Finite Group Databasebeta

← C2×#19146199 #25971698

Subgroups — C2×#19146199 #25971698

Order 11008.

3042 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063352C211yesmaximal, characteristic, complemented
2C22×#13063350C211yesmaximal, characteristic, complemented
3C2×#14583540C211yesmaximal, characteristic, complemented
4C2×#14583537C211yesmaximal, characteristic, complemented
5#19146199C2116yesmaximal, direct product factor
6C2×#14583284C211yesmaximal, characteristic, complemented
7C2×#14583148C211yesmaximal, characteristic, complemented
8C2×#14583147C211yesmaximal, characteristic, complemented
9C2×#14583117C211yesmaximal, characteristic, complemented
10C2×#14583116C211yesmaximal, characteristic, complemented
11C2×#14583060C211yesmaximal, characteristic, complemented
12C2×#14583035C211yesmaximal, characteristic, complemented
13C2×#14583034C211yesmaximal, characteristic, complemented
14C2×#14582979C211yesmaximal, characteristic, complemented
15C2×#14582974C211yesmaximal, characteristic, complemented
16C2×C43×#452C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C23×D172C2211yescharacteristic, complemented
19C22×D4×D43C2211yescharacteristic, complemented
20C2×#13063352—28no—
21C2×#13063352C2218yescomplemented
22C2×#13063350—28no—
23C2×#13063350C2218yescomplemented
24C22×#10621884C2211yescharacteristic, complemented
25C22×#10621884C2211yescharacteristic, complemented
26C22×#10621884C2211yescharacteristic, complemented
27C22×D344C2211yescharacteristic
28C22×D344C2211yescharacteristic
29C22×#10621882C2211yescharacteristic
30C22×#10621882C2211yescharacteristic
31C22×#10621877C2211yescharacteristic, complemented
32C22×#10621872C2211yescharacteristic, complemented
33#14583540—24no—
34#14583540C2218yescomplemented
35#14583537—24no—
36#14583537C2218yescomplemented
37C2×#13063314C2211yescharacteristic, complemented
38C2×#13063314C2211yescharacteristic, complemented
39C2×#13063310—21no—
40C2×#13063308—21no—
41C2×#13063301C2211yescharacteristic, complemented
42C2×#13063300—21no—
43C2×#13063300C2211yescharacteristic
44C2×#13063299C2211yescharacteristic
45C2×#13063297—21no—
46C2×#13063295—21no—
47C2×#13063293—21no—
48C2×D4×Dic43C2211yescharacteristic, complemented
49C2×#13063287C2211yescharacteristic, complemented
50C2×C4×C22⋊D43C2211yescharacteristic
51C22×(C2×D43)⋊C4—21no—
52C2×C22⋊C4×D43—21no—
53#14583284C2218yescomplemented
54#14583148C2218yescomplemented
55#14583147C2218yescomplemented
56#14583117C2218yescomplemented
57#14583116C2218yescomplemented
58#14583060C2218yescomplemented
59#14583035C2218yescomplemented
60#14583034C2218yescomplemented
61#14582979C2218yescomplemented
62#14582974C2218yescomplemented
63C2×#13063258C2211yescharacteristic, complemented
64C2×Dic43⋊C8C2211yescharacteristic, complemented
65C2×#13063249C2211yescharacteristic, complemented
66C2×#13063247C2211yescharacteristic, complemented
67C2×#13063247C2211yescharacteristic, complemented
68C2×#13063245C2211yescharacteristic, complemented
