Finite Group Databasebeta

← #15786318

Subgroups — #15786318

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×#11718646C211yesmaximal, characteristic, complemented
4C2×#11718611C212yesmaximal, complemented
5C2×C4×C4⋊Dic13C211yesmaximal, characteristic, complemented
6#13113081C212yesmaximal, complemented
7#13113081C212yesmaximal, complemented
8#13113066C211yesmaximal, 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×C4⋊Dic13C2212yes—
27C22×C4⋊Dic13C2211yescharacteristic
28C22×C4⋊Dic13C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C13×#390C418yescomplemented
32#11718882—24no—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2211yescharacteristic
37C2×#88071C2211yescharacteristic
38C2×#88071C2212yes—
39C2×#88071C2212yes—
40#11718646—24no—
41#11718611—28no—
42C4×C4⋊Dic13—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×Dic13C2312yes—
63C23×Dic13C2311yescharacteristic
64C23×Dic13C2311yescharacteristic
65C23×Dic13C2312yes—
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C2×C13×C4⋊C4—22no—
69C2×C13×C4⋊C4—22no—
70C2×C13×C4⋊C4C2×C414yescomplemented
71C2×C13×C22⋊C4—24no—
72C2×C13×C22⋊C4—24no—
73C2×C13×C22⋊C4—42no—
74C2×C13×C22⋊C4—42no—
75C2×C13×C22⋊C4C2×C418yescomplemented
76C2×C13×C22⋊C4C2×C418yescomplemented
77C2×C42×C13—22no—
78C2×C42×C13—22no—
79C2×C42×C13C2×C414yescomplemented
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—24no—
87C2×C22⋊Dic13—42no—
88C2×C22⋊Dic13—42no—
89D4×Dic13—232no—
90C2×C4⋊Dic13—22no—
91C2×C4⋊Dic13—22no—
92C2×C4⋊Dic13—22no—
93C2×C4⋊Dic13—22no—
94C2×C4⋊Dic13—22no—
95C2×C4⋊Dic13—22no—
96C2×C4⋊Dic13—22no—
97C2×C4⋊Dic13—22no—
98C2×C4⋊Dic13—22no—
99C2×C4⋊Dic13—22no—
100C2×C4⋊Dic13—24no—
101C2×C4⋊Dic13—24no—
102C2×C4⋊Dic13—42no—
103C2×C4⋊Dic13D414yes—
104C2×C4⋊Dic13D414yescomplemented
105C2×C4×Dic13—22no—
106C2×C4×Dic13—22no—
107C2×C4×Dic13—22no—
108C2×C4×Dic13—22no—
109C2×C4×Dic13—22no—
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—22no—
148C22×C4×C13—22no—
149C22×C4×C13—21no—
150C22×C4×C13—22no—
151C22×C4×C13—22no—
152C22×C4×C13—21no—
153C22×C4×C13—22no—
154C22×C4×C13—22no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13C22×C412yes—
159C22×C4×C13C22×C414yes—
160C22×C4×C13C22×C412yes—
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—216no—
175C22×Dic13—21no—
176C22×Dic13—21no—
177C22×Dic13—21no—
178C22×Dic13—22no—
179C22×Dic13—21no—
180C22×Dic13—21no—
181C22×Dic13—21no—
182C22×Dic13—21no—
183C22×Dic13—21no—
184C22×Dic13—22no—
185C22×Dic13—22no—
186C22×Dic13—21no—
187C22×Dic13—21no—
188C22×Dic13—21no—
189C22×Dic13—21no—
190C22×Dic13—22no—
191C22×Dic13—21no—
192C22×Dic13—22no—
193C22×Dic13—21no—
194C22×Dic13—22no—
195C22×Dic13—21no—
196C22×Dic13—21no—
197C22×Dic13—21no—
198C22×Dic13—21no—
199C22×Dic13—22no—
200C22×Dic13—22no—
201C22×Dic13—22no—
202C22×Dic13—22no—
203C22×Dic13—22no—
204C22×Dic13—22no—
205C22×Dic13—22no—
206C22×Dic13—48no—
