Finite Group Databasebeta

← #25140172

Subgroups — #25140172

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×#14583211C211yesmaximal, characteristic, complemented
2#19137945C211yesmaximal, characteristic
3#19137525C211yesmaximal, characteristic, complemented
4#19136114C211yesmaximal, characteristic, complemented
5#19136011C211yesmaximal, characteristic, complemented
6#19135783C211yesmaximal, characteristic, complemented
7#19135782C211yesmaximal, characteristic, complemented
8#19135224C211yesmaximal, characteristic, complemented
9#19135218C211yesmaximal, characteristic, complemented
10#19134909C211yesmaximal, characteristic, complemented
11#19134892C211yesmaximal, characteristic, complemented
12#19134794C211yesmaximal, characteristic, complemented
13#19134628C211yesmaximal, characteristic, complemented
14#19134526C211yesmaximal, characteristic, complemented
15C2×C43×#418C211yesmaximal, characteristic, complemented
16C2×#13063296C2211yescharacteristic
17C2×#13063296C2211yescharacteristic
18C2×#13063294—21no—
19C2×C4×C22⋊D43C2211yescharacteristic
20C2×C4⋊C4×D43C2211yescharacteristic, complemented
21#14583211—24no—
22C2×#13063259C2211yescharacteristic, complemented
23C2×#13063258C2211yescharacteristic, complemented
24C2×#13063257C2211yescharacteristic, complemented
25C2×#13063256C2211yescharacteristic, complemented
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×C22⋊(C43⋊C8)C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
32C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
33#14582813—21no—
34#14582807—21no—
35#14582802C2211yescharacteristic
36#14582802C2211yescharacteristic
37#14582793—21no—
38#14582783—21no—
39#14582775—21no—
40#14582764C2211yescharacteristic, complemented
41#14582759C2211yescharacteristic
42#14582759C2211yescharacteristic
43#14582756C2211yescharacteristic, complemented
44#14582755—21no—
45C4⋊C4×Dic43C2211yescharacteristic, complemented
46C4×(C2×D43)⋊C4—21no—
47#14582662C2211yescharacteristic, complemented
48#14582662C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582661C2211yescharacteristic, complemented
51#14582653C2211yescharacteristic, complemented
52#14582653C2211yescharacteristic, complemented
53C23×D4×C43C2211yescharacteristic
54C22×M16×C43C2211yescharacteristic
55C2×#117×C43C2211yescharacteristic
56C43×#418—24no—
57C2×#102×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C22×C22⋊D43—21no—
62C22×C22⋊D43—21no—
63C22×C22⋊D43D411yescharacteristic
64C22×C4×D43—21no—
65C22×C4×D43C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68#13063296—22no—
69#13063296—22no—
70#13063296—41no—
71#13063296—41no—
72#13063294—44no—
73C4×C22⋊D43—22no—
74C4×C22⋊D43—22no—
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4D411yescharacteristic
81C4⋊C4×D43—22no—
82C4⋊C4×D43—41no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43D411yescharacteristic
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4D411yescharacteristic
94C2×C4×Dic43—21no—
95C2×C4×Dic43C2311yescharacteristic
96#13063259—22no—
97#13063258—22no—
98#13063257—41no—
99#13063256—41no—
100#13063246—22no—
101#13063246—22no—
102#13063246—41no—
103#13063246—41no—
104C22⋊(C43⋊C8)—22no—
105(C2×D43)⋊C8—22no—
106(C2×D43)⋊C8—41no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C25×C43—21no—
114C22×D4×C43—22no—
115C22×D4×C43—22no—
116C22×D4×C43—21no—
117C22×D4×C43—22no—
118C22×D4×C43—22no—
119C22×D4×C43—41no—
120C22×D4×C43—41no—
121C22×D4×C43C2311yescharacteristic
122C22×D4×C43C2311yescharacteristic
123C23×C4×C43C2311yescharacteristic
124C2×M16×C43—22no—
125C2×M16×C43—22no—
126C2×M16×C43—41no—
127C22×C8×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129#117×C43—22no—
130#117×C43—41no—
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C22⋊C4×C43—21no—
134C2×C42×C43—21no—
135#102×C43—22no—
136#102×C43—22no—
137#102×C43—22no—
138#102×C43D414yescomplemented
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—
204M16×C43—44no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43C2×D412yes—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43C2×D412yes—
215C22⋊C4×C43—42no—
216C42×C43—42no—
217C22⋊Dic43—22no—
218C22⋊Dic43—42no—
219C22⋊Dic43—42no—
220C22⋊Dic43—42no—
221C22⋊Dic43—42no—
222C22⋊Dic43—42no—
223C22⋊Dic43—81no—
224C22⋊Dic43—81no—
225C22⋊Dic43—81no—
226(C2×D43)⋊C4—22no—
227(C2×D43)⋊C4—42no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234C4⋊Dic43—21no—
235C4⋊Dic43—21no—
236Dic43⋊C4—22no—
237Dic43⋊C4—42no—
238C4×Dic43—21no—
239C4×Dic43—21no—
240C4×Dic43—81no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
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—22no—
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—21no—
318C2×Dic43—21no—
319C2×Dic43—21no—
320C2×Dic43—21no—
321C2×Dic43—21no—
322C2×Dic43—21no—
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—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—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—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—42no—
383C4×C43—81no—
384C4×C43#52511yescharacteristic
385C4×C43#53811yescharacteristic
386C4×C43#54611yescharacteristic
387C4×C43#55111yescharacteristic
388Dic43—41no—
389Dic43—41no—
390Dic43—41no—
391Dic43—81no—
392Dic43—81no—
393Dic43—81no—
394Dic43—81no—
395C2×#480—431no—
396C2×#418D4311yescharacteristic, complemented
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—82no—
413C2×C43#241811yescharacteristic
414C2×C43#309411yescharacteristic
415C2×C43#309611yescharacteristic
416C2×C43#326411yescharacteristic
417C2×C43#327511yescharacteristic
418C2×C43#331011yescharacteristic
419C2×C43#332211yescharacteristic
420D43—42no—
421C23×D4C2×D4311yescharacteristic
422C22×M16C2×D4311yescharacteristic
423C2×#121—431no—
424C2×#121—431no—
425C2×#120—861no—
426C2×C4×D4—431no—
427C2×#117C2×D4311yescharacteristic
428C22×C4⋊C4—431no—
429#480—864no—
430C2×#107—431no—
431C2×#107—431no—
432C2×#106—431no—
433C2×#106—431no—
434#418—24no—
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⋊C8—431no—
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—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—22no—
484C2×M16—22no—
485C2×M16—41no—
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—22no—
498#117—41no—
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—21no—
522C2×C42—431no—
523C2×C42—861no—
524#107—862no—
525#107—862no—
526#106—1721no—
527#106—1721no—
528#102—22no—
529#102—22no—
530#102—22no—
531#102—862no—
532#102—862no—
533#102—1721no—
534#102—1721no—
535#102C22⋊D4314yescomplemented
536C22⋊C8—862no—
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—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×D4#1062189812yes—
583C2×D4C2×C22⋊D4312yes—
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—44no—
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—862no—
627C4⋊C4—861no—
628C4⋊C4—861no—
629C4⋊C4—861no—
630C4⋊C4—861no—
631C4⋊C4—861no—
632C4⋊C4—861no—
633C4⋊C4—861no—
634C4⋊C4—861no—
635C4⋊C4—1722no—
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—42no—
650C42—861no—
651C42—861no—
652C42—3441no—
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—22no—
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—861no—
721C2×C4—861no—
722C2×C4—3444no—
723C2×C4—1721no—
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×C4C22×C22⋊D4311yescharacteristic
741C2×C4C2×#1062190011yescharacteristic
742C2×C4C2×#1062189811yescharacteristic
743C2×C4C2×#1062189811yescharacteristic
744C2×C4#1306337011yescharacteristic
745C2×C4#1306337011yescharacteristic
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—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
780C22D4×C22⋊D4311yescharacteristic
781C22#1458353911yescharacteristic
782C22AGL(1,ℤ/8)×D4311yescharacteristic
783C22#1458369511yescharacteristic
784C22#1458370311yescharacteristic
785C22#1458370911yescharacteristic
786C4—22no—
787C4—42no—
788C4—81no—
789C4—3441no—
790C4—3441no—
791C4—3441no—
792C4—3441no—
793C4—1721no—
794C4—1721no—
795C4—1721no—
796C4#1458341011yescharacteristic
797C4#1458348711yescharacteristic
798C4#1458354311yescharacteristic
799C4#1458357511yescharacteristic
800C2—42no—
801C2—82no—
802C2—82no—
803C2—1722no—
804C2#1913805711yescharacteristic
805C2#1914453311yescharacteristic
806C2#1914455111yescharacteristic
807C2#1914606911yescharacteristic
808C2#1914622611yescharacteristic
809C2#1914661711yescharacteristic
810C2#1914679211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#418C2
socleC23×C43C22×D4
prime radical#19137945C2
hypercenterC2×#418D43
hypocenterC43#24882
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#418

