Finite Group Databasebeta

← C4×#14583088 #25102584

Subgroups — C4×#14583088 #25102584

Order 11008.

1538 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13063370C211yesmaximal, characteristic
2C2×#14583088C211yesmaximal, characteristic
3C4×#13063308C212yesmaximal, complemented
4#19135009C211yesmaximal, characteristic, complemented
5#19135005C212yesmaximal, complemented
6#19134875C211yesmaximal, characteristic, complemented
7#19134874C212yesmaximal, complemented
8#19134542C211yesmaximal, characteristic
9C4×#13063239C212yesmaximal, complemented
10C4×#13063240C211yesmaximal, characteristic, complemented
11C4×#123×C43C211yesmaximal, characteristic, complemented
12C2×#13063370C2211yescharacteristic
13C2×#13063308C2212yes—
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—21no—
23C2×C4×C22⋊D43C2212yes—
24C4×D4×D43—22no—
25#14583088C418yesdirect product factor
26C2×#13063240C2211yescharacteristic
27C2×#13063240C2211yescharacteristic
28C2×#13063239C2212yes—
29C2×#13063239C2212yes—
30#14582790—22no—
31#14582783—22no—
32#14582778C2212yes—
33#14582772C2212yescomplemented
34#14582762C2212yescomplemented
35C4×Dic43⋊C4—22no—
36C4×(C2×D43)⋊C4—22no—
37C4×C22⋊Dic43C2212yescomplemented
38#14582666C2212yescomplemented
39#14582665C2212yescomplemented
40#14582665C2212yescomplemented
41C2×#123×C43C2211yescharacteristic
42C2×C4×D4×C43C2211yescharacteristic
43C22×C42×C43C2211yescharacteristic, complemented
44C43×#388—21no—
45C43×#387—21no—
46C43×#386C2211yescharacteristic
47C43×#385C2211yescharacteristic, complemented
48C43×#381C2211yescharacteristic, complemented
49C4×C4⋊C4×C43—21no—
50C4×C22⋊C4×C43—21no—
51C4×C22⋊C4×C43C2211yescharacteristic, complemented
52#13063370—22no—
53#13063370—24no—
54#13063370C2×C414yes—
55C2×#10621898—21no—
56C2×#10621900—22no—
57C22×C22⋊D43—21no—
58C22×C22⋊D43C2312yes—
59C2×D4×D43—22no—
60C22×C4×D43—21no—
61C22×C4×D43D412yes—
62#13063308—24no—
63#13063308C2×C418yescomplemented
64C4×Dic86—21no—
65C4×Dic86—21no—
66#13063290—22no—
67C4×D172—21no—
68C4×D172—21no—
69D4×Dic43—22no—
70D4×Dic43—22no—
71#13063287—22no—
72C4×C22⋊D43—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—
80(C22⋊D43)⋊C4—22no—
81(C22⋊D43)⋊C4—22no—
82(C22⋊D43)⋊C4—22no—
83(C22⋊D43)⋊C4—22no—
84#13063284—21no—
85#13063283—22no—
86#13063282—22no—
87#13063281—22no—
88#13063281—22no—
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—22no—
91C2×Dic43⋊C4—22no—
92C2×Dic43⋊C4D412yes—
93C4⋊C4×D43—22no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43C2312yes—
96C2×C22⋊Dic43C2312yes—
97C2×C22⋊Dic43C2312yes—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—22no—
100C2×(C2×D43)⋊C4—22no—
101C2×(C2×D43)⋊C4D412yes—
102C22⋊C4×D43—22no—
103C22⋊C4×D43—22no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43—22no—
