Finite Group Databasebeta

← #15786363

Subgroups — #15786363

Order 3328.

1954 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718600C211yesmaximal, characteristic
2C2×#11718649C211yesmaximal, characteristic
3C2×#11718649C211yesmaximal, characteristic
4C2×#11718330C212yesmaximal, complemented
5C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
6C2×C4×#6101C211yesmaximal, characteristic, complemented
7#13113084C212yesmaximal, complemented
8#13113080C212yesmaximal, complemented
9#13113072C212yesmaximal, complemented
10#13113065C211yesmaximal, characteristic, complemented
11C13×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×D52C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C42×C13C2211yescharacteristic
16C22×#6103C2212yes—
17C22×#6103C2212yes—
18C22×#6103C2212yes—
19C22×#6103C2212yes—
20C22×#6103C2212yes—
21C22×#6103C2212yes—
22C22×C4⋊Dic13C2211yescharacteristic
23C22×#6101C2211yescharacteristic
24C22×#6101C2211yescharacteristic
25C22×C4×Dic13C2212yes—
26C22×C4×Dic13C2211yescharacteristic
27C22×C4×Dic13C2211yescharacteristic
28C2×C13×#95C2212yes—
29C2×C13×#95C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2211yescharacteristic
32C2×#88071C2211yescharacteristic
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35#11718649—24no—
36#11718649C418yescomplemented
37C4⋊C4×Dic13—24no—
38#11718600—24no—
39C4×#6101—24no—
40#11718330—28no—
41C24×D13C2312yes—
42C23×C4×C13C2312yes—
43C23×C4×C13C2312yes—
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2311yescharacteristic
46C23×C4×C13C2311yescharacteristic
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2312yes—
50C23×Dic13C2311yescharacteristic
51C23×Dic13C2311yescharacteristic
52C22×D52—22no—
53C22×D52—22no—
54C22×D52—22no—
55C22×D52—22no—
56C22×D52—22no—
57C22×D52—22no—
58C22×D52C2×C414yes—
59C2×C13×C4⋊C4—22no—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—22no—
62C2×C13×C4⋊C4—22no—
63C2×C13×C4⋊C4—22no—
64C2×C13×C4⋊C4C2×C414yes—
65C2×C42×C13—22no—
66C2×C42×C13—22no—
67C2×C42×C13—22no—
68C2×#6103—24no—
69C2×#6103—24no—
70C2×#6103—24no—
71C2×#6103—24no—
72C2×#6103—24no—
73C2×#6103—24no—
74C2×#6103—24no—
75C2×#6103—24no—
76C2×#6103—24no—
77C2×#6103—24no—
78C2×#6103—42no—
79C2×#6103—42no—
80C2×#6103—42no—
81C2×#6103—42no—
82C2×#6103—42no—
83C2×#6103—42no—
84C2×#6103C2×C418yes—
85C2×#6103C2×C418yes—
86C2×C4⋊Dic13—22no—
87C2×C4⋊Dic13—22no—
88C2×C4⋊Dic13D414yes—
89C2×#6101—22no—
90C2×#6101—22no—
91C2×#6101—22no—
92C2×#6101—22no—
93C2×#6101—22no—
94C2×#6101D414yescomplemented
95C2×C4×Dic13—22no—
96C2×C4×Dic13—22no—
97C2×C4×Dic13—22no—
98C2×C4×Dic13—22no—
99C2×C4×Dic13—24no—
100C2×C4×Dic13—24no—
101C2×C4×Dic13—42no—
102C2×C4×Dic13C2×C414yes—
103C2×C4×Dic13D414yes—
104C13×#95—24no—
105C13×#95—42no—
106#88071—24no—
107#88071—22no—
108#88071—22no—
109#88071—24no—
110#88071—42no—
111#14022—131nomaximal, Sylow
112C24×C13C2411yescharacteristic
113C23×D13—22no—
114C23×D13—22no—
