Finite Group Databasebeta

← #25140116

Subgroups — #25140116

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×#14583216C211yesmaximal, characteristic, complemented
2C2×#14582904C211yesmaximal, characteristic, complemented
3#19137945C211yesmaximal, characteristic
4#19137517C211yesmaximal, characteristic, complemented
5#19136114C211yesmaximal, characteristic, complemented
6#19136011C211yesmaximal, characteristic, complemented
7#19135776C211yesmaximal, characteristic, complemented
8#19135775C211yesmaximal, characteristic, complemented
9#19135224C211yesmaximal, characteristic, complemented
10#19135218C211yesmaximal, characteristic, complemented
11#19134909C211yesmaximal, characteristic, complemented
12#19134890C211yesmaximal, characteristic, complemented
13#19134796C211yesmaximal, characteristic, complemented
14#19134626C211yesmaximal, characteristic, complemented
15C43×#1786C211yesmaximal, characteristic, complemented
16C22×#10621877C2211yescharacteristic
17C2×#13063296C2211yescharacteristic
18C2×#13063296C2211yescharacteristic
19C2×#13063294—21no—
20C2×C4×C22⋊D43C2211yescharacteristic
21C2×#13063284C2211yescharacteristic
22C2×C4⋊C4×D43C2211yescharacteristic, complemented
23#14583216—24no—
24C2×#13063259C2211yescharacteristic, complemented
25C2×#13063258C2211yescharacteristic, complemented
26C2×#13063257C2211yescharacteristic, complemented
27C2×#13063256C2211yescharacteristic, complemented
28#14582904—24no—
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
34C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
35#14582813—21no—
36#14582807—21no—
37#14582802C2211yescharacteristic
38#14582802C2211yescharacteristic
39#14582787—21no—
40#14582781—21no—
41#14582775—21no—
42#14582764C2211yescharacteristic, complemented
43#14582759C2211yescharacteristic
44#14582756C2211yescharacteristic, complemented
45#14582755—21no—
46C4⋊C4×Dic43C2211yescharacteristic, complemented
47#14582746—21no—
48#14582662C2211yescharacteristic, complemented
49#14582662C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582661C2211yescharacteristic, complemented
52#14582653C2211yescharacteristic, complemented
53#14582653C2211yescharacteristic, complemented
54C23×D4×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C43×#380C2211yescharacteristic
61C22×C22⋊D43—21no—
62C22×C22⋊D43—21no—
63C22×C22⋊D43D411yescharacteristic
64C22×C4×D43—21no—
65C22×C4×D43C2311yescharacteristic
66C2×#10621877—22no—
67C2×#10621877—22no—
68C2×#10621877—41no—
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71#13063296—22no—
72#13063296—22no—
73#13063296—41no—
74#13063296—41no—
75#13063294—44no—
76C4×C22⋊D43—22no—
77C4×C22⋊D43—22no—
78#13063284—22no—
79#13063284—41no—
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4D411yescharacteristic
86C4⋊C4×D43—22no—
87C4⋊C4×D43—41no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×C22⋊Dic43—21no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—21no—
96C2×C22⋊Dic43D411yescharacteristic
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4D411yescharacteristic
99C2×C4×Dic43—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43C2311yescharacteristic
102#13063259—41no—
103#13063258—41no—
104#13063257—22no—
105#13063256—22no—
106#13063246—22no—
107#13063246—22no—
108#13063246—22no—
109#13063246D414yescomplemented
110(C2×D43)⋊C8—22no—
111(C2×D43)⋊C8—41no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C25×C43—21no—
118C22×D4×C43—22no—
119C22×D4×C43—22no—
120C22×D4×C43—21no—
121C22×D4×C43—22no—
122C22×D4×C43—22no—
123C22×D4×C43—41no—
124C22×D4×C43—41no—
125C22×D4×C43C2311yescharacteristic
126C22×D4×C43C2311yescharacteristic
127C23×C4×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129C22×C8×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C22⋊C4×C43—21no—
133#102×C43—22no—
134#102×C43—22no—
135#102×C43—41no—
136#102×C43—41no—
137C22⋊C8×C43—22no—
138#95×C43—21no—
139C24×C43—21no—
140C24×C43—21no—
141C24×C43—42no—
142C24×C43—42no—
143C24×C43—42no—
144C24×C43—42no—
145C24×C43—42no—
146C24×C43—81no—
147C24×C43—81no—
148C24×C43C2×D411yescharacteristic
149C23×D43C2×D411yescharacteristic
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—28no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—42no—
162C2×D4×C43—42no—
163C2×D4×C43—44no—
164C2×D4×C43—44no—
165C2×D4×C43—44no—
166C2×D4×C43—42no—
167C2×D4×C43C2×D412yes—
168C2×D4×C43#4112yes—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43#4112yes—
177C22×C4×C43#4112yes—
178C22×C4×C43C2411yescharacteristic
179C2×C22⋊D43—22no—
180C2×C22⋊D43—22no—
181C2×C22⋊D43—41no—
182C2×C22⋊D43—42no—
183C2×C22⋊D43—42no—
