Finite Group Databasebeta

← C4×#14583085 #25102577

Subgroups — C4×#14583085 #25102577

Order 11008.

1910 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13063370C211yesmaximal, characteristic, complemented
2C2×#14583085C211yesmaximal, characteristic
3C4×#13063294C212yesmaximal, complemented
4#19135004C211yesmaximal, characteristic, complemented
5#19135000C212yesmaximal, complemented
6#19134875C211yesmaximal, characteristic, complemented
7#19134874C212yesmaximal, complemented
8#19134542C211yesmaximal, characteristic, complemented
9C4×#13063239C212yesmaximal, complemented
10C4×#13063240C211yesmaximal, characteristic, complemented
11C4×#120×C43C211yesmaximal, characteristic, complemented
12C2×#13063370C2211yescharacteristic
13C2×#13063294C2212yes—
14#14583380—21no—
15#14583378—22no—
16#14583374C2211yescharacteristic
17#14583372—21no—
18#14583372C2212yes—
19#14583371—22no—
20C4×#10621898—21no—
21C4×#10621900—22no—
22C2×C4×C22⋊D43—22no—
23C2×C4×C22⋊D43—21no—
24C2×C4×C22⋊D43C2212yes—
25C4×D4×D43—22no—
26#14583085C418yesdirect product factor
27C2×#13063240C2211yescharacteristic
28C2×#13063240C2211yescharacteristic
29C2×#13063239C2212yes—
30C2×#13063239C2212yes—
31#14582778—22no—
32#14582778C2212yes—
33#14582772—22no—
34#14582772C2212yescomplemented
35#14582755C2212yescomplemented
36C4×C22⋊Dic43—22no—
37C4×C22⋊Dic43C2212yescomplemented
38#14582666C2212yescomplemented
39#14582665C2212yescomplemented
40#14582665C2212yescomplemented
41C24×C4×C43C2211yescharacteristic, complemented
42C2×#120×C43C2211yescharacteristic
43C2×C4×D4×C43—21no—
44C2×C4×D4×C43C2211yescharacteristic
45C43×#386—21no—
46C43×#386C2211yescharacteristic
47C43×#385—21no—
48C43×#385C2211yescharacteristic, complemented
49C43×#379C2211yescharacteristic, complemented
50C4×C22⋊C4×C43—21no—
51C4×C22⋊C4×C43C2211yescharacteristic, complemented
52#13063370—22no—
53#13063370—24no—
54#13063370C2×C414yescomplemented
55C2×#10621898—21no—
56C2×#10621900—22no—
57C22×C22⋊D43—21no—
58C22×C22⋊D43—22no—
59C22×C22⋊D43C2312yes—
60C2×D4×D43—22no—
61C22×C4×D43—21no—
62C22×C4×D43D412yescomplemented
63#13063294—24no—
64#13063294C2×C418yescomplemented
65C4×Dic86—21no—
66C4×Dic86—21no—
67#13063290—22no—
68C4×D172—21no—
69C4×D172—21no—
70D4×Dic43—22no—
71D4×Dic43—22no—
72#13063287—22no—
73C4×C22⋊D43—22no—
74C4×C22⋊D43—22no—
75C4×C22⋊D43—22no—
76C4×C22⋊D43—22no—
77C4×C22⋊D43—22no—
78C4×C22⋊D43—22no—
79C4×C22⋊D43—22no—
80C4×C22⋊D43—22no—
81C4×C22⋊D43—48no—
82(C22⋊D43)⋊C4—22no—
83(C22⋊D43)⋊C4—22no—
84(C22⋊D43)⋊C4—22no—
85(C22⋊D43)⋊C4—22no—
86#13063284—21no—
87#13063283—22no—
88#13063282—22no—
89#13063281—22no—
90#13063281—22no—
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—22no—
93C2×Dic43⋊C4D412yescomplemented
94C4⋊C4×D43—22no—
95C2×C22⋊Dic43—21no—
