Finite Group Databasebeta

← #15786310

Subgroups — #15786310

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
1C2×#11718882C211yesmaximal, characteristic
2C2×#11718882C211yesmaximal, characteristic
3C2×#11718634C211yesmaximal, characteristic, complemented
4C2×#11718871C212yesmaximal, complemented
5C2×C4×#6101C211yesmaximal, characteristic, complemented
6#13113079C212yesmaximal, complemented
7#13113079C212yesmaximal, complemented
8#13113066C211yesmaximal, characteristic, complemented
9#13113065C211yesmaximal, characteristic, complemented
10#13113059C212yesmaximal, complemented
11C22×C4×D4×C13C211yesmaximal, characteristic
12C23×D4×C13C2211yescharacteristic
13C24×C4×C13C2212yes—
14C2×C4×D4×C13—24no—
15C2×C4×D4×C13—24no—
16C2×C4×D4×C13—24no—
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2212yes—
19C22×C42×C13C2211yescharacteristic
20C22×C22⋊Dic13C2212yes—
21C22×C22⋊Dic13C2212yes—
22C22×C22⋊Dic13C2212yes—
23C22×C22⋊Dic13C2212yes—
24C22×C4⋊Dic13C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2212yes—
28C22×#6101C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31#11718882—24no—
32#11718882C418yescomplemented
33#11718871—28no—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2211yescharacteristic
38C2×#88071C2211yescharacteristic
39C2×#88071C2212yes—
40C2×#88071C2212yes—
41#11718634—24no—
42C4×#6101—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×C13—24no—
52C23×C4×C13—24no—
53C23×C4×C13—24no—
54C23×C4×C13—24no—
55C23×C4×C13—24no—
56C23×C4×C13—42no—
57C23×C4×C13—42no—
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2312yes—
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×Dic13C2312yes—
63C23×Dic13C2311yescharacteristic
64C23×Dic13C2312yes—
65C23×Dic13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C4×D4×C13—232no—
69C2×C13×C4⋊C4—22no—
70C2×C13×C4⋊C4—22no—
71C2×C13×C4⋊C4D414yes—
72C2×C13×C22⋊C4—24no—
73C2×C13×C22⋊C4—24no—
74C2×C13×C22⋊C4—24no—
75C2×C42×C13—22no—
76C2×C42×C13—22no—
77C2×C42×C13D414yes—
78C2×C22⋊Dic13—24no—
79C2×C22⋊Dic13—24no—
80C2×C22⋊Dic13—24no—
81C2×C22⋊Dic13—24no—
82C2×C22⋊Dic13—24no—
83C2×C22⋊Dic13—24no—
84C2×C22⋊Dic13—42no—
85C2×C22⋊Dic13—42no—
86C2×C22⋊Dic13—42no—
87C2×C22⋊Dic13—42no—
88C2×C22⋊Dic13C2×C418yescomplemented
89C2×C22⋊Dic13C2×C418yescomplemented
90C2×C4⋊Dic13—22no—
91C2×C4⋊Dic13—22no—
92C2×C4⋊Dic13—22no—
93C2×C4⋊Dic13—22no—
94C2×C4⋊Dic13—22no—
95C2×C4⋊Dic13C2×C414yescomplemented
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×Dic13—22no—
110C2×C4×Dic13C2×C414yescomplemented
111#88071—22no—
112#88071—22no—
113#88071—24no—
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—216no—
147C22×C4×C13—22no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—22no—
151C22×C4×C13—22no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—22no—
155C22×C4×C13—21no—
156C22×C4×C13—22no—
157C22×C4×C13—22no—
158C22×C4×C13—21no—
159C22×C4×C13—48no—
160C22×C4×C13—48no—
161C22×C4×C13—48no—
162C22×C4×C13—48no—
163C22×C4×C13—48no—
164C22×C4×C13—48no—
165C22×C4×C13C22×C412yes—
166C22×C4×C13C2×D412yes—
167C22×C4×C13C2×D412yes—
168C22×C4×C13C2×D414yes—
169C22×C4×C13C2×D412yes—
