Finite Group Databasebeta

← C2×#19146119 #25971593

Subgroups — C2×#19146119 #25971593

Order 11008.

2914 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063352C211yesmaximal, characteristic, complemented
2C22×#13063348C211yesmaximal, characteristic, complemented
3C2×#14583552C211yesmaximal, characteristic, complemented
4C2×#14583542C211yesmaximal, characteristic, complemented
5#19146119C2116yesmaximal, direct product factor
6C2×#14583154C211yesmaximal, characteristic, complemented
7C2×#14583125C211yesmaximal, characteristic, complemented
8C2×#14583111C211yesmaximal, characteristic, complemented
9C2×#14583101C211yesmaximal, characteristic, complemented
10C2×#14583060C211yesmaximal, characteristic, complemented
11C2×#14583060C211yesmaximal, characteristic, complemented
12C2×#14583043C211yesmaximal, characteristic, complemented
13C2×#14583048C211yesmaximal, characteristic, complemented
14C2×#14583012C211yesmaximal, characteristic, complemented
15C2×#14582972C211yesmaximal, characteristic, complemented
16C2×C43×#497C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621902C2211yescharacteristic
19C22×#10621902C2211yescharacteristic, complemented
20C22×D4×D43C2211yescharacteristic
21C2×#13063352—28no—
22C2×#13063352C2218yescomplemented
23C2×#13063348—28no—
24C2×#13063348C2218yescomplemented
25C22×#10621884C2211yescharacteristic
26C22×#10621884C2211yescharacteristic
27C22×#10621884C2211yescharacteristic, complemented
28C22×D344C2211yescharacteristic
29C22×#10621882C2211yescharacteristic
30C22×#10621872C2211yescharacteristic
31C22×C8×D43C2211yescharacteristic, complemented
32#14583552—24no—
33#14583552C2218yescomplemented
34#14583542—24no—
35#14583542C2218yescomplemented
36C2×#13063310—21no—
37C2×#13063310—21no—
38C2×#13063307—21no—
39C2×#13063301C2211yescharacteristic
40C2×#13063301C2211yescharacteristic
41C2×#13063301C2211yescharacteristic, complemented
42C2×#13063300—21no—
43C2×#13063298—21no—
44C2×#13063296C2211yescharacteristic
45C2×#13063295—21no—
46C2×C4×D172C2211yescharacteristic
47C2×C4×D172C2211yescharacteristic
48C2×C4×D172C2211yescharacteristic, complemented
49C2×C4⋊C4×D43—21no—
50C2×C22⋊C4×D43—21no—
51#14583154C2218yescomplemented
52#14583125C2218yescomplemented
53#14583111C2218yescomplemented
54#14583101C2218yescomplemented
55#14583060C2218yescomplemented
56#14583060C2218yescomplemented
57#14583048C2218yescomplemented
58#14583043C2218yescomplemented
59#14583012C2218yescomplemented
60#14582972C2218yescomplemented
61C2×#13063257C2211yescharacteristic, complemented
62C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
63C2×#13063249C2211yescharacteristic, complemented
64C2×#13063249C2211yescharacteristic, complemented
65C2×#13063249C2211yescharacteristic, complemented
66C2×#13063247C2211yescharacteristic