96C2×C22⋊Dic43—22no—
97C2×C22⋊Dic43—22no—
98C2×C22⋊Dic43—22no—
99C2×C22⋊Dic43C2312yes—
100C2×C22⋊Dic43C2312yes—
101C2×C22⋊Dic43C2312yes—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—22no—
104C2×(C2×D43)⋊C4D412yescomplemented
105C22⋊C4×D43—22no—
106C22⋊C4×D43—22no—
107C2×C4×Dic43—21no—
108C2×C4×Dic43—22no—
109C2×C4×Dic43D412yescomplemented
110C42×D43—22no—
111#13063240—22no—
112#13063240C2×C414yescomplemented
113#13063239—24no—
114#13063239C2×C418yescomplemented
115C43⋊#95—22no—
116C43⋊#95—22no—
117C43⋊#95—22no—
118C25×C43C2311yescharacteristic
119C22×D4×C43—21no—
120C22×D4×C43C2311yescharacteristic
121C23×C4×C43—21no—
122C23×C4×C43—22no—
123C23×C4×C43—21no—
124C23×C4×C43—22no—
125C23×C4×C43—44no—
126C23×C4×C43D411yescharacteristic, complemented
127C23×C4×C43C2311yescharacteristic
128C23×C4×C43C2311yescharacteristic
129#120×C43—22no—
130#120×C43C2×C414yescomplemented
131C4×D4×C43—22no—
132C4×D4×C43—22no—
133C4×D4×C43—44no—
134C2×C4⋊C4×C43—21no—
135C2×C4⋊C4×C43D411yescharacteristic, complemented
136C2×C22⋊C4×C43—21no—
137C2×C22⋊C4×C43—21no—
138C2×C22⋊C4×C43—21no—
139C2×C22⋊C4×C43—21no—
140C2×C22⋊C4×C43D411yescharacteristic, complemented
141C2×C22⋊C4×C43C2311yescharacteristic
142C2×C22⋊C4×C43C2311yescharacteristic
143C2×C22⋊C4×C43C2311yescharacteristic
144C2×C42×C43—21no—
145C2×C42×C43D411yescharacteristic, complemented
146#95×C43—21no—
147#95×C43—21no—
148#95×C43—21no—
149C24×C43—21no—
150C24×C43—22no—
151C24×C43—21no—
152C24×C43—22no—
153C24×C43—42no—
154C24×C43—42no—
155C24×C43C22×C412yescomplemented
156C24×C43C2×D411yescharacteristic
157C24×C43C2411yescharacteristic
158C23×D43—21no—
159C23×D43C2×D412yes—
160C2×D4×C43—24no—
161C2×D4×C43—22no—
162C2×D4×C43—22no—
163C2×D4×C43—42no—
164C2×D4×C43—42no—
165C2×D4×C43C22×C412yes—
166C2×D4×C43#4112yes—
167C22×C4×C43—24no—
168C22×C4×C43—28no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—22no—
174C22×C4×C43—21no—
175C22×C4×C43—44no—
176C22×C4×C43—42no—
177C22×C4×C43—42no—
178C22×C4×C43—42no—
179C22×C4×C43—44no—
180C22×C4×C43—42no—
181C22×C4×C43—44no—
182C22×C4×C43—42no—
183C22×C4×C43—42no—
184C22×C4×C43—42no—
185C22×C4×C43—41no—
186C22×C4×C43—41no—
187C22×C4×C43C2×D412yes—
188C22×C4×C43C2×D412yes—
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D411yescharacteristic
194C2×C22⋊D43—22no—
195C2×C22⋊D43—24no—
196C2×C22⋊D43—24no—
197C2×C22⋊D43—22no—
198C2×C22⋊D43—22no—
199C2×C22⋊D43—22no—
200C2×C22⋊D43—22no—
201C2×C22⋊D43—28no—
202C2×C22⋊D43—44no—
203C2×C22⋊D43—44no—
204C2×C22⋊D43C22×C414yes—
205C2×C22⋊D43#4114yes—
206C22×Dic43—21no—
207C22×Dic43—21no—
208C22×Dic43—21no—
209C22×Dic43—22no—
210C22×Dic43—22no—
211C22×Dic43C2×D412yes—
212C22×Dic43C2×D412yes—
213C22×Dic43C2×D412yes—
214#10621900—28no—
215#10621900—28no—
