Finite Group Databasebeta

← #25134278

Subgroups — #25134278

Order 11008.

1922 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583126C211yesmaximal, characteristic, complemented
2C2×#14583050C211yesmaximal, characteristic, complemented
3C2×#14583050C211yesmaximal, characteristic, complemented
4C22×#13063246C211yesmaximal, characteristic, complemented
5#19138046C211yesmaximal, characteristic, complemented
6#19135826C211yesmaximal, characteristic, complemented
7#19135781C211yesmaximal, characteristic, complemented
8#19135683C211yesmaximal, characteristic, complemented
9#19135598C211yesmaximal, characteristic, complemented
10#19134929C211yesmaximal, characteristic, complemented
11#19134913C211yesmaximal, characteristic, complemented
12#19134888C211yesmaximal, characteristic, complemented
13#19134856C211yesmaximal, characteristic, complemented
14#19134526C211yesmaximal, characteristic, complemented
15C2×D42×C43C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C22×#10621883C2211yescharacteristic, complemented
18C22×#10621883C2211yescharacteristic, complemented
19C23×C43⋊C8C2211yescharacteristic, complemented
20C2×#13063304C2211yescharacteristic, complemented
21C2×#13063304C2211yescharacteristic, complemented
22C22×C4⋊Dic43C2211yescharacteristic, complemented
23#14583126—24no—
24#14583050—24no—
25#14583050—24no—
26C2×#13063256C2211yescharacteristic, complemented
27C2×#13063248C2211yescharacteristic, complemented
28C2×#13063246—24no—
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic, complemented
33C2×#13063246C2211yescharacteristic, complemented
34C2×#13063246C2211yescharacteristic, complemented
35C2×#13063246C2211yescharacteristic, complemented
36C2×#13063246C2211yescharacteristic, complemented
37C2×#13063246C2211yescharacteristic, complemented
38C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
39C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
40C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
41#14582832—21no—
42#14582822—21no—
43#14582805C2211yescharacteristic, complemented
44#14582797C2211yescharacteristic, complemented
45#14582779—21no—
46#14582759C2211yescharacteristic, complemented
47#14582757—21no—
48#14582661C2211yescharacteristic, complemented
49#14582661C2211yescharacteristic, complemented
50#14582654C2211yescharacteristic, complemented
51#14582654C2211yescharacteristic, complemented
52C23×D4×C43—21no—
53C23×D4×C43C2211yescharacteristic
54C23×D4×C43C2211yescharacteristic
55D42×C43—24no—
56D42×C43—24no—
57C2×#127×C43C2211yescharacteristic
58C2×#121×C43—21no—
59C2×#121×C43C2211yescharacteristic
60C2×#121×C43C2211yescharacteristic
61C2×#120×C43—21no—
62C2×#120×C43—21no—
63C2×C4×D4×C43C2211yescharacteristic
