Finite Group Databasebeta

← C2×#19144321 #25963999

Subgroups — C2×#19144321 #25963999

Order 11008.

2746 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583695C211yesmaximal, characteristic, complemented
2C22×#13063349C211yesmaximal, characteristic, complemented
3C2×AGL(1,ℤ/8)×D43C211yesmaximal, characteristic, complemented
4C2×#14583664C211yesmaximal, characteristic, complemented
5#19144321C2116yesmaximal, direct product factor
6C2×#14583168C211yesmaximal, characteristic, complemented
7C2×#14583167C211yesmaximal, characteristic, complemented
8C2×#14583166C211yesmaximal, characteristic, complemented
9C2×#14583163C211yesmaximal, characteristic, complemented
10C2×#14583162C211yesmaximal, characteristic, complemented
11C2×#14583161C211yesmaximal, characteristic, complemented
12C2×#14583160C211yesmaximal, characteristic, complemented
13C2×#14582946C211yesmaximal, characteristic, complemented
14C2×#14582880C211yesmaximal, characteristic, complemented
15C2×#100×D43C211yesmaximal, characteristic, complemented
16C2×C43×#472C211yesmaximal, characteristic, complemented
17C22×#10621900C2211yescharacteristic
18C2×#41×D43C2211yescharacteristic
19C22×D4×D43C2211yescharacteristic
20#14583695—24no—
21#14583695C2218yescomplemented
22C2×#13063358C2211yescharacteristic, complemented
23C2×#13063355C2211yescharacteristic, complemented
24C2×#13063354—21no—
25C2×#13063353C2211yescharacteristic
26C2×#13063352—21no—
27C2×#13063351C2211yescharacteristic
28C2×#13063351C2211yescharacteristic, complemented
29C2×#13063350C2211yescharacteristic
30C2×#13063349—21no—
31C2×#13063349—21no—
32C2×#13063349—21no—
33C2×#13063349—21no—
34C2×#13063349—21no—
35C2×#13063349—21no—
36C2×#13063349—24no—
37C2×#13063349C2218yescomplemented
38AGL(1,ℤ/8)×D43—24no—
39AGL(1,ℤ/8)×D43C2218yescomplemented
40C2×#13063346—21no—
41C2×#13063344—21no—
42C22×#10621873C2211yescharacteristic, complemented
43C22×#10621883C2211yescharacteristic, complemented
44C2×SD16×D43—21no—
45C22×#10621882C2211yescharacteristic, complemented
46C2×D8×D43—21no—
47#14583664—24no—
48#14583664C2218yescomplemented
49C2×#13063333—21no—
50C2×#13063333C2211yescharacteristic, complemented
51C2×#13063332C2211yescharacteristic, complemented
52C2×#13063331—21no—
53C2×#13063331C2211yescharacteristic, complemented
54C22×#10621872—21no—
55C22×#10621872C2211yescharacteristic
56C2×M16×D43—21no—
57C2×M16×D43C2211yescharacteristic
58C2×M16×D43C2211yescharacteristic
59C2×M16×D43C2211yescharacteristic
60#14583168C2218yescomplemented
61#14583167C2218yescomplemented
62#14583166C2218yescomplemented
63#14583163C2218yescomplemented
64#14583162C2218yescomplemented
65#14583161C2218yescomplemented
66#14583160C2218yescomplemented
67#14582946C2218yescomplemented
68C2×#13063261C2211yescharacteristic, complemented
69C2×#13063260C2211yescharacteristic, complemented
70C2×#13063260C2211yescharacteristic, complemented
71#14582880C2218yescomplemented
72C2×#13063243C2211yescharacteristic, complemented
73C2×#13063243C2211yescharacteristic, complemented
74C2×#13063242C2211yescharacteristic, complemented
75C2×#13063242C2211yescharacteristic, complemented
76C2×#13063241C2211yescharacteristic, complemented
77C2×#13063241C2211yescharacteristic, complemented
78#100×D43C2218yescomplemented
79C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
80C2×AGL(1,ℤ/8)×C43C2211yescharacteristic, complemented
81C22×D8×C43C2211yescharacteristic, complemented
82C2×#131×C43C2211yescharacteristic, complemented
83C43×#472C2218yescomplemented