216D4×D43—28no—
217D4×D43—28no—
218#10621898—24no—
219#10621898—24no—
220C2×D172—21no—
221C2×C4×D43—22no—
222C2×C4×D43—22no—
223C2×C4×D43—22no—
224C2×C4×D43—22no—
225C2×C4×D43—22no—
226C2×C4×D43—44no—
227C2×C4×D43—82no—
228C2×Dic86—21no—
229C4⋊C4×C43—22no—
230C4⋊C4×C43—42no—
231C22⋊C4×C43—24no—
232C22⋊C4×C43—22no—
233C22⋊C4×C43—22no—
234C22⋊C4×C43—21no—
235C22⋊C4×C43—22no—
236C22⋊C4×C43—42no—
237C22⋊C4×C43—42no—
238C22⋊C4×C43—42no—
239C22⋊C4×C43C22×C412yescomplemented
240C42×C43—21no—
241C42×C43—21no—
242C42×C43—42no—
243C22⋊Dic43—22no—
244C22⋊Dic43—28no—
245C22⋊Dic43—22no—
246C22⋊Dic43—22no—
247C22⋊Dic43—22no—
248C22⋊Dic43—22no—
249C22⋊Dic43—22no—
250C22⋊Dic43—44no—
251C22⋊Dic43—44no—
252C22⋊Dic43C22×C414yescomplemented
253(C2×D43)⋊C4—22no—
254(C2×D43)⋊C4—22no—
255(C2×D43)⋊C4—22no—
256(C2×D43)⋊C4—22no—
257(C2×D43)⋊C4—44no—
258C4⋊Dic43—21no—
259C4⋊Dic43—21no—
260Dic43⋊C4—22no—
261Dic43⋊C4—22no—
262Dic43⋊C4—22no—
263Dic43⋊C4—22no—
264Dic43⋊C4—44no—
265C4×Dic43—22no—
266C4×Dic43—22no—
267C4×Dic43—22no—
268C4×Dic43—22no—
269C4×Dic43—22no—
270C4×Dic43—44no—
271C23×C43—24no—
272C23×C43—24no—
273C23×C43—22no—
274C23×C43—22no—
275C23×C43—24no—
276C23×C43—22no—
277C23×C43—21no—
278C23×C43—21no—
279C23×C43—41no—
280C23×C43—44no—
281C23×C43—41no—
282C23×C43—42no—
283C23×C43—41no—
284C23×C43—42no—
285C23×C43—41no—
286C23×C43—48no—
287C23×C43—44no—
288C23×C43—41no—
289C23×C43—41no—
290C23×C43—41no—
291C23×C43—41no—
292C23×C43—42no—
293C23×C43C4×D412yescomplemented
294C23×C43C23×C411yescharacteristic
295C23×C43C22×D412yes—
296C23×C43C22×D411yescharacteristic
297C23×C43C2×#4112yes—
298C23×C43C2×#4111yescharacteristic
299C22×D43—22no—
300C22×D43—24no—
301C22×D43—22no—
302C22×D43—42no—
303C22×D43—42no—
304C22×D43—81no—
305C22×D43—81no—
306C22×D43C4×D414yescomplemented
307D4×C43—24no—
308D4×C43—24no—
309D4×C43—48no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—24no—
313C2×C4×C43—22no—
314C2×C4×C43—24no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—21no—
318C2×C4×C43—21no—
319C2×C4×C43—42no—
320C2×C4×C43—41no—
321C2×C4×C43—48no—
322C2×C4×C43—44no—
323C2×C4×C43—41no—
324C2×C4×C43—42no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43—42no—
329C2×C4×C43—44no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43—81no—
336C2×C4×C43C4×D412yescomplemented
337C2×C4×C43#12012yes—
338C2×C4×C43#12011yescharacteristic
339C2×C4×C43#12011yescharacteristic
340C22⋊D43—28no—
341C22⋊D43—24no—
342C22⋊D43—24no—
343C22⋊D43—24no—
344C22⋊D43—24no—
345C22⋊D43—416no—
346C2×Dic43—24no—
347C2×Dic43—22no—
348C2×Dic43—22no—
349C2×Dic43—24no—
350C2×Dic43—22no—
351C2×Dic43—22no—
352C2×Dic43—42no—
353C2×Dic43—42no—
354C2×Dic43—42no—
355C2×Dic43—42no—
356C2×Dic43—42no—
357C2×Dic43—42no—
358C2×Dic43—42no—
359C2×Dic43—81no—
