Finite Group Databasebeta

← #25023351

Subgroups — #25023351

Order 11008.

2566 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D172C211yesmaximal, characteristic, complemented
2C2×#14582808C211yesmaximal, characteristic
3C2×#14582775C212yesmaximal, complemented
4#19132851C211yesmaximal, characteristic, complemented
5#19132840C211yesmaximal, characteristic, complemented
6#19132837C212yesmaximal, complemented
7#19132835C211yesmaximal, characteristic, complemented
8#19132834C212yesmaximal, complemented
9#19132822C211yesmaximal, characteristic, complemented
10(C2×D43)⋊#95C212yesmaximal, complemented
11C2×C43×#388C211yesmaximal, characteristic, complemented
12C23×D172C2211yescharacteristic
13C23×C22⋊D43C2212yes—
14C23×C4×D43C2212yes—
15C2×C4×D172—28no—
16C2×C4×D172—24no—
17C22×C4⋊Dic43C2211yescharacteristic
18C22×C22⋊Dic43C2212yes—
19C22×(C2×D43)⋊C4C2212yes—
20C22×(C2×D43)⋊C4C2212yes—
21C22×(C2×D43)⋊C4C2212yes—
22C22×(C2×D43)⋊C4C2212yes—
23#14582808C418yescomplemented
24#14582775—28no—
25C2×C43⋊#95C2212yes—
26C2×C43⋊#95C2211yescharacteristic
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2211yescharacteristic
32C22×C4⋊C4×C43C2211yescharacteristic
33C22×C22⋊C4×C43C2211yescharacteristic
34C22×C22⋊C4×C43C2211yescharacteristic
35C22×C22⋊C4×C43C2211yescharacteristic
36C22×C42×C43C2211yescharacteristic
37C43×#388—24no—
38C2×#95×C43C2211yescharacteristic
39C2×#95×C43C2211yescharacteristic
40C24×D43C2312yes—
41C22×D172—24no—
42C22×D172—24no—
43C22×D172—22no—
44C22×D172—22no—
45C22×D172C2×C414yes—
46C22×C22⋊D43—24no—
47C22×C22⋊D43—24no—
48C22×C22⋊D43—42no—
49C22×C22⋊D43—42no—
50C22×C22⋊D43—42no—
51C22×C22⋊D43—42no—
52C22×C22⋊D43C2×C418yescomplemented
53C23×Dic43C2312yes—
54C23×Dic43C2312yes—
55C23×Dic43C2312yes—
56C22×C4×D43—24no—
57C22×C4×D43—24no—
58C22×C4×D43—42no—
59C22×C4×D43—42no—
60C22×C4×D43—42no—
61C22×C4×D43—42no—
62C22×C4×D43D418yescomplemented
63C4×D172—232no—
64C2×C4⋊Dic43—22no—
65C2×C4⋊Dic43—24no—
66C2×C22⋊Dic43—24no—
67C2×C22⋊Dic43—42no—
68C2×C22⋊Dic43—42no—
69C2×(C2×D43)⋊C4—24no—
70C2×(C2×D43)⋊C4—24no—
71C2×(C2×D43)⋊C4—24no—
72C2×(C2×D43)⋊C4—24no—
73C2×(C2×D43)⋊C4—24no—
74C2×(C2×D43)⋊C4—42no—
75C2×(C2×D43)⋊C4—42no—
76C2×(C2×D43)⋊C4—42no—
77C2×(C2×D43)⋊C4—42no—
78C2×(C2×D43)⋊C4—42no—
79C2×(C2×D43)⋊C4—42no—
80C2×(C2×D43)⋊C4C2×C418yescomplemented
81C43⋊#95—24no—
82C43⋊#95—22no—
83C43⋊#95—24no—
84C43⋊#95—42no—
85C43⋊#95—42no—
86C43⋊#95—42no—
87C43⋊#95C2×C414yescomplemented
88C25×C43C2311yescharacteristic
89C23×C4×C43C2311yescharacteristic
90C23×C4×C43C2311yescharacteristic
91C23×C4×C43C2311yescharacteristic
92C23×C4×C43C2311yescharacteristic
93C23×C4×C43C2311yescharacteristic
94C23×C4×C43C2311yescharacteristic
95C2×C4⋊C4×C43—22no—
96C2×C4⋊C4×C43—42no—
97C2×C22⋊C4×C43—22no—
98C2×C22⋊C4×C43—22no—
99C2×C22⋊C4×C43—22no—
