Finite Group Databasebeta

← C4×#14583151 #25103239

Subgroups — C4×#14583151 #25103239

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×C4×#10621882C211yesmaximal, characteristic, complemented
3C2×C4×#10621872C211yesmaximal, characteristic, complemented
4C4×#13063300C211yesmaximal, characteristic, complemented
5C4×#13063296C211yesmaximal, characteristic, complemented
6#19135468C211yesmaximal, characteristic, complemented
7#19135337C211yesmaximal, characteristic, complemented
8#19135294C211yesmaximal, characteristic, complemented
9#19135290C211yesmaximal, characteristic, complemented
10#19135032C211yesmaximal, characteristic, complemented
11#19135030C211yesmaximal, characteristic, complemented
12#19134627C211yesmaximal, characteristic, complemented
13C4×#13063256C211yesmaximal, characteristic, complemented
14C4×#13063247C211yesmaximal, characteristic, complemented
15C4×#102×C43C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C2×#13063300C2211yescharacteristic
20C2×#13063296C2211yescharacteristic
21C2×C4×D172—21no—
22C2×C4×D172C2211yescharacteristic
23C2×C4×C22⋊D43—21no—
24C2×C42×D43C2211yescharacteristic
25#14583151C418yesdirect product factor
26C4×#10621882—24no—
27C2×#13063258C2211yescharacteristic
28C2×#13063256C2211yescharacteristic
29C2×#13063256C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31C2×#13063247C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C4×#10621872—24no—
35C2×#13063235C2211yescharacteristic
36C2×#13063235C2211yescharacteristic
37C2×C4×C43⋊C8C2211yescharacteristic
38#14582802C2211yescharacteristic
39#14582800C2211yescharacteristic
40#14582798C2211yescharacteristic
41#14582795C2211yescharacteristic
42#14582791—21no—
43#14582787—21no—
44#14582777—21no—
45#14582775—21no—
46#14582756C2211yescharacteristic
47#14582756C2211yescharacteristic
48C4×C4⋊Dic43C2211yescharacteristic
49C4×(C2×D43)⋊C4—21no—
50C4×C22⋊Dic43—21no—
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×C4×C8×C43C2211yescharacteristic
59C4×C4⋊C4×C43C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×D172—21no—
63C22×D172C2311yescharacteristic
64C22×C22⋊D43—21no—
65C22×C4×D43—21no—
66C22×C4×D43D411yescharacteristic
67C22×C4×D43D411yescharacteristic
68C22×C4×D43C2311yescharacteristic
69C2×#10621882—22no—
70C2×#10621882—22no—
71C2×#10621882C2×C414yescomplemented
72C2×#10621872—22no—
73C2×#10621872—22no—
74C2×#10621872—22no—
75C2×#10621872—22no—
76C2×#10621872—22no—
77C2×#10621872C2×C414yescomplemented
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80#13063300—22no—
81#13063300C2×C414yescomplemented
82#13063296—22no—
83#13063296C2×C414yescomplemented
84C4×D172—22no—
85C4×D172—22no—
86C4×D172—44no—
87C4×C22⋊D43—44no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×Dic43⋊C4—21no—
93C2×C22⋊Dic43—21no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—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)⋊C4—21no—
102C2×C4×Dic43—21no—
103C2×C4×Dic43D411yescharacteristic
104C2×C4×Dic43D411yescharacteristic
105C2×C4×Dic43C2311yescharacteristic
106C42×D43—22no—
107C42×D43—22no—
108#13063258—22no—
109#13063256—22no—
110#13063256C2×C414yescomplemented
111#13063247—22no—
112#13063247C2×C414yescomplemented
113#13063246—22no—
114#13063245—22no—
115#13063235—22no—
116#13063235—22no—
117C4×C43⋊C8D414yescomplemented
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C22×D4×C43C2311yescharacteristic
124C23×C4×C43—21no—
125C22×C8×C43C2311yescharacteristic
126C22×C8×C43C2311yescharacteristic
127C4×D4×C43—22no—
128C4×D4×C43—22no—
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C4⋊C4×C43C2311yescharacteristic
132C2×C22⋊C4×C43—21no—
133C2×C42×C43—21no—
134C2×C42×C43C2311yescharacteristic
135#102×C43—22no—
136#102×C43C2×C414yescomplemented
137C4×C8×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×C43—42no—
