Finite Group Databasebeta

← #25103240

Subgroups — #25103240

Order 11008.

1170 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583151C211yesmaximal, characteristic
2C2×#14582979C211yesmaximal, characteristic, complemented
3C2×#14582851C211yesmaximal, characteristic, complemented
4#19137111C211yesmaximal, characteristic, complemented
5#19137103C211yesmaximal, characteristic, complemented
6#19135470C211yesmaximal, characteristic, complemented
7#19135335C211yesmaximal, characteristic, complemented
8#19135292C211yesmaximal, characteristic, complemented
9#19135032C211yesmaximal, characteristic, complemented
10#19135030C211yesmaximal, characteristic, complemented
11#19134627C211yesmaximal, characteristic, complemented
12#19134483C211yesmaximal, characteristic, complemented
13#102×Dic43C211yesmaximal, characteristic, complemented
14#19134409C211yesmaximal, characteristic, complemented
15C43×#1936C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C2×#13063300C2211yescharacteristic
20C2×#13063296C2211yescharacteristic
21C2×D4×Dic43C2211yescharacteristic
22C2×#13063287—21no—
23C2×#13063287C2211yescharacteristic
24C2×(C22⋊D43)⋊C4—21no—
25C2×C42×D43C2211yescharacteristic
26#14583151C418yescomplemented
27#14582979—24no—
28C2×#13063258C2211yescharacteristic
29C2×#13063256C2211yescharacteristic
30C2×#13063256C2211yescharacteristic
31C2×#13063247C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35#14582851—24no—
36C2×#13063236C2211yescharacteristic
37C2×C8×Dic43C2211yescharacteristic
38C2×C8×Dic43C2211yescharacteristic
39#14582801C2211yescharacteristic
40#14582797C2211yescharacteristic
41#14582793—21no—
42#14582789—21no—
43#14582777—21no—
44#14582775—21no—
45#14582756C2211yescharacteristic
46#14582756C2211yescharacteristic
47C4⋊C4×Dic43C2211yescharacteristic
48C4⋊C4×Dic43C2211yescharacteristic
49C22⋊C4×Dic43—21no—
50#14582746—21no—
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#97×C43C2211yescharacteristic
58C43×#390C2211yescharacteristic
59C43×#389C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×D172—21no—
63C22×D172C2311yescharacteristic
64C22×C22⋊D43—21no—
65C23×Dic43—21no—
66C22×C4×D43—21no—
67C22×C4×D43D411yescharacteristic
68C22×C4×D43D411yescharacteristic
69C22×C4×D43C2311yescharacteristic
70C2×#10621882—22no—
71C2×#10621882—22no—
72C2×#10621882C2×C414yescomplemented
73C2×#10621872—22no—
74C2×#10621872—22no—
75C2×#10621872—22no—
76C2×#10621872—22no—
77C2×#10621872—22no—
78C2×#10621872C2×C414yescomplemented
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81#13063300—22no—
82#13063300C2×C414yescomplemented
83#13063296—22no—
84#13063296C2×C414yescomplemented
85D4×Dic43—22no—
86D4×Dic43—22no—
87#13063287—22no—
88#13063287—22no—
89#13063287—44no—
90(C22⋊D43)⋊C4—44no—
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×Dic43⋊C4—21no—
95C2×C22⋊Dic43—21no—
96C2×C22⋊Dic43—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×C4×Dic43—21no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43D411yescharacteristic
106C2×C4×Dic43D411yescharacteristic
107C2×C4×Dic43C2311yescharacteristic
108C42×D43—22no—
109C42×D43—22no—
110#13063258—22no—
111#13063256—22no—
112#13063256C2×C414yescomplemented
113#13063247—22no—
114#13063247C2×C414yescomplemented
115#13063246—22no—
116#13063245—22no—
