Finite Group Databasebeta

← C2×#471×D43 #25963966

Subgroups — C2×#471×D43 #25963966

Order 11008.

2758 conjugacy classes of subgroups.

The subgroup lattice has 1150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#137×D43C211yesmaximal, characteristic, complemented
2C2×AGL(1,ℤ/8)×D43C211yesmaximal, characteristic
3C22×SD16×D43C211yesmaximal, characteristic, complemented
4C2×#131×D43C211yesmaximal, characteristic, complemented
5C2×#14583165C211yesmaximal, characteristic, complemented
6C2×#14583164C211yesmaximal, characteristic, complemented
7C2×#14583163C211yesmaximal, characteristic, complemented
8C2×#14583162C211yesmaximal, characteristic, complemented
9C2×#14583161C211yesmaximal, characteristic, complemented
10C2×#14583160C211yesmaximal, characteristic, complemented
11C2×#14583159C211yesmaximal, characteristic, complemented
12#471×D43C2116yesmaximal, direct product factor
13C2×#108×D43C211yesmaximal, characteristic, complemented
14C2×#101×D43C211yesmaximal, characteristic, complemented
15C2×#100×D43C211yesmaximal, characteristic, complemented
16C2×C43×#471C211yesmaximal, characteristic, complemented
17C2×#41×D43C2211yescharacteristic
18C22×Q8×D43C2211yescharacteristic
19C22×D4×D43C2211yescharacteristic
20C2×#13063358C2211yescharacteristic, complemented
21C2×#13063357—21no—
22C2×#13063356C2211yescharacteristic, complemented
23C2×#13063355C2211yescharacteristic, complemented
24C2×#13063354—21no—
25#137×D43—24no—
26#137×D43C2218yescomplemented
27C2×#13063353C2211yescharacteristic
28C2×#13063352—21no—
29C2×#13063351C2211yescharacteristic
30C2×#13063350C2211yescharacteristic
31C2×#13063349—21no—
32AGL(1,ℤ/8)×D43—24no—
33AGL(1,ℤ/8)×D43C2218yes—
34C2×Q16×D43—21no—
35C22×#10621873C2211yescharacteristic, complemented
36C22×#10621883C2211yescharacteristic, complemented
37C22×#10621884C2211yescharacteristic, complemented
38C2×SD16×D43—21no—
39C2×SD16×D43—21no—
40C2×SD16×D43—21no—
41C2×SD16×D43—21no—
42C2×SD16×D43—24no—
43C2×SD16×D43—21no—
44C2×SD16×D43—21no—
45C2×SD16×D43C2218yescomplemented
46C2×D8×D43—21no—
47C2×#13063333—21no—
48C2×#13063333C2211yescharacteristic, complemented
49C2×#13063332C2211yescharacteristic, complemented
50C2×#13063331—21no—
51C2×#13063331C2211yescharacteristic, complemented
52#131×D43—24no—
53#131×D43C2218yescomplemented
54C2×M16×D43—21no—
55C2×M16×D43C2211yescharacteristic
56C2×M16×D43C2211yescharacteristic
57C2×M16×D43C2211yescharacteristic
58C22×C8×D43—21no—
59C22×C8×D43C2211yescharacteristic
60#14583165C2218yescomplemented
61#14583164C2218yescomplemented
62#14583163C2218yescomplemented
63#14583162C2218yescomplemented
64#14583161C2218yescomplemented
65#14583160C2218yescomplemented
66#14583159C2218yescomplemented
67C2×#13063261C2211yescharacteristic, complemented
68C2×#13063260C2211yescharacteristic, complemented
69C2×#13063260C2211yescharacteristic, complemented
70#108×D43C2218yescomplemented
71C2×#13063244C2211yescharacteristic, complemented
72C2×#13063243C2211yescharacteristic, complemented
73C2×#13063243C2211yescharacteristic, complemented
74#101×D43C2218yescomplemented
75C2×#13063242C2211yescharacteristic, complemented
76C2×#13063241C2211yescharacteristic, complemented
77C2×#13063241C2211yescharacteristic, complemented
78#100×D43C2218yescomplemented
