Finite Group Databasebeta

← #15786319

Subgroups — #15786319

Order 3328.

2474 conjugacy classes of subgroups.

The subgroup lattice has 862 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×#11718607C212yesmaximal, complemented
5C2×C4×#6101C211yesmaximal, characteristic, complemented
6#13113079C212yesmaximal, complemented
7#13113079C212yesmaximal, complemented
8#13113065C211yesmaximal, characteristic, complemented
9#13113065C211yesmaximal, characteristic, complemented
10#13113058C212yesmaximal, 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×Dic13—24no—
24C22×C4⋊Dic13C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2212yes—
28C22×#6101C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C13×#390—24no—
32#11718882C418yescomplemented
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2211yescharacteristic
37C2×#88071C2211yescharacteristic
38C2×#88071C2212yes—
39C2×#88071C2212yes—
40#11718607—28no—
41C4×#6101—24no—
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—24no—
60C23×Dic13—42no—
61C23×Dic13—42no—
62C23×Dic13C2311yescharacteristic
63C23×Dic13C2312yes—
64C23×Dic13C2311yescharacteristic
65C23×Dic13C2312yes—
66C23×Dic13C2311yescharacteristic
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—42no—
86C2×C22⋊Dic13—42no—
87C2×C22⋊Dic13C2×C418yescomplemented
88C2×C22⋊Dic13C2×C418yescomplemented
89D4×Dic13—232no—
90C2×C4⋊Dic13—22no—
91C2×C4⋊Dic13—22no—
92C2×C4⋊Dic13—22no—
93C2×C4⋊Dic13—22no—
94C2×C4⋊Dic13C2×C414yescomplemented
95C2×C4⋊Dic13D414yes—
96C2×#6101—22no—
97C2×#6101—22no—
98C2×#6101—22no—
99C2×#6101—22no—
100C2×#6101—22no—
101C2×#6101—24no—
102C2×#6101—24no—
103C2×#6101—42no—
104C2×#6101D414yescomplemented
105C2×C4×Dic13—22no—
106C2×C4×Dic13—22no—
107C2×C4×Dic13—22no—
108C2×C4×Dic13—22no—
109C2×C4×Dic13C2×C414yescomplemented
110C2×C4×Dic13D414yes—
111#88071—24no—
112#88071—22no—
113#88071—22no—
114#88071—24no—
115#88071—24no—
116#88071—42no—
117#88071—42no—
118#14018—131nomaximal, Sylow
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×C13—22no—
130C24×C13—22no—
131C24×C13C22×C414yes—
132C24×C13C2×D414yes—
133C24×C13C2×Q814yes—
134C24×C13C2411yescharacteristic
135C2×D4×C13—28no—
136C2×D4×C13—28no—
137C2×D4×C13—28no—
138C2×D4×C13—28no—
139C2×D4×C13—28no—
140C2×D4×C13—28no—
141C2×D4×C13C4⋊C4116yescomplemented
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—21no—
153C22×C4×C13—21no—
154C22×C4×C13—22no—
155C22×C4×C13—22no—
156C22×C4×C13—22no—
157C22×C4×C13—22no—
158C22×C4×C13—22no—
159C22×C4×C13—22no—
160C22×C4×C13—22no—
161C22×C4×C13C22×C412yes—
162C22×C4×C13C2×D412yes—
163C22×C4×C13C2×D412yes—
164C22×C4×C13C2×D412yes—
165C22×C4×C13C2×D412yes—
166C22×C4×C13C2×Q812yes—
167C22×C4×C13#4112yes—
168C22×C4×C13#4112yes—
169C22×C4×C13#4112yes—
