Finite Group Databasebeta

← #15785290

Subgroups — #15785290

Order 3328.

2458 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic13C211yesmaximal, characteristic
2C2×#11718882C211yesmaximal, characteristic
3C2×#11718589C211yesmaximal, characteristic, complemented
4C2×#11718634C211yesmaximal, characteristic, complemented
5C2×#11718603C212yesmaximal, complemented
6#13113079C212yesmaximal, complemented
7#13113079C212yesmaximal, complemented
8#13113065C211yesmaximal, characteristic, complemented
9#13113058C212yesmaximal, complemented
10C4×#88071C211yesmaximal, characteristic, complemented
11C2×C13×#390C211yesmaximal, characteristic
12C23×D4×C13C2211yescharacteristic
13C24×Dic13C2212yes—
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C13×C22⋊C4C2212yes—
16C22×C13×C22⋊C4C2212yes—
17C22×C42×C13C2211yescharacteristic
18C22×C22⋊Dic13C2212yes—
19C22×C22⋊Dic13C2212yes—
20C22×C22⋊Dic13C2212yes—
21C2×D4×Dic13—24no—
22C2×D4×Dic13—24no—
23C2×D4×Dic13C418yescomplemented
24C22×C4⋊Dic13C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×#6101C2212yes—
27C22×#6101C2212yes—
28C22×C4×Dic13C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C13×#390—24no—
31#11718882—24no—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2211yescharacteristic
36C2×#88071C2211yescharacteristic
37C2×#88071C2211yescharacteristic
38C2×#88071C2212yes—
39C2×#88071C2211yescharacteristic
40#11718634—24no—
41#11718603—28no—
42#11718589—24no—
43C25×C13C2312yes—
44C22×D4×C13—22no—
45C22×D4×C13—22no—
46C22×D4×C13—22no—
47C22×D4×C13—22no—
48C22×D4×C13C2×C414yes—
49C22×D4×C13D414yes—
50C22×D4×C13Q814yes—
51C23×C4×C13C2312yes—
52C23×C4×C13C2311yescharacteristic
53C23×C4×C13C2311yescharacteristic
54C23×C4×C13C2311yescharacteristic
55C23×Dic13—24no—
56C23×Dic13—24no—
57C23×Dic13—24no—
58C23×Dic13—24no—
59C23×Dic13—42no—
60C23×Dic13—42no—
61C23×Dic13C2×C418yes—
62C23×Dic13C2312yes—
63C23×Dic13C2311yescharacteristic
64C23×Dic13C2311yescharacteristic
65C23×Dic13C2311yescharacteristic
66C23×Dic13C2312yes—
67C23×Dic13C2311yescharacteristic
68C2×C13×C4⋊C4—22no—
69C2×C13×C4⋊C4—22no—
70C2×C13×C4⋊C4—22no—
71C2×C13×C22⋊C4—24no—
72C2×C13×C22⋊C4—24no—
73C2×C13×C22⋊C4—24no—
74C2×C13×C22⋊C4—24no—
75C2×C13×C22⋊C4—42no—
76C2×C13×C22⋊C4—42no—
77C2×C42×C13—22no—
78C2×C42×C13—22no—
79C2×C42×C13—22no—
80C2×C22⋊Dic13—24no—
81C2×C22⋊Dic13—24no—
82C2×C22⋊Dic13—24no—
83C2×C22⋊Dic13—24no—
84C2×C22⋊Dic13—24no—
85C2×C22⋊Dic13—24no—
86C2×C22⋊Dic13—42no—
87C2×C22⋊Dic13—42no—
88C2×C22⋊Dic13C2×C418yes—
89D4×Dic13—232no—
90C2×C4⋊Dic13—22no—
91C2×C4⋊Dic13—22no—
92C2×C4⋊Dic13—22no—
93C2×C4⋊Dic13C2×C414yes—
94C2×C4⋊Dic13D414yes—
95C2×C4⋊Dic13D414yes—
96C2×#6101—24no—
97C2×#6101—24no—
98C2×#6101—24no—
99C2×#6101—24no—
100C2×#6101—42no—
101C2×#6101—42no—
102C2×C4×Dic13—22no—
103C2×C4×Dic13—22no—
104C2×C4×Dic13—22no—
105C2×C4×Dic13—22no—
106C2×C4×Dic13—22no—
107C2×C4×Dic13C2×C414yes—
108#88071—22no—
109#88071—24no—
110#88071—24no—