67C2×#13063247C2211yescharacteristic, complemented
68C2×#13063246C2211yescharacteristic
69C2×(C2×D43)⋊C8C2211yescharacteristic
70C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
71C22×Q16×C43C2211yescharacteristic, complemented
72C22×Q16×C43C2211yescharacteristic, complemented
73C22×SD16×C43C2211yescharacteristic
74C22×SD16×C43C2211yescharacteristic
75C2×C4⋊Q8×C43C2211yescharacteristic, complemented
76C2×#124×C43C2211yescharacteristic
77C43×#497C2218yescomplemented
78C2×#97×C43C2211yescharacteristic, complemented
79C24×D43—21no—
80C2×#10621902—22no—
81C2×#10621902—22no—
82C2×#10621902—22no—
83C2×#10621902—24no—
84C2×#10621902—24no—
85C2×#10621902—24no—
86C2×#10621902—42no—
87C2×#10621902—42no—
88C2×#10621902—42no—
89C2×#10621902C2314yes—
90C2×#10621902C2314yes—
91C2×#10621902C2314yescomplemented
92C22×D172—21no—
93C22×D172—21no—
94C22×D172—21no—
95C22×D172D411yescharacteristic
96C22×D172C2311yescharacteristic
97C22×D172C2311yescharacteristic
98C22×C22⋊D43—21no—
99C22×C22⋊D43—21no—
100C2×D4×D43—24no—
101C2×D4×D43—22no—
102C2×D4×D43—42no—
103C2×D4×D43C2314yes—
104C22×C4×D43—21no—
105C22×C4×D43—21no—
106C22×C4×D43—21no—
107C22×C4×D43—21no—
108C22×C4×D43—21no—
109C22×C4×D43C2311yescharacteristic
110C22×C4×D43C2311yescharacteristic
111#13063352—232no—
112#13063348—232no—
113C2×#10621884—24no—
114C2×#10621884—24no—
115C2×#10621884—24no—
116C2×#10621884C2314yes—
117C2×#10621884C2314yes—
118C2×#10621884C2314yescomplemented
119C2×D344D418yescomplemented
120C2×D344C2314yes—
121C2×#10621882—24no—
122C2×#10621882C2314yes—
123C2×#10621872—24no—
124C2×#10621872C2314yes—
125C22×C43⋊C8C2311yescharacteristic
126C22×C43⋊C8C2311yescharacteristic
127C2×C8×D43—24no—
128C2×C8×D43C2314yescomplemented
129#13063310—28no—
130#13063310—28no—
131#13063307—28no—
132#13063301—22no—
133#13063301—22no—
134#13063301—22no—
135#13063301C2314yes—
136#13063301C2314yes—
137#13063301C2314yescomplemented
138#13063300—28no—
139#13063298—28no—
140#13063296—22no—
141#13063296C2314yes—
142#13063295—28no—
143C4×D172—22no—
144C4×D172—22no—
145C4×D172D414yes—
146C4×D172C2314yes—
147C4×D172C2314yes—
148C4×D172C2314yescomplemented
149C2×C4⋊Dic43D411yescharacteristic
150C2×C4⋊Dic43C2311yescharacteristic
151C2×C4⋊Dic43C2311yescharacteristic
152C2×Dic43⋊C4—21no—
153C2×Dic43⋊C4—21no—
154C2×Dic43⋊C4—21no—
155C4⋊C4×D43—28no—
156C2×C22⋊Dic43—21no—
157C2×(C2×D43)⋊C4—21no—
158C2×(C2×D43)⋊C4—21no—
159C2×(C2×D43)⋊C4—21no—
160C2×(C2×D43)⋊C4—21no—
161C2×(C2×D43)⋊C4—21no—
162C2×(C2×D43)⋊C4D411yescharacteristic
163C2×(C2×D43)⋊C4D411yescharacteristic
164C22⋊C4×D43—28no—
165#13063257C2314yescomplemented
166C4⋊(C43⋊C8)C2314yescomplemented
167#13063249C2314yescomplemented
168#13063249C2314yescomplemented
169#13063249C2314yescomplemented
170#13063247C2314yes—
171#13063247C2314yescomplemented
