Finite Group Databasebeta

← #15785291

Subgroups — #15785291

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×#88147C211yesmaximal, characteristic
2C2×#11718600C211yesmaximal, characteristic
3C2×#11718649C211yesmaximal, characteristic
4C2×#11718646C211yesmaximal, characteristic, complemented
5C2×#11718648C212yesmaximal, complemented
6#13113082C212yesmaximal, complemented
7#13113078C212yesmaximal, complemented
8#13113065C211yesmaximal, characteristic, complemented
9#13113057C212yesmaximal, complemented
10C4×#88071C211yesmaximal, characteristic, complemented
11C2×C13×#389C211yesmaximal, characteristic, complemented
12C23×D52C2211yescharacteristic
13C23×C4×D13C2212yes—
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C13×C4⋊C4C2212yes—
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C42×C13C2211yescharacteristic
18C22×#6103C2212yes—
19C22×#6103C2212yes—
20C22×#6103C2212yes—
21C22×#6103C2212yes—
22C22×#6103C2212yes—
23C22×C4⋊Dic13C2211yescharacteristic
24C22×C4⋊Dic13C2212yes—
25C22×C4×Dic13C2211yescharacteristic
26C22×C4×Dic13C2211yescharacteristic
27C2×#88147—24no—
28C2×#88147—24no—
29C2×#88147C418yescomplemented
30C13×#389—24no—
31C2×C13×#95C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2211yescharacteristic
35C2×#88071C2211yescharacteristic
36C2×#88071C2211yescharacteristic
37C2×#88071C2212yes—
38C2×#88071C2211yescharacteristic
39#11718649—24no—
40#11718648—28no—
41#11718646—24no—
42#11718600—24no—
43C24×D13C2312yes—
44C23×C4×C13C2312yes—
45C23×C4×C13C2311yescharacteristic
46C23×C4×C13C2311yescharacteristic
47C23×C4×C13C2312yes—
48C23×C4×C13C2311yescharacteristic
49C23×Dic13C2312yes—
50C23×Dic13C2311yescharacteristic
51C23×Dic13C2311yescharacteristic
52C23×Dic13C2311yescharacteristic
53C23×Dic13C2311yescharacteristic
54C22×D52—22no—
55C22×D52—22no—
56C22×D52—22no—
57C22×D52—22no—
58C22×D52C2×C414yes—
59C22×D52D414yes—
60C22×D52Q814yes—
61C22×C4×D13—24no—
62C22×C4×D13—24no—
63C22×C4×D13—24no—
64C22×C4×D13—24no—
65C22×C4×D13—42no—
66C22×C4×D13—42no—
67C22×C4×D13C2×C418yes—
68C2×C13×C4⋊C4—24no—
69C2×C13×C4⋊C4—22no—
70C2×C13×C4⋊C4—24no—
71C2×C13×C4⋊C4—22no—
72C2×C13×C4⋊C4—22no—
73C2×C13×C4⋊C4—42no—
74C2×C13×C4⋊C4C2×C414yes—
75C2×C13×C4⋊C4D414yes—
76C2×C13×C4⋊C4D414yes—
77C2×C42×C13—22no—
78C2×C42×C13—22no—
79C2×C42×C13—22no—
80C2×#6103—24no—
81C2×#6103—24no—
82C2×#6103—24no—
83C2×#6103—24no—
84C2×#6103—24no—
85C2×#6103—24no—
86C2×#6103—24no—
87C2×#6103—24no—
88C2×#6103—24no—
89C2×#6103—24no—
90C2×#6103—42no—
91C2×#6103—42no—
92C2×#6103—42no—
93C2×#6103—42no—
94C2×#6103C2×C418yes—
95C2×C4⋊Dic13—22no—
96C2×C4⋊Dic13—24no—
97C2×C4⋊Dic13—22no—
98C2×C4⋊Dic13—22no—
99C2×C4⋊Dic13—24no—
100C2×C4⋊Dic13—42no—
101C2×C4×Dic13—22no—
102C2×C4×Dic13—22no—
103C2×C4×Dic13—22no—
104C2×C4×Dic13—22no—
105C2×C4×Dic13—22no—
106C2×C4×Dic13C2×C414yes—
107#88147—232no—
108C13×#95—24no—
109#88071—24no—