69C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
70C2×C8×Dic43C2211yescharacteristic, complemented
71C22×#41×C43C2211yescharacteristic
72C22×Q16×C43C2211yescharacteristic, complemented
73C22×SD16×C43C2211yescharacteristic, complemented
74C2×C22⋊Q8×C43C2211yescharacteristic, complemented
75C43×#452C2218yescomplemented
76C2×#103×C43C2211yescharacteristic, complemented
77C2×#102×C43C2211yescharacteristic, complemented
78C2×C22⋊C8×C43C2211yescharacteristic, complemented
79C24×D43—21no—
80C24×D43—21no—
81C2×#10621902—22no—
82C2×#10621902—24no—
83C2×#10621902—42no—
84C2×#10621902C2314yes—
85C22×D172—24no—
86C22×D172—21no—
87C22×D172—21no—
88C22×D172—22no—
89C22×D172—21no—
90C22×D172—42no—
91C22×D172C2311yescharacteristic
92C22×D172C2311yescharacteristic
93C22×D172C2311yescharacteristic
94C22×D172C2314yescomplemented
95C22×C22⋊D43—21no—
96C22×C22⋊D43—21no—
97C22×C22⋊D43D411yescharacteristic
98C2×D4×D43—24no—
99C2×D4×D43—22no—
100C2×D4×D43—42no—
101C2×D4×D43C2314yescomplemented
102C23×Dic43—21no—
103C22×C4×D43—21no—
104C22×C4×D43—21no—
105C22×C4×D43C2311yescharacteristic
106#13063352—232no—
107#13063350—232no—
108C2×#10621884—24no—
109C2×#10621884—24no—
110C2×#10621884—24no—
111C2×#10621884C2314yescomplemented
112C2×#10621884C2314yescomplemented
113C2×#10621884C2314yescomplemented
114C2×D344—24no—
115C2×D344—42no—
116C2×D344C2314yes—
117C2×D344C2314yes—
118C2×#10621882—24no—
119C2×#10621882D418yescomplemented
120C2×#10621882C2314yes—
121C2×#10621882C2314yes—
122C2×#10621877—24no—
123C2×#10621877C2314yescomplemented
124C2×#10621872—24no—
125C2×#10621872C2314yescomplemented
126C22×C43⋊C8C2311yescharacteristic
127C22×C43⋊C8C2311yescharacteristic
128#13063314—22no—
129#13063314—22no—
130#13063314C2314yescomplemented
131#13063314C2314yescomplemented
132#13063310—28no—
133#13063308—28no—
134#13063301—22no—
135#13063301C2314yescomplemented
136#13063300—22no—
137#13063300—28no—
138#13063300C2314yes—
139#13063299—22no—
140#13063299C2314yes—
141#13063297—28no—
142#13063295—28no—
143#13063293—28no—
144D4×Dic43—22no—
145D4×Dic43C2314yescomplemented
146#13063287—22no—
147#13063287C2314yescomplemented
148C4×C22⋊D43D414yes—
149C4×C22⋊D43C2314yes—
150C2×C4⋊Dic43C2311yescharacteristic
151C2×Dic43⋊C4—21no—
152C2×Dic43⋊C4D411yescharacteristic
153C2×C22⋊Dic43—21no—
154C2×C22⋊Dic43D411yescharacteristic
155C2×(C2×D43)⋊C4—21no—
156C2×(C2×D43)⋊C4—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)⋊C4—21no—
163C2×(C2×D43)⋊C4—28no—
164C2×(C2×D43)⋊C4D411yescharacteristic
165C22⋊C4×D43—28no—
166C2×C4×Dic43C2311yescharacteristic
167#13063258C2314yescomplemented
168Dic43⋊C8C2314yescomplemented
169#13063249C2314yescomplemented
170#13063247C2314yescomplemented
171#13063247C2314yescomplemented
172#13063245C2314yescomplemented
173(C2×D43)⋊C8C2314yescomplemented
174C8×Dic43C2314yescomplemented
175C2×#41×C43—22no—
176C2×#41×C43—24no—
177C2×#41×C43—42no—
178C2×#41×C43C2314yes—
179C22×Q8×C43C2311yescharacteristic