170C22×C4×C13C2×D412yes—
171C22×C4×C13C2×D412yes—
172C22×C4×C13C2×D412yes—
173C22×C4×C13C2×Q812yes—
174C22×C4×C13#4112yes—
175C22×C4×C13#4112yes—
176C22×C4×C13#4112yes—
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—22no—
186C22×Dic13—22no—
187C22×Dic13—21no—
188C22×Dic13—21no—
189C22×Dic13—21no—
190C22×Dic13—21no—
191C22×Dic13—21no—
192C22×Dic13—21no—
193C22×Dic13—22no—
194C22×Dic13—22no—
195C22×Dic13—21no—
196C22×Dic13—22no—
197C22×Dic13—21no—
198C22×Dic13—22no—
199C22×Dic13—21no—
200C22×Dic13—21no—
201C22×Dic13—21no—
202C22×Dic13—21no—
203C22×Dic13—21no—
204C22×Dic13—21no—
205C22×Dic13—22no—
206C22×Dic13—22no—
207C22×Dic13—22no—
208C22×Dic13—22no—
209C22×Dic13—22no—
210C22×Dic13—22no—
211C22×Dic13—22no—
212C22×Dic13C22×C412yes—
213C22×Dic13C22×C414yes—
214C22×Dic13C22×C412yes—
215C22×Dic13C2×D412yes—
216C22×Dic13C2×D412yes—
217C22×Dic13#4112yes—
218C22×Dic13#4112yes—
219C13×C4⋊C4—28no—
220C13×C22⋊C4—216no—
221C42×C13—28no—
222C22⋊Dic13—216no—
223C22⋊Dic13—48no—
224C22⋊Dic13—48no—
225C22⋊Dic13—48no—
226C4⋊Dic13—28no—
227C4⋊Dic13—44no—
228#6101—28no—
229#6101—28no—
230#6101—48no—
231C4×Dic13—28no—
232C4×Dic13—44no—
233C22×C4×D4D1311yescharacteristic
234C2×#390—131no—
235C2×#390—131no—
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—22no—
304C2×C4×C13—22no—
305C2×C4×C13—24no—
306C2×C4×C13—24no—
307C2×C4×C13—432no—
308C2×C4×C13—42no—
309C2×C4×C13—42no—
310C2×C4×C13—42no—
311C2×C4×C13—41no—
312C2×C4×C13—42no—
313C2×C4×C13—41no—
314C2×C4×C13—41no—
315C2×C4×C13—41no—
316C2×C4×C13C2×C4⋊C414yes—
317C2×C4×C13C4×D414yes—
318C2×C4×C13C4×D414yes—
319C2×C4×C13#12014yes—
320C2×C4×C13#12114yes—
321C2×C4×C13C22⋊Q814yes—
322C2×C4×C13C22⋊Q814yes—
323C2×C4×C13#12314yes—
324C2×Dic13—22no—
325C2×Dic13—22no—
326C2×Dic13—22no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—22no—
330C2×Dic13—22no—
331C2×Dic13—24no—
332C2×Dic13—24no—
333C2×Dic13—22no—
334C2×Dic13—24no—
335C2×Dic13—22no—
336C2×Dic13—22no—
337C2×Dic13—22no—
338C2×Dic13—22no—
339C2×Dic13—22no—
340C2×Dic13—22no—
341C2×Dic13—22no—
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—42no—
351C2×Dic13—41no—
352C2×Dic13—41no—
353C2×Dic13—41no—
354C2×Dic13—42no—
355C2×Dic13—42no—
356C2×Dic13—41no—
357C2×Dic13—42no—
358C2×Dic13—42no—
359C2×Dic13—42no—
360C2×Dic13—42no—
361C2×Dic13—42no—
362C2×Dic13—42no—
363C2×Dic13—42no—
364C2×Dic13—42no—
365C2×Dic13C4×D414yescomplemented
366C23×D4C2×D1311yescharacteristic
367C24×C4C2×D1312yes—
368C2×C4×D4—24no—
369C2×C4×D4—24no—
370C2×C4×D4—24no—
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⋊C4—132no—
381C22×C22⋊C4C2×D1312yes—
382C22×C42—131no—
383C22×C42—131no—
384C22×C42C2×D1311yescharacteristic
385#390—138no—
386#390—264no—
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—44no—
454Dic13—42no—
455Dic13—42no—
456Dic13—82no—
457C25C22×D1312yes—
458C22×D4—22no—
459C22×D4—22no—
460C22×D4—22no—
461C22×D4—22no—
462C22×D4Dic2614yes—
463C22×D4C4×D1314yes—
464C22×D4C22⋊D1314yes—
465C23×C4—24no—
466C23×C4—24no—
467C23×C4—24no—
468C23×C4—24no—
469C23×C4—24no—
470C23×C4—42no—
471C23×C4—42no—
472C23×C4—131no—
473C23×C4—131no—
474C23×C4—132no—
