Finite Group Databasebeta

← #25019374

Subgroups — #25019374

Order 11008.

2742 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063306C211yesmaximal, characteristic
2C2×#14582779C211yesmaximal, characteristic
3C2×#14582760C211yesmaximal, characteristic, complemented
4C22×C43⋊#95C211yesmaximal, characteristic, complemented
5#19132845C212yesmaximal, complemented
6#19132842C212yesmaximal, complemented
7#19132828C212yesmaximal, complemented
8#19132818C211yesmaximal, characteristic, complemented
9#19132818C212yesmaximal, complemented
10#19132817C211yesmaximal, characteristic, complemented
11C22×C4×D4×C43C211yesmaximal, characteristic
12C24×Dic43C2211yescharacteristic
13C24×Dic43C2211yescharacteristic
14C2×#13063306—24no—
15C2×#13063306—24no—
16C2×#13063306C418yescomplemented
17C22×Dic43⋊C4C2212yes—
18C22×C22⋊Dic43C2211yescharacteristic
19C22×C22⋊Dic43C2212yes—
20C22×C22⋊Dic43C2211yescharacteristic
21C22×C22⋊Dic43C2212yes—
22#14582779—24no—
23#14582760—24no—
24C2×C43⋊#95—24no—
25C2×C43⋊#95C2212yes—
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2212yes—
34C23×D4×C43C2211yescharacteristic
35C24×C4×C43C2211yescharacteristic
36C24×C4×C43C2211yescharacteristic
37C2×C4×D4×C43—24no—
38C2×C4×D4×C43—24no—
39C2×C4×D4×C43—24no—
40C22×C4⋊C4×C43C2211yescharacteristic
41C22×C22⋊C4×C43C2211yescharacteristic
42C22×C22⋊C4×C43C2211yescharacteristic
43C22×C42×C43C2211yescharacteristic
44C23×Dic43—22no—
45C23×Dic43—22no—
46C23×Dic43—22no—
47C23×Dic43—22no—
48C23×Dic43—22no—
49C23×Dic43—22no—
50C23×Dic43—22no—
51C23×Dic43—24no—
52C23×Dic43—22no—
53C23×Dic43—22no—
54C23×Dic43—42no—
55C23×Dic43C2×C414yescomplemented
56C23×Dic43C2312yes—
57C23×Dic43C2312yes—
58C23×Dic43C2312yes—
59C23×Dic43C2312yes—
60#13063306—232no—
61C2×Dic43⋊C4—24no—
62C2×Dic43⋊C4—24no—
63C2×Dic43⋊C4C2×C418yescomplemented
64C2×C22⋊Dic43—22no—
65C2×C22⋊Dic43—24no—
66C2×C22⋊Dic43—22no—
67C2×C22⋊Dic43—24no—
68C2×C22⋊Dic43—22no—
69C2×C22⋊Dic43—24no—
70C2×C22⋊Dic43—22no—
71C2×C22⋊Dic43—22no—
72C2×C22⋊Dic43—24no—
73C2×C22⋊Dic43—42no—
74C2×C22⋊Dic43C2×C414yescomplemented
75C2×C22⋊Dic43C2×C418yescomplemented
76C43⋊#95—24no—
77C43⋊#95—24no—
78C43⋊#95—24no—
79C43⋊#95—24no—
80C43⋊#95—24no—
81C43⋊#95—24no—
82C43⋊#95—24no—
83C43⋊#95—42no—
84C43⋊#95—42no—
85C25×C43C2311yescharacteristic
86C25×C43C2311yescharacteristic
87C22×D4×C43—22no—
88C22×D4×C43—22no—
89C22×D4×C43—22no—
90C22×D4×C43—22no—
91C22×D4×C43C2×C414yes—
92C22×D4×C43D414yes—
93C22×D4×C43D414yes—
94C23×C4×C43—22no—
95C23×C4×C43—22no—
96C23×C4×C43—22no—
97C23×C4×C43—22no—
98C23×C4×C43—22no—
99C23×C4×C43—24no—
100C23×C4×C43—24no—
101C23×C4×C43—42no—
102C23×C4×C43—42no—
103C23×C4×C43D414yes—
104C23×C4×C43C2311yescharacteristic
105C23×C4×C43C2311yescharacteristic
106C23×C4×C43C2311yescharacteristic
107C23×C4×C43C2311yescharacteristic
108C23×C4×C43C2311yescharacteristic
109C4×D4×C43—232no—
110C2×C4⋊C4×C43—22no—