64C2×C4×D4×C43C2211yescharacteristic
65C22×Dic86C2311yescharacteristic
66C23×Dic43—21no—
67C2×#10621883—22no—
68C2×#10621883—22no—
69C2×#10621883—22no—
70C2×#10621883—22no—
71C2×#10621883—22no—
72C2×#10621883—22no—
73C2×#10621883—41no—
74C2×#10621883—41no—
75C2×#10621883—41no—
76C22×C43⋊C8—22no—
77C22×C43⋊C8—22no—
78C22×C43⋊C8—41no—
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83#13063304—22no—
84#13063304—22no—
85#13063304—22no—
86#13063304—41no—
87C2×C4⋊Dic43—22no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43—41no—
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×C22⋊Dic43—21no—
97C2×C22⋊Dic43—21no—
98C2×C22⋊Dic43—21no—
99#13063256—22no—
100#13063248—22no—
101#13063246—22no—
102#13063246—22no—
103#13063246—22no—
104#13063246—22no—
105#13063246—22no—
106#13063246—22no—
107#13063246—22no—
108#13063246—41no—
109#13063246D414yescomplemented
110C22⋊(C43⋊C8)—22no—
111C22⋊(C43⋊C8)—22no—
112C22⋊(C43⋊C8)—41no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C25×C43—21no—
118C25×C43—21no—
119C22×D4×C43—22no—
120C22×D4×C43—22no—
121C22×D4×C43—28no—
122C22×D4×C43—21no—
123C22×D4×C43—21no—
124C22×D4×C43—22no—
125C22×D4×C43—22no—
126C22×D4×C43—22no—
127C22×D4×C43—22no—
128C22×D4×C43—21no—
129C22×D4×C43—21no—
130C22×D4×C43—21no—
131C22×D4×C43—22no—
132C22×D4×C43—21no—
133C22×D4×C43—41no—
134C22×D4×C43—41no—
135C22×D4×C43—41no—
136C22×D4×C43—41no—
137C22×D4×C43—44no—
138C22×D4×C43—44no—
139C22×D4×C43D411yescharacteristic
140C22×D4×C43D414yes—
141C22×D4×C43C2311yescharacteristic
142C22×D4×C43C2311yescharacteristic
143C22×D4×C43C2311yescharacteristic
144C23×C4×C43—21no—
145C23×C4×C43C2311yescharacteristic
146C23×C4×C43C2311yescharacteristic
147#127×C43—22no—
148#127×C43—22no—
149#121×C43—28no—
150#121×C43—22no—
151#121×C43—22no—
152#121×C43—22no—
153#121×C43D414yes—
154#120×C43—28no—
155#120×C43—28no—
156C4×D4×C43—22no—
157C4×D4×C43—22no—
158C4×D4×C43—22no—
159C4×D4×C43—22no—
160C2×C4⋊C4×C43D411yescharacteristic
161C2×C4⋊C4×C43C2311yescharacteristic
162C2×C22⋊C4×C43—21no—
163C2×C22⋊C4×C43—21no—
164C2×C22⋊C4×C43—21no—
165C2×C22⋊C4×C43D411yescharacteristic
166C2×C22⋊C4×C43D411yescharacteristic
167C2×C42×C43C2311yescharacteristic
168C24×C43—21no—
169C24×C43—24no—
170C24×C43—21no—
171C24×C43—21no—
172C24×C43—24no—
173C24×C43—42no—
174C24×C43—42no—
175C24×C43—42no—
176C24×C43—42no—
177C24×C43—42no—
178C24×C43—42no—
179C24×C43—42no—
180C24×C43—42no—
181C24×C43—81no—
182C24×C43—81no—
183C24×C43—81no—
184C24×C43—81no—
185C24×C43C2×D411yescharacteristic
186C24×C43C2×D411yescharacteristic
187C2×D4×C43—24no—
188C2×D4×C43—24no—
189C2×D4×C43—24no—
190C2×D4×C43—24no—
191C2×D4×C43—24no—
192C2×D4×C43—21no—
193C2×D4×C43—21no—
194C2×D4×C43—21no—
