Finite Group Databasebeta

← #25140169

Subgroups — #25140169

Order 11008.

1168 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582902C211yesmaximal, characteristic, complemented
2#19137947C211yesmaximal, characteristic
3#19137520C211yesmaximal, characteristic, complemented
4#19136113C211yesmaximal, characteristic, complemented
5#19136011C211yesmaximal, characteristic, complemented
6#19135785C211yesmaximal, characteristic, complemented
7#19135781C211yesmaximal, characteristic, complemented
8#19135224C211yesmaximal, characteristic, complemented
9#19135214C211yesmaximal, characteristic, complemented
10#19134912C211yesmaximal, characteristic, complemented
11#19134889C211yesmaximal, characteristic, complemented
12#19134791C211yesmaximal, characteristic, complemented
13#19134629C211yesmaximal, characteristic, complemented
14#19134524C211yesmaximal, characteristic, complemented
15C2×C43×#480C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C2×#13063299C2211yescharacteristic
19C2×#13063293—21no—
20C2×C4×C22⋊D43C2211yescharacteristic
21C2×#13063283C2211yescharacteristic
22C2×#13063257C2211yescharacteristic, complemented
23C2×#13063256C2211yescharacteristic, complemented
24#14582902—24no—
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
32C2×(C2×D43)⋊C8C2211yescharacteristic
33#14582814—21no—
34#14582807—21no—
35#14582802C2211yescharacteristic
36#14582800C2211yescharacteristic
37#14582789—21no—
38#14582780—21no—
39#14582778—21no—
40#14582764C2211yescharacteristic, complemented
41#14582759C2211yescharacteristic, complemented
42#14582756C2211yescharacteristic
43#14582756C2211yescharacteristic
44#14582754—21no—
45C4⋊C4×Dic43C2211yescharacteristic, complemented
46C4×C22⋊Dic43—21no—
47#14582662C2211yescharacteristic, complemented
48#14582661C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582653C2211yescharacteristic, complemented
52#14582653C2211yescharacteristic, complemented
53C2×#121×C43C2211yescharacteristic
54C22×C4⋊C4×C43C2211yescharacteristic, complemented
55C43×#480—24no—
56C2×#107×C43C2211yescharacteristic, complemented
57C2×#107×C43C2211yescharacteristic, complemented
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic, complemented
61C24×D43—21no—
62C22×D172C2311yescharacteristic
63C22×C22⋊D43—21no—
64C22×C22⋊D43—21no—
65C22×C22⋊D43D411yescharacteristic
66C2×D4×D43—22no—
67C2×D4×D43—22no—
68C2×D4×D43—22no—
69C2×D4×D43—22no—
70C2×D4×D43—41no—
71C2×D4×D43—41no—
72C22×C4×D43C2311yescharacteristic
73C2×#10621872—22no—
74C2×#10621872—22no—
75C2×#10621872—41no—
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78#13063299—22no—
79#13063299—41no—
80#13063293—44no—
81C4×C22⋊D43—22no—
82C4×C22⋊D43—22no—
83#13063283—22no—
84#13063283—41no—
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×Dic43⋊C4D411yescharacteristic
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43D411yescharacteristic
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4D411yescharacteristic
100C2×C4×Dic43—21no—
101C2×C4×Dic43—21no—
102C2×C4×Dic43C2311yescharacteristic
103#13063257—41no—
104#13063256—41no—
105#13063247—22no—
106#13063247—22no—
107#13063246—22no—
108#13063246—41no—
109#13063245—22no—
110#13063245—41no—
111C22⋊(C43⋊C8)—41no—
112(C2×D43)⋊C8—22no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C22×D4×C43—21no—