111#88071—24no—
112#88071—22no—
113#88071—22no—
114#88071—42no—
115#88071D414yescomplemented
116#13920—131nomaximal, Sylow
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×C13C22×C414yes—
130C24×C13C2×D414yes—
131C24×C13C2×Q814yes—
132C24×C13C2411yescharacteristic
133C2×D4×C13—28no—
134C2×D4×C13—28no—
135C2×D4×C13—28no—
136C2×D4×C13—28no—
137C2×D4×C13—28no—
138C2×D4×C13—28no—
139C2×D4×C13C4⋊C4116yescomplemented
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—22no—
153C22×C4×C13—22no—
154C22×C4×C13—22no—
155C22×C4×C13—22no—
156C22×C4×C13—22no—
157C22×C4×C13—22no—
158C22×C4×C13—22no—
159C22×C4×C13C22×C412yes—
160C22×C4×C13C2×D412yes—
161C22×C4×C13C2×D412yes—
162C22×C4×C13C2×D412yes—
163C22×C4×C13C2×D412yes—
164C22×C4×C13C2×Q812yes—
165C22×C4×C13#4112yes—
166C22×C4×C13#4112yes—
167C22×C4×C13#4112yes—
168C22×Dic13—21no—
169C22×Dic13—21no—
170C22×Dic13—22no—
171C22×Dic13—22no—
172C22×Dic13—22no—
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—21no—
182C22×Dic13—21no—
183C22×Dic13—21no—
184C22×Dic13—21no—
185C22×Dic13—21no—
186C22×Dic13—21no—
187C22×Dic13—21no—
188C22×Dic13—21no—
189C22×Dic13—21no—
190C22×Dic13—21no—
191C22×Dic13—21no—
192C22×Dic13—21no—
193C22×Dic13—21no—
194C22×Dic13—216no—
195C22×Dic13—216no—
196C22×Dic13—22no—
197C22×Dic13—22no—
198C22×Dic13—22no—
199C22×Dic13—22no—
200C22×Dic13—22no—
201C22×Dic13—22no—
202C22×Dic13—22no—
203C22×Dic13—48no—
204C22×Dic13—48no—
205C22×Dic13—48no—
206C22×Dic13—48no—
207C22×Dic13—48no—
208C22×Dic13C22×C412yes—
209C22×Dic13C22×C414yes—
210C22×Dic13C22×C412yes—
211C22×Dic13C2×D412yes—
212C22×Dic13C2×D414yes—
213C22×Dic13C2×D414yes—
214C22×Dic13C2×D412yes—
215C22×Dic13#4112yes—
216C22×Dic13#4112yes—
217C13×C4⋊C4—44no—
218C13×C22⋊C4—48no—
219C13×C22⋊C4—48no—
220C42×C13—44no—
221C22⋊Dic13—216no—
222C22⋊Dic13—48no—
223C22⋊Dic13—48no—
224C4⋊Dic13—44no—
225C4⋊Dic13C22⋊C4116yescomplemented
226#6101—48no—
227#6101—48no—
228C4×Dic13—28no—
229C4×Dic13—44no—
230C22×C4×D4—131no—
231C2×#390—131no—
232C2×#390D1311yescharacteristic
233C2×#389—131no—
234C2×#389—131no—
235C2×#380—132no—
236#1439—132no—
237#1439—132no—
238C4⋊#95—131no—
239C22⋊#95—132no—
240C4×#95—131no—
241C23×C13—24no—
242C23×C13—24no—
243C23×C13—24no—
244C23×C13—24no—
245C23×C13—24no—
246C23×C13—24no—
247C23×C13—24no—
248C23×C13—24no—
249C23×C13—24no—
250C23×C13—24no—
251C23×C13—24no—
252C23×C13—24no—
253C23×C13—24no—
254C23×C13—24no—
255C23×C13—24no—
256C23×C13—24no—
257C23×C13—24no—
258C23×C13—24no—
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×C13—42no—
271C23×C13—42no—
272C23×C13—42no—
273C23×C13—42no—
274C23×C13—42no—
275C23×C13C2×C4⋊C418yes—
276C23×C13C23×C411yescharacteristic
277C23×C13C22×D411yescharacteristic
278C23×C13C22×D411yescharacteristic
279C23×C13C22×D411yescharacteristic
280C23×C13C22×D411yescharacteristic
281C23×C13C22×Q811yescharacteristic
282C23×C13C2×#4111yescharacteristic
283C23×C13C2×#4111yescharacteristic