360C2×Dic43—81no—
361C2×Dic43C4×D414yescomplemented
362D172—24no—
363C4×D43—28no—
364C4×D43—44no—
365C4×D43—82no—
366C4×D43—82no—
367C4×D43—82no—
368Dic86—24no—
369C4×B(4,𝔽2)—431nomaximal, Sylow
370C22×C43—22no—
371C22×C43—21no—
372C22×C43—22no—
373C22×C43—21no—
374C22×C43—28no—
375C22×C43—24no—
376C22×C43—22no—
377C22×C43—41no—
378C22×C43—42no—
379C22×C43—41no—
380C22×C43—42no—
381C22×C43—44no—
382C22×C43—44no—
383C22×C43—44no—
384C22×C43—42no—
385C22×C43—42no—
386C22×C43—42no—
387C22×C43—41no—
388C22×C43—42no—
389C22×C43—41no—
390C22×C43—42no—
391C22×C43—42no—
392C22×C43—81no—
393C22×C43C2×C4×D412yes—
394C22×C43C2×C4×D411yescharacteristic
395C22×C43C2×#12011yescharacteristic
396C22×C43#52511yescharacteristic
397C22×C43#52512yes—
398C2×D43—24no—
399C2×D43—42no—
400C2×D43—42no—
401C2×D43—44no—
402C2×D43—82no—
403C2×D43—84no—
404C4×C43—22no—
405C4×C43—21no—
406C4×C43—22no—
407C4×C43—42no—
408C4×C43—41no—
409C4×C43—42no—
410C4×C43—41no—
411C4×C43—81no—
412C4×C43B(4,𝔽2)12yescomplemented
413Dic43—24no—
414Dic43—44no—
415Dic43—42no—
416Dic43—42no—
417Dic43—82no—
418C4×H(5,𝔽2)—431no—
419C2×B(4,𝔽2)—431no—
420C4×#120—432no—
421C4×#120D4311yescharacteristic, complemented
422#1889—432no—
423#1889—431no—
424#1867—431no—
425#1867—432no—
426#1790—431no—
427C4×#99—432no—
428C4×#99—431no—
429C2×C43—22no—
430C2×C43—22no—
431C2×C43—21no—
432C2×C43—21no—
433C2×C43—42no—
434C2×C43—44no—
435C2×C43C4×#12011yescharacteristic
436C2×C43C2×B(4,𝔽2)11yescharacteristic
437C2×C43#302511yescharacteristic
438D43—44no—
439C2×H(5,𝔽2)—431no—
440C24×C4C2×D4311yescharacteristic, complemented
441C2×#120—432no—
442C2×#120C2×D4311yescharacteristic
443#520—862no—
444#520—861no—
445#518—431no—
446#518—432no—
447#518—862no—
448#518—861no—
449C4×#41—862no—
450C4×#41—861no—
451C2×C4×D4—21no—
452C2×C4×D4—432no—
453C2×C4×D4—862no—
454C2×C4×D4—861no—
455C2×C4×D4—862no—
456C2×C4×D4C2×D4311yescharacteristic
457B(4,𝔽2)—438no—
458C2×#99—431no—
459C2×#99—432no—
460C2×#99—431no—
461C2×#99—432no—
462#386—21no—
463#386—432no—
464#386—862no—
465#386C2×D4311yescharacteristic
466#385—21no—
467#385—432no—
468#385—862no—
469#385C2×D4311yescharacteristic, complemented
470#379—432no—
471#379C2×D4311yescharacteristic, complemented
472C4×C22⋊C4—21no—
473C4×C22⋊C4—432no—
474C4×C22⋊C4—862no—
475C4×C22⋊C4C2×D4311yescharacteristic, complemented
476#342—432no—
477#342—432no—
478#342—432no—
479C43C4×B(4,𝔽2)11yescharacteristic, complemented, Sylow
480C25C22×D4311yescharacteristic
481H(5,𝔽2)—434no—
482H(5,𝔽2)—864no—
483H(5,𝔽2)—862no—
484C2×#41—862no—
485C2×#41—861no—
486C22×D4—21no—
487C22×D4—432no—
488C22×D4—862no—
489C22×D4—861no—
490C22×D4—862no—
491C22×D4C22×D4311yescharacteristic
492C23×C4—22no—
493C23×C4—21no—
494C23×C4—22no—
495C23×C4—21no—
496C23×C4—44no—