475C23×C4—131no—
476C23×C4—131no—
477C23×C4—132no—
478C23×C4C22×D1311yescharacteristic
479C23×C4C22×D1312yes—
480C23×C4C22×D1311yescharacteristic
481C23×C4C22×D1311yescharacteristic
482C4×D4—232no—
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—262no—
496C2×C4⋊C4—262no—
497C2×C4⋊C4—264no—
498C2×C4⋊C4—262no—
499C2×C4⋊C4—522no—
500C2×C4⋊C4C22⋊D1314yes—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—138no—
505C2×C22⋊C4—138no—
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⋊C4—522no—
515C2×C22⋊C4—522no—
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×C42C22⋊D1314yes—
525#95—264no—
526#95—264no—
527#95—262no—
528#95—262no—
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—216no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—132no—
595C22×C4—132no—
596C22×C4—132no—
597C22×C4—132no—
598C22×C4—134no—
599C22×C4—132no—
600C22×C4—132no—
601C22×C4—261no—
602C22×C4—261no—
603C22×C4—261no—
604C22×C4—261no—
605C22×C4—261no—
606C22×C4—262no—
607C22×C4—262no—
608C22×C4—261no—
609C22×C4—261no—
610C22×C4—261no—
611C22×C4—261no—
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—261no—
621C22×C4—261no—
622C22×C4—261no—
623C22×C4—261no—
624C22×C4—261no—
625C22×C4—262no—
626C22×C4—261no—
627C22×C4—261no—
628C22×C4—261no—
629C22×C4—262no—
630C22×C4—262no—
631C22×C4—262no—
632C22×C4—262no—
633C22×C4—262no—
634C22×C4—262no—
635C22×C4—262no—
636C22×C4C2×Dic2612yes—
637C22×C4C2×C4×D1312yes—
638C22×C4#612712yes—
639C22×C4#612712yes—
640C22×C4D4×D1312yes—
641C22×C4#612912yes—
642C22×C4C2×C22⋊D1312yes—
643C22×C4C2×C22⋊D1314yes—
644C22×C4C2×C22⋊D1312yes—
645C22×C4C2×C22⋊D1312yes—
646C22×C4C2×C22⋊D1312yes—
647C22×C4C2×C22⋊D1312yes—
648C4⋊C4—28no—
649C4⋊C4—268no—
650C4⋊C4—268no—
651C4⋊C4—268no—
652C4⋊C4—528no—
653C4⋊C4—524no—
654C22⋊C4—216no—
655C22⋊C4—2616no—
656C22⋊C4—528no—
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×#610118yes—
698C23C22×Dic2611yescharacteristic
699C23C22×C4×D1311yescharacteristic
700C23C2×#612711yescharacteristic
701C23C2×#612711yescharacteristic
702C23C2×D4×D1311yescharacteristic
703C23C2×#612911yescharacteristic
704C23#8825111yescharacteristic
705C23#8825111yescharacteristic
706C23#41×D1311yescharacteristic
707C23#41×D1311yescharacteristic
708C23#8825611yescharacteristic
709C23#8825711yescharacteristic
710C23C22×C22⋊D1311yescharacteristic
711C23C22×C22⋊D1311yescharacteristic
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—24no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—432no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—134no—
736C2×C4—262no—
737C2×C4—262no—
738C2×C4—262no—
739C2×C4—262no—
740C2×C4—262no—
741C2×C4—262no—
742C2×C4—262no—
743C2×C4—264no—
744C2×C4—264no—
745C2×C4—262no—
746C2×C4—262no—
747C2×C4—264no—
748C2×C4—262no—
749C2×C4—262no—
750C2×C4—262no—
751C2×C4—262no—
752C2×C4—262no—
753C2×C4—262no—
754C2×C4—522no—
755C2×C4—521no—
756C2×C4—521no—
757C2×C4—521no—
758C2×C4—521no—
759C2×C4—522no—
760C2×C4—522no—
761C2×C4—521no—
762C2×C4—521no—
763C2×C4—521no—
764C2×C4—521no—
765C2×C4—521no—
766C2×C4—522no—
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×C4C2×#610114yes—