84C2×#108×C43C2211yescharacteristic, complemented
85C2×#100×C43C2211yescharacteristic, complemented
86C2×#100×C43C2211yescharacteristic, complemented
87C24×D43—21no—
88C2×#10621902D411yescharacteristic
89C2×#10621898—21no—
90C2×#10621898C2311yescharacteristic
91C2×#10621900—21no—
92C2×#10621900—21no—
93C2×#10621900—21no—
94C2×#10621900—22no—
95C2×#10621900—21no—
96C2×#10621900—21no—
97C2×#10621900—22no—
98C2×#10621900—22no—
99C2×#10621900D411yescharacteristic
100C2×#10621900C2314yes—
101#41×D43—22no—
102#41×D43—22no—
103#41×D43D414yes—
104#41×D43C2314yes—
105C22×Dic86C2311yescharacteristic
106C2×Q8×D43D411yescharacteristic
107C22×D172C2311yescharacteristic
108C22×C22⋊D43—21no—
109C22×C22⋊D43—21no—
110C2×D4×D43—21no—
111C2×D4×D43—21no—
112C2×D4×D43—22no—
113C2×D4×D43—21no—
114C2×D4×D43—22no—
115C2×D4×D43—21no—
116C2×D4×D43—21no—
117C2×D4×D43—22no—
118C2×D4×D43D411yescharacteristic
119C2×D4×D43C2314yes—
120C23×Dic43—21no—
121C22×C4×D43—21no—
122C22×C4×D43C2311yescharacteristic
123#13063358—22no—
124#13063358C2314yescomplemented
125#13063355—22no—
126#13063355C2314yescomplemented
127#13063354—28no—
128#13063353—22no—
129#13063353C2314yes—
130#13063352—28no—
131#13063351—22no—
132#13063351—22no—
133#13063351C2314yes—
134#13063351C2314yescomplemented
135#13063350—22no—
136#13063350C2314yes—
137#13063349—28no—
138#13063349—28no—
139#13063349—28no—
140#13063349—28no—
141#13063349—28no—
142#13063349—28no—
143#13063346—28no—
144#13063344—28no—
145C2×Dic172—21no—
146C2×#10621885—21no—
147C2×#10621873—21no—
148C2×#10621873—21no—
149C2×#10621873—21no—
150C2×#10621873—21no—
151C2×#10621873—22no—
152C2×#10621873C2314yescomplemented
153C2×#10621883—21no—
154C2×#10621883—21no—
155C2×#10621883—21no—
156C2×#10621883—21no—
157C2×#10621883—21no—
158C2×#10621883—22no—
159C2×#10621883C2314yescomplemented
160C2×#10621884—21no—
161SD16×D43—28no—
162C2×D344—21no—
163C2×#10621882—21no—
164C2×#10621882—21no—
165C2×#10621882—21no—
166C2×#10621882—21no—
167C2×#10621882—21no—
168C2×#10621882—22no—
169C2×#10621882C2314yescomplemented
170D8×D43—28no—
171#13063333—22no—
172#13063333—28no—
173#13063333C2314yescomplemented
174#13063332—22no—
175#13063332C2314yescomplemented
176#13063331—22no—
177#13063331—28no—
178#13063331C2314yescomplemented
179C2×#10621877—21no—
180C2×#10621877C2311yescharacteristic
181C2×#10621877C2311yescharacteristic
182C2×#10621877C2311yescharacteristic
183C2×#10621872—21no—
184C2×#10621872—21no—
185C2×#10621872—21no—
186C2×#10621872—21no—
187C2×#10621872—21no—
188C2×#10621872—28no—
189C2×#10621872D411yescharacteristic
190C2×#10621872D411yescharacteristic
191C2×#10621872D411yescharacteristic
192C2×#10621872D411yescharacteristic
193C2×#10621872D414yes—
194C2×#10621872C2314yes—
195M16×D43—22no—
196M16×D43—22no—
197M16×D43—22no—
198M16×D43—28no—
199M16×D43C2314yes—
200M16×D43C2314yes—
201M16×D43C2314yes—
202C22×C43⋊C8—21no—
203C22×C43⋊C8C2311yescharacteristic
204C2×C8×D43—21no—
205C2×C8×D43—21no—
206C2×C8×D43—21no—
207C2×C8×D43—21no—
208C2×C8×D43—21no—
209#13063261C2314yescomplemented
210#13063260C2314yescomplemented
211#13063260C2314yescomplemented
212#13063243C2314yescomplemented
213#13063243C2314yescomplemented
214#13063242C2314yescomplemented
215#13063242C2314yescomplemented
216#13063241C2314yescomplemented
217#13063241C2314yescomplemented
218C2×#41×C43C2311yescharacteristic
219C22×D4×C43C2311yescharacteristic
220C22×D4×C43C2311yescharacteristic
221AGL(1,ℤ/8)×C43—22no—
222AGL(1,ℤ/8)×C43—22no—
223AGL(1,ℤ/8)×C43C2314yes—