111C2×C4⋊C4×C43—22no—
112C2×C4⋊C4×C43—22no—
113C2×C22⋊C4×C43—22no—
114C2×C22⋊C4×C43—22no—
115C2×C22⋊C4×C43—22no—
116C2×C22⋊C4×C43—22no—
117C2×C22⋊C4×C43—22no—
118C2×C22⋊C4×C43D414yes—
119C2×C42×C43—22no—
120C2×C42×C43—22no—
121C2×C42×C43—22no—
122C24×C43—22no—
123C24×C43—22no—
124C24×C43—22no—
125C24×C43—22no—
126C24×C43—21no—
127C24×C43—21no—
128C24×C43—22no—
129C24×C43—21no—
130C24×C43—21no—
131C24×C43—22no—
132C24×C43—22no—
133C24×C43—22no—
134C24×C43C22×C412yes—
135C24×C43C22×C412yes—
136C24×C43C2×D412yes—
137C24×C43C2×D412yes—
138C24×C43C2×D412yes—
139C24×C43C2×D412yes—
140C24×C43C2×D412yes—
141C24×C43C2×D412yes—
142C24×C43#4112yes—
143C24×C43#4112yes—
144C24×C43C2411yescharacteristic
145C2×D4×C43—28no—
146C2×D4×C43—28no—
147C2×D4×C43—28no—
148C2×D4×C43—28no—
149C2×D4×C43—28no—
150C2×D4×C43—28no—
151C2×D4×C43C22⋊C4116yes—
152C22×C4×C43—28no—
153C22×C4×C43—28no—
154C22×C4×C43—28no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—22no—
168C22×C4×C43—22no—
169C22×C4×C43—22no—
170C22×C4×C43—22no—
171C22×C4×C43—22no—
172C22×C4×C43—22no—
173C22×C4×C43—22no—
174C22×C4×C43—44no—
175C22×C4×C43—48no—
176C22×C4×C43—48no—
177C22×C4×C43—48no—
178C22×C4×C43—48no—
179C22×C4×C43—44no—
180C22×C4×C43—44no—
181C22×C4×C43C22×C412yes—
182C22×C4×C43C2×D412yes—
183C22×C4×C43C2×D412yes—
184C22×C4×C43C2×D412yes—
185C22×C4×C43C2×D412yes—
186C22×C4×C43C2×D412yes—
187C22×C4×C43C2×D412yes—
188C22×C4×C43#4114yes—
189C22×Dic43—28no—
190C22×Dic43—28no—
191C22×Dic43—28no—
192C22×Dic43—28no—
193C22×Dic43—22no—
194C22×Dic43—22no—
195C22×Dic43—22no—
196C22×Dic43—22no—
197C22×Dic43—22no—
198C22×Dic43—22no—
199C22×Dic43—22no—
200C22×Dic43—22no—
201C22×Dic43—22no—
202C22×Dic43—22no—
203C22×Dic43—22no—
204C22×Dic43—22no—
205C22×Dic43—22no—
206C22×Dic43—22no—
207C22×Dic43—22no—
208C22×Dic43—22no—
209C22×Dic43—22no—
210C22×Dic43—22no—
211C22×Dic43—22no—
212C22×Dic43—22no—
213C22×Dic43—22no—
214C22×Dic43—22no—
215C22×Dic43—22no—
216C22×Dic43—22no—
217C22×Dic43—22no—
218C22×Dic43—48no—
219C22×Dic43—48no—
220C22×Dic43—44no—
221C22×Dic43—44no—
222C22×Dic43—44no—
223C22×Dic43—44no—
224C22×Dic43—44no—
225C22×Dic43—44no—
226C22×Dic43C22×C414yes—
227C22×Dic43C22×C414yes—
228C22×Dic43#4114yes—
229C4⋊C4×C43—28no—
230C22⋊C4×C43—28no—
231C22⋊C4×C43—28no—
232C42×C43—28no—
233C22⋊Dic43—216no—
234C22⋊Dic43—28no—
235C22⋊Dic43—48no—
236C22⋊Dic43—44no—
237Dic43⋊C4—216no—
238C23×C43—24no—
239C23×C43—24no—
240C23×C43—22no—
241C23×C43—22no—
242C23×C43—24no—
243C23×C43—22no—
244C23×C43—22no—
245C23×C43—24no—
246C23×C43—24no—
247C23×C43—24no—
248C23×C43—24no—
249C23×C43—24no—
250C23×C43—24no—
251C23×C43—24no—
252C23×C43—24no—
253C23×C43—24no—
254C23×C43—22no—
255C23×C43—22no—
256C23×C43—24no—
257C23×C43—24no—
258C23×C43—22no—
259C23×C43—22no—
260C23×C43—22no—
261C23×C43—22no—
262C23×C43—24no—
263C23×C43—24no—
264C23×C43—24no—
