Finite Group Databasebeta

← #25140229

Subgroups — #25140229

Order 11008.

1154 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582902C211yesmaximal, characteristic, complemented
2#19137947C211yesmaximal, characteristic
3#19137545C211yesmaximal, characteristic, complemented
4#19136125C211yesmaximal, characteristic, complemented
5#19136001C211yesmaximal, characteristic, complemented
6#19135781C211yesmaximal, characteristic, complemented
7#19135778C211yesmaximal, characteristic, complemented
8#19135217C211yesmaximal, characteristic, complemented
9#19135214C211yesmaximal, characteristic, complemented
10#19134917C211yesmaximal, characteristic, complemented
11#19134889C211yesmaximal, characteristic, complemented
12#19134791C211yesmaximal, characteristic, complemented
13#19134625C211yesmaximal, characteristic, complemented
14#19134524C211yesmaximal, characteristic, complemented
15C2×C43×#482C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C2×#13063299C2211yescharacteristic
19C2×#13063293—21no—
20C2×C4×C22⋊D43C2211yescharacteristic
21C2×#13063283C2211yescharacteristic
22C2×#13063259C2211yescharacteristic, 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#14582799—21no—
38#14582790—21no—
39#14582787—21no—
40#14582768C2211yescharacteristic, complemented
41#14582759C2211yescharacteristic, complemented
42#14582756C2211yescharacteristic
43#14582756C2211yescharacteristic
44#14582754—21no—
45C4⋊C4×Dic43C2211yescharacteristic, complemented
46C4×Dic43⋊C4—21no—
47#14582662C2211yescharacteristic, complemented
48#14582661C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582653C2211yescharacteristic, complemented
52#14582653C2211yescharacteristic, complemented
53C2×#121×C43C2211yescharacteristic
54C2×#117×C43C2211yescharacteristic, complemented
55C43×#482—24no—
56C2×#107×C43C2211yescharacteristic, complemented
57C2×#106×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⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4D411yescharacteristic
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×C22⋊Dic43—21no—
94C2×C22⋊Dic43D411yescharacteristic
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4D411yescharacteristic
102C2×C4×Dic43—21no—
103C2×C4×Dic43—21no—
104C2×C4×Dic43C2311yescharacteristic
105#13063259—41no—
106#13063256—41no—
107#13063247—22no—
108#13063247—22no—
109#13063246—22no—
110#13063246—41no—
111#13063245—22no—
112#13063245—41no—
113C22⋊(C43⋊C8)—41no—
114(C2×D43)⋊C8—22no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C22×D4×C43—21no—
120C22×D4×C43C2311yescharacteristic
121C23×C4×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123C22×C8×C43C2311yescharacteristic
124#121×C43—22no—
125#121×C43—41no—
126#117×C43—22no—
127#117×C43—41no—
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43—21no—
133C2×C42×C43—21no—
134#107×C43—22no—
135#106×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×C43C2×D411yescharacteristic
169C22×C4×C43C2411yescharacteristic
170C2×C22⋊D43—22no—
171C2×C22⋊D43—22no—
172C2×C22⋊D43—41no—
173C2×C22⋊D43—42no—
174C2×C22⋊D43—42no—
175C2×C22⋊D43—42no—
176C2×C22⋊D43—42no—
177C2×C22⋊D43—42no—
178C2×C22⋊D43—81no—
179C22×Dic43—21no—
180C22×Dic43—21no—
181C22×Dic43—21no—
182C22×Dic43C2×D411yescharacteristic
183C22×Dic43C2×D411yescharacteristic
184C22×Dic43C2×D411yescharacteristic
185D4×D43—28no—
186D4×D43—44no—
187D4×D43—44no—
188D4×D43—44no—
189C2×D172—21no—
190C2×D172—21no—
191C2×D172—21no—
192C2×D172—21no—
193C2×D172—21no—
194C2×D172#4112yes—
195C2×C4×D43—21no—
196C2×C4×D43—21no—
197C2×C4×D43—21no—
198C2×C4×D43—21no—
199C2×C4×D43#4112yes—