120C22×D4×C43C2311yescharacteristic
121C23×C4×C43—21no—
122C23×C4×C43C2311yescharacteristic
123C22×C8×C43C2311yescharacteristic
124C22×C8×C43C2311yescharacteristic
125#121×C43—22no—
126#121×C43—41no—
127C2×C4⋊C4×C43—22no—
128C2×C4⋊C4×C43—21no—
129C2×C4⋊C4×C43—41no—
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C22⋊C4×C43—21no—
134#107×C43—22no—
135#107×C43—22no—
136#102×C43—22no—
137#102×C43D414yescomplemented
138C22⋊C8×C43—22no—
139C24×C43—21no—
140C24×C43C2×D411yescharacteristic
141C23×D43—21no—
142C23×D43—42no—
143C23×D43—42no—
144C23×D43—42no—
145C23×D43—42no—
146C23×D43—42no—
147C23×D43—81no—
148C23×D43—81no—
149C23×D43C2×D411yescharacteristic
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—42no—
156C2×D4×C43—42no—
157C2×D4×C43—81no—
158C2×D4×C43C2×D412yes—
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—21no—
168C22×C4×C43—42no—
169C22×C4×C43—42no—
170C22×C4×C43—81no—
171C22×C4×C43C2×D411yescharacteristic
172C22×C4×C43C2411yescharacteristic
173C2×C22⋊D43—22no—
174C2×C22⋊D43—22no—
175C2×C22⋊D43—41no—
176C2×C22⋊D43—42no—
177C2×C22⋊D43—42no—
178C2×C22⋊D43—42no—
179C2×C22⋊D43—42no—
180C2×C22⋊D43—42no—
181C2×C22⋊D43—81no—
182C22×Dic43—21no—
183C22×Dic43—21no—
184C22×Dic43—21no—
185C22×Dic43C2×D411yescharacteristic
186C22×Dic43C2×D411yescharacteristic
187C22×Dic43C2×D411yescharacteristic
188D4×D43—28no—
189D4×D43—44no—
190D4×D43—44no—
191D4×D43—44no—
192C2×D172—21no—
193C2×D172—21no—
194C2×D172—21no—
195C2×D172—21no—
196C2×D172—21no—
197C2×D172#4112yes—
198C2×C4×D43—21no—
199C2×C4×D43—21no—
200C2×C4×D43—21no—
201C2×C4×D43—21no—
202C2×C4×D43#4112yes—
203C2×C4×D43#4112yes—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43C2×D412yes—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43—42no—
216C4⋊C4×C43C2×D412yes—
217C22⋊C4×C43—42no—
218C22⋊Dic43—22no—
219C22⋊Dic43—42no—
220C22⋊Dic43—42no—
221C22⋊Dic43—81no—
222(C2×D43)⋊C4—22no—
223(C2×D43)⋊C4—42no—
224(C2×D43)⋊C4—42no—
225(C2×D43)⋊C4—42no—
226(C2×D43)⋊C4—42no—
227(C2×D43)⋊C4—81no—
228(C2×D43)⋊C4—81no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235Dic43⋊C4—22no—
236C4×Dic43—21no—
237C4×Dic43—21no—
238C4×Dic43—42no—
239C4×Dic43—81no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246#10621872—44no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—22no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43AGL(1,ℤ/8)12yes—
261C23×C43C22×D411yescharacteristic
262C22×D43—21no—
263C22×D43—21no—
264C22×D43—21no—
265C22×D43—21no—
266C22×D43—21no—
267C22×D43—21no—
268C22×D43—22no—
269C22×D43—48no—
270C22×D43—41no—
271C22×D43—41no—
272C22×D43—41no—
273C22×D43—41no—
274C22×D43—41no—
275C22×D43—41no—
276C22×D43—84no—
277C22×D43—84no—
278C22×D43—84no—
279C22×D43—84no—
280C22×D43—84no—
281C22×D43—84no—
282C22×D43#12312yes—
283D4×C43—22no—
284D4×C43—22no—
285D4×C43—41no—
286D4×C43—41no—
287D4×C43—84no—
288C2×C4×C43—21no—
289C2×C4×C43—22no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—41no—
304C2×C4×C43—84no—
305C2×C4×C43C22×D411yescharacteristic
306C2×C4×C43C2×#4111yescharacteristic
307C2×C4×C43C2×#4111yescharacteristic
308C2×C4×C43C2×#4111yescharacteristic
309C2×C4×C43H(5,𝔽2)11yescharacteristic
310C2×C4×C43H(5,𝔽2)11yescharacteristic
311C22⋊D43—48no—
312C22⋊D43—44no—
313C22⋊D43—84no—
314C2×Dic43—21no—
315C2×Dic43—21no—
316C2×Dic43—21no—