265C23×C43—24no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—42no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43—42no—
272C23×C43—42no—
273C23×C43—42no—
274C23×C43—42no—
275C23×C43—42no—
276C23×C43C2×C22⋊C414yes—
277C23×C43C2×C22⋊C414yes—
278C23×C43C4×D414yes—
279C23×C43C4×D414yes—
280C23×C43#12014yes—
281C23×C43#12114yes—
282C23×C43#12114yes—
283C23×C43#12314yes—
284C23×C43C23×C411yescharacteristic
285C23×C43C22×D411yescharacteristic
286C23×C43C22×D411yescharacteristic
287C23×C43C22×D411yescharacteristic
288C23×C43C22×D411yescharacteristic
289C23×C43C2×#4112yes—
290C23×C43C2×#4112yes—
291C23×C43C2×#4111yescharacteristic
292C23×C43C2×#4111yescharacteristic
293C23×C43H(5,𝔽2)12yes—
294C23×C432−1+412yes—
295D4×C43—232no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—24no—
305C2×C4×C43—24no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—24no—
312C2×C4×C43—24no—
313C2×C4×C43—416no—
314C2×C4×C43—416no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43—41no—
318C2×C4×C43—41no—
319C2×C4×C43—42no—
320C2×C4×C43—42no—
321C2×C4×C43—42no—
322C2×C4×C43—42no—
323C2×C4×C43C2×C22⋊C414yes—
324C2×C4×C43#12314yescomplemented
325C2×Dic43—24no—
326C2×Dic43—24no—
327C2×Dic43—24no—
328C2×Dic43—24no—
329C2×Dic43—24no—
330C2×Dic43—24no—
331C2×Dic43—24no—
332C2×Dic43—24no—
333C2×Dic43—24no—
334C2×Dic43—416no—
335C2×Dic43—42no—
336C2×Dic43—42no—
337C2×Dic43—42no—
338C2×Dic43—42no—
339C2×Dic43—42no—
340C2×Dic43—42no—
341C2×Dic43—42no—
342C2×Dic43—42no—
343C2×Dic43—42no—
344C2×Dic43—42no—
345C2×Dic43—42no—
346C2×Dic43—42no—
347C2×Dic43—416no—
348C2×Dic43—42no—
349C2×Dic43—42no—
350C2×Dic43—42no—
351C2×Dic43—42no—
352C2×Dic43—42no—
353C2×Dic43—42no—
354C2×Dic43—42no—
355#13968—431nomaximal, Sylow
356C22×C43—24no—
357C22×C43—28no—
358C22×C43—28no—
359C22×C43—24no—
360C22×C43—24no—
361C22×C43—28no—
362C22×C43—28no—
363C22×C43—24no—
364C22×C43—24no—
365C22×C43—24no—
366C22×C43—28no—
367C22×C43—24no—
368C22×C43—42no—
369C22×C43—44no—
370C22×C43—42no—
371C22×C43—42no—
372C22×C43—44no—
373C22×C43—44no—
374C22×C43—42no—
375C22×C43—42no—
376C22×C43—42no—
377C22×C43#38618yes—
378C22×C43C22×C22⋊C411yescharacteristic
379C22×C43C2×C4×D411yescharacteristic
380C22×C43C2×C4×D411yescharacteristic
381C22×C43C4×#4112yes—
382C22×C43#52012yes—
383C22×C43C2×#12011yescharacteristic
384C22×C43C2×#12111yescharacteristic
385C22×C43C2×#12111yescharacteristic
386C22×C43C2×#12311yescharacteristic
387C22×C43C2×#12311yescharacteristic
388C22×C43#52511yescharacteristic
389C22×C43#52912yes—
390C22×C43#53411yescharacteristic
391C22×C43#53611yescharacteristic
392C22×C43#53912yes—
393C22×C43#54612yes—
394C22×C43#54612yes—
395C22×C43#54612yes—
396C22×C43#54712yes—
397C22×C43#54712yes—
398C22×C43#54712yes—
399C22×C43#55112yes—
400C22×C43#55212yes—
401C4×C43—24no—
402C4×C43—24no—
403C4×C43—42no—
404C4×C43—42no—
405C4×C43—42no—
406Dic43—44no—
407Dic43—44no—
