Finite Group Databasebeta

← #25112076

Subgroups — #25112076

Order 11008.

1670 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583542C211yesmaximal, characteristic
2C2×#14582972C211yesmaximal, characteristic, complemented
3C2×#14582899C211yesmaximal, characteristic, complemented
4C2×#102×D43C211yesmaximal, characteristic, complemented
5#19137495C211yesmaximal, characteristic, complemented
6#19135528C211yesmaximal, characteristic, complemented
7#19135030C211yesmaximal, characteristic, complemented
8#19135015C211yesmaximal, characteristic, complemented
9#19134909C211yesmaximal, characteristic, complemented
10#19134899C211yesmaximal, characteristic, complemented
11#19134592C211yesmaximal, characteristic, complemented
12#19134534C211yesmaximal, characteristic, complemented
13#19134524C211yesmaximal, characteristic, complemented
14#19134421C211yesmaximal, characteristic, complemented
15C43×#1959C211yesmaximal, characteristic, complemented
16C22×#10621902C2211yescharacteristic
17C22×D4×D43C2211yescharacteristic
18C22×#10621872C2211yescharacteristic, complemented
19C22×C8×D43C2211yescharacteristic
20#14583542—24no—
21#14583542C418yescomplemented
22C2×#13063307—21no—
23C2×#13063301C2211yescharacteristic
24C2×#13063298—21no—
25C2×#13063296C2211yescharacteristic
26C2×#13063295—21no—
27C2×C4×D172C2211yescharacteristic
28C2×C4×D172C2211yescharacteristic
29C2×#13063287—21no—
30C2×C4⋊C4×D43C2211yescharacteristic
31C2×C4⋊C4×D43C2211yescharacteristic, complemented
32C2×C22⋊C4×D43—21no—
33#14582972—24no—
34C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
35#14582899—24no—
36C2×#13063249C2211yescharacteristic, complemented
37C2×#13063249C2211yescharacteristic, complemented
38C2×#13063247C2211yescharacteristic
39C2×#13063247C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×#13063246C2211yescharacteristic
42C2×#13063245C2211yescharacteristic
43C2×#13063245C2211yescharacteristic
44#102×D43—24no—
45C2×(C2×D43)⋊C8C2211yescharacteristic
46C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
47#14582795—21no—
48#14582770—21no—
49#14582770—21no—
50#14582756C2211yescharacteristic
51#14582756C2211yescharacteristic, complemented
52C4×C4⋊Dic43C2211yescharacteristic, complemented
53#14582662C2211yescharacteristic, complemented
54#14582662C2211yescharacteristic, complemented
55#14582661C2211yescharacteristic, complemented
56#14582661C2211yescharacteristic, complemented
57C2×#124×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic, complemented
59C2×#103×C43C2211yescharacteristic, complemented
60C2×#102×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C2×#97×C43C2211yescharacteristic, complemented
63C43×#384C2211yescharacteristic, complemented
64C24×D43—21no—
65C2×#10621902—22no—
66C2×#10621902—22no—
67C2×#10621902—22no—
68C2×#10621902—41no—
69C2×#10621902—41no—
70C2×#10621902C2×C414yescomplemented
71C22×D172—21no—
72C22×D172D411yescharacteristic
73C22×D172C2311yescharacteristic