110#88071—22no—
111#88071—24no—
112#88071—22no—
113#88071—22no—
114#88071—42no—
115#88071D414yescomplemented
116#13920—131nomaximal, Sylow
117C24×C13C2411yescharacteristic
118C23×D13—22no—
119C23×D13—22no—
120C23×D13—22no—
121C23×D13—22no—
122C23×D13—22no—
123C23×D13—22no—
124C23×D13—22no—
125C23×D13—22no—
126C23×D13—22no—
127C23×D13—22no—
128C23×D13—22no—
129C23×D13—22no—
130C23×D13C22×C414yes—
131C23×D13C2×D414yes—
132C23×D13C2×Q814yes—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—22no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
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—22no—
150C22×C4×C13—22no—
151C22×C4×C13—22no—
152C22×C4×C13—22no—
153C22×C4×C13—22no—
154C22×C4×C13—22no—
155C22×C4×C13—22no—
156C22×C4×C13C22×C414yes—
157C22×C4×C13C22×C412yes—
158C22×C4×C13C2×D414yes—
159C22×C4×C13C2×D412yes—
160C22×C4×C13C2×D412yes—
161C22×C4×C13C2×D412yes—
162C22×C4×C13C2×D414yes—
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—21no—
171C22×Dic13—21no—
172C22×Dic13—21no—
173C22×Dic13—21no—
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—22no—
191C22×Dic13—22no—
192C22×Dic13—22no—
193C22×Dic13—22no—
194C22×Dic13—22no—
195C22×Dic13—22no—
196C22×Dic13—22no—
197C22×Dic13C22×C412yes—
198C22×Dic13C22×C412yes—
199C22×Dic13C2×D412yes—
200C22×Dic13C2×D412yes—
201C22×Dic13#4112yes—
202C22×Dic13#4112yes—
203C2×D52—28no—
204C2×D52—28no—
205C2×D52—28no—
206C2×D52—28no—
207C2×D52—28no—
208C2×D52—28no—
209C2×D52C4⋊C4116yescomplemented
210C2×C4×D13—216no—
211C2×C4×D13—216no—
212C2×C4×D13—48no—
213C2×C4×D13—48no—
214C2×C4×D13—48no—
215C2×C4×D13—48no—
216C2×C4×D13—48no—
217C13×C4⋊C4—48no—
218C13×C4⋊C4—44no—
219C13×C4⋊C4C22⋊C4116yescomplemented
220C42×C13—44no—
221#6103—216no—
222#6103—48no—
223#6103—48no—
224#6103—48no—
225#6103—48no—
226C4⋊Dic13—48no—
227C4⋊Dic13—44no—
228C4×Dic13—28no—
229C4×Dic13—44no—
230C22×C4×D4—131no—
231C2×#390—131no—
232C2×#390—131no—
233C2×#389—131no—
234C2×#389D1311yescharacteristic, complemented
235C2×#380—132no—
236#1439—132no—
237#1439—132no—
238C4⋊#95—131no—
239C22⋊#95—132no—
240C4×#95—131no—
241C23×C13C23×C411yescharacteristic
242C23×C13C22×D411yescharacteristic
243C23×C13C22×D411yescharacteristic
244C23×C13C22×D411yescharacteristic
245C23×C13C22×D411yescharacteristic
246C23×C13C22×Q811yescharacteristic
247C23×C13C2×#4111yescharacteristic
248C23×C13C2×#4111yescharacteristic
249C23×C13C2×#4111yescharacteristic
250C23×C13C2×#4111yescharacteristic
251C23×C13C2×#4111yescharacteristic
252C23×C13H(5,𝔽2)11yescharacteristic
253C23×C13H(5,𝔽2)11yescharacteristic
254C23×C13H(5,𝔽2)11yescharacteristic
255C23×C132−1+411yescharacteristic
256C22×D13—24no—
257C22×D13—24no—
258C22×D13—24no—
259C22×D13—24no—
260C22×D13—24no—
261C22×D13—24no—
262C22×D13—24no—
263C22×D13—24no—
264C22×D13—24no—
265C22×D13—24no—
266C22×D13—24no—
267C22×D13—24no—
268C22×D13—24no—
269C22×D13—24no—