224AGL(1,ℤ/8)×C43C2314yescomplemented
225C2×SD16×C43—21no—
226C2×SD16×C43—21no—
227C2×D8×C43—21no—
228C2×D8×C43—21no—
229C2×D8×C43—21no—
230C2×D8×C43—21no—
231C2×D8×C43—22no—
232C2×D8×C43C2314yescomplemented
233#131×C43—22no—
234#131×C43C2314yescomplemented
235C2×M16×C43—21no—
236C2×M16×C43C2311yescharacteristic
237C2×M16×C43C2311yescharacteristic
238C2×M16×C43C2311yescharacteristic
239C22×C8×C43—21no—
240C22×C8×C43C2311yescharacteristic
241#108×C43C2314yescomplemented
242#100×C43C2314yescomplemented
243#100×C43C2314yescomplemented
244C24×C43—21no—
245C24×C43—21no—
246C23×D43—21no—
247C23×D43—21no—
248C23×D43—24no—
249C23×D43—41no—
250C23×D43—41no—
251C23×D43—42no—
252C23×D43—84no—
253C23×D43#4111yescharacteristic
254#41×C43—21no—
255#41×C43—21no—
256#41×C43C2×D412yes—
257#41×C43C2412yes—
258C2×Q8×C43C2×D411yescharacteristic
259C2×D4×C43—21no—
260C2×D4×C43—21no—
261C2×D4×C43—21no—
262C2×D4×C43—21no—
263C2×D4×C43—21no—
264C2×D4×C43—21no—
265C2×D4×C43—21no—
266C2×D4×C43—21no—
267C2×D4×C43—21no—
268C2×D4×C43—21no—
269C2×D4×C43—21no—
270C2×D4×C43C2×D411yescharacteristic
271C2×D4×C43C2412yes—
272C2×D4×C43C2412yes—
273C22×C4×C43—21no—
274C22×C4×C43C2411yescharacteristic
275C2×C22⋊D43—21no—
276C2×C22⋊D43—24no—
277C2×C22⋊D43—21no—
278C2×C22⋊D43—21no—
279C2×C22⋊D43—24no—
280C2×C22⋊D43—41no—
281C2×C22⋊D43—41no—
282C2×C22⋊D43—42no—
283C2×C22⋊D43—41no—
284C2×C22⋊D43—41no—
285C2×C22⋊D43—42no—
286C22×Dic43—21no—
287C22×Dic43—24no—
288C22×Dic43—21no—
289C22×Dic43—41no—
290C22×Dic43—41no—
291C22×Dic43—42no—
292C22×Dic43#4111yescharacteristic
293#10621902—22no—
294#10621902C2×D414yes—
295Q8×D43—22no—
296Q8×D43C2×D414yes—
297#10621900—24no—
298#10621900—24no—
299#10621900—22no—
300#10621900—24no—
301#10621900—24no—
302#10621900—24no—
303#10621900—24no—
304#10621900—42no—
305#10621900—42no—
306#10621900—42no—
307#10621900—42no—
308#10621900C2×D414yes—
309D4×D43—22no—
310D4×D43—24no—
311D4×D43—24no—
312D4×D43—24no—
313D4×D43—24no—
314D4×D43—24no—
315D4×D43—24no—
316D4×D43—42no—
317D4×D43—42no—
318D4×D43—42no—
319D4×D43—42no—
320D4×D43C2×D414yes—
321#10621898—21no—
322#10621898—21no—
323#10621898—24no—
324#10621898—24no—
325#10621898C2×D412yes—
326#10621898C2412yes—
327C2×D172—21no—
328C2×D172—21no—
329C2×D172—21no—
330C2×D172—21no—
331C2×D172—21no—
332C2×D172—21no—
333C2×D172C2×D411yescharacteristic
334C2×D172C2412yes—
335C2×C4×D43—21no—
336C2×C4×D43—21no—
337C2×C4×D43—24no—
338C2×C4×D43—24no—
339C2×C4×D43—21no—
340C2×C4×D43C2×D411yescharacteristic
341C2×C4×D43C2×D411yescharacteristic
342C2×C4×D43C2×D411yescharacteristic
343C2×C4×D43C2×D412yes—
344C2×C4×D43C2×D412yes—
345C2×C4×D43C2×D411yescharacteristic
346C2×C4×D43#4112yes—
347C2×C4×D43C2412yes—
348C2×Dic86—21no—
349C2×Dic86—21no—
350C2×Dic86—21no—
351C2×Dic86—21no—
352C2×Dic86—21no—
353C2×Dic86—21no—
354C2×Dic86C2×D411yescharacteristic
355C2×Dic86C2412yes—
356SD16×C43—24no—
357SD16×C43—24no—
358D8×C43—24no—
359D8×C43—24no—
360D8×C43—24no—
361D8×C43—24no—
362M16×C43—21no—
363M16×C43—21no—
364M16×C43—21no—
365M16×C43—24no—
366M16×C43C2412yes—
367M16×C43C2412yes—
368M16×C43C2412yes—
369C2×C8×C43—21no—
370C2×C8×C43—21no—
371C2×C8×C43—21no—
372C2×C8×C43—24no—
373C2×C8×C43C2×D411yescharacteristic
374C2×C8×C43C2×D411yescharacteristic
375C2×C8×C43C2×D412yes—
376C2×C8×C43C2412yes—
377#10621885—24no—
378#10621884—24no—
379#10621883—24no—
380#10621883—24no—
381#10621883—24no—
382#10621883—24no—
383#10621883—24no—
384#10621882—24no—
385#10621882—24no—
386#10621882—24no—
387#10621882—24no—