106C2×C4×Dic43D412yes—
107C42×D43—22no—
108#13063240—22no—
109#13063240C2×C414yescomplemented
110#13063239—24no—
111#13063239C2×C418yescomplemented
112C43⋊#95—22no—
113C43⋊#95—22no—
114C43⋊#95—22no—
115C43⋊#95—22no—
116C43⋊#95—22no—
117C22×D4×C43C2311yescharacteristic
118C23×C4×C43D411yescharacteristic
119C23×C4×C43C2311yescharacteristic
120C23×C4×C43C2311yescharacteristic
121C23×C4×C43C2311yescharacteristic
122#123×C43—22no—
123#123×C43C2×C414yescomplemented
124C4×D4×C43—22no—
125C4×D4×C43—22no—
126C2×C4⋊C4×C43—21no—
127C2×C4⋊C4×C43—21no—
128C2×C4⋊C4×C43D411yescharacteristic
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43D411yescharacteristic
132C2×C22⋊C4×C43C2311yescharacteristic
133C2×C22⋊C4×C43C2311yescharacteristic
134C2×C22⋊C4×C43C2311yescharacteristic
135C2×C42×C43—22no—
136C2×C42×C43—21no—
137C2×C42×C43—21no—
138C2×C42×C43—22no—
139C2×C42×C43—21no—
140C2×C42×C43D411yescharacteristic
141#95×C43—21no—
142#95×C43—21no—
143#95×C43—21no—
144#95×C43—21no—
145#95×C43—21no—
146C24×C43C2×D411yescharacteristic
147C24×C43C2411yescharacteristic
148C23×D43—21no—
149C23×D43C2×D412yes—
150C2×D4×C43—22no—
151C2×D4×C43—22no—
152C2×D4×C43C22×C412yes—
153C2×D4×C43#4112yes—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—22no—
160C22×C4×C43—22no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—22no—
164C22×C4×C43—42no—
165C22×C4×C43—42no—
166C22×C4×C43—42no—
167C22×C4×C43C22×C412yescomplemented
168C22×C4×C43C2×D412yes—
169C22×C4×C43C2×D412yes—
170C22×C4×C43C2×D411yescharacteristic
171C22×C4×C43C2×D411yescharacteristic
172C22×C4×C43C2×D411yescharacteristic
173C22×C4×C43C2×D411yescharacteristic
174C22×C4×C43C2×D411yescharacteristic
175C2×C22⋊D43—22no—
176C2×C22⋊D43—24no—
177C2×C22⋊D43—24no—
178C2×C22⋊D43—22no—
179C2×C22⋊D43—22no—
180C2×C22⋊D43—22no—
181C2×C22⋊D43—22no—
182C2×C22⋊D43C22×C414yes—
183C2×C22⋊D43#4114yes—
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43—21no—
187C22×Dic43—22no—
188C22×Dic43—22no—
189C22×Dic43C2×D412yes—
190C22×Dic43C2×D412yes—
191C22×Dic43C2×D412yes—
192#10621900—28no—
193#10621900—28no—
194D4×D43—28no—
195D4×D43—28no—
196#10621898—24no—
197#10621898—24no—
198C2×D172—21no—
199C2×C4×D43—22no—
200C2×C4×D43—22no—
201C2×C4×D43—22no—
202C2×C4×D43—22no—
203C2×C4×D43—22no—
204C2×C4×D43—44no—
205C2×C4×D43—82no—
206C2×Dic86—21no—
207C4⋊C4×C43—24no—
208C4⋊C4×C43—22no—
209C4⋊C4×C43—42no—
210C22⋊C4×C43—22no—
211C22⋊C4×C43—24no—
212C22⋊C4×C43—22no—
213C22⋊C4×C43—21no—
214C22⋊C4×C43—22no—
215C22⋊C4×C43—42no—
216C22⋊C4×C43C22×C412yescomplemented
217C42×C43—21no—
218C42×C43—21no—
219C42×C43—42no—
220C42×C43—42no—
221C42×C43—41no—
222C42×C43—41no—
223C22⋊Dic43—22no—
224C22⋊Dic43—22no—
225C22⋊Dic43—22no—
226C22⋊Dic43—22no—