172#13063246C2314yes—
173(C2×D43)⋊C8C2314yes—
174(C2×D43)⋊C8C2314yescomplemented
175C22×Q8×C43C2311yescharacteristic
176C22×Q8×C43C2311yescharacteristic
177C22×Q8×C43C2311yescharacteristic
178C22×D4×C43C2311yescharacteristic
179C2×Q16×C43—24no—
180C2×Q16×C43—42no—
181C2×Q16×C43C2314yescomplemented
182C2×Q16×C43C2314yescomplemented
183C2×SD16×C43—24no—
184C2×SD16×C43—42no—
185C2×SD16×C43C2314yes—
186C2×SD16×C43C2314yes—
187C22×C8×C43C2311yescharacteristic
188C22×C8×C43C2311yescharacteristic
189C4⋊Q8×C43—22no—
190C4⋊Q8×C43C2314yescomplemented
191#124×C43—22no—
192#124×C43C2314yes—
193C2×C4⋊C4×C43—21no—
194C2×C4⋊C4×C43—21no—
195C2×C22⋊C4×C43—21no—
196C2×C22⋊C4×C43—21no—
197C2×C42×C43C2311yescharacteristic
198#97×C43C2314yescomplemented
199C24×C43—21no—
200C23×D43—21no—
201C23×D43—21no—
202C23×D43—24no—
203C23×D43—44no—
204C23×D43—44no—
205C23×D43—82no—
206C23×D43C2×D411yescharacteristic
207C23×D43C2×D411yescharacteristic
208C2×Q8×C43—21no—
209C2×Q8×C43—21no—
210C2×Q8×C43—21no—
211C2×Q8×C43—22no—
212C2×Q8×C43—22no—
213C2×Q8×C43—22no—
214C2×Q8×C43—22no—
215C2×Q8×C43—22no—
216C2×Q8×C43—22no—
217C2×Q8×C43C2412yes—
218C2×Q8×C43C2412yes—
219C2×Q8×C43C2412yes—
220C2×D4×C43—21no—
221C2×D4×C43—22no—
222C2×D4×C43—22no—
223C2×D4×C43C2412yes—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43C2×D411yescharacteristic
228C22×C4×C43C2×D411yescharacteristic
229C22×C4×C43C2411yescharacteristic
230C2×C22⋊D43—24no—
231C2×C22⋊D43—24no—
232C2×C22⋊D43—44no—
233C2×C22⋊D43—82no—
234C22×Dic43—21no—
235C22×Dic43—21no—
236C22×Dic43C2×D411yescharacteristic
237C22×Dic43C2×D411yescharacteristic
238#10621902—28no—
239#10621902—28no—
240#10621902—28no—
241#10621902—44no—
242#10621902—44no—
243#10621902—44no—
244#10621902—48no—
245#10621902—48no—
246#10621902—48no—
247D4×D43—28no—
248D4×D43—44no—
249D4×D43—48no—
250C2×D172—21no—
251C2×D172—21no—
252C2×D172—22no—
253C2×D172—22no—
254C2×D172—24no—
255C2×D172—24no—
256C2×D172—24no—
257C2×D172—42no—
258C2×D172—44no—
259C2×D172—44no—
260C2×D172—44no—
261C2×D172C2×D414yes—
262C2×D172C2×D414yes—
263C2×D172C2×D414yes—
264C2×D172C2412yes—
265C2×D172C2412yes—
266C2×C4×D43—22no—
267C2×C4×D43—22no—
268C2×C4×D43—22no—
269C2×C4×D43—22no—
270C2×C4×D43—24no—
271C2×C4×D43—24no—
272C2×C4×D43—24no—
273C2×C4×D43—24no—
274C2×C4×D43—24no—
275C2×C4×D43—44no—
276C2×C4×D43—44no—
277C2×C4×D43—44no—
278C2×C4×D43—44no—
279C2×C4×D43—82no—
280C2×C4×D43C2×D412yes—
281C2×C4×D43C2×D412yes—
282C2×C4×D43C2412yes—
283C2×C4×D43C2412yes—
284Q16×C43—28no—
285Q16×C43—44no—
286SD16×C43—28no—
287SD16×C43—44no—
288C2×C8×C43—22no—
289C2×C8×C43C2×D414yes—
290C2×C8×C43C2412yes—
291C2×C8×C43C2412yes—
292C4⋊C4×C43—24no—
293C4⋊C4×C43—24no—
294C22⋊C4×C43—24no—
295C22⋊C4×C43—24no—
296C42×C43C2×D412yes—
297C42×C43C2412yes—
298C22⋊Dic43—24no—