200C2×C4×D43#4112yes—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43C2×D412yes—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43C2×D412yes—
213C22⋊C4×C43—42no—
214C22⋊C4×C43—42no—
215C42×C43—42no—
216C22⋊Dic43—22no—
217C22⋊Dic43—42no—
218C22⋊Dic43—81no—
219C22⋊Dic43—81no—
220(C2×D43)⋊C4—22no—
221(C2×D43)⋊C4—42no—
222(C2×D43)⋊C4—42no—
223(C2×D43)⋊C4—42no—
224(C2×D43)⋊C4—42no—
225(C2×D43)⋊C4—81no—
226(C2×D43)⋊C4—81no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233Dic43⋊C4—22no—
234Dic43⋊C4—42no—
235Dic43⋊C4—81no—
236C4×Dic43—21no—
237C4×Dic43—21no—
238C4×Dic43—42no—
239C4×Dic43—42no—
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—22no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
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×C43C22×D411yescharacteristic
305C2×C4×C43C2×#4111yescharacteristic
306C2×C4×C43C2×#4111yescharacteristic
307C2×C4×C43C2×#4111yescharacteristic
308C2×C4×C43H(5,𝔽2)11yescharacteristic
309C2×C4×C43H(5,𝔽2)11yescharacteristic
310C22⋊D43—44no—
311C22⋊D43—48no—
312C22⋊D43—84no—
313C2×Dic43—21no—
314C2×Dic43—21no—
315C2×Dic43—21no—
316C2×Dic43—21no—
317C2×Dic43—21no—
318C2×Dic43—21no—
319C2×Dic43—21no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43#12312yes—
330C2×Dic43AGL(1,ℤ/8)12yes—
331D172—22no—
332D172—22no—
333D172—41no—
334D172—41no—
335C4×D43—22no—
336C4×D43—22no—
337C4×D43—22no—
338C4×D43—22no—
339C8×C43—22no—
340C8×C43—41no—
341C43⋊C8—41no—
342C43⋊C8—41no—
343#24886—431nomaximal, Sylow
344C22×C43—41no—
345C22×C43—41no—
346C22×C43—42no—
347C22×C43—41no—
348C22×C43—42no—
349C22×C43—41no—
350C22×C43—42no—
351C22×C43—41no—
352C22×C43—41no—
353C22×C43—41no—
354C22×C43—81no—
355C22×C43—81no—
356C22×C43—81no—
357C22×C43—81no—
358C22×C43C2×#12311yescharacteristic
359C22×C43D4211yescharacteristic
360C22×C43#54611yescharacteristic
361C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
362C22×C43#57511yescharacteristic
363C22×C43#57611yescharacteristic
364C22×C43#57711yescharacteristic
365C2×D43—22no—
366C2×D43—22no—
367C2×D43—22no—
368C2×D43—41no—
369C2×D43—41no—
370C2×D43—41no—
371C2×D43—41no—
372C2×D43—42no—
373C2×D43—42no—
374C2×D43—42no—
375C2×D43—816no—
376C2×D43—81no—
377C2×D43—81no—
378C2×D43—81no—
379C2×D43—81no—
380C4×C43—41no—
381C4×C43—42no—
382C4×C43—81no—
383C4×C43—81no—
384C4×C43#52511yescharacteristic
385C4×C43#53811yescharacteristic
386C4×C43#54611yescharacteristic
387C4×C43#55111yescharacteristic
388Dic43—22no—
389Dic43—22no—
390Dic43—41no—
391Dic43—81no—
392Dic43—81no—
393Dic43—81no—
394C2×#482D4311yescharacteristic, complemented
395C2×#418—431no—
396#2408—431no—
397#2354—431no—
398#2094—431no—
399#2071—431no—
400#2034—431no—
401#2033—431no—
402#1925—431no—
403#1925—431no—
404#1875—431no—
405#1870—431no—
406#1854—431no—
407#1809—431no—
408#1786—431no—
409C2×C43—82no—
410C2×C43—81no—
411C2×C43#241811yescharacteristic
412C2×C43#309411yescharacteristic
413C2×C43#309611yescharacteristic
414C2×C43#326811yescharacteristic
415C2×C43#327211yescharacteristic
416C2×C43#331111yescharacteristic
417C2×C43#332511yescharacteristic
418D43—42no—
419D43—82no—
420C23×D4—431no—
421C22×M16—431no—
422C2×#121—431no—
423C2×#121C2×D4311yescharacteristic
424C2×#120—861no—
425C2×C4×D4—431no—
426C2×#117—431no—
427C2×#117C2×D4311yescharacteristic, complemented
428#482—24no—
429C2×#107—431no—
430C2×#107C2×D4311yescharacteristic, complemented
431C2×#106—431no—
432C2×#106C2×D4311yescharacteristic, complemented
433#418—864no—
434C2×#102—431no—
435C2×#102—431no—
436C2×#102—431no—
437C2×#102—431no—
438C2×#102—431no—
439C2×#102—431no—