227C22⋊Dic43—22no—
228C22⋊Dic43—22no—
229C22⋊Dic43C22×C414yescomplemented
230(C2×D43)⋊C4—22no—
231(C2×D43)⋊C4—22no—
232(C2×D43)⋊C4—22no—
233(C2×D43)⋊C4—22no—
234(C2×D43)⋊C4—28no—
235(C2×D43)⋊C4—44no—
236C4⋊Dic43—21no—
237C4⋊Dic43—21no—
238Dic43⋊C4—22no—
239Dic43⋊C4—22no—
240Dic43⋊C4—22no—
241Dic43⋊C4—22no—
242Dic43⋊C4—28no—
243Dic43⋊C4—44no—
244C4×Dic43—22no—
245C4×Dic43—22no—
246C4×Dic43—22no—
247C4×Dic43—22no—
248C4×Dic43—22no—
249C4×Dic43—44no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43C4×D412yes—
257C23×C43C23×C411yescharacteristic
258C23×C43C22×D412yes—
259C23×C43C22×D411yescharacteristic
260C23×C43C2×#4112yes—
261C23×C43C2×#4111yescharacteristic
262C22×D43—22no—
263C22×D43—24no—
264C22×D43—22no—
265C22×D43—42no—
266C22×D43—42no—
267C22×D43—81no—
268C22×D43—81no—
269C22×D43C4×D414yes—
270D4×C43—24no—
271D4×C43—24no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—24no—
275C2×C4×C43—22no—
276C2×C4×C43—24no—
277C2×C4×C43—22no—
278C2×C4×C43—24no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—21no—
282C2×C4×C43—21no—
283C2×C4×C43—42no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—42no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—42no—
293C2×C4×C43—42no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
299C2×C4×C43—81no—
300C2×C4×C43C4×D412yes—
301C2×C4×C43#12012yes—
302C2×C4×C43#12011yescharacteristic
303C2×C4×C43#12011yescharacteristic
304C22⋊D43—28no—
305C22⋊D43—24no—
306C22⋊D43—24no—
307C22⋊D43—24no—
308C22⋊D43—24no—
309C2×Dic43—24no—
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—24no—
313C2×Dic43—22no—
314C2×Dic43—22no—
315C2×Dic43—42no—
316C2×Dic43—42no—
317C2×Dic43—42no—
318C2×Dic43—42no—
319C2×Dic43—42no—
320C2×Dic43—42no—
321C2×Dic43—42no—
322C2×Dic43—81no—
323C2×Dic43—81no—
324C2×Dic43C4×D414yes—
325D172—24no—
326C4×D43—28no—
327C4×D43—44no—
328C4×D43—82no—
329C4×D43—82no—
330C4×D43—82no—
331Dic86—24no—
332C4×#458—431nomaximal, Sylow
333C22×C43—22no—
334C22×C43—21no—
335C22×C43—22no—
336C22×C43—21no—
337C22×C43—22no—
338C22×C43—41no—
339C22×C43—42no—
340C22×C43—41no—
341C22×C43—42no—
342C22×C43—41no—
343C22×C43—41no—
344C22×C43—81no—
345C22×C43C2×C4×D412yes—
346C22×C43C2×C4×D411yescharacteristic
347C22×C43C2×#12011yescharacteristic
348C22×C43#52511yescharacteristic
349C22×C43#52512yes—
350C2×D43—24no—
351C2×D43—42no—
352C2×D43—42no—
353C2×D43—44no—
354C2×D43—82no—
355C2×D43—84no—
356C4×C43—22no—
357C4×C43—21no—
358C4×C43—22no—
359C4×C43—42no—
360C4×C43—41no—
361C4×C43—41no—
362C4×C43—42no—
363C4×C43—42no—
364C4×C43—81no—
365C4×C43#45812yescomplemented
366Dic43—24no—
367Dic43—44no—
368Dic43—42no—
369Dic43—42no—
370Dic43—82no—
371C4×H(5,𝔽2)—431no—
372C2×#458—431no—
373C4×#123—432no—
374C4×#123D4311yescharacteristic, complemented