388#10621882—24no—
389#10621877—21no—
390#10621877—21no—
391#10621877—21no—
392#10621877—24no—
393#10621877C2412yes—
394#10621877C2412yes—
395#10621877C2412yes—
396C2×C43⋊C8—21no—
397C2×C43⋊C8—21no—
398C2×C43⋊C8—21no—
399C2×C43⋊C8—24no—
400C2×C43⋊C8C2×D411yescharacteristic
401C2×C43⋊C8C2×D411yescharacteristic
402C2×C43⋊C8C2×D412yes—
403C2×C43⋊C8C2412yes—
404Dic172—24no—
405D344—24no—
406#10621873—24no—
407#10621873—24no—
408#10621873—24no—
409#10621873—24no—
410#10621872—24no—
411#10621872—24no—
412#10621872—24no—
413#10621872—24no—
414#10621872—24no—
415#10621872C2×D414yes—
416#10621872C2×D414yes—
417#10621872C2×D414yes—
418#10621872C2×D414yes—
419C8×D43—24no—
420C8×D43—24no—
421C8×D43—24no—
422C8×D43—24no—
423C8×D43—24no—
424C23×C43—21no—
425C23×C43—22no—
426C23×C43—22no—
427C23×C43—41no—
428C23×C43—41no—
429C23×C43—41no—
430C23×C43—41no—
431C23×C43—82no—
432C23×C43—82no—
433C23×C43C2×#4111yescharacteristic
434C22×D43—21no—
435C22×D43—24no—
436C22×D43—22no—
437C22×D43—42no—
438C22×D43—41no—
439C22×D43—41no—
440C22×D43—44no—
441C22×D43—44no—
442C22×D43—82no—
443C22×D43—84no—
444C22×D43—84no—
445C22×D43—88no—
446C22×D43—88no—
447C22×D43—82no—
448C22×D43#12111yescharacteristic
449C22×D43#12111yescharacteristic
450C22×D43#12112yes—
451C22×D43C2×#4112yes—
452Q8×C43—21no—
453Q8×C43C22×D412yes—
454D4×C43—22no—
455D4×C43—22no—
456D4×C43—21no—
457D4×C43—22no—
458D4×C43—22no—
459D4×C43—22no—
460D4×C43—22no—
461D4×C43—41no—
462D4×C43—41no—
463D4×C43—41no—
464D4×C43—41no—
465D4×C43C22×D412yes—
466C2×C4×C43—21no—
467C2×C4×C43—22no—
468C2×C4×C43—22no—
469C2×C4×C43C22×D411yescharacteristic
470C2×C4×C43C22×D411yescharacteristic
471C2×C4×C43C22×D411yescharacteristic
472C2×C4×C43C22×D411yescharacteristic
473C2×C4×C43C2×#4111yescharacteristic
474C2×C4×C43C2511yescharacteristic
475C22⋊D43—22no—
476C22⋊D43—22no—
477C22⋊D43—24no—
478C22⋊D43—24no—
479C22⋊D43—44no—
480C22⋊D43—44no—
481C22⋊D43—44no—
482C22⋊D43—44no—
483C2×Dic43—21no—
484C2×Dic43—24no—
485C2×Dic43—22no—
486C2×Dic43—41no—
487C2×Dic43—41no—
488C2×Dic43—44no—
489C2×Dic43—44no—
490C2×Dic43#12111yescharacteristic
491C2×Dic43#12111yescharacteristic
492C2×Dic43#12112yes—
493C2×Dic43C2×#4112yes—
494D172—24no—
495D172—21no—
496D172—22no—
497D172—22no—
498D172—41no—
499D172—41no—
500D172C22×D412yes—
501C4×D43—24no—
502C4×D43—22no—
503C4×D43—22no—
504C4×D43—24no—
505C4×D43#12112yes—
506C4×D43#12112yes—
507C4×D43#12112yes—
508C4×D43#12112yes—
509C4×D43C22×D412yes—
510C4×D43C22×D412yes—
511C4×D43C22×D412yes—
512C4×D43C22×D412yes—
513Dic86—21no—
514Dic86—24no—
515Dic86—22no—
516Dic86—22no—
517Dic86—41no—
518Dic86—41no—
519Dic86C22×D412yes—
520C8×C43—22no—
521C8×C43—22no—
522C8×C43—22no—
523C8×C43C22×D412yes—
524C8×C43C22×D412yes—
525C43⋊C8—22no—
526C43⋊C8—22no—
527C43⋊C8—22no—
528C43⋊C8C22×D412yes—
529C43⋊C8C22×D412yes—
530C2×#3068—431nomaximal, Sylow
531C22×C43—22no—
532C22×C43—22no—
533C22×C43—42no—
534C22×C43—42no—
535C22×C43—42no—
536C22×C43—82no—
537C22×C43—82no—
538C22×C43—82no—
539C22×C43—82no—
540C22×C43—82no—
541C22×C43—82no—
542C22×C43C2×#12111yescharacteristic
543C22×C43C2×#12111yescharacteristic
544C22×C43C22×#4111yescharacteristic
545C2×D43—22no—
546C2×D43—22no—
547C2×D43—22no—
548C2×D43—42no—
549C2×D43—42no—
550C2×D43—42no—
551C2×D43—42no—
552C2×D43—84no—
553C2×D43—88no—
554C2×D43—88no—
555C2×D43—82no—
556C2×D43—82no—
557C2×D43—82no—
558C2×D43C2×#12112yes—
559C2×D43C2×#12112yes—
560C4×C43—22no—
561C4×C43C2×#12111yescharacteristic
562C4×C43C2×#12111yescharacteristic
