Finite Group Databasebeta

← #25019723

Subgroups — #25019723

Order 11008.

2474 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
1C22×#13063309C211yesmaximal, characteristic
2C2×#14582778C211yesmaximal, characteristic
3C2×#14582776C211yesmaximal, characteristic
4C2×#14582760C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×Dic43C211yesmaximal, characteristic, complemented
6C22×C43⋊#95C211yesmaximal, characteristic, complemented
7#19132864C212yesmaximal, complemented
8#19132837C212yesmaximal, complemented
9#19132831C212yesmaximal, complemented
10#19132824C212yesmaximal, complemented
11C2×C43×#385C211yesmaximal, characteristic, complemented
12C23×C22⋊D43C2211yescharacteristic
13C24×Dic43C2211yescharacteristic
14C24×Dic43C2211yescharacteristic
15C2×#13063309—24no—
16C2×#13063309—24no—
17C2×#13063309C418yescomplemented
18C22×C4⋊Dic43C2212yes—
19C22×C22⋊Dic43C2211yescharacteristic
20C22×(C2×D43)⋊C4C2211yescharacteristic
21C22×(C2×D43)⋊C4C2212yes—
22C22×(C2×D43)⋊C4C2212yes—
23C22×(C2×D43)⋊C4C2211yescharacteristic
24C22×C4×Dic43C2212yes—
25#14582778—24no—
26#14582776—24no—
27#14582760—24no—
28C22⋊C4×Dic43—24no—
29C2×C43⋊#95—24no—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2211yescharacteristic
33C2×C43⋊#95C2212yes—
34C2×C43⋊#95C2212yes—
35C2×C43⋊#95C2212yes—
36C2×C43⋊#95C2212yes—
37C2×C43⋊#95C2211yescharacteristic
38C24×C4×C43C2211yescharacteristic
39C22×C4⋊C4×C43C2212yes—
40C22×C22⋊C4×C43C2211yescharacteristic
41C22×C22⋊C4×C43C2211yescharacteristic
42C43×#385—24no—
43C2×#95×C43C2212yes—
44C24×D43C2311yescharacteristic
45C22×C22⋊D43—22no—
46C22×C22⋊D43—22no—
47C22×C22⋊D43—22no—
48C22×C22⋊D43—22no—
49C22×C22⋊D43—22no—
50C22×C22⋊D43—22no—
51C22×C22⋊D43C2×C414yes—
52C23×Dic43—22no—
53C23×Dic43—22no—
54C23×Dic43—22no—
55C23×Dic43—22no—
56C23×Dic43—22no—
57C23×Dic43—22no—
58C23×Dic43—22no—
59C23×Dic43—22no—
60C23×Dic43—24no—
61C23×Dic43—42no—
62C23×Dic43C2×C414yes—
63C23×Dic43D414yes—
64C23×Dic43C2312yes—
65C23×Dic43C2311yescharacteristic
66C23×Dic43C2312yes—
67C23×Dic43C2311yescharacteristic
68C23×Dic43C2311yescharacteristic
69#13063309—232no—
70C2×C4⋊Dic43—24no—
71C2×C4⋊Dic43—24no—
72C2×C4⋊Dic43C2×C418yescomplemented
73C2×C22⋊Dic43—22no—
74C2×C22⋊Dic43—22no—
75C2×C22⋊Dic43D414yes—
76C2×(C2×D43)⋊C4—24no—
77C2×(C2×D43)⋊C4—24no—
78C2×(C2×D43)⋊C4—24no—
79C2×(C2×D43)⋊C4—22no—
80C2×(C2×D43)⋊C4—22no—
81C2×(C2×D43)⋊C4—24no—
82C2×(C2×D43)⋊C4—24no—
83C2×(C2×D43)⋊C4—42no—
84C2×(C2×D43)⋊C4—42no—
85C2×(C2×D43)⋊C4C2×C418yescomplemented
86C2×C4×Dic43—24no—
87C2×C4×Dic43—24no—
88C2×C4×Dic43—42no—
89C43⋊#95—24no—
90C43⋊#95—24no—
91C43⋊#95—24no—
92C43⋊#95—24no—
93C43⋊#95—24no—
94C43⋊#95—22no—
95C43⋊#95—22no—
96C43⋊#95—24no—
97C25×C43C2311yescharacteristic
98C23×C4×C43—22no—
99C23×C4×C43—24no—
100C23×C4×C43—22no—
101C23×C4×C43—22no—
102C23×C4×C43—42no—
103C23×C4×C43C2311yescharacteristic