74C22×C22⋊D43—21no—
75C22×C22⋊D43—21no—
76C2×D4×D43—22no—
77C2×D4×D43—22no—
78C2×D4×D43—22no—
79C2×D4×D43—41no—
80C2×D4×D43—41no—
81C2×D4×D43C2×C414yescomplemented
82C22×C4×D43—21no—
83C22×C4×D43—21no—
84C22×C4×D43—21no—
85C22×C4×D43—21no—
86C22×C4×D43C2311yescharacteristic
87C22×C4×D43C2311yescharacteristic
88C2×#10621872—22no—
89C2×#10621872—22no—
90C2×#10621872—41no—
91C22×C43⋊C8C2311yescharacteristic
92C22×C43⋊C8C2311yescharacteristic
93C2×C8×D43—22no—
94C2×C8×D43—22no—
95C2×C8×D43—41no—
96#13063307—28no—
97#13063301—22no—
98#13063301C2×C414yescomplemented
99#13063298—28no—
100#13063296—22no—
101#13063296C2×C414yescomplemented
102#13063295—28no—
103C4×D172—22no—
104C4×D172C2×C414yes—
105C4×D172C2×C414yescomplemented
106C4×D172D414yes—
107#13063287—44no—
108C2×C4⋊Dic43D411yescharacteristic
109C2×C4⋊Dic43C2311yescharacteristic
110C2×C4⋊Dic43C2311yescharacteristic
111C2×C4⋊Dic43C2311yescharacteristic
112C2×Dic43⋊C4—21no—
113C2×Dic43⋊C4—21no—
114C2×Dic43⋊C4—21no—
115C4⋊C4×D43—22no—
116C4⋊C4×D43—22no—
117C4⋊C4×D43—41no—
118C4⋊C4×D43—41no—
119C2×C22⋊Dic43—21no—
120C2×(C2×D43)⋊C4—21no—
121C2×(C2×D43)⋊C4—21no—
122C2×(C2×D43)⋊C4—21no—
123C2×(C2×D43)⋊C4—21no—
124C2×(C2×D43)⋊C4D411yescharacteristic
125C2×(C2×D43)⋊C4D411yescharacteristic
126C22⋊C4×D43—28no—
127C2×C4×Dic43—21no—
128C4⋊(C43⋊C8)—22no—
129#13063249—22no—
130#13063249—41no—
131#13063247—22no—
132#13063247D414yescomplemented
133#13063246—22no—
134#13063246—41no—
135#13063245—22no—
136#13063245—22no—
137(C2×D43)⋊C8—22no—
138(C2×D43)⋊C8—22no—
139C43⋊#95—21no—
140C43⋊#95—21no—
141C43⋊#95—21no—
142C22×Q8×C43C2311yescharacteristic
143C22×D4×C43C2311yescharacteristic
144C22×C8×C43C2311yescharacteristic
145C22×C8×C43C2311yescharacteristic
146#124×C43—22no—
147#124×C43C2×C414yescomplemented
148C2×C4⋊C4×C43—21no—
149C2×C4⋊C4×C43—21no—
150C2×C4⋊C4×C43C2311yescharacteristic
151C2×C4⋊C4×C43C2311yescharacteristic
152C2×C22⋊C4×C43—21no—
153C2×C22⋊C4×C43—21no—
154C2×C42×C43C2311yescharacteristic
155#103×C43—22no—
156#103×C43—41no—
157#102×C43—22no—
158#102×C43—41no—
159#97×C43—22no—
160C24×C43—21no—
161C23×D43—21no—
162C23×D43—24no—
163C23×D43—42no—
164C23×D43—42no—
165C23×D43—42no—
166C23×D43—42no—
167C23×D43—81no—
168C23×D43—81no—
169C23×D43C2×D411yescharacteristic
170C23×D43C2×D411yescharacteristic
171C2×Q8×C43—21no—
172C2×Q8×C43—21no—
173C2×Q8×C43—21no—
174C2×Q8×C43—21no—
175C2×Q8×C43—21no—
176C2×Q8×C43C22×C412yes—
177C2×D4×C43—21no—
178C2×D4×C43—21no—
179C2×D4×C43—21no—
180C2×D4×C43—21no—
181C2×D4×C43—21no—
182C2×D4×C43C22×C412yes—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2411yescharacteristic
189C2×C22⋊D43—24no—
190C2×C22⋊D43—24no—
191C2×C22⋊D43—42no—
192C2×C22⋊D43—42no—
193C2×C22⋊D43—81no—
194C2×C22⋊D43—81no—
195C22×Dic43—21no—
196C22×Dic43—21no—
197C22×Dic43—21no—
198C22×Dic43C2×D411yescharacteristic
199C22×Dic43C2×D411yescharacteristic
200#10621902—28no—
201#10621902—44no—
202#10621902—44no—
203#10621902—44no—