497C23×C4—432no—
498C23×C4—861no—
499C23×C4C22⋊D4311yescharacteristic, complemented
500C23×C4C22×D4311yescharacteristic
501C23×C4C22×D4311yescharacteristic
502#120—22no—
503#120—438no—
504#120—864no—
505#120C4×D4314yescomplemented
506C4×Q8—861no—
507C4×Q8—861no—
508C4×Q8—862no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—44no—
512C4×D4—861no—
513C4×D4—861no—
514C4×D4—862no—
515C4×D4—862no—
516C4×D4—862no—
517C4×D4—862no—
518C4×D4—862no—
519C4×D4—862no—
520C4×D4—862no—
521C4×D4—862no—
522C4×D4—862no—
523C4×D4—862no—
524C4×D4—862no—
525C4×D4—862no—
526C4×D4—862no—
527C4×D4—862no—
528C4×D4—862no—
529C4×D4—1728no—
530#117—862no—
531#117—862no—
532#117—862no—
533#117—862no—
534#117—861no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—432no—
537C2×C4⋊C4—862no—
538C2×C4⋊C4—861no—
539C2×C4⋊C4—862no—
540C2×C4⋊C4C22⋊D4311yescharacteristic, complemented
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—432no—
546C2×C22⋊C4—432no—
547C2×C22⋊C4—432no—
548C2×C22⋊C4—432no—
549C2×C22⋊C4—862no—
550C2×C22⋊C4—862no—
551C2×C22⋊C4—861no—
552C2×C22⋊C4—862no—
553C2×C22⋊C4—861no—
554C2×C22⋊C4—862no—
555C2×C22⋊C4—862no—
556C2×C22⋊C4—862no—
557C2×C22⋊C4C22⋊D4311yescharacteristic, complemented
558C2×C22⋊C4C22×D4311yescharacteristic
559C2×C22⋊C4C22×D4311yescharacteristic
560C2×C22⋊C4C22×D4311yescharacteristic
561C2×C42—21no—
562C2×C42—432no—
563C2×C42—862no—
564C2×C42—861no—
565C2×C42—862no—
566C2×C42C22⋊D4311yescharacteristic, complemented
567#99—434no—
568#99—438no—
569#99—864no—
570#99—862no—
571#95—21no—
572#95—21no—
573#95—21no—
574#95—862no—
575#95—862no—
576#95—862no—
577C24—22no—
578C24—21no—
579C24—22no—
580C24—21no—
581C24—42no—
582C24—42no—
583C24—432no—
584C24—861no—
585C24C2×C4×D4312yescomplemented
586C24C2×C22⋊D4311yescharacteristic
587C24C23×D4311yescharacteristic
588#41—864no—
589#41—868no—
590#41—868no—
591#41—864no—
592C2×Q8—861no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—24no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—434no—
599C2×D4—434no—
600C2×D4—861no—
601C2×D4—868no—
602C2×D4—868no—
603C2×D4—862no—
604C2×D4—864no—
605C2×D4—864no—
606C2×D4—862no—
607C2×D4—862no—
608C2×D4—862no—
609C2×D4—862no—
610C2×D4—868no—
611C2×D4—1724no—
612C2×D4—1724no—
613C2×D4C2×C4×D4312yes—
614C2×D4#1062189812yes—
615C22×C4—24no—
616C22×C4—28no—
617C22×C4—22no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—44no—
627C22×C4—42no—
628C22×C4—44no—
629C22×C4—42no—
630C22×C4—44no—
631C22×C4—42no—
632C22×C4—41no—
633C22×C4—42no—
634C22×C4—41no—
635C22×C4—432no—
636C22×C4—432no—
637C22×C4—432no—
638C22×C4—862no—
639C22×C4—862no—
640C22×C4—862no—
641C22×C4—861no—
642C22×C4—861no—
643C22×C4—861no—
644C22×C4—862no—
645C22×C4—862no—
646C22×C4—862no—
647C22×C4—862no—
648C22×C4—3442no—