100C2×C22⋊C4×C43—22no—
101C2×C22⋊C4×C43—24no—
102C2×C22⋊C4×C43—42no—
103C2×C22⋊C4×C43C2×C414yescomplemented
104C2×C42×C43—24no—
105C2×C42×C43D414yescomplemented
106#95×C43—22no—
107#95×C43—22no—
108C24×C43—21no—
109C24×C43—22no—
110C24×C43—21no—
111C24×C43—22no—
112C24×C43—22no—
113C24×C43—21no—
114C24×C43—22no—
115C24×C43—21no—
116C24×C43—21no—
117C24×C43—21no—
118C24×C43C22×C412yes—
119C24×C43C2411yescharacteristic
120C23×D43—22no—
121C23×D43—22no—
122C23×D43—22no—
123C23×D43—22no—
124C23×D43—22no—
125C23×D43—22no—
126C23×D43—22no—
127C23×D43—22no—
128C23×D43—22no—
129C23×D43—22no—
130C23×D43—22no—
131C23×D43—22no—
132C23×D43C22×C414yes—
133C23×D43C2×D414yes—
134C23×D43#4114yes—
135C22×C4×C43—22no—
136C22×C4×C43—21no—
137C22×C4×C43—22no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—22no—
141C22×C4×C43—22no—
142C22×C4×C43—21no—
143C22×C4×C43—22no—
144C22×C4×C43—21no—
145C22×C4×C43—22no—
146C22×C4×C43—21no—
147C22×C4×C43—22no—
148C22×C4×C43—22no—
149C22×C4×C43—21no—
150C22×C4×C43—22no—
151C22×C4×C43—22no—
152C22×C4×C43—22no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43C22×C412yes—
159C22×C4×C43C22×C412yes—
160C22×C4×C43C2×D414yes—
161C22×C4×C43C2×D412yes—
162C22×C4×C43C2×D412yes—
163C22×C4×C43C2×D412yes—
164C22×C4×C43#4112yes—
165C2×C22⋊D43—216no—
166C2×C22⋊D43—48no—
167C2×C22⋊D43—48no—
168C2×C22⋊D43—48no—
169C2×C22⋊D43—48no—
170C2×C22⋊D43—48no—
171C2×C22⋊D43—48no—
172C22×Dic43—22no—
173C22×Dic43—22no—
174C22×Dic43—22no—
175C22×Dic43—22no—
176C22×Dic43—22no—
177C22×Dic43—22no—
178C22×Dic43—22no—
179C22×Dic43—22no—
180C22×Dic43—22no—
181C22×Dic43—22no—
182C22×Dic43—22no—
183C22×Dic43—22no—
184C22×Dic43—22no—
185C22×Dic43—22no—
186C22×Dic43—22no—
187C22×Dic43—22no—
188C22×Dic43—22no—
189C22×Dic43—22no—
190C22×Dic43—22no—
191C22×Dic43C22×C414yes—
192C22×Dic43C2×D414yes—
193C2×D172—28no—
194C2×D172—216no—
195C2×D172—28no—
196C2×D172—28no—
197C2×D172—216no—
198C2×C4×D43—216no—
199C2×C4×D43—48no—
200C2×C4×D43—48no—
201C2×C4×D43—48no—
202C2×C4×D43—48no—
203C2×C4×D43—48no—
204C2×C4×D43—48no—
205C4⋊C4×C43—44no—
206C22⋊C4×C43—28no—
207C22⋊C4×C43—44no—
208C22⋊C4×C43—44no—
209C42×C43—28no—
210C22⋊Dic43—48no—
211(C2×D43)⋊C4—216no—
212(C2×D43)⋊C4—48no—
213(C2×D43)⋊C4—48no—
214(C2×D43)⋊C4—48no—
215C4⋊Dic43—28no—
216C23×C43—22no—
217C23×C43—24no—
218C23×C43—22no—
219C23×C43—24no—
220C23×C43—22no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—42no—
224C23×C43—42no—
225C23×C43—42no—
226C23×C43—41no—
227C23×C43—42no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43—41no—
231C23×C43—42no—
232C23×C43—42no—
233C23×C43—42no—
234C23×C43—42no—
235C23×C43—42no—
236C23×C43—42no—
237C23×C43—41no—
238C23×C43—41no—
239C23×C43C23×C411yescharacteristic
240C23×C43C22×D412yes—
241C23×C43C22×D411yescharacteristic
242C23×C43C2×#4112yes—
