Finite Group Databasebeta

← #15785759

Subgroups — #15785759

Order 3328.

1746 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718646C211yesmaximal, characteristic, complemented
2C2×#11718873C211yesmaximal, characteristic
3C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Dic13C211yesmaximal, characteristic
5#13113093C212yesmaximal, complemented
6#13113081C212yesmaximal
7#13113073C212yesmaximal
8#13113065C211yesmaximal, characteristic, complemented
9#13113065C211yesmaximal, characteristic, complemented
10#13113061C212yesmaximal, complemented
11C2×C13×#380C211yesmaximal, characteristic
12C24×C4×C13C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C13×C22⋊C4C2212yes—
16C22×C22⋊Dic13C2211yescharacteristic
17C22×C22⋊Dic13C2212yes—
18C22×C22⋊Dic13C2211yescharacteristic
19C22×C4⋊Dic13C2211yescharacteristic
20C22×C4⋊Dic13C2211yescharacteristic
21C22×C4⋊Dic13C2212yes—
22C22×C4×Dic13C2211yescharacteristic
23C22×C4×Dic13C2212yes—
24C22×C4×Dic13C2211yescharacteristic
25C13×#380C418yescomplemented
26C2×C13×#95C2212yes—
27#11718873—24no—
28C4×C22⋊Dic13—24no—
29C2×#88071C2211yescharacteristic
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2211yescharacteristic
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38#11718646—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×C13C2312yes—
50C23×C4×C13C2311yescharacteristic
51C23×C4×C13C2311yescharacteristic
52C23×Dic13C2312yes—
53C23×Dic13C2311yescharacteristic
54C23×Dic13C2312yes—
55C23×Dic13C2311yescharacteristic
56C23×Dic13C2311yescharacteristic
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⋊C4C2×C414yes—
63C2×C13×C4⋊C4C2×C414yes—
64C2×C13×C22⋊C4—42no—
65C2×C13×C22⋊C4—42no—
66C2×C13×C22⋊C4C2×C418yes—
67C2×C22⋊Dic13—22no—
68C2×C22⋊Dic13—22no—
69C2×C22⋊Dic13—22no—
70C2×C22⋊Dic13—22no—
71C2×C22⋊Dic13—22no—
72C2×C22⋊Dic13—24no—
73C2×C22⋊Dic13—24no—
74C2×C22⋊Dic13—42no—
75C2×C22⋊Dic13Q814yes—
76C2×C4⋊Dic13—22no—
77C2×C4⋊Dic13—22no—
78C2×C4⋊Dic13—22no—
79C2×C4⋊Dic13—22no—
80C2×C4⋊Dic13—22no—
81C2×C4⋊Dic13—24no—
82C2×C4⋊Dic13—42no—
83C2×C4⋊Dic13—42no—
84C2×C4⋊Dic13D414yes—
85C2×C4×Dic13—22no—
86C2×C4×Dic13—22no—
87C2×C4×Dic13—22no—
88C2×C4×Dic13—22no—
89C2×C4×Dic13—22no—
90C2×C4×Dic13—24no—
91C2×C4×Dic13—24no—
92C2×C4×Dic13—42no—
93C2×C4×Dic13D414yes—
94C13×#95C2×C418yes—
95#88071—22no—
96#88071—22no—
97#88071—24no—
98#88071—24no—
99#88071—24no—
100#88071—24no—
101#88071—42no—
102#88071—42no—
103#88071—42no—
104#13973—131nomaximal, Sylow
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×C13—21no—
116C24×C13—21no—
117C24×C13C22×C412yes—
118C24×C13C2×Q812yes—
119C24×C13#4112yes—
120C24×C13C2411yescharacteristic
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—22no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—28no—
140C22×C4×C13—28no—
141C22×C4×C13—28no—
142C22×C4×C13—44no—
143C22×C4×C13—44no—
144C22×C4×C13—44no—
145C22×C4×C13—44no—
146C22×C4×C13C22×C412yes—
147C22×C4×C13C22×C414yes—
148C22×C4×C13C22×C414yes—
149C22×C4×C13C22×C412yes—
150C22×C4×C13C2×D412yes—
151C22×C4×C13C2×D412yes—
152C22×C4×C13#4112yes—
153C22×C4×C13#4112yes—
154C22×C4×C13#4112yes—
155C22×C4×C13#4112yes—