563C4×C43C23×D411yescharacteristic
564C4×C43C23×D411yescharacteristic
565Dic43—22no—
566Dic43—42no—
567Dic43C2×#12112yes—
568Dic43C2×#12112yes—
569C2×#575—431no—
570C22×AGL(1,ℤ/8)—431no—
571C22×AGL(1,ℤ/8)—431no—
572C2×#568—431no—
573#3068—4316no—
574C2×#472—431no—
575C2×#472—431no—
576C2×#472—431no—
577C2×#472D4311yescharacteristic, complemented
578C2×#471—431no—
579C2×#471—431no—
580C2×#471—431no—
581C2×#471—431no—
582C2×#430—431no—
583C2×#413—431no—
584C22×#100—431no—
585C2×C43—21no—
586C2×C43—21no—
587C2×C43—42no—
588C2×C43—82no—
589C2×C43—82no—
590C2×C43#306812yescomplemented
591C2×C43C22×#12111yescharacteristic
592D43—22no—
593D43—22no—
594D43—42no—
595D43—82no—
596C22×#41—431no—
597C22×#41—431no—
598C23×D4—431no—
599#575—438no—
600#575—864no—
601C2×#137—431no—
602C2×#137—431no—
603C2×#137—861no—
604C2×AGL(1,ℤ/8)—438no—
605C2×AGL(1,ℤ/8)—431no—
606C2×AGL(1,ℤ/8)—431no—
607C2×AGL(1,ℤ/8)—431no—
608C2×AGL(1,ℤ/8)—438no—
609C2×AGL(1,ℤ/8)—431no—
610C2×AGL(1,ℤ/8)—861no—
611C2×AGL(1,ℤ/8)—861no—
612C2×AGL(1,ℤ/8)—861no—
613C2×AGL(1,ℤ/8)—861no—
614C2×AGL(1,ℤ/8)—864no—
615C2×AGL(1,ℤ/8)—861no—
616C2×AGL(1,ℤ/8)—861no—
617C2×AGL(1,ℤ/8)—861no—
618C2×AGL(1,ℤ/8)—864no—
619C2×AGL(1,ℤ/8)C2×D4311yescharacteristic
620C2×AGL(1,ℤ/8)C2×D4311yescharacteristic, complemented
621C2×#135—861no—
622C2×#135—861no—
623C22×SD16—431no—
624C22×SD16—431no—
625C22×SD16—861no—
626C22×D8—431no—
627C22×D8—861no—
628C22×D8C2×D4311yescharacteristic, complemented
629#568—438no—
630#568—864no—
631C2×#131—431no—
632C2×#131—431no—
633C2×#131—431no—
634C2×#131—861no—
635C2×#131—861no—
636C2×#131C2×D4311yescharacteristic, complemented
637C22×M16—431no—
638C22×M16—431no—
639C22×M16—431no—
640C22×M16—431no—
641C22×M16—861no—
642C22×M16—861no—
643#472—438no—
644#472—438no—
645#472—438no—
646#472C2×D4318yescomplemented
647#471—438no—
648#471—438no—
649#471—438no—
650#471—438no—
651#430—438no—
652C2×#108—431no—
653C2×#108—431no—
654C2×#108—431no—
655C2×#108C2×D4311yescharacteristic, complemented
656#413—438no—
657C2×#101—431no—
658C2×#101—431no—
659C2×#100—431no—
660C2×#100—431no—
661C2×#100—431no—
662C2×#100—431no—
663C2×#100—438no—
664C2×#100C2×D4311yescharacteristic, complemented
665C2×#100C2×D4311yescharacteristic, complemented
666C43C2×#306811yescharacteristic, complemented, Sylow
667C25—861no—
668C2×#41—434no—
669C2×#41—434no—
670C2×#41—431no—
671C2×#41—431no—
672C2×#41—434no—
673C2×#41—431no—
674C2×#41—861no—
675C2×#41—861no—
676C2×#41—862no—
677C2×#41—862no—
678C2×#41—862no—
679C2×#41—861no—
680C2×#41—861no—
681C2×#41—861no—
682C2×#41—862no—
683C2×#41—861no—
684C2×#41—862no—
685C2×#41C22×D4311yescharacteristic
686C22×Q8—431no—
687C22×Q8—431no—
688C22×D4—431no—
689C22×D4—434no—
690C22×D4—431no—
691C22×D4—861no—
692C22×D4—861no—
693C22×D4—861no—
694C22×D4—861no—
695C22×D4—862no—
696C22×D4—862no—
697C22×D4—862no—
698C22×D4—861no—
699C22×D4—861no—
700C22×D4—861no—
701C22×D4C22×D4311yescharacteristic
702C22×D4C22×D4311yescharacteristic
703C23×C4—431no—
704C23×C4—861no—
705C23×C4—861no—
706#137—434no—
707#137—434no—
708#137—862no—
709#137—868no—
710#137—862no—
711AGL(1,ℤ/8)—22no—
712AGL(1,ℤ/8)—22no—
713AGL(1,ℤ/8)—434no—
714AGL(1,ℤ/8)—434no—
715AGL(1,ℤ/8)—434no—
716AGL(1,ℤ/8)—434no—
717AGL(1,ℤ/8)—862no—
718AGL(1,ℤ/8)—868no—
719AGL(1,ℤ/8)—868no—
720AGL(1,ℤ/8)—868no—
721AGL(1,ℤ/8)—868no—
722AGL(1,ℤ/8)—868no—
723AGL(1,ℤ/8)—868no—
724AGL(1,ℤ/8)—868no—
725AGL(1,ℤ/8)—862no—
726AGL(1,ℤ/8)—862no—
727AGL(1,ℤ/8)—862no—
728AGL(1,ℤ/8)C22×D4314yes—
729AGL(1,ℤ/8)C22×D4314yescomplemented