243C23×C43C2×#4111yescharacteristic
244C23×C43H(5,𝔽2)12yes—
245C23×C43H(5,𝔽2)11yescharacteristic
246C23×C43H(5,𝔽2)12yes—
247C23×C43H(5,𝔽2)11yescharacteristic
248C23×C43H(5,𝔽2)11yescharacteristic
249C23×C432−1+411yescharacteristic
250C22×D43—24no—
251C22×D43—24no—
252C22×D43—24no—
253C22×D43—24no—
254C22×D43—24no—
255C22×D43—24no—
256C22×D43—24no—
257C22×D43—24no—
258C22×D43—24no—
259C22×D43—24no—
260C22×D43—24no—
261C22×D43—24no—
262C22×D43—24no—
263C22×D43—24no—
264C22×D43—24no—
265C22×D43—24no—
266C22×D43—24no—
267C22×D43—24no—
268C22×D43—42no—
269C22×D43—42no—
270C22×D43—42no—
271C22×D43—42no—
272C22×D43—42no—
273C22×D43—42no—
274C22×D43—42no—
275C22×D43—42no—
276C22×D43—42no—
277C22×D43—42no—
278C22×D43—42no—
279C22×D43—42no—
280C22×D43—42no—
281C22×D43—42no—
282C22×D43—42no—
283C22×D43—42no—
284C22×D43C4×D418yes—
285C2×C4×C43—24no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—24no—
289C2×C4×C43—24no—
290C2×C4×C43—24no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—24no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—42no—
301C2×C4×C43—42no—
302C2×C4×C43—42no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—42no—
306C2×C4×C43—41no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—42no—
311C2×C4×C43—42no—
312C2×C4×C43—42no—
313C2×C4×C43C4×D414yes—
314C2×C4×C43#12014yes—
315C22⋊D43—432no—
316C2×Dic43—24no—
317C2×Dic43—24no—
318C2×Dic43—24no—
319C2×Dic43—24no—
320C2×Dic43—24no—
321C2×Dic43—24no—
322C2×Dic43—42no—
323C2×Dic43—42no—
324C2×Dic43—42no—
325C2×Dic43—42no—
326C2×Dic43—42no—
327C2×Dic43—42no—
328C2×Dic43—42no—
329C2×Dic43—42no—
330C2×Dic43—42no—
331C2×Dic43—42no—
332C2×Dic43—42no—
333C2×Dic43—42no—
334C2×Dic43—42no—
335C2×Dic43—42no—
336C2×Dic43—42no—
337D172—232no—
338C4×D43—432no—
339#14299—431nomaximal, Sylow
340C22×C43—44no—
341C22×C43—42no—
342C22×C43—44no—
343C22×C43—42no—
344C22×C43—42no—
345C22×C43—81no—
346C22×C43—81no—
347C22×C43—82no—
348C22×C43—81no—
349C22×C43—82no—
350C22×C43—81no—
351C22×C43C2×C4×D412yes—
352C22×C43C2×C4×D411yescharacteristic
353C22×C43#51812yes—
354C22×C43#51811yescharacteristic
355C22×C43#52011yescharacteristic
356C22×C43C2×#12011yescharacteristic
357C22×C43#52511yescharacteristic
358C22×C43#52512yes—
359C22×C43#53412yes—
360C22×C43#53412yes—
361C22×C43#53511yescharacteristic
362C22×C43#53511yescharacteristic
363C22×C43#53512yes—
364C22×C43#53511yescharacteristic
365C22×C43#53711yescharacteristic
366C22×C43#53712yes—
367C22×C43#53812yes—
368C22×C43#53812yes—
369C22×C43#53812yes—
370C22×C43#53912yes—
371C22×C43#54012yes—
372C22×C43#54011yescharacteristic
373C22×C43#54211yescharacteristic
374C2×D43—28no—
375C2×D43—28no—
376C2×D43—28no—
377C2×D43—44no—
378C2×D43—44no—
379C2×D43—44no—
380C2×D43—44no—
381C2×D43—44no—
382C2×D43—44no—
383C2×D43—44no—
384C2×D43—44no—