104C23×C4×C43C2311yescharacteristic
105C23×C4×C43C2312yes—
106C23×C4×C43C2312yes—
107C2×C4⋊C4×C43—24no—
108C2×C4⋊C4×C43—24no—
109C2×C4⋊C4×C43—42no—
110C2×C22⋊C4×C43—22no—
111C2×C22⋊C4×C43—22no—
112C2×C22⋊C4×C43—22no—
113C2×C22⋊C4×C43C2×C414yes—
114C2×C22⋊C4×C43D414yes—
115C2×C22⋊C4×C43D414yes—
116#95×C43—24no—
117C24×C43—22no—
118C24×C43—22no—
119C24×C43—22no—
120C24×C43—22no—
121C24×C43C22×C412yes—
122C24×C43C2×D412yes—
123C24×C43C2×D412yes—
124C24×C43C2×D412yes—
125C24×C43C2×D412yes—
126C24×C43#4112yes—
127C24×C43#4112yes—
128C24×C43C2411yescharacteristic
129C23×D43—21no—
130C23×D43—21no—
131C23×D43—21no—
132C23×D43—21no—
133C23×D43—22no—
134C23×D43—22no—
135C23×D43—21no—
136C23×D43—21no—
137C23×D43—22no—
138C23×D43—22no—
139C23×D43C22×C412yes—
140C22×C4×C43—28no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—22no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—22no—
151C22×C4×C43—22no—
152C22×C4×C43—22no—
153C22×C4×C43—22no—
154C22×C4×C43—22no—
155C22×C4×C43—22no—
156C22×C4×C43—22no—
157C22×C4×C43—22no—
158C22×C4×C43—22no—
159C22×C4×C43—22no—
160C22×C4×C43—22no—
161C22×C4×C43—48no—
162C22×C4×C43—48no—
163C22×C4×C43—44no—
164C22×C4×C43—44no—
165C22×C4×C43C22×C414yes—
166C22×C4×C43C2×D414yes—
167C22×C4×C43C2×D414yes—
168C22×C4×C43#4114yes—
169C2×C22⋊D43—28no—
170C2×C22⋊D43—28no—
171C2×C22⋊D43—28no—
172C2×C22⋊D43—44no—
173C2×C22⋊D43—44no—
174C2×C22⋊D43—44no—
175C2×C22⋊D43—44no—
176C22×Dic43—28no—
177C22×Dic43—28no—
178C22×Dic43—28no—
179C22×Dic43—28no—
180C22×Dic43—28no—
181C22×Dic43—21no—
182C22×Dic43—22no—
183C22×Dic43—22no—
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43—21no—
187C22×Dic43—22no—
188C22×Dic43—22no—
189C22×Dic43—22no—
190C22×Dic43—21no—
191C22×Dic43—21no—
192C22×Dic43—21no—
193C22×Dic43—22no—
194C22×Dic43—22no—
195C22×Dic43—22no—
196C22×Dic43—22no—
197C22×Dic43—22no—
198C22×Dic43—22no—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43—22no—
203C22×Dic43—22no—
204C22×Dic43—22no—
205C22×Dic43—22no—
206C22×Dic43—44no—
207C22×Dic43—48no—
208C22×Dic43—48no—
209C22×Dic43—44no—
210C22×Dic43—44no—
211C22×Dic43—44no—
212C22×Dic43—44no—
213C22×Dic43C22×C414yes—
214C22×Dic43C22×C412yes—
215C22×Dic43C2×D414yes—
216C22×Dic43C2×D412yes—
217C22×Dic43C2×D412yes—
218C22×Dic43#4114yes—
219C4⋊C4×C43—48no—
220C22⋊C4×C43—44no—
221C22⋊C4×C43C22⋊C4116yescomplemented
222C22⋊Dic43—28no—
223(C2×D43)⋊C4—216no—
224(C2×D43)⋊C4—48no—
225(C2×D43)⋊C4—44no—
226(C2×D43)⋊C4—44no—
227C4⋊Dic43—216no—
228C4×Dic43—48no—
229C23×C43—24no—
230C23×C43—24no—
231C23×C43—22no—
232C23×C43—22no—
233C23×C43—24no—
234C23×C43—22no—
235C23×C43—22no—
236C23×C43—24no—
237C23×C43—24no—
238C23×C43—24no—
239C23×C43—24no—
240C23×C43—24no—
241C23×C43—24no—
242C23×C43—24no—
243C23×C43—24no—
244C23×C43—24no—
245C23×C43C2×C22⋊C414yes—
246C23×C43C4×D414yes—
247C23×C43C4×D414yes—
248C23×C43#12114yes—