204D4×D43—28no—
205D4×D43—44no—
206D4×D43—44no—
207D4×D43—44no—
208C2×D172—21no—
209C2×D172—21no—
210C2×D172—21no—
211C2×D172—24no—
212C2×D172—22no—
213C2×D172—22no—
214C2×D172—42no—
215C2×D172—42no—
216C2×D172C22⋊C414yes—
217C2×D172C22×C412yes—
218C2×D172C2×D412yes—
219C2×D172#4112yes—
220C2×C4×D43—21no—
221C2×C4×D43—21no—
222C2×C4×D43—21no—
223C2×C4×D43—21no—
224C2×C4×D43—21no—
225C2×C4×D43—21no—
226C2×C4×D43—21no—
227C2×C4×D43—21no—
228C2×C4×D43—24no—
229C2×C4×D43—24no—
230C2×C4×D43—42no—
231C2×C4×D43—42no—
232C2×C4×D43—42no—
233C2×C4×D43—42no—
234C2×C4×D43—42no—
235C2×C4×D43—42no—
236C2×C4×D43—81no—
237C2×C4×D43—81no—
238C2×C4×D43—81no—
239C2×C4×D43—81no—
240C2×C4×D43C22×C412yes—
241C2×C4×D43C22×C412yes—
242C2×C4×D43C2×D412yes—
243C2×C4×D43C2×D412yes—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C2×C8×C43—21no—
249C2×C8×C43C2×D412yes—
250C4⋊C4×C43—21no—
251C4⋊C4×C43—21no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43—21no—
254C4⋊C4×C43—42no—
255C4⋊C4×C43—81no—
256C22⋊C4×C43—24no—
257C22⋊C4×C43—24no—
258C42×C43C22×C412yes—
259C42×C43C2×D412yes—
260C22⋊Dic43—24no—
261(C2×D43)⋊C4—24no—
262(C2×D43)⋊C4—24no—
263(C2×D43)⋊C4—42no—
264(C2×D43)⋊C4—42no—
265(C2×D43)⋊C4C22⋊C414yes—
266(C2×D43)⋊C4C22⋊C414yes—
267C4⋊Dic43—21no—
268C4⋊Dic43—21no—
269C4⋊Dic43—21no—
270C4⋊Dic43—21no—
271C4⋊Dic43C22⋊C414yes—
272C4⋊Dic43C22×C412yes—
273C4⋊Dic43C2×D412yes—
274Dic43⋊C4—24no—
275Dic43⋊C4—42no—
276Dic43⋊C4—42no—
277C4×Dic43—42no—
278C2×C43⋊C8—21no—
279C2×C43⋊C8—21no—
280C2×C43⋊C8—21no—
281C2×C43⋊C8—21no—
282C2×C43⋊C8—21no—
283C2×C43⋊C8—21no—
284#10621872—44no—
285C8×D43—44no—
286C23×C43—22no—
287C23×C43—41no—
288C23×C43—41no—
289C23×C43—41no—
290C23×C43—41no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43C22×D411yescharacteristic
294C22×D43—21no—
295C22×D43—21no—
296C22×D43—21no—
297C22×D43—21no—
298C22×D43—22no—
299C22×D43—21no—
300C22×D43—22no—
301C22×D43—21no—
302C22×D43—22no—
303C22×D43—21no—
304C22×D43—21no—
305C22×D43—21no—
306C22×D43—21no—
307C22×D43—48no—
308C22×D43—41no—
309C22×D43—41no—
310C22×D43—41no—
311C22×D43—41no—
312C22×D43—48no—
313C22×D43—84no—
314C22×D43—84no—
315C22×D43—84no—
316C22×D43—84no—
317C22×D43—84no—
318C22×D43C2×C22⋊C412yes—
319C22×D43C2×C22⋊C412yes—
320C22×D43AGL(1,ℤ/8)12yes—
321C22×D43#13712yes—
322Q8×C43—22no—
323Q8×C43—22no—
324Q8×C43—41no—
325Q8×C43—41no—
326D4×C43—22no—
327D4×C43—22no—
328D4×C43—41no—
329D4×C43—41no—
330C2×C4×C43—21no—
331C2×C4×C43—21no—
332C2×C4×C43—21no—
333C2×C4×C43—21no—
334C2×C4×C43—22no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
341C2×C4×C43—41no—
342C2×C4×C43—41no—
343C2×C4×C43C2×C22⋊C412yes—
344C2×C4×C43C2×C22⋊C412yes—
345C2×C4×C43C23×C411yescharacteristic
346C2×C4×C43C22×D411yescharacteristic
347C2×C4×C43C22×D411yescharacteristic
348C2×C4×C43C2×#4111yescharacteristic
349C2×C4×C43H(5,𝔽2)11yescharacteristic
350C2×C4×C43H(5,𝔽2)11yescharacteristic
351C22⋊D43—48no—
352C22⋊D43—84no—
353C2×Dic43—21no—