152C22×C4×C43—42no—
153C22×C4×C43—42no—
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2411yescharacteristic
157C2×C22⋊D43—24no—
158C2×C22⋊D43—42no—
159C2×C22⋊D43—42no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—21no—
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×C43#4112yes—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43C22×C412yes—
202C22⋊C4×C43—42no—
203C42×C43—42no—
204C42×C43C2×D412yes—
205C42×C43#4112yes—
206C22⋊Dic43—24no—
207C22⋊Dic43—42no—
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⋊Dic43—42no—
222C4⋊Dic43C22×C412yes—
223Dic43⋊C4—42no—
224C4×Dic43—22no—
225C4×Dic43—22no—
226C4×Dic43—21no—
227C4×Dic43—21no—
228C4×Dic43—42no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8C22×C412yes—
232C2×C43⋊C8C2×D412yes—
233C2×C43⋊C8C2×D412yes—
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—21no—
264C2×C4×C43—21no—
265C2×C4×C43—22no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43—41no—
269C2×C4×C43—41no—
270C2×C4×C43—41no—
271C2×C4×C43—41no—
272C2×C4×C43—41no—
273C2×C4×C43—41no—
274C2×C4×C43—84no—
275C2×C4×C43#12112yes—
276C2×C4×C43#12112yes—
277C2×C4×C43AGL(1,ℤ/8)12yes—
278C2×C4×C43AGL(1,ℤ/8)12yes—
279C2×C4×C43C23×C411yescharacteristic
280C2×C4×C43C22×D411yescharacteristic
281C2×C4×C43C2×#4111yescharacteristic
282C2×C4×C43C2×#4111yescharacteristic
283C2×C4×C43C2×#4111yescharacteristic
284C2×C4×C43C2×#4111yescharacteristic
285C22⋊D43—48no—
286C2×Dic43—21no—
287C2×Dic43—21no—
288C2×Dic43—22no—
289C2×Dic43—21no—
290C2×Dic43—21no—
291C2×Dic43—21no—
292C2×Dic43—21no—
293C2×Dic43—21no—
294C2×Dic43—21no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297C2×Dic43—41no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300C2×Dic43—41no—
301C2×Dic43—41no—
302C2×Dic43—41no—
303C2×Dic43C4×D412yes—
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—22no—
350C4×C43—42no—
351C4×C43—81no—
352C4×C43—81no—
353C4×C43#46914yescomplemented
354C4×C43C2×C4×D411yescharacteristic
355C4×C43C4×#4111yescharacteristic
356C4×C43#52511yescharacteristic
357C4×C43#52911yescharacteristic
358Dic43—22no—
359Dic43—42no—
360Dic43—41no—
361Dic43—41no—
362Dic43—81no—
363Dic43—81no—
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#1936—431no—
373#1895—431no—
374#1895—431no—
375#1809—431no—
376C4×#106—431no—
377C4×#102—431no—
378C4×#102D4311yescharacteristic, complemented
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—861no—
396C2×C4×D4—861no—
397C2×C4×D4C2×D4311yescharacteristic
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×#97—431no—
413C2×C4×C8—431no—
414C2×C4×C8C2×D4311yescharacteristic
415#390—431no—
416#390—431no—
417#389—431no—
418#389—431no—
419#388—861no—
420#388—861no—
421#386—861no—
422#386—861no—
423#380—431no—
424#380—431no—
425C4×C4⋊C4—431no—
426C4×C4⋊C4C2×D4311yescharacteristic
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—21no—
441C23×C4—431no—
442C23×C4—431no—
443C23×C4—431no—
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—22no—
463C4×D4—22no—
464C4×D4—862no—
465C4×D4—862no—
466C4×D4—1724no—
467C4×D4—1724no—
468C2×C4⋊C4—431no—
469C2×C4⋊C4—431no—
470C2×C4⋊C4—431no—
471C2×C4⋊C4—861no—
472C2×C4⋊C4—861no—
473C2×C4⋊C4C22×D4311yescharacteristic
474C2×C4⋊C4C22×D4311yescharacteristic
475C2×C4⋊C4C22×D4311yescharacteristic
476C2×C22⋊C4—21no—
477C2×C22⋊C4—861no—
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—21no—
487C2×C42—431no—
488C2×C42—431no—
489C2×C42—431no—
490C2×C42—862no—
491C2×C42—862no—
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—862no—
504#97—862no—
505C4×C8—22no—
506C4×C8—434no—
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—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—431no—
541C22×C4—432no—
542C22×C4—432no—
543C22×C4—431no—
544C22×C4—431no—
545C22×C4—861no—
546C22×C4—861no—