117#13063236—22no—
118C8×Dic43—22no—
119C8×Dic43D414yescomplemented
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C22×D4×C43C2311yescharacteristic
126C22×C8×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C2×C4⋊C4×C43—21no—
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C22⋊C4×C43—21no—
133C2×C22⋊C4×C43—21no—
134C2×C42×C43C2311yescharacteristic
135#102×C43—22no—
136#102×C43C2×C414yescomplemented
137#97×C43—22no—
138#95×C43—21no—
139C24×C43—21no—
140C23×D43—21no—
141C23×D43C2×D411yescharacteristic
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43C22×C412yes—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2411yescharacteristic
154C2×C22⋊D43—24no—
155C2×C22⋊D43—42no—
156C2×C22⋊D43—42no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—42no—
161C22×Dic43—42no—
162C22×Dic43—42no—
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D411yescharacteristic
165C22×Dic43C2×D411yescharacteristic
166C2×D172—21no—
167C2×D172—24no—
168C2×D172—21no—
169C2×D172—21no—
170C2×D172—21no—
171C2×D172—21no—
172C2×D172—42no—
173C2×D172—42no—
174C2×D172C22×C412yes—
175C2×C4×D43—21no—
176C2×C4×D43—21no—
177C2×C4×D43—21no—
178C2×C4×D43—21no—
179C2×C4×D43—22no—
180C2×C4×D43—22no—
181C2×C4×D43—22no—
182C2×C4×D43—22no—
183C2×C4×D43—41no—
184C2×C4×D43—41no—
185C2×C4×D43—42no—
186C2×C4×D43—42no—
187C2×C4×D43—42no—
188C2×C4×D43C22×C412yes—
189C2×C4×D43#4112yes—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43C22×C412yes—
195C2×C8×C43C2×D412yes—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—42no—
202C4⋊C4×C43C22×C412yes—
203C22⋊C4×C43—42no—
204C22⋊C4×C43—42no—
205C42×C43—21no—
206C42×C43—21no—
207C22⋊Dic43—24no—
208C22⋊Dic43—42no—
209#10621882—28no—
210(C2×D43)⋊C4—24no—
211(C2×D43)⋊C4—42no—
212(C2×D43)⋊C4—42no—
213(C2×D43)⋊C4—42no—
214(C2×D43)⋊C4—42no—
215(C2×D43)⋊C4—42no—
216C4⋊Dic43—21no—
217C4⋊Dic43—21no—
218C4⋊Dic43—21no—
219C4⋊Dic43—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43C22×C412yes—
222Dic43⋊C4—42no—
223C4×Dic43—22no—
224C4×Dic43—22no—
225C4×Dic43—42no—
226C4×Dic43—42no—
227C4×Dic43C2×D412yes—
228C4×Dic43#4112yes—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8C22×C412yes—
232C2×C43⋊C8C2×D412yes—
233C2×C43⋊C8#4112yes—
234C2×C43⋊C8#4112yes—
235#10621872—28no—
236#10621872—28no—
237C23×C43—22no—
238C23×C43—41no—
239C23×C43—41no—
240C23×C43—41no—
241C23×C43—41no—
242C23×C43—41no—
243C23×C43—41no—
244C23×C43C22×D411yescharacteristic
245C22×D43—21no—
246C22×D43—21no—
247C22×D43—21no—
248C22×D43—21no—
249C22×D43—21no—
250C22×D43—21no—
251C22×D43—22no—
252C22×D43—41no—
253C22×D43—41no—
254C22×D43—41no—
255C22×D43—41no—
256C22×D43—41no—
257C22×D43—41no—
258C22×D43C4×D412yes—
259D4×C43—22no—
260D4×C43—22no—
261D4×C43—41no—
262D4×C43—41no—
263C2×C4×C43—22no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
270C2×C4×C43—41no—
271C2×C4×C43—41no—
272C2×C4×C43—41no—
273C2×C4×C43—41no—
274C2×C4×C43—41no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43C23×C411yescharacteristic
279C2×C4×C43C22×D411yescharacteristic
280C2×C4×C43C2×#4111yescharacteristic
281C2×C4×C43C2×#4111yescharacteristic
282C2×C4×C43C2×#4111yescharacteristic
283C2×C4×C43C2×#4111yescharacteristic
284C22⋊D43—48no—
285C2×Dic43—21no—
286C2×Dic43—21no—
287C2×Dic43—21no—
288C2×Dic43—21no—
