Finite Group Databasebeta

← #15799665

Subgroups — #15799665

Order 3328.

1778 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718336C212yesmaximal, complemented
2C2×#11718600C211yesmaximal, characteristic
3C2×#11718649C211yesmaximal, characteristic
4C2×#11718649C211yesmaximal, characteristic
5C2×C4×#6101C211yesmaximal, characteristic, complemented
6#13113084C212yesmaximal, complemented
7#13113084C212yesmaximal, complemented
8#13113080C212yesmaximal, complemented
9#13113065C211yesmaximal, characteristic, 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×Dic13C2211yescharacteristic
26C22×C4×Dic13C2211yescharacteristic
27C2×C13×#95C2212yes—
28C2×C13×#95C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2211yescharacteristic
32C2×#88071C2211yescharacteristic
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35#11718649—24no—
36#11718649—24no—
37#11718600—24no—
38C4×#6101—24no—
39#11718336—28no—
40C24×D13C2312yes—
41C23×C4×C13C2312yes—
42C23×C4×C13C2312yes—
43C23×C4×C13C2311yescharacteristic
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2311yescharacteristic
46C23×Dic13C2312yes—
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2311yescharacteristic
51C22×D52—22no—
52C22×D52—22no—
53C22×D52—22no—
54C22×D52—22no—
55C22×D52—22no—
56C22×D52—22no—
57C22×D52D414yes—
58C2×C13×C4⋊C4—22no—
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×C42×C13—22no—
65C2×C42×C13—22no—
66C2×C42×C13—22no—
67C2×#6103—24no—
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—24no—
79C2×#6103—42no—
80C2×#6103—42no—
81C2×#6103—42no—
82C2×#6103—42no—
83C2×#6103—42no—
84C2×#6103—42no—
85C2×C4⋊Dic13—22no—
86C2×C4⋊Dic13—22no—
87C2×C4⋊Dic13—22no—
88C2×#6101—22no—
89C2×#6101—22no—
90C2×#6101—22no—
91C2×#6101—22no—
92C2×#6101—22no—
93C2×#6101D414yescomplemented
94C2×C4×Dic13—22no—
95C2×C4×Dic13—22no—
96C2×C4×Dic13—22no—
97C2×C4×Dic13—22no—
98C2×C4×Dic13—22no—
99C2×C4×Dic13D414yes—
100C13×#95—24no—
101C13×#95—42no—
102#88071—24no—
103#88071—24no—
104#88071—22no—
105#88071—22no—
106#88071—42no—
107#88071—42no—
108#15147—131nomaximal, Sylow
109C24×C13C2411yescharacteristic
110C23×D13—22no—
111C23×D13—22no—
112C23×D13—22no—
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×D13C2×D414yes—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—22no—
140C22×C4×C13—22no—
141C22×C4×C13—22no—
142C22×C4×C13—22no—
143C22×C4×C13—22no—
144C22×C4×C13—22no—
145C22×C4×C13—22no—
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13—22no—
149C22×C4×C13—22no—
150C22×C4×C13—22no—
151C22×C4×C13C2×D412yes—
152C22×C4×C13C2×D412yes—
153C22×C4×C13C2×D412yes—
154C22×C4×C13#4112yes—
155C22×C4×C13#4112yes—
156C22×C4×C13#4112yes—
157C22×C4×C13#4112yes—
158C22×C4×C13#4112yes—
159C22×C4×C13#4112yes—
160C22×Dic13—21no—
161C22×Dic13—21no—
162C22×Dic13—21no—
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—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—22no—
183C22×Dic13—22no—
184C22×Dic13—22no—
185C22×Dic13—22no—
186C22×Dic13—22no—
187C22×Dic13—22no—
188C22×Dic13—22no—
189C22×Dic13C2×D412yes—
190C22×Dic13C2×D412yes—
191C22×Dic13C2×D412yes—