440C2×#102C2×D4311yescharacteristic
441C2×#102C2×D4311yescharacteristic
442C2×C22⋊C8—431no—
443C2×C22⋊C8—431no—
444C2×C22⋊C8C2×D4311yescharacteristic, complemented
445#394—861no—
446#392—861no—
447#390—431no—
448#390—431no—
449#390—861no—
450#388—861no—
451#388—861no—
452#384—431no—
453#380—431no—
454#380—431no—
455#380—431no—
456#379—861no—
457C4×C4⋊C4—431no—
458C4×C4⋊C4—861no—
459#340—431no—
460#340—431no—
461#340—431no—
462#340—431no—
463#336—431no—
464#336—431no—
465C43#2488611yescharacteristic, complemented, Sylow
466C25—861no—
467C22×D4—21no—
468C22×D4—431no—
469C22×D4—431no—
470C22×D4—862no—
471C22×D4—862no—
472C22×D4—861no—
473C22×D4—862no—
474C22×D4—862no—
475C22×D4—861no—
476C22×D4—1721no—
477C22×D4—1721no—
478C22×D4C22×D4311yescharacteristic
479C23×C4—431no—
480C23×C4C22×D4311yescharacteristic
481C2×M16—862no—
482C2×M16—862no—
483C2×M16—1721no—
484C22×C8—431no—
485C22×C8—431no—
486C22×C8C22×D4311yescharacteristic
487C22×C8C22×D4311yescharacteristic
488#121—22no—
489#121—41no—
490#121—862no—
491#121—1721no—
492#120—1724no—
493C4×D4—862no—
494C4×D4—862no—
495#117—22no—
496#117—41no—
497#117—862no—
498#117—1721no—
499C2×C4⋊C4—431no—
500C2×C4⋊C4—431no—
501C2×C4⋊C4—431no—
502C2×C4⋊C4—431no—
503C2×C4⋊C4—861no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4C22×D4311yescharacteristic
506C2×C4⋊C4C22×D4311yescharacteristic
507C2×C4⋊C4C22×D4311yescharacteristic
508C2×C22⋊C4—21no—
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—21no—
522C2×C42—431no—
523C2×C42—861no—
524C2×C42—861no—
525#107—22no—
526#107—1721no—
527#106—22no—
528#106—1721no—
529#102—22no—
530#102—862no—
531#102—862no—
532#102—862no—
533#102—862no—
534#102—1721no—
535#102—1721no—
536#102C22⋊D4314yescomplemented
537C22⋊C8—22no—
538C22⋊C8—862no—
539C22⋊C8—1721no—
540#95—861no—
541#95—861no—
542#95—861no—
543#95—861no—
544C24—21no—
545C24—431no—
546C24—861no—
547C24—3441no—
548C24—3441no—
549C24—1722no—
550C24—1722no—
551C24—1722no—
552C24—1722no—
553C24—1722no—
554C24D4×D4311yescharacteristic
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—81no—
563C2×D4—432no—
564C2×D4—862no—
565C2×D4—868no—
566C2×D4—862no—
567C2×D4—861no—
568C2×D4—861no—
569C2×D4—861no—
570C2×D4—861no—
571C2×D4—861no—
572C2×D4—3441no—
573C2×D4—1722no—
574C2×D4—1724no—
575C2×D4—1724no—
576C2×D4—1724no—
577C2×D4—1721no—
578C2×D4—1722no—
579C2×D4—1722no—
580C2×D4—1722no—
581C2×D4—1722no—
582C2×D4C2×C22⋊D4312yes—
583C22×C4—21no—
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—431no—
593C22×C4—431no—
594C22×C4—432no—
595C22×C4—432no—
596C22×C4—431no—
597C22×C4—861no—
598C22×C4—861no—
599C22×C4—861no—
600C22×C4—861no—
601C22×C4—861no—
602C22×C4—861no—
603C22×C4—861no—
604C22×C4D4×D4311yescharacteristic
605C22×C4C23×D4311yescharacteristic
606M16—1724no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—861no—
613C2×C8—861no—
614C2×C8—861no—
615C2×C8—861no—
616C2×C8—861no—
617C2×C8—861no—
618C2×C8C2×C22⋊D4312yes—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—862no—
625C4⋊C4—861no—
626C4⋊C4—861no—
627C4⋊C4—861no—
628C4⋊C4—861no—
629C4⋊C4—861no—
630C4⋊C4—861no—
631C4⋊C4—3441no—
632C4⋊C4—1722no—
633C4⋊C4C2×C22⋊D4312yes—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—862no—
637C22⋊C4—862no—
638C22⋊C4—3441no—
639C22⋊C4—3441no—
640C22⋊C4—3441no—
641C22⋊C4—3441no—
642C22⋊C4—1722no—
643C22⋊C4—1722no—
644C22⋊C4—1722no—
645C22⋊C4—1722no—
646C22⋊C4—1722no—
647C42—42no—
648C42—861no—
649C42—861no—
650C42—1722no—
651C42—1722no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—22no—
659C23—21no—