284C23×C13C2×#4111yescharacteristic
285C23×C13C2×#4111yescharacteristic
286C23×C13C2×#4111yescharacteristic
287C23×C13H(5,𝔽2)11yescharacteristic
288C23×C13H(5,𝔽2)11yescharacteristic
289C23×C13H(5,𝔽2)11yescharacteristic
290C23×C132−1+411yescharacteristic
291D4×C13—232no—
292C2×C4×C13—22no—
293C2×C4×C13—22no—
294C2×C4×C13—22no—
295C2×C4×C13—22no—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—41no—
299C2×C4×C13—41no—
300C2×C4×C13—41no—
301C2×C4×C13—41no—
302C2×C4×C13—41no—
303C2×C4×C13—41no—
304C2×C4×C13—41no—
305C2×C4×C13—41no—
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×C13C2×C22⋊C414yes—
314C2×C4×C13C2×C4⋊C414yes—
315C2×C4×C13#11714yes—
316C2×C4×C13#12114yes—
317C2×C4×C13#12114yes—
318C2×C4×C13C22⋊Q814yes—
319C2×C4×C13C22⋊Q814yes—
320C2×Dic13—22no—
321C2×Dic13—24no—
322C2×Dic13—22no—
323C2×Dic13—24no—
324C2×Dic13—24no—
325C2×Dic13—24no—
326C2×Dic13—22no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—22no—
330C2×Dic13—24no—
331C2×Dic13—24no—
332C2×Dic13—22no—
333C2×Dic13—22no—
334C2×Dic13—22no—
335C2×Dic13—22no—
336C2×Dic13—22no—
337C2×Dic13—22no—
338C2×Dic13—22no—
339C2×Dic13—22no—
340C2×Dic13—22no—
341C2×Dic13—432no—
342C2×Dic13—41no—
343C2×Dic13—41no—
344C2×Dic13—41no—
345C2×Dic13—41no—
346C2×Dic13—41no—
347C2×Dic13—41no—
348C2×Dic13—41no—
349C2×Dic13—41no—
350C2×Dic13—41no—
351C2×Dic13—41no—
352C2×Dic13—41no—
353C2×Dic13—41no—
354C2×Dic13—42no—
355C2×Dic13—42no—
356C2×Dic13—42no—
357C2×Dic13—42no—
358C2×Dic13—42no—
359C2×Dic13—42no—
360C2×Dic13—42no—
361C2×Dic13C2×C22⋊C418yes—
362C2×Dic13C4×D414yes—
363C23×D4C2×D1311yescharacteristic
364C24×C4—132no—
365C2×C4×D4—138no—
366C2×C4×D4—264no—
367C2×C4×D4—264no—
368C22×C4⋊C4—131no—
369C22×C4⋊C4—131no—
370C22×C4⋊C4—132no—
371C22×C4⋊C4—132no—
372C22×C4⋊C4C2×D1311yescharacteristic
373C22×C22⋊C4—132no—
374C22×C22⋊C4—132no—
375C22×C22⋊C4—132no—
376C22×C22⋊C4C2×D1312yes—
377C22×C22⋊C4C2×D1312yes—
378C22×C42—131no—
379C22×C42—131no—
380C22×C42C2×D1311yescharacteristic
381#390—24no—
382#390—264no—
383#389—264no—
384#389—264no—
385#380—268no—
386C2×#95—131no—
387C2×#95—131no—
388C2×#95—131no—
389C2×#95—131no—
390C2×#95—132no—
391C2×#95—132no—
392C2×#95—132no—
393C2×#95—132no—
394C22×C13—28no—
395C22×C13—28no—
396C22×C13—28no—
397C22×C13—44no—
398C22×C13—44no—
399C22×C13—44no—
400C22×C13—44no—
401C22×C13—44no—
402C22×C13—44no—
403C22×C13—44no—
404C22×C13—44no—
405C22×C13—44no—
406C22×C13—44no—
407C22×C13—44no—
408C22×C13—44no—
409C22×C13C22×C22⋊C411yescharacteristic
410C22×C13C22×C4⋊C411yescharacteristic
411C22×C13C2×#11711yescharacteristic
412C22×C13C2×C4×D411yescharacteristic
413C22×C13C4×#4111yescharacteristic
414C22×C13#51811yescharacteristic
415C22×C13#52011yescharacteristic
416C22×C13C2×#12111yescharacteristic
417C22×C13C2×#12111yescharacteristic
418C22×C13C2×C22⋊Q811yescharacteristic
419C22×C13C2×C22⋊Q811yescharacteristic
420C22×C13#52911yescharacteristic
421C22×C13#52911yescharacteristic