778C2×C4#8817814yes—
779C2×C4#8817814yes—
780C2×C4C4×C22⋊D1314yes—
781C2×C4C4×C22⋊D1314yes—
782C2×C4#8818314yes—
783C2×C4#8819214yes—
784C2×C4#8820714yes—
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—
800C22C4×#612911yescharacteristic
801C22D4×Dic2611yescharacteristic
802C22#1171924411yescharacteristic
803C22#1171924411yescharacteristic
804C22#1171924711yescharacteristic
805C22#1171924811yescharacteristic
806C22C4×D4×D1311yescharacteristic
807C22#1171925011yescharacteristic
808C22#1171925111yescharacteristic
809C22#1171925311yescharacteristic
810C22#1171925811yescharacteristic
811C22#1171926211yescharacteristic
812C22#1171926411yescharacteristic
813C22#1171926411yescharacteristic
814C22#1171926611yescharacteristic
815C22#1171926711yescharacteristic
816C22C22×#610111yescharacteristic
817C22C2×#8817811yescharacteristic
818C22C2×#8817811yescharacteristic
819C22C2×C4×C22⋊D1311yescharacteristic
820C22C2×C4×C22⋊D1311yescharacteristic
821C22C2×#8818311yescharacteristic
822C22C2×#8819211yescharacteristic
823C22D4×C22⋊D1311yescharacteristic
824C22D4×C22⋊D1311yescharacteristic
825C22#1171951011yescharacteristic
826C22#1171951111yescharacteristic
827C22#1171951111yescharacteristic
828C22#1171952911yescharacteristic
829C22#1171953311yescharacteristic
830C22#1171953411yescharacteristic
831C22#1171953611yescharacteristic
832C22#1171953811yescharacteristic
833C22#1171953911yescharacteristic
834C22C2×#8820711yescharacteristic
835C4—24no—
836C4—42no—
837C4—44no—
838C4—264no—
839C4—522no—
840C4—524no—
841C4—522no—
842C4—522no—
843C4—1042no—
844C4#1171887118yescomplemented
845C2—48no—
846C2C2×#1171887111yescharacteristic
847C2C4×#8819211yescharacteristic
848C2#1311752311yescharacteristic
849C2D4×#610111yescharacteristic
850C2#1311774111yescharacteristic
851C2#1311789811yescharacteristic
852C2#1311790911yescharacteristic
853C2#1311817511yescharacteristic
854C2#1311818611yescharacteristic
855C2#1311859511yescharacteristic
856C2#1311861711yescharacteristic
857C2#1311868011yescharacteristic
858C2#1311870211yescharacteristic
859C2#1311975811yescharacteristic
860C2#1312019011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC22×C4×D4×C13C2
socle, cosocleC24×C13C24
prime radicalC23×D4×C13C22
hypercenterC22×C4×D4D13
hypocenterC13#14018
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
3. C2×#11718634C2semidirect
4. C2×#11718871C2semidirect
5. C2×C4×#6101C2semidirect
6. #13113079C2semidirect
7. #13113079C2semidirect
8. #13113066C2semidirect
9. #13113065C2semidirect
10. #13113059C2semidirect
32. #11718882C4semidirect
88. C2×C22⋊Dic13C2×C4semidirect
89. C2×C22⋊Dic13C2×C4semidirect
95. C2×C4⋊Dic13C2×C4semidirect
104. C2×#6101D4semidirect
110. C2×C4×Dic13C2×C4semidirect
141. C2×D4×C13C4⋊C4semidirect
365. C2×Dic13C4×D4semidirect
450. C4×C13#385semidirect
570. C2×D4#6101semidirect
662. C13#14018semidirect
844. C4#11718871semidirect

Maximal subgroups

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

subgroupindex
C2×#117188822
C2×#117186342
C2×#117188712
C2×C4×#61012
#131130792
#131130662
#131130652
#131130592
C22×C4×D4×C132
#1401813