730#135—868no—
731#135—868no—
732C2×Q16—861no—
733C2×Q16—861no—
734C2×SD16—21no—
735C2×SD16—21no—
736C2×SD16—434no—
737C2×SD16—434no—
738C2×SD16—861no—
739C2×SD16—861no—
740C2×SD16—861no—
741C2×SD16—861no—
742C2×SD16—862no—
743C2×SD16—868no—
744C2×SD16—861no—
745C2×SD16—861no—
746C2×SD16—861no—
747C2×SD16—861no—
748C2×SD16—861no—
749C2×SD16—861no—
750C2×SD16—862no—
751C2×D8—21no—
752C2×D8—21no—
753C2×D8—21no—
754C2×D8—21no—
755C2×D8—22no—
756C2×D8—434no—
757C2×D8—861no—
758C2×D8—861no—
759C2×D8—861no—
760C2×D8—862no—
761C2×D8—868no—
762C2×D8—861no—
763C2×D8—861no—
764C2×D8—861no—
765C2×D8C22×D4314yescomplemented
766#131—22no—
767#131—434no—
768#131—434no—
769#131—434no—
770#131—868no—
771#131—862no—
772#131—862no—
773#131—868no—
774#131—862no—
775#131C22×D4314yescomplemented
776C2×M16—21no—
777C2×M16—431no—
778C2×M16—431no—
779C2×M16—431no—
780C2×M16—431no—
781C2×M16—434no—
782C2×M16—434no—
783C2×M16—431no—
784C2×M16—431no—
785C2×M16—431no—
786C2×M16—434no—
787C2×M16—434no—
788C2×M16—434no—
789C2×M16—861no—
790C2×M16—868no—
791C2×M16—861no—
792C2×M16—861no—
793C2×M16—861no—
794C2×M16—861no—
795C2×M16—868no—
796C2×M16—862no—
797C2×M16—862no—
798C2×M16—862no—
799C2×M16—861no—
800C2×M16C22×D4311yescharacteristic
801C2×M16C22×D4311yescharacteristic
802C2×M16C22×D4311yescharacteristic
803C22×C8—21no—
804C22×C8—431no—
805C22×C8—861no—
806C22×C8—861no—
807C22×C8—861no—
808C22×C8—861no—
809C22×C8—861no—
810C22×C8—861no—
811C22×C8C22×D4311yescharacteristic
812#108—434no—
813#108—434no—
814#108—434no—
815#108C22×D4314yescomplemented
816#101—434no—
817#101—434no—
818#100—434no—
819#100—434no—
820#100—434no—
821#100—434no—
822#100C22×D4314yescomplemented
823#100C22×D4314yescomplemented
824C24—21no—
825C24—21no—
826C24—431no—
827C24—861no—
828C24—864no—
829C24—861no—
830C24—3444no—
831C24—1722no—
832C24—1721no—
833C24—1721no—
834#41—21no—
835#41—21no—
836#41—434no—
837#41—434no—
838#41—432no—
839#41—432no—
840#41—864no—
841#41—864no—
842#41—864no—
843#41—864no—
844#41—862no—
845#41—862no—
846#41—864no—
847#41—864no—
848#41—864no—
849#41—864no—
850#41—861no—
851#41—861no—
852#41—1722no—
853#41—1722no—
854#41—1722no—
855#41—1722no—
856#41D4×D4312yes—
857#41C23×D4312yes—
858C2×Q8—434no—
859C2×Q8—431no—
860C2×Q8—432no—
861C2×Q8—861no—
862C2×Q8—862no—
863C2×Q8—861no—
864C2×Q8—861no—
865C2×Q8—861no—
866C2×Q8—861no—
867C2×Q8—861no—
868C2×Q8D4×D4311yescharacteristic
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—434no—
881C2×D4—431no—
882C2×D4—432no—
883C2×D4—861no—
884C2×D4—862no—
885C2×D4—864no—
886C2×D4—864no—
887C2×D4—864no—
888C2×D4—864no—
889C2×D4—861no—
890C2×D4—864no—
891C2×D4—864no—
892C2×D4—864no—
893C2×D4—861no—
894C2×D4—861no—
895C2×D4—864no—
896C2×D4—861no—
897C2×D4—861no—
898C2×D4—861no—
899C2×D4—861no—
900C2×D4—861no—
901C2×D4—1722no—
902C2×D4—1722no—
903C2×D4—1722no—
904C2×D4—1722no—
905C2×D4—1722no—
906C2×D4—1721no—
907C2×D4—1721no—
908C2×D4—1722no—
909C2×D4—1721no—
910C2×D4—1721no—
911C2×D4D4×D4311yescharacteristic
912C2×D4C23×D4312yes—
913C2×D4C23×D4312yes—
914C22×C4—21no—
915C22×C4—431no—
916C22×C4—431no—
917C22×C4—431no—
918C22×C4—431no—
919C22×C4—431no—
920C22×C4—432no—
921C22×C4—432no—
922C22×C4—432no—
923C22×C4—432no—
924C22×C4—864no—
925C22×C4—861no—
926C22×C4—864no—
927C22×C4—861no—
928C22×C4—861no—
929C22×C4—864no—
930C22×C4—861no—
931C22×C4—861no—
932C22×C4—1722no—
933C22×C4—1721no—
934C22×C4—1721no—
935C22×C4C23×D4311yescharacteristic
936Q16—864no—
937Q16—864no—
938SD16—24no—
939SD16—24no—