195C2×D4×C43—21no—
196C2×D4×C43—21no—
197C2×D4×C43—22no—
198C2×D4×C43—24no—
199C2×D4×C43—22no—
200C2×D4×C43—28no—
201C2×D4×C43—21no—
202C2×D4×C43—21no—
203C2×D4×C43—21no—
204C2×D4×C43—21no—
205C2×D4×C43—21no—
206C2×D4×C43—21no—
207C2×D4×C43—21no—
208C2×D4×C43—21no—
209C2×D4×C43—42no—
210C2×D4×C43—42no—
211C2×D4×C43—42no—
212C2×D4×C43—42no—
213C2×D4×C43—42no—
214C2×D4×C43—44no—
215C2×D4×C43—44no—
216C2×D4×C43—44no—
217C2×D4×C43—42no—
218C2×D4×C43—44no—
219C2×D4×C43—44no—
220C2×D4×C43—44no—
221C2×D4×C43—432no—
222C2×D4×C43—44no—
223C2×D4×C43—42no—
224C2×D4×C43—42no—
225C2×D4×C43—42no—
226C2×D4×C43—42no—
227C2×D4×C43—81no—
228C2×D4×C43—81no—
229C2×D4×C43SD1614yescomplemented
230C2×D4×C43C2×D412yes—
231C2×D4×C43C2×D412yes—
232C2×D4×C43C2×D412yes—
233C2×D4×C43C2×D412yes—
234C2×D4×C43#4112yes—
235C22×C4×C43—21no—
236C22×C4×C43—21no—
237C22×C4×C43—21no—
238C22×C4×C43—21no—
239C22×C4×C43—24no—
240C22×C4×C43—21no—
241C22×C4×C43—21no—
242C22×C4×C43—21no—
243C22×C4×C43—21no—
244C22×C4×C43—21no—
245C22×C4×C43—21no—
246C22×C4×C43—21no—
247C22×C4×C43—42no—
248C22×C4×C43—42no—
249C22×C4×C43C2×D412yes—
250C22×C4×C43C2×D412yes—
251C22×C4×C43C2×D411yescharacteristic
252C22×C4×C43C2×D411yescharacteristic
253C22×C4×C43C2×D411yescharacteristic
254C22×C4×C43C2×D411yescharacteristic
255C22×C4×C43C2411yescharacteristic
256C22×Dic43—21no—
257C22×Dic43—21no—
258C22×Dic43—21no—
259C22×Dic43—21no—
260C22×Dic43—42no—
261C22×Dic43—42no—
262C22×Dic43—81no—
263C2×Dic86—21no—
264C2×Dic86—21no—
265C2×Dic86—21no—
266C2×Dic86—21no—
267C2×Dic86—21no—
268C2×Dic86—21no—
269C4⋊C4×C43—22no—
270C4⋊C4×C43—21no—
271C4⋊C4×C43C2×D412yes—
272C22⋊C4×C43—24no—
273C22⋊C4×C43—24no—
274C22⋊C4×C43—24no—
275C22⋊C4×C43—22no—
276C22⋊C4×C43—22no—
277C42×C43—21no—
278C42×C43—21no—
279C22⋊Dic43—42no—
280C22⋊Dic43—42no—
281C22⋊Dic43—81no—
282#10621883—44no—
283#10621883—44no—
284#10621883—44no—
285C4⋊Dic43—21no—
286C4⋊Dic43—21no—
287C4⋊Dic43—21no—
288C4⋊Dic43—21no—
289C4⋊Dic43—21no—
290C4⋊Dic43—42no—
291C4⋊Dic43C2×D412yescomplemented
292Dic43⋊C4—42no—
293Dic43⋊C4—42no—
294Dic43⋊C4—81no—
295C2×C43⋊C8—21no—
296C2×C43⋊C8—21no—
297C2×C43⋊C8—21no—
298C2×C43⋊C8—21no—
299C2×C43⋊C8—21no—
300C2×C43⋊C8—21no—
301C2×C43⋊C8—21no—
302C2×C43⋊C8—21no—
303C2×C43⋊C8—21no—
304C2×C43⋊C8—21no—
305C2×C43⋊C8—21no—
306C2×C43⋊C8—44no—
307C2×C43⋊C8C2×D412yescomplemented
308C23×C43—21no—
309C23×C43—21no—
310C23×C43—21no—
311C23×C43—21no—
312C23×C43—21no—
313C23×C43—22no—
314C23×C43—21no—
315C23×C43—22no—
316C23×C43—21no—
317C23×C43—22no—
318C23×C43—21no—
319C23×C43—21no—
320C23×C43—21no—
321C23×C43—22no—
322C23×C43—22no—
323C23×C43—48no—
324C23×C43—48no—
325C23×C43—48no—
326C23×C43—41no—
327C23×C43—41no—
328C23×C43—41no—