180C22×Q8×C43C2311yescharacteristic
181C22×D4×C43—21no—
182C22×D4×C43C2311yescharacteristic
183C23×C4×C43—21no—
184C23×C4×C43C2311yescharacteristic
185C2×Q16×C43—42no—
186C2×Q16×C43C2314yescomplemented
187C2×SD16×C43—24no—
188C2×SD16×C43C2314yescomplemented
189C22×C8×C43C2311yescharacteristic
190C22×C8×C43C2311yescharacteristic
191C22⋊Q8×C43—22no—
192C22⋊Q8×C43C2314yescomplemented
193C2×C4⋊C4×C43—21no—
194C2×C4⋊C4×C43C2311yescharacteristic
195C2×C22⋊C4×C43—21no—
196#103×C43C2314yescomplemented
197#102×C43C2314yescomplemented
198C22⋊C8×C43C2314yescomplemented
199C24×C43—21no—
200C24×C43C2×D411yescharacteristic
201C23×D43—21no—
202C23×D43—21no—
203C23×D43—21no—
204C23×D43—24no—
205C23×D43—24no—
206C23×D43—44no—
207C23×D43—44no—
208C23×D43—44no—
209C23×D43—44no—
210C23×D43—82no—
211C23×D43—82no—
212C23×D43C2×D411yescharacteristic
213#41×C43—28no—
214#41×C43—44no—
215#41×C43—48no—
216C2×Q8×C43—21no—
217C2×Q8×C43—21no—
218C2×Q8×C43—22no—
219C2×Q8×C43—22no—
220C2×Q8×C43—22no—
221C2×Q8×C43—22no—
222C2×Q8×C43C2412yes—
223C2×Q8×C43C2412yes—
224C2×D4×C43—21no—
225C2×D4×C43—22no—
226C2×D4×C43—24no—
227C2×D4×C43—44no—
228C2×D4×C43C2×D414yes—
229C2×D4×C43C2412yes—
230C22×C4×C43—22no—
231C22×C4×C43—22no—
232C22×C4×C43—24no—
233C22×C4×C43—21no—
234C22×C4×C43—21no—
235C22×C4×C43—21no—
236C22×C4×C43—44no—
237C22×C4×C43C2×D411yescharacteristic
238C22×C4×C43C2×D412yes—
239C22×C4×C43C2412yes—
240C22×C4×C43C2411yescharacteristic
241C2×C22⋊D43—24no—
242C2×C22⋊D43—24no—
243C2×C22⋊D43—42no—
244C2×C22⋊D43—44no—
245C2×C22⋊D43—82no—
246C2×C22⋊D43C2×D414yes—
247C22×Dic43—24no—
248C22×Dic43—21no—
249C22×Dic43—82no—
250C22×Dic43C2×D411yescharacteristic
251C22×Dic43C2×D411yescharacteristic
252C22×Dic43C2×D411yescharacteristic
253#10621902—28no—
254#10621902—44no—
255#10621902—48no—
256D4×D43—28no—
257D4×D43—44no—
258D4×D43—48no—
259C2×D172—21no—
260C2×D172—22no—
261C2×D172—21no—
262C2×D172—24no—
263C2×D172—21no—
264C2×D172—24no—
265C2×D172—24no—
266C2×D172—22no—
267C2×D172—22no—
268C2×D172—22no—
269C2×D172—22no—
270C2×D172—28no—
271C2×D172—44no—
272C2×D172—44no—
273C2×D172—44no—
274C2×D172—48no—
275C2×D172—82no—
276C2×D172C2×D414yes—
277C2×D172C2412yes—
278C2×D172C2412yes—
279C2×D172C2412yes—
280C2×C4×D43—22no—
281C2×C4×D43—22no—
282C2×C4×D43—24no—
283C2×C4×D43—24no—
284C2×C4×D43—44no—
285C2×C4×D43—82no—
286C2×C4×D43C2×D412yes—
287C2×C4×D43C2412yes—
288Q16×C43—44no—
289SD16×C43—28no—
290C2×C8×C43—22no—
291C2×C8×C43—22no—
292C2×C8×C43C2412yes—
293C2×C8×C43C2412yes—
294C4⋊C4×C43—24no—
295C4⋊C4×C43—21no—
296C4⋊C4×C43C2412yes—
297C22⋊C4×C43—24no—
298C22⋊Dic43—24no—
299C22⋊Dic43C2×D414yes—
300#10621884—28no—
301#10621884—28no—
302#10621884—28no—
303#10621882—28no—
304#10621882C2×D4116yescomplemented
305(C2×D43)⋊C4—24no—
306(C2×D43)⋊C4—24no—
307(C2×D43)⋊C4—24no—
308(C2×D43)⋊C4—24no—
309(C2×D43)⋊C4—24no—
310(C2×D43)⋊C4—24no—
311(C2×D43)⋊C4—24no—
312(C2×D43)⋊C4—24no—
313(C2×D43)⋊C4C2×D414yes—
314C4⋊Dic43—21no—