170C22×Dic13—21no—
171C22×Dic13—21no—
172C22×Dic13—21no—
173C22×Dic13—21no—
174C22×Dic13—21no—
175C22×Dic13—21no—
176C22×Dic13—21no—
177C22×Dic13—21no—
178C22×Dic13—216no—
179C22×Dic13—21no—
180C22×Dic13—22no—
181C22×Dic13—22no—
182C22×Dic13—22no—
183C22×Dic13—21no—
184C22×Dic13—21no—
185C22×Dic13—22no—
186C22×Dic13—22no—
187C22×Dic13—21no—
188C22×Dic13—21no—
189C22×Dic13—21no—
190C22×Dic13—22no—
191C22×Dic13—22no—
192C22×Dic13—22no—
193C22×Dic13—21no—
194C22×Dic13—21no—
195C22×Dic13—22no—
196C22×Dic13—22no—
197C22×Dic13—22no—
198C22×Dic13—22no—
199C22×Dic13—21no—
200C22×Dic13—21no—
201C22×Dic13—21no—
202C22×Dic13—21no—
203C22×Dic13—48no—
204C22×Dic13—48no—
205C22×Dic13—48no—
206C22×Dic13—48no—
207C22×Dic13—48no—
208C22×Dic13—48no—
209C22×Dic13C22×C412yes—
210C22×Dic13C22×C414yes—
211C22×Dic13C22×C412yes—
212C22×Dic13C2×D412yes—
213C22×Dic13C2×D414yes—
214C22×Dic13C2×D412yes—
215C22×Dic13C2×D412yes—
216C22×Dic13C2×D412yes—
217C22×Dic13#4112yes—
218C22×Dic13#4112yes—
219C13×C4⋊C4—44no—
220C13×C22⋊C4—48no—
221C13×C22⋊C4—48no—
222C42×C13—44no—
223C22⋊Dic13—216no—
224C22⋊Dic13—216no—
225C22⋊Dic13—48no—
226C4⋊Dic13—28no—
227C4⋊Dic13—28no—
228#6101—28no—
229#6101—28no—
230#6101—48no—
231C4×Dic13—28no—
232C4×Dic13—28no—
233C22×C4×D4—131no—
234C2×#390—131no—
235C2×#390D1311yescharacteristic
236C2×#389—131no—
237C2×#385—132no—
238C2×C4×C4⋊C4—131no—
239#1439—132no—
240#1439—132no—
241C4⋊#95—131no—
242C4⋊#95—131no—
243C22⋊#95—132no—
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—24no—
260C23×C13—24no—
261C23×C13—24no—
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×C13—42no—
276C23×C13—42no—
277C23×C13—42no—
278C23×C13C2×C4⋊C418yes—
279C23×C13C23×C411yescharacteristic
280C23×C13C22×D411yescharacteristic
281C23×C13C22×D411yescharacteristic
282C23×C13C22×D411yescharacteristic
283C23×C13C22×D411yescharacteristic
284C23×C13C22×Q811yescharacteristic
285C23×C13C2×#4111yescharacteristic
286C23×C13C2×#4111yescharacteristic
287C23×C13C2×#4111yescharacteristic
288C23×C13C2×#4111yescharacteristic
289C23×C13C2×#4111yescharacteristic
290C23×C13H(5,𝔽2)11yescharacteristic
291C23×C13H(5,𝔽2)11yescharacteristic
292C23×C13H(5,𝔽2)11yescharacteristic
293C23×C132−1+411yescharacteristic
294D4×C13—232no—
295C2×C4×C13—22no—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
299C2×C4×C13—22no—
300C2×C4×C13—22no—
301C2×C4×C13—41no—
302C2×C4×C13—41no—
303C2×C4×C13—41no—
304C2×C4×C13—41no—
305C2×C4×C13—41no—
306C2×C4×C13—41no—
307C2×C4×C13—41no—
308C2×C4×C13—41no—
309C2×C4×C13—42no—
310C2×C4×C13—42no—
311C2×C4×C13—42no—
312C2×C4×C13—42no—
313C2×C4×C13—42no—
314C2×C4×C13—42no—
315C2×C4×C13—42no—
316C2×C4×C13C2×C4⋊C414yes—
317C2×C4×C13C4×D414yes—
318C2×C4×C13C4×D414yes—
319C2×C4×C13#12014yes—
