Finite Group Databasebeta

← C2×#19134567 #25095935

Subgroups — C2×#19134567 #25095935

Order 11008.

3602 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063373C211yesmaximal, characteristic
2C2×#14582917C211yesmaximal, characteristic, complemented
3C2×#14582915C211yesmaximal, characteristic, complemented
4C2×#14582908C211yesmaximal, characteristic, complemented
5C2×#14582881C211yesmaximal, characteristic, complemented
6C2×#14582872C211yesmaximal, characteristic, complemented
7#19134567C218yesmaximal, direct product factor
8C2×C43×#419C211yesmaximal, characteristic, complemented
9C2×#13063373—22no—
10C2×#13063373—22no—
11C2×#13063373—22no—
12C2×#13063373—22no—
13C2×#13063373—22no—
14C2×#13063373—22no—
15C2×#13063373—22no—
16C2×#13063373—22no—
17C2×#13063373—22no—
18C2×#13063373—22no—
19C2×#13063373C414yescomplemented
20C2×#13063373C2214yes—
21C22×#10621902—21no—
22C22×#10621902C412yescomplemented
23C22×#10621898—22no—
24C22×#10621898C2211yescharacteristic
25C22×#10621898C2211yescharacteristic
26C22×Q8×D43—21no—
27C22×Q8×D43C412yescomplemented
28C22×#10621877C2211yescharacteristic
29C2×#13063284C2211yescharacteristic
30#14582917—22no—
31#14582917C2214yescomplemented
32#14582915—22no—
33#14582915C2214yescomplemented
34C2×#13063253—22no—
35C2×#13063251—22no—
36#14582908—22no—
37#14582908C2214yescomplemented
38C2×#13063249—22no—
39#14582881—22no—
40#14582881C2214yescomplemented
41C2×#13063243—21no—
42C2×#13063241—21no—
43#14582872—22no—
44#14582872C2214yescomplemented
45C2×#13063239—22no—
46C23×Q8×C43C2211yescharacteristic
47C22×M16×C43C2211yescharacteristic
48C2×#117×C43C2211yescharacteristic
49C43×#419—22no—
50C43×#419C2214yescomplemented
51C2×#103×C43—22no—
52#13063373—28no—
53#13063373—28no—
54#13063373—28no—
55#13063373—28no—
56#13063373—28no—
57#13063373—28no—
58#13063373—28no—
59#13063373—28no—
60#13063373—28no—
61#13063373—28no—
62#13063373—28no—
63#13063373—28no—
64#13063373—28no—
65#13063373—28no—
66#13063373—28no—
67#13063373—28no—
68C2×#10621902—24no—
69C2×#10621902—24no—
70C2×#10621902—24no—
71C2×#10621902—24no—
72C2×#10621902—24no—
73C2×#10621902—24no—
74C2×#10621902—24no—
75C2×#10621902—24no—
76C2×#10621902—24no—
77C2×#10621902—24no—
78C2×#10621902—24no—
79C2×#10621902C2×C418yescomplemented
80C2×#10621898—28no—
81C2×#10621898—28no—
82C2×#10621898—28no—
83C2×#10621898—28no—
84C2×#10621898—21no—
85C2×#10621898—21no—
86C2×#10621898—21no—
87C2×#10621898—21no—
88C2×#10621898—21no—
89C2×#10621898—21no—
90C2×#10621898—21no—
91C2×#10621898—21no—
92C2×#10621898—21no—
93C2×#10621898—21no—
94C2×#10621898—21no—
95C2×#10621898—21no—
96C2×#10621898—21no—