354C2×Dic43—21no—
355C2×Dic43—21no—
356C2×Dic43—21no—
357C2×Dic43—22no—
358C2×Dic43—22no—
359C2×Dic43—41no—
360C2×Dic43—41no—
361C2×Dic43—41no—
362C2×Dic43—41no—
363C2×Dic43—41no—
364C2×Dic43—41no—
365C2×Dic43—41no—
366C2×Dic43C2×C22⋊C412yes—
367C2×Dic43C2×C22⋊C412yes—
368D172—28no—
369D172—22no—
370D172—22no—
371D172—22no—
372D172—48no—
373D172C4×D414yescomplemented
374C4×D43—22no—
375C4×D43—22no—
376C4×D43—22no—
377C4×D43—22no—
378C4×D43—22no—
379C4×D43—22no—
380C4×D43—22no—
381C4×D43—22no—
382C4×D43—48no—
383C4×D43—84no—
384C4×D43—84no—
385C4×D43—84no—
386C8×C43—22no—
387C8×C43—41no—
388C43⋊C8—41no—
389C43⋊C8—41no—
390#22419—431nomaximal, Sylow
391C22×C43—42no—
392C22×C43—42no—
393C22×C43—42no—
394C22×C43—81no—
395C22×C43—81no—
396C22×C43—81no—
397C22×C43—81no—
398C22×C43C22×C22⋊C411yescharacteristic
399C22×C43D4211yescharacteristic
400C22×C43#54611yescharacteristic
401C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
402C22×C43C2×#13711yescharacteristic
403C22×C43#57611yescharacteristic
404C22×C43#57711yescharacteristic
405C2×D43—22no—
406C2×D43—22no—
407C2×D43—22no—
408C2×D43—22no—
409C2×D43—22no—
410C2×D43—22no—
411C2×D43—24no—
412C2×D43—22no—
413C2×D43—22no—
414C2×D43—22no—
415C2×D43—42no—
416C2×D43—42no—
417C2×D43—41no—
418C2×D43—42no—
419C2×D43—41no—
420C2×D43—42no—
421C2×D43—41no—
422C2×D43—42no—
423C2×D43—41no—
424C2×D43—42no—
425C2×D43—816no—
426C2×D43#41714yescomplemented
427C4×C43—22no—
428C4×C43—22no—
429C4×C43—42no—
430C4×C43—81no—
431C4×C43—81no—
432C4×C43C2×C4×D411yescharacteristic
433C4×C43#51811yescharacteristic
434C4×C43D4211yescharacteristic
435C4×C43#54611yescharacteristic
436Dic43—22no—
437Dic43—22no—
438Dic43—42no—
439Dic43—42no—
440Dic43—81no—
441C2×#546—431no—
442C2×#435—431no—
443C2×#417—431no—
444C22×#102—431no—
445D4×C4⋊C4—431no—
446#1983—431no—
447#1959D4311yescharacteristic, complemented
448#1895—431no—
449#1892—431no—
450#1874—431no—
451#1872—431no—
452#1802—431no—
453#1788—431no—
454#1786—431no—
455#1762—431no—
456C2×C43—82no—
457C2×C43D4×C22⋊C411yescharacteristic
458C2×C43C2×#41711yescharacteristic
459C2×C43#289711yescharacteristic
460C2×C43#326411yescharacteristic
461C2×C43#326611yescharacteristic
462C2×C43#330611yescharacteristic
463C2×C43#331411yescharacteristic
464D43—24no—
465D43—42no—
466D43—44no—
467C22×#41—431no—
468C23×D4—431no—
469C22×M16—431no—
470C23×C8—431no—
471#546—438no—
472#546—864no—
473C2×#124C2×D4311yescharacteristic
474C2×#123—861no—
475C2×C22⋊Q8—431no—
476C2×#121—431no—
477C2×#121—861no—
478C2×#120—861no—
479C2×C4×D4—431no—
480C2×C4×D4—431no—
481C2×C4×D4—861no—
482C22×C4⋊C4—431no—
483C22×C4⋊C4—431no—
484C22×C22⋊C4—861no—
485#435—864no—
486C2×C4⋊C8—431no—
487#417—864no—
488C2×#103—431no—
489C2×#103—431no—
490C2×#103C2×D4311yescharacteristic, complemented
491C2×#103C2×D4311yescharacteristic, complemented
492C2×#102—431no—
493C2×#102—431no—
494C2×#102—431no—
495C2×#102—431no—
496C2×#102—431no—
497C2×#102—431no—