79C2×#137×C43C2211yescharacteristic, complemented
80C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
81C22×SD16×C43C2211yescharacteristic, complemented
82C2×#131×C43C2211yescharacteristic, complemented
83C43×#471C2218yescomplemented
84C2×#108×C43C2211yescharacteristic, complemented
85C2×#101×C43C2211yescharacteristic, complemented
86C2×#100×C43C2211yescharacteristic, complemented
87C24×D43—21no—
88C2×#10621902D411yescharacteristic
89C2×#10621898—21no—
90C2×#10621898C2311yescharacteristic
91C2×#10621900—21no—
92C2×#10621900D411yescharacteristic
93#41×D43—22no—
94#41×D43—22no—
95#41×D43D414yes—
96#41×D43C2314yes—
97C22×Dic86—21no—
98C22×Dic86C2311yescharacteristic
99C2×Q8×D43—22no—
100C2×Q8×D43—21no—
101C2×Q8×D43—22no—
102C2×Q8×D43—21no—
103C2×Q8×D43—21no—
104C2×Q8×D43—22no—
105C2×Q8×D43—21no—
106C2×Q8×D43D411yescharacteristic
107C2×Q8×D43C2314yes—
108C22×D172C2311yescharacteristic
109C22×C22⋊D43—21no—
110C2×D4×D43—21no—
111C2×D4×D43—21no—
112C2×D4×D43—21no—
113C2×D4×D43—22no—
114C2×D4×D43—21no—
115C2×D4×D43—22no—
116C2×D4×D43—21no—
117C2×D4×D43—22no—
118C2×D4×D43D411yescharacteristic
119C2×D4×D43C2314yes—
120C22×C4×D43—21no—
121C22×C4×D43—21no—
122C22×C4×D43C2311yescharacteristic
123#13063358—22no—
124#13063358C2314yescomplemented
125#13063357—28no—
126#13063356—22no—
127#13063356C2314yescomplemented
128#13063355—22no—
129#13063355C2314yescomplemented
130#13063354—28no—
131#13063353—22no—
132#13063353C2314yes—
133#13063352—28no—
134#13063351—22no—
135#13063351C2314yes—
136#13063350—22no—
137#13063350C2314yes—
138#13063349—28no—
139C2×Dic172—21no—
140C2×#10621885—21no—
141C2×#10621885—21no—
142Q16×D43—28no—
143C2×#10621873—21no—
144C2×#10621873—21no—
145C2×#10621873—21no—
146C2×#10621873—21no—
147C2×#10621873—22no—
148C2×#10621873C2314yescomplemented
149C2×#10621883—21no—
150C2×#10621883—21no—
151C2×#10621883—21no—
152C2×#10621883—21no—
153C2×#10621883—22no—
154C2×#10621883C2314yescomplemented
155C2×#10621884—21no—
156C2×#10621884—21no—
157C2×#10621884—21no—
158C2×#10621884—21no—
159C2×#10621884—22no—
160C2×#10621884C2314yescomplemented
161SD16×D43—28no—
162SD16×D43—28no—
163SD16×D43—28no—
164SD16×D43—28no—
165SD16×D43—28no—
166SD16×D43—28no—
167C2×D344—21no—
168C2×#10621882—21no—
169C2×#10621882—21no—
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—
188M16×D43—22no—
189M16×D43—22no—
190M16×D43—22no—
191M16×D43—28no—
192M16×D43C2314yes—
193M16×D43C2314yes—
194M16×D43C2314yes—
195C22×C43⋊C8—21no—
196C22×C43⋊C8C2311yescharacteristic
197C2×C8×D43—21no—
198C2×C8×D43—21no—
199C2×C8×D43—21no—
200C2×C8×D43—21no—
201C2×C8×D43—21no—
202C2×C8×D43—28no—
203C2×C8×D43D411yescharacteristic
204C2×C8×D43D411yescharacteristic
205C2×C8×D43D414yes—
206C2×C8×D43D411yescharacteristic
207C2×C8×D43D411yescharacteristic
208C2×C8×D43C2314yes—
209#13063261C2314yescomplemented
210#13063260C2314yescomplemented
211#13063260C2314yescomplemented
212#13063244C2314yescomplemented
213#13063243C2314yescomplemented
214#13063243C2314yescomplemented
215#13063242C2314yescomplemented
216#13063241C2314yescomplemented
217#13063241C2314yescomplemented
218C2×#41×C43C2311yescharacteristic
219C22×Q8×C43C2311yescharacteristic
220C22×D4×C43C2311yescharacteristic
221#137×C43—22no—
222#137×C43C2314yescomplemented
223AGL(1,ℤ/8)×C43—22no—