270C22×D13—24no—
271C22×D13—24no—
272C22×D13—24no—
273C22×D13—24no—
274C22×D13—42no—
275C22×D13—42no—
276C22×D13—42no—
277C22×D13—42no—
278C22×D13—42no—
279C22×D13—42no—
280C22×D13—42no—
281C22×D13—42no—
282C22×D13—42no—
283C22×D13—42no—
284C22×D13—42no—
285C22×D13—42no—
286C22×D13—42no—
287C22×D13—42no—
288C22×D13—42no—
289C22×D13—42no—
290C22×D13C2×C4⋊C418yes—
291C2×C4×C13—24no—
292C2×C4×C13—24no—
293C2×C4×C13—24no—
294C2×C4×C13—24no—
295C2×C4×C13—24no—
296C2×C4×C13—24no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
299C2×C4×C13—22no—
300C2×C4×C13—22no—
301C2×C4×C13—22no—
302C2×C4×C13—22no—
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—41no—
310C2×C4×C13—41no—
311C2×C4×C13—42no—
312C2×C4×C13—42no—
313C2×C4×C13—42no—
314C2×C4×C13—42no—
315C2×C4×C13—42no—
316C2×C4×C13—42no—
317C2×C4×C13—42no—
318C2×C4×C13C2×C22⋊C418yes—
319C2×C4×C13C2×C22⋊C414yes—
320C2×C4×C13C2×C4⋊C414yes—
321C2×C4×C13#11714yes—
322C2×C4×C13#12114yes—
323C2×C4×C13#12114yes—
324C2×C4×C13C22⋊Q814yes—
325C2×C4×C13C22⋊Q814yes—
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—22no—
337C2×Dic13—22no—
338C2×Dic13—22no—
339C2×Dic13—22no—
340C2×Dic13—22no—
341C2×Dic13—41no—
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—42no—
354C2×Dic13—42no—
355C2×Dic13—42no—
356C2×Dic13—42no—
357C2×Dic13—42no—
358C2×Dic13—42no—
359C2×Dic13—42no—
360C2×Dic13C4×D414yes—
361D52—232no—
362C4×D13—432no—
363C23×D4—131no—
364C24×C4—132no—
365C2×C4×D4—138no—
366C2×C4×D4—264no—
367C2×C4×D4—264no—
368C22×C4⋊C4—131no—
369C22×C4⋊C4—132no—
370C22×C4⋊C4C2×D1311yescharacteristic
371C22×C4⋊C4C2×D1312yes—
372C22×C4⋊C4C2×D1311yescharacteristic
373C22×C22⋊C4—132no—
374C22×C22⋊C4—132no—
375C22×C22⋊C4—132no—
376C22×C22⋊C4—132no—
377C22×C22⋊C4—132no—
378C22×C42—131no—
379C22×C42—131no—
380C22×C42C2×D1311yescharacteristic
381#390—264no—
382#390—264no—
383#389—24no—
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×#95C2×D1312yes—
394C22×C13C22×C22⋊C411yescharacteristic
395C22×C13C22×C4⋊C411yescharacteristic
396C22×C13C2×#11711yescharacteristic
397C22×C13C2×C4×D411yescharacteristic
398C22×C13C4×#4111yescharacteristic
399C22×C13#51811yescharacteristic
400C22×C13#52011yescharacteristic
401C22×C13C2×#12111yescharacteristic
402C22×C13C2×#12111yescharacteristic
403C22×C13C2×C22⋊Q811yescharacteristic
404C22×C13C2×C22⋊Q811yescharacteristic
405C22×C13#52911yescharacteristic
406C22×C13#52911yescharacteristic
407C22×C13#53211yescharacteristic
408C22×C13#53211yescharacteristic
409C22×C13#54011yescharacteristic
410C22×C13#54011yescharacteristic
411C22×C13#54211yescharacteristic
412C22×C13#54211yescharacteristic
413C22×C13D4211yescharacteristic
414C22×C13D4211yescharacteristic
415C22×C13D4211yescharacteristic
416C22×C13#54611yescharacteristic
417C22×C13#54611yescharacteristic
418C22×C13#54611yescharacteristic
419C22×C13#54611yescharacteristic