249C23×C43#12114yes—
250C23×C43#12414yes—
251C23×C43#12714yes—
252C23×C43C23×C411yescharacteristic
253C23×C43C22×D411yescharacteristic
254C23×C43C22×D411yescharacteristic
255C23×C43C22×D411yescharacteristic
256C23×C43C22×D411yescharacteristic
257C23×C43C2×#4112yes—
258C23×C43C2×#4112yes—
259C23×C43C2×#4111yescharacteristic
260C23×C43C2×#4111yescharacteristic
261C23×C43H(5,𝔽2)12yes—
262C23×C432−1+412yes—
263C22×D43—22no—
264C22×D43—22no—
265C22×D43—22no—
266C22×D43—24no—
267C22×D43—24no—
268C22×D43—41no—
269C22×D43—41no—
270C22×D43—41no—
271C22×D43—41no—
272C22×D43—41no—
273C22×D43—42no—
274C22×D43—41no—
275C22×D43—41no—
276C22×D43—41no—
277C22×D43—42no—
278C22×D43—42no—
279C22×D43—42no—
280C22×D43—42no—
281C22×D43—42no—
282C22×D43—42no—
283C22×D43—42no—
284C22×D43—42no—
285C22×D43—42no—
286C2×C4×C43—24no—
287C2×C4×C43—24no—
288C2×C4×C43—24no—
289C2×C4×C43—24no—
290C2×C4×C43—24no—
291C2×C4×C43—24no—
292C2×C4×C43—24no—
293C2×C4×C43—24no—
294C2×C4×C43—24no—
295C2×C4×C43—416no—
296C2×C4×C43—42no—
297C2×C4×C43—42no—
298C2×C4×C43—42no—
299C2×C4×C43—42no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—42no—
307C2×C4×C43—42no—
308C2×C4×C43—42no—
309C2×C4×C43—42no—
310C2×C4×C43C2×C22⋊C418yes—
311C22⋊D43—416no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—24no—
315C2×Dic43—24no—
316C2×Dic43—22no—
317C2×Dic43—24no—
318C2×Dic43—24no—
319C2×Dic43—24no—
320C2×Dic43—22no—
321C2×Dic43—22no—
322C2×Dic43—24no—
323C2×Dic43—22no—
324C2×Dic43—22no—
325C2×Dic43—22no—
326C2×Dic43—24no—
327C2×Dic43—24no—
328C2×Dic43—416no—
329C2×Dic43—42no—
330C2×Dic43—42no—
331C2×Dic43—41no—
332C2×Dic43—41no—
333C2×Dic43—42no—
334C2×Dic43—41no—
335C2×Dic43—42no—
336C2×Dic43—42no—
337C2×Dic43—41no—
338C2×Dic43—42no—
339C2×Dic43—42no—
340C2×Dic43—42no—
341C2×Dic43—42no—
342C2×Dic43—42no—
343C2×Dic43—416no—
344C2×Dic43#12314yescomplemented
345#13996—431nomaximal, Sylow
346C22×C43—24no—
347C22×C43—28no—
348C22×C43—28no—
349C22×C43—24no—
350C22×C43—24no—
351C22×C43—28no—
352C22×C43—28no—
353C22×C43—24no—
354C22×C43—24no—
355C22×C43—24no—
356C22×C43#39018yes—
357C22×C43C22×C22⋊C411yescharacteristic
358C22×C43C2×C4×D411yescharacteristic
359C22×C43C2×C4×D411yescharacteristic
360C22×C43C4×#4112yes—
361C22×C43#52012yes—
362C22×C43C2×#12111yescharacteristic
363C22×C43C2×#12111yescharacteristic
364C22×C43C2×#12311yescharacteristic
365C22×C43#52511yescharacteristic
366C22×C43C2×#12411yescharacteristic
367C22×C43#52912yes—
368C22×C43C2×#12711yescharacteristic
369C22×C43#53411yescharacteristic
370C22×C43#53611yescharacteristic
371C22×C43#53912yes—
372C22×C43#54612yes—
373C22×C43#54612yes—
374C22×C43#54612yes—
375C22×C43#54712yes—
376C22×C43#54712yes—
377C22×C43#54712yes—
378C22×C43#55112yes—
379C22×C43#55212yes—
380C2×D43—42no—
381C2×D43—44no—
382C2×D43—44no—
383C2×D43—42no—
384C2×D43—42no—
385C2×D43—81no—
386C2×D43—81no—