224AGL(1,ℤ/8)×C43C2314yes—
225C2×Q16×C43—21no—
226C2×SD16×C43—21no—
227C2×SD16×C43—21no—
228C2×SD16×C43—21no—
229C2×SD16×C43—21no—
230C2×SD16×C43—22no—
231C2×SD16×C43C2314yescomplemented
232C2×D8×C43—21no—
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#101×C43C2314yescomplemented
243#100×C43C2314yescomplemented
244C24×C43—21no—
245C23×D43—21no—
246C23×D43—21no—
247C23×D43—24no—
248C23×D43—41no—
249C23×D43—42no—
250C23×D43—41no—
251C23×D43—84no—
252C23×D43#4111yescharacteristic
253#41×C43—21no—
254#41×C43—21no—
255#41×C43C2×D412yes—
256#41×C43C2412yes—
257C2×Q8×C43—21no—
258C2×Q8×C43—21no—
259C2×Q8×C43—21no—
260C2×Q8×C43—21no—
261C2×Q8×C43—21no—
262C2×Q8×C43C2×D411yescharacteristic
263C2×Q8×C43C2412yes—
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—
272C22×C4×C43—21no—
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—41no—
280C2×C22⋊D43—41no—
281C2×C22⋊D43—42no—
282C22×Dic43—21no—
283C22×Dic43—21no—
284C22×Dic43#4111yescharacteristic
285#10621902—22no—
286#10621902C2×D414yes—
287Q8×D43—22no—
288Q8×D43—24no—
289Q8×D43—24no—
290Q8×D43—24no—
291Q8×D43—24no—
292Q8×D43—42no—
293Q8×D43—42no—
294Q8×D43—42no—
295Q8×D43—42no—
296Q8×D43C2×D414yes—
297#10621900—24no—
298#10621900—24no—
299#10621900—22no—
300#10621900C2×D414yes—
301D4×D43—22no—
302D4×D43—24no—
303D4×D43—24no—
304D4×D43—24no—
305D4×D43—24no—
306D4×D43—24no—
307D4×D43—24no—
308D4×D43—42no—
309D4×D43—42no—
310D4×D43—42no—
311D4×D43—42no—
312D4×D43C2×D414yes—
313#10621898—21no—
314#10621898—21no—
315#10621898—24no—
316#10621898—24no—
317#10621898C2×D412yes—
318#10621898C2412yes—
319C2×D172—21no—
320C2×D172—21no—
321C2×D172—21no—
322C2×D172—21no—
323C2×D172—21no—
324C2×D172—21no—
325C2×D172C2×D411yescharacteristic
326C2×D172C2412yes—
327C2×C4×D43—21no—
328C2×C4×D43—21no—
329C2×C4×D43—24no—
330C2×C4×D43—24no—
331C2×C4×D43—21no—
332C2×C4×D43—24no—
333C2×C4×D43—41no—
334C2×C4×D43—42no—
335C2×C4×D43—41no—
336C2×C4×D43C2×D411yescharacteristic
337C2×C4×D43C2×D411yescharacteristic
338C2×C4×D43C2×D412yes—
339C2×C4×D43C2×D411yescharacteristic
340C2×C4×D43C2×D412yes—
341C2×C4×D43C2×D411yescharacteristic
342C2×C4×D43#4112yes—
343C2×C4×D43C2412yes—
344C2×Dic86—21no—
345C2×Dic86—21no—
346C2×Dic86—21no—
347C2×Dic86—21no—
348C2×Dic86—21no—
349C2×Dic86—21no—
350C2×Dic86—24no—
351C2×Dic86—41no—
352C2×Dic86—41no—
353C2×Dic86—42no—
354C2×Dic86C2×D411yescharacteristic
355C2×Dic86C2412yes—
356Q16×C43—24no—
357SD16×C43—24no—
358SD16×C43—24no—
359SD16×C43—24no—
360SD16×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#10621885—24no—
379#10621884—24no—
380#10621884—24no—
381#10621884—24no—
382#10621884—24no—
383#10621883—24no—
384#10621883—24no—
385#10621883—24no—
386#10621883—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—
415C8×D43—24no—
416C8×D43—24no—
417C8×D43—24no—
418C8×D43—24no—
419C8×D43—24no—
420C8×D43C2×D414yes—
421C8×D43C2×D414yes—
422C8×D43C2×D414yes—
423C8×D43C2×D414yes—
424C23×C43—21no—
425C23×C43—22no—
426C23×C43—41no—
427C23×C43—41no—
428C23×C43—82no—
429C23×C43C2×#4111yescharacteristic
430C22×D43—24no—
431C22×D43—21no—
432C22×D43—24no—
433C22×D43—22no—
434C22×D43—44no—
435C22×D43—41no—
436C22×D43—41no—
437C22×D43—44no—
438C22×D43—44no—
439C22×D43—84no—
440C22×D43—88no—
441C22×D43—88no—
442C22×D43—84no—