289C2×Dic43—22no—
290C2×Dic43—41no—
291C2×Dic43—41no—
292C2×Dic43—41no—
293C2×Dic43—41no—
294C2×Dic43—41no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297C2×Dic43—41no—
298C2×Dic43—84no—
299C2×Dic43C4×D412yes—
300C2×Dic43#12112yes—
301C2×Dic43#12112yes—
302C2×Dic43AGL(1,ℤ/8)12yes—
303C2×Dic43AGL(1,ℤ/8)12yes—
304D172—22no—
305D172—22no—
306D172—48no—
307D172—41no—
308D172—41no—
309C4×D43—22no—
310C4×D43—22no—
311C4×D43—22no—
312C4×D43—22no—
313C4×D43—44no—
314C4×D43—44no—
315C4×D43—84no—
316C8×C43—22no—
317C8×C43—22no—
318C43⋊C8—22no—
319C43⋊C8C4×D414yescomplemented
320C4×#469—431nomaximal, Sylow
321C22×C43—42no—
322C22×C43—42no—
323C22×C43—42no—
324C22×C43—81no—
325C22×C43—81no—
326C22×C43—81no—
327C22×C43—81no—
328C22×C43C2×C4×D411yescharacteristic
329C22×C43C2×#12111yescharacteristic
330C22×C43#53211yescharacteristic
331C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
332C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
333C22×C43#57511yescharacteristic
334C22×C43#57511yescharacteristic
335C2×D43—22no—
336C2×D43—22no—
337C2×D43—22no—
338C2×D43—41no—
339C2×D43—41no—
340C2×D43—41no—
341C2×D43—41no—
342C2×D43—42no—
343C2×D43—42no—
344C2×D43—42no—
345C2×D43—81no—
346C2×D43—81no—
347C2×D43—81no—
348C2×D43—81no—
349C4×C43—42no—
350C4×C43—41no—
351C4×C43—41no—
352C4×C43—81no—
353C4×C43—81no—
354C4×C43C2×C4×D411yescharacteristic
355C4×C43C4×#4111yescharacteristic
356C4×C43#52511yescharacteristic
357C4×C43#52911yescharacteristic
358Dic43—22no—
359Dic43—22no—
360Dic43—42no—
361Dic43—81no—
362Dic43—81no—
363Dic43#46914yescomplemented
364C2×#469—431no—
365C2×C4×D8—431no—
366C2×C4×M16—431no—
367C4×#121—431no—
368C4×#121—431no—
369#1972—431no—
370#1944—431no—
371#1936—431no—
372#1936D4311yescharacteristic, complemented
373#1895—431no—
374#1895—431no—
375#1809—431no—
376C4×#106—431no—
377C4×#102—431no—
378C4×#102—431no—
379C2×C43—82no—
380C2×C43C4×#12111yescharacteristic
381C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
382C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
383C2×C43C2×#46911yescharacteristic
384C2×C43#305411yescharacteristic
385C2×C43#317111yescharacteristic
386C2×C43#317111yescharacteristic
387D43—42no—
388D43—82no—
389C22×D8—431no—
390C22×M16—431no—
391C22×M16—431no—
392C2×#121—431no—
393C2×#121—431no—
394C2×C4×D4—431no—
395C2×C4×D4—431no—
396C2×C4×D4—861no—
397C2×C4×D4—861no—
398C22×C42—431no—
399#469—438no—
400C4×D8—864no—
401C2×#107—431no—
402C2×#106—431no—
403C2×#106—431no—
404C2×#102—431no—
405C2×#102—431no—
406C2×#102—431no—
407C2×#102—431no—
408C2×#102C2×D4311yescharacteristic
409C2×#102C2×D4311yescharacteristic
410C4×M16—864no—
411C2×#97—431no—
412C2×#97C2×D4311yescharacteristic
413C2×C4×C8—431no—
414C2×C4×C8—431no—
415#390—431no—
416#390C2×D4311yescharacteristic
417#389—431no—
418#389C2×D4311yescharacteristic
419#388—861no—
420#388—861no—
421#386—861no—
422#386—861no—
423#380—431no—
424#380—431no—
425C4×C4⋊C4—431no—
426C4×C4⋊C4—431no—
427C4×C22⋊C4—861no—
428C4×C22⋊C4—861no—
429#340—431no—
430#340—431no—
431#340—431no—
432#340—431no—
433#340C2×D4311yescharacteristic
434#340C2×D4311yescharacteristic
435C43C4×#46911yescharacteristic, complemented, Sylow
436C22×D4—431no—
437C22×D4—861no—
438C22×D4—861no—
439C22×D4C22×D4311yescharacteristic