547C22×C4—861no—
548C22×C4—861no—
549C22×C4—861no—
550C22×C4—862no—
551C22×C4—862no—
552C22×C4—862no—
553C22×C4—862no—
554C22×C4—861no—
555C22×C4—861no—
556C22×C4—1721no—
557C22×C4—1721no—
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×C8#1062189812yes—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—432no—
585C4⋊C4—861no—
586C4⋊C4—861no—
587C4⋊C4—861no—
588C4⋊C4—861no—
589C4⋊C4—861no—
590C4⋊C4—1722no—
591C4⋊C4—1722no—
592C4⋊C4C2×C4×D4312yes—
593C22⋊C4—42no—
594C22⋊C4—864no—
595C22⋊C4—864no—
596C22⋊C4—1722no—
597C22⋊C4—1722no—
598C22⋊C4—1722no—
599C22⋊C4—1722no—
600C22⋊C4—1722no—
601C22⋊C4—1722no—
602C22⋊C4—1722no—
603C42—42no—
604C42—862no—
605C42—862no—
606C42—861no—
607C42—861no—
608C42—1722no—
609C42#1062189812yes—
610C42D4×D4312yes—
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—21no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—84no—
655C2×C4—432no—
656C2×C4—861no—
657C2×C4—861no—
658C2×C4—862no—
659C2×C4—862no—
660C2×C4—862no—
661C2×C4—862no—
662C2×C4—862no—
663C2×C4—861no—
664C2×C4—861no—
665C2×C4—861no—
666C2×C4—861no—
667C2×C4—861no—
668C2×C4—861no—
669C2×C4—3444no—
670C2×C4—1724no—
671C2×C4—1721no—
672C2×C4—1721no—
673C2×C4—1721no—
674C2×C4—1721no—
675C2×C4—1721no—
676C2×C4—1721no—
677C2×C4—1721no—
678C2×C4—1721no—
679C2×C4—1724no—
680C2×C4#1306329812yes—
681C2×C4#1306329812yes—
682C2×C4#1306334912yes—
683C2×C4#1306335212yes—
684C2×C4C22×C4×D4311yescharacteristic
685C2×C4C2×D4×D4311yescharacteristic
686C2×C4#41×D4311yescharacteristic
687C2×C4#41×D4311yescharacteristic
688C2×C4C2×#1062189811yescharacteristic
689C2×C4C2×#1062189811yescharacteristic
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
716C22C2×#1306329811yescharacteristic
717C22#1458344611yescharacteristic
718C22C2×#1306334911yescharacteristic
719C22C2×#1306335211yescharacteristic
720C22#1458369611yescharacteristic
721C22#1458369611yescharacteristic
722C4—22no—
723C4—42no—
724C4—81no—
725C4—81no—
726C4—862no—
727C4—3441no—
728C4—3441no—
729C4—1721no—
730C4—1722no—
731C4—1721no—
732C4#1458315114yesdirect product factor
733C4C4×D4×D4311yescharacteristic
734C4C4×#1062189811yescharacteristic
735C4#1458340811yescharacteristic
736C4#1458342711yescharacteristic
737C2—82no—
738C2—3442no—
739C2—1722no—
740C2C4×#1306329811yescharacteristic
741C2C4×#1306334911yescharacteristic
742C2C4×#1306335211yescharacteristic
743C2C2×#1458315111yescharacteristic
744C2#1914420311yescharacteristic
745C2#1914518611yescharacteristic
746C2#1914518811yescharacteristic
subgroupG/H
centerC22×C4D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#102×C43C2
socleC23×C43C22×D4
prime radicalC2×#14583151C2
cosocleC22×C4×C43C24
hypercenterC4×#102D43
hypocenterC43C4×#469
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10621882C2semidirect
3. C2×C4×#10621872C2semidirect
4. C4×#13063300C2semidirect
5. C4×#13063296C2semidirect
6. #19135468C2semidirect
7. #19135337C2semidirect
8. #19135294C2semidirect
9. #19135290C2semidirect
10. #19135032C2semidirect
11. #19135030C2semidirect
12. #19134627C2semidirect
13. C4×#13063256C2semidirect
14. C4×#13063247C2semidirect
15. C4×#102×C43C2semidirect
25. #14583151C4direct (N × H)
71. C2×#10621882C2×C4semidirect
77. C2×#10621872C2×C4semidirect
81. #13063300C2×C4semidirect
83. #13063296C2×C4semidirect
110. #13063256C2×C4semidirect
112. #13063247C2×C4semidirect
117. C4×C43⋊C8D4semidirect
136. #102×C43C2×C4semidirect
319. C43⋊C8C4×D4semidirect
353. C4×C43#469semidirect
378. C4×#102D43semidirect
435. C43C4×#469semidirect
502. #102C4×D43semidirect
732. C4#14583151direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145831512
C2×C4×#106218822
C2×C4×#106218722
C4×#130633002
C4×#130632962
#191354682
#191353372
#191352942
#191352902
#191350322
#191350302
#191346272
C4×#130632562
C4×#130632472
C4×#102×C432
C4×#46943