329C23×C43—41no—
330C23×C43—41no—
331C23×C43—41no—
332C23×C43—41no—
333C23×C43—41no—
334C23×C43—41no—
335C23×C43—41no—
336C23×C43—41no—
337C23×C43—41no—
338C23×C43—41no—
339C23×C43—41no—
340C23×C43—41no—
341C23×C43—41no—
342C23×C43—48no—
343C23×C43—84no—
344C23×C43—84no—
345C23×C43—84no—
346C23×C43—84no—
347C23×C43—84no—
348C23×C43—84no—
349C23×C43—84no—
350C23×C43—84no—
351C23×C43—84no—
352C23×C43—84no—
353C23×C43#12012yes—
354C23×C43C2×SD1612yes—
355C23×C43C2×SD1612yes—
356C23×C43AGL(1,ℤ/8)12yes—
357C23×C43C22×D411yescharacteristic
358D4×C43—28no—
359D4×C43—22no—
360D4×C43—22no—
361D4×C43—22no—
362D4×C43—22no—
363D4×C43—22no—
364D4×C43—22no—
365D4×C43—22no—
366D4×C43—48no—
367D4×C43—48no—
368D4×C43—48no—
369D4×C43—48no—
370D4×C43—48no—
371D4×C43—41no—
372D4×C43—41no—
373D4×C43—41no—
374D4×C43—41no—
375D4×C43—84no—
376D4×C43#12114yes—
377C2×C4×C43—21no—
378C2×C4×C43—21no—
379C2×C4×C43—21no—
380C2×C4×C43—21no—
381C2×C4×C43—22no—
382C2×C4×C43—22no—
383C2×C4×C43—22no—
384C2×C4×C43—22no—
385C2×C4×C43—21no—
386C2×C4×C43—21no—
387C2×C4×C43—22no—
388C2×C4×C43—21no—
389C2×C4×C43—21no—
390C2×C4×C43—21no—
391C2×C4×C43—21no—
392C2×C4×C43—48no—
393C2×C4×C43—41no—
394C2×C4×C43—41no—
395C2×C4×C43—41no—
396C2×C4×C43—41no—
397C2×C4×C43—41no—
398C2×C4×C43—41no—
399C2×C4×C43#12012yes—
400C2×C4×C43C2×SD1612yes—
401C2×C4×C43C22×D411yescharacteristic
402C2×C4×C43C22×D411yescharacteristic
403C2×C4×C43C22×D411yescharacteristic
404C2×C4×C43C2×#4111yescharacteristic
405C2×C4×C43H(5,𝔽2)11yescharacteristic
406C2×C4×C43H(5,𝔽2)11yescharacteristic
407C2×Dic43—22no—
408C2×Dic43—41no—
409C2×Dic43—41no—
410C2×Dic43—41no—
411C2×Dic43—41no—
412C2×Dic43—41no—
413C2×Dic43—41no—
414C2×Dic43—41no—
415C2×Dic43—41no—
416C2×Dic43—41no—
417C2×Dic43—41no—
418C2×Dic43—41no—
419C2×Dic43—84no—
420Dic86—41no—
421Dic86—41no—
422Dic86—41no—
423Dic86—41no—
424C43⋊C8—22no—
425C43⋊C8—41no—
426C43⋊C8—41no—
427C43⋊C8—41no—
428#24432—431nomaximal, Sylow
429C22×C43—22no—
430C22×C43—22no—
431C22×C43—22no—
432C22×C43—22no—
433C22×C43—22no—
434C22×C43—22no—
435C22×C43—24no—
436C22×C43—22no—
437C22×C43—22no—
438C22×C43—22no—
439C22×C43—41no—
440C22×C43—42no—
441C22×C43—41no—
442C22×C43—42no—
443C22×C43—41no—
444C22×C43—42no—
445C22×C43—42no—
446C22×C43—42no—
447C22×C43—41no—
448C22×C43—42no—
449C22×C43—42no—
450C22×C43—42no—
451C22×C43—42no—
452C22×C43—42no—
453C22×C43—42no—
454C22×C43—42no—
455C22×C43—816no—
456C22×C43—816no—
457C22×C43—81no—
458C22×C43—81no—
459C22×C43—81no—
460C22×C43—81no—
461C22×C43—81no—
462C22×C43—81no—
463C22×C43—81no—
464C22×C43—81no—
465C22×C43#45014yescomplemented
466C22×C43C2×#12011yescharacteristic
467C22×C43D4211yescharacteristic
468C22×C43#54611yescharacteristic