320C2×C4×C13C22⋊Q814yes—
321C2×C4×C13C22⋊Q814yes—
322C2×C4×C13#12314yes—
323C2×Dic13—22no—
324C2×Dic13—22no—
325C2×Dic13—22no—
326C2×Dic13—22no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—22no—
330C2×Dic13—22no—
331C2×Dic13—22no—
332C2×Dic13—22no—
333C2×Dic13—22no—
334C2×Dic13—22no—
335C2×Dic13—22no—
336C2×Dic13—24no—
337C2×Dic13—24no—
338C2×Dic13—22no—
339C2×Dic13—24no—
340C2×Dic13—22no—
341C2×Dic13—22no—
342C2×Dic13—24no—
343C2×Dic13—22no—
344C2×Dic13—22no—
345C2×Dic13—24no—
346C2×Dic13—24no—
347C2×Dic13—432no—
348C2×Dic13—42no—
349C2×Dic13—41no—
350C2×Dic13—42no—
351C2×Dic13—41no—
352C2×Dic13—41no—
353C2×Dic13—41no—
354C2×Dic13—42no—
355C2×Dic13—42no—
356C2×Dic13—41no—
357C2×Dic13—42no—
358C2×Dic13—41no—
359C2×Dic13—41no—
360C2×Dic13—42no—
361C2×Dic13—42no—
362C2×Dic13—41no—
363C2×Dic13—42no—
364C2×Dic13C4×D414yescomplemented
365C2×Dic13#12114yes—
366C23×D4C2×D1311yescharacteristic
367C24×C4—132no—
368C2×C4×D4—264no—
369C2×C4×D4—264no—
370C2×C4×D4—264no—
371C22×C4⋊C4—131no—
372C22×C4⋊C4—131no—
373C22×C4⋊C4—131no—
374C22×C4⋊C4—131no—
375C22×C4⋊C4—132no—
376C22×C4⋊C4C2×D1311yescharacteristic
377C22×C22⋊C4—132no—
378C22×C22⋊C4—132no—
379C22×C22⋊C4—132no—
380C22×C22⋊C4C2×D1312yes—
381C22×C22⋊C4C2×D1312yes—
382C22×C42—131no—
383C22×C42—131no—
384C22×C42C2×D1311yescharacteristic
385#390—24no—
386#390—138no—
387#389—264no—
388#385—268no—
389C4×C4⋊C4—264no—
390C2×#95—131no—
391C2×#95—132no—
392C2×#95—132no—
393C2×#95—132no—
394C2×#95—131no—
395C2×#95—132no—
396C2×#95—132no—
397C22×C13—28no—
398C22×C13—28no—
399C22×C13—28no—
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×C13—44no—
410C22×C13—44no—
411C22×C13—44no—
412C22×C13C22×C4⋊C411yescharacteristic
413C22×C13C2×C4×D411yescharacteristic
414C22×C13C2×C4×D411yescharacteristic
415C22×C13C2×C4×D411yescharacteristic
416C22×C13C4×#4111yescharacteristic
417C22×C13#51811yescharacteristic
418C22×C13#52011yescharacteristic
419C22×C13C2×#12011yescharacteristic
420C22×C13C2×#12111yescharacteristic
421C22×C13C2×C22⋊Q811yescharacteristic
422C22×C13C2×C22⋊Q811yescharacteristic
423C22×C13C2×#12311yescharacteristic
424C22×C13#52511yescharacteristic
425C22×C13#52911yescharacteristic
426C22×C13#53211yescharacteristic
427C22×C13#53511yescharacteristic
428C22×C13#53711yescharacteristic
429C22×C13#54011yescharacteristic
430C22×C13#54211yescharacteristic
431C22×C13D4211yescharacteristic
432C22×C13D4211yescharacteristic
433C22×C13#54611yescharacteristic
434C22×C13#54611yescharacteristic
435C22×C13#54611yescharacteristic
436C22×C13#54711yescharacteristic
437C22×C13#54811yescharacteristic
438C22×C13D4×Q811yescharacteristic
439C22×C13#55011yescharacteristic
440C22×C13#55011yescharacteristic
441C22×C13#55411yescharacteristic