97C2×#10621898—21no—
98C2×#10621898—28no—
99C2×#10621898—28no—
100C2×#10621898C2×C412yes—
101C2×#10621898C2×C412yes—
102C2×#10621898D412yes—
103C2×#10621898D412yes—
104C2×#10621898D412yes—
105C2×#10621898D412yes—
106C2×#10621898D412yes—
107C2×#10621898D412yes—
108C2×#10621898C2312yes—
109C2×#10621898C2312yes—
110C22×Dic86—22no—
111C22×Dic86C2×C411yescharacteristic
112C22×Dic86D411yescharacteristic
113C2×Q8×D43—24no—
114C2×Q8×D43—24no—
115C2×Q8×D43—24no—
116C2×Q8×D43—24no—
117C2×Q8×D43—24no—
118C2×Q8×D43—24no—
119C2×Q8×D43—24no—
120C2×Q8×D43—24no—
121C2×Q8×D43—24no—
122C2×Q8×D43—24no—
123C2×Q8×D43—24no—
124C2×Q8×D43C2×C418yescomplemented
125C22×D172—22no—
126C22×D172C2×C411yescharacteristic
127C22×D172D411yescharacteristic
128C22×C22⋊D43—21no—
129C22×C22⋊D43D412yes—
130C22×C4×D43—22no—
131C22×C4×D43—21no—
132C22×C4×D43—22no—
133C22×C4×D43C2×C412yes—
134C2×#10621877—21no—
135C2×#10621877—21no—
136C2×#10621877—21no—
137C2×#10621877—21no—
138C2×#10621877—21no—
139C2×#10621877C2312yes—
140C22×C43⋊C8—21no—
141#13063284—21no—
142#13063284—21no—
143#13063284—21no—
144#13063284C2312yes—
145C2×C4⋊Dic43—21no—
146C2×C22⋊Dic43—21no—
147C2×C4×Dic43—21no—
148#13063253—28no—
149#13063251—28no—
150#13063249—28no—
151#13063243—24no—
152#13063241—24no—
153#13063239—28no—
154C22×Q8×C43—21no—
155C22×Q8×C43—21no—
156C22×Q8×C43—21no—
157C22×Q8×C43—21no—
158C22×Q8×C43—21no—
159C22×Q8×C43—21no—
160C22×Q8×C43—21no—
161C22×Q8×C43C2×C412yes—
162C22×Q8×C43C2×C412yes—
163C22×Q8×C43D412yes—
164C22×Q8×C43D412yes—
165C22×Q8×C43D412yes—
166C22×Q8×C43D412yes—
167C22×Q8×C43C2312yes—
168C23×C4×C43—21no—
169C23×C4×C43C2311yescharacteristic
170C2×M16×C43—21no—
171C2×M16×C43—21no—
172C2×M16×C43—21no—
173C2×M16×C43—21no—
174C2×M16×C43—21no—
175C2×M16×C43C2312yes—
176C22×C8×C43—21no—
177#117×C43—21no—
178#117×C43—21no—
179#117×C43—21no—
180#117×C43C2312yes—
181C2×C4⋊C4×C43—21no—
182C2×C22⋊C4×C43—21no—
183C2×C42×C43—21no—
184#103×C43—28no—
185C24×C43C2×D411yescharacteristic
186C23×D43—21no—
187C23×D43C22⋊C412yes—
188C2×Q8×C43—22no—
189C2×Q8×C43—22no—
190C2×Q8×C43—22no—
191C2×Q8×C43—22no—
192C2×Q8×C43—22no—
193C2×Q8×C43—22no—
194C2×Q8×C43—22no—
195C2×Q8×C43—22no—
196C2×Q8×C43—22no—
197C2×Q8×C43—22no—
198C2×Q8×C43—22no—
199C2×Q8×C43—22no—
200C2×Q8×C43—22no—
201C2×Q8×C43—22no—
202C2×Q8×C43—22no—
203C2×Q8×C43—22no—
204C2×Q8×C43—22no—
205C2×Q8×C43—22no—
206C2×Q8×C43—22no—
207C2×Q8×C43—22no—
208C2×Q8×C43—22no—
209C2×Q8×C43C22⋊C414yes—
210C2×Q8×C43C22⋊C414yes—
211C2×Q8×C43C22⋊C414yes—
212C2×Q8×C43C22⋊C414yes—
213C2×Q8×C43C22×C414yes—
214C2×Q8×C43C2×D414yes—
215C2×Q8×C43C2×D414yes—
216C22×C4×C43—22no—