192C22×Dic13C2×D412yes—
193C22×Dic13#4112yes—
194C22×Dic13#4112yes—
195C2×D52—28no—
196C2×D52—28no—
197C2×D52—28no—
198C2×D52—44no—
199C2×D52—44no—
200C2×D52—44no—
201C2×D52—44no—
202C13×C4⋊C4—44no—
203C13×C4⋊C4—44no—
204C42×C13—44no—
205#6103—48no—
206#6103—48no—
207#6103—48no—
208#6103—48no—
209#6103—48no—
210#6103—48no—
211C4⋊Dic13—44no—
212#6101—28no—
213#6101—28no—
214C4×Dic13—28no—
215C4×Dic13—44no—
216C2×#397—132no—
217C2×#390—131no—
218C2×#390—131no—
219C2×#390—131no—
220C2×C4×C4⋊C4—131no—
221#1440—132no—
222#1440—132no—
223#1439—132no—
224C4⋊#95—131no—
225C4⋊#95—131no—
226C4⋊#95D1311yescharacteristic, complemented
227C23×C13C22×D411yescharacteristic
228C23×C13C22×D411yescharacteristic
229C23×C13C22×D411yescharacteristic
230C23×C13C2×#4111yescharacteristic
231C23×C13C2×#4111yescharacteristic
232C23×C13C2×#4111yescharacteristic
233C23×C13C2×#4111yescharacteristic
234C23×C13C2×#4111yescharacteristic
235C23×C13C2×#4111yescharacteristic
236C23×C13C2×#4111yescharacteristic
237C23×C13C2×#4111yescharacteristic
238C23×C13H(5,𝔽2)11yescharacteristic
239C23×C13H(5,𝔽2)11yescharacteristic
240C23×C13H(5,𝔽2)11yescharacteristic
241C23×C132−1+411yescharacteristic
242C22×D13—24no—
243C22×D13—24no—
244C22×D13—24no—
245C22×D13—24no—
246C22×D13—24no—
247C22×D13—24no—
248C22×D13—24no—
249C22×D13—42no—
250C22×D13—42no—
251C22×D13—42no—
252C22×D13—42no—
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—
277C2×C4×C13—22no—
278C2×C4×C13—22no—
279C2×C4×C13—22no—
280C2×C4×C13—22no—
281C2×C4×C13—22no—
282C2×C4×C13—22no—
283C2×C4×C13—41no—
284C2×C4×C13—41no—
285C2×C4×C13—41no—
286C2×C4×C13—41no—
287C2×C4×C13—41no—
288C2×C4×C13—41no—
289C2×C4×C13—41no—
290C2×C4×C13—41no—
291C2×C4×C13—42no—
292C2×C4×C13—42no—
293C2×C4×C13—42no—
294C2×C4×C13—42no—
295C2×C4×C13—42no—
296C2×C4×C13—42no—
297C2×C4×C13—42no—
298C2×C4×C13—42no—
299C2×C4×C13—42no—
300C2×C4×C13—42no—
301C2×C4×C13—42no—
302C2×C4×C13—42no—
303C2×C4×C13—42no—
304C2×C4×C13—42no—
305C2×C4×C13#12114yes—
306C2×C4×C13#12314yes—
307C2×C4×C13#12314yes—
308C2×C4×C13#12314yes—
309C2×C4×C13#12414yes—
310C2×C4×C13#12614yes—
311C2×C4×C13#12614yes—
312C2×Dic13—22no—
313C2×Dic13—22no—
314C2×Dic13—22no—
315C2×Dic13—22no—
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—41no—
328C2×Dic13—41no—
329C2×Dic13—41no—
330C2×Dic13—41no—
331C2×Dic13—41no—
332C2×Dic13—41no—
333C2×Dic13—41no—
334C2×Dic13—41no—
335C2×Dic13—41no—
336C2×Dic13—41no—
337C2×Dic13—41no—
338C2×Dic13—41no—
339C2×Dic13—42no—
340C2×Dic13—42no—
341C2×Dic13—42no—
342C2×Dic13—42no—
343C2×Dic13—42no—
344C2×Dic13—42no—
345C2×Dic13—42no—
346C2×Dic13#12114yes—
347D52—416no—
348C23×D4—131no—
349C22×C4⋊C4—131no—
350C22×C4⋊C4—131no—
351C22×C4⋊C4—131no—
352C22×C4⋊C4C2×D1311yescharacteristic
353C22×C4⋊C4C2×D1311yescharacteristic
354C22×C22⋊C4—132no—
355C22×C22⋊C4—132no—
356C22×C22⋊C4—132no—
357C22×C22⋊C4—132no—
358C22×C22⋊C4—132no—
359C22×C22⋊C4—132no—
360C22×C42—131no—
361C22×C42—131no—
362C22×C42C2×D1311yescharacteristic
363#397—268no—
364#390—264no—
365#390—264no—
366#390—264no—
367C4×C4⋊C4—264no—
368C2×#95—132no—
369C2×#95—132no—