156C22×Dic13—21no—
157C22×Dic13—21no—
158C22×Dic13—21no—
159C22×Dic13—21no—
160C22×Dic13—21no—
161C22×Dic13—21no—
162C22×Dic13—21no—
163C22×Dic13—21no—
164C22×Dic13—22no—
165C22×Dic13—21no—
166C22×Dic13—21no—
167C22×Dic13—21no—
168C22×Dic13—21no—
169C22×Dic13—22no—
170C22×Dic13—22no—
171C22×Dic13—21no—
172C22×Dic13—21no—
173C22×Dic13—21no—
174C22×Dic13—21no—
175C22×Dic13—22no—
176C22×Dic13—21no—
177C22×Dic13—21no—
178C22×Dic13—21no—
179C22×Dic13—22no—
180C22×Dic13—22no—
181C22×Dic13—21no—
182C22×Dic13—21no—
183C22×Dic13—21no—
184C22×Dic13—22no—
185C22×Dic13—22no—
186C22×Dic13—22no—
187C22×Dic13—22no—
188C22×Dic13—22no—
189C22×Dic13—22no—
190C22×Dic13—22no—
191C22×Dic13C2×D414yes—
192C22×Dic13C2×D412yes—
193C22×Dic13C2×D412yes—
194C22×Dic13C2×Q812yes—
195C22×Dic13C2×Q812yes—
196C22×Dic13#4112yes—
197C22×Dic13#4112yes—
198C13×C4⋊C4—28no—
199C13×C4⋊C4—28no—
200C13×C22⋊C4—48no—
201C22⋊Dic13—28no—
202C22⋊Dic13—28no—
203C22⋊Dic13—48no—
204C4⋊Dic13—28no—
205C4⋊Dic13—48no—
206C4⋊Dic13—44no—
207C4×Dic13—28no—
208C4×Dic13—48no—
209C4×Dic13—44no—
210C2×#389—131no—
211C2×#380—131no—
212C2×#380D1311yescharacteristic
213C2×C4×C4⋊C4—131no—
214C2×C4×C22⋊C4—131no—
215#1442—132no—
216#1439—132no—
217#1437—132no—
218C4⋊#95—131no—
219C4⋊#95—131no—
220#1434—132no—
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—22no—
237C23×C13—22no—
238C23×C13—22no—
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—41no—
253C23×C13—41no—
254C23×C13—41no—
255C23×C13C4×Q814yes—
256C23×C13C23×C411yescharacteristic
257C23×C13C22×D411yescharacteristic
258C23×C13C22×D411yescharacteristic
259C23×C13C22×Q811yescharacteristic
260C23×C13C2×#4111yescharacteristic
261C23×C13C2×#4111yescharacteristic
262C23×C13C2×#4111yescharacteristic
263C23×C13C2×#4111yescharacteristic
264C23×C13C2×#4111yescharacteristic
265C23×C13C2×#4111yescharacteristic
266C23×C13C2×#4111yescharacteristic
267C23×C13H(5,𝔽2)11yescharacteristic
268C23×C13H(5,𝔽2)11yescharacteristic
269C23×C13H(5,𝔽2)11yescharacteristic
270C23×C132−1+411yescharacteristic
271C2×C4×C13—22no—
272C2×C4×C13—24no—
273C2×C4×C13—24no—
274C2×C4×C13—22no—
275C2×C4×C13—22no—
276C2×C4×C13—24no—
277C2×C4×C13—24no—
278C2×C4×C13—24no—
279C2×C4×C13—24no—
280C2×C4×C13—41no—
281C2×C4×C13—41no—
282C2×C4×C13—41no—
283C2×C4×C13—41no—
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—42no—
291C2×C4×C13—42no—
292C2×C4×C13—416no—
293C2×C4×C13#11714yes—
294C2×C4×C13C4×D414yes—
295C2×C4×C13C4×D414yes—
296C2×C4×C13#12114yes—
297C2×C4×C13#12314yes—
298C2×C4×C13#12414yes—
299C2×C4×C13#12614yes—
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—24no—
309C2×Dic13—22no—
310C2×Dic13—22no—
311C2×Dic13—22no—
312C2×Dic13—24no—
313C2×Dic13—24no—
314C2×Dic13—22no—
315C2×Dic13—22no—
316C2×Dic13—22no—
317C2×Dic13—22no—
318C2×Dic13—41no—
319C2×Dic13—41no—
320C2×Dic13—42no—
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—42no—
330C2×Dic13—41no—
331C2×Dic13—41no—
332C2×Dic13—41no—
333C2×Dic13—42no—
334C2×Dic13—42no—
335C2×Dic13—42no—
336C2×Dic13—42no—
337C2×Dic13—42no—
338C2×Dic13—42no—
339C2×Dic13—42no—
340C2×Dic13—42no—
341C2×Dic13C22⋊Q814yes—
342C24×C4C2×D1311yescharacteristic