207C22×Dic13—48no—
208C22×Dic13—48no—
209C22×Dic13—48no—
210C22×Dic13—48no—
211C22×Dic13—48no—
212C22×Dic13C2×D412yes—
213C22×Dic13C2×D414yes—
214C22×Dic13C2×D412yes—
215C22×Dic13C2×D412yes—
216C22×Dic13C2×D412yes—
217C22×Dic13#4112yes—
218C22×Dic13#4112yes—
219C13×C4⋊C4—28no—
220C13×C22⋊C4—216no—
221C13×C22⋊C4—48no—
222C42×C13—28no—
223C22⋊Dic13—216no—
224C22⋊Dic13—48no—
225C22⋊Dic13—48no—
226C4⋊Dic13—28no—
227C4⋊Dic13—28no—
228C4⋊Dic13—28no—
229C4⋊Dic13—48no—
230C4⋊Dic13—44no—
231C4×Dic13—28no—
232C4×Dic13—44no—
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—22no—
302C2×C4×C13—24no—
303C2×C4×C13—24no—
304C2×C4×C13—22no—
305C2×C4×C13—24no—
306C2×C4×C13—22no—
307C2×C4×C13—41no—
308C2×C4×C13—41no—
309C2×C4×C13—41no—
310C2×C4×C13—41no—
311C2×C4×C13—42no—
312C2×C4×C13—42no—
313C2×C4×C13—42no—
314C2×C4×C13—42no—
315C2×C4×C13C2×C4⋊C414yes—
316C2×C4×C13C4×D414yes—
317C2×C4×C13C4×D414yes—
318C2×C4×C13C4×D414yescomplemented
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—24no—
331C2×Dic13—22no—
332C2×Dic13—22no—
333C2×Dic13—22no—
334C2×Dic13—22no—
335C2×Dic13—22no—
336C2×Dic13—24no—
337C2×Dic13—22no—
338C2×Dic13—22no—
339C2×Dic13—24no—
340C2×Dic13—22no—
341C2×Dic13—432no—
342C2×Dic13—41no—
343C2×Dic13—41no—
344C2×Dic13—42no—
345C2×Dic13—41no—
346C2×Dic13—42no—
347C2×Dic13—41no—
348C2×Dic13—42no—
349C2×Dic13—41no—
350C2×Dic13—41no—
351C2×Dic13—41no—
352C2×Dic13—42no—
353C2×Dic13—41no—
354C2×Dic13—41no—
355C2×Dic13—41no—
356C2×Dic13—41no—
357C2×Dic13—41no—
358C2×Dic13—42no—
359C2×Dic13—42no—
360C2×Dic13—42no—
361C2×Dic13—42no—
362C2×Dic13—42no—
363C2×Dic13—42no—
364C2×Dic13—42no—
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—264no—
386#390Dic1318yescomplemented
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—24no—
448C4×C13—42no—
449C4×C13—44no—
450C4×C13#38518yescomplemented
451Dic13—24no—
452Dic13—42no—
453Dic13—42no—
454Dic13—42no—
455Dic13—44no—
456Dic13—82no—
457C25C22×D1312yes—
458C22×D4—22no—
459C22×D4—22no—
460C22×D4—22no—
461C22×D4—22no—
462C22×D4Dic2614yes—
463C22×D4D5214yes—
464C22×D4C2×Dic1314yes—
465C23×C4—131no—
466C23×C4—131no—
467C23×C4—131no—
468C23×C4—131no—
469C23×C4—132no—
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—134no—
486C2×C4⋊C4—134no—
487C2×C4⋊C4—262no—
488C2×C4⋊C4—262no—
489C2×C4⋊C4—262no—
490C2×C4⋊C4—262no—
491C2×C4⋊C4—262no—
492C2×C4⋊C4—262no—
493C2×C4⋊C4—262no—
494C2×C4⋊C4—264no—
495C2×C4⋊C4—264no—
496C2×C4⋊C4—262no—
497C2×C4⋊C4—262no—
498C2×C4⋊C4—262no—
499C2×C4⋊C4—522no—
500C2×C4⋊C4C2×Dic1314yescomplemented
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—42no—
504C2×C22⋊C4—42no—
505C2×C22⋊C4—264no—
506C2×C22⋊C4—264no—
507C2×C22⋊C4—264no—
508C2×C22⋊C4—264no—
509C2×C22⋊C4—264no—
510C2×C22⋊C4—264no—
511C2×C22⋊C4—264no—
512C2×C22⋊C4—522no—
513C2×C22⋊C4—522no—
514C2×C22⋊C4C2×Dic1318yescomplemented
515C2×C22⋊C4C2×Dic1318yescomplemented