315C4⋊Dic43C2412yes—
316Dic43⋊C4—24no—
317Dic43⋊C4C2×D414yes—
318C4×Dic43C2×D412yes—
319C4×Dic43C2412yes—
320#10621877—28no—
321C2×C43⋊C8—22no—
322C2×C43⋊C8C2×D414yes—
323C2×C43⋊C8C2412yes—
324C2×C43⋊C8C2412yes—
325D344—28no—
326D344—44no—
327#10621872—28no—
328C23×C43—24no—
329C23×C43—22no—
330C23×C43—22no—
331C23×C43—22no—
332C23×C43—22no—
333C23×C43—42no—
334C23×C43—42no—
335C23×C43C22×D412yes—
336C23×C43C22×D411yescharacteristic
337C22×D43—22no—
338C22×D43—24no—
339C22×D43—22no—
340C22×D43—22no—
341C22×D43—22no—
342C22×D43—22no—
343C22×D43—22no—
344C22×D43—48no—
345C22×D43—48no—
346C22×D43—48no—
347C22×D43—42no—
348C22×D43—42no—
349C22×D43—48no—
350C22×D43—42no—
351C22×D43—42no—
352C22×D43—42no—
353C22×D43—42no—
354C22×D43—42no—
355C22×D43—42no—
356C22×D43—84no—
357C22×D43—84no—
358C22×D43—816no—
359C22×D43—816no—
360C22×D43C22×D412yes—
361Q8×C43—22no—
362Q8×C43—22no—
363Q8×C43—22no—
364Q8×C43—22no—
365Q8×C43—42no—
366Q8×C43—42no—
367D4×C43—24no—
368D4×C43—22no—
369D4×C43—48no—
370D4×C43C22×D414yes—
371C2×C4×C43—22no—
372C2×C4×C43—24no—
373C2×C4×C43—22no—
374C2×C4×C43—22no—
375C2×C4×C43—22no—
376C2×C4×C43—22no—
377C2×C4×C43—22no—
378C2×C4×C43—48no—
379C2×C4×C43—42no—
380C2×C4×C43—42no—
381C2×C4×C43—42no—
382C2×C4×C43C22×D412yes—
383C2×C4×C43C22×D411yescharacteristic
384C2×C4×C43C22×D412yes—
385C2×C4×C43H(5,𝔽2)12yes—
386C2×C4×C43C2511yescharacteristic
387C22⋊D43—44no—
388C22⋊D43—48no—
389C22⋊D43—84no—
390C2×Dic43—22no—
391C2×Dic43—22no—
392C2×Dic43—22no—
393C2×Dic43—22no—
394C2×Dic43—42no—
395C2×Dic43—84no—
396C2×Dic43C22×D412yes—
397C2×Dic43C22×D412yes—
398C2×Dic43C22×D412yes—
399D172—24no—
400D172—22no—
401D172—22no—
402D172—22no—
403D172—22no—
404D172—22no—
405D172—48no—
406D172—48no—
407D172—42no—
408D172—42no—
409D172—84no—
410D172C22×D414yes—
411C4×D43—24no—
412C4×D43—22no—
413C4×D43—22no—
414C4×D43—48no—
415C4×D43—84no—
416C8×C43—22no—
417C8×C43—22no—
418C43⋊C8—22no—
419C43⋊C8C22×D414yes—
420C2×#3273—431nomaximal, Sylow
421C22×C43—22no—
422C22×C43—24no—
423C22×C43—22no—
424C22×C43—22no—
425C22×C43—44no—
426C22×C43—48no—
427C22×C43—42no—
428C22×C43—42no—
429C22×C43D4212yes—
430C22×C43#57512yes—
431C22×C43#57612yes—
432C22×C43C23×D411yescharacteristic
433C2×D43—24no—
434C2×D43—22no—
435C2×D43—22no—
436C2×D43—22no—
437C2×D43—44no—
438C2×D43—48no—
439C2×D43—42no—
440C2×D43—42no—
441C2×D43—42no—
442C2×D43—42no—
443C2×D43—42no—
444C2×D43—42no—
445C2×D43—42no—
446C2×D43—42no—
447C2×D43—816no—
448C2×D43—816no—
449C2×D43—84no—
450C2×D43—84no—
451C4×C43—22no—
452C4×C43—42no—
453C4×C43—42no—
454C4×C43—42no—
455C4×C43D4212yes—
456C4×C43C23×D411yescharacteristic
457C4×C43C2×H(5,𝔽2)11yescharacteristic
458Dic43—22no—
459Dic43—22no—
460Dic43—22no—
461Dic43—42no—
462C22×AGL(1,ℤ/8)—431no—
463C22×AGL(1,ℤ/8)—431no—
464C2×#546—431no—
465C2×#546—431no—
466#3273—4316no—
467C2×#495—431no—
468C2×#468—431no—
469C2×#468—431no—
470C2×#463—431no—
471C2×#463—431no—
472C2×#452—431no—
473C2×#452D4311yescharacteristic, complemented