317C2×Dic43—21no—
318C2×Dic43—21no—
319C2×Dic43—21no—
320C2×Dic43—21no—
321C2×Dic43—21no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43#12312yes—
332D172—22no—
333D172—22no—
334D172—41no—
335D172—41no—
336C4×D43—22no—
337C4×D43—22no—
338C4×D43—22no—
339C4×D43—22no—
340C8×C43—22no—
341C8×C43—41no—
342C43⋊C8—41no—
343C43⋊C8—41no—
344#24882—431nomaximal, Sylow
345C22×C43—22no—
346C22×C43—22no—
347C22×C43—22no—
348C22×C43—41no—
349C22×C43—41no—
350C22×C43—41no—
351C22×C43—41no—
352C22×C43—42no—
353C22×C43—42no—
354C22×C43—42no—
355C22×C43—81no—
356C22×C43—81no—
357C22×C43—81no—
358C22×C43—81no—
359C22×C43C2×#12311yescharacteristic
360C22×C43D4211yescharacteristic
361C22×C43#54611yescharacteristic
362C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
363C22×C43#57511yescharacteristic
364C22×C43#57611yescharacteristic
365C22×C43#57711yescharacteristic
366C2×D43—22no—
367C2×D43—22no—
368C2×D43—22no—
369C2×D43—41no—
370C2×D43—41no—
371C2×D43—41no—
372C2×D43—41no—
373C2×D43—42no—
374C2×D43—42no—
375C2×D43—42no—
376C2×D43—816no—
377C2×D43—81no—
378C2×D43—81no—
379C2×D43—81no—
380C2×D43—81no—
381C4×C43—41no—
382C4×C43—42no—
383C4×C43—81no—
384C4×C43—81no—
385C4×C43#52511yescharacteristic
386C4×C43#53811yescharacteristic
387C4×C43#54611yescharacteristic
388C4×C43#55111yescharacteristic
389Dic43—22no—
390Dic43—41no—
391Dic43—41no—
392Dic43—81no—
393Dic43—81no—
394Dic43—81no—
395C2×#480D4311yescharacteristic, complemented
396C2×#418—431no—
397#2408—431no—
398#2352—431no—
399#2092—431no—
400#2073—431no—
401#2034—431no—
402#2034—431no—
403#1926—431no—
404#1925—431no—
405#1874—431no—
406#1870—431no—
407#1854—431no—
408#1809—431no—
409#1786—431no—
410C2×C43—42no—
411C2×C43—82no—
412C2×C43#241811yescharacteristic
413C2×C43#309411yescharacteristic
414C2×C43#309611yescharacteristic
415C2×C43#326411yescharacteristic
416C2×C43#327511yescharacteristic
417C2×C43#331011yescharacteristic
418C2×C43#332211yescharacteristic
419D43—42no—
420D43—82no—
421C23×D4—431no—
422C22×M16—431no—
423C2×#121—431no—
424C2×#121C2×D4311yescharacteristic
425C2×#120—861no—
426C2×C4×D4—431no—
427C2×#117—431no—
428C22×C4⋊C4C2×D4311yescharacteristic, complemented
429#480—24no—
430C2×#107C2×D4311yescharacteristic, complemented
431C2×#107C2×D4311yescharacteristic, complemented
432C2×#106—431no—
433C2×#106—431no—
434#418—864no—
435C2×#102—431no—
436C2×#102—431no—
437C2×#102—431no—
438C2×#102—431no—
439C2×#102—431no—
440C2×#102—431no—
441C2×#102C2×D4311yescharacteristic
442C2×#102C2×D4311yescharacteristic
443C2×C22⋊C8—431no—
444C2×C22⋊C8—431no—
445C2×C22⋊C8C2×D4311yescharacteristic, complemented
446#394—861no—
447#392—861no—
448#390—431no—
449#390—431no—
450#388—861no—
451#387—861no—
452#386—861no—
453#382—431no—
454#380—431no—
455#380—431no—
456#380—431no—
457#379—861no—
458C4×C4⋊C4—431no—
459C4×C22⋊C4—861no—
460#340—431no—
461#340—431no—
462#340—431no—
463#340—431no—
464#336—431no—
465#336—431no—
466C43#2488211yescharacteristic, complemented, Sylow
467C25—861no—
468C22×D4—21no—
469C22×D4—431no—
470C22×D4—431no—
471C22×D4—862no—
472C22×D4—862no—
473C22×D4—861no—
474C22×D4—862no—
475C22×D4—862no—
476C22×D4—861no—
477C22×D4—1721no—
478C22×D4—1721no—
479C22×D4C22×D4311yescharacteristic
480C23×C4—21no—
481C23×C4—431no—
482C23×C4C22×D4311yescharacteristic