440C23×C4—431no—
441C23×C4—431no—
442C23×C4—431no—
443C23×C4—861no—
444C23×C4—861no—
445C2×D8—434no—
446C2×D8—862no—
447C2×D8—862no—
448C2×M16—434no—
449C2×M16—862no—
450C2×M16—862no—
451C2×M16—862no—
452C2×M16—862no—
453C2×M16—862no—
454C22×C8—431no—
455C22×C8—431no—
456C22×C8C22×D4311yescharacteristic
457C22×C8C22×D4311yescharacteristic
458#121—434no—
459#121—434no—
460#121—862no—
461#121—862no—
462C4×D4—862no—
463C4×D4—862no—
464C4×D4—862no—
465C4×D4—862no—
466C4×D4—1724no—
467C4×D4—1724no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—431no—
470C2×C4⋊C4—431no—
471C2×C4⋊C4—431no—
472C2×C4⋊C4—861no—
473C2×C4⋊C4C22×D4311yescharacteristic
474C2×C4⋊C4C22×D4311yescharacteristic
475C2×C4⋊C4C22×D4311yescharacteristic
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—861no—
479C2×C22⋊C4—861no—
480C2×C22⋊C4—861no—
481C2×C22⋊C4—861no—
482C2×C22⋊C4—861no—
483C2×C22⋊C4—861no—
484C2×C22⋊C4—861no—
485C2×C22⋊C4—861no—
486C2×C42—431no—
487C2×C42—431no—
488C2×C42—431no—
489C2×C42—862no—
490C2×C42—862no—
491C2×C42—861no—
492C2×C42—861no—
493C2×C42C22×D4311yescharacteristic
494#107—862no—
495#106—434no—
496#106—862no—
497#102—22no—
498#102—434no—
499#102—862no—
500#102—862no—
501#102—862no—
502#102C4×D4314yescomplemented
503#97—22no—
504#97—862no—
505C4×C8—434no—
506C4×C8—862no—
507#95—21no—
508#95—861no—
509#95—861no—
510#95—861no—
511#95—861no—
512#95—861no—
513C24—21no—
514C24—431no—
515C24—861no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—432no—
522C2×D4—864no—
523C2×D4—864no—
524C2×D4—861no—
525C2×D4—861no—
526C2×D4—861no—
527C2×D4—861no—
528C2×D4—861no—
529C2×D4—1722no—
530C2×D4—1722no—
531C2×D4—1722no—
532C2×D4—1722no—
533C2×D4C2×C4×D4312yes—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—431no—
538C22×C4—431no—
539C22×C4—431no—
540C22×C4—432no—
541C22×C4—432no—
542C22×C4—862no—
543C22×C4—862no—
544C22×C4—862no—
545C22×C4—862no—
546C22×C4—861no—
547C22×C4—861no—
548C22×C4—861no—
549C22×C4—861no—
550C22×C4—861no—
551C22×C4—861no—
552C22×C4—861no—
553C22×C4—1721no—
554C22×C4—1721no—
555C22×C4—1722no—
556C22×C4—1722no—
557C22×C4—1722no—
558C22×C4—1722no—
559C22×C4—1722no—
560C22×C4—1722no—
561C22×C4D4×D4311yescharacteristic
562C22×C4D4×D4311yescharacteristic
563C22×C4C23×D4311yescharacteristic
564D8—868no—
565M16—868no—
566M16—868no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—432no—
572C2×C8—432no—
573C2×C8—432no—
574C2×C8—432no—
575C2×C8—861no—
576C2×C8—861no—
577C2×C8C2×C4×D4312yes—
578C2×C8D4×D4312yes—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—42no—
585C4⋊C4—432no—
586C4⋊C4—861no—
587C4⋊C4—861no—
588C4⋊C4—861no—
589C4⋊C4—861no—
590C4⋊C4—861no—
591C4⋊C4—1722no—
592C4⋊C4C2×C4×D4312yes—
593C22⋊C4—42no—
594C22⋊C4—42no—
595C22⋊C4—864no—
596C22⋊C4—864no—
597C22⋊C4—1722no—
598C22⋊C4—1722no—
599C22⋊C4—1722no—
600C22⋊C4—1722no—
601C22⋊C4—1722no—
602C22⋊C4—1722no—
603C42—21no—
604C42—21no—
605C42—432no—
606C42—432no—
607C42—862no—
608C42—862no—
609C42—1722no—
610C42—1722no—
611C23—22no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—432no—
619C23—861no—
620C23—861no—
621C23—861no—
622C23—861no—
623C23—861no—
624C23—861no—
625C23—862no—
626C23—1721no—
627C23—1721no—
628C23—1721no—
629C23—1721no—
630C23—1721no—
631C23—1721no—
632C23C2×D4×D4311yescharacteristic