422C22×C13#53211yescharacteristic
423C22×C13#53211yescharacteristic
424C22×C13#54011yescharacteristic
425C22×C13#54011yescharacteristic
426C22×C13#54211yescharacteristic
427C22×C13#54211yescharacteristic
428C22×C13D4211yescharacteristic
429C22×C13D4211yescharacteristic
430C22×C13D4211yescharacteristic
431C22×C13#54611yescharacteristic
432C22×C13#54611yescharacteristic
433C22×C13#54611yescharacteristic
434C22×C13#54611yescharacteristic
435C22×C13#54711yescharacteristic
436C22×C13#54811yescharacteristic
437C22×C13#54811yescharacteristic
438C22×C13D4×Q811yescharacteristic
439C22×C13#55011yescharacteristic
440C22×C13#55011yescharacteristic
441C22×C13#55411yescharacteristic
442C22×C13#55411yescharacteristic
443C22×C13#55411yescharacteristic
444C4×C13—42no—
445C4×C13—42no—
446C4×C13—82no—
447C4×C13#38018yescomplemented
448Dic13—24no—
449Dic13—28no—
450Dic13—42no—
451Dic13—42no—
452Dic13—42no—
453Dic13—82no—
454C25C22×D1312yes—
455C22×D4—22no—
456C22×D4—22no—
457C22×D4—22no—
458C22×D4—22no—
459C22×D4Dic2614yes—
460C22×D4C4×D1314yes—
461C22×D4C22⋊D1314yes—
462C23×C4—132no—
463C23×C4—131no—
464C23×C4—131no—
465C23×C4—131no—
466C23×C4—131no—
467C23×C4—138no—
468C23×C4—132no—
469C23×C4—264no—
470C23×C4—264no—
471C23×C4—264no—
472C23×C4—264no—
473C23×C4—522no—
474C23×C4—522no—
475C23×C4C22×D1312yes—
476C23×C4C22×D1311yescharacteristic
477C23×C4C22×D1311yescharacteristic
478C23×C4C22×D1311yescharacteristic
479C4×D4—2632no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—134no—
484C2×C4⋊C4—134no—
485C2×C4⋊C4—134no—
486C2×C4⋊C4—264no—
487C2×C4⋊C4—264no—
488C2×C4⋊C4—264no—
489C2×C4⋊C4—264no—
490C2×C4⋊C4—262no—
491C2×C4⋊C4—262no—
492C2×C4⋊C4—262no—
493C2×C4⋊C4—522no—
494C2×C4⋊C4—522no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—42no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—138no—
502C2×C22⋊C4—264no—
503C2×C22⋊C4—264no—
504C2×C22⋊C4—264no—
505C2×C22⋊C4—264no—
506C2×C22⋊C4—264no—
507C2×C22⋊C4—264no—
508C2×C22⋊C4—522no—
509C2×C22⋊C4—522no—
510C2×C42—22no—
511C2×C42—22no—
512C2×C42—22no—
513C2×C42—134no—
514C2×C42—262no—
515C2×C42—262no—
516C2×C42—262no—
517C2×C42—262no—
518C2×C42—262no—
519#95—134no—
520#95—262no—
521#95—262no—
522#95—264no—
523#95—264no—
524#95—264no—
525#95—262no—
526#95—522no—
527C2×C13—48no—
528C2×C13C2×#38011yescharacteristic
529C2×C13#229311yescharacteristic
530C2×C13#231911yescharacteristic
531C2×C13D4×C22⋊C411yescharacteristic
532C2×C13#234111yescharacteristic
533C2×C13D4×C4⋊C411yescharacteristic
534C2×C13#234911yescharacteristic
535C2×C13#242711yescharacteristic
536C2×C13#242711yescharacteristic
537C2×C13#242811yescharacteristic
538C2×C13#242811yescharacteristic
539C2×C13#245211yescharacteristic
540C2×C13#245211yescharacteristic
541C2×C13#245411yescharacteristic
542C2×C13#245411yescharacteristic
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24C2×Dic2614yes—
556C24C2×C4×D1314yes—
557C24C2×C22⋊D1314yes—
558C24C23×D1311yescharacteristic