375#1890—432no—
376#1890—431no—
377#1867—431no—
378#1867—432no—
379#1790—431no—
380C4×#99—432no—
381C4×#99—431no—
382C2×C43—22no—
383C2×C43—22no—
384C2×C43—21no—
385C2×C43—21no—
386C2×C43—42no—
387C2×C43C4×#12011yescharacteristic
388C2×C43C2×#45811yescharacteristic
389C2×C43#302511yescharacteristic
390D43—44no—
391C2×H(5,𝔽2)—431no—
392C2×#123—432no—
393C2×#123C2×D4311yescharacteristic
394#520—862no—
395#520—861no—
396#518—431no—
397#518—432no—
398#518—862no—
399#518—861no—
400C4×#41—862no—
401C4×#41—861no—
402C2×C4×D4—432no—
403C2×C4×D4—862no—
404C2×C4×D4—861no—
405C2×C4×D4C2×D4311yescharacteristic
406C22×C42C2×D4311yescharacteristic, complemented
407#458—438no—
408C2×#99—431no—
409C2×#99—432no—
410C2×#99—431no—
411C2×#99—432no—
412#388—21no—
413#388—862no—
414#387—21no—
415#387—862no—
416#386—432no—
417#386C2×D4311yescharacteristic
418#385—432no—
419#385C2×D4311yescharacteristic, complemented
420#381—432no—
421#381C2×D4311yescharacteristic, complemented
422C4×C4⋊C4—21no—
423C4×C4⋊C4—862no—
424C4×C22⋊C4—21no—
425C4×C22⋊C4—432no—
426C4×C22⋊C4—862no—
427C4×C22⋊C4C2×D4311yescharacteristic, complemented
428#342—432no—
429#342—432no—
430#342—432no—
431C43C4×#45811yescharacteristic, complemented, Sylow
432H(5,𝔽2)—434no—
433H(5,𝔽2)—864no—
434H(5,𝔽2)—862no—
435C2×#41—862no—
436C2×#41—861no—
437C22×D4—432no—
438C22×D4—862no—
439C22×D4—861no—
440C22×D4C22×D4311yescharacteristic
441C23×C4—432no—
442C23×C4—861no—
443C23×C4C22⋊D4311yescharacteristic
444C23×C4C22×D4311yescharacteristic
445C23×C4C22×D4311yescharacteristic
446C23×C4C22×D4311yescharacteristic
447#123—22no—
448#123—438no—
449#123—864no—
450#123C4×D4314yescomplemented
451C4×Q8—861no—
452C4×Q8—861no—
453C4×Q8—862no—
454C4×D4—22no—
455C4×D4—22no—
456C4×D4—861no—
457C4×D4—861no—
458C4×D4—862no—
459C4×D4—862no—
460C4×D4—862no—
461C4×D4—862no—
462C4×D4—862no—
463C4×D4—862no—
464C4×D4—862no—
465C4×D4—862no—
466C4×D4—862no—
467C4×D4—862no—
468C4×D4—862no—
469C4×D4—862no—
470C4×D4—862no—
471C4×D4—862no—
472C4×D4—862no—
473#117—862no—
474#117—862no—
475#117—862no—
476#117—862no—
477#117—861no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—432no—
481C2×C4⋊C4—862no—
482C2×C4⋊C4—862no—
483C2×C4⋊C4—861no—
484C2×C4⋊C4—862no—
485C2×C4⋊C4C22⋊D4311yescharacteristic
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—432no—
489C2×C22⋊C4—432no—
490C2×C22⋊C4—432no—
491C2×C22⋊C4—432no—
492C2×C22⋊C4—862no—
493C2×C22⋊C4—862no—
494C2×C22⋊C4—862no—
495C2×C22⋊C4—861no—
496C2×C22⋊C4—861no—
497C2×C22⋊C4—862no—
498C2×C22⋊C4C22⋊D4311yescharacteristic
499C2×C22⋊C4C22×D4311yescharacteristic
500C2×C22⋊C4C22×D4311yescharacteristic
501C2×C22⋊C4C22×D4311yescharacteristic
502C2×C42—22no—
503C2×C42—22no—
504C2×C42—21no—
505C2×C42—21no—
506C2×C42—21no—