474C2×#447—431no—
475C2×#447—431no—
476C2×C4×D8—431no—
477C2×#436—431no—
478C2×C43—42no—
479C2×C43—44no—
480C2×C43#327314yescomplemented
481C2×C43C2×D4211yescharacteristic
482C2×C43C2×#57511yescharacteristic
483C2×C43C2×#57611yescharacteristic
484D43—42no—
485D43—44no—
486D43—82no—
487D43—82no—
488C22×#41—431no—
489C22×#41C2×D4311yescharacteristic
490C23×D4—431no—
491C23×D4—431no—
492C2×AGL(1,ℤ/8)—438no—
493C2×AGL(1,ℤ/8)—438no—
494C2×AGL(1,ℤ/8)—868no—
495C2×AGL(1,ℤ/8)—868no—
496C22×Q16C2×D4311yescharacteristic, complemented
497C22×SD16—431no—
498C22×SD16—431no—
499C22×SD16—431no—
500C22×SD16C2×D4311yescharacteristic, complemented
501C22×D8—431no—
502C22×D8—431no—
503C22×D8—431no—
504C22×D8—431no—
505C22×M16—431no—
506C22×M16—431no—
507#546—438no—
508#546—438no—
509#546—864no—
510#546—864no—
511C2×#124—431no—
512C2×#124—431no—
513C2×#123—861no—
514C2×#123—861no—
515C2×C22⋊Q8—431no—
516C2×C22⋊Q8C2×D4311yescharacteristic, complemented
517C2×#121—431no—
518C2×#121—431no—
519C2×#121—861no—
520C2×#121—861no—
521C2×#120—861no—
522C2×#120—861no—
523C2×C4×D4—431no—
524C2×C4×D4—431no—
525C2×C4×D4—431no—
526C22×C22⋊C4—861no—
527C22×C22⋊C4—861no—
528#495—438no—
529#468—438no—
530#468—438no—
531#463—438no—
532#463—438no—
533#452—438no—
534#452C2×D4318yescomplemented
535#447—438no—
536#447—438no—
537C4×D8—438no—
538#436—438no—
539C2×#107—431no—
540C2×C4⋊C8—431no—
541C2×#103—431no—
542C2×#103C2×D4311yescharacteristic, complemented
543C2×#102—431no—
544C2×#102—431no—
545C2×#102—431no—
546C2×#102C2×D4311yescharacteristic, complemented
547C2×C22⋊C8—431no—
548C2×C22⋊C8C2×D4311yescharacteristic, complemented
549C2×C4×C8—431no—
550C43C2×#327311yescharacteristic, complemented, Sylow
551C25—861no—
552C25—861no—
553C2×#41—22no—
554C2×#41—24no—
555C2×#41—42no—
556C2×#41—434no—
557C2×#41—862no—
558C2×#41—864no—
559C2×#41—1722no—
560C2×#41C22×D4314yes—
561C22×Q8C22×D4311yescharacteristic
562C22×Q8C22×D4311yescharacteristic
563C22×D4—21no—
564C22×D4—431no—
565C22×D4—434no—
566C22×D4—431no—
567C22×D4—431no—
568C22×D4—431no—
569C22×D4—434no—
570C22×D4—864no—
571C22×D4—861no—
572C22×D4—861no—
573C22×D4—862no—
574C22×D4—861no—
575C22×D4—864no—
576C22×D4—861no—
577C22×D4—861no—
578C22×D4—862no—
579C22×D4—1722no—
580C22×D4—1722no—
581C22×D4C22×D4311yescharacteristic
582C23×C4—21no—
583C23×C4—431no—
584C23×C4—861no—
585C23×C4—861no—
586C23×C4—861no—
587C23×C4C22×D4311yescharacteristic
588AGL(1,ℤ/8)—8632no—
589AGL(1,ℤ/8)—8632no—
590C2×Q16—42no—
591C2×Q16C22×D4314yescomplemented
592C2×SD16—24no—
593C2×SD16—434no—
594C2×SD16—434no—
595C2×SD16—434no—
596C2×SD16—864no—
597C2×SD16—864no—
598C2×SD16—864no—
599C2×SD16C22×D4314yescomplemented
600C2×D8—438no—
601C2×D8—434no—
602C2×D8—434no—
603C2×D8—434no—
604C2×D8—434no—
605C2×D8—864no—
606C2×D8—864no—
607C2×D8—1722no—
608C2×M16—434no—
609C2×M16—434no—
610C2×M16—864no—
611C2×M16—864no—
612C22×C8—431no—
613C22×C8—431no—
614C22×C8C22×D4311yescharacteristic