299#10621884—28no—
300#10621884—28no—
301#10621884—28no—
302#10621882—28no—
303(C2×D43)⋊C4—24no—
304(C2×D43)⋊C4—24no—
305(C2×D43)⋊C4—24no—
306(C2×D43)⋊C4—24no—
307(C2×D43)⋊C4—24no—
308(C2×D43)⋊C4C2×D414yes—
309(C2×D43)⋊C4C2×D414yes—
310C4⋊Dic43—21no—
311C4⋊Dic43—21no—
312C4⋊Dic43C2×D414yes—
313C4⋊Dic43C2412yes—
314C4⋊Dic43C2412yes—
315Dic43⋊C4—24no—
316Dic43⋊C4—24no—
317Dic43⋊C4—24no—
318C2×C43⋊C8—22no—
319C2×C43⋊C8—22no—
320C2×C43⋊C8C2412yes—
321C2×C43⋊C8C2412yes—
322D344C2×D4116yescomplemented
323#10621872—28no—
324C8×D43—28no—
325C23×C43—22no—
326C23×C43—42no—
327C23×C43—42no—
328C23×C43—42no—
329C23×C43C22×D411yescharacteristic
330C22×D43—22no—
331C22×D43—22no—
332C22×D43—24no—
333C22×D43—24no—
334C22×D43—22no—
335C22×D43—22no—
336C22×D43—22no—
337C22×D43—22no—
338C22×D43—22no—
339C22×D43—22no—
340C22×D43—48no—
341C22×D43—48no—
342C22×D43—42no—
343C22×D43—42no—
344C22×D43—42no—
345C22×D43—42no—
346C22×D43—84no—
347C22×D43—816no—
348C22×D43C22×D412yes—
349C22×D43C22×D412yes—
350Q8×C43—22no—
351Q8×C43—22no—
352Q8×C43—22no—
353Q8×C43—22no—
354Q8×C43—22no—
355Q8×C43—22no—
356Q8×C43—42no—
357Q8×C43—42no—
358Q8×C43—42no—
359D4×C43—22no—
360D4×C43—22no—
361D4×C43—42no—
362C2×C4×C43—22no—
363C2×C4×C43—22no—
364C2×C4×C43—22no—
365C2×C4×C43—22no—
366C2×C4×C43—22no—
367C2×C4×C43—42no—
368C2×C4×C43—42no—
369C2×C4×C43—42no—
370C2×C4×C43C22×D412yes—
371C2×C4×C43C22×D412yes—
372C2×C4×C43C22×D411yescharacteristic
373C2×C4×C43C22×D412yes—
374C2×C4×C43H(5,𝔽2)12yes—
375C2×C4×C43C2511yescharacteristic
376C22⋊D43—48no—
377C22⋊D43—84no—
378C2×Dic43—22no—
379C2×Dic43—22no—
380C2×Dic43—22no—
381C2×Dic43—22no—
382C2×Dic43—42no—
383C2×Dic43—42no—
384C2×Dic43C22×D412yes—
385C2×Dic43C22×D412yes—
386D172—24no—
387D172—24no—
388D172—22no—
389D172—22no—
390D172—44no—
391D172—48no—
392D172—48no—
393D172—48no—
394D172C22×D414yes—
395D172C22×D414yes—
396C4×D43—24no—
397C4×D43—24no—
398C4×D43—22no—
399C4×D43—22no—
400C4×D43—22no—
401C4×D43—22no—
402C4×D43—48no—
403C4×D43—48no—
404C4×D43—48no—
405C4×D43—48no—
406C4×D43—84no—
407C8×C43—22no—
408C8×C43C22×D414yes—
409C43⋊C8—22no—
410C43⋊C8—22no—
411C2×#3267—431nomaximal, Sylow
412C22×C43—42no—
413C22×C43—42no—
414C22×C43—42no—
415C22×C43—84no—
416C22×C43D4212yes—
417C22×C43#57512yes—
418C22×C43#57712yes—
419C22×C43C23×D411yescharacteristic
420C2×D43—24no—
421C2×D43—24no—
422C2×D43—22no—
423C2×D43—22no—
424C2×D43—22no—
425C2×D43—22no—
426C2×D43—22no—
427C2×D43—22no—
428C2×D43—44no—
429C2×D43—44no—
430C2×D43—48no—
431C2×D43—48no—
432C2×D43—42no—
433C2×D43—42no—
434C2×D43—42no—
435C2×D43—42no—
436C2×D43—816no—
437C4×C43—22no—
438C4×C43—22no—
439C4×C43—42no—
440C4×C43—42no—
441C4×C43—42no—
442C4×C43D4212yes—
443C4×C43C23×D411yescharacteristic
444C4×C43C2×H(5,𝔽2)11yescharacteristic
445Dic43—22no—
446Dic43—22no—
447Dic43—42no—