498C2×#102—864no—
499C2×#102C2×D4311yescharacteristic
500C2×#102C2×D4311yescharacteristic
501C2×C22⋊C8—431no—
502C2×C22⋊C8—431no—
503C2×#97C2×D4311yescharacteristic, complemented
504#389—861no—
505#385—861no—
506#385—861no—
507#384C2×D4311yescharacteristic, complemented
508#380—431no—
509#380—431no—
510C4×C4⋊C4—431no—
511#340—431no—
512#340—431no—
513#340—431no—
514#340—431no—
515C43#2241911yescharacteristic, complemented, Sylow
516C25—861no—
517C2×#41—434no—
518C2×#41—862no—
519C2×#41—862no—
520C2×#41—862no—
521C2×#41—1721no—
522C2×#41—1721no—
523C22×Q8C22×D4311yescharacteristic
524C22×D4—434no—
525C22×D4—431no—
526C22×D4—431no—
527C22×D4—861no—
528C22×D4—862no—
529C22×D4—861no—
530C22×D4—862no—
531C22×D4—862no—
532C22×D4—861no—
533C22×D4—1721no—
534C22×D4—1721no—
535C22×D4C22×D4311yescharacteristic
536C23×C4—431no—
537C23×C4—431no—
538C23×C4—861no—
539C23×C4—861no—
540C23×C4—861no—
541C23×C4—861no—
542C2×M16—862no—
543C2×M16—862no—
544C2×M16—1721no—
545C22×C8—431no—
546C22×C8—431no—
547C22×C8—862no—
548C22×C8—862no—
549C22×C8—1721no—
550C22×C8C22×D4311yescharacteristic
551C22×C8C22×D4311yescharacteristic
552#124—22no—
553#124C4×D4314yescomplemented
554#123—868no—
555C22⋊Q8—434no—
556C22⋊Q8—862no—
557#121—434no—
558#121—868no—
559#121—862no—
560#120—868no—
561C4×D4—434no—
562C4×D4—434no—
563C4×D4—434no—
564C4×D4—862no—
565C4×D4—1724no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—431no—
569C2×C4⋊C4—431no—
570C2×C4⋊C4—431no—
571C2×C4⋊C4—431no—
572C2×C4⋊C4—862no—
573C2×C4⋊C4—862no—
574C2×C4⋊C4—861no—
575C2×C4⋊C4—861no—
576C2×C4⋊C4—861no—
577C2×C4⋊C4—1721no—
578C2×C4⋊C4—1721no—
579C2×C4⋊C4C22×D4311yescharacteristic
580C2×C4⋊C4C22×D4311yescharacteristic
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—431no—
584C2×C22⋊C4—431no—
585C2×C22⋊C4—868no—
586C2×C22⋊C4—861no—
587C2×C22⋊C4—861no—
588C2×C22⋊C4—861no—
589C2×C22⋊C4—861no—
590C2×C22⋊C4—861no—
591C2×C42—861no—
592C2×C42C22×D4311yescharacteristic
593C4⋊C8—862no—
594#103—22no—
595#103—41no—
596#103—862no—
597#103—1721no—
598#102—22no—
599#102—41no—
600#102—434no—
601#102—862no—
602#102—862no—
603#102—862no—
604#102—862no—
605#102—1721no—
606C22⋊C8—862no—
607C22⋊C8—862no—
608#97—22no—
609#95—861no—
610#95—861no—
611#95—861no—
612C24—21no—
613C24—431no—
614C24—431no—
615C24—864no—
616C24—861no—
617C24—3441no—
618C24—3441no—
619C24—1722no—
620C24—1722no—
621C24—1722no—
622C24—1722no—
623#41—868no—
624#41—1724no—
625#41—1724no—
626#41—1724no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8C2×C4×D4312yes—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—434no—
639C2×D4—432no—
640C2×D4—432no—
641C2×D4—432no—
642C2×D4—862no—
643C2×D4—862no—
644C2×D4—864no—
645C2×D4—864no—
646C2×D4—868no—
647C2×D4—864no—
648C2×D4—861no—
649C2×D4—861no—
650C2×D4—861no—
651C2×D4—3441no—
652C2×D4—3441no—
653C2×D4—1722no—
654C2×D4—1722no—
655C2×D4—1724no—
656C2×D4—1724no—
657C2×D4—1724no—
658C2×D4—1722no—
659C2×D4—1722no—