649C22×C4—1724no—
650C22×C4D4×D4312yes—
651C22×C4D4×D4312yes—
652C22×C4C2×C22⋊D4311yescharacteristic
653C22×C4C2×C22⋊D4311yescharacteristic
654C22×C4C2×C22⋊D4311yescharacteristic
655C22×C4C2×C22⋊D4311yescharacteristic
656C22×C4C2×C22⋊D4311yescharacteristic
657C4⋊C4—22no—
658C4⋊C4—42no—
659C4⋊C4—862no—
660C4⋊C4—861no—
661C4⋊C4—862no—
662C4⋊C4—861no—
663C4⋊C4—862no—
664C4⋊C4—862no—
665C4⋊C4—1724no—
666C22⋊C4—22no—
667C22⋊C4—21no—
668C22⋊C4—24no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—434no—
675C22⋊C4—862no—
676C22⋊C4—862no—
677C22⋊C4—868no—
678C22⋊C4—862no—
679C22⋊C4—862no—
680C22⋊C4—862no—
681C22⋊C4—862no—
682C22⋊C4—862no—
683C22⋊C4—862no—
684C22⋊C4—862no—
685C22⋊C4—862no—
686C22⋊C4—1724no—
687C22⋊C4—1724no—
688C22⋊C4—1724no—
689C22⋊C4C2×C4×D4312yescomplemented
690C42—21no—
691C42—21no—
692C42—42no—
693C42—862no—
694C42—862no—
695C42—862no—
696C42—862no—
697C42—862no—
698C42—1724no—
699C23—22no—
700C23—22no—
701C23—24no—
702C23—24no—
703C23—24no—
704C23—22no—
705C23—21no—
706C23—21no—
707C23—41no—
708C23—44no—
709C23—41no—
710C23—41no—
711C23—42no—
712C23—41no—
713C23—42no—
714C23—44no—
715C23—48no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—42no—
721C23—434no—
722C23—864no—
723C23—862no—
724C23—862no—
725C23—3441no—
726C23—3441no—
727C23—1722no—
728C23—1722no—
729C23C4×C22⋊D4312yescomplemented
730C23C22×C4×D4311yescharacteristic
731C23C2×D4×D4312yes—
732C23C22×C22⋊D4311yescharacteristic
733C23#41×D4312yes—
734C23C2×#1062189811yescharacteristic
735Q8—864no—
736D4—24no—
737D4—24no—
738D4—48no—
739D4—864no—
740D4—868no—
741D4—864no—
742D4—864no—
743D4—864no—
744D4—864no—
745D4—17216no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—22no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—42no—
756C2×C4—41no—
757C2×C4—44no—
758C2×C4—48no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—44no—
765C2×C4—42no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—81no—
772C2×C4—434no—
773C2×C4—868no—
774C2×C4—864no—
775C2×C4—862no—
776C2×C4—862no—
777C2×C4—864no—
778C2×C4—862no—
779C2×C4—862no—
780C2×C4—3442no—
781C2×C4—3442no—
782C2×C4—3442no—
783C2×C4—3441no—
784C2×C4—3441no—
785C2×C4—1722no—
786C2×C4—1722no—
787C2×C4—1722no—
788C2×C4—1722no—
789C2×C4—1722no—
790C2×C4—1724no—
791C2×C4—1722no—
792C2×C4—1722no—
793C2×C4C4×C22⋊D4312yescomplemented
794C2×C4#1306329311yescharacteristic
795C2×C4#1306329312yes—
796C2×C4#1306329311yescharacteristic
797C22—21no—
798C22—22no—
799C22—21no—
800C22—22no—
801C22—24no—
802C22—28no—
803C22—22no—
804C22—41no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—44no—
812C22—44no—
813C22—44no—
814C22—42no—
815C22—41no—
816C22—41no—
817C22—42no—
818C22—42no—
819C22—81no—
820C22—864no—
821C22—3442no—
822C22—3444no—
823C22—1724no—