385C2×D43—44no—
386C2×D43—44no—
387C2×D43—44no—
388C2×D43—44no—
389C4×C43—24no—
390C4×C43—24no—
391C4×C43—42no—
392C4×C43—42no—
393C4×C43—81no—
394C4×C43—81no—
395Dic43—44no—
396Dic43—44no—
397Dic43—82no—
398C22×C4×D4—431no—
399C2×#392—431no—
400C2×#388D4311yescharacteristic, complemented
401C2×#386—432no—
402#1442—431no—
403#1439—432no—
404#1439—431no—
405#1438—431no—
406#1438—432no—
407#1434—431no—
408C22⋊#95—432no—
409C2×C43—82no—
410C2×C43C4×#12011yescharacteristic
411C2×C43#232112yes—
412C2×C43#232411yescharacteristic
413C2×C43#232512yes—
414C2×C43#232811yescharacteristic
415C2×C43#261311yescharacteristic
416C2×C43#261511yescharacteristic
417C2×C43#263012yes—
418C2×C43#263111yescharacteristic
419C2×C43#263512yes—
420C2×C43#263611yescharacteristic
421D43—48no—
422C23×D4—432no—
423C23×D4—431no—
424C24×C4—432no—
425C2×C4×D4—868no—
426C2×C4×D4—864no—
427C22×C4⋊C4—431no—
428C22×C4⋊C4C2×D4311yescharacteristic
429C22×C22⋊C4—432no—
430C22×C22⋊C4—432no—
431C22×C22⋊C4—432no—
432C22×C22⋊C4—432no—
433C22×C22⋊C4—432no—
434C22×C22⋊C4C2×D4311yescharacteristic
435C22×C22⋊C4C2×D4311yescharacteristic
436C22×C22⋊C4C2×D4311yescharacteristic
437C22×C42C2×D4311yescharacteristic
438#392—438no—
439#388—24no—
440#386—868no—
441C2×#95—431no—
442C2×#95—432no—
443C2×#95—431no—
444C2×#95—432no—
445C2×#95—432no—
446C2×#95—432no—
447C2×#95—432no—
448C2×#95C2×D4311yescharacteristic
449C2×#95C2×D4311yescharacteristic
450C43#1429911yescharacteristic, complemented, Sylow
451C25—432no—
452C25C22×D4311yescharacteristic
453C22×D4—438no—
454C22×D4—434no—
455C22×D4—864no—
456C22×D4—864no—
457C22×D4—864no—
458C22×D4—864no—
459C22×D4—862no—
460C22×D4—862no—
461C22×D4—1722no—
462C22×D4—1722no—
463C22×D4—1722no—
464C22×D4—1722no—
465C23×C4—432no—
466C23×C4—432no—
467C23×C4—438no—
468C23×C4—432no—
469C23×C4—864no—
470C23×C4—864no—
471C23×C4—1722no—
472C23×C4—1722no—
473C23×C4—1722no—
474C23×C4—1722no—
475C23×C4C22×D4311yescharacteristic
476C23×C4C22×D4311yescharacteristic
477C23×C4C22×D4311yescharacteristic
478C23×C4C22×D4311yescharacteristic
479C23×C4C22×D4311yescharacteristic
480C23×C4C22×D4311yescharacteristic
481C4×D4—8632no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—42no—
484C2×C4⋊C4—864no—
485C2×C4⋊C4—862no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—42no—
492C2×C22⋊C4—438no—
493C2×C22⋊C4—864no—
494C2×C22⋊C4—864no—
495C2×C22⋊C4—864no—
496C2×C22⋊C4—864no—
497C2×C22⋊C4—864no—
498C2×C22⋊C4—864no—
499C2×C22⋊C4—1722no—
500C2×C22⋊C4—1722no—
501C2×C22⋊C4—1722no—
502C2×C22⋊C4—1722no—
503C2×C22⋊C4—1722no—
504C2×C22⋊C4—1722no—
505C2×C22⋊C4—1722no—
506C2×C22⋊C4—1722no—
507C2×C22⋊C4C4×D4314yescomplemented
508C2×C42—24no—
509C2×C42C22⋊D4314yescomplemented
510#95—22no—
511#95—22no—
512#95—434no—
513#95—864no—
514#95—862no—
515#95—864no—
516#95—1722no—