408Dic43—44no—
409Dic43—82no—
410C22×#123—431no—
411C22×C4×D4D4311yescharacteristic
412C2×#386—431no—
413C2×#381—431no—
414C22×#95—431no—
415#1441—432no—
416#1440—432no—
417#1436—432no—
418C22⋊#95—431no—
419C22⋊#95—432no—
420C22⋊#95—431no—
421C2×C43—28no—
422C2×C43—44no—
423C2×C43C2×#38611yescharacteristic
424C2×C43C4×#12311yescharacteristic
425C2×C43#232211yescharacteristic
426C2×C43#233912yes—
427C2×C43#235912yes—
428C2×C43#240511yescharacteristic
429C2×C43#240611yescharacteristic
430C2×C43#241912yes—
431C2×C43#242512yes—
432C2×C43#248611yescharacteristic
433C2×C43#253411yescharacteristic
434C23×D4C2×D4311yescharacteristic
435C24×C4—431no—
436C24×C4—431no—
437C24×C4C2×D4311yescharacteristic
438C24×C4C2×D4311yescharacteristic
439C2×#123—438no—
440C2×#123—864no—
441C2×#123—864no—
442C2×C4×D4—24no—
443C2×C4×D4—24no—
444C2×C4×D4—24no—
445C22×C4⋊C4—432no—
446C22×C4⋊C4C2×D4311yescharacteristic
447C22×C22⋊C4—431no—
448C22×C22⋊C4—432no—
449C22×C22⋊C4—431no—
450C22×C22⋊C4—432no—
451C22×C22⋊C4C2×D4311yescharacteristic
452C22×C22⋊C4C2×D4311yescharacteristic
453C22×C42C2×D4311yescharacteristic
454#386—864no—
455#381—864no—
456C2×#95—432no—
457C2×#95—432no—
458C2×#95—432no—
459C2×#95—432no—
460C2×#95—432no—
461C2×#95—432no—
462C2×#95—432no—
463C2×#95—432no—
464C2×#95—432no—
465C2×#95—864no—
466C43#1396811yescharacteristic, complemented, Sylow
467C25C22×D4311yescharacteristic
468C25C22×D4311yescharacteristic
469C22×D4—22no—
470C22×D4—22no—
471C22×D4—22no—
472C22×D4—22no—
473C22×D4C4×D4314yes—
474C22×D4D17214yes—
475C22×D4C22⋊D4314yes—
476C23×C4—22no—
477C23×C4—22no—
478C23×C4—22no—
479C23×C4—24no—
480C23×C4—22no—
481C23×C4—22no—
482C23×C4—24no—
483C23×C4—42no—
484C23×C4—42no—
485C23×C4—434no—
486C23×C4—432no—
487C23×C4—432no—
488C23×C4—432no—
489C23×C4—432no—
490C23×C4—864no—
491C23×C4—862no—
492C23×C4—862no—
493C23×C4—862no—
494C23×C4—862no—
495C23×C4—862no—
496C23×C4—862no—
497C23×C4—862no—
498C23×C4—862no—
499C23×C4—862no—
500C23×C4—1722no—
501C23×C4C22⋊D4314yes—
502C23×C4C22×D4311yescharacteristic
503C23×C4C22×D4311yescharacteristic
504C23×C4C22×D4311yescharacteristic
505C23×C4C22×D4311yescharacteristic
506C23×C4C22×D4311yescharacteristic
507#123—8632no—
508C4×D4—232no—
509C2×C4⋊C4—22no—
510C2×C4⋊C4—22no—
511C2×C4⋊C4—22no—
512C2×C4⋊C4—438no—
513C2×C4⋊C4—864no—
514C2×C4⋊C4—864no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—434no—
521C2×C22⋊C4—438no—
522C2×C22⋊C4—862no—
523C2×C22⋊C4—864no—
524C2×C22⋊C4—862no—
525C2×C22⋊C4—864no—
526C2×C22⋊C4—864no—
527C2×C22⋊C4—864no—
528C2×C22⋊C4—862no—
529C2×C22⋊C4—862no—
530C2×C22⋊C4—862no—
531C2×C22⋊C4—1722no—
532C2×C22⋊C4C22⋊D4314yes—
533C2×C42—22no—
534C2×C42—22no—
535C2×C42—22no—
536#95—864no—
537#95—864no—
538#95—864no—
539#95—864no—
540#95—864no—
541#95—864no—
542#95—864no—
543#95—1722no—
544#95—1722no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—21no—