483C2×M16—862no—
484C2×M16—862no—
485C2×M16—1721no—
486C22×C8—431no—
487C22×C8—431no—
488C22×C8C22×D4311yescharacteristic
489C22×C8C22×D4311yescharacteristic
490#121—22no—
491#121—41no—
492#121—862no—
493#121—1721no—
494#120—1724no—
495C4×D4—862no—
496C4×D4—862no—
497#117—862no—
498#117—1721no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—41no—
502C2×C4⋊C4—431no—
503C2×C4⋊C4—431no—
504C2×C4⋊C4—431no—
505C2×C4⋊C4—431no—
506C2×C4⋊C4C22×D4311yescharacteristic
507C2×C4⋊C4C22×D4311yescharacteristic
508C2×C4⋊C4C22×D4311yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—431no—
511C2×C22⋊C4—431no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C22⋊C4—861no—
515C2×C22⋊C4—861no—
516C2×C22⋊C4—861no—
517C2×C22⋊C4—861no—
518C2×C22⋊C4—861no—
519C2×C22⋊C4—861no—
520C2×C22⋊C4—861no—
521C2×C42—431no—
522C2×C42—861no—
523C2×C42—861no—
524#107—22no—
525#107—22no—
526#106—1721no—
527#106—1721no—
528#102—22no—
529#102—862no—
530#102—862no—
531#102—862no—
532#102—862no—
533#102—1721no—
534#102—1721no—
535#102C22⋊D4314yescomplemented
536C22⋊C8—22no—
537C22⋊C8—862no—
538C22⋊C8—1721no—
539#95—861no—
540#95—861no—
541#95—861no—
542#95—861no—
543#95—861no—
544#95—861no—
545C24—21no—
546C24—431no—
547C24—861no—
548C24—3441no—
549C24—3441no—
550C24—1722no—
551C24—1722no—
552C24—1722no—
553C24—1722no—
554C24—1722no—
555C24D4×D4311yescharacteristic
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—81no—
564C2×D4—432no—
565C2×D4—868no—
566C2×D4—862no—
567C2×D4—862no—
568C2×D4—861no—
569C2×D4—861no—
570C2×D4—861no—
571C2×D4—861no—
572C2×D4—861no—
573C2×D4—3441no—
574C2×D4—1722no—
575C2×D4—1724no—
576C2×D4—1724no—
577C2×D4—1724no—
578C2×D4—1721no—
579C2×D4—1722no—
580C2×D4—1722no—
581C2×D4—1722no—
582C2×D4—1722no—
583C2×D4C2×C22⋊D4312yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—81no—
596C22×C4—431no—
597C22×C4—432no—
598C22×C4—432no—
599C22×C4—431no—
600C22×C4—431no—
601C22×C4—861no—
602C22×C4—861no—
603C22×C4—861no—
604C22×C4—861no—
605C22×C4—861no—
606C22×C4—861no—
607C22×C4—861no—
608C22×C4D4×D4311yescharacteristic
609C22×C4C23×D4311yescharacteristic
610M16—1724no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—861no—
617C2×C8—861no—
618C2×C8—861no—
619C2×C8—861no—
620C2×C8—861no—
621C2×C8—861no—
622C2×C8C2×C22⋊D4312yes—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—42no—
629C4⋊C4—862no—
630C4⋊C4—861no—
631C4⋊C4—861no—
632C4⋊C4—861no—
633C4⋊C4—861no—
634C4⋊C4—861no—
635C4⋊C4—861no—
636C4⋊C4C2×C22⋊D4312yes—
637C22⋊C4—42no—
638C22⋊C4—862no—
639C22⋊C4—862no—
640C22⋊C4—3441no—
641C22⋊C4—3441no—
642C22⋊C4—3441no—
643C22⋊C4—1722no—
644C22⋊C4—1722no—
645C22⋊C4—1722no—
646C22⋊C4—1722no—
647C22⋊C4—1722no—
648C22⋊C4—1722no—
649C42—861no—
650C42—861no—
651C42—3441no—
652C42—1722no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—22no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—432no—
667C23—861no—
668C23—861no—
669C23—861no—
670C23—861no—
671C23—861no—
672C23—861no—
673C23—862no—
674C23—3444no—
675C23—3444no—
676C23—3444no—
677C23—3444no—
678C23—3444no—
679C23—3444no—
680C23—1728no—
681C23—1721no—
682C23—1721no—
683C23—1721no—
684C23—1721no—
685C23—1721no—
686C23—1721no—
687C23#1306334912yes—
688C23C2×D4×D4311yescharacteristic
689D4—22no—
690D4—22no—
691D4—41no—
692D4—41no—
693D4—84no—
694D4—862no—