115C23×D13—22no—
116C23×D13—22no—
117C23×D13—22no—
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×D13C22×C414yes—
128C22×C4×C13—22no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—22no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—22no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—22no—
140C22×C4×C13—21no—
141C22×C4×C13—22no—
142C22×C4×C13—22no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13—22no—
149C22×C4×C13—22no—
150C22×C4×C13—22no—
151C22×C4×C13—22no—
152C22×C4×C13—22no—
153C22×C4×C13C22×C414yes—
154C22×C4×C13C22×C412yes—
155C22×C4×C13C2×D412yes—
156C22×C4×C13C2×D412yes—
157C22×C4×C13C2×D412yes—
158C22×C4×C13#4112yes—
159C22×C4×C13#4112yes—
160C22×C4×C13#4112yes—
161C22×C4×C13#4112yes—
162C22×C4×C13#4112yes—
163C22×Dic13—21no—
164C22×Dic13—21no—
165C22×Dic13—21no—
166C22×Dic13—21no—
167C22×Dic13—21no—
168C22×Dic13—21no—
169C22×Dic13—21no—
170C22×Dic13—21no—
171C22×Dic13—21no—
172C22×Dic13—21no—
173C22×Dic13—22no—
174C22×Dic13—21no—
175C22×Dic13—21no—
176C22×Dic13—21no—
177C22×Dic13—21no—
178C22×Dic13—22no—
179C22×Dic13—22no—
180C22×Dic13—22no—
181C22×Dic13—21no—
182C22×Dic13—22no—
183C22×Dic13—22no—
184C22×Dic13—21no—
185C22×Dic13—21no—
186C22×Dic13—21no—
187C22×Dic13—21no—
188C22×Dic13—21no—
189C22×Dic13C22×C412yes—
190C22×Dic13C22×C412yes—
191C22×Dic13C2×D414yes—
192C22×Dic13C2×D412yes—
193C22×Dic13C2×D412yes—
194C22×Dic13C2×D412yes—
195C22×Dic13C2×D412yes—
196C22×Dic13#4112yes—
197C22×Dic13#4112yes—
198C2×D52—28no—
199C2×D52—28no—
200C2×D52—28no—
201C2×D52—44no—
202C2×D52—44no—
203C2×D52—44no—
204C2×D52—44no—
205C13×C4⋊C4—28no—
206C13×C4⋊C4—44no—
207C42×C13—44no—
208#6103—216no—
209#6103—48no—
210#6103—48no—
211#6103—48no—
212#6103—48no—
213#6103—48no—
214C4⋊Dic13—28no—
215#6101—28no—
216#6101—28no—
217C4×Dic13—28no—
218C4×Dic13—28no—
219C4×Dic13—48no—
220C2×#390—131no—
221C2×#390—131no—
222C2×#390—131no—
223C2×#388—132no—
224C2×C4×C4⋊C4—131no—
225C2×C4×C4⋊C4—131no—
226#1440—132no—
227#1439—132no—
228#1437—132no—
229C4⋊#95—131no—
230C4⋊#95D1311yescharacteristic, complemented
231C23×C13C23×C411yescharacteristic
232C23×C13C22×D411yescharacteristic
233C23×C13C22×D411yescharacteristic
234C23×C13C22×D411yescharacteristic
235C23×C13C2×#4111yescharacteristic
236C23×C13C2×#4111yescharacteristic
237C23×C13C2×#4111yescharacteristic
238C23×C13C2×#4111yescharacteristic
239C23×C13C2×#4111yescharacteristic
240C23×C13C2×#4111yescharacteristic
241C23×C13C2×#4111yescharacteristic
242C23×C13H(5,𝔽2)11yescharacteristic
243C23×C13H(5,𝔽2)11yescharacteristic
244C23×C13H(5,𝔽2)11yescharacteristic
245C23×C132−1+411yescharacteristic
246C22×D13—24no—
247C22×D13—24no—
248C22×D13—24no—
249C22×D13—24no—
250C22×D13—24no—
251C22×D13—24no—
252C22×D13—24no—
253C22×D13—42no—
254C22×D13—42no—
255C22×D13—42no—
256C22×D13—42no—
257C22×D13—42no—
258C22×D13—42no—
259C22×D13—42no—
260C22×D13—42no—
261C22×D13—42no—
262C22×D13—42no—
263C22×D13—42no—