507C2×C42—432no—
508C2×C42—862no—
509C2×C42—861no—
510C2×C42—862no—
511C2×C42C22⋊D4311yescharacteristic
512#99—434no—
513#99—438no—
514#99—864no—
515#99—862no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—862no—
522#95—862no—
523#95—862no—
524#95—862no—
525#95—862no—
526C24—432no—
527C24—861no—
528C24C2×C22⋊D4311yescharacteristic
529C24C23×D4311yescharacteristic
530#41—864no—
531#41—868no—
532#41—868no—
533#41—864no—
534C2×Q8—861no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—434no—
538C2×D4—434no—
539C2×D4—861no—
540C2×D4—868no—
541C2×D4—868no—
542C2×D4—862no—
543C2×D4—864no—
544C2×D4—864no—
545C2×D4—862no—
546C2×D4—862no—
547C2×D4—862no—
548C2×D4—862no—
549C2×D4C2×C4×D4312yes—
550C2×D4#1062189812yes—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—432no—
565C22×C4—432no—
566C22×C4—432no—
567C22×C4—862no—
568C22×C4—862no—
569C22×C4—862no—
570C22×C4—861no—
571C22×C4—861no—
572C22×C4—861no—
573C22×C4—862no—
574C22×C4—862no—
575C22×C4—862no—
576C22×C4—862no—
577C22×C4—3442no—
578C22×C4—1724no—
579C22×C4C2×C4×D4312yescomplemented
580C22×C4D4×D4312yes—
581C22×C4D4×D4312yes—
582C22×C4C2×C22⋊D4311yescharacteristic
583C22×C4C2×C22⋊D4311yescharacteristic
584C22×C4C2×C22⋊D4311yescharacteristic
585C22×C4C2×C22⋊D4311yescharacteristic
586C22×C4C2×C22⋊D4311yescharacteristic
587C4⋊C4—24no—
588C4⋊C4—22no—
589C4⋊C4—42no—
590C4⋊C4—868no—
591C4⋊C4—862no—
592C4⋊C4—861no—
593C4⋊C4—862no—
594C4⋊C4—861no—
595C4⋊C4—862no—
596C4⋊C4—862no—
597C4⋊C4—1724no—
598C22⋊C4—24no—
599C22⋊C4—22no—
600C22⋊C4—21no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—42no—
604C22⋊C4—434no—
605C22⋊C4—868no—
606C22⋊C4—862no—
607C22⋊C4—862no—
608C22⋊C4—862no—
609C22⋊C4—862no—
610C22⋊C4—862no—
611C22⋊C4—862no—
612C22⋊C4—862no—
613C22⋊C4—862no—
614C22⋊C4—862no—
615C22⋊C4—862no—
616C22⋊C4—1724no—
617C22⋊C4C2×C4×D4312yescomplemented
618C42—21no—
619C42—21no—
620C42—42no—
621C42—41no—
622C42—42no—
623C42—41no—
624C42—862no—
625C42—862no—
626C42—862no—
627C42—862no—
628C42—862no—
629C42—1724no—
630C23—21no—
631C23—21no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—434no—
637C23—864no—
638C23—862no—
639C23—862no—
640C23—3441no—
641C23—3441no—
642C23—1722no—
643C23—1722no—
644C23C4×C22⋊D4312yes—
645C23C22×C4×D4311yescharacteristic
646C23C2×D4×D4312yes—
647C23C22×C22⋊D4311yescharacteristic
648C23#41×D4312yes—
649C23C2×#1062189811yescharacteristic
650Q8—864no—
651D4—24no—
652D4—24no—
653D4—864no—
654D4—868no—
655D4—864no—
656D4—864no—
657D4—864no—
658D4—864no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—42no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—42no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—81no—
687C2×C4—434no—
688C2×C4—868no—
689C2×C4—864no—
690C2×C4—862no—