184C2×C22⋊D43—42no—
185C2×C22⋊D43—42no—
186C2×C22⋊D43—81no—
187C2×C22⋊D43—81no—
188C22×Dic43—21no—
189C22×Dic43—21no—
190C22×Dic43—21no—
191C22×Dic43—21no—
192C22×Dic43C2×D411yescharacteristic
193C22×Dic43C2×D411yescharacteristic
194C22×Dic43C2×D411yescharacteristic
195C2×C4×D43—21no—
196C2×C4×D43—21no—
197C2×C4×D43—21no—
198C2×C4×D43—21no—
199C2×C4×D43—21no—
200C2×C4×D43—21no—
201C2×C4×D43—42no—
202C2×C4×D43—42no—
203C2×C4×D43—81no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—21no—
214C22⋊C4×C43—81no—
215C22⋊Dic43—22no—
216C22⋊Dic43—42no—
217C22⋊Dic43—42no—
218C22⋊Dic43—42no—
219C22⋊Dic43—42no—
220C22⋊Dic43—42no—
221C22⋊Dic43—42no—
222C22⋊Dic43—81no—
223C22⋊Dic43—81no—
224(C2×D43)⋊C4—22no—
225(C2×D43)⋊C4—42no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43C2×D412yes—
234Dic43⋊C4—22no—
235Dic43⋊C4—42no—
236C4×Dic43—21no—
237C4×Dic43—21no—
238C4×Dic43—42no—
239C4×Dic43—81no—
240#10621877—44no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8C2×D412yes—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—22no—
254C23×C43—22no—
255C23×C43—48no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—84no—
269C23×C43—84no—
270C23×C43—84no—
271C23×C43—84no—
272C23×C43—84no—
273C23×C43—84no—
274C23×C43#12312yes—
275C23×C43C22×D411yescharacteristic
276C22×D43—21no—
277C22×D43—21no—
278C22×D43—21no—
279C22×D43—21no—
280C22×D43—21no—
281C22×D43—21no—
282C22×D43AGL(1,ℤ/8)12yes—
283D4×C43—22no—
284D4×C43—22no—
285D4×C43—22no—
286D4×C43—22no—
287D4×C43—48no—
288D4×C43—41no—
289D4×C43—41no—
290D4×C43—41no—
291D4×C43—41no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
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#12312yes—
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—44no—
312C22⋊D43—84no—
313C22⋊D43—84no—
314C2×Dic43—21no—
315C2×Dic43—21no—
316C2×Dic43—21no—
317C2×Dic43—22no—
318C2×Dic43—21no—
319C2×Dic43—21no—
320C2×Dic43—21no—
321C2×Dic43—21no—
322C2×Dic43—21no—
323C2×Dic43—21no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43—41no—
332C2×Dic43—41no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335C4×D43—41no—
336C4×D43—41no—
337C4×D43—41no—
338C4×D43—41no—
339C4×D43—84no—
340C8×C43—41no—
341C8×C43—41no—
342C43⋊C8—22no—
343C43⋊C8—41no—
344#24878—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—42no—
356C22×C43—42no—
357C22×C43—42no—
358C22×C43—816no—
359C22×C43—81no—
360C22×C43—81no—
361C22×C43—81no—
362C22×C43—81no—
363C22×C43—81no—
364C22×C43—81no—
365C22×C43—81no—
366C22×C43—81no—
367C22×C43C2×#12311yescharacteristic
368C22×C43D4211yescharacteristic
369C22×C43#54611yescharacteristic
370C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
371C22×C43#57511yescharacteristic
372C22×C43#57611yescharacteristic
373C22×C43#57711yescharacteristic
374C2×D43—22no—
375C2×D43—22no—
376C2×D43—22no—
377C2×D43—41no—
378C2×D43—41no—
379C2×D43—41no—
380C2×D43—41no—
381C4×C43—22no—
382C4×C43—81no—
383C4×C43—81no—
384C4×C43#52511yescharacteristic
385C4×C43#53811yescharacteristic
386C4×C43#54611yescharacteristic
387C4×C43#55111yescharacteristic
388Dic43—41no—
389Dic43—41no—
390Dic43—41no—
391Dic43—42no—
392Dic43—81no—
393Dic43—81no—
394Dic43—81no—
395C2×#481—431no—
396C2×#418—431no—
397#2408—431no—
398#2352—431no—
399#2092—431no—
400#2073—431no—
401#2033—431no—
402#2033—431no—
403#1926—431no—
404#1925—431no—
405#1874—431no—
406#1870—431no—
407#1854—431no—
408#1809—431no—
409#1786D4311yescharacteristic, complemented
410C2×C43—42no—
411C2×C43—82no—
412C2×C43—82no—
413C2×C43#241811yescharacteristic
414C2×C43#309411yescharacteristic
415C2×C43#309611yescharacteristic
416C2×C43#326511yescharacteristic
417C2×C43#327311yescharacteristic
418C2×C43#331811yescharacteristic
419C2×C43#332311yescharacteristic
420D43—42no—
421C23×D4C2×D4311yescharacteristic
422C22×M16—431no—
423C2×#121—431no—
424C2×#121—431no—
425C2×#120—861no—
426C2×C4×D4—431no—
427C2×#117—431no—
428C22×C4⋊C4—431no—
429#481—864no—
430C2×#107—431no—
431C2×#107—431no—
432C2×#106—431no—
433C2×#106—431no—
434#418—864no—
435C2×#102—431no—
436C2×#102—431no—
437C2×#102—431no—
438C2×#102—431no—
439C2×#102C2×D4311yescharacteristic
440C2×#102C2×D4311yescharacteristic
441C2×#102C2×D4311yescharacteristic
442C2×#102C2×D4311yescharacteristic
443C2×C22⋊C8—431no—
444C2×C22⋊C8—431no—
445C2×C22⋊C8C2×D4311yescharacteristic
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#380C2×D4311yescharacteristic
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#2487811yescharacteristic, complemented, Sylow
467C25—21no—
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—22no—
471C22×D4—21no—