517#95—1722no—
518#95—1722no—
519C24—22no—
520C24—21no—
521C24—22no—
522C24—21no—
523C24—22no—
524C24—21no—
525C24—22no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24—434no—
530C24—434no—
531C24—434no—
532C24—862no—
533C24—862no—
534C24—862no—
535C24—862no—
536C24—862no—
537C24—862no—
538C24—862no—
539C24—862no—
540C24—862no—
541C24—862no—
542C24—862no—
543C24—862no—
544C24C2×C4×D4312yes—
545C24C23×D4311yescharacteristic
546C2×D4—8616no—
547C2×D4—868no—
548C2×D4—868no—
549C2×D4—8616no—
550C2×D4—8616no—
551C2×D4—868no—
552C2×D4—1728no—
553C2×D4—1728no—
554C2×D4—1728no—
555C2×D4—1728no—
556C2×D4—1728no—
557C2×D4—1728no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—434no—
582C22×C4—434no—
583C22×C4—862no—
584C22×C4—862no—
585C22×C4—862no—
586C22×C4—862no—
587C22×C4—862no—
588C22×C4—862no—
589C22×C4—862no—
590C22×C4—862no—
591C22×C4—862no—
592C22×C4—862no—
593C22×C4—862no—
594C22×C4—862no—
595C22×C4—8616no—
596C22×C4—862no—
597C22×C4—862no—
598C22×C4—862no—
599C22×C4—862no—
600C22×C4—862no—
601C22×C4—862no—
602C22×C4—862no—
603C22×C4—1728no—
604C22×C4—1728no—
605C22×C4—1728no—
606C22×C4—1728no—
607C22×C4—1728no—
608C22×C4—1728no—
609C22×C4C2×C4×D4312yes—
610C22×C4C2×C4×D4312yes—
611C22×C4#1062189812yes—
612C22×C4D4×D4314yes—
613C22×C4C2×C22⋊D4312yes—
614C22×C4C2×C22⋊D4312yes—
615C22×C4C2×C22⋊D4312yes—
616C4⋊C4—44no—
617C4⋊C4—868no—
618C22⋊C4—28no—
619C22⋊C4—44no—
620C22⋊C4—44no—
621C22⋊C4—8616no—
622C22⋊C4—1728no—
623C22⋊C4—1728no—
624C22⋊C4—1728no—
625C22⋊C4—1728no—
626C42—28no—
627C23—24no—
628C23—22no—
629C23—24no—
630C23—22no—
631C23—22no—
632C23—41no—
633C23—41no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—41no—
638C23—41no—
639C23—42no—
640C23—41no—
641C23—41no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—41no—
649C23—41no—
650C23—438no—
651C23—864no—
652C23—864no—
653C23—864no—
654C23—864no—
655C23—864no—
656C23—864no—
657C23—864no—
658C23—864no—
659C23—864no—
660C23—864no—
661C23—864no—
662C23—864no—
663C23—864no—
664C23—864no—
665C23—864no—
666C23—864no—
667C23—864no—
668C23—864no—
669C23—1722no—
670C23—1722no—
671C23—1722no—
672C23—1722no—
673C23—1722no—
674C23—1722no—
675C23—1722no—
676C23—1722no—
677C23—1722no—
678C23—1722no—
679C23—1722no—
680C23—1722no—
681C23—1722no—
682C23—1722no—
683C23—1722no—
684C23—1722no—
685C23C22×C4×D4311yescharacteristic
686C23C2×D4×D4312yes—
687C23C22×C22⋊D4311yescharacteristic
688C23#41×D4312yes—
689C23C2×#1062189811yescharacteristic
690C23#1306337012yes—
691C23#1306337112yes—
692C23#1306337111yescharacteristic
693C23#1306337111yescharacteristic
694C23#1306337111yescharacteristic
695C23#1306337211yescharacteristic
696D4—8632no—
697D4—17232no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—864no—
727C2×C4—864no—
728C2×C4—864no—
729C2×C4—864no—