516C2×C42—22no—
517C2×C42—22no—
518C2×C42—134no—
519C2×C42—262no—
520C2×C42—262no—
521C2×C42—262no—
522C2×C42—262no—
523C2×C42—262no—
524C2×C42C2×Dic1314yescomplemented
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×D5214yes—
562C24C22×Dic1314yes—
563C24C23×D1311yescharacteristic
564C2×D4—28no—
565C2×D4—28no—
566C2×D4—28no—
567C2×D4—28no—
568C2×D4—28no—
569C2×D4—28no—
570C2×D4C4⋊Dic13116yescomplemented
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—132no—
588C22×C4—132no—
589C22×C4—132no—
590C22×C4—132no—
591C22×C4—134no—
592C22×C4—132no—
593C22×C4—132no—
594C22×C4—261no—
595C22×C4—261no—
596C22×C4—261no—
597C22×C4—261no—
598C22×C4—2616no—
599C22×C4—261no—
600C22×C4—261no—
601C22×C4—261no—
602C22×C4—262no—
603C22×C4—261no—
604C22×C4—261no—
605C22×C4—261no—
606C22×C4—262no—
607C22×C4—261no—
608C22×C4—261no—
609C22×C4—262no—
610C22×C4—261no—
611C22×C4—261no—
612C22×C4—261no—
613C22×C4—261no—
614C22×C4—261no—
615C22×C4—262no—
616C22×C4—261no—
617C22×C4—261no—
618C22×C4—262no—
619C22×C4—262no—
620C22×C4—261no—
621C22×C4—261no—
622C22×C4—261no—
623C22×C4—262no—
624C22×C4—262no—
625C22×C4—262no—
626C22×C4—262no—
627C22×C4—262no—
628C22×C4—262no—
629C22×C4—262no—
630C22×C4—528no—
631C22×C4—528no—
632C22×C4—528no—
633C22×C4—528no—
634C22×C4—528no—
635C22×C4—528no—
636C22×C4C2×Dic2612yes—
637C22×C4C2×D5212yes—
638C22×C4D4×D1312yes—
639C22×C4D4×D1312yes—
640C22×C4D4×D1312yes—
641C22×C4#612912yes—
642C22×C4#612912yes—
643C22×C4#612912yes—
644C22×C4C22×Dic1312yes—
645C22×C4C22×Dic1314yes—
646C22×C4C22×Dic1312yes—
647C22×C4C22×Dic1312yes—
648C4⋊C4—28no—
649C4⋊C4—268no—
650C4⋊C4—268no—
651C4⋊C4—268no—
652C4⋊C4—528no—
653C4⋊C4—524no—
654C22⋊C4—216no—
655C22⋊C4—48no—
656C22⋊C4—2616no—
657C22⋊C4—528no—
658C22⋊C4—528no—
659C42—28no—
660C42—268no—
661C42—524no—
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×C4⋊Dic1318yes—
698C23C22×Dic2611yescharacteristic
699C23C22×D5211yescharacteristic
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
712C23C23×Dic1311yescharacteristic
713D4—232no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—134no—
735C2×C4—262no—
736C2×C4—262no—
737C2×C4—262no—
738C2×C4—262no—
739C2×C4—262no—
740C2×C4—262no—
741C2×C4—262no—
742C2×C4—264no—
743C2×C4—262no—
744C2×C4—262no—
745C2×C4—262no—
746C2×C4—262no—
747C2×C4—262no—
748C2×C4—262no—
749C2×C4—264no—
750C2×C4—262no—
751C2×C4—262no—
752C2×C4—264no—
753C2×C4—5232no—
754C2×C4—521no—
755C2×C4—521no—
756C2×C4—522no—
757C2×C4—521no—
758C2×C4—521no—
759C2×C4—522no—
760C2×C4—521no—
761C2×C4—521no—
762C2×C4—522no—
763C2×C4—521no—
764C2×C4—522no—
765C2×C4—521no—
766C2×C4—521no—
767C2×C4—521no—
768C2×C4—521no—
769C2×C4—521no—
770C2×C4—522no—
771C2×C4—522no—
772C2×C4—522no—
773C2×C4—522no—
774C2×C4—522no—
775C2×C4—522no—
776C2×C4—522no—
777C2×C4#8813214yes—
778C2×C4#8813214yes—
779C2×C4#8813614yes—
780C2×C4#8814014yes—
781C2×C4C2×C4⋊Dic1314yes—