443C22×D43—82no—
444C22×D43#12111yescharacteristic
445C22×D43#12112yes—
446C22×D43#12111yescharacteristic
447C22×D43C2×#4112yes—
448Q8×C43—21no—
449Q8×C43—22no—
450Q8×C43—22no—
451Q8×C43—41no—
452Q8×C43—41no—
453Q8×C43C22×D412yes—
454D4×C43—22no—
455D4×C43—22no—
456D4×C43—21no—
457D4×C43—22no—
458D4×C43—22no—
459D4×C43—41no—
460D4×C43—41no—
461D4×C43C22×D412yes—
462C2×C4×C43—21no—
463C2×C4×C43—22no—
464C2×C4×C43—22no—
465C2×C4×C43—22no—
466C2×C4×C43—41no—
467C2×C4×C43—41no—
468C2×C4×C43C22×D411yescharacteristic
469C2×C4×C43C22×D411yescharacteristic
470C2×C4×C43C22×D411yescharacteristic
471C2×C4×C43C22×D411yescharacteristic
472C2×C4×C43C2×#4111yescharacteristic
473C2×C4×C43C2511yescharacteristic
474C22⋊D43—22no—
475C22⋊D43—22no—
476C22⋊D43—24no—
477C22⋊D43—24no—
478C22⋊D43—44no—
479C22⋊D43—44no—
480C2×Dic43—21no—
481C2×Dic43—24no—
482C2×Dic43—22no—
483C2×Dic43—41no—
484C2×Dic43—41no—
485C2×Dic43#12111yescharacteristic
486C2×Dic43#12111yescharacteristic
487C2×Dic43#12112yes—
488C2×Dic43C2×#4112yes—
489D172—24no—
490D172—21no—
491D172—22no—
492D172—22no—
493D172—41no—
494D172—41no—
495D172C22×D412yes—
496C4×D43—24no—
497C4×D43—22no—
498C4×D43—22no—
499C4×D43—24no—
500C4×D43—44no—
501C4×D43—44no—
502C4×D43#12112yes—
503C4×D43#12112yes—
504C4×D43#12112yes—
505C4×D43#12112yes—
506C4×D43C22×D412yes—
507C4×D43C22×D412yes—
508C4×D43C22×D412yes—
509C4×D43C22×D412yes—
510Dic86—21no—
511Dic86—24no—
512Dic86—22no—
513Dic86—22no—
514Dic86—41no—
515Dic86—41no—
516Dic86—44no—
517Dic86—44no—
518Dic86C22×D412yes—
519C8×C43—22no—
520C8×C43—22no—
521C8×C43—22no—
522C8×C43C22×D412yes—
523C8×C43C22×D412yes—
524C43⋊C8—22no—
525C43⋊C8—22no—
526C43⋊C8—22no—
527C43⋊C8C22×D412yes—
528C43⋊C8C22×D412yes—
529C22×#471—431nomaximal, Sylow
530C22×C43—22no—
531C22×C43—22no—
532C22×C43—42no—
533C22×C43—42no—
534C22×C43—82no—
535C22×C43—82no—
536C22×C43—82no—
537C22×C43C2×#12111yescharacteristic
538C22×C43C2×#12111yescharacteristic
539C22×C43C22×#4111yescharacteristic
540C2×D43—22no—
541C2×D43—24no—
542C2×D43—24no—
543C2×D43—22no—
544C2×D43—42no—
545C2×D43—48no—
546C2×D43—42no—
547C2×D43—88no—
548C2×D43—82no—
549C2×D43—82no—
550C2×D43—88no—
551C2×D43—82no—
552C2×D43#47114yesdirect product factor
553C2×D43C2×#12112yes—
554C2×D43C2×#12112yes—
555C4×C43—22no—
556C4×C43—42no—
557C4×C43C2×#12111yescharacteristic
558C4×C43C2×#12111yescharacteristic
559C4×C43C23×D411yescharacteristic
560C4×C43C23×D411yescharacteristic
561Dic43—22no—
562Dic43—42no—
563Dic43C2×#12112yes—
564Dic43C2×#12112yes—
565C22×#137—431no—
566C22×AGL(1,ℤ/8)—431no—
567C23×SD16—431no—
568C22×#131—431no—
569C2×#471—4316no—
570C2×#471—431no—
571C2×#471—431no—
572C2×#471—431no—
573C2×#471—431no—
574C2×#471—431no—
575C2×#471—431no—
576C2×#471—431no—
577C2×#471D4311yescharacteristic, direct product factor
578C22×#108—431no—
579C22×#101—431no—
580C22×#100—431no—
581C2×C43—21no—
582C2×C43—21no—
583C2×C43—42no—
584C2×C43—82no—
585C2×C43C2×#47112yescomplemented
586C2×C43C22×#12111yescharacteristic
587D43—22no—
588D43—42no—
589D43—82no—
590D43C2×#47114yesdirect product factor
591C22×#41—431no—
592C23×Q8—431no—
593C23×D4—431no—
594C2×#137—431no—
595C2×#137—431no—
596C2×#137—438no—
597C2×#137—431no—
598C2×#137—861no—
599C2×#137—861no—
600C2×#137—864no—