370C2×#95—131no—
371C2×#95—131no—
372C2×#95—132no—
373C2×#95—132no—
374C2×#95C2×D1312yes—
375C2×#95C2×D1312yes—
376C22×C13C2×#12111yescharacteristic
377C22×C13C2×#12111yescharacteristic
378C22×C13C2×#12311yescharacteristic
379C22×C13C2×#12311yescharacteristic
380C22×C13C2×#12311yescharacteristic
381C22×C13#52511yescharacteristic
382C22×C13C2×#12411yescharacteristic
383C22×C13C2×#12611yescharacteristic
384C22×C13C2×#12611yescharacteristic
385C22×C13#52911yescharacteristic
386C22×C13#52911yescharacteristic
387C22×C13#53211yescharacteristic
388C22×C13#53211yescharacteristic
389C22×C13#53511yescharacteristic
390C22×C13#53711yescharacteristic
391C22×C13#54011yescharacteristic
392C22×C13#54011yescharacteristic
393C22×C13#54211yescharacteristic
394C22×C13#54211yescharacteristic
395C22×C13D4211yescharacteristic
396C22×C13#54611yescharacteristic
397C22×C13#54611yescharacteristic
398C22×C13#54711yescharacteristic
399C22×C13#54711yescharacteristic
400C22×C13#55011yescharacteristic
401C22×C13#55011yescharacteristic
402C22×C13#55311yescharacteristic
403C22×C13#55311yescharacteristic
404C22×C13#55511yescharacteristic
405C22×C13#55611yescharacteristic
406C22×C13#55611yescharacteristic
407C22×C13#55911yescharacteristic
408C22×C13#55911yescharacteristic
409C22×C13#55911yescharacteristic
410C22×C13#55911yescharacteristic
411C2×D13—44no—
412C2×D13—44no—
413C2×D13—44no—
414C2×D13—44no—
415C2×D13—44no—
416C2×D13—44no—
417C2×D13—44no—
418C2×D13—82no—
419C2×D13—82no—
420C2×D13—82no—
421C2×D13—82no—
422C2×D13—82no—
423C2×D13—82no—
424C2×D13—82no—
425C2×D13—82no—
426C4×C13—42no—
427C4×C13—42no—
428C4×C13—82no—
429C4×C13—82no—
430C4×C13#39718yescomplemented
431Dic13—24no—
432Dic13—42no—
433Dic13—42no—
434Dic13—42no—
435Dic13—82no—
436C25—132no—
437C22×D4—134no—
438C22×D4—262no—
439C22×D4—262no—
440C22×D4—262no—
441C22×D4—262no—
442C22×D4—262no—
443C22×D4—262no—
444C23×C4—131no—
445C23×C4—131no—
446C23×C4—131no—
447C23×C4—131no—
448C23×C4—132no—
449C23×C4C22×D1312yes—
450C23×C4C22×D1312yes—
451C23×C4C22×D1311yescharacteristic
452C23×C4C22×D1311yescharacteristic
453C23×C4C22×D1311yescharacteristic
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—134no—
461C2×C4⋊C4—262no—
462C2×C4⋊C4—262no—
463C2×C4⋊C4—262no—
464C2×C4⋊C4—262no—
465C2×C4⋊C4—262no—
466C2×C4⋊C4—262no—
467C2×C4⋊C4—262no—
468C2×C4⋊C4—262no—
469C2×C22⋊C4—264no—
470C2×C22⋊C4—264no—
471C2×C22⋊C4—264no—
472C2×C22⋊C4—264no—
473C2×C22⋊C4—264no—
474C2×C22⋊C4—264no—
475C2×C22⋊C4—264no—
476C2×C22⋊C4—264no—
477C2×C22⋊C4—264no—
478C2×C22⋊C4—264no—
479C2×C22⋊C4—264no—
480C2×C22⋊C4—264no—
481C2×C22⋊C4—522no—
482C2×C22⋊C4—522no—
483C2×C22⋊C4—522no—
484C2×C22⋊C4—522no—
485C2×C22⋊C4—522no—
486C2×C22⋊C4—522no—
487C2×C42—22no—
488C2×C42—22no—
489C2×C42—22no—
490C2×C42—134no—
491C2×C42—262no—
492C2×C42—262no—
493C2×C42—262no—
494C2×C42—262no—
495C2×C42—262no—
496#95—24no—
497#95—42no—
498#95—262no—
499#95—262no—
500#95—264no—
501#95—264no—
502#95—522no—
503#95—522no—
504C2×C13C2×#39711yescharacteristic
505C2×C13#244511yescharacteristic
506C2×C13#244511yescharacteristic
507C2×C13#244711yescharacteristic