264C22×D13—42no—
265C22×D13—42no—
266C22×D13—42no—
267C22×D13—42no—
268C22×D13—42no—
269C22×D13—42no—
270C22×D13—42no—
271C22×D13—42no—
272C22×D13—42no—
273C22×D13—42no—
274C22×D13—42no—
275C22×D13—42no—
276C22×D13—42no—
277C22×D13—42no—
278C22×D13—42no—
279C22×D13—42no—
280C22×D13—42no—
281C2×C4×C13—24no—
282C2×C4×C13—24no—
283C2×C4×C13—24no—
284C2×C4×C13—22no—
285C2×C4×C13—22no—
286C2×C4×C13—22no—
287C2×C4×C13—22no—
288C2×C4×C13—22no—
289C2×C4×C13—22no—
290C2×C4×C13—41no—
291C2×C4×C13—41no—
292C2×C4×C13—41no—
293C2×C4×C13—41no—
294C2×C4×C13—42no—
295C2×C4×C13—41no—
296C2×C4×C13—42no—
297C2×C4×C13—42no—
298C2×C4×C13—41no—
299C2×C4×C13—41no—
300C2×C4×C13—41no—
301C2×C4×C13—42no—
302C2×C4×C13—42no—
303C2×C4×C13—42no—
304C2×C4×C13—42no—
305C2×C4×C13—42no—
306C2×C4×C13—42no—
307C2×C4×C13—42no—
308C2×C4×C13—42no—
309C2×C4×C13#11714yes—
310C2×C4×C13C4×D414yes—
311C2×C4×C13C4×D414yes—
312C2×C4×C13#12114yes—
313C2×C4×C13#12314yes—
314C2×C4×C13#12414yes—
315C2×C4×C13#12614yes—
316C2×Dic13—22no—
317C2×Dic13—22no—
318C2×Dic13—22no—
319C2×Dic13—22no—
320C2×Dic13—22no—
321C2×Dic13—22no—
322C2×Dic13—22no—
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—24no—
333C2×Dic13—22no—
334C2×Dic13—22no—
335C2×Dic13—24no—
336C2×Dic13—24no—
337C2×Dic13—42no—
338C2×Dic13—41no—
339C2×Dic13—41no—
340C2×Dic13—41no—
341C2×Dic13—42no—
342C2×Dic13—41no—
343C2×Dic13—41no—
344C2×Dic13—41no—
345C2×Dic13—42no—
346C2×Dic13—41no—
347C2×Dic13—41no—
348C2×Dic13—42no—
349C2×Dic13C4×D414yes—
350C2×Dic13#12114yes—
351D52—416no—
352C23×D4—131no—
353C22×C4⋊C4—131no—
354C22×C4⋊C4—131no—
355C22×C4⋊C4—131no—
356C22×C4⋊C4C2×D1311yescharacteristic
357C22×C4⋊C4C2×D1311yescharacteristic
358C22×C22⋊C4—132no—
359C22×C22⋊C4—132no—
360C22×C22⋊C4—132no—
361C22×C22⋊C4—132no—
362C22×C22⋊C4—132no—
363C22×C22⋊C4—132no—
364C22×C42—131no—
365C22×C42—131no—
366C22×C42—132no—
367C22×C42C2×D1311yescharacteristic
368#390—138no—
369#390—264no—
370#390—264no—
371#388—268no—
372C4×C4⋊C4—264no—
373C4×C4⋊C4—264no—
374C2×#95—132no—
375C2×#95—131no—
376C2×#95—132no—
377C2×#95—131no—
378C2×#95—132no—
379C2×#95C2×D1312yes—
380C2×#95C2×D1312yes—
381C22×C13C2×#11711yescharacteristic
382C22×C13C2×C4×D411yescharacteristic
383C22×C13C2×C4×D411yescharacteristic
384C22×C13C2×C4×D411yescharacteristic
385C22×C13C4×#4111yescharacteristic
386C22×C13#51811yescharacteristic
387C22×C13#52011yescharacteristic
388C22×C13C2×#12111yescharacteristic
389C22×C13C2×#12111yescharacteristic
390C22×C13C2×#12311yescharacteristic
391C22×C13#52511yescharacteristic
392C22×C13C2×#12411yescharacteristic
393C22×C13C2×#12611yescharacteristic
394C22×C13#52911yescharacteristic
395C22×C13#53211yescharacteristic
396C22×C13#53511yescharacteristic
397C22×C13#53711yescharacteristic
398C22×C13#54011yescharacteristic
399C22×C13#54211yescharacteristic
400C22×C13D4211yescharacteristic
401C22×C13#54611yescharacteristic
402C22×C13#54711yescharacteristic