469C22×C43C22×SD1611yescharacteristic
470C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
471C22×C43#57611yescharacteristic
472C22×C43#57711yescharacteristic
473C4×C43—22no—
474C4×C43—22no—
475C4×C43—41no—
476C4×C43—42no—
477C4×C43—41no—
478C4×C43C2×#12111yescharacteristic
479C4×C43#53411yescharacteristic
480C4×C43D4211yescharacteristic
481C4×C43#54611yescharacteristic
482Dic43—42no—
483Dic43—81no—
484Dic43—81no—
485Dic43—81no—
486C2×D42D4311yescharacteristic
487C2×#465—431no—
488C2×#450—431no—
489C2×#450—431no—
490C22×#102—431no—
491#2417—431no—
492#2041—431no—
493#2034—431no—
494#2014—431no—
495#2000—431no—
496#1877—431no—
497#1874—431no—
498#1869—431no—
499#1864—431no—
500#1786—431no—
501C2×C43—24no—
502C2×C43—42no—
503C2×C43—44no—
504C2×C43—82no—
505C2×C43—82no—
506C2×C43#241011yescharacteristic
507C2×C43C2×#45011yescharacteristic
508C2×C43#301211yescharacteristic
509C2×C43#326411yescharacteristic
510C2×C43D4×SD1611yescharacteristic
511C2×C43#329511yescharacteristic
512C2×C43#331011yescharacteristic
513C23×D4—21no—
514C23×D4C2×D4311yescharacteristic
515C23×D4C2×D4311yescharacteristic
516C22×SD16—431no—
517C22×SD16—431no—
518C22×SD16—431no—
519C23×C8—431no—
520D42—24no—
521D42—24no—
522C2×#127C2×D4311yescharacteristic
523C2×C22⋊Q8—431no—
524C2×C22⋊Q8—431no—
525C2×#121—21no—
526C2×#121C2×D4311yescharacteristic
527C2×#121C2×D4311yescharacteristic
528C2×#120—21no—
529C2×#120—21no—
530C2×C4×D4C2×D4311yescharacteristic
531C2×C4×D4C2×D4311yescharacteristic
532C22×C4⋊C4—431no—
533#465—864no—
534#450—864no—
535#450—864no—
536C2×#106—431no—
537C2×#103—431no—
538C2×#102—431no—
539C2×#102—431no—
540C2×#102—431no—
541C2×#102—431no—
542C2×#102—431no—
543C2×#102—431no—
544C2×#102—431no—
545C2×#102—431no—
546C2×#102—431no—
547C2×#102—864no—
548C2×C22⋊C8—431no—
549C2×C22⋊C8—431no—
550C2×C22⋊C8—431no—
551#398—861no—
552#396—861no—
553#391—431no—
554#389—431no—
555#386—861no—
556#380—431no—
557#380—861no—
558#340—431no—
559#340—431no—
560#336—431no—
561#336—431no—
562C43#2443211yescharacteristic, complemented, Sylow
563C25—21no—
564C25—21no—
565C22×Q8—431no—
566C22×D4—22no—
567C22×D4—22no—
568C22×D4—28no—
569C22×D4—21no—
570C22×D4—21no—
571C22×D4—22no—
572C22×D4—22no—
573C22×D4—22no—
574C22×D4—22no—
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4—22no—
579C22×D4—21no—
580C22×D4—41no—
581C22×D4—41no—
582C22×D4—41no—
583C22×D4—41no—
584C22×D4—44no—
585C22×D4—44no—
586C22×D4C22⋊D4311yescharacteristic
587C22×D4C22⋊D4314yes—
588C22×D4C22×D4311yescharacteristic
589C22×D4C22×D4311yescharacteristic
590C22×D4C22×D4311yescharacteristic
591C23×C4—21no—
592C23×C4—861no—
593C23×C4C22×D4311yescharacteristic
594C23×C4C22×D4311yescharacteristic