550C24—21no—
551C24—22no—
552C24—22no—
553C24—21no—
554C24—21no—
555C24—22no—
556C24—22no—
557C24C2×C4×D4312yes—
558C24C2×C4×D4312yes—
559C24C2×D17212yes—
560C24C2×D17212yes—
561C24#1062189812yes—
562C24#1062189812yes—
563C24C2×C22⋊D4312yes—
564C24C2×C22⋊D4312yes—
565C24C2×C22⋊D4312yes—
566C24C2×C22⋊D4312yes—
567C24C23×D4311yescharacteristic
568C2×D4—28no—
569C2×D4—28no—
570C2×D4—28no—
571C2×D4—28no—
572C2×D4—28no—
573C2×D4—28no—
574C2×D4(C2×D43)⋊C4116yes—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—28no—
583C22×C4—28no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—28no—
597C22×C4—44no—
598C22×C4—48no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—48no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—434no—
605C22×C4—434no—
606C22×C4—434no—
607C22×C4—868no—
608C22×C4—868no—
609C22×C4—868no—
610C22×C4—868no—
611C22×C4—862no—
612C22×C4—862no—
613C22×C4—862no—
614C22×C4—862no—
615C22×C4—862no—
616C22×C4—862no—
617C22×C4—862no—
618C22×C4—862no—
619C22×C4—862no—
620C22×C4—862no—
621C22×C4—862no—
622C22×C4—862no—
623C22×C4—862no—
624C22×C4—862no—
625C22×C4—862no—
626C22×C4—862no—
627C22×C4—862no—
628C22×C4—862no—
629C22×C4—862no—
630C22×C4—862no—
631C22×C4—862no—
632C22×C4—862no—
633C22×C4—862no—
634C22×C4—862no—
635C22×C4—862no—
636C22×C4—1728no—
637C22×C4—1728no—
638C22×C4—1724no—
639C22×C4—1724no—
640C22×C4—1724no—
641C22×C4—1724no—
642C22×C4—1724no—
643C22×C4—1724no—
644C22×C4C2×C4×D4312yes—
645C22×C4C2×D17212yes—
646C22×C4#1062190014yes—
647C22×C4C2×C22⋊D4312yes—
648C22×C4C2×C22⋊D4312yes—
649C22×C4C2×C22⋊D4312yes—
650C22×C4C2×C22⋊D4312yes—
651C22×C4C2×C22⋊D4312yes—
652C4⋊C4—28no—
653C4⋊C4—8616no—
654C22⋊C4—28no—
655C22⋊C4—28no—
656C22⋊C4—868no—
657C22⋊C4—8616no—
658C22⋊C4—1728no—
659C22⋊C4—1724no—
660C42—28no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—22no—
667C23—22no—
668C23—24no—
669C23—22no—
670C23—22no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—22no—
679C23—22no—
680C23—24no—
681C23—24no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—42no—
690C23—42no—
691C23—41no—
692C23—41no—
693C23—42no—
694C23—41no—
695C23—41no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23C2×(C2×D43)⋊C414yes—
700C23C2×(C2×D43)⋊C414yes—
701C23C4×C22⋊D4314yes—
702C23C4×C22⋊D4314yes—
703C23#1306329414yes—
704C23#1306329914yes—
705C23#1306329914yes—
706C23#1306330814yes—
707C23C22×C4×D4311yescharacteristic
708C23C22×C22⋊D4311yescharacteristic
709C23C22×C22⋊D4311yescharacteristic
710C23C22×C22⋊D4311yescharacteristic
711C23C22×D17211yescharacteristic
712C23#41×D4312yes—
713C23C2×#1062190012yes—
714C23C2×#1062189811yescharacteristic
715C23C2×#1062189811yescharacteristic
716C23#1306337012yes—
717C23#1306337212yes—
718D4—232no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—416no—
737C2×C4—416no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—864no—
