113065C2semidirect
10. #13113060C2semidirect
27. C4×C22⋊Dic13C4semidirect
609. C13#13875semidirect

Maximal subgroups

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

subgroupindex
C2×#117186382
C2×#117188732
C2×C4⋊C4×Dic132
C2×C4×C22⋊Dic132
#131130972
#131130832
#131130732
#131130652
#131130602
C2×C13×#3802
#1387513