420C22×C13#54711yescharacteristic
421C22×C13#54811yescharacteristic
422C22×C13#54811yescharacteristic
423C22×C13D4×Q811yescharacteristic
424C22×C13#55011yescharacteristic
425C22×C13#55011yescharacteristic
426C22×C13#55411yescharacteristic
427C22×C13#55411yescharacteristic
428C22×C13#55411yescharacteristic
429C2×D13—28no—
430C2×D13—28no—
431C2×D13—28no—
432C2×D13—44no—
433C2×D13—44no—
434C2×D13—44no—
435C2×D13—44no—
436C2×D13—44no—
437C2×D13—44no—
438C2×D13—44no—
439C2×D13—44no—
440C2×D13—44no—
441C2×D13—44no—
442C2×D13—44no—
443C2×D13—44no—
444C4×C13—28no—
445C4×C13—42no—
446C4×C13—42no—
447C4×C13—82no—
448C4×C13#38018yescomplemented
449Dic13—24no—
450Dic13—42no—
451Dic13—42no—
452Dic13—42no—
453Dic13—82no—
454C25—132no—
455C22×D4—134no—
456C22×D4—134no—
457C22×D4—134no—
458C22×D4—262no—
459C22×D4—262no—
460C22×D4—262no—
461C22×D4—262no—
462C23×C4—131no—
463C23×C4—131no—
464C23×C4—131no—
465C23×C4—131no—
466C23×C4—138no—
467C23×C4—132no—
468C23×C4—264no—
469C23×C4—264no—
470C23×C4—264no—
471C23×C4—264no—
472C23×C4—522no—
473C23×C4—522no—
474C23×C4C22×D1312yes—
475C23×C4C22×D1311yescharacteristic
476C23×C4C22×D1311yescharacteristic
477C23×C4C22×D1312yes—
478C23×C4C22×D1311yescharacteristic
479C4×D4—2632no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—24no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—42no—
486C2×C4⋊C4—264no—
487C2×C4⋊C4—264no—
488C2×C4⋊C4—262no—
489C2×C4⋊C4—262no—
490C2×C4⋊C4—262no—
491C2×C4⋊C4—522no—
492C2×C4⋊C4C4×D1314yes—
493C2×C4⋊C4D5214yes—
494C2×C4⋊C4C22⋊D1314yes—
495C2×C22⋊C4—138no—
496C2×C22⋊C4—264no—
497C2×C22⋊C4—264no—
498C2×C22⋊C4—264no—
499C2×C22⋊C4—264no—
500C2×C22⋊C4—264no—
501C2×C22⋊C4—264no—
502C2×C22⋊C4—264no—
503C2×C22⋊C4—264no—
504C2×C22⋊C4—264no—
505C2×C22⋊C4—264no—
506C2×C22⋊C4—522no—
507C2×C22⋊C4—522no—
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—24no—
520#95—134no—
521#95—262no—
522#95—262no—
523#95—264no—
524#95—264no—
525#95—262no—
526#95—522no—
527C2×C13C2×#38011yescharacteristic
528C2×C13#229311yescharacteristic
529C2×C13#231911yescharacteristic
530C2×C13D4×C22⋊C411yescharacteristic
531C2×C13#234111yescharacteristic
532C2×C13D4×C4⋊C411yescharacteristic
533C2×C13#234911yescharacteristic
534C2×C13#242711yescharacteristic
535C2×C13#242711yescharacteristic
536C2×C13#242811yescharacteristic
537C2×C13#242811yescharacteristic
538C2×C13#245211yescharacteristic
539C2×C13#245211yescharacteristic
540C2×C13#245411yescharacteristic
541C2×C13#245411yescharacteristic
542D13—48no—
543C24—134no—
544C24—134no—
545C24—134no—
546C24—262no—
547C24—262no—
548C24—262no—
549C24—262no—
550C24—262no—
551C24—262no—
552C24—262no—
553C24—262no—
554C24—262no—
555C24—262no—
556C24—262no—
557C24—262no—
558C24C23×D1311yescharacteristic
559C2×D4—1316no—
560C2×D4—268no—
561C2×D4—268no—
562C2×D4—268no—
563C2×D4—268no—
564C2×D4—268no—
565C2×D4—268no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
