Finite Group Databasebeta

← #25102598

Subgroups — #25102598

Order 11008.

1630 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13063370C211yesmaximal, characteristic, complemented
2C2×#14583085C211yesmaximal, characteristic
3#19137253C212yesmaximal, 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
11C43×#2321C211yesmaximal, 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—21no—
23C2×C4×C22⋊D43C2212yes—
24C4×D4×D43—22no—
25#14583085C418yescomplemented
26C2×#13063240C2211yescharacteristic
27C2×#13063240C2211yescharacteristic
28C2×#13063239C2212yes—
29C2×#13063239C2212yes—
30#14582799—22no—
31#14582793—22no—
32#14582787—22no—
33#14582778C2212yes—
34#14582775—22no—
35#14582772C2212yescomplemented
36#14582755C2212yescomplemented
37C4×C22⋊Dic43C2212yescomplemented
38#14582666C2212yescomplemented
39#14582665C2212yescomplemented
40#14582665C2212yescomplemented
41C2×#120×C43C2211yescharacteristic
42C2×C4×D4×C43C2211yescharacteristic
43C22×C22⋊C4×C43C2211yescharacteristic, complemented
44C43×#390—21no—
45C43×#388—21no—
46C43×#388—21no—
47C43×#386—21no—
48C43×#386C2211yescharacteristic
49C43×#385C2211yescharacteristic, complemented
50C43×#379C2211yescharacteristic, complemented
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⋊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—
81(C22⋊D43)⋊C4—22no—
82(C22⋊D43)⋊C4—22no—
83(C22⋊D43)⋊C4—22no—
84(C22⋊D43)⋊C4—22no—
85#13063284—21no—
86#13063283—22no—
87#13063282—22no—
88#13063281—22no—
89#13063281—22no—
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—22no—
92C2×Dic43⋊C4D412yescomplemented
93C4⋊C4×D43—22no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—22no—
96C2×C22⋊Dic43—22no—
97C2×C22⋊Dic43—22no—
98C2×C22⋊Dic43C2312yes—
99C2×C22⋊Dic43C2312yes—
100C2×C22⋊Dic43C2312yes—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—22no—
103C2×(C2×D43)⋊C4D412yescomplemented
104C22⋊C4×D43—22no—
105C22⋊C4×D43—22no—
106C2×C4×Dic43—21no—
107C2×C4×Dic43—22no—
108C2×C4×Dic43D412yescomplemented
109C42×D43—22no—
110#13063240—22no—
111#13063240C2×C414yescomplemented
112#13063239—24no—
113#13063239C2×C418yescomplemented
114C43⋊#95—22no—
115C43⋊#95—22no—
116C43⋊#95—22no—
117C25×C43C2311yescharacteristic
118C22×D4×C43—21no—
119C22×D4×C43C2311yescharacteristic
120C23×C4×C43D411yescharacteristic, complemented
121C23×C4×C43C2311yescharacteristic
122C23×C4×C43C2311yescharacteristic
123#120×C43—22no—
124#120×C43C2×C414yescomplemented
125C4×D4×C43—22no—
126C4×D4×C43—22no—
127C2×C4⋊C4×C43—21no—
128C2×C4⋊C4×C43D411yescharacteristic, complemented
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43—22no—
131C2×C22⋊C4×C43—22no—
132C2×C22⋊C4×C43—21no—
133C2×C22⋊C4×C43—21no—
134C2×C22⋊C4×C43—21no—
135C2×C22⋊C4×C43—21no—
136C2×C22⋊C4×C43—21no—
137C2×C22⋊C4×C43D411yescharacteristic, complemented
138C2×C22⋊C4×C43C2311yescharacteristic
139C2×C22⋊C4×C43C2311yescharacteristic