824C22—1722no—
825C22—1722no—
826C22C4×D4×D4312yes—
827C22C2×C4×C22⋊D4311yescharacteristic
828C22C2×#1306329311yescharacteristic
829C22#1458340611yescharacteristic
830C22#1458340812yes—
831C4—21no—
832C4—22no—
833C4—22no—
834C4—42no—
835C4—42no—
836C4—41no—
837C4—41no—
838C4—81no—
839C4—864no—
840C4—3442no—
841C4—1724no—
842C4—1722no—
843C4—1722no—
844C4#1458308512yesdirect product factor
845C2—21no—
846C2—21no—
847C2—22no—
848C2—22no—
849C2—44no—
850C2—42no—
851C2—1724no—
852C2C4×#1306329311yescharacteristic
853C2C2×#1458308511yescharacteristic
854C2#1914398611yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC4×#120×C43C2
socleC22×C43C2×#120
prime radicalC2×#14583085C2
cosocleC24×C43C24
hypercenterC4×#120D43
hypocenterC43C4×B(4,𝔽2)
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×#120

Complements

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

NH ≅ G/Ntype
1. C4×#13063370C2semidirect
3. C4×#13063294C2semidirect
4. #19135004C2semidirect
5. #19135000C2semidirect
6. #19134875C2semidirect
7. #19134874C2semidirect
8. #19134542C2semidirect
9. C4×#13063239C2semidirect
10. C4×#13063240C2semidirect
11. C4×#120×C43C2semidirect
26. #14583085C4direct (N × H)
34. #14582772C22semidirect
35. #14582755C22semidirect
37. C4×C22⋊Dic43C22semidirect
38. #14582666C22semidirect
39. #14582665C22semidirect
40. #14582665C22semidirect
41. C24×C4×C43C22semidirect
48. C43×#385C22semidirect
49. C43×#379C22semidirect
51. C4×C22⋊C4×C43C22semidirect
54. #13063370C2×C4semidirect
62. C22×C4×D43D4semidirect
64. #13063294C2×C4semidirect
93. C2×Dic43⋊C4D4semidirect
104. C2×(C2×D43)⋊C4D4semidirect
109. C2×C4×Dic43D4semidirect
112. #13063240C2×C4semidirect
114. #13063239C2×C4semidirect
126. C23×C4×C43D4semidirect
130. #120×C43C2×C4semidirect
135. C2×C4⋊C4×C43D4semidirect
140. C2×C22⋊C4×C43D4semidirect
145. C2×C42×C43D4semidirect
155. C24×C43C22×C4semidirect
239. C22⋊C4×C43C22×C4semidirect
252. C22⋊Dic43C22×C4semidirect
293. C23×C43C4×D4semidirect
306. C22×D43C4×D4semidirect
336. C2×C4×C43C4×D4semidirect
361. C2×Dic43C4×D4semidirect
412. C4×C43B(4,𝔽2)semidirect
421. C4×#120D43semidirect
440. C24×C4C2×D43semidirect
469. #385C2×D43semidirect
471. #379C2×D43semidirect
475. C4×C22⋊C4C2×D43semidirect
479. C43C4×B(4,𝔽2)semidirect
499. C23×C4C22⋊D43semidirect
505. #120C4×D43semidirect
540. C2×C4⋊C4C22⋊D43semidirect
557. C2×C22⋊C4C22⋊D43semidirect
566. C2×C42C22⋊D43semidirect
585. C24C2×C4×D43semidirect
689. C22⋊C4C2×C4×D43semidirect
729. C23C4×C22⋊D43semidirect
793. C2×C4C4×C22⋊D43semidirect
844. C4#14583085direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#130633702
C2×#145830852
C4×#130632942
#191350042
#191350002
#191348752
#191348742
#191345422
C4×#130632392
C4×#130632402
C4×#120×C432
C4×B(4,𝔽2)43