387C2×D43—82no—
388C2×D43—82no—
389C2×D43—81no—
390C2×D43—81no—
391C4×C43—28no—
392C4×C43—44no—
393C4×C43—81no—
394C4×C43—81no—
395Dic43—24no—
396Dic43—42no—
397Dic43—44no—
398Dic43—44no—
399Dic43—42no—
400C22×#123—431no—
401C2×#386—431no—
402C2×#386—431no—
403C2×#385D4311yescharacteristic, complemented
404C2×#381—431no—
405C2×C4×C22⋊C4—431no—
406C22×#95—431no—
407#1445—432no—
408#1439—432no—
409#1437—432no—
410C4⋊#95—432no—
411C2×C43—28no—
412C2×C43C2×#39011yescharacteristic
413C2×C43C4×#12311yescharacteristic
414C2×C43#232211yescharacteristic
415C2×C43#233912yes—
416C2×C43#235912yes—
417C2×C43#241211yescharacteristic
418C2×C43#241311yescharacteristic
419C2×C43#242512yes—
420C2×C43#248812yes—
421C2×C43#250111yescharacteristic
422C2×C43#253911yescharacteristic
423D43—82no—
424C23×D4—431no—
425C24×C4—431no—
426C24×C4—431no—
427C24×C4C2×D4311yescharacteristic
428C2×#123—438no—
429C2×#123—864no—
430C2×#123—864no—
431C22×C4⋊C4—432no—
432C22×C4⋊C4C2×D4312yes—
433C22×C22⋊C4—431no—
434C22×C22⋊C4—432no—
435C22×C22⋊C4—431no—
436C22×C22⋊C4—432no—
437C22×C22⋊C4—431no—
438C22×C22⋊C4C2×D4311yescharacteristic
439C22×C22⋊C4C2×D4311yescharacteristic
440C22×C42—432no—
441#386—864no—
442#386—864no—
443#385—24no—
444#381—864no—
445C4×C22⋊C4—864no—
446C2×#95—431no—
447C2×#95—432no—
448C2×#95—432no—
449C2×#95—432no—
450C2×#95—432no—
451C2×#95—432no—
452C2×#95—432no—
453C2×#95—431no—
454C2×#95—864no—
455C2×#95C2×D4312yes—
456C43#1399611yescharacteristic, complemented, Sylow
457C25—431no—
458C25C22×D4311yescharacteristic
459C22×D4—434no—
460C22×D4—862no—
461C22×D4—862no—
462C22×D4—862no—
463C22×D4—862no—
464C22×D4—862no—
465C22×D4—862no—
466C23×C4—22no—
467C23×C4—24no—
468C23×C4—22no—
469C23×C4—22no—
470C23×C4—42no—
471C23×C4—431no—
472C23×C4—434no—
473C23×C4—432no—
474C23×C4—432no—
475C23×C4—431no—
476C23×C4—431no—
477C23×C4—434no—
478C23×C4—864no—
479C23×C4—862no—
480C23×C4—862no—
481C23×C4—862no—
482C23×C4—862no—
483C23×C4—862no—
484C23×C4—862no—
485C23×C4—862no—
486C23×C4—862no—
487C23×C4—1722no—
488C23×C4C22×D4311yescharacteristic
489C23×C4C22×D4311yescharacteristic
490C23×C4C22×D4312yes—
491C23×C4C22×D4312yes—
492#123—8632no—
493C2×C4⋊C4—24no—
494C2×C4⋊C4—24no—
495C2×C4⋊C4—42no—
496C2×C4⋊C4—438no—
497C2×C4⋊C4—864no—
498C2×C4⋊C4—864no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—434no—
503C2×C22⋊C4—438no—
504C2×C22⋊C4—862no—
505C2×C22⋊C4—862no—
506C2×C22⋊C4—864no—
507C2×C22⋊C4—864no—
508C2×C22⋊C4—864no—
509C2×C22⋊C4—864no—
510C2×C22⋊C4—862no—
511C2×C22⋊C4—862no—
512C2×C22⋊C4—864no—
513C2×C22⋊C4—1722no—
514C2×C22⋊C4—1722no—
515C2×C22⋊C4C4×D4314yes—
516C2×C22⋊C4D17214yes—
517C2×C22⋊C4C22⋊D4314yes—
518C2×C42—864no—
519C2×C42—864no—
520C2×C42—1722no—
521#95—24no—
522#95—864no—
523#95—864no—
524#95—864no—
525#95—864no—
526#95—864no—
527#95—862no—
528#95—862no—