782C2×C4D4×Dic1314yes—
783C2×C4D4×Dic1314yes—
784C2×C4D4×Dic1314yescomplemented
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×#8813611yescharacteristic
803C22C2×#8814011yescharacteristic
804C22D4×Dic2611yescharacteristic
805C22#1171924411yescharacteristic
806C22#1171924411yescharacteristic
807C22#1171924811yescharacteristic
808C22D4×D5211yescharacteristic
809C22#1171925911yescharacteristic
810C22#1171925911yescharacteristic
811C22#1171926011yescharacteristic
812C22#1171930111yescharacteristic
813C22#1171930511yescharacteristic
814C22#1171930811yescharacteristic
815C22D13×#12111yescharacteristic
816C22#1171931111yescharacteristic
817C22#1171931211yescharacteristic
818C22#1171931311yescharacteristic
819C22#1171932411yescharacteristic
820C22#1171937611yescharacteristic
821C22#1171938111yescharacteristic
822C22#1171938211yescharacteristic
823C22#1171938611yescharacteristic
824C22#1171941811yescharacteristic
825C22#1171942211yescharacteristic
826C22#1171942311yescharacteristic
827C22#1171942311yescharacteristic
828C22C22×C4⋊Dic1311yescharacteristic
829C22C2×D4×Dic1311yescharacteristic
830C22C2×D4×Dic1311yescharacteristic
831C22C2×D4×Dic1311yescharacteristic
832C22#1171950311yescharacteristic
833C22#41×Dic1311yescharacteristic
834C22#1171953211yescharacteristic
835C4—24no—
836C4—42no—
837C4—44no—
838C4—264no—
839C4—522no—
840C4—522no—
841C4—522no—
842C4—524no—
843C4—1042no—
844C4#1171861118yescomplemented
845C2—48no—
846C2C2×#1171861111yescharacteristic
847C2#121×Dic1311yescharacteristic
848C2#1311753111yescharacteristic
849C2D4×C4⋊Dic1311yescharacteristic
850C2#1311774611yescharacteristic
851C2#1311790111yescharacteristic
852C2#1311791111yescharacteristic
853C2#1311817911yescharacteristic
854C2#1311819011yescharacteristic
855C2#1311859911yescharacteristic
856C2#1311862111yescharacteristic
857C2#1311868911yescharacteristic
858C2#1311871111yescharacteristic
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×#11718646C2semidirect
4. C2×#11718611C2semidirect
5. C2×C4×C4⋊Dic13C2semidirect
6. #13113081C2semidirect
7. #13113081C2semidirect
8. #13113066C2semidirect
9. #13113065C2semidirect
10. #13113058C2semidirect
31. C13×#390C4semidirect
70. C2×C13×C4⋊C4C2×C4semidirect
75. C2×C13×C22⋊C4C2×C4semidirect
76. C2×C13×C22⋊C4C2×C4semidirect
79. C2×C42×C13C2×C4semidirect
104. C2×C4⋊Dic13D4semidirect
141. C2×D4×C13C4⋊C4semidirect
318. C2×C4×C13C4×D4semidirect
386. #390Dic13semidirect
450. C4×C13#385semidirect
500. C2×C4⋊C4C2×Dic13semidirect
514. C2×C22⋊C4C2×Dic13semidirect
515. C2×C22⋊C4C2×Dic13semidirect
524. C2×C42C2×Dic13semidirect
570. C2×D4C4⋊Dic13semidirect
662. C13#14018semidirect
784. C2×C4D4×Dic13semidirect
844. C4#11718611semidirect

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×#117186462
C2×#117186112
C2×C4×C4⋊Dic132
#131130812
#131130662
#131130652
#131130582
C2×C13×#3902
#1401813