601C2×#137C2×D4311yescharacteristic, complemented
602C2×AGL(1,ℤ/8)—431no—
603C2×AGL(1,ℤ/8)—431no—
604C2×AGL(1,ℤ/8)—438no—
605C2×AGL(1,ℤ/8)—431no—
606C2×AGL(1,ℤ/8)—861no—
607C2×AGL(1,ℤ/8)—861no—
608C2×AGL(1,ℤ/8)—864no—
609C2×AGL(1,ℤ/8)C2×D4311yescharacteristic
610C22×Q16—861no—
611C22×SD16—431no—
612C22×SD16—431no—
613C22×SD16—438no—
614C22×SD16—431no—
615C22×SD16—861no—
616C22×SD16—861no—
617C22×SD16—861no—
618C22×SD16—861no—
619C22×SD16—864no—
620C22×SD16—861no—
621C22×SD16—861no—
622C22×SD16C2×D4311yescharacteristic, complemented
623C22×D8—861no—
624C2×#131—431no—
625C2×#131—438no—
626C2×#131—431no—
627C2×#131—431no—
628C2×#131—861no—
629C2×#131—861no—
630C2×#131—864no—
631C2×#131C2×D4311yescharacteristic, complemented
632C22×M16—431no—
633C22×M16—431no—
634C22×M16—431no—
635C22×M16—861no—
636C23×C8—431no—
637C23×C8—861no—
638#471—438no—
639#471—438no—
640#471—438no—
641#471—438no—
642#471—438no—
643#471—438no—
644#471—438no—
645#471C2×D4318yesdirect product factor
646C2×#108—431no—
647C2×#108—431no—
648C2×#108—431no—
649C2×#108—438no—
650C2×#108C2×D4311yescharacteristic, complemented
651C2×#101—431no—
652C2×#101—431no—
653C2×#101—431no—
654C2×#101—438no—
655C2×#101C2×D4311yescharacteristic, complemented
656C2×#100—431no—
657C2×#100—431no—
658C2×#100—431no—
659C2×#100—438no—
660C2×#100C2×D4311yescharacteristic, complemented
661C43C22×#47111yescharacteristic, complemented, Sylow
662C25—861no—
663C2×#41—434no—
664C2×#41—434no—
665C2×#41—431no—
666C2×#41—431no—
667C2×#41—431no—
668C2×#41—861no—
669C2×#41—861no—
670C2×#41—862no—
671C2×#41—862no—
672C2×#41C22×D4311yescharacteristic
673C22×Q8—431no—
674C22×Q8—434no—
675C22×Q8—431no—
676C22×Q8—861no—
677C22×Q8—862no—
678C22×Q8—861no—
679C22×Q8—862no—
680C22×Q8—861no—
681C22×Q8—861no—
682C22×Q8—861no—
683C22×Q8—862no—
684C22×Q8C22×D4311yescharacteristic
685C22×D4—431no—
686C22×D4—434no—
687C22×D4—431no—
688C22×D4—861no—
689C22×D4—861no—
690C22×D4—862no—
691C22×D4—861no—
692C22×D4—861no—
693C22×D4—862no—
694C22×D4—862no—
695C22×D4—861no—
696C22×D4—861no—
697C22×D4C22×D4311yescharacteristic
698C23×C4—431no—
699C23×C4—861no—
700C23×C4—861no—
701#137—22no—
702#137—434no—
703#137—434no—
704#137—434no—
705#137—862no—
706#137—868no—
707#137—868no—
708#137—862no—
709#137—862no—
710#137C22×D4314yescomplemented
711AGL(1,ℤ/8)—22no—
712AGL(1,ℤ/8)—434no—
713AGL(1,ℤ/8)—434no—
714AGL(1,ℤ/8)—434no—
715AGL(1,ℤ/8)—862no—
716AGL(1,ℤ/8)—868no—
717AGL(1,ℤ/8)—868no—
718AGL(1,ℤ/8)—862no—
719AGL(1,ℤ/8)—862no—
720AGL(1,ℤ/8)C22×D4314yes—
721C2×Q16—21no—
722C2×Q16—861no—
723C2×Q16—868no—
724C2×Q16—861no—
725C2×Q16—861no—
726C2×SD16—21no—
727C2×SD16—21no—
728C2×SD16—21no—
729C2×SD16—21no—
730C2×SD16—22no—
731C2×SD16—434no—
732C2×SD16—434no—
733C2×SD16—434no—
734C2×SD16—861no—
735C2×SD16—861no—
736C2×SD16—868no—
737C2×SD16—868no—
738C2×SD16—868no—
739C2×SD16—868no—
740C2×SD16—861no—
741C2×SD16—861no—
742C2×SD16—862no—
743C2×SD16—861no—
744C2×SD16—861no—
745C2×SD16—862no—
746C2×SD16—868no—
747C2×SD16—868no—
748C2×SD16—861no—
749C2×SD16—861no—
750C2×SD16—861no—
751C2×SD16—861no—
752C2×SD16—861no—
753C2×SD16—861no—
754C2×SD16—862no—
755C2×SD16C22×D4314yescomplemented
756C2×D8—21no—
757C2×D8—861no—
758C2×D8—868no—
759C2×D8—861no—
760C2×D8—861no—
761#131—22no—
762#131—434no—
763#131—434no—
764#131—434no—