508C2×C13#244711yescharacteristic
509C2×C13#251211yescharacteristic
510C2×C13#251211yescharacteristic
511C2×C13#251311yescharacteristic
512C2×C13#251311yescharacteristic
513C2×C13#253511yescharacteristic
514C2×C13#253711yescharacteristic
515C2×C13#254811yescharacteristic
516C2×C13#259211yescharacteristic
517C2×C13#262411yescharacteristic
518C2×C13#285411yescharacteristic
519D13—84no—
520C24—134no—
521C24—262no—
522C24—262no—
523C24—262no—
524C24—262no—
525C24—262no—
526C24—262no—
527C24—262no—
528C24—262no—
529C24—262no—
530C24—262no—
531C24—262no—
532C24—262no—
533C24—262no—
534C24—262no—
535C24C23×D1311yescharacteristic
536C2×D4—268no—
537C2×D4—268no—
538C2×D4—268no—
539C2×D4—524no—
540C2×D4—524no—
541C2×D4—524no—
542C2×D4—524no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—132no—
570C22×C4—132no—
571C22×C4—132no—
572C22×C4—132no—
573C22×C4—132no—
574C22×C4—132no—
575C22×C4—261no—
576C22×C4—261no—
577C22×C4—261no—
578C22×C4—261no—
579C22×C4—261no—
580C22×C4—261no—
581C22×C4—261no—
582C22×C4—261no—
583C22×C4—261no—
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—261no—
594C22×C4—261no—
595C22×C4—261no—
596C22×C4—261no—
597C22×C4—262no—
598C22×C4—262no—
599C22×C4—262no—
600C22×C4—262no—
601C22×C4—262no—
602C22×C4—262no—
603C22×C4—262no—
604C22×C4#612712yes—
605C22×C4#612712yes—
606C22×C4#612712yes—
607C22×C4D4×D1312yes—
608C22×C4D4×D1312yes—
609C22×C4D4×D1312yes—
610C22×C4#612912yes—
611C22×C4#613112yes—
612C22×C4#613112yes—
613C4⋊C4—44no—
614C4⋊C4—44no—
615C4⋊C4—268no—
616C4⋊C4—268no—
617C4⋊C4—524no—
618C22⋊C4—528no—
619C22⋊C4—528no—
620C22⋊C4—528no—
621C22⋊C4—528no—
622C22⋊C4—528no—
623C22⋊C4—528no—
624C42—44no—
625C42—268no—
626C42—524no—
627C13#1514711yescharacteristic, complemented, Sylow
628C23—264no—
629C23—264no—
630C23—264no—
631C23—264no—
632C23—264no—
633C23—264no—
634C23—264no—
635C23—522no—
636C23—522no—
637C23—522no—
638C23—522no—
639C23—522no—
640C23—522no—
641C23—522no—
642C23—522no—
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—
663C23C2×#612711yescharacteristic
664C23C2×#612711yescharacteristic
665C23C2×#612711yescharacteristic
666C23C2×D4×D1311yescharacteristic
667C23C2×D4×D1311yescharacteristic
668C23C2×D4×D1311yescharacteristic
669C23C2×#612911yescharacteristic
670C23#8825111yescharacteristic
671C23C2×#613111yescharacteristic
672C23C2×#613111yescharacteristic
673C23#8825411yescharacteristic
674C23#41×D1311yescharacteristic
675C23#41×D1311yescharacteristic
676C23#8825611yescharacteristic
677C23#8825611yescharacteristic
678D4—5216no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—134no—
708C2×C4—262no—
709C2×C4—262no—
710C2×C4—262no—
711C2×C4—262no—
712C2×C4—262no—
713C2×C4—262no—
714C2×C4—262no—
715C2×C4—262no—
716C2×C4—262no—
717C2×C4—262no—
718C2×C4—262no—
719C2×C4—262no—
720C2×C4—262no—
721C2×C4—262no—
722C2×C4—262no—
723C2×C4—521no—
724C2×C4—521no—
725C2×C4—521no—
726C2×C4—521no—
727C2×C4—521no—
728C2×C4—521no—
729C2×C4—521no—
730C2×C4—521no—
731C2×C4—521no—
732C2×C4—521no—
733C2×C4—521no—
734C2×C4—521no—
735C2×C4—522no—
736C2×C4—522no—
737C2×C4—522no—
738C2×C4—522no—