472C22×D4—22no—
473C22×D4—41no—
474C22×D4—41no—
475C22×D4—431no—
476C22×D4—861no—
477C22×D4—861no—
478C22×D4C22×D4311yescharacteristic
479C22×D4C22×D4311yescharacteristic
480C23×C4—431no—
481C23×C4—861no—
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—862no—
491#121—862no—
492#121—1721no—
493#121—1721no—
494#120—1724no—
495C4×D4—862no—
496C4×D4—862no—
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—431no—
504C2×C4⋊C4—862no—
505C2×C4⋊C4—861no—
506C2×C4⋊C4—1721no—
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—1721no—
525#107—1721no—
526#106—862no—
527#106—862no—
528#102—22no—
529#102—22no—
530#102—41no—
531#102—41no—
532#102—434no—
533#102—862no—
534#102—862no—
535#102—862no—
536C22⋊C8—22no—
537C22⋊C8—862no—
538C22⋊C8—1721no—
539#95—21no—
540#95—861no—
541#95—861no—
542#95—861no—
543#95—861no—
544#95—861no—
545C24—21no—
546C24—21no—
547C24—42no—
548C24—42no—
549C24—42no—
550C24—42no—
551C24—42no—
552C24—81no—
553C24—81no—
554C24—431no—
555C24D4×D4311yescharacteristic
556C2×D4—28no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—44no—
572C2×D4—42no—
573C2×D4—862no—
574C2×D4—862no—
575C2×D4—3441no—
576C2×D4—3441no—
577C2×D4—1721no—
578C2×D4—1722no—
579C2×D4—1722no—
580C2×D4—1722no—
581C2×D4—1722no—
582C2×D4D4×D4312yes—
583C2×D4#1062190012yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—431no—
591C22×C4—431no—
592C22×C4—431no—
593C22×C4—861no—
594C22×C4—861no—
595C22×C4—861no—
596C22×C4—861no—
597C22×C4—861no—
598C22×C4—861no—
599C22×C4—861no—
600C22×C4—861no—
601C22×C4—861no—
602C22×C4—861no—
603C22×C4—3441no—
604C22×C4—1722no—
605C22×C4—1722no—
606C22×C4#1062189812yes—
607C22×C4D4×D4311yescharacteristic
608C22×C4#1062190012yes—
609C22×C4C23×D4311yescharacteristic
610M16—1724no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—432no—
618C2×C8—861no—
619C2×C8—861no—
620C2×C8—861no—
621C2×C8—861no—
622C2×C8—861no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—432no—
628C4⋊C4—862no—
629C4⋊C4—861no—
630C4⋊C4—861no—
631C4⋊C4—861no—
632C4⋊C4—861no—
633C4⋊C4—861no—
634C4⋊C4—861no—
635C4⋊C4—861no—
636C4⋊C4—1722no—
637C22⋊C4—81no—
638C22⋊C4—862no—
639C22⋊C4—862no—
640C22⋊C4—3441no—
641C22⋊C4—3441no—
642C22⋊C4—1722no—
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—22no—
661C23—48no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—84no—
675C23—84no—
676C23—84no—
677C23—84no—
678C23—84no—
679C23—84no—
680C23—432no—
681C23—861no—
682C23—861no—
683C23—861no—
684C23—861no—
685C23—861no—
686C23—861no—
687C23#1306330712yes—
688C23C2×D4×D4311yescharacteristic
689D4—22no—
690D4—22no—
691D4—22no—
692D4—22no—
693D4—48no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—3444no—
699D4—3444no—
700D4—1724no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—861no—
714C2×C4—861no—
715C2×C4—861no—
716C2×C4—861no—
717C2×C4—861no—
718C2×C4—861no—
719C2×C4—861no—
720C2×C4—862no—
721C2×C4—861no—
722C2×C4—861no—
723C2×C4—3444no—
724C2×C4—1721no—
725C2×C4—1721no—
726C2×C4—1721no—
727C2×C4—1721no—
728C2×C4—1721no—
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×C4—1721no—
739C2×C4#1306330712yes—
740C2×C4C2×D4×D4311yescharacteristic
741C2×C4C2×#1062190011yescharacteristic
742C2×C4C2×#1062190011yescharacteristic
743C2×C4C2×#1062189811yescharacteristic
744C2×C4#1306337011yescharacteristic
745C2×C4#1306337011yescharacteristic
746C8—41no—
747C8—41no—
748C8—862no—
749C8—1721no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—816no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—862no—
773C22—862no—
774C22—862no—
775C22—1721no—
776C22—1721no—
777C22—1721no—
778C22—1721no—
779C22C2×#1306330711yescharacteristic
780C22#1458353111yescharacteristic
781C22#1458353611yescharacteristic
782C22AGL(1,ℤ/8)×D4311yescharacteristic
783C22#1458369511yescharacteristic
784C22#1458370011yescharacteristic
785C22#1458370511yescharacteristic
786C4—22no—
787C4—81no—
788C4—81no—
789C4—3441no—
790C4—3441no—
791C4—3441no—
792C4—1721no—
793C4—1721no—
794C4—1721no—
795C4—1722no—
796C4#1458340511yescharacteristic
797C4#1458348411yescharacteristic
798C4#1458353911yescharacteristic
799C4#1458357511yescharacteristic
800C2—42no—
801C2—82no—
802C2—82no—
803C2—1722no—
804C2#1913806111yescharacteristic
805C2#1914453311yescharacteristic
806C2#1914454911yescharacteristic
807C2#1914608811yescharacteristic
808C2#1914620611yescharacteristic
809C2#1914672911yescharacteristic
810C2#1914681511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1786C2
socleC23×C43C22×D4
prime radical#19137945C2
hypercenter#1786D43
hypocenterC43#24878
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