Complements

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

NH ≅ G/Ntype
1. C2×#14583211C2semidirect
3. #19137525C2semidirect
4. #19136114C2semidirect
5. #19136011C2semidirect
6. #19135783C2semidirect
7. #19135782C2semidirect
8. #19135224C2semidirect
9. #19135218C2semidirect
10. #19134909C2semidirect
11. #19134892C2semidirect
12. #19134794C2semidirect
13. #19134628C2semidirect
14. #19134526C2semidirect
15. C2×C43×#418C2semidirect
20. C2×C4⋊C4×D43C22semidirect
22. C2×#13063259C22semidirect
23. C2×#13063258C22semidirect
24. C2×#13063257C22semidirect
25. C2×#13063256C22semidirect
31. C2×(C2×D43)⋊C8C22semidirect
32. C2×(C2×D43)⋊C8C22semidirect
40. #14582764C22semidirect
43. #14582756C22semidirect
45. C4⋊C4×Dic43C22semidirect
47. #14582662C22semidirect
48. #14582662C22semidirect
49. #14582661C22semidirect
50. #14582661C22semidirect
51. #14582653C22semidirect
52. #14582653C22semidirect
138. #102×C43D4semidirect
396. C2×#418D43semidirect
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×#145832112
#191379452
#191375252
#191361142
#191360112
#191357832
#191357822
#191352242
#191352182
#191349092
#191348922
#191347942
#191346282
#191345262
C2×C43×#4182
#2488243