442C22×C13#55411yescharacteristic
443C22×C13#55411yescharacteristic
444C22×C13#55611yescharacteristic
445C22×C13#55911yescharacteristic
446C22×C13#55911yescharacteristic
447C4×C13—42no—
448C4×C13—42no—
449C4×C13—82no—
450C4×C13#38518yescomplemented
451Dic13—24no—
452Dic13—24no—
453Dic13—42no—
454Dic13—44no—
455Dic13—42no—
456Dic13—44no—
457C25C22×D1312yes—
458C22×D4—22no—
459C22×D4—22no—
460C22×D4—22no—
461C22×D4—22no—
462C22×D4Dic2614yes—
463C22×D4C4×D1314yes—
464C22×D4C22⋊D1314yes—
465C23×C4—131no—
466C23×C4—131no—
467C23×C4—132no—
468C23×C4—131no—
469C23×C4—131no—
470C23×C4—132no—
471C23×C4—264no—
472C23×C4—264no—
473C23×C4—264no—
474C23×C4—264no—
475C23×C4—264no—
476C23×C4—522no—
477C23×C4—522no—
478C23×C4C22×D1312yes—
479C23×C4C22×D1311yescharacteristic
480C23×C4C22×D1311yescharacteristic
481C23×C4C22×D1311yescharacteristic
482C4×D4—2632no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—134no—
487C2×C4⋊C4—134no—
488C2×C4⋊C4—134no—
489C2×C4⋊C4—262no—
490C2×C4⋊C4—262no—
491C2×C4⋊C4—262no—
492C2×C4⋊C4—262no—
493C2×C4⋊C4—262no—
494C2×C4⋊C4—262no—
495C2×C4⋊C4—262no—
496C2×C4⋊C4—262no—
497C2×C4⋊C4—262no—
498C2×C4⋊C4—264no—
499C2×C4⋊C4—264no—
500C2×C4⋊C4—522no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—42no—
506C2×C22⋊C4—42no—
507C2×C22⋊C4—138no—
508C2×C22⋊C4—138no—
509C2×C22⋊C4—264no—
510C2×C22⋊C4—264no—
511C2×C22⋊C4—264no—
512C2×C22⋊C4—264no—
513C2×C22⋊C4—264no—
514C2×C22⋊C4—522no—
515C2×C22⋊C4—522no—
516C2×C42—22no—
517C2×C42—22no—
518C2×C42—22no—
519C2×C42—134no—
520C2×C42—134no—
521C2×C42—262no—
522C2×C42—262no—
523C2×C42—262no—
524C2×C42—262no—
525#95—262no—
526#95—262no—
527#95—264no—
528#95—264no—
529#95—264no—
530#95—522no—
531#95—522no—
532C2×C13—48no—
533C2×C13C2×#38511yescharacteristic
534C2×C13C4×#12111yescharacteristic
535C2×C13#232411yescharacteristic
536C2×C13D4×C4⋊C411yescharacteristic
537C2×C13#234911yescharacteristic
538C2×C13#236611yescharacteristic
539C2×C13#236711yescharacteristic
540C2×C13#240711yescharacteristic
541C2×C13#240811yescharacteristic
542C2×C13#244511yescharacteristic
543C2×C13#244711yescharacteristic
544C2×C13#245211yescharacteristic
545C2×C13#245411yescharacteristic
546C2×C13#253811yescharacteristic
547C2×C13#258011yescharacteristic
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24C2×Dic2614yes—
561C24C2×C4×D1314yes—
562C24C2×C22⋊D1314yes—
563C24C23×D1311yescharacteristic
564C2×D4—28no—
565C2×D4—28no—
566C2×D4—28no—
567C2×D4—28no—
568C2×D4—28no—
569C2×D4—28no—
570C2×D4#6101116yescomplemented
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—132no—
591C22×C4—132no—
592C22×C4—132no—
593C22×C4—132no—
594C22×C4—132no—
595C22×C4—132no—
596C22×C4—132no—
597C22×C4—134no—
598C22×C4—132no—
599C22×C4—134no—
600C22×C4—261no—
601C22×C4—261no—