403C22×C13#54811yescharacteristic
404C22×C13#55011yescharacteristic
405C22×C13#55011yescharacteristic
406C22×C13#55011yescharacteristic
407C22×C13#55311yescharacteristic
408C22×C13#55311yescharacteristic
409C22×C13#55511yescharacteristic
410C22×C13#55611yescharacteristic
411C22×C13#55611yescharacteristic
412C22×C13#55911yescharacteristic
413C22×C13#55911yescharacteristic
414C22×C13#55911yescharacteristic
415C22×C13#55911yescharacteristic
416C2×D13—44no—
417C2×D13—44no—
418C2×D13—44no—
419C2×D13—44no—
420C2×D13—44no—
421C2×D13—44no—
422C2×D13—44no—
423C2×D13—82no—
424C2×D13—82no—
425C2×D13—82no—
426C2×D13—82no—
427C2×D13—82no—
428C2×D13—82no—
429C2×D13—82no—
430C2×D13—82no—
431C4×C13—44no—
432C4×C13—42no—
433C4×C13—42no—
434C4×C13—82no—
435C4×C13#38818yescomplemented
436Dic13—24no—
437Dic13—24no—
438Dic13—42no—
439Dic13—42no—
440Dic13—44no—
441C25—132no—
442C22×D4—134no—
443C22×D4—262no—
444C22×D4—262no—
445C22×D4—262no—
446C22×D4—262no—
447C22×D4—262no—
448C22×D4—262no—
449C23×C4—131no—
450C23×C4—131no—
451C23×C4—131no—
452C23×C4—132no—
453C23×C4—131no—
454C23×C4C22×D1312yes—
455C23×C4C22×D1312yes—
456C23×C4C22×D1311yescharacteristic
457C23×C4C22×D1311yescharacteristic
458C23×C4C22×D1311yescharacteristic
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—134no—
465C2×C4⋊C4—134no—
466C2×C4⋊C4—262no—
467C2×C4⋊C4—262no—
468C2×C4⋊C4—262no—
469C2×C4⋊C4—262no—
470C2×C4⋊C4—262no—
471C2×C4⋊C4—262no—
472C2×C4⋊C4—262no—
473C2×C4⋊C4C4×D1314yes—
474C2×C22⋊C4—138no—
475C2×C22⋊C4—138no—
476C2×C22⋊C4—264no—
477C2×C22⋊C4—264no—
478C2×C22⋊C4—264no—
479C2×C22⋊C4—264no—
480C2×C22⋊C4—264no—
481C2×C22⋊C4—264no—
482C2×C22⋊C4—264no—
483C2×C22⋊C4—264no—
484C2×C22⋊C4—264no—
485C2×C22⋊C4—264no—
486C2×C22⋊C4—522no—
487C2×C22⋊C4—522no—
488C2×C22⋊C4—522no—
489C2×C22⋊C4—522no—
490C2×C22⋊C4—522no—
491C2×C22⋊C4—522no—
492C2×C42—22no—
493C2×C42—22no—
494C2×C42—22no—
495C2×C42—134no—
496C2×C42—134no—
497C2×C42—262no—
498C2×C42—262no—
499C2×C42—262no—
500C2×C42—262no—
501C2×C42—264no—
502C2×C42—264no—
503C2×C42—522no—
504#95—24no—
505#95—42no—
506#95—262no—
507#95—262no—
508#95—264no—
509#95—264no—
510#95—522no—
511C2×C13C2×#38811yescharacteristic
512C2×C13C4×#12111yescharacteristic
513C2×C13#232411yescharacteristic
514C2×C13#235411yescharacteristic
515C2×C13#235711yescharacteristic
516C2×C13#236611yescharacteristic
517C2×C13#236711yescharacteristic
518C2×C13#241411yescharacteristic
519C2×C13#241611yescharacteristic
520C2×C13#244511yescharacteristic
521C2×C13#244811yescharacteristic
522C2×C13#251211yescharacteristic
523C2×C13#251311yescharacteristic
524C2×C13#254811yescharacteristic
525C2×C13#259211yescharacteristic
526D13—84no—
527C24—134no—
528C24—262no—
529C24—262no—
530C24—262no—
531C24—262no—
532C24—262no—
533C24—262no—
534C24—262no—
535C24—262no—
536C24—262no—
537C24—262no—
538C24—262no—
539C24—262no—
540C24—262no—
541C24—262no—
542C24C23×D1311yescharacteristic
543C2×D4—268no—
544C2×D4—268no—