529#95—864no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—432no—
535C24—861no—
536C24—861no—
537C24—861no—
538C24—861no—
539C24—862no—
540C24—862no—
541C24—861no—
542C24—861no—
543C24—862no—
544C24—862no—
545C24C2×C4×D4312yes—
546C24C2×D17212yes—
547C24D4×D4312yes—
548C24D4×D4312yes—
549C24#1062190212yes—
550C24#1062190212yes—
551C24C2×C22⋊D4312yes—
552C24C23×D4311yescharacteristic
553C2×D4—868no—
554C2×D4—868no—
555C2×D4—868no—
556C2×D4—1724no—
557C2×D4—1724no—
558C2×D4—1724no—
559C2×D4—1724no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—28no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—48no—
582C22×C4—48no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—432no—
586C22×C4—434no—
587C22×C4—434no—
588C22×C4—432no—
589C22×C4—434no—
590C22×C4—432no—
591C22×C4—868no—
592C22×C4—861no—
593C22×C4—861no—
594C22×C4—862no—
595C22×C4—868no—
596C22×C4—868no—
597C22×C4—868no—
598C22×C4—868no—
599C22×C4—862no—
600C22×C4—862no—
601C22×C4—861no—
602C22×C4—861no—
603C22×C4—862no—
604C22×C4—861no—
605C22×C4—861no—
606C22×C4—862no—
607C22×C4—862no—
608C22×C4—861no—
609C22×C4—862no—
610C22×C4—862no—
611C22×C4—862no—
612C22×C4—862no—
613C22×C4—862no—
614C22×C4—862no—
615C22×C4—861no—
616C22×C4—861no—
617C22×C4—861no—
618C22×C4—862no—
619C22×C4—862no—
620C22×C4—862no—
621C22×C4—1724no—
622C22×C4—1728no—
623C22×C4—1728no—
624C22×C4—1724no—
625C22×C4—1724no—
626C22×C4—1724no—
627C22×C4—1724no—
628C22×C4C2×C4×D4314yes—
629C22×C4C2×D17214yes—
630C22×C4#1062190014yes—
631C22×C4C2×C22⋊D4314yes—
632C4⋊C4—48no—
633C4⋊C4—8616no—
634C22⋊C4—44no—
635C22⋊C4—868no—
636C22⋊C4—8616no—
637C22⋊C4—1728no—
638C22⋊C4—1724no—
639C22⋊C4—1724no—
640C22⋊C4(C2×D43)⋊C4116yescomplemented
641C42—1728no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—22no—
648C23—22no—
649C23—24no—
650C23—22no—
651C23—22no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—862no—
659C23—862no—
660C23—862no—
661C23—864no—
662C23—864no—
663C23—1722no—
664C23—1722no—
665C23—1722no—
666C23—1721no—
667C23—1721no—
668C23—1721no—
669C23—1721no—
670C23—1721no—
671C23—1722no—
672C23—1721no—
673C23—1721no—
674C23—1721no—
675C23—1722no—
676C23—1722no—
677C23—1722no—
678C23—1722no—
679C23—1722no—
680C23—1722no—
681C23C2×(C2×D43)⋊C414yes—
682C23#1306328714yes—
683C23#1306328714yes—
684C23#1306330014yes—
685C23#1306330014yes—
686C23#1306331414yes—
687C23#1306332114yes—
688C23C22×C4×D4311yescharacteristic
689C23C2×D4×D4311yescharacteristic
690C23C2×D4×D4311yescharacteristic
691C23C22×C22⋊D4311yescharacteristic
692C23C22×D17211yescharacteristic
693C23#41×D4312yes—
694C23C2×#1062190012yes—
695C23C2×#1062190211yescharacteristic
696C23C2×#1062190211yescharacteristic
697C23#1306337012yes—
698C23#1306337212yes—
699D4—17216no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—416no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—434no—
725C2×C4—864no—