602C22×C4—261no—
603C22×C4—261no—
604C22×C4—261no—
605C22×C4—261no—
606C22×C4—261no—
607C22×C4—261no—
608C22×C4—2616no—
609C22×C4—261no—
610C22×C4—262no—
611C22×C4—262no—
612C22×C4—262no—
613C22×C4—261no—
614C22×C4—262no—
615C22×C4—261no—
616C22×C4—262no—
617C22×C4—261no—
618C22×C4—261no—
619C22×C4—261no—
620C22×C4—262no—
621C22×C4—262no—
622C22×C4—261no—
623C22×C4—262no—
624C22×C4—261no—
625C22×C4—262no—
626C22×C4—261no—
627C22×C4—262no—
628C22×C4—262no—
629C22×C4—261no—
630C22×C4—261no—
631C22×C4—261no—
632C22×C4—262no—
633C22×C4—528no—
634C22×C4—528no—
635C22×C4—528no—
636C22×C4—528no—
637C22×C4—528no—
638C22×C4—528no—
639C22×C4C2×Dic2612yes—
640C22×C4C2×C4×D1312yes—
641C22×C4D4×D1312yes—
642C22×C4D4×D1312yes—
643C22×C4D4×D1312yes—
644C22×C4#612912yes—
645C22×C4#612912yes—
646C22×C4#612912yes—
647C22×C4C2×C22⋊D1312yes—
648C4⋊C4—44no—
649C4⋊C4—268no—
650C4⋊C4—268no—
651C4⋊C4—268no—
652C4⋊C4—268no—
653C4⋊C4—528no—
654C22⋊C4—48no—
655C22⋊C4—48no—
656C22⋊C4—2616no—
657C22⋊C4—2616no—
658C22⋊C4—528no—
659C42—44no—
660C42—268no—
661C42—268no—
662C13#1401811yescharacteristic, complemented, Sylow
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—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23C2×#610118yes—
698C23C22×Dic2611yescharacteristic
699C23C22×C4×D1311yescharacteristic
700C23C2×D4×D1311yescharacteristic
701C23C2×D4×D1311yescharacteristic
702C23C2×D4×D1311yescharacteristic
703C23C2×#612911yescharacteristic
704C23C2×#612911yescharacteristic
705C23C2×#612911yescharacteristic
706C23#8825111yescharacteristic
707C23#8825111yescharacteristic
708C23#41×D1311yescharacteristic
709C23#41×D1311yescharacteristic
710C23#8825611yescharacteristic
711C23#8825711yescharacteristic
712C23C22×C22⋊D1311yescharacteristic
713D4—232no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—134no—
736C2×C4—134no—
737C2×C4—262no—
738C2×C4—262no—
739C2×C4—262no—
740C2×C4—262no—
741C2×C4—262no—
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—264no—
751C2×C4—262no—
752C2×C4—264no—
753C2×C4—264no—
754C2×C4—262no—
755C2×C4—264no—
756C2×C4—262no—
757C2×C4—262no—
758C2×C4—262no—
759C2×C4—264no—
760C2×C4—264no—
761C2×C4—5232no—
762C2×C4—521no—
763C2×C4—522no—
764C2×C4—521no—
765C2×C4—521no—
766C2×C4—522no—
767C2×C4—521no—
768C2×C4—522no—
769C2×C4—521no—
770C2×C4—522no—
771C2×C4—521no—
772C2×C4—522no—
773C2×C4—521no—
774C2×C4—522no—
775C2×C4—522no—
776C2×C4—521no—
777C2×C4—522no—
778C2×C4#8813214yes—
779C2×C4#8813214yes—
780C2×C4#8813514yes—
781C2×C4#8813514yes—
782C2×C4C2×#610114yes—
783C2×C4#8818914yes—
784C2×C4#8819114yes—
785C22—28no—
786C22—28no—
787C22—28no—
788C22—44no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—44no—
797C22—44no—
798C22—44no—
799C22—44no—