595C2×SD16—862no—
596C2×SD16—862no—
597C2×SD16—862no—
598C2×SD16—862no—
599C2×SD16—862no—
600C2×SD16—862no—
601C2×SD16—1721no—
602C2×SD16—1721no—
603C2×SD16—1721no—
604C22×C8—431no—
605C22×C8—431no—
606C22×C8—431no—
607C22×C8—431no—
608C22×C8—862no—
609C22×C8—862no—
610C22×C8—1721no—
611#127—22no—
612#127—22no—
613C22⋊Q8—862no—
614C22⋊Q8—862no—
615C22⋊Q8—862no—
616C22⋊Q8—1721no—
617#121—28no—
618#121—22no—
619#121—22no—
620#121—22no—
621#121C22⋊D4314yes—
622#120—28no—
623#120—28no—
624C4×D4—22no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—22no—
628C2×C4⋊C4—431no—
629C2×C4⋊C4—431no—
630C2×C4⋊C4—431no—
631C2×C4⋊C4—862no—
632C2×C4⋊C4—861no—
633C2×C4⋊C4—861no—
634C2×C4⋊C4—861no—
635C2×C4⋊C4—861no—
636C2×C4⋊C4—1721no—
637C2×C4⋊C4C22⋊D4311yescharacteristic
638C2×C4⋊C4C22×D4311yescharacteristic
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—861no—
643C2×C22⋊C4—861no—
644C2×C22⋊C4—861no—
645C2×C22⋊C4C22⋊D4311yescharacteristic
646C2×C22⋊C4C22⋊D4311yescharacteristic
647C2×C42C22×D4311yescharacteristic
648#106—862no—
649#103—862no—
650#102—434no—
651#102—862no—
652#102—862no—
653#102—862no—
654#102—862no—
655#102—862no—
656#102—862no—
657#102—862no—
658#102—1721no—
659C22⋊C8—862no—
660C22⋊C8—862no—
661C22⋊C8—1721no—
662#95—861no—
663#95—861no—
664#95—861no—
665#95—861no—
666C24—21no—
667C24—24no—
668C24—21no—
669C24—21no—
670C24—24no—
671C24—42no—
672C24—42no—
673C24—42no—
674C24—42no—
675C24—42no—
676C24—42no—
677C24—42no—
678C24—42no—
679C24—81no—
680C24—81no—
681C24—81no—
682C24—81no—
683C24C2×C22⋊D4311yescharacteristic
684C24C2×C22⋊D4311yescharacteristic
685C2×Q8—861no—
686C2×Q8—861no—
687C2×Q8—861no—
688C2×Q8—861no—
689C2×Q8—861no—
690C2×Q8—861no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—28no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—24no—
698C2×D4—24no—
699C2×D4—24no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—42no—
720C2×D4—42no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—432no—
724C2×D4—44no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—42no—
728C2×D4—42no—
729C2×D4—44no—
730C2×D4—42no—
731C2×D4—81no—
732C2×D4—81no—
733C2×D4#1062188314yescomplemented
734C2×D4D4×D4312yes—
735C2×D4#1062190012yes—
736C2×D4C2×C22⋊D4312yes—
737C2×D4C2×C22⋊D4312yes—
738C2×D4C2×C22⋊D4312yes—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—24no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—42no—
752C22×C4—42no—
753C22×C4—861no—
754C22×C4—861no—
755C22×C4—861no—
756C22×C4—861no—
757C22×C4—3441no—
758C22×C4—1722no—
759C22×C4—1722no—
760C22×C4C2×C22⋊D4311yescharacteristic
761C22×C4C2×C22⋊D4311yescharacteristic
762C22×C4C2×C22⋊D4311yescharacteristic
763C22×C4C2×C22⋊D4312yes—
764C22×C4C2×C22⋊D4312yes—