448Dic43—42no—
449C22×AGL(1,ℤ/8)—431no—
450C22×#135—431no—
451C2×#547—431no—
452C2×#546—431no—
453#3267—4316no—
454C2×#497D4311yescharacteristic, complemented
455C2×#470—431no—
456C2×#465—431no—
457C2×#463—431no—
458C2×#461—431no—
459C2×#452—431no—
460C2×#452—431no—
461C2×#449—431no—
462C2×#450—431no—
463C2×#442—431no—
464C2×#435—431no—
465C2×C43—82no—
466C2×C43#326714yescomplemented
467C2×C43C2×D4211yescharacteristic
468C2×C43C2×#57511yescharacteristic
469C2×C43C2×#57711yescharacteristic
470D43—42no—
471D43—42no—
472D43—44no—
473D43—44no—
474C22×#41—431no—
475C22×#41—431no—
476C22×#41—431no—
477C23×D4—431no—
478C2×AGL(1,ℤ/8)—438no—
479C2×AGL(1,ℤ/8)—868no—
480C2×#135—438no—
481C2×#135—868no—
482C22×Q16C2×D4311yescharacteristic, complemented
483C22×Q16C2×D4311yescharacteristic, complemented
484C22×SD16—431no—
485C22×SD16—431no—
486C22×SD16—431no—
487C22×SD16C2×D4311yescharacteristic
488C22×SD16C2×D4311yescharacteristic
489C22×D8—431no—
490C22×D8—431no—
491C22×M16—431no—
492C23×C8—431no—
493#547—438no—
494#547—864no—
495#546—438no—
496#546—864no—
497C2×C4⋊Q8C2×D4311yescharacteristic, complemented
498C2×#124C2×D4311yescharacteristic
499C2×#123—861no—
500C2×#123—861no—
501C2×#123—861no—
502C2×C22⋊Q8—431no—
503C2×C22⋊Q8—431no—
504C2×C22⋊Q8—431no—
505C2×#121—431no—
506C2×#121—861no—
507C2×#121—861no—
508C2×#120—861no—
509C2×C4×D4—431no—
510C2×C4×D4—431no—
511C2×C4×D4—431no—
512C22×C4⋊C4—861no—
513C22×C22⋊C4—861no—
514#497C2×D4318yescomplemented
515#470—438no—
516#465—438no—
517#463—438no—
518#461—438no—
519#452—438no—
520#452—438no—
521#450—438no—
522#449—438no—
523#442—438no—
524#435—438no—
525C2×#106—431no—
526C2×C4⋊C8—431no—
527C2×#103—431no—
528C2×#103—431no—
529C2×#103—431no—
530C2×#102—431no—
531C2×#102—431no—
532C2×#102—431no—
533C2×C22⋊C8—431no—
534C2×C22⋊C8—431no—
535C2×#97C2×D4311yescharacteristic, complemented
536C43C2×#326711yescharacteristic, complemented, Sylow
537C25—861no—
538C2×#41—434no—
539C2×#41—434no—
540C2×#41—434no—
541C2×#41—862no—
542C2×#41—862no—
543C2×#41—862no—
544C2×#41—864no—
545C2×#41—864no—
546C2×#41—864no—
547C2×#41—1722no—
548C2×#41—1722no—
549C2×#41—1722no—
550C22×Q8C22×D4311yescharacteristic
551C22×Q8C22×D4311yescharacteristic
552C22×Q8C22×D4311yescharacteristic
553C22×D4—434no—
554C22×D4—431no—
555C22×D4—431no—
556C22×D4—431no—
557C22×D4—861no—
558C22×D4—861no—
559C22×D4—861no—
560C22×D4—862no—
561C22×D4—861no—
562C22×D4—864no—
563C22×D4—861no—
564C22×D4—1722no—
565C22×D4C22×D4311yescharacteristic
566C23×C4—431no—
567C23×C4—431no—
568C23×C4—861no—
569C23×C4—861no—
570C23×C4—861no—
571C23×C4—861no—
572C23×C4—861no—
573AGL(1,ℤ/8)—8632no—
574#135—8632no—
575C2×Q16—24no—
576C2×Q16—42no—
577C2×Q16C22×D4314yescomplemented
578C2×Q16C22×D4314yescomplemented
579C2×SD16—24no—
580C2×SD16—42no—