726C2×C4—862no—
727C2×C4—862no—
728C2×C4—864no—
729C2×C4—864no—
730C2×C4—862no—
731C2×C4—864no—
732C2×C4—864no—
733C2×C4—862no—
734C2×C4—862no—
735C2×C4—864no—
736C2×C4—862no—
737C2×C4—862no—
738C2×C4—862no—
739C2×C4—864no—
740C2×C4—864no—
741C2×C4—17216no—
742C2×C4—1722no—
743C2×C4—17216no—
744C2×C4—1722no—
745C2×C4—1722no—
746C2×C4—1722no—
747C2×C4—1721no—
748C2×C4—1721no—
749C2×C4—1722no—
750C2×C4—1721no—
751C2×C4—1722no—
752C2×C4—1722no—
753C2×C4—1721no—
754C2×C4—1722no—
755C2×C4—1722no—
756C2×C4—1722no—
757C2×C4C2×(C2×D43)⋊C418yes—
758C22—28no—
759C22—24no—
760C22—28no—
761C22—28no—
762C22—28no—
763C22—24no—
764C22—24no—
765C22—24no—
766C22—24no—
767C22—24no—
768C22—3442no—
769C22—3442no—
770C22—3441no—
771C22—3441no—
772C22—3441no—
773C22—3441no—
774C22—1722no—
775C22—1724no—
776C22—1722no—
777C22—1724no—
778C22—1722no—
779C22#1458280018yes—
780C22C22×(C2×D43)⋊C411yescharacteristic
781C22C2×#1306328711yescharacteristic
782C22C2×#1306328711yescharacteristic
783C22C4×#1062190012yes—
784C22#1458337812yes—
785C22C2×#1306330011yescharacteristic
786C22C2×#1306330011yescharacteristic
787C22#123×D4311yescharacteristic
788C22#1458340511yescharacteristic
789C22C2×#1306331411yescharacteristic
790C22#1458343512yes—
791C22C2×#1306332111yescharacteristic
792C22#1458345911yescharacteristic
793C22#1458347111yescharacteristic
794C22#1458349812yes—
795C22#1458353612yes—
796C22#1458354312yes—
797C22#1458354412yes—
798C22#1458354712yes—
799C22#1458354812yes—
800C22#1458355312yes—
801C22#1458357612yes—
802C22#1458359112yes—
803C4—28no—
804C4—44no—
805C4—81no—
806C4—81no—
807C4—864no—
808C4—1724no—
809C4—1722no—
810C4—1724no—
811C4—1722no—
812C2—28no—
813C2—3442no—
814C2C2×#1458280011yescharacteristic
815C2#1913711411yescharacteristic
816C2#1913726311yescharacteristic
817C2#1913742012yes—
818C2#1913758512yes—
819C2#1913798911yescharacteristic
820C2#1913800011yescharacteristic
821C2#1913814412yes—
822C2#1913892712yes—
823C2#1913906411yescharacteristic
824C2#1913952311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#385C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenterC2×#385D43
hypocenterC43#13996
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
4. C2×#14582760C2semidirect
5. C2×C22⋊C4×Dic43C2semidirect
6. C22×C43⋊#95C2semidirect
7. #19132864C2semidirect
8. #19132837C2semidirect
9. #19132831C2semidirect
10. #19132824C2semidirect
11. C2×C43×#385C2semidirect
17. C2×#13063309C4semidirect
72. C2×C4⋊Dic43C2×C4semidirect
85. C2×(C2×D43)⋊C4C2×C4semidirect
221. C22⋊C4×C43C22⋊C4semidirect
344. C2×Dic43#123semidirect
403. C2×#385D43semidirect
456. C43#13996semidirect
640. C22⋊C4(C2×D43)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#130633092
C2×#145827782
C2×#145827762
C2×#145827602
C2×C22⋊C4×Dic432
C22×C43⋊#952
#191328642
#191328372
#191328312
#191328242
C2×C43×#3852
#1399643