343C22×C4⋊C4—131no—
344C22×C4⋊C4—131no—
345C22×C4⋊C4—132no—
346C22×C4⋊C4C2×D1311yescharacteristic
347C22×C4⋊C4C2×D1311yescharacteristic
348C22×C22⋊C4—131no—
349C22×C22⋊C4—131no—
350C22×C22⋊C4—132no—
351C22×C22⋊C4C2×D1312yes—
352C22×C42—131no—
353C22×C42—131no—
354C22×C42—132no—
355#389—264no—
356#380—264no—
357#380Dic1318yescomplemented
358C4×C4⋊C4—264no—
359C4×C22⋊C4—264no—
360C2×#95—131no—
361C2×#95—132no—
362C2×#95—132no—
363C2×#95—132no—
364C2×#95—132no—
365C2×#95—131no—
366C2×#95—132no—
367C2×#95—132no—
368C2×#95—132no—
369C2×#95C2×D1312yes—
370C22×C13—24no—
371C22×C13—24no—
372C22×C13—24no—
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×C13—42no—
383C22×C13—42no—
384C22×C13—42no—
385C22×C13C2×#11711yescharacteristic
386C22×C13C2×C4×D411yescharacteristic
387C22×C13C2×C4×D411yescharacteristic
388C22×C13C2×C4×Q811yescharacteristic
389C22×C13C4×#4111yescharacteristic
390C22×C13#51811yescharacteristic
391C22×C13#52011yescharacteristic
392C22×C13C2×#12111yescharacteristic
393C22×C13C2×C22⋊Q811yescharacteristic
394C22×C13C2×#12311yescharacteristic
395C22×C13#52511yescharacteristic
396C22×C13C2×#12411yescharacteristic
397C22×C13C2×#12611yescharacteristic
398C22×C13#52911yescharacteristic
399C22×C13#53311yescharacteristic
400C22×C13#53511yescharacteristic
401C22×C13#53711yescharacteristic
402C22×C13#54011yescharacteristic
403C22×C13#54211yescharacteristic
404C22×C13#54611yescharacteristic
405C22×C13#54611yescharacteristic
406C22×C13D4×Q811yescharacteristic
407C22×C13#55011yescharacteristic
408C22×C13#55211yescharacteristic
409C22×C13#55211yescharacteristic
410C22×C13#55211yescharacteristic
411C22×C13#55311yescharacteristic
412C22×C13#55311yescharacteristic
413C22×C13#55311yescharacteristic
414C22×C13#55411yescharacteristic
415C22×C13#55411yescharacteristic
416C22×C13#55411yescharacteristic
417C22×C13#55511yescharacteristic
418C22×C13#55511yescharacteristic
419C22×C13#55511yescharacteristic
420C4×C13—44no—
421C4×C13—44no—
422C4×C13—42no—
423C4×C13#38818yes—
424Dic13—24no—
425Dic13—42no—
426Dic13—42no—
427Dic13—42no—
428Dic13—44no—
429Dic13—82no—
430C25C22×D1311yescharacteristic
431C23×C4—22no—
432C23×C4—22no—
433C23×C4—22no—
434C23×C4—22no—
435C23×C4—22no—
436C23×C4—22no—
437C23×C4—131no—
438C23×C4—131no—
439C23×C4—132no—
440C23×C4—131no—
441C23×C4—131no—
442C23×C4—132no—
443C23×C4C2×Dic1314yes—
444C23×C4C22×D1312yes—
445C23×C4C22×D1312yes—
446C23×C4C22×D1311yescharacteristic
447C23×C4C22×D1311yescharacteristic
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—134no—
453C2×C4⋊C4—262no—
454C2×C4⋊C4—262no—
455C2×C4⋊C4—264no—
456C2×C4⋊C4—262no—
457C2×C4⋊C4—262no—
458C2×C4⋊C4—262no—
459C2×C4⋊C4—522no—
460C2×C4⋊C4—522no—
461C2×C4⋊C4C2×Dic1314yes—
462C2×C4⋊C4C2×Dic1314yes—
463C2×C22⋊C4—42no—
464C2×C22⋊C4—42no—
465C2×C22⋊C4—134no—
466C2×C22⋊C4—262no—
467C2×C22⋊C4—262no—
468C2×C22⋊C4—262no—
469C2×C22⋊C4—262no—
470C2×C22⋊C4—262no—
471C2×C22⋊C4—264no—
472C2×C22⋊C4—264no—
473C2×C22⋊C4—522no—
474C2×C22⋊C4C2×Dic1318yes—
475C2×C42—134no—
476C2×C42—262no—
477C2×C42—262no—
478C2×C42—264no—
479C2×C42—264no—
480C2×C42—262no—
481C2×C42—262no—
482C2×C42—262no—