Complements

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

NH ≅ G/Ntype
1. C2×#14583216C2semidirect
2. C2×#14582904C2semidirect
4. #19137517C2semidirect
5. #19136114C2semidirect
6. #19136011C2semidirect
7. #19135776C2semidirect
8. #19135775C2semidirect
9. #19135224C2semidirect
10. #19135218C2semidirect
11. #19134909C2semidirect
12. #19134890C2semidirect
13. #19134796C2semidirect
14. #19134626C2semidirect
15. C43×#1786C2semidirect
22. C2×C4⋊C4×D43C22semidirect
24. C2×#13063259C22semidirect
25. C2×#13063258C22semidirect
26. C2×#13063257C22semidirect
27. C2×#13063256C22semidirect
33. C2×(C2×D43)⋊C8C22semidirect
34. C2×(C2×D43)⋊C8C22semidirect
42. #14582764C22semidirect
44. #14582756C22semidirect
46. C4⋊C4×Dic43C22semidirect
48. #14582662C22semidirect
49. #14582662C22semidirect
50. #14582661C22semidirect
51. #14582661C22semidirect
52. #14582653C22semidirect
53. #14582653C22semidirect
109. #13063246D4semidirect
409. #1786D43semidirect
466. C43#24878semidirect

Maximal subgroups

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

subgroupindex
C2×#145832162
C2×#145829042
#191379452
#191375172
#191361142
#191360112
#191357762
#191357752
#191352242
#191352182
#191349092
#191348902
#191347962
#191346262
C43×#17862
#2487843