765#131—868no—
766#131—862no—
767#131—868no—
768#131—862no—
769#131—862no—
770#131C22×D4314yescomplemented
771C2×M16—21no—
772C2×M16—431no—
773C2×M16—431no—
774C2×M16—431no—
775C2×M16—434no—
776C2×M16—434no—
777C2×M16—434no—
778C2×M16—861no—
779C2×M16—861no—
780C2×M16—861no—
781C2×M16—861no—
782C2×M16—868no—
783C2×M16—861no—
784C2×M16—862no—
785C2×M16—862no—
786C2×M16—862no—
787C2×M16—861no—
788C2×M16C22×D4311yescharacteristic
789C2×M16C22×D4311yescharacteristic
790C2×M16C22×D4311yescharacteristic
791C22×C8—21no—
792C22×C8—431no—
793C22×C8—431no—
794C22×C8—431no—
795C22×C8—431no—
796C22×C8—431no—
797C22×C8—434no—
798C22×C8—434no—
799C22×C8—861no—
800C22×C8—868no—
801C22×C8—861no—
802C22×C8—861no—
803C22×C8—861no—
804C22×C8—861no—
805C22×C8—861no—
806C22×C8C22×D4311yescharacteristic
807#108—434no—
808#108—434no—
809#108—434no—
810#108C22×D4314yescomplemented
811#101—434no—
812#101—434no—
813#101—434no—
814#101C22×D4314yescomplemented
815#100—434no—
816#100—434no—
817#100—434no—
818#100C22×D4314yescomplemented
819C24—21no—
820C24—431no—
821C24—861no—
822C24—864no—
823C24—861no—
824C24—3444no—
825C24—1722no—
826C24—1721no—
827C24—1721no—
828#41—21no—
829#41—21no—
830#41—434no—
831#41—434no—
832#41—432no—
833#41—432no—
834#41—864no—
835#41—864no—
836#41—864no—
837#41—864no—
838#41—862no—
839#41—862no—
840#41—861no—
841#41—861no—
842#41D4×D4312yes—
843#41C23×D4312yes—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—434no—
850C2×Q8—431no—
851C2×Q8—432no—
852C2×Q8—861no—
853C2×Q8—864no—
854C2×Q8—862no—
855C2×Q8—864no—
856C2×Q8—864no—
857C2×Q8—864no—
858C2×Q8—864no—
859C2×Q8—861no—
860C2×Q8—861no—
861C2×Q8—861no—
862C2×Q8—861no—
863C2×Q8—861no—
864C2×Q8—1722no—
865C2×Q8—1721no—
866C2×Q8—1721no—
867C2×Q8—1722no—
868C2×Q8—1722no—
869C2×Q8—1722no—
870C2×Q8—1722no—
871C2×Q8D4×D4311yescharacteristic
872C2×Q8C23×D4312yes—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—434no—
880C2×D4—431no—
881C2×D4—432no—
882C2×D4—861no—
883C2×D4—862no—
884C2×D4—864no—
885C2×D4—864no—
886C2×D4—864no—
887C2×D4—864no—
888C2×D4—861no—
889C2×D4—864no—
890C2×D4—864no—
891C2×D4—864no—
892C2×D4—861no—
893C2×D4—861no—
894C2×D4—861no—
895C2×D4—861no—
896C2×D4—861no—
897C2×D4—861no—
898C2×D4—861no—
899C2×D4—1722no—
900C2×D4—1722no—
901C2×D4—1722no—
902C2×D4—1722no—
903C2×D4—1722no—
904C2×D4—1721no—
905C2×D4—1721no—
906C2×D4D4×D4311yescharacteristic
907C2×D4C23×D4312yes—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—431no—
911C22×C4—431no—
912C22×C4—432no—
913C22×C4—431no—
914C22×C4—431no—
915C22×C4—432no—
916C22×C4—431no—
917C22×C4—432no—
918C22×C4—432no—
919C22×C4—864no—
920C22×C4—861no—
921C22×C4—864no—
922C22×C4—861no—
923C22×C4—864no—
924C22×C4—861no—
925C22×C4—861no—
926C22×C4—861no—
927C22×C4—1722no—
928C22×C4—1721no—
929C22×C4—1721no—
930C22×C4C23×D4311yescharacteristic
931Q16—24no—
932Q16—864no—
933Q16—864no—
934Q16—864no—
935SD16—24no—
936SD16—24no—
937SD16—24no—
938SD16—24no—
939SD16—864no—
940SD16—864no—
941SD16—864no—
942SD16—864no—
943SD16—864no—
944SD16—864no—
945SD16—864no—
946SD16—864no—
947SD16—864no—
948SD16—864no—
949SD16—864no—
950SD16—864no—
951D8—24no—
952D8—864no—
953D8—864no—
954D8—864no—
955M16—21no—
956M16—21no—
957M16—21no—
958M16—24no—
959M16—432no—
960M16—432no—
961M16—432no—