140C2×C22⋊C4×C43C2311yescharacteristic
141C2×C42×C43—21no—
142C2×C42×C43D411yescharacteristic, complemented
143#95×C43—21no—
144#95×C43—21no—
145#95×C43—21no—
146C24×C43—21no—
147C24×C43—22no—
148C24×C43—21no—
149C24×C43—22no—
150C24×C43—81no—
151C24×C43—81no—
152C24×C43C22×C412yescomplemented
153C24×C43C2×D411yescharacteristic
154C24×C43C2411yescharacteristic
155C23×D43—21no—
156C23×D43C2×D412yes—
157C2×D4×C43—24no—
158C2×D4×C43—22no—
159C2×D4×C43—22no—
160C2×D4×C43—81no—
161C2×D4×C43—81no—
162C2×D4×C43C22×C412yes—
163C2×D4×C43#4112yes—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—22no—
170C22×C4×C43—81no—
171C22×C4×C43—81no—
172C22×C4×C43—81no—
173C22×C4×C43C2×D412yes—
174C22×C4×C43C2×D412yes—
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2×D411yescharacteristic
180C2×C22⋊D43—22no—
181C2×C22⋊D43—24no—
182C2×C22⋊D43—24no—
183C2×C22⋊D43—22no—
184C2×C22⋊D43—22no—
185C2×C22⋊D43—22no—
186C2×C22⋊D43—22no—
187C2×C22⋊D43—28no—
188C2×C22⋊D43—82no—
189C2×C22⋊D43—82no—
190C2×C22⋊D43C22×C414yes—
191C2×C22⋊D43#4114yes—
192C22×Dic43—21no—
193C22×Dic43—21no—
194C22×Dic43—21no—
195C22×Dic43—22no—
196C22×Dic43—22no—
197C22×Dic43C2×D412yes—
198C22×Dic43C2×D412yes—
199C22×Dic43C2×D412yes—
200#10621900—28no—
201#10621900—28no—
202D4×D43—28no—
203D4×D43—28no—
204#10621898—24no—
205#10621898—24no—
206C2×D172—21no—
207C2×C4×D43—22no—
208C2×C4×D43—22no—
209C2×C4×D43—22no—
210C2×C4×D43—22no—
211C2×C4×D43—22no—
212C2×C4×D43—82no—
213C2×C4×D43—82no—
214C2×Dic86—21no—
215C4⋊C4×C43—22no—
216C4⋊C4×C43—81no—
217C22⋊C4×C43—24no—
218C22⋊C4×C43—22no—
219C22⋊C4×C43—22no—
220C22⋊C4×C43—21no—
221C22⋊C4×C43—22no—
222C22⋊C4×C43—41no—
223C22⋊C4×C43—42no—
224C22⋊C4×C43—41no—
225C22⋊C4×C43—81no—
226C22⋊C4×C43—81no—
227C22⋊C4×C43—81no—
228C22⋊C4×C43C22×C412yescomplemented
229C42×C43—21no—
230C42×C43—21no—
231C42×C43—81no—
232C22⋊Dic43—22no—
233C22⋊Dic43—28no—
234C22⋊Dic43—22no—
235C22⋊Dic43—22no—
236C22⋊Dic43—22no—
237C22⋊Dic43—22no—
238C22⋊Dic43—22no—
239C22⋊Dic43—82no—
240C22⋊Dic43—82no—
241C22⋊Dic43C22×C414yescomplemented
242(C2×D43)⋊C4—22no—
243(C2×D43)⋊C4—22no—
244(C2×D43)⋊C4—22no—
245(C2×D43)⋊C4—22no—
246(C2×D43)⋊C4—82no—
247C4⋊Dic43—21no—
248C4⋊Dic43—21no—
249Dic43⋊C4—22no—
250Dic43⋊C4—22no—
251Dic43⋊C4—22no—
252Dic43⋊C4—22no—
253Dic43⋊C4—82no—
254C4×Dic43—22no—
255C4×Dic43—22no—
256C4×Dic43—22no—
257C4×Dic43—22no—
258C4×Dic43—22no—
259C4×Dic43—82no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—24no—
263C23×C43—22no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—42no—
269C23×C43—42no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—42no—
273C23×C43—42no—
274C23×C43—41no—
275C23×C43—41no—
276C23×C43—41no—
277C23×C43—41no—
278C23×C43—42no—
279C23×C43—82no—
280C23×C43—84no—
281C23×C43—82no—
282C23×C43C4×D412yes—
283C23×C43C23×C411yescharacteristic
284C23×C43C22×D412yes—
285C23×C43C22×D411yescharacteristic