940SD16—864no—
941SD16—864no—
942SD16—864no—
943SD16—864no—
944SD16—864no—
945SD16—864no—
946SD16—864no—
947SD16—864no—
948SD16—864no—
949SD16—864no—
950D8—24no—
951D8—24no—
952D8—24no—
953D8—24no—
954D8—864no—
955D8—864no—
956D8—864no—
957D8—864no—
958D8—864no—
959D8—864no—
960M16—21no—
961M16—21no—
962M16—21no—
963M16—24no—
964M16—434no—
965M16—434no—
966M16—434no—
967M16—434no—
968M16—432no—
969M16—432no—
970M16—432no—
971M16—864no—
972M16—864no—
973M16—864no—
974M16—864no—
975M16—864no—
976M16—861no—
977M16—861no—
978M16—861no—
979M16—864no—
980M16C23×D4312yes—
981M16C23×D4312yes—
982M16C23×D4312yes—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—24no—
987C2×C8—431no—
988C2×C8—431no—
989C2×C8—432no—
990C2×C8—432no—
991C2×C8—864no—
992C2×C8—864no—
993C2×C8—864no—
994C2×C8—864no—
995C2×C8—864no—
996C2×C8—861no—
997C2×C8—861no—
998C2×C8—861no—
999C2×C8—864no—
1000C2×C8D4×D4311yescharacteristic
1001C2×C8D4×D4311yescharacteristic
1002C2×C8D4×D4312yes—
1003C2×C8C23×D4312yes—
1004C23—21no—
1005C23—22no—
1006C23—22no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—82no—
1012C23—82no—
1013C23—431no—
1014C23—431no—
1015C23—432no—
1016C23—432no—
1017C23—864no—
1018C23—861no—
1019C23—862no—
1020C23—3442no—
1021C23—3442no—
1022C23—3444no—
1023C23—3444no—
1024C23—3448no—
1025C23—3448no—
1026C23—1722no—
1027C23—1724no—
1028C23—1724no—
1029C23—1721no—
1030C23—1721no—
1031C23#41×D4311yescharacteristic
1032Q8—21no—
1033Q8—432no—
1034Q8—864no—
1035Q8—861no—
1036Q8—862no—
1037Q8—862no—
1038Q8—1721no—
1039Q8—1721no—
1040Q8C2×D4×D4312yes—
1041D4—22no—
1042D4—22no—
1043D4—21no—
1044D4—22no—
1045D4—22no—
1046D4—22no—
1047D4—22no—
1048D4—41no—
1049D4—41no—
1050D4—41no—
1051D4—41no—
1052D4—432no—
1053D4—864no—
1054D4—864no—
1055D4—864no—
1056D4—862no—
1057D4—862no—
1058D4—861no—
1059D4—862no—
1060D4—862no—
1061D4—1724no—
1062D4—1724no—
1063D4—1724no—
1064D4—1724no—
1065D4—1721no—
1066D4—1721no—
1067D4C2×D4×D4312yes—
1068C2×C4—21no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—432no—
1072C2×C4—431no—
1073C2×C4—431no—
1074C2×C4—432no—
1075C2×C4—432no—
1076C2×C4—432no—
1077C2×C4—432no—
1078C2×C4—432no—
1079C2×C4—432no—
1080C2×C4—432no—
1081C2×C4—432no—
1082C2×C4—432no—
1083C2×C4—864no—
1084C2×C4—864no—
1085C2×C4—864no—
1086C2×C4—861no—
1087C2×C4—862no—
1088C2×C4—862no—
1089C2×C4—862no—
1090C2×C4—1724no—
1091C2×C4—1724no—
1092C2×C4—1721no—
1093C2×C4—1721no—
1094C2×C4C2×D4×D4311yescharacteristic
1095C2×C4C2×D4×D4311yescharacteristic
1096C2×C4C2×D4×D4311yescharacteristic
1097C2×C4C2×D4×D4311yescharacteristic
1098C2×C4#41×D4311yescharacteristic
1099C2×C4C24×D4311yescharacteristic
1100C8—22no—
1101C8—22no—
1102C8—22no—
1103C8—432no—
1104C8—432no—
1105C8—862no—
1106C8—862no—
1107C8—862no—
1108C8C2×D4×D4312yes—
1109C8C2×D4×D4312yes—
1110C22—22no—
1111C22—22no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—82no—
1116C22—82no—
1117C22—82no—
1118C22—82no—
1119C22—82no—
1120C22—82no—
1121C22—432no—
1122C22—432no—
1123C22—862no—
1124C22—862no—
1125C22—862no—
1126C22—3442no—
1127C22—3442no—
1128C22—3444no—
1129C22—3448no—
1130C22—3448no—
1131C22—3442no—
1132C22—1722no—
1133C22—1722no—
1134C22—1722no—
1135C22—1722no—
1136C22#121×D4311yescharacteristic
1137C22#121×D4311yescharacteristic
1138C22C2×#41×D4311yescharacteristic
1139C4—22no—
1140C4—432no—
1141C4—432no—
1142C4—862no—
1143C4—1722no—
1144C4#121×D4311yescharacteristic
1145C4#121×D4311yescharacteristic
1146C4C22×D4×D4311yescharacteristic
1147C4C22×D4×D4311yescharacteristic