962M16—864no—
963M16—864no—
964M16—864no—
965M16—864no—
966M16—864no—
967M16—861no—
968M16—861no—
969M16—861no—
970M16—864no—
971M16C23×D4312yes—
972M16C23×D4312yes—
973M16C23×D4312yes—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—24no—
978C2×C8—431no—
979C2×C8—431no—
980C2×C8—432no—
981C2×C8—432no—
982C2×C8—434no—
983C2×C8—434no—
984C2×C8—434no—
985C2×C8—434no—
986C2×C8—864no—
987C2×C8—864no—
988C2×C8—864no—
989C2×C8—864no—
990C2×C8—864no—
991C2×C8—861no—
992C2×C8—861no—
993C2×C8—861no—
994C2×C8—864no—
995C2×C8D4×D4311yescharacteristic
996C2×C8D4×D4311yescharacteristic
997C2×C8D4×D4312yes—
998C2×C8C23×D4312yes—
999C23—21no—
1000C23—22no—
1001C23—41no—
1002C23—41no—
1003C23—82no—
1004C23—431no—
1005C23—432no—
1006C23—431no—
1007C23—432no—
1008C23—864no—
1009C23—864no—
1010C23—861no—
1011C23—862no—
1012C23—3442no—
1013C23—3444no—
1014C23—3448no—
1015C23—3448no—
1016C23—3444no—
1017C23—1724no—
1018C23—1724no—
1019C23—1724no—
1020C23—1721no—
1021C23—1721no—
1022C23#41×D4311yescharacteristic
1023Q8—21no—
1024Q8—22no—
1025Q8—22no—
1026Q8—41no—
1027Q8—41no—
1028Q8—432no—
1029Q8—864no—
1030Q8—861no—
1031Q8—862no—
1032Q8—862no—
1033Q8—1724no—
1034Q8—1724no—
1035Q8—1721no—
1036Q8—1721no—
1037Q8C2×D4×D4312yes—
1038D4—22no—
1039D4—22no—
1040D4—21no—
1041D4—22no—
1042D4—22no—
1043D4—41no—
1044D4—41no—
1045D4—432no—
1046D4—864no—
1047D4—864no—
1048D4—864no—
1049D4—862no—
1050D4—862no—
1051D4—861no—
1052D4—862no—
1053D4—862no—
1054D4—1724no—
1055D4—1724no—
1056D4—1721no—
1057D4—1721no—
1058D4C2×D4×D4312yes—
1059C2×C4—21no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—432no—
1066C2×C4—431no—
1067C2×C4—431no—
1068C2×C4—432no—
1069C2×C4—432no—
1070C2×C4—432no—
1071C2×C4—432no—
1072C2×C4—432no—
1073C2×C4—432no—
1074C2×C4—432no—
1075C2×C4—432no—
1076C2×C4—432no—
1077C2×C4—864no—
1078C2×C4—864no—
1079C2×C4—864no—
1080C2×C4—861no—
1081C2×C4—862no—
1082C2×C4—862no—
1083C2×C4—862no—
1084C2×C4—1724no—
1085C2×C4—1724no—
1086C2×C4—1721no—
1087C2×C4—1721no—
1088C2×C4C2×D4×D4311yescharacteristic
1089C2×C4C2×D4×D4311yescharacteristic
1090C2×C4C2×D4×D4311yescharacteristic
1091C2×C4C2×D4×D4311yescharacteristic
1092C2×C4#41×D4311yescharacteristic
1093C2×C4C24×D4311yescharacteristic
1094C8—22no—
1095C8—22no—
1096C8—22no—
1097C8—432no—
1098C8—432no—
1099C8—862no—
1100C8—862no—
1101C8—862no—
1102C8C2×D4×D4312yes—
1103C8C2×D4×D4312yes—
1104C22—22no—
1105C22—22no—
1106C22—42no—
1107C22—42no—
1108C22—82no—
1109C22—82no—
1110C22—82no—
1111C22—432no—
1112C22—434no—
1113C22—432no—
1114C22—864no—
1115C22—864no—
1116C22—862no—
1117C22—862no—
1118C22—3442no—
1119C22—3442no—
1120C22—3448no—
1121C22—3448no—
1122C22—3442no—
1123C22—1728no—
1124C22—1722no—
1125C22—1722no—
1126C22#121×D4311yescharacteristic
1127C22#121×D4311yescharacteristic
1128C22C2×#41×D4311yescharacteristic
1129C4—22no—
1130C4—42no—
1131C4—432no—
1132C4—432no—
1133C4—862no—
1134C4—1722no—
1135C4#121×D4311yescharacteristic
1136C4#121×D4311yescharacteristic
1137C4C22×D4×D4311yescharacteristic
1138C4C22×D4×D4311yescharacteristic
1139C2—21no—
1140C2—21no—
1141C2—42no—
1142C2—82no—
1143C2—434no—
1144C2—862no—
1145C2—3442no—
1146C2—1722no—
1147C2#471×D4312yesdirect product factor
1148C2C2×#121×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#471C2