691C2×C4—862no—
692C2×C4—864no—
693C2×C4—862no—
694C2×C4—862no—
695C2×C4—3442no—
696C2×C4—3442no—
697C2×C4—3442no—
698C2×C4—3441no—
699C2×C4—3441no—
700C2×C4—1722no—
701C2×C4—1722no—
702C2×C4—1722no—
703C2×C4—1722no—
704C2×C4—1722no—
705C2×C4—1724no—
706C2×C4—1722no—
707C2×C4—1722no—
708C2×C4C4×C22⋊D4312yes—
709C2×C4#1306329311yescharacteristic
710C2×C4#1306329312yes—
711C2×C4#1306329311yescharacteristic
712C22—21no—
713C22—22no—
714C22—21no—
715C22—22no—
716C22—22no—
717C22—41no—
718C22—42no—
719C22—41no—
720C22—42no—
721C22—41no—
722C22—41no—
723C22—81no—
724C22—864no—
725C22—3442no—
726C22—3444no—
727C22—1724no—
728C22—1722no—
729C22—1722no—
730C22C4×D4×D4312yes—
731C22C2×C4×C22⋊D4311yescharacteristic
732C22C2×#1306329311yescharacteristic
733C22#1458340611yescharacteristic
734C22#1458340812yes—
735C4—21no—
736C4—22no—
737C4—22no—
738C4—42no—
739C4—41no—
740C4—42no—
741C4—41no—
742C4—42no—
743C4—81no—
744C4—864no—
745C4—3442no—
746C4—1724no—
747C4—1722no—
748C4—1722no—
749C4#1458308812yesdirect product factor
750C2—21no—
751C2—21no—
752C2—22no—
753C2—22no—
754C2—42no—
755C2—1724no—
756C2C4×#1306329311yescharacteristic
757C2C2×#1458308811yescharacteristic
758C2#1914398611yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC4×#123×C43C2
socleC22×C43C2×#120
prime radicalC2×#13063370C22
cosocleC24×C43C24
hypercenterC4×#123D43
hypocenterC43C4×#458
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×#123

Complements

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

NH ≅ G/Ntype
3. C4×#13063308C2semidirect
4. #19135009C2semidirect
5. #19135005C2semidirect
6. #19134875C2semidirect
7. #19134874C2semidirect
9. C4×#13063239C2semidirect
10. C4×#13063240C2semidirect
11. C4×#123×C43C2semidirect
25. #14583088C4direct (N × H)
33. #14582772C22semidirect
34. #14582762C22semidirect
37. C4×C22⋊Dic43C22semidirect
38. #14582666C22semidirect
39. #14582665C22semidirect
40. #14582665C22semidirect
43. C22×C42×C43C22semidirect
47. C43×#385C22semidirect
48. C43×#381C22semidirect
51. C4×C22⋊C4×C43C22semidirect
63. #13063308C2×C4semidirect
109. #13063240C2×C4semidirect
111. #13063239C2×C4semidirect
123. #123×C43C2×C4semidirect
167. C22×C4×C43C22×C4semidirect
216. C22⋊C4×C43C22×C4semidirect
229. C22⋊Dic43C22×C4semidirect
365. C4×C43#458semidirect
374. C4×#123D43semidirect
406. C22×C42C2×D43semidirect
419. #385C2×D43semidirect
421. #381C2×D43semidirect
427. C4×C22⋊C4C2×D43semidirect
431. C43C4×#458semidirect
450. #123C4×D43semidirect
579. C22×C4C2×C4×D43semidirect
617. C22⋊C4C2×C4×D43semidirect
749. C4#14583088direct (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×#145830882
C4×#130633082
#191350092
#191350052
#191348752
#191348742
#191345422
C4×#130632392
C4×#130632402
C4×#123×C432
C4×#45843