1148C2—21no—
1149C2—21no—
1150C2—42no—
1151C2—82no—
1152C2—82no—
1153C2—862no—
1154C2—862no—
1155C2—3442no—
1156C2—1722no—
1157C2#1914432112yesdirect product factor
1158C2C2×#121×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#472C2
socleC22×C43C2×#121
hypercenterC2×#472D43
hypocenterC43C2×#3068
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#472

Complements

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

NH ≅ G/Ntype
1. C2×#14583695C2semidirect
2. C22×#13063349C2semidirect
3. C2×AGL(1,ℤ/8)×D43C2semidirect
4. C2×#14583664C2semidirect
5. #19144321C2direct (N × H)
6. C2×#14583168C2semidirect
7. C2×#14583167C2semidirect
8. C2×#14583166C2semidirect
9. C2×#14583163C2semidirect
10. C2×#14583162C2semidirect
11. C2×#14583161C2semidirect
12. C2×#14583160C2semidirect
13. C2×#14582946C2semidirect
14. C2×#14582880C2semidirect
15. C2×#100×D43C2semidirect
16. C2×C43×#472C2semidirect
21. #14583695C22semidirect
22. C2×#13063358C22semidirect
23. C2×#13063355C22semidirect
28. C2×#13063351C22semidirect
37. C2×#13063349C22semidirect
39. AGL(1,ℤ/8)×D43C22semidirect
42. C22×#10621873C22semidirect
43. C22×#10621883C22semidirect
45. C22×#10621882C22semidirect
48. #14583664C22semidirect
50. C2×#13063333C22semidirect
51. C2×#13063332C22semidirect
53. C2×#13063331C22semidirect
60. #14583168C22semidirect
61. #14583167C22semidirect
62. #14583166C22semidirect
63. #14583163C22semidirect
64. #14583162C22semidirect
65. #14583161C22semidirect
66. #14583160C22semidirect
67. #14582946C22semidirect
68. C2×#13063261C22semidirect
69. C2×#13063260C22semidirect
70. C2×#13063260C22semidirect
71. #14582880C22semidirect
72. C2×#13063243C22semidirect
73. C2×#13063243C22semidirect
74. C2×#13063242C22semidirect
75. C2×#13063242C22semidirect
76. C2×#13063241C22semidirect
77. C2×#13063241C22semidirect
78. #100×D43C22semidirect
80. C2×AGL(1,ℤ/8)×C43C22semidirect
81. C22×D8×C43C22semidirect
82. C2×#131×C43C22semidirect
83. C43×#472C22semidirect
84. C2×#108×C43C22semidirect
85. C2×#100×C43C22semidirect
86. C2×#100×C43C22semidirect
124. #13063358C23semidirect
126. #13063355C23semidirect
134. #13063351C23semidirect
152. C2×#10621873C23semidirect
159. C2×#10621883C23semidirect
169. C2×#10621882C23semidirect
173. #13063333C23semidirect
175. #13063332C23semidirect
178. #13063331C23semidirect
209. #13063261C23semidirect
210. #13063260C23semidirect
211. #13063260C23semidirect
212. #13063243C23semidirect
213. #13063243C23semidirect
214. #13063242C23semidirect
215. #13063242C23semidirect
216. #13063241C23semidirect
217. #13063241C23semidirect
224. AGL(1,ℤ/8)×C43C23semidirect
232. C2×D8×C43C23semidirect
234. #131×C43C23semidirect
241. #108×C43C23semidirect
242. #100×C43C23semidirect
243. #100×C43C23semidirect
577. C2×#472D43semidirect
590. C2×C43#3068semidirect
620. C2×AGL(1,ℤ/8)C2×D43semidirect
628. C22×D8C2×D43semidirect
636. C2×#131C2×D43semidirect
646. #472C2×D43semidirect
655. C2×#108C2×D43semidirect
664. C2×#100C2×D43semidirect
665. C2×#100C2×D43semidirect
666. C43C2×#3068semidirect
729. AGL(1,ℤ/8)C22×D43semidirect
765. C2×D8C22×D43semidirect
775. #131C22×D43semidirect
815. #108C22×D43semidirect
822. #100C22×D43semidirect
823. #100C22×D43semidirect
1157. C2#19144321direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836952
C22×#130633492
C2×AGL(1,ℤ/8)×D432
C2×#145836642
#191443212
C2×#145831682
C2×#145831672
C2×#145831662
C2×#145831632
C2×#145831622
C2×#145831612
C2×#145831602
C2×#145829462
C2×#145828802
C2×#100×D432
C2×C43×#4722
C2×#306843