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—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—132no—
590C22×C4—132no—
591C22×C4—132no—
592C22×C4—132no—
593C22×C4—132no—
594C22×C4—132no—
595C22×C4—2616no—
596C22×C4—261no—
597C22×C4—261no—
598C22×C4—261no—
599C22×C4—261no—
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—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—2616no—
619C22×C4—262no—
620C22×C4—262no—
621C22×C4—262no—
622C22×C4—262no—
623C22×C4—262no—
624C22×C4—262no—
625C22×C4—262no—
626C22×C4—528no—
627C22×C4—528no—
628C22×C4—528no—
629C22×C4—528no—
630C22×C4—528no—
631C22×C4C2×C4×D1314yes—
632C22×C4C2×C4×D1312yes—
633C22×C4C2×D5214yes—
634C22×C4C2×D5212yes—
635C22×C4D4×D1312yes—
636C22×C4D4×D1312yes—
637C22×C4#612912yes—
638C22×C4Q8×D1312yes—
639C22×C4#613112yes—
640C22×C4#613112yes—
641C22×C4C2×C22⋊D1314yes—
642C22×C4C2×C22⋊D1312yes—
643C4⋊C4—48no—
644C4⋊C4—44no—
645C4⋊C4—528no—
646C4⋊C4—524no—
647C4⋊C4#6103116yescomplemented
648C22⋊C4—2616no—
649C22⋊C4—528no—
650C22⋊C4—528no—
651C22⋊C4—528no—
652C22⋊C4—528no—
653C42—44no—
654C42—268no—
655C42—524no—
656C13#1392011yescharacteristic, complemented, Sylow
657C23—138no—
658C23—264no—
659C23—264no—
660C23—264no—
661C23—264no—
662C23—264no—
663C23—264no—
664C23—264no—
665C23—264no—
666C23—264no—
667C23—264no—
668C23—264no—
669C23—264no—
670C23—264no—
671C23—264no—
672C23—264no—
673C23—264no—
674C23—264no—
675C23—264no—
676C23—522no—
677C23—522no—
678C23—522no—
679C23—522no—
680C23—522no—
681C23—522no—
682C23—522no—
683C23—522no—
684C23—522no—
685C23—522no—
686C23—522no—
687C23—522no—
688C23—522no—
689C23—522no—
690C23—522no—
691C23—522no—
692C23C22×C4×D1311yescharacteristic
693C23C22×D5211yescharacteristic
694C23C2×D4×D1311yescharacteristic
695C23C2×D4×D1311yescharacteristic
696C23C2×#612911yescharacteristic
697C23#8825111yescharacteristic
698C23C2×Q8×D1311yescharacteristic
699C23C2×#613111yescharacteristic
700C23C2×#613111yescharacteristic
701C23#8825411yescharacteristic
702C23#41×D1311yescharacteristic
703C23#41×D1311yescharacteristic
704C23#8825611yescharacteristic
705C23#8825611yescharacteristic
706C23C22×C22⋊D1311yescharacteristic
707D4—2632no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
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—262no—
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—262no—
751C2×C4—5232no—
752C2×C4—521no—
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—522no—
765C2×C4—522no—
766C2×C4—522no—
767C2×C4—522no—
768C2×C4—522no—
769C2×C4—522no—
770C2×C4—522no—
771C2×C4C4⋊C4×D1314yes—
772C2×C4#8814614yes—
773C2×C4#8814914yes—
774C2×C4#8815114yes—
775C2×C4C2×#610318yes—
776C2×C4C2×#610314yes—
777C2×C4#8819214yes—
778C2×C4#8820014yes—
779C22—268no—
780C22—268no—
781C22—268no—
782C22—524no—
783C22—524no—
784C22—524no—
785C22—524no—
786C22—524no—
787C22—524no—