730C2×C4—864no—
731C2×C4—864no—
732C2×C4—17232no—
733C2×C4—1722no—
734C2×C4—1722no—
735C2×C4—1722no—
736C2×C4—1722no—
737C2×C4—1722no—
738C2×C4—1722no—
739C2×C4—1722no—
740C2×C4—1722no—
741C2×C4—1722no—
742C2×C4—1722no—
743C2×C4—1722no—
744C2×C4—1722no—
745C2×C4—1722no—
746C2×C4—1722no—
747C2×C4—1722no—
748C2×C4C4×C22⋊D4314yes—
749C2×C4#1306329314yes—
750C22—42no—
751C22—44no—
752C22—42no—
753C22—42no—
754C22—44no—
755C22—82no—
756C22—81no—
757C22—82no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—868no—
762C22—868no—
763C22—868no—
764C22—1724no—
765C22—1724no—
766C22—1724no—
767C22—1724no—
768C22—1724no—
769C22—1724no—
770C22—1724no—
771C22—1724no—
772C22—1724no—
773C22—1724no—
774C22—1724no—
775C22—1724no—
776C22C4×D4×D4312yes—
777C22C2×C4×C22⋊D4311yescharacteristic
778C22#1458337112yes—
779C22#1458337311yescharacteristic
780C22#1458337911yescharacteristic
781C22C2×#1306329311yescharacteristic
782C22#1458340611yescharacteristic
783C22#1458340812yes—
784C22#1458346012yes—
785C22#1458346012yes—
786C22#1458346311yescharacteristic
787C22#1458346311yescharacteristic
788C22#1458346512yes—
789C22#1458346611yescharacteristic
790C22#1458347711yescharacteristic
791C22#1458347812yes—
792C22#1458348312yes—
793C22#1458348312yes—
794C22#1458348812yes—
795C22#1458349012yes—
796C22#1458350012yes—
797C22#1458350411yescharacteristic
798C22#1458352011yescharacteristic
799C4—24no—
800C4—24no—
801C4—42no—
802C4—42no—
803C4—81no—
804C4—81no—
805C4—3442no—
806C4—1724no—
807C4—1724no—
808C2—82no—
809C2—1728no—
810C2C4×#1306329311yescharacteristic
811C2#1913725712yes—
812C2#1913728811yescharacteristic
813C2#1913729912yes—
814C2#1913731711yescharacteristic
815C2#1914031111yescharacteristic
816C2#1914032011yescharacteristic
817C2#1914044212yes—
818C2#1914044811yescharacteristic
819C2#1914048612yes—
820C2#1914049211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#388C2
socle, cosocleC24×C43C24
prime radicalC2×#14582808C2
hypercenterC2×#388D43
hypocenterC43#14299
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C22×C4×D172C2semidirect
3. C2×#14582775C2semidirect
4. #19132851C2semidirect
5. #19132840C2semidirect
6. #19132837C2semidirect
7. #19132835C2semidirect
8. #19132834C2semidirect
9. #19132822C2semidirect
10. (C2×D43)⋊#95C2semidirect
11. C2×C43×#388C2semidirect
23. #14582808C4semidirect
52. C22×C22⋊D43C2×C4semidirect
62. C22×C4×D43D4semidirect
80. C2×(C2×D43)⋊C4C2×C4semidirect
87. C43⋊#95C2×C4semidirect
103. C2×C22⋊C4×C43C2×C4semidirect
105. C2×C42×C43D4semidirect
400. C2×#388D43semidirect
450. C43#14299semidirect
507. C2×C22⋊C4C4×D43semidirect
509. C2×C42C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D1722
C2×#145828082
C2×#145827752
#191328512
#191328402
#191328372
#191328352
#191328342
#191328222
(C2×D43)⋊#952
C2×C43×#3882
#1429943