695D4—862no—
696D4—3444no—
697D4—1728no—
698D4—1724no—
699D4—1721no—
700D4—1721no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—84no—
718C2×C4—432no—
719C2×C4—861no—
720C2×C4—861no—
721C2×C4—862no—
722C2×C4—862no—
723C2×C4—862no—
724C2×C4—862no—
725C2×C4—861no—
726C2×C4—861no—
727C2×C4—861no—
728C2×C4—861no—
729C2×C4—861no—
730C2×C4—861no—
731C2×C4—1721no—
732C2×C4—1721no—
733C2×C4—1721no—
734C2×C4—1721no—
735C2×C4—1721no—
736C2×C4—1721no—
737C2×C4—1721no—
738C2×C4—1721no—
739C2×C4—1721no—
740C2×C4C22×C22⋊D4311yescharacteristic
741C2×C4#41×D4311yescharacteristic
742C2×C4#41×D4311yescharacteristic
743C2×C4#41×D4311yescharacteristic
744C2×C4#1306337011yescharacteristic
745C2×C4#1306337111yescharacteristic
746C8—22no—
747C8—41no—
748C8—1721no—
749C8—1721no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—862no—
765C22—862no—
766C22—862no—
767C22—34416no—
768C22—3441no—
769C22—3441no—
770C22—3441no—
771C22—3441no—
772C22—1722no—
773C22—1722no—
774C22—1722no—
775C22—1721no—
776C22—1721no—
777C22—1721no—
778C22—1721no—
779C22#123×D4311yescharacteristic
780C22D4×C22⋊D4311yescharacteristic
781C22#1458354111yescharacteristic
782C22C2×#1306334911yescharacteristic
783C22#1458369811yescharacteristic
784C22#1458370011yescharacteristic
785C22#1458370811yescharacteristic
786C4—41no—
787C4—42no—
788C4—81no—
789C4—81no—
790C4—862no—
791C4—3441no—
792C4—3441no—
793C4—3441no—
794C4—1721no—
795C4—1721no—
796C4#1458340611yescharacteristic
797C4#1458348511yescharacteristic
798C4#1458353711yescharacteristic
799C4#1458357711yescharacteristic
800C2—42no—
801C2—82no—
802C2—3442no—
803C2—1722no—
804C2#1913805411yescharacteristic
805C2#1914453011yescharacteristic
806C2#1914454611yescharacteristic
807C2#1914607511yescharacteristic
808C2#1914622011yescharacteristic
809C2#1914661411yescharacteristic
810C2#1914679911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#480C2
socleC23×C43C22×D4
prime radical#19137947C2
hypercenterC2×#480D43
hypocenterC43#24882
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
1. C2×#14582902C2semidirect
3. #19137520C2semidirect
4. #19136113C2semidirect
5. #19136011C2semidirect
6. #19135785C2semidirect
7. #19135781C2semidirect
8. #19135224C2semidirect
9. #19135214C2semidirect
10. #19134912C2semidirect
11. #19134889C2semidirect
12. #19134791C2semidirect
13. #19134629C2semidirect
14. #19134524C2semidirect
15. C2×C43×#480C2semidirect
22. C2×#13063257C22semidirect
23. C2×#13063256C22semidirect
31. C2×C22⋊(C43⋊C8)C22semidirect
40. #14582764C22semidirect
41. #14582759C22semidirect
45. C4⋊C4×Dic43C22semidirect
47. #14582662C22semidirect
48. #14582661C22semidirect
49. #14582661C22semidirect
50. #14582661C22semidirect
51. #14582653C22semidirect
52. #14582653C22semidirect
54. C22×C4⋊C4×C43C22semidirect
56. C2×#107×C43C22semidirect
57. C2×#107×C43C22semidirect
60. C2×C22⋊C8×C43C22semidirect
137. #102×C43D4semidirect
395. C2×#480D43semidirect
428. C22×C4⋊C4C2×D43semidirect
430. C2×#107C2×D43semidirect
431. C2×#107C2×D43semidirect
445. C2×C22⋊C8C2×D43semidirect
466. C43#24882semidirect
535. #102C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145829022
#191379472
#191375202
#191361132
#191360112
#191357852
#191357812
#191352242
#191352142
#191349122
#191348892
#191347912
#191346292
#191345242
C2×C43×#4802
#2488243