581C2×SD16—434no—
582C2×SD16—434no—
583C2×SD16—434no—
584C2×SD16—864no—
585C2×SD16—864no—
586C2×SD16—864no—
587C2×SD16C22×D4314yes—
588C2×SD16C22×D4314yes—
589C2×D8—434no—
590C2×D8—438no—
591C2×D8—434no—
592C2×D8—864no—
593C2×M16—434no—
594C2×M16—864no—
595C22×C8—431no—
596C22×C8—431no—
597C22×C8—434no—
598C22×C8—864no—
599C22×C8C22×D4311yescharacteristic
600C22×C8C22×D4311yescharacteristic
601C4⋊Q8—22no—
602C4⋊Q8C22×D4314yescomplemented
603#124—22no—
604#124C22×D4314yes—
605#123—868no—
606#123—868no—
607#123—868no—
608C22⋊Q8—434no—
609C22⋊Q8—434no—
610C22⋊Q8—434no—
611C22⋊Q8—862no—
612C22⋊Q8—862no—
613C22⋊Q8—862no—
614#121—434no—
615#121—868no—
616#121—868no—
617#121—862no—
618#120—868no—
619C4×D4—434no—
620C4×D4—434no—
621C4×D4—434no—
622C4×D4—434no—
623C4×D4—862no—
624C4×D4—862no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—431no—
628C2×C4⋊C4—431no—
629C2×C4⋊C4—431no—
630C2×C4⋊C4—868no—
631C2×C4⋊C4—861no—
632C2×C4⋊C4—861no—
633C2×C4⋊C4—861no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—431no—
637C2×C22⋊C4—431no—
638C2×C22⋊C4—868no—
639C2×C22⋊C4—861no—
640C2×C22⋊C4—861no—
641C2×C22⋊C4—861no—
642C2×C22⋊C4—861no—
643C2×C22⋊C4—861no—
644C2×C22⋊C4—861no—
645C2×C42C22×D4311yescharacteristic
646#106—434no—
647C4⋊C8—434no—
648#103—434no—
649#103—434no—
650#103—434no—
651#102—434no—
652#102—434no—
653#102—434no—
654C22⋊C8—434no—
655C22⋊C8—434no—
656#97C22×D4314yescomplemented
657C24—21no—
658C24—431no—
659C24—431no—
660C24—864no—
661C24—861no—
662C24—861no—
663C24—3442no—
664C24—1724no—
665C24—1724no—
666#41—868no—
667#41—868no—
668#41—868no—
669#41—1724no—
670#41—1724no—
671#41—1724no—
672#41—1728no—
673#41—1728no—
674#41—1728no—
675C2×Q8—21no—
676C2×Q8—21no—
677C2×Q8—21no—
678C2×Q8—22no—
679C2×Q8—22no—
680C2×Q8—22no—
681C2×Q8—22no—
682C2×Q8—22no—
683C2×Q8—22no—
684C2×Q8C23×D4312yes—
685C2×Q8C23×D4312yes—
686C2×Q8C23×D4312yes—
687C2×D4—22no—
688C2×D4—21no—
689C2×D4—22no—
690C2×D4—434no—
691C2×D4—434no—
692C2×D4—434no—
693C2×D4—432no—
694C2×D4—432no—
695C2×D4—864no—
696C2×D4—864no—
697C2×D4—864no—
698C2×D4—864no—
699C2×D4—868no—
700C2×D4—864no—
701C2×D4—861no—
702C2×D4—861no—
703C2×D4—862no—
704C2×D4—862no—
705C2×D4—3442no—
706C2×D4—1722no—
707C2×D4—1724no—
708C2×D4—1724no—
709C2×D4—1724no—
710C2×D4—1724no—
711C2×D4—1728no—
712C2×D4—1724no—
713C2×D4C23×D4312yes—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—431no—
718C22×C4—431no—
719C22×C4—432no—
720C22×C4—432no—
721C22×C4—432no—
722C22×C4—432no—
723C22×C4—864no—
724C22×C4—864no—
725C22×C4—864no—
726C22×C4—862no—
727C22×C4—862no—
728C22×C4—862no—
729C22×C4—862no—
730C22×C4—861no—
731C22×C4—861no—
732C22×C4—864no—
733C22×C4—864no—
734C22×C4—3442no—
735C22×C4—1724no—
736C22×C4—1724no—
737C22×C4—1724no—
738C22×C4—1724no—
739C22×C4D4×D4311yescharacteristic