559C2×D4—28no—
560C2×D4—28no—
561C2×D4—28no—
562C2×D4—28no—
563C2×D4—28no—
564C2×D4—28no—
565C2×D4#6101116yescomplemented
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—132no—
586C22×C4—134no—
587C22×C4—132no—
588C22×C4—134no—
589C22×C4—134no—
590C22×C4—132no—
591C22×C4—132no—
592C22×C4—132no—
593C22×C4—132no—
594C22×C4—2616no—
595C22×C4—2616no—
596C22×C4—261no—
597C22×C4—261no—
598C22×C4—262no—
599C22×C4—262no—
600C22×C4—261no—
601C22×C4—262no—
602C22×C4—262no—
603C22×C4—261no—
604C22×C4—261no—
605C22×C4—261no—
606C22×C4—261no—
607C22×C4—261no—
608C22×C4—261no—
609C22×C4—261no—
610C22×C4—261no—
611C22×C4—261no—
612C22×C4—261no—
613C22×C4—261no—
614C22×C4—261no—
615C22×C4—261no—
616C22×C4—261no—
617C22×C4—261no—
618C22×C4—261no—
619C22×C4—261no—
620C22×C4—261no—
621C22×C4—261no—
622C22×C4—262no—
623C22×C4—262no—
624C22×C4—262no—
625C22×C4—262no—
626C22×C4—262no—
627C22×C4—262no—
628C22×C4—262no—
629C22×C4—528no—
630C22×C4—528no—
631C22×C4—528no—
632C22×C4—528no—
633C22×C4—528no—
634C22×C4C2×Dic2612yes—
635C22×C4C2×C4×D1312yes—
636C22×C4D4×D1312yes—
637C22×C4D4×D1312yes—
638C22×C4D4×D1312yes—
639C22×C4#612912yes—
640C22×C4#612912yes—
641C22×C4#612912yes—
642C22×C4C2×C22⋊D1312yes—
643C4⋊C4—44no—
644C4⋊C4—1316no—
645C4⋊C4—528no—
646C4⋊C4—528no—
647C4⋊C4—524no—
648C22⋊C4—48no—
649C22⋊C4—48no—
650C22⋊C4—2616no—
651C22⋊C4—528no—
652C22⋊C4—528no—
653C42—44no—
654C42—268no—
655C42—524no—
656C13#1392011yescharacteristic, complemented, Sylow
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23C2×#610118yes—
692C23C22×Dic2611yescharacteristic
693C23C22×C4×D1311yescharacteristic
694C23C2×D4×D1311yescharacteristic
695C23C2×D4×D1311yescharacteristic
696C23C2×D4×D1311yescharacteristic
697C23C2×#612911yescharacteristic
698C23C2×#612911yescharacteristic
699C23C2×#612911yescharacteristic
700C23#8825111yescharacteristic
701C23#8825111yescharacteristic
702C23#41×D1311yescharacteristic
703C23#41×D1311yescharacteristic
704C23#8825611yescharacteristic
705C23#8825711yescharacteristic
706C23C22×C22⋊D1311yescharacteristic
707D4—232no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—138no—
730C2×C4—134no—
731C2×C4—262no—
732C2×C4—264no—
733C2×C4—264no—
734C2×C4—262no—
735C2×C4—264no—
736C2×C4—262no—
737C2×C4—264no—
738C2×C4—262no—
739C2×C4—264no—
740C2×C4—262no—
741C2×C4—264no—
742C2×C4—262no—
743C2×C4—262no—
744C2×C4—262no—
745C2×C4—262no—
746C2×C4—262no—
747C2×C4—262no—
748C2×C4—262no—
749C2×C4—262no—
750C2×C4—262no—
751C2×C4—262no—
752C2×C4—5232no—
753C2×C4—521no—
754C2×C4—521no—
755C2×C4—521no—
756C2×C4—521no—
757C2×C4—521no—
758C2×C4—521no—
759C2×C4—521no—
760C2×C4—521no—
761C2×C4—521no—
762C2×C4—521no—
763C2×C4—521no—
764C2×C4—521no—
765C2×C4—522no—
766C2×C4—522no—
767C2×C4—522no—
768C2×C4—522no—
769C2×C4—522no—
770C2×C4—522no—
771C2×C4—522no—
772C2×C4#8813114yes—
773C2×C4#8813214yes—
774C2×C4#8813214yes—
775C2×C4C22⋊C4×D1314yes—
776C2×C4C2×#610114yes—