286C23×C43C2×#4112yes—
287C23×C43C2×#4111yescharacteristic
288C22×D43—22no—
289C22×D43—24no—
290C22×D43—22no—
291C22×D43—42no—
292C22×D43—42no—
293C22×D43—81no—
294C22×D43—81no—
295C22×D43C4×D414yes—
296D4×C43—24no—
297D4×C43—24no—
298D4×C43—84no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43—22no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—42no—
305C2×C4×C43—41no—
306C2×C4×C43—42no—
307C2×C4×C43—41no—
308C2×C4×C43—42no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—42no—
314C2×C4×C43—42no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43—41no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43—81no—
322C2×C4×C43C4×D412yes—
323C2×C4×C43#12011yescharacteristic
324C2×C4×C43#12012yes—
325C2×C4×C43#12011yescharacteristic
326C22⋊D43—28no—
327C22⋊D43—24no—
328C22⋊D43—24no—
329C22⋊D43—24no—
330C22⋊D43—24no—
331C22⋊D43—88no—
332C2×Dic43—24no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—24no—
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—42no—
339C2×Dic43—42no—
340C2×Dic43—42no—
341C2×Dic43—42no—
342C2×Dic43—42no—
343C2×Dic43—42no—
344C2×Dic43—42no—
345C2×Dic43—81no—
346C2×Dic43—81no—
347C2×Dic43C4×D414yes—
348D172—24no—
349C4×D43—28no—
350C4×D43—44no—
351C4×D43—82no—
352C4×D43—82no—
353C4×D43—82no—
354Dic86—24no—
355#21482—431nomaximal, Sylow
356C22×C43—22no—
357C22×C43—21no—
358C22×C43—22no—
359C22×C43—21no—
360C22×C43—22no—
361C22×C43—41no—
362C22×C43—42no—
363C22×C43—41no—
364C22×C43—42no—
365C22×C43—44no—
366C22×C43—42no—
367C22×C43—44no—
368C22×C43—42no—
369C22×C43—41no—
370C22×C43—41no—
371C22×C43—42no—
372C22×C43—81no—
373C22×C43—82no—
374C22×C43—82no—
375C22×C43—81no—
376C22×C43—81no—
377C22×C43—81no—
378C22×C43—81no—
379C22×C43C2×C4×D412yes—
380C22×C43C2×C4×D411yescharacteristic
381C22×C43C2×#12011yescharacteristic
382C22×C43#52511yescharacteristic
383C22×C43#52512yes—
384C2×D43—24no—
385C2×D43—42no—
386C2×D43—42no—
387C2×D43—44no—
388C2×D43—82no—
389C2×D43—84no—
390C4×C43—21no—
391C4×C43—22no—
392C4×C43—21no—
393C4×C43—22no—
394C4×C43—42no—
395C4×C43—41no—
396C4×C43—41no—
397C4×C43—81no—
398C4×C43—81no—
399Dic43—24no—
400Dic43—44no—
401Dic43—42no—
402Dic43—42no—
403Dic43—82no—
404C4×H(5,𝔽2)—431no—
405C2×B(4,𝔽2)—431no—
406#2321—432no—
407#2321D4311yescharacteristic, complemented
408#1889—432no—
409#1889—431no—
410#1867—431no—
411#1867—432no—
412#1790—431no—
413C4×#99—432no—
414C4×#99—431no—
415C2×C43—22no—
416C2×C43—22no—
417C2×C43—21no—
418C2×C43—21no—
419C2×C43—42no—
420C2×C43—82no—
421C2×C43C4×#12011yescharacteristic
422C2×C43#302611yescharacteristic
423C2×C43#302711yescharacteristic
424D43—44no—
425C2×H(5,𝔽2)—431no—
426C2×#120—432no—
427C2×#120C2×D4311yescharacteristic
428#520—862no—
429#520—861no—
430#518—431no—
431#518—432no—
432#518—862no—
433#518—861no—
434C4×#41—862no—
435C4×#41—861no—
436C2×C4×D4—432no—
437C2×C4×D4—862no—