483C2×C42—522no—
484#95—264no—
485#95—262no—
486#95—262no—
487#95—264no—
488#95—264no—
489#95—264no—
490#95—522no—
491#95—522no—
492#95—522no—
493#95C2×Dic1318yes—
494C2×C13—44no—
495C2×C13C2×#38811yescharacteristic
496C2×C13C4×C22⋊Q811yescharacteristic
497C2×C13#232411yescharacteristic
498C2×C13#234511yescharacteristic
499C2×C13#234611yescharacteristic
500C2×C13#236011yescharacteristic
501C2×C13#236311yescharacteristic
502C2×C13#241411yescharacteristic
503C2×C13#241711yescharacteristic
504C2×C13#242011yescharacteristic
505C2×C13#242311yescharacteristic
506C2×C13#249511yescharacteristic
507C2×C13#249711yescharacteristic
508C2×C13#256211yescharacteristic
509C2×C13#256311yescharacteristic
510C24—21no—
511C24—21no—
512C24—21no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—21no—
517C24—21no—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24Q8×D1312yes—
523C24#613112yes—
524C24C22×Dic1312yes—
525C24C23×D1311yescharacteristic
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—28no—
545C22×C4—28no—
546C22×C4—28no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—132no—
552C22×C4—132no—
553C22×C4—132no—
554C22×C4—134no—
555C22×C4—132no—
556C22×C4—132no—
557C22×C4—132no—
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—261no—
571C22×C4—262no—
572C22×C4—261no—
573C22×C4—261no—
574C22×C4—262no—
575C22×C4—261no—
576C22×C4—261no—
577C22×C4—261no—
578C22×C4—262no—
579C22×C4—262no—
580C22×C4—261no—
581C22×C4—261no—
582C22×C4—261no—
583C22×C4—262no—
584C22×C4—261no—
585C22×C4—261no—
586C22×C4—262no—
587C22×C4—262no—
588C22×C4—262no—
589C22×C4—262no—
590C22×C4—262no—
591C22×C4—262no—
592C22×C4—262no—
593C22×C4#612712yes—
594C22×C4#612712yes—
595C22×C4D4×D1312yes—
596C22×C4D4×D1312yes—
597C22×C4#612912yes—
598C22×C4#612912yes—
599C22×C4C22×Dic1312yes—
600C22×C4C22×Dic1314yes—
601C22×C4C22×Dic1314yes—
602C22×C4C22×Dic1312yes—
603C4⋊C4—28no—
604C4⋊C4—28no—
605C4⋊C4—268no—
606C4⋊C4—528no—
607C4⋊C4—524no—
608C22⋊C4—48no—
609C22⋊C4—268no—
610C22⋊C4—268no—
611C22⋊C4—528no—
612C42—268no—
613C42—528no—
614C42—524no—
615C13#1397311yescharacteristic, complemented, Sylow
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—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23Q8×Dic1314yes—
651C23C2×#612711yescharacteristic
652C23C2×#612711yescharacteristic
653C23C2×D4×D1311yescharacteristic
654C23C2×D4×D1311yescharacteristic
655C23C2×#612911yescharacteristic
656C23C2×#612911yescharacteristic
657C23#8825111yescharacteristic
658C23#8825111yescharacteristic
659C23C2×Q8×D1311yescharacteristic
660C23C2×#613111yescharacteristic
661C23#41×D1311yescharacteristic
662C23#41×D1311yescharacteristic
663C23#8825611yescharacteristic
664C23#8825711yescharacteristic
665C23C23×Dic1311yescharacteristic
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—416no—
688C2×C4—134no—
689C2×C4—262no—
690C2×C4—262no—
691C2×C4—262no—
692C2×C4—262no—
693C2×C4—262no—
694C2×C4—262no—
695C2×C4—264no—
696C2×C4—262no—
697C2×C4—262no—
698C2×C4—262no—
699C2×C4—262no—
700C2×C4—264no—
701C2×C4—262no—
702C2×C4—262no—
703C2×C4—262no—
704C2×C4—262no—
705C2×C4—264no—
706C2×C4—262no—
707C2×C4—521no—