739C2×C4—522no—
740C2×C4—522no—
741C2×C4—522no—
742C2×C4#8813014yes—
743C2×C4#8813714yes—
744C2×C4#8813814yes—
745C2×C4#8813914yes—
746C2×C4#8814814yes—
747C2×C4#8814814yes—
748C2×C4#8815214yes—
749C22—524no—
750C22—524no—
751C22—524no—
752C22—524no—
753C22—524no—
754C22—524no—
755C22—524no—
756C22—1042no—
757C22—1042no—
758C22—1042no—
759C22—1042no—
760C22—1042no—
761C22—1042no—
762C22—1042no—
763C22—1042no—
764C22C2×#8813011yescharacteristic
765C22C2×#8813711yescharacteristic
766C22C2×#8813811yescharacteristic
767C22C2×#8813911yescharacteristic
768C22C2×#8814811yescharacteristic
769C22C2×#8814811yescharacteristic
770C22#1171921211yescharacteristic
771C22C2×#8815211yescharacteristic
772C22#1171921911yescharacteristic
773C22#1171923511yescharacteristic
774C22#1171923711yescharacteristic
775C22#1171925311yescharacteristic
776C22#1171925811yescharacteristic
777C22#1171926411yescharacteristic
778C22#1171926711yescharacteristic
779C22#1171927311yescharacteristic
780C22#1171928511yescharacteristic
781C22#1171928711yescharacteristic
782C22#1171929011yescharacteristic
783C22D13×#12111yescharacteristic
784C22#1171931211yescharacteristic
785C22#1171931411yescharacteristic
786C22#1171931711yescharacteristic
787C22#1171933211yescharacteristic
788C22#1171933411yescharacteristic
789C22#1171933511yescharacteristic
790C22#1171933611yescharacteristic
791C22#1171938611yescharacteristic
792C22#1171938611yescharacteristic
793C22#1171939611yescharacteristic
794C22#1171940311yescharacteristic
795C22#1171942311yescharacteristic
796C22#1171943011yescharacteristic
797C22#1171943711yescharacteristic
798C22#1171943811yescharacteristic
799C4—42no—
800C4—42no—
801C4—82no—
802C4—82no—
803C4—264no—
804C4—522no—
805C4—522no—
806C4—522no—
807C4—1042no—
808C4#1171833618yescomplemented
809C2—1044no—
810C2C2×#1171833611yescharacteristic
811C2#1311860211yescharacteristic
812C2#1311860311yescharacteristic
813C2#1311862411yescharacteristic
814C2#1311862511yescharacteristic
815C2#1311941611yescharacteristic
816C2#1311941811yescharacteristic
817C2#1311942711yescharacteristic
818C2#1311942911yescharacteristic
819C2#1311973911yescharacteristic
820C2#1311975111yescharacteristic
821C2#1311983711yescharacteristic
822C2#1312032311yescharacteristic
823C2#1312063011yescharacteristic
824C2#1312316911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutator, socle, cosocleC24×C13C24
FittingC13×C4⋊#95C2
prime radicalC23×D52C22
hypercenterC4⋊#95D13
hypocenterC13#15147
LCSG ▷ C24×C13 ▷ C13
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
1. C2×#11718336C2semidirect
5. C2×C4×#6101C2semidirect
6. #13113084C2semidirect
7. #13113084C2semidirect
8. #13113080C2semidirect
9. #13113065C2semidirect
10. #13113065C2semidirect
11. C13×C4⋊#95C2semidirect
93. C2×#6101D4semidirect
226. C4⋊#95D13semidirect
430. C4×C13#397semidirect
627. C13#15147semidirect
808. C4#11718336semidirect

Maximal subgroups

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

subgroupindex
C2×#117183362
C2×#117186002
C2×#117186492
C2×C4×#61012
#131130842
#131130802
#131130652
C13×C4⋊#952
#1514713