765C22×C4C2×C22⋊D4311yescharacteristic
766C22×C4C23×D4311yescharacteristic
767SD16—1724no—
768SD16—1724no—
769SD16—1724no—
770C2×C8—432no—
771C2×C8—861no—
772C2×C8—861no—
773C2×C8—861no—
774C2×C8—861no—
775C2×C8—861no—
776C2×C8—861no—
777C2×C8—861no—
778C2×C8—861no—
779C2×C8—861no—
780C2×C8—861no—
781C2×C8—861no—
782C2×C8—1724no—
783C4⋊C4—22no—
784C4⋊C4—21no—
785C4⋊C4—432no—
786C4⋊C4—861no—
787C4⋊C4—861no—
788C4⋊C4—861no—
789C4⋊C4—861no—
790C4⋊C4—861no—
791C4⋊C4—3441no—
792C4⋊C4—1722no—
793C4⋊C4—1722no—
794C4⋊C4—1722no—
795C4⋊C4C2×C22⋊D4312yes—
796C22⋊C4—24no—
797C22⋊C4—24no—
798C22⋊C4—22no—
799C22⋊C4—24no—
800C22⋊C4—22no—
801C22⋊C4—3441no—
802C22⋊C4—1722no—
803C22⋊C4—1722no—
804C42—21no—
805C42—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—22no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—22no—
817C23—21no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—48no—
822C23—48no—
823C23—48no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—48no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—84no—
842C23—84no—
843C23—84no—
844C23—84no—
845C23—84no—
846C23—84no—
847C23—84no—
848C23—84no—
849C23—84no—
850C23—84no—
851C23#1306329412yes—
852C23C2×#1062188312yes—
853C23C2×#1062188312yes—
854C23#1306335112yes—
855C23C22×C22⋊D4311yescharacteristic
856Q8—1721no—
857Q8—1721no—
858Q8—1721no—
859Q8—1721no—
860D4—28no—
861D4—22no—
862D4—22no—
863D4—22no—
864D4—22no—
865D4—22no—
866D4—22no—
867D4—22no—
868D4—48no—
869D4—48no—
870D4—48no—
871D4—48no—
872D4—48no—
873D4—41no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—84no—
878D4#1306329714yes—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—22no—
890C2×C4—21no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—48no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—862no—
902C2×C4—3444no—
903C2×C4—1721no—
904C2×C4—1721no—
905C2×C4—1721no—
906C2×C4—1721no—
907C2×C4—1721no—
908C2×C4—1721no—
909C2×C4—1721no—
910C2×C4—1721no—
911C2×C4—1721no—
912C2×C4—1721no—
913C2×C4—1721no—
914C2×C4#1306329412yes—
915C2×C4C2×#1062188312yes—
916C2×C4C2×D4×D4311yescharacteristic
917C2×C4C22×C22⋊D4311yescharacteristic
918C2×C4C22×C22⋊D4311yescharacteristic
919C2×C4C2×#1062190011yescharacteristic
920C2×C4#1306337011yescharacteristic
921C2×C4#1306337011yescharacteristic
922C8—862no—
923C8—1721no—
924C8—1721no—
925C8—1721no—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—22no—
933C22—22no—
934C22—24no—
935C22—22no—
936C22—42no—
937C22—41no—
938C22—42no—
939C22—42no—
940C22—41no—
941C22—42no—
942C22—41no—
943C22—42no—
944C22—41no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—816no—
953C22—816no—
954C22—81no—
955C22—81no—
956C22—81no—
957C22—81no—
958C22—81no—
959C22—81no—