740C22×C4D4×D4311yescharacteristic
741C22×C4C23×D4311yescharacteristic
742Q16—28no—
743Q16—44no—
744SD16—28no—
745SD16—44no—
746SD16—868no—
747SD16—868no—
748SD16—868no—
749D8—4316no—
750D8—868no—
751M16—868no—
752C2×C8—22no—
753C2×C8—432no—
754C2×C8—432no—
755C2×C8—862no—
756C2×C8—862no—
757C2×C8—868no—
758C2×C8D4×D4314yes—
759C2×C8C23×D4312yes—
760C2×C8C23×D4312yes—
761C4⋊C4—24no—
762C4⋊C4—24no—
763C4⋊C4—434no—
764C4⋊C4—432no—
765C4⋊C4—432no—
766C4⋊C4—864no—
767C4⋊C4—864no—
768C4⋊C4—864no—
769C4⋊C4—861no—
770C4⋊C4—861no—
771C22⋊C4—24no—
772C22⋊C4—24no—
773C22⋊C4—434no—
774C22⋊C4—434no—
775C22⋊C4—864no—
776C22⋊C4—864no—
777C22⋊C4—864no—
778C22⋊C4—864no—
779C22⋊C4—864no—
780C22⋊C4—864no—
781C42D4×D4312yes—
782C42C23×D4312yes—
783C23—22no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—432no—
788C23—432no—
789C23—862no—
790C23—862no—
791C23—862no—
792C23—862no—
793C23—862no—
794C23—862no—
795C23—862no—
796C23—862no—
797C23—864no—
798C23—864no—
799C23—3444no—
800C23—34416no—
801C23—1728no—
802C23—1728no—
803C23—1722no—
804C23—1722no—
805C23—1722no—
806C23—1722no—
807C23C2×D4×D4311yescharacteristic
808Q8—22no—
809Q8—22no—
810Q8—22no—
811Q8—22no—
812Q8—22no—
813Q8—22no—
814Q8—42no—
815Q8—42no—
816Q8—42no—
817D4—22no—
818D4—22no—
819D4—42no—
820D4—434no—
821D4—434no—
822D4—862no—
823D4—862no—
824D4—864no—
825D4—864no—
826D4—3444no—
827D4—1724no—
828D4—1728no—
829D4—1728no—
830D4—1728no—
831D4—1728no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—432no—
841C2×C4—432no—
842C2×C4—862no—
843C2×C4—862no—
844C2×C4—862no—
845C2×C4—862no—
846C2×C4—862no—
847C2×C4—862no—
848C2×C4—864no—
849C2×C4—864no—
850C2×C4—862no—
851C2×C4—862no—
852C2×C4—3444no—
853C2×C4—1728no—
854C2×C4—1728no—
855C2×C4—1728no—
856C2×C4—1728no—
857C2×C4—1722no—
858C2×C4—1722no—
859C2×C4C2×D4×D4312yes—
860C2×C4C2×D4×D4312yes—
861C2×C4C2×D4×D4312yes—
862C2×C4C2×D4×D4311yescharacteristic
863C2×C4#1306337012yes—
864C2×C4C24×D4311yescharacteristic
865C8—22no—
866C8—862no—
867C8—862no—
868C8C2×D4×D4314yes—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—84no—
873C22—862no—
874C22—862no—
875C22—864no—
876C22—864no—
877C22—862no—
878C22—862no—
879C22—862no—
880C22—862no—
881C22—34416no—
882C22—1722no—
883C22—1722no—
884C22—1722no—
885C22—1722no—
886C22—1724no—
887C22—1724no—
888C22—1728no—
889C22—1728no—
890C22#1458353412yes—
891C22#1458369812yes—
892C22#1458370812yes—
893C22C22×D4×D4311yescharacteristic
894C4—22no—
895C4—22no—
896C4—42no—
897C4—42no—
898C4—42no—
899C4—862no—
900C4—862no—
901C4—1722no—
902C4—1722no—
903C4#1458353412yes—
904C4C22×D4×D4311yescharacteristic
905C4C2×#1306337011yescharacteristic
906C2—82no—
907C2—1722no—
908C2—1722no—
909C2—1724no—
910C2—1724no—
911C2#1914611914yesdirect product factor
912C2C2×#1458353411yescharacteristic