633D4—22no—
634D4—22no—
635D4—41no—
636D4—41no—
637D4—862no—
638D4—862no—
639D4—1728no—
640D4—1728no—
641D4—1721no—
642D4—1721no—
643C2×C4—22no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—432no—
659C2×C4—432no—
660C2×C4—432no—
661C2×C4—432no—
662C2×C4—432no—
663C2×C4—861no—
664C2×C4—861no—
665C2×C4—861no—
666C2×C4—861no—
667C2×C4—862no—
668C2×C4—862no—
669C2×C4—862no—
670C2×C4—862no—
671C2×C4—862no—
672C2×C4—3444no—
673C2×C4—3444no—
674C2×C4—1724no—
675C2×C4—1724no—
676C2×C4—1721no—
677C2×C4—1721no—
678C2×C4—1721no—
679C2×C4—1721no—
680C2×C4—1721no—
681C2×C4—1721no—
682C2×C4—1721no—
683C2×C4—1721no—
684C2×C4C22×C4×D4311yescharacteristic
685C2×C4C2×D4×D4311yescharacteristic
686C2×C4#41×D4311yescharacteristic
687C2×C4#41×D4311yescharacteristic
688C2×C4#41×D4311yescharacteristic
689C2×C4#41×D4311yescharacteristic
690C8—22no—
691C8—22no—
692C8—434no—
693C8—862no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—81no—
698C22—81no—
699C22—81no—
700C22—81no—
701C22—862no—
702C22—862no—
703C22—862no—
704C22—3441no—
705C22—3441no—
706C22—3441no—
707C22—3441no—
708C22—1722no—
709C22—1722no—
710C22—1722no—
711C22—1721no—
712C22—1721no—
713C22—1721no—
714C22—1721no—
715C22C4×D4×D4311yescharacteristic
716C22#121×D4311yescharacteristic
717C22#1458344811yescharacteristic
718C22AGL(1,ℤ/8)×D4311yescharacteristic
719C22AGL(1,ℤ/8)×D4311yescharacteristic
720C22#1458369511yescharacteristic
721C22#1458369811yescharacteristic
722C4—41no—
723C4—42no—
724C4—41no—
725C4—81no—
726C4—81no—
727C4—434no—
728C4—862no—
729C4—862no—
730C4—3441no—
731C4—3441no—
732C4—1722no—
733C4C4×D4×D4311yescharacteristic
734C4#1458336711yescharacteristic
735C4#1458340711yescharacteristic
736C4#1458343211yescharacteristic
737C2—82no—
738C2—3442no—
739C2—1722no—
740C2#1913710711yescharacteristic
741C2#1914340011yescharacteristic
742C2#1914340611yescharacteristic
743C2#469×D4311yescharacteristic
744C2#1914419911yescharacteristic
745C2#1914518911yescharacteristic
746C2#1914519311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1936C2
socleC23×C43C22×D4
prime radicalC2×#14583151C2
cosocleC22×C4×C43C24
hypercenter#1936D43
hypocenterC43C4×#469
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1936

Complements

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

NH ≅ G/Ntype
2. C2×#14582979C2semidirect
3. C2×#14582851C2semidirect
4. #19137111C2semidirect
5. #19137103C2semidirect
6. #19135470C2semidirect
7. #19135335C2semidirect
8. #19135292C2semidirect
9. #19135032C2semidirect
10. #19135030C2semidirect
11. #19134627C2semidirect
12. #19134483C2semidirect
13. #102×Dic43C2semidirect
14. #19134409C2semidirect
15. C43×#1936C2semidirect
26. #14583151C4semidirect
72. C2×#10621882C2×C4semidirect
78. C2×#10621872C2×C4semidirect
82. #13063300C2×C4semidirect
84. #13063296C2×C4semidirect
112. #13063256C2×C4semidirect
114. #13063247C2×C4semidirect
119. C8×Dic43D4semidirect
136. #102×C43C2×C4semidirect
319. C43⋊C8C4×D4semidirect
363. Dic43#469semidirect
372. #1936D43semidirect
435. C43C4×#469semidirect
502. #102C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831512
C2×#145829792
C2×#145828512
#191371112
#191371032
#191354702
#191353352
#191352922
#191350322
#191350302
#191346272
#191344832
#102×Dic432
#191344092
C43×#19362
C4×#46943