438C2×C4×D4—861no—
439C2×C4×D4C2×D4311yescharacteristic
440C22×C22⋊C4C2×D4311yescharacteristic, complemented
441B(4,𝔽2)—438no—
442C2×#99—431no—
443C2×#99—432no—
444C2×#99—431no—
445C2×#99—432no—
446#390—21no—
447#390—862no—
448#388—21no—
449#388—21no—
450#388—862no—
451#388—862no—
452#386—21no—
453#386—432no—
454#386—862no—
455#386C2×D4311yescharacteristic
456#385—432no—
457#385C2×D4311yescharacteristic, complemented
458#379—432no—
459#379C2×D4311yescharacteristic, complemented
460C4×C22⋊C4—432no—
461C4×C22⋊C4C2×D4311yescharacteristic, complemented
462#342—432no—
463#342—432no—
464#342—432no—
465C43#2148211yescharacteristic, complemented, Sylow
466C25C22×D4311yescharacteristic
467H(5,𝔽2)—434no—
468H(5,𝔽2)—864no—
469H(5,𝔽2)—862no—
470C2×#41—862no—
471C2×#41—861no—
472C22×D4—21no—
473C22×D4—432no—
474C22×D4—862no—
475C22×D4—861no—
476C22×D4—862no—
477C22×D4C22×D4311yescharacteristic
478C23×C4—432no—
479C23×C4—861no—
480C23×C4C22⋊D4311yescharacteristic, complemented
481C23×C4C22×D4311yescharacteristic
482C23×C4C22×D4311yescharacteristic
483#120—22no—
484#120—438no—
485#120—864no—
486#120C4×D4314yescomplemented
487C4×Q8—861no—
488C4×Q8—861no—
489C4×Q8—862no—
490C4×D4—22no—
491C4×D4—22no—
492C4×D4—861no—
493C4×D4—861no—
494C4×D4—862no—
495C4×D4—862no—
496C4×D4—862no—
497C4×D4—862no—
498C4×D4—862no—
499C4×D4—862no—
500C4×D4—862no—
501C4×D4—862no—
502C4×D4—862no—
503C4×D4—862no—
504C4×D4—862no—
505C4×D4—862no—
506C4×D4—862no—
507C4×D4—862no—
508C4×D4—862no—
509#117—862no—
510#117—862no—
511#117—862no—
512#117—862no—
513#117—861no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—432no—
516C2×C4⋊C4—862no—
517C2×C4⋊C4—861no—
518C2×C4⋊C4—862no—
519C2×C4⋊C4C22⋊D4311yescharacteristic, complemented
520C2×C22⋊C4—21no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—432no—
529C2×C22⋊C4—432no—
530C2×C22⋊C4—432no—
531C2×C22⋊C4—432no—
532C2×C22⋊C4—862no—
533C2×C22⋊C4—862no—
534C2×C22⋊C4—861no—
535C2×C22⋊C4—862no—
536C2×C22⋊C4—861no—
537C2×C22⋊C4—862no—
538C2×C22⋊C4—862no—
539C2×C22⋊C4—862no—
540C2×C22⋊C4C22⋊D4311yescharacteristic, complemented
541C2×C22⋊C4C22×D4311yescharacteristic
542C2×C22⋊C4C22×D4311yescharacteristic
543C2×C22⋊C4C22×D4311yescharacteristic
544C2×C42—21no—
545C2×C42—432no—
546C2×C42—862no—
547C2×C42—861no—
548C2×C42—862no—
549C2×C42C22⋊D4311yescharacteristic, complemented
550#99—434no—
551#99—438no—
552#99—864no—
553#99—862no—
554#95—21no—
555#95—21no—
556#95—21no—
557#95—862no—
558#95—862no—
559#95—862no—
560C24—22no—
561C24—21no—
562C24—22no—
563C24—21no—
564C24—81no—
565C24—81no—
566C24—432no—
567C24—861no—
568C24C2×C4×D4312yescomplemented
569C24C2×C22⋊D4311yescharacteristic
570C24C23×D4311yescharacteristic
571#41—864no—
572#41—868no—
573#41—868no—
574#41—864no—
575C2×Q8—861no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—24no—
579C2×D4—81no—
580C2×D4—81no—
581C2×D4—434no—
582C2×D4—434no—