615C22×C8C22×D4311yescharacteristic
616#124—434no—
617#124—434no—
618#124—862no—
619#124—862no—
620#123—868no—
621#123—868no—
622C22⋊Q8—22no—
623C22⋊Q8—434no—
624C22⋊Q8—862no—
625C22⋊Q8C22×D4314yescomplemented
626#121—434no—
627#121—434no—
628#121—868no—
629#121—868no—
630#121—862no—
631#121—862no—
632#120—868no—
633#120—868no—
634C4×D4—434no—
635C4×D4—434no—
636C4×D4—434no—
637C4×D4—434no—
638C4×D4—862no—
639C4×D4—862no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—431no—
642C2×C4⋊C4—431no—
643C2×C4⋊C4—861no—
644C2×C4⋊C4C22×D4311yescharacteristic
645C2×C22⋊C4—21no—
646C2×C22⋊C4—431no—
647C2×C22⋊C4—431no—
648C2×C22⋊C4—868no—
649C2×C22⋊C4—868no—
650C2×C22⋊C4—861no—
651C2×C22⋊C4—861no—
652C2×C22⋊C4—861no—
653C2×C22⋊C4—861no—
654C2×C22⋊C4—861no—
655C2×C22⋊C4—861no—
656C2×C22⋊C4—861no—
657C2×C22⋊C4—861no—
658C2×C22⋊C4—861no—
659C2×C42—431no—
660#107—434no—
661C4⋊C8—434no—
662#103—434no—
663#103C22×D4314yescomplemented
664#102—434no—
665#102—434no—
666#102—434no—
667#102C22×D4314yescomplemented
668C22⋊C8—434no—
669C22⋊C8C22×D4314yescomplemented
670C4×C8—434no—
671C24—21no—
672C24—431no—
673C24—864no—
674C24—861no—
675C24—864no—
676C24—861no—
677C24—861no—
678C24—3442no—
679C24—3442no—
680C24—1724no—
681C24—1724no—
682C24—1724no—
683C24—1724no—
684C24D4×D4311yescharacteristic
685#41—28no—
686#41—44no—
687#41—48no—
688#41—868no—
689#41—1724no—
690#41—1728no—
691C2×Q8—21no—
692C2×Q8—21no—
693C2×Q8—22no—
694C2×Q8—22no—
695C2×Q8—22no—
696C2×Q8—22no—
697C2×Q8C23×D4312yes—
698C2×Q8C23×D4312yes—
699C2×D4—24no—
700C2×D4—21no—
701C2×D4—22no—
702C2×D4—44no—
703C2×D4—434no—
704C2×D4—434no—
705C2×D4—432no—
706C2×D4—432no—
707C2×D4—432no—
708C2×D4—868no—
709C2×D4—864no—
710C2×D4—864no—
711C2×D4—864no—
712C2×D4—868no—
713C2×D4—864no—
714C2×D4—861no—
715C2×D4—862no—
716C2×D4—862no—
717C2×D4—864no—
718C2×D4—861no—
719C2×D4—861no—
720C2×D4—862no—
721C2×D4—862no—
722C2×D4—862no—
723C2×D4—3442no—
724C2×D4—3442no—
725C2×D4—1724no—
726C2×D4—1728no—
727C2×D4—1724no—
728C2×D4—1724no—
729C2×D4—1724no—
730C2×D4—1728no—
731C2×D4—1722no—
732C2×D4—1724no—
733C2×D4D4×D4314yes—
734C2×D4C23×D4312yes—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—24no—
741C22×C4—44no—
742C22×C4—431no—
743C22×C4—431no—
744C22×C4—431no—
745C22×C4—432no—
746C22×C4—432no—
747C22×C4—864no—
748C22×C4—864no—
749C22×C4—864no—
750C22×C4—862no—
751C22×C4—862no—
752C22×C4—861no—
753C22×C4—3442no—
754C22×C4—3442no—
755C22×C4—1724no—
756C22×C4D4×D4312yes—
757C22×C4D4×D4311yescharacteristic
758C22×C4C23×D4312yes—
759C22×C4C23×D4311yescharacteristic
760Q16—44no—
761SD16—28no—
762SD16—868no—
763SD16—868no—
764SD16—868no—
765D8—4316no—
766D8—868no—
767D8—868no—
768D8—1724no—
769M16—868no—
770M16—868no—
771C2×C8—22no—
772C2×C8—22no—
773C2×C8—434no—
774C2×C8—432no—
775C2×C8—432no—
776C2×C8—862no—
777C2×C8C23×D4312yes—
778C2×C8C23×D4312yes—
779C4⋊C4—24no—
780C4⋊C4—21no—
781C4⋊C4—434no—
782C4⋊C4—432no—
783C4⋊C4—864no—
784C4⋊C4—861no—
785C4⋊C4C23×D4312yes—
786C22⋊C4—24no—