777C2×C4#8819314yes—
778C2×C4#8819314yes—
779C22—28no—
780C22—28no—
781C22—28no—
782C22—44no—
783C22—44no—
784C22—44no—
785C22—44no—
786C22—44no—
787C22—44no—
788C22—44no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22C2×#8813111yescharacteristic
795C22C2×#8813211yescharacteristic
796C22C2×#8813211yescharacteristic
797C22C2×C22⋊C4×D1311yescharacteristic
798C22C4×#612911yescharacteristic
799C22D4×Dic2611yescharacteristic
800C22#1171924411yescharacteristic
801C22#1171924411yescharacteristic
802C22#1171924811yescharacteristic
803C22C4×D4×D1311yescharacteristic
804C22#1171925011yescharacteristic
805C22#1171925111yescharacteristic
806C22#1171930111yescharacteristic
807C22#1171930311yescharacteristic
808C22#1171930411yescharacteristic
809C22#1171930511yescharacteristic
810C22#1171930811yescharacteristic
811C22#1171931411yescharacteristic
812C22#1171931711yescharacteristic
813C22#1171932411yescharacteristic
814C22#1171938111yescharacteristic
815C22#1171938211yescharacteristic
816C22#1171938511yescharacteristic
817C22#1171938711yescharacteristic
818C22#1171942111yescharacteristic
819C22#1171942211yescharacteristic
820C22#1171942311yescharacteristic
821C22#1171942411yescharacteristic
822C22C22×#610111yescharacteristic
823C22D4×C22⋊D1311yescharacteristic
824C22C2×#8819311yescharacteristic
825C22C2×#8819311yescharacteristic
826C22#1171951111yescharacteristic
827C22#1171952911yescharacteristic
828C22#1171953411yescharacteristic
829C4—42no—
830C4—42no—
831C4—82no—
832C4—268no—
833C4—264no—
834C4—522no—
835C4—522no—
836C4—522no—
837C4—1042no—
838C4#1171860318yescomplemented
839C2—48no—
840C2C2×#1171860311yescharacteristic
841C2#1311729811yescharacteristic
842C2#1311747311yescharacteristic
843C2#1311765711yescharacteristic
844C2#1311767511yescharacteristic
845C2D4×#610111yescharacteristic
846C2#1311774111yescharacteristic
847C2#1311841511yescharacteristic
848C2#1311841611yescharacteristic
849C2#1311842611yescharacteristic
850C2#1311842711yescharacteristic
851C2#1311868811yescharacteristic
852C2#1311868911yescharacteristic
853C2#1311871011yescharacteristic
854C2#1311871111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#390C2
socle, cosocleC24×C13C24
prime radicalC23×D4×C13C22
hypercenterC2×#390D13
hypocenterC13#13920
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
3. C2×#11718589C2semidirect
4. C2×#11718634C2semidirect
5. C2×#11718603C2semidirect
6. #13113079C2semidirect
7. #13113079C2semidirect
8. #13113065C2semidirect
9. #13113058C2semidirect
10. C4×#88071C2semidirect
23. C2×D4×Dic13C4semidirect
115. #88071D4semidirect
139. C2×D4×C13C4⋊C4semidirect
225. C4⋊Dic13C22⋊C4semidirect
447. C4×C13#380semidirect
565. C2×D4#6101semidirect
656. C13#13920semidirect
838. C4#11718603semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic132
C2×#117188822
C2×#117185892
C2×#117186342
C2×#117186032
#131130792
#131130652
#131130582
C4×#880712
C2×C13×#3902
#1392013