583C2×D4—861no—
584C2×D4—868no—
585C2×D4—868no—
586C2×D4—862no—
587C2×D4—864no—
588C2×D4—864no—
589C2×D4—862no—
590C2×D4—862no—
591C2×D4—862no—
592C2×D4—862no—
593C2×D4—868no—
594C2×D4—3442no—
595C2×D4—3442no—
596C2×D4C2×C4×D4312yes—
597C2×D4#1062189812yes—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—22no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—81no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—432no—
608C22×C4—432no—
609C22×C4—432no—
610C22×C4—862no—
611C22×C4—862no—
612C22×C4—862no—
613C22×C4—861no—
614C22×C4—861no—
615C22×C4—861no—
616C22×C4—862no—
617C22×C4—862no—
618C22×C4—862no—
619C22×C4—862no—
620C22×C4—3442no—
621C22×C4—3442no—
622C22×C4D4×D4312yes—
623C22×C4D4×D4312yes—
624C22×C4C2×C22⋊D4311yescharacteristic
625C22×C4C2×C22⋊D4311yescharacteristic
626C22×C4C2×C22⋊D4311yescharacteristic
627C22×C4C2×C22⋊D4311yescharacteristic
628C22×C4C2×C22⋊D4311yescharacteristic
629C4⋊C4—22no—
630C4⋊C4—81no—
631C4⋊C4—862no—
632C4⋊C4—861no—
633C4⋊C4—862no—
634C4⋊C4—861no—
635C4⋊C4—862no—
636C4⋊C4—862no—
637C4⋊C4—3442no—
638C22⋊C4—22no—
639C22⋊C4—21no—
640C22⋊C4—24no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—41no—
644C22⋊C4—41no—
645C22⋊C4—42no—
646C22⋊C4—81no—
647C22⋊C4—81no—
648C22⋊C4—81no—
649C22⋊C4—434no—
650C22⋊C4—862no—
651C22⋊C4—862no—
652C22⋊C4—868no—
653C22⋊C4—862no—
654C22⋊C4—862no—
655C22⋊C4—862no—
656C22⋊C4—862no—
657C22⋊C4—862no—
658C22⋊C4—862no—
659C22⋊C4—862no—
660C22⋊C4—862no—
661C22⋊C4—3442no—
662C22⋊C4—3442no—
663C22⋊C4—3442no—
664C22⋊C4C2×C4×D4312yescomplemented
665C42—21no—
666C42—21no—
667C42—81no—
668C42—862no—
669C42—862no—
670C42—862no—
671C42—862no—
672C42—862no—
673C42—3442no—
674C23—21no—
675C23—21no—
676C23—24no—
677C23—22no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—42no—
685C23—42no—
686C23—41no—
687C23—41no—
688C23—42no—
689C23—42no—
690C23—41no—
691C23—41no—
692C23—42no—
693C23—82no—
694C23—84no—
695C23—82no—
696C23—434no—
697C23—864no—
698C23—862no—
699C23—862no—
700C23—3441no—
701C23—3441no—
702C23—1722no—
703C23—1722no—
704C23C4×C22⋊D4312yes—
705C23C22×C4×D4311yescharacteristic
706C23C2×D4×D4312yes—
707C23C22×C22⋊D4311yescharacteristic
708C23#41×D4312yes—
709C23C2×#1062189811yescharacteristic
710Q8—864no—
711D4—24no—
712D4—24no—
713D4—84no—
714D4—864no—
715D4—868no—
716D4—864no—
717D4—864no—
718D4—864no—
719D4—864no—
720D4—3448no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—81no—
744C2×C4—434no—
745C2×C4—868no—
746C2×C4—864no—
747C2×C4—862no—
748C2×C4—862no—
749C2×C4—864no—
750C2×C4—862no—
751C2×C4—862no—
752C2×C4—3442no—
753C2×C4—3442no—
754C2×C4—3442no—
755C2×C4—3441no—
756C2×C4—3441no—
757C2×C4—1724no—
758C2×C4—1722no—
759C2×C4—1722no—
760C2×C4—1722no—
761C2×C4—1722no—
762C2×C4—1722no—
763C2×C4—1722no—
764C2×C4—1722no—
765C2×C4C4×C22⋊D4312yes—
766C2×C4#1306329311yescharacteristic
767C2×C4#1306329311yescharacteristic