787C22⋊C4—434no—
788C22⋊C4—434no—
789C22⋊C4—864no—
790C22⋊C4—864no—
791C22⋊C4—864no—
792C22⋊C4—864no—
793C22⋊C4—864no—
794C22⋊C4—864no—
795C22⋊C4—864no—
796C22⋊C4—864no—
797C22⋊C4—864no—
798C42—432no—
799C42—432no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—24no—
805C23—42no—
806C23—42no—
807C23—432no—
808C23—862no—
809C23—862no—
810C23—862no—
811C23—862no—
812C23—864no—
813C23—862no—
814C23—862no—
815C23—3444no—
816C23—3444no—
817C23—34416no—
818C23—34416no—
819C23—1728no—
820C23—1728no—
821C23—1728no—
822C23—1728no—
823C23—1722no—
824C23—1722no—
825C23—1722no—
826C23—1722no—
827C23—1722no—
828C23—1722no—
829C23—1722no—
830C23—1722no—
831C23C2×D4×D4312yes—
832C23C2×D4×D4311yescharacteristic
833Q8—22no—
834Q8—22no—
835Q8—22no—
836Q8—22no—
837Q8—42no—
838Q8—42no—
839D4—22no—
840D4—24no—
841D4—48no—
842D4—434no—
843D4—862no—
844D4—862no—
845D4—862no—
846D4—862no—
847D4—862no—
848D4—864no—
849D4—3444no—
850D4—3444no—
851D4—1728no—
852D4—1728no—
853D4—1724no—
854D4—1728no—
855D4—1722no—
856D4—1722no—
857D4C2×D4×D4314yes—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—24no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—48no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—432no—
870C2×C4—432no—
871C2×C4—432no—
872C2×C4—862no—
873C2×C4—862no—
874C2×C4—862no—
875C2×C4—862no—
876C2×C4—862no—
877C2×C4—864no—
878C2×C4—862no—
879C2×C4—3444no—
880C2×C4—3444no—
881C2×C4—1728no—
882C2×C4—1722no—
883C2×C4C2×D4×D4312yes—
884C2×C4C2×D4×D4312yes—
885C2×C4C2×D4×D4311yescharacteristic
886C2×C4#1306337012yes—
887C2×C4C24×D4311yescharacteristic
888C8—22no—
889C8—22no—
890C8—434no—
891C8—862no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—24no—
896C22—42no—
897C22—42no—
898C22—44no—
899C22—48no—
900C22—862no—
901C22—862no—
902C22—862no—
903C22—864no—
904C22—34416no—
905C22—34416no—
906C22—3444no—
907C22—3444no—
908C22—1722no—
909C22—1722no—
910C22—1722no—
911C22—1722no—
912C22—1722no—
913C22—1722no—
914C22—1722no—
915C22—1722no—
916C22—1724no—
917C22—1728no—
918C22#1458353112yes—
919C22#1458369812yes—
920C22#1458370112yes—
921C22C22×D4×D4311yescharacteristic
922C4—22no—
923C4—42no—
924C4—42no—
925C4—42no—
926C4—862no—
927C4—862no—
928C4—862no—
929C4—1722no—
930C4#1458353112yes—
931C4C22×D4×D4311yescharacteristic
932C4C2×#1306337011yescharacteristic
933C2—42no—
934C2—44no—
935C2—3442no—
936C2—3442no—
937C2—1722no—
938C2—1724no—
939C2#1914619914yesdirect product factor
940C2C2×#1458353111yescharacteristic
941C2C2×#1458369811yescharacteristic
942C2C2×#1458370111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#452C2
socleC23×C43C22×D4
hypercenterC2×#452D43
hypocenterC43C2×#3273
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C22×#13063352C2semidirect
2. C22×#13063350C2semidirect
3. C2×#14583540C2semidirect
4. C2×#14583537C2semidirect
5. #19146199C2direct (N × H)
6. C2×#14583284C2semidirect
7. C2×#14583148C2semidirect
8. C2×#14583147C2semidirect
9. C2×#14583117C2semidirect