708C2×C4—521no—
709C2×C4—521no—
710C2×C4—521no—
711C2×C4—522no—
712C2×C4—521no—
713C2×C4—521no—
714C2×C4—522no—
715C2×C4—521no—
716C2×C4—521no—
717C2×C4—521no—
718C2×C4—521no—
719C2×C4—522no—
720C2×C4—522no—
721C2×C4—521no—
722C2×C4—521no—
723C2×C4—522no—
724C2×C4—522no—
725C2×C4—522no—
726C2×C4—522no—
727C2×C4—522no—
728C2×C4—522no—
729C2×C4—522no—
730C2×C4#8813314yes—
731C2×C4#8813714yes—
732C2×C4#8813814yes—
733C2×C4#8813914yes—
734C2×C4#8818014yes—
735C2×C4D4×Dic1314yes—
736C2×C4D4×Dic1314yes—
737C22—24no—
738C22—24no—
739C22—24no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22C2×#8813311yescharacteristic
753C22C2×#8813711yescharacteristic
754C22C2×#8813811yescharacteristic
755C22C2×#8813911yescharacteristic
756C22#1171921611yescharacteristic
757C22#1171921611yescharacteristic
758C22#1171921911yescharacteristic
759C22#1171921911yescharacteristic
760C22#1171923411yescharacteristic
761C22#1171923411yescharacteristic
762C22#1171923711yescharacteristic
763C22#1171923711yescharacteristic
764C22#1171930411yescharacteristic
765C22#1171930811yescharacteristic
766C22#1171931211yescharacteristic
767C22#1171931311yescharacteristic
768C22#1171931711yescharacteristic
769C22#1171931911yescharacteristic
770C22#1171932111yescharacteristic
771C22#1171932411yescharacteristic
772C22#1171932711yescharacteristic
773C22#1171932911yescharacteristic
774C22D13×C22⋊Q811yescharacteristic
775C22#1171933211yescharacteristic
776C22#1171933511yescharacteristic
777C22#1171933711yescharacteristic
778C22#1171934011yescharacteristic
779C22#1171934711yescharacteristic
780C22C2×#8818011yescharacteristic
781C22C2×D4×Dic1311yescharacteristic
782C22C2×D4×Dic1311yescharacteristic
783C22#1171950311yescharacteristic
784C22C2×Q8×Dic1311yescharacteristic
785C22#41×Dic1311yescharacteristic
786C22#1171953211yescharacteristic
787C4—42no—
788C4—44no—
789C4—44no—
790C4—264no—
791C4—522no—
792C4—522no—
793C4—522no—
794C4—524no—
795C4—1042no—
796C4#1171861218yes—
797C2—44no—
798C2C2×#1171861211yescharacteristic
799C2C22⋊Q8×Dic1311yescharacteristic
800C2#1311753111yescharacteristic
801C2#1311771311yescharacteristic
802C2#1311772111yescharacteristic
803C2#1311784511yescharacteristic
804C2#1311787811yescharacteristic
805C2#1311825611yescharacteristic
806C2#1311828911yescharacteristic
807C2#1311833011yescharacteristic
808C2#1311836311yescharacteristic
809C2#1311924311yescharacteristic
810C2#1311926511yescharacteristic
811C2#1312000111yescharacteristic
812C2#1312000611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#380C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×#380D13
hypocenterC13#13973
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C2×#11718646C2semidirect
3. C2×C4⋊C4×Dic13C2semidirect
5. #13113093C2semidirect
8. #13113065C2semidirect
9. #13113065C2semidirect
10. #13113061C2semidirect
25. C13×#380C4semidirect
357. #380Dic13semidirect
615. C13#13973semidirect

Maximal subgroups

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

subgroupindex
C2×#117186462
C2×#117188732
C2×C4⋊C4×Dic132
C2×C4×C22⋊Dic132
#131130932
#131130812
#131130732
#131130652
#131130612
C2×C13×#3802
#1397313