960C22—81no—
961C22—81no—
962C22#1458305014yescomplemented
963C22C2×#1306329411yescharacteristic
964C22D4×C22⋊D4311yescharacteristic
965C22#1458354311yescharacteristic
966C22C22×#1062188311yescharacteristic
967C22C2×#1306335111yescharacteristic
968C22#1458370211yescharacteristic
969C22#1458371011yescharacteristic
970C4—22no—
971C4—22no—
972C4—42no—
973C4—41no—
974C4—41no—
975C4—3441no—
976C4—3441no—
977C4—3441no—
978C4—1722no—
979C4C2×#1306329711yescharacteristic
980C4#1458345811yescharacteristic
981C4D4×C22⋊D4311yescharacteristic
982C4#1458354311yescharacteristic
983C2—24no—
984C2—42no—
985C2—44no—
986C2—82no—
987C2—82no—
988C2#1913796911yescharacteristic
989C2C2×#1458305011yescharacteristic
990C2#1914389911yescharacteristic
991C2#1914607111yescharacteristic
992C2D4×#1062188311yescharacteristic
993C2#1914641911yescharacteristic
994C2#1914661611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×D42×C43C2
socleC23×C43C22×D4
hypercenterC2×D42D43
hypocenterC43#24432
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D42

Complements

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

NH ≅ G/Ntype
1. C2×#14583126C2semidirect
2. C2×#14583050C2semidirect
3. C2×#14583050C2semidirect
4. C22×#13063246C2semidirect
5. #19138046C2semidirect
6. #19135826C2semidirect
7. #19135781C2semidirect
8. #19135683C2semidirect
9. #19135598C2semidirect
10. #19134929C2semidirect
11. #19134913C2semidirect
12. #19134888C2semidirect
13. #19134856C2semidirect
14. #19134526C2semidirect
17. C22×#10621883C22semidirect
18. C22×#10621883C22semidirect
19. C23×C43⋊C8C22semidirect
20. C2×#13063304C22semidirect
21. C2×#13063304C22semidirect
22. C22×C4⋊Dic43C22semidirect
26. C2×#13063256C22semidirect
27. C2×#13063248C22semidirect
32. C2×#13063246C22semidirect
33. C2×#13063246C22semidirect
34. C2×#13063246C22semidirect
35. C2×#13063246C22semidirect
36. C2×#13063246C22semidirect
37. C2×#13063246C22semidirect
38. C2×C22⋊(C43⋊C8)C22semidirect
39. C2×C22⋊(C43⋊C8)C22semidirect
40. C2×C22⋊(C43⋊C8)C22semidirect
43. #14582805C22semidirect
44. #14582797C22semidirect
46. #14582759C22semidirect
48. #14582661C22semidirect
49. #14582661C22semidirect
50. #14582654C22semidirect
51. #14582654C22semidirect
109. #13063246D4semidirect
229. C2×D4×C43SD16semidirect
291. C4⋊Dic43C2×D4semidirect
307. C2×C43⋊C8C2×D4semidirect
465. C22×C43#450semidirect
562. C43#24432semidirect
733. C2×D4#10621883semidirect
962. C22#14583050semidirect

Maximal subgroups

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

subgroupindex
C2×#145831262
C2×#145830502
C22×#130632462
#191380462
#191358262
#191357812
#191356832
#191355982
#191349292
#191349132
#191348882
#191348562
#191345262
C2×D42×C432
#2443243