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—
687C23C2×D4×D4311yescharacteristic
688D4—22no—
689D4—22no—
690D4—41no—
691D4—41no—
692D4—84no—
693D4—862no—
694D4—862no—
695D4—3444no—
696D4—1724no—
697D4—1728no—
698D4—1721no—
699D4—1721no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—41no—
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—432no—
717C2×C4—432no—
718C2×C4—861no—
719C2×C4—861no—
720C2×C4—861no—
721C2×C4—861no—
722C2×C4—862no—
723C2×C4—862no—
724C2×C4—862no—
725C2×C4—862no—
726C2×C4—861no—
727C2×C4—861no—
728C2×C4—861no—
729C2×C4—1721no—
730C2×C4—1721no—
731C2×C4—1721no—
732C2×C4—1721no—
733C2×C4—1721no—
734C2×C4—1721no—
735C2×C4—1721no—
736C2×C4—1721no—
737C2×C4—1721no—
738C2×C4C22×C22⋊D4311yescharacteristic
739C2×C4#41×D4311yescharacteristic
740C2×C4#41×D4311yescharacteristic
741C2×C4#41×D4311yescharacteristic
742C2×C4#1306337011yescharacteristic
743C2×C4#1306337111yescharacteristic
744C8—22no—
745C8—41no—
746C8—1721no—
747C8—1721no—
748C22—41no—
749C22—42no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—42no—
756C22—41no—
757C22—42no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—862no—
763C22—862no—
764C22—862no—
765C22—34416no—
766C22—3441no—
767C22—3441no—
768C22—3441no—
769C22—3441no—
770C22—1722no—
771C22—1722no—
772C22—1722no—
773C22—1721no—
774C22—1721no—
775C22—1721no—
776C22—1721no—
777C22#123×D4311yescharacteristic
778C22D4×C22⋊D4311yescharacteristic
779C22#1458354111yescharacteristic
780C22AGL(1,ℤ/8)×D4311yescharacteristic
781C22#1458369611yescharacteristic
782C22#1458370111yescharacteristic
783C22#1458370911yescharacteristic
784C4—41no—
785C4—42no—
786C4—81no—
787C4—81no—
788C4—862no—
789C4—862no—
790C4—3441no—
791C4—3441no—
792C4—3441no—
793C4—1721no—
794C4#1458340611yescharacteristic
795C4#1458348511yescharacteristic
796C4#1458353711yescharacteristic
797C4#1458357711yescharacteristic
798C2—81no—
799C2—82no—
800C2—3442no—
801C2—1722no—
802C2#1913805411yescharacteristic
803C2#1914453411yescharacteristic
804C2#1914455011yescharacteristic
805C2#1914613511yescharacteristic
806C2#1914618911yescharacteristic
807C2#1914662911yescharacteristic
808C2#1914683511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#482C2
socleC23×C43C22×D4
prime radical#19137947C2
hypercenterC2×#482D43
hypocenterC43#24886
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
1. C2×#14582902C2semidirect
3. #19137545C2semidirect
4. #19136125C2semidirect
5. #19136001C2semidirect
6. #19135781C2semidirect
7. #19135778C2semidirect
8. #19135217C2semidirect
9. #19135214C2semidirect
10. #19134917C2semidirect
11. #19134889C2semidirect
12. #19134791C2semidirect
13. #19134625C2semidirect
14. #19134524C2semidirect
15. C2×C43×#482C2semidirect
22. C2×#13063259C22semidirect
23. C2×#13063256C22semidirect
31. C2×C22⋊(C43⋊C8)C22semidirect
40. #14582768C22semidirect
41. #14582759C22semidirect
45. C4⋊C4×Dic43C22semidirect
47. #14582662C22semidirect
48. #14582661C22semidirect
49. #14582661C22semidirect
50. #14582661C22semidirect
51. #14582653C22semidirect
52. #14582653C22semidirect
54. C2×#117×C43C22semidirect
56. C2×#107×C43C22semidirect
57. C2×#106×C43C22semidirect
60. C2×C22⋊C8×C43C22semidirect
137. #102×C43D4semidirect
394. C2×#482D43semidirect
427. C2×#117C2×D43semidirect
430. C2×#107C2×D43semidirect
432. C2×#106C2×D43semidirect
444. C2×C22⋊C8C2×D43semidirect
465. C43#24886semidirect
536. #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
#191375452
#191361252
#191360012
#191357812
#191357782
#191352172
#191352142
#191349172
#191348892
#191347912
#191346252
#191345242
C2×C43×#4822
#2488643