545C2×D4—268no—
546C2×D4—524no—
547C2×D4—524no—
548C2×D4—524no—
549C2×D4—524no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—132no—
576C22×C4—132no—
577C22×C4—132no—
578C22×C4—132no—
579C22×C4—132no—
580C22×C4—132no—
581C22×C4—132no—
582C22×C4—132no—
583C22×C4—134no—
584C22×C4—261no—
585C22×C4—261no—
586C22×C4—261no—
587C22×C4—261no—
588C22×C4—261no—
589C22×C4—261no—
590C22×C4—261no—
591C22×C4—261no—
592C22×C4—261no—
593C22×C4—262no—
594C22×C4—261no—
595C22×C4—261no—
596C22×C4—262no—
597C22×C4—261no—
598C22×C4—261no—
599C22×C4—261no—
600C22×C4—262no—
601C22×C4—262no—
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×C4C2×C4×D1314yes—
611C22×C4C2×C4×D1312yes—
612C22×C4#612712yes—
613C22×C4#612712yes—
614C22×C4D4×D1312yes—
615C22×C4D4×D1312yes—
616C22×C4D4×D1312yes—
617C22×C4#612912yes—
618C22×C4#613112yes—
619C22×C4#613112yes—
620C4⋊C4—28no—
621C4⋊C4—44no—
622C4⋊C4—268no—
623C4⋊C4—268no—
624C4⋊C4—268no—
625C22⋊C4—2616no—
626C22⋊C4—528no—
627C22⋊C4—528no—
628C22⋊C4—528no—
629C22⋊C4—528no—
630C22⋊C4—528no—
631C42—44no—
632C42—268no—
633C42—268no—
634C42—528no—
635C13#1402211yescharacteristic, complemented, Sylow
636C23—264no—
637C23—264no—
638C23—264no—
639C23—264no—
640C23—264no—
641C23—264no—
642C23—264no—
643C23—522no—
644C23—522no—
645C23—522no—
646C23—522no—
647C23—522no—
648C23—522no—
649C23—522no—
650C23—522no—
651C23—522no—
652C23—522no—
653C23—522no—
654C23—522no—
655C23—522no—
656C23—522no—
657C23—522no—
658C23—522no—
659C23—522no—
660C23—522no—
661C23—522no—
662C23—522no—
663C23—522no—
664C23—522no—
665C23—522no—
666C23—522no—
667C23—522no—
668C23—522no—
669C23—522no—
670C23—522no—
671C23C22×C4×D1311yescharacteristic
672C23C2×#612711yescharacteristic
673C23C2×#612711yescharacteristic
674C23C2×D4×D1311yescharacteristic
675C23C2×D4×D1311yescharacteristic
676C23C2×D4×D1311yescharacteristic
677C23C2×#612911yescharacteristic
678C23#8825111yescharacteristic
679C23C2×#613111yescharacteristic
680C23C2×#613111yescharacteristic
681C23#8825411yescharacteristic
682C23#41×D1311yescharacteristic
683C23#41×D1311yescharacteristic
684C23#8825611yescharacteristic
685C23#8825611yescharacteristic
686D4—5216no—
687C2×C4—24no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—134no—
716C2×C4—134no—
717C2×C4—262no—
718C2×C4—262no—
719C2×C4—262no—
720C2×C4—262no—
721C2×C4—262no—
722C2×C4—262no—
723C2×C4—262no—
724C2×C4—262no—
725C2×C4—262no—
726C2×C4—262no—
727C2×C4—262no—
728C2×C4—262no—
729C2×C4—262no—
730C2×C4—262no—
731C2×C4—264no—
732C2×C4—262no—
733C2×C4—262no—
734C2×C4—262no—
735C2×C4—264no—
736C2×C4—262no—
737C2×C4—264no—
738C2×C4—522no—
739C2×C4—521no—
740C2×C4—521no—
741C2×C4—521no—
742C2×C4—522no—
743C2×C4—522no—
744C2×C4—521no—
745C2×C4—521no—
746C2×C4—521no—
747C2×C4—521no—
748C2×C4—521no—
749C2×C4—522no—
750C2×C4#8812614yes—
751C2×C4#8813514yes—
752C2×C4#8813814yes—
753C2×C4#8813914yes—
754C2×C4#8814714yes—
755C2×C4#8814814yes—