788C22—524no—
789C22—524no—
790C22—524no—
791C22—524no—
792C22—524no—
793C22—524no—
794C22C2×C4⋊C4×D1311yescharacteristic
795C22C2×#8814611yescharacteristic
796C22C2×#8814911yescharacteristic
797C22C2×#8815111yescharacteristic
798C22C4×D4×D1311yescharacteristic
799C22#1171925011yescharacteristic
800C22D4×D5211yescharacteristic
801C22#1171925911yescharacteristic
802C22C4×#613111yescharacteristic
803C22#1171927911yescharacteristic
804C22#1171928111yescharacteristic
805C22#1171928211yescharacteristic
806C22#1171930111yescharacteristic
807C22#1171931411yescharacteristic
808C22#1171931711yescharacteristic
809C22#1171932411yescharacteristic
810C22#1171932911yescharacteristic
811C22#1171933511yescharacteristic
812C22#1171933611yescharacteristic
813C22#1171934811yescharacteristic
814C22#1171939511yescharacteristic
815C22#1171939511yescharacteristic
816C22#1171939611yescharacteristic
817C22#1171940311yescharacteristic
818C22#1171943011yescharacteristic
819C22#1171943211yescharacteristic
820C22#1171943511yescharacteristic
821C22#1171943811yescharacteristic
822C22C22×#610311yescharacteristic
823C22C2×#8819211yescharacteristic
824C22D4×C22⋊D1311yescharacteristic
825C22C2×#8820011yescharacteristic
826C22#1171952211yescharacteristic
827C22#1171953411yescharacteristic
828C22#1171953911yescharacteristic
829C4—28no—
830C4—42no—
831C4—42no—
832C4—82no—
833C4—264no—
834C4—522no—
835C4—522no—
836C4—522no—
837C4—1042no—
838C4#1171864818yescomplemented
839C2—528no—
840C2C2×#1171864811yescharacteristic
841C2#1311729411yescharacteristic
842C2#1311747511yescharacteristic
843C2D4×#610311yescharacteristic
844C2#1311767411yescharacteristic
845C2#1311773711yescharacteristic
846C2#1311774511yescharacteristic
847C2#1311840911yescharacteristic
848C2#1311841111yescharacteristic
849C2#1311842011yescharacteristic
850C2#1311842211yescharacteristic
851C2#1311868211yescharacteristic
852C2#1311868411yescharacteristic
853C2#1311870411yescharacteristic
854C2#1311870611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#389C2
socle, cosocleC24×C13C24
prime radicalC23×D52C22
hypercenterC2×#389D13
hypocenterC13#13920
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
4. C2×#11718646C2semidirect
5. C2×#11718648C2semidirect
6. #13113082C2semidirect
7. #13113078C2semidirect
8. #13113065C2semidirect
9. #13113057C2semidirect
10. C4×#88071C2semidirect
11. C2×C13×#389C2semidirect
29. C2×#88147C4semidirect
115. #88071D4semidirect
209. C2×D52C4⋊C4semidirect
219. C13×C4⋊C4C22⋊C4semidirect
234. C2×#389D13semidirect
448. C4×C13#380semidirect
647. C4⋊C4#6103semidirect
656. C13#13920semidirect
838. C4#11718648semidirect

Maximal subgroups

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

subgroupindex
C22×#881472
C2×#117186002
C2×#117186492
C2×#117186462
C2×#117186482
#131130822
#131130782
#131130652
#131130572
C4×#880712
C2×C13×#3892
#1392013