660C2×D4C2×C4×D4312yes—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—431no—
665C22×C4—431no—
666C22×C4—432no—
667C22×C4—432no—
668C22×C4—432no—
669C22×C4—432no—
670C22×C4—864no—
671C22×C4—861no—
672C22×C4—861no—
673C22×C4—861no—
674C22×C4—861no—
675C22×C4—861no—
676C22×C4—861no—
677C22×C4—861no—
678C22×C4—861no—
679C22×C4—861no—
680C22×C4—861no—
681C22×C4—864no—
682C22×C4—861no—
683C22×C4—3441no—
684C22×C4—3441no—
685C22×C4—3441no—
686C22×C4—3441no—
687C22×C4—1722no—
688C22×C4—1722no—
689C22×C4—1722no—
690C22×C4—1722no—
691C22×C4—1722no—
692C22×C4—1722no—
693C22×C4D4×D4311yescharacteristic
694C22×C4D4×D4311yescharacteristic
695C22×C4C23×D4311yescharacteristic
696M16—1724no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—861no—
703C2×C8—861no—
704C2×C8—861no—
705C2×C8—861no—
706C2×C8—861no—
707C2×C8—861no—
708C2×C8—1724no—
709C2×C8D4×D4312yes—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—42no—
715C4⋊C4—81no—
716C4⋊C4—434no—
717C4⋊C4—432no—
718C4⋊C4—432no—
719C4⋊C4—864no—
720C4⋊C4—861no—
721C4⋊C4—861no—
722C4⋊C4—861no—
723C4⋊C4—861no—
724C4⋊C4—1722no—
725C4⋊C4—1722no—
726C22⋊C4—24no—
727C22⋊C4—24no—
728C22⋊C4—434no—
729C22⋊C4—434no—
730C22⋊C4—864no—
731C22⋊C4—864no—
732C22⋊C4—864no—
733C22⋊C4—1722no—
734C22⋊C4—1722no—
735C42—1722no—
736C42C2×C4×D4312yes—
737C42D4×D4312yes—
738C23—22no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—432no—
746C23—432no—
747C23—432no—
748C23—432no—
749C23—861no—
750C23—861no—
751C23—861no—
752C23—861no—
753C23—862no—
754C23—861no—
755C23—861no—
756C23—861no—
757C23—861no—
758C23—861no—
759C23—862no—
760C23—861no—
761C23—862no—
762C23—3444no—
763C23—3444no—
764C23—3444no—
765C23—3444no—
766C23—3444no—
767C23—1728no—
768C23—1728no—
769C23—1721no—
770C23—1721no—
771C23—1721no—
772C23—1721no—
773C23C2×D4×D4311yescharacteristic
774Q8—22no—
775Q8—22no—
776Q8—41no—
777Q8—41no—
778D4—22no—
779D4—22no—
780D4—41no—
781D4—41no—
782D4—434no—
783D4—868no—
784D4—862no—
785D4—862no—
786D4—862no—
787D4—3444no—
788D4—1728no—
789D4—1728no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—22no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—432no—
804C2×C4—432no—
805C2×C4—861no—
806C2×C4—861no—
807C2×C4—861no—
808C2×C4—861no—
809C2×C4—862no—
810C2×C4—862no—
811C2×C4—862no—
812C2×C4—862no—
813C2×C4—862no—
814C2×C4—862no—
815C2×C4—862no—
816C2×C4—862no—
817C2×C4—862no—
818C2×C4—862no—
819C2×C4—3444no—
820C2×C4—3444no—
821C2×C4—3444no—
822C2×C4—1728no—
823C2×C4—1721no—
824C2×C4—1721no—
825C2×C4—1721no—
826C2×C4—1721no—
827C2×C4—1721no—
828C2×C4—1721no—
829C2×C4—1721no—
830C2×C4C22⋊C4×D4312yes—
831C2×C4C22⋊C4×D4312yes—
832C2×C4C22×C4×D4311yescharacteristic
833C2×C4C2×D4×D4311yescharacteristic
834C2×C4C2×D4×D4311yescharacteristic
835C2×C4#41×D4311yescharacteristic
836C2×C4#1306337011yescharacteristic
837C2×C4#1306337111yescharacteristic
838C8—22no—
839C8—41no—
840C8—1721no—
841C8—1721no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—434no—