socleC22×C43C2×#121
prime radicalC2×AGL(1,ℤ/8)×D43C2
hypercenterC2×#471D43
hypocenterC43C22×#471
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#471

Complements

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

NH ≅ G/Ntype
1. C2×#137×D43C2semidirect
3. C22×SD16×D43C2semidirect
4. C2×#131×D43C2semidirect
5. C2×#14583165C2semidirect
6. C2×#14583164C2semidirect
7. C2×#14583163C2semidirect
8. C2×#14583162C2semidirect
9. C2×#14583161C2semidirect
10. C2×#14583160C2semidirect
11. C2×#14583159C2semidirect
12. #471×D43C2direct (N × H)
13. C2×#108×D43C2semidirect
14. C2×#101×D43C2semidirect
15. C2×#100×D43C2semidirect
16. C2×C43×#471C2semidirect
20. C2×#13063358C22semidirect
22. C2×#13063356C22semidirect
23. C2×#13063355C22semidirect
26. #137×D43C22semidirect
35. C22×#10621873C22semidirect
36. C22×#10621883C22semidirect
37. C22×#10621884C22semidirect
45. C2×SD16×D43C22semidirect
48. C2×#13063333C22semidirect
49. C2×#13063332C22semidirect
51. C2×#13063331C22semidirect
53. #131×D43C22semidirect
60. #14583165C22semidirect
61. #14583164C22semidirect
62. #14583163C22semidirect
63. #14583162C22semidirect
64. #14583161C22semidirect
65. #14583160C22semidirect
66. #14583159C22semidirect
67. C2×#13063261C22semidirect
68. C2×#13063260C22semidirect
69. C2×#13063260C22semidirect
70. #108×D43C22semidirect
71. C2×#13063244C22semidirect
72. C2×#13063243C22semidirect
73. C2×#13063243C22semidirect
74. #101×D43C22semidirect
75. C2×#13063242C22semidirect
76. C2×#13063241C22semidirect
77. C2×#13063241C22semidirect
78. #100×D43C22semidirect
79. C2×#137×C43C22semidirect
81. C22×SD16×C43C22semidirect
82. C2×#131×C43C22semidirect
83. C43×#471C22semidirect
84. C2×#108×C43C22semidirect
85. C2×#101×C43C22semidirect
86. C2×#100×C43C22semidirect
124. #13063358C23semidirect
127. #13063356C23semidirect
129. #13063355C23semidirect
148. C2×#10621873C23semidirect
154. C2×#10621883C23semidirect
160. C2×#10621884C23semidirect
173. #13063333C23semidirect
175. #13063332C23semidirect
178. #13063331C23semidirect
209. #13063261C23semidirect
210. #13063260C23semidirect
211. #13063260C23semidirect
212. #13063244C23semidirect
213. #13063243C23semidirect
214. #13063243C23semidirect
215. #13063242C23semidirect
216. #13063241C23semidirect
217. #13063241C23semidirect
222. #137×C43C23semidirect
231. C2×SD16×C43C23semidirect
234. #131×C43C23semidirect
241. #108×C43C23semidirect
242. #101×C43C23semidirect
243. #100×C43C23semidirect
552. C2×D43#471direct (N × H)
577. C2×#471D43direct (N × H)
585. C2×C43C2×#471semidirect
590. D43C2×#471direct (N × H)
601. C2×#137C2×D43semidirect
622. C22×SD16C2×D43semidirect
631. C2×#131C2×D43semidirect
645. #471C2×D43direct (N × H)
650. C2×#108C2×D43semidirect
655. C2×#101C2×D43semidirect
660. C2×#100C2×D43semidirect
661. C43C22×#471semidirect
710. #137C22×D43semidirect
755. C2×SD16C22×D43semidirect
770. #131C22×D43semidirect
810. #108C22×D43semidirect
814. #101C22×D43semidirect
818. #100C22×D43semidirect
1147. C2#471×D43direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#137×D432
C2×AGL(1,ℤ/8)×D432
C22×SD16×D432
C2×#131×D432
C2×#145831652
C2×#145831642
C2×#145831632
C2×#145831622
C2×#145831612
C2×#145831602
C2×#145831592
#471×D432
C2×#108×D432
C2×#101×D432
C2×#100×D432
C2×C43×#4712
C22×#47143