913C2C2×#1458369811yescharacteristic
914C2C2×#1458370811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#497C2
socleC23×C43C22×D4
hypercenterC2×#497D43
hypocenterC43C2×#3267
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#497

Complements

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

NH ≅ G/Ntype
1. C22×#13063352C2semidirect
2. C22×#13063348C2semidirect
3. C2×#14583552C2semidirect
4. C2×#14583542C2semidirect
5. #19146119C2direct (N × H)
6. C2×#14583154C2semidirect
7. C2×#14583125C2semidirect
8. C2×#14583111C2semidirect
9. C2×#14583101C2semidirect
10. C2×#14583060C2semidirect
11. C2×#14583060C2semidirect
12. C2×#14583043C2semidirect
13. C2×#14583048C2semidirect
14. C2×#14583012C2semidirect
15. C2×#14582972C2semidirect
16. C2×C43×#497C2semidirect
19. C22×#10621902C22semidirect
22. C2×#13063352C22semidirect
24. C2×#13063348C22semidirect
27. C22×#10621884C22semidirect
31. C22×C8×D43C22semidirect
33. #14583552C22semidirect
35. #14583542C22semidirect
41. C2×#13063301C22semidirect
48. C2×C4×D172C22semidirect
51. #14583154C22semidirect
52. #14583125C22semidirect
53. #14583111C22semidirect
54. #14583101C22semidirect
55. #14583060C22semidirect
56. #14583060C22semidirect
57. #14583048C22semidirect
58. #14583043C22semidirect
59. #14583012C22semidirect
60. #14582972C22semidirect
61. C2×#13063257C22semidirect
62. C2×C4⋊(C43⋊C8)C22semidirect
63. C2×#13063249C22semidirect
64. C2×#13063249C22semidirect
65. C2×#13063249C22semidirect
67. C2×#13063247C22semidirect
70. C2×(C2×D43)⋊C8C22semidirect
71. C22×Q16×C43C22semidirect
72. C22×Q16×C43C22semidirect
75. C2×C4⋊Q8×C43C22semidirect
77. C43×#497C22semidirect
78. C2×#97×C43C22semidirect
91. C2×#10621902C23semidirect
118. C2×#10621884C23semidirect
119. C2×D344D4semidirect
128. C2×C8×D43C23semidirect
137. #13063301C23semidirect
148. C4×D172C23semidirect
165. #13063257C23semidirect
166. C4⋊(C43⋊C8)C23semidirect
167. #13063249C23semidirect
168. #13063249C23semidirect
169. #13063249C23semidirect
171. #13063247C23semidirect
174. (C2×D43)⋊C8C23semidirect
181. C2×Q16×C43C23semidirect
182. C2×Q16×C43C23semidirect
190. C4⋊Q8×C43C23semidirect
198. #97×C43C23semidirect
322. D344C2×D4semidirect
454. C2×#497D43semidirect
466. C2×C43#3267semidirect
482. C22×Q16C2×D43semidirect
483. C22×Q16C2×D43semidirect
497. C2×C4⋊Q8C2×D43semidirect
514. #497C2×D43semidirect
535. C2×#97C2×D43semidirect
536. C43C2×#3267semidirect
577. C2×Q16C22×D43semidirect
578. C2×Q16C22×D43semidirect
602. C4⋊Q8C22×D43semidirect
656. #97C22×D43semidirect
911. C2#19146119direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633522
C22×#130633482
C2×#145835522
C2×#145835422
#191461192
C2×#145831542
C2×#145831252
C2×#145831112
C2×#145831012
C2×#145830602
C2×#145830432
C2×#145830482
C2×#145830122
C2×#145829722
C2×C43×#4972
C2×#326743