850C22—862no—
851C22—862no—
852C22—862no—
853C22—862no—
854C22—862no—
855C22—862no—
856C22—862no—
857C22—864no—
858C22—862no—
859C22—862no—
860C22—34416no—
861C22—1721no—
862C22—1722no—
863C22—1721no—
864C22—1722no—
865C22—1721no—
866C22—1722no—
867C22—1721no—
868C22—1722no—
869C22—1722no—
870C22—1722no—
871C22C2×C22⋊C4×D4311yescharacteristic
872C22#1458353411yescharacteristic
873C22#1458354211yescharacteristic
874C22AGL(1,ℤ/8)×D4311yescharacteristic
875C22#137×D4311yescharacteristic
876C22#1458370311yescharacteristic
877C22#1458370811yescharacteristic
878C4—22no—
879C4—22no—
880C4—42no—
881C4—81no—
882C4—81no—
883C4—862no—
884C4—862no—
885C4—3441no—
886C4—1722no—
887C4—1722no—
888C4C4×D4×D4311yescharacteristic
889C4#1458337111yescharacteristic
890C4#1458353311yescharacteristic
891C4#1458354611yescharacteristic
892C2—82no—
893C2—864no—
894C2—1722no—
895C2—1724no—
896C2#1913741611yescharacteristic
897C2#417×D4311yescharacteristic
898C2#1914311911yescharacteristic
899C2#1914607411yescharacteristic
900C2#1914610411yescharacteristic
901C2#1914655511yescharacteristic
902C2#1914667511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1959C2
socleC23×C43C22×D4
prime radicalC2×#14583542C2
cosocleC22×C4×C43C24
hypercenter#1959D43
hypocenterC43#22419
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1959

Complements

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

NH ≅ G/Ntype
2. C2×#14582972C2semidirect
3. C2×#14582899C2semidirect
4. C2×#102×D43C2semidirect
5. #19137495C2semidirect
6. #19135528C2semidirect
7. #19135030C2semidirect
8. #19135015C2semidirect
9. #19134909C2semidirect
10. #19134899C2semidirect
11. #19134592C2semidirect
12. #19134534C2semidirect
13. #19134524C2semidirect
14. #19134421C2semidirect
15. C43×#1959C2semidirect
18. C22×#10621872C22semidirect
21. #14583542C4semidirect
31. C2×C4⋊C4×D43C22semidirect
34. C2×C4⋊(C43⋊C8)C22semidirect
36. C2×#13063249C22semidirect
37. C2×#13063249C22semidirect
46. C2×(C2×D43)⋊C8C22semidirect
51. #14582756C22semidirect
52. C4×C4⋊Dic43C22semidirect
53. #14582662C22semidirect
54. #14582662C22semidirect
55. #14582661C22semidirect
56. #14582661C22semidirect
58. C2×#103×C43C22semidirect
59. C2×#103×C43C22semidirect
62. C2×#97×C43C22semidirect
63. C43×#384C22semidirect
70. C2×#10621902C2×C4semidirect
81. C2×D4×D43C2×C4semidirect
98. #13063301C2×C4semidirect
101. #13063296C2×C4semidirect
105. C4×D172C2×C4semidirect
132. #13063247D4semidirect
147. #124×C43C2×C4semidirect
373. D172C4×D4semidirect
426. C2×D43#417semidirect
447. #1959D43semidirect
490. C2×#103C2×D43semidirect
491. C2×#103C2×D43semidirect
503. C2×#97C2×D43semidirect
507. #384C2×D43semidirect
515. C43#22419semidirect
553. #124C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145835422
C2×#145829722
C2×#145828992
C2×#102×D432
#191374952
#191355282
#191350302
#191350152
#191349092
#191348992
#191345922
#191345342
#191345242
#191344212
C43×#19592
#2241943