800C22C2×#8813211yescharacteristic
801C22C2×#8813211yescharacteristic
802C22C2×#8813511yescharacteristic
803C22C2×#8813511yescharacteristic
804C22C4×#612911yescharacteristic
805C22D4×Dic2611yescharacteristic
806C22#1171924411yescharacteristic
807C22#1171924411yescharacteristic
808C22#1171924811yescharacteristic
809C22C4×D4×D1311yescharacteristic
810C22#1171925011yescharacteristic
811C22#1171925111yescharacteristic
812C22#1171930311yescharacteristic
813C22#1171930411yescharacteristic
814C22D13×#12111yescharacteristic
815C22#1171931111yescharacteristic
816C22#1171931211yescharacteristic
817C22#1171931311yescharacteristic
818C22#1171931411yescharacteristic
819C22#1171931711yescharacteristic
820C22#1171937611yescharacteristic
821C22#1171938511yescharacteristic
822C22#1171938611yescharacteristic
823C22#1171938711yescharacteristic
824C22#1171941811yescharacteristic
825C22#1171942111yescharacteristic
826C22#1171942311yescharacteristic
827C22#1171942411yescharacteristic
828C22C22×#610111yescharacteristic
829C22C2×#8818911yescharacteristic
830C22C2×#8819111yescharacteristic
831C22D4×C22⋊D1311yescharacteristic
832C22#1171951111yescharacteristic
833C22#1171952911yescharacteristic
834C22#1171953411yescharacteristic
835C4—42no—
836C4—42no—
837C4—82no—
838C4—264no—
839C4—264no—
840C4—522no—
841C4—524no—
842C4—522no—
843C4—524no—
844C4#1171860718yescomplemented
845C2—48no—
846C2C2×#1171860711yescharacteristic
847C2#1311735211yescharacteristic
848C2#1311753211yescharacteristic
849C2D4×#610111yescharacteristic
850C2#1311774111yescharacteristic
851C2#1311789711yescharacteristic
852C2#1311790611yescharacteristic
853C2#1311817711yescharacteristic
854C2#1311818811yescharacteristic
855C2#1311859711yescharacteristic
856C2#1311861911yescharacteristic
857C2#1311868811yescharacteristic
858C2#1311871011yescharacteristic
859C2#1311975611yescharacteristic
860C2#1312019211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#390C2
socle, cosocleC24×C13C24
prime radicalC23×D4×C13C22
hypercenterC2×#390D13
hypocenterC13#14018
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×#11718607C2semidirect
5. C2×C4×#6101C2semidirect
6. #13113079C2semidirect
7. #13113079C2semidirect
8. #13113065C2semidirect
9. #13113065C2semidirect
10. #13113058C2semidirect
32. #11718882C4semidirect
87. C2×C22⋊Dic13C2×C4semidirect
88. C2×C22⋊Dic13C2×C4semidirect
94. C2×C4⋊Dic13C2×C4semidirect
104. C2×#6101D4semidirect
109. C2×C4×Dic13C2×C4semidirect
141. C2×D4×C13C4⋊C4semidirect
364. C2×Dic13C4×D4semidirect
450. C4×C13#385semidirect
570. C2×D4#6101semidirect
662. C13#14018semidirect
844. C4#11718607semidirect

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×#117186072
C2×C4×#61012
#131130792
#131130652
#131130582
C2×C13×#3902
#1401813