10. C2×#14583116C2semidirect
11. C2×#14583060C2semidirect
12. C2×#14583035C2semidirect
13. C2×#14583034C2semidirect
14. C2×#14582979C2semidirect
15. C2×#14582974C2semidirect
16. C2×C43×#452C2semidirect
18. C23×D172C22semidirect
19. C22×D4×D43C22semidirect
21. C2×#13063352C22semidirect
23. C2×#13063350C22semidirect
24. C22×#10621884C22semidirect
25. C22×#10621884C22semidirect
26. C22×#10621884C22semidirect
31. C22×#10621877C22semidirect
32. C22×#10621872C22semidirect
34. #14583540C22semidirect
36. #14583537C22semidirect
37. C2×#13063314C22semidirect
38. C2×#13063314C22semidirect
41. C2×#13063301C22semidirect
48. C2×D4×Dic43C22semidirect
49. C2×#13063287C22semidirect
53. #14583284C22semidirect
54. #14583148C22semidirect
55. #14583147C22semidirect
56. #14583117C22semidirect
57. #14583116C22semidirect
58. #14583060C22semidirect
59. #14583035C22semidirect
60. #14583034C22semidirect
61. #14582979C22semidirect
62. #14582974C22semidirect
63. C2×#13063258C22semidirect
64. C2×Dic43⋊C8C22semidirect
65. C2×#13063249C22semidirect
66. C2×#13063247C22semidirect
67. C2×#13063247C22semidirect
68. C2×#13063245C22semidirect
69. C2×(C2×D43)⋊C8C22semidirect
70. C2×C8×Dic43C22semidirect
72. C22×Q16×C43C22semidirect
73. C22×SD16×C43C22semidirect
74. C2×C22⋊Q8×C43C22semidirect
75. C43×#452C22semidirect
76. C2×#103×C43C22semidirect
77. C2×#102×C43C22semidirect
78. C2×C22⋊C8×C43C22semidirect
94. C22×D172C23semidirect
101. C2×D4×D43C23semidirect
111. C2×#10621884C23semidirect
112. C2×#10621884C23semidirect
113. C2×#10621884C23semidirect
119. C2×#10621882D4semidirect
123. C2×#10621877C23semidirect
125. C2×#10621872C23semidirect
130. #13063314C23semidirect
131. #13063314C23semidirect
135. #13063301C23semidirect
145. D4×Dic43C23semidirect
147. #13063287C23semidirect
167. #13063258C23semidirect
168. Dic43⋊C8C23semidirect
169. #13063249C23semidirect
170. #13063247C23semidirect
171. #13063247C23semidirect
172. #13063245C23semidirect
173. (C2×D43)⋊C8C23semidirect
174. C8×Dic43C23semidirect
186. C2×Q16×C43C23semidirect
188. C2×SD16×C43C23semidirect
192. C22⋊Q8×C43C23semidirect
196. #103×C43C23semidirect
197. #102×C43C23semidirect
198. C22⋊C8×C43C23semidirect
304. #10621882C2×D4semidirect
473. C2×#452D43semidirect
480. C2×C43#3273semidirect
496. C22×Q16C2×D43semidirect
500. C22×SD16C2×D43semidirect
516. C2×C22⋊Q8C2×D43semidirect
534. #452C2×D43semidirect
542. C2×#103C2×D43semidirect
546. C2×#102C2×D43semidirect
548. C2×C22⋊C8C2×D43semidirect
550. C43C2×#3273semidirect
591. C2×Q16C22×D43semidirect
599. C2×SD16C22×D43semidirect
625. C22⋊Q8C22×D43semidirect
663. #103C22×D43semidirect
667. #102C22×D43semidirect
669. C22⋊C8C22×D43semidirect
939. C2#19146199direct (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×#130633502
C2×#145835402
C2×#145835372
#191461992
C2×#145832842
C2×#145831482
C2×#145831472
C2×#145831172
C2×#145831162
C2×#145830602
C2×#145830352
C2×#145830342
C2×#145829792
C2×#145829742
C2×C43×#4522
C2×#327343