747C2×C4—864no—
748C2×C4—864no—
749C2×C4—864no—
750C2×C4—864no—
751C2×C4—864no—
752C2×C4—864no—
753C2×C4—864no—
754C2×C4—864no—
755C2×C4—1722no—
756C2×C4—1722no—
757C2×C4—1722no—
758C2×C4—1722no—
759C2×C4—1722no—
760C2×C4—1722no—
761C2×C4—1722no—
762C2×C4—17216no—
763C2×C4—1722no—
764C2×C4—1722no—
765C2×C4—1722no—
766C2×C4—1722no—
767C2×C4—1722no—
768C2×C4—1722no—
769C2×C4—1722no—
770C2×C4—1722no—
771C2×C4—1722no—
772C2×C4—1722no—
773C2×C4—1722no—
774C2×C4—17216no—
775C2×C4—1722no—
776C2×C4C2×(C2×D43)⋊C414yes—
777C2×C4#1306330614yescomplemented
778C22—28no—
779C22—28no—
780C22—24no—
781C22—24no—
782C22—28no—
783C22—24no—
784C22—24no—
785C22—28no—
786C22—24no—
787C22—24no—
788C22—28no—
789C22—24no—
790C22—44no—
791C22—44no—
792C22—42no—
793C22—42no—
794C22—44no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22#1458277818yes—
800C22C22×(C2×D43)⋊C411yescharacteristic
801C22C2×C4×C22⋊D4311yescharacteristic
802C22C2×C4×C22⋊D4311yescharacteristic
803C22C4×#1062190012yes—
804C22#1458337812yes—
805C22C2×#1306329411yescharacteristic
806C22C2×#1306329911yescharacteristic
807C22C2×#1306329911yescharacteristic
808C22C2×#1306330611yescharacteristic
809C22C2×#1306330811yescharacteristic
810C22#1458340611yescharacteristic
811C22#1458342912yes—
812C22#1458345811yescharacteristic
813C22#1458347011yescharacteristic
814C22#1458349112yes—
815C22#1458354312yes—
816C22#1458354312yes—
817C22#1458354412yes—
818C22#1458354812yes—
819C22#1458354812yes—
820C22#1458355312yes—
821C22#1458357812yes—
822C22#1458358912yes—
823C4—24no—
824C4—24no—
825C4—42no—
826C4—42no—
827C4—42no—
828C4—3442no—
829C4—1724no—
830C4—1724no—
831C4—1724no—
832C2—28no—
833C2—44no—
834C2C2×#1458277811yescharacteristic
835C2C4×#1306330611yescharacteristic
836C2#1913726011yescharacteristic
837C2#1913742012yes—
838C2#1913758112yes—
839C2#1913791811yescharacteristic
840C2#1913792611yescharacteristic
841C2#1913806612yes—
842C2#1913814012yes—
843C2#1913890311yescharacteristic
844C2#1913948111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC22×C4×D4×C43C2
socle, cosocleC24×C43C24
prime radicalC23×D4×C43C22
hypercenterC22×C4×D4D43
hypocenterC43#13968
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
3. C2×#14582760C2semidirect
4. C22×C43⋊#95C2semidirect
5. #19132845C2semidirect
6. #19132842C2semidirect
7. #19132828C2semidirect
8. #19132818C2semidirect
9. #19132818C2semidirect
10. #19132817C2semidirect
16. C2×#13063306C4semidirect
55. C23×Dic43C2×C4semidirect
63. C2×Dic43⋊C4C2×C4semidirect
74. C2×C22⋊Dic43C2×C4semidirect
75. C2×C22⋊Dic43C2×C4semidirect
324. C2×C4×C43#123semidirect
466. C43#13968semidirect
777. C2×C4#13063306semidirect

Maximal subgroups

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

subgroupindex
C22×#130633062
C2×#145827792
C2×#145827602
C22×C43⋊#952
#191328452
#191328422
#191328282
#191328182
#191328172
C22×C4×D4×C432
#1396843