768C2×C4#1306329312yes—
769C22—21no—
770C22—22no—
771C22—21no—
772C22—22no—
773C22—22no—
774C22—41no—
775C22—42no—
776C22—41no—
777C22—42no—
778C22—42no—
779C22—44no—
780C22—42no—
781C22—44no—
782C22—41no—
783C22—41no—
784C22—42no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—82no—
789C22—82no—
790C22—81no—
791C22—81no—
792C22—864no—
793C22—3442no—
794C22—3444no—
795C22—1724no—
796C22—1722no—
797C22—1722no—
798C22C4×D4×D4312yes—
799C22C2×C4×C22⋊D4311yescharacteristic
800C22C2×#1306329311yescharacteristic
801C22#1458340611yescharacteristic
802C22#1458340812yes—
803C4—21no—
804C4—21no—
805C4—22no—
806C4—22no—
807C4—42no—
808C4—41no—
809C4—41no—
810C4—81no—
811C4—81no—
812C4—864no—
813C4—3442no—
814C4—1724no—
815C4—1722no—
816C4—1722no—
817C2—21no—
818C2—21no—
819C2—22no—
820C2—22no—
821C2—42no—
822C2—82no—
823C2—1724no—
824C2C4×#1306329311yescharacteristic
825C2#1914399111yescharacteristic
826C2#1914399611yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#2321C2
socleC22×C43C2×#120
prime radicalC2×#14583085C2
cosocleC24×C43C24
hypercenter#2321D43
hypocenterC43#21482
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2321

Complements

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

NH ≅ G/Ntype
1. C4×#13063370C2semidirect
3. #19137253C2semidirect
4. #19135004C2semidirect
5. #19135000C2semidirect
6. #19134875C2semidirect
7. #19134874C2semidirect
8. #19134542C2semidirect
9. C4×#13063239C2semidirect
10. C4×#13063240C2semidirect
11. C43×#2321C2semidirect
25. #14583085C4semidirect
35. #14582772C22semidirect
36. #14582755C22semidirect
37. C4×C22⋊Dic43C22semidirect
38. #14582666C22semidirect
39. #14582665C22semidirect
40. #14582665C22semidirect
43. C22×C22⋊C4×C43C22semidirect
49. C43×#385C22semidirect
50. C43×#379C22semidirect
51. C4×C22⋊C4×C43C22semidirect
62. C22×C4×D43D4semidirect
64. #13063294C2×C4semidirect
92. C2×Dic43⋊C4D4semidirect
103. C2×(C2×D43)⋊C4D4semidirect
108. C2×C4×Dic43D4semidirect
111. #13063240C2×C4semidirect
113. #13063239C2×C4semidirect
120. C23×C4×C43D4semidirect
124. #120×C43C2×C4semidirect
128. C2×C4⋊C4×C43D4semidirect
137. C2×C22⋊C4×C43D4semidirect
142. C2×C42×C43D4semidirect
152. C24×C43C22×C4semidirect
228. C22⋊C4×C43C22×C4semidirect
241. C22⋊Dic43C22×C4semidirect
407. #2321D43semidirect
440. C22×C22⋊C4C2×D43semidirect
457. #385C2×D43semidirect
459. #379C2×D43semidirect
461. C4×C22⋊C4C2×D43semidirect
465. C43#21482semidirect
480. C23×C4C22⋊D43semidirect
486. #120C4×D43semidirect
519. C2×C4⋊C4C22⋊D43semidirect
540. C2×C22⋊C4C22⋊D43semidirect
549. C2×C42C22⋊D43semidirect
568. C24C2×C4×D43semidirect
664. C22⋊C4C2×C4×D43semidirect

Maximal subgroups

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

subgroupindex
C4×#130633702
C2×#145830852
#191372532
#191350042
#191350002
#191348752
#191348742
#191345422
C4×#130632392
C4×#130632402
C43×#23212
#2148243