756C2×C4#8815214yes—
757C22—524no—
758C22—524no—
759C22—524no—
760C22—524no—
761C22—524no—
762C22—524no—
763C22—524no—
764C22—1042no—
765C22—1042no—
766C22—1042no—
767C22—1042no—
768C22—1042no—
769C22—1042no—
770C22—1042no—
771C22—1042no—
772C22C2×#8812611yescharacteristic
773C22C2×#8813511yescharacteristic
774C22C2×#8813811yescharacteristic
775C22C2×#8813911yescharacteristic
776C22C2×#8814711yescharacteristic
777C22C2×#8814811yescharacteristic
778C22#1171921211yescharacteristic
779C22C2×#8815211yescharacteristic
780C22#1171921911yescharacteristic
781C22#1171923511yescharacteristic
782C22#1171923711yescharacteristic
783C22C4×D4×D1311yescharacteristic
784C22#1171925011yescharacteristic
785C22#1171925811yescharacteristic
786C22#1171926411yescharacteristic
787C22#1171927311yescharacteristic
788C22C4×#613111yescharacteristic
789C22#1171927911yescharacteristic
790C22#1171929011yescharacteristic
791C22#1171930411yescharacteristic
792C22D13×#12111yescharacteristic
793C22#1171931211yescharacteristic
794C22#1171931411yescharacteristic
795C22#1171933211yescharacteristic
796C22#1171933411yescharacteristic
797C22#1171933511yescharacteristic
798C22#1171933811yescharacteristic
799C22#1171938611yescharacteristic
800C22#1171938611yescharacteristic
801C22#1171939611yescharacteristic
802C22#1171940311yescharacteristic
803C22#1171942311yescharacteristic
804C22#1171943011yescharacteristic
805C22#1171943711yescharacteristic
806C22#1171943811yescharacteristic
807C4—42no—
808C4—42no—
809C4—44no—
810C4—82no—
811C4—264no—
812C4—264no—
813C4—522no—
814C4—522no—
815C4—524no—
816C4#1171833018yescomplemented
817C2—1044no—
818C2C2×#1171833011yescharacteristic
819C2#1311734411yescharacteristic
820C2#1311752711yescharacteristic
821C2#1311778111yescharacteristic
822C2#1311780511yescharacteristic
823C2#1311789711yescharacteristic
824C2#1311791211yescharacteristic
825C2#1311825611yescharacteristic
826C2#1311827811yescharacteristic
827C2#1311860311yescharacteristic
828C2#1311863611yescharacteristic
829C2#1311941811yescharacteristic
830C2#1311942911yescharacteristic
831C2#1311983711yescharacteristic
832C2#1312032311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×C4⋊#95C2
socle, cosocleC24×C13C24
prime radicalC23×D52C22
hypercenterC4⋊#95D13
hypocenterC13#14022
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#11718330C2semidirect
5. C2×C4⋊C4×Dic13C2semidirect
6. C2×C4×#6101C2semidirect
7. #13113084C2semidirect
8. #13113080C2semidirect
9. #13113072C2semidirect
10. #13113065C2semidirect
11. C13×C4⋊#95C2semidirect
36. #11718649C4semidirect
94. C2×#6101D4semidirect
230. C4⋊#95D13semidirect
435. C4×C13#388semidirect
635. C13#14022semidirect
816. C4#11718330semidirect

Maximal subgroups

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

subgroupindex
C2×#117186002
C2×#117186492
C2×#117183302
C2×C4⋊C4×Dic132
C2×C4×#61012
#131130842
#131130802
#131130722
#131130652
C13×C4⋊#952
#1402213