217C22×C4×C43—22no—
218C22×C4×C43—22no—
219C22×C4×C43—22no—
220C22×C4×C43—22no—
221C22×C4×C43—22no—
222C22×C4×C43—22no—
223C22×C4×C43—41no—
224C22×C4×C43C22×C411yescharacteristic
225C22×C4×C43C22×C411yescharacteristic
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43C2×D411yescharacteristic
228C22×C4×C43C2×D411yescharacteristic
229C22×C4×C43C2×D411yescharacteristic
230C22×C4×C43C2×D411yescharacteristic
231C22×C4×C43C2×D411yescharacteristic
232C22×C4×C43C2×D411yescharacteristic
233C22×C4×C43C2×D411yescharacteristic
234C22×C4×C43C2×D411yescharacteristic
235C22×C4×C43C2×D411yescharacteristic
236C22×C4×C43C2×D411yescharacteristic
237C22×C4×C43C2411yescharacteristic
238C2×C22⋊D43—22no—
239C2×C22⋊D43—22no—
240C2×C22⋊D43—22no—
241C2×C22⋊D43—22no—
242C2×C22⋊D43—22no—
243C2×C22⋊D43—22no—
244C2×C22⋊D43—22no—
245C2×C22⋊D43—22no—
246C2×C22⋊D43—22no—
247C2×C22⋊D43—22no—
248C2×C22⋊D43C22⋊C414yes—
249C2×C22⋊D43C2×D414yes—
250C22×Dic43—21no—
251C22×Dic43—41no—
252C22×Dic43C22⋊C412yes—
253#10621902—216no—
254#10621902—216no—
255#10621902—216no—
256#10621902—216no—
257#10621902—216no—
258#10621902—216no—
259#10621902—216no—
260#10621902—216no—
261Q8×D43—216no—
262Q8×D43—216no—
263Q8×D43—216no—
264Q8×D43—216no—
265Q8×D43—216no—
266Q8×D43—216no—
267Q8×D43—216no—
268Q8×D43—216no—
269#10621898—232no—
270#10621898—232no—
271#10621898—232no—
272#10621898—232no—
273#10621898—22no—
274#10621898—22no—
275#10621898—22no—
276#10621898—22no—
277#10621898—22no—
278#10621898—22no—
279#10621898—22no—
280#10621898—22no—
281#10621898—22no—
282#10621898—22no—
283#10621898—22no—
284#10621898—22no—
285#10621898—22no—
286#10621898—22no—
287#10621898—22no—
288#10621898—22no—
289#10621898—22no—
290#10621898—22no—
291#10621898—22no—
292#10621898—22no—
293#10621898—22no—
294#10621898—22no—
295#10621898—22no—
296#10621898—22no—
297#10621898—22no—
298#10621898—22no—
299#10621898—22no—
300#10621898—22no—
301#10621898C22⋊C414yes—
302#10621898C22⋊C414yes—
303#10621898C2×D414yes—
304#10621898C2×D414yes—
305C2×D172—28no—
306C2×D172—28no—
307C2×D172—21no—
308C2×D172—21no—
309C2×D172—21no—
310C2×D172—21no—
311C2×D172—21no—
312C2×D172—21no—
313C2×D172—21no—
314C2×D172—28no—
315C2×D172C22⋊C412yes—
316C2×D172C22⋊C412yes—
317C2×D172C22⋊C412yes—
318C2×D172C22×C412yes—
319C2×D172C2×D412yes—
320C2×C4×D43—28no—
321C2×C4×D43—28no—
322C2×C4×D43—28no—
323C2×C4×D43—28no—
324C2×C4×D43—22no—
325C2×C4×D43—22no—
326C2×C4×D43—22no—
327C2×C4×D43—22no—
328C2×C4×D43—22no—
329C2×C4×D43—22no—
330C2×C4×D43—22no—
331C2×C4×D43—22no—
332C2×C4×D43—22no—
333C2×C4×D43—22no—
334C2×C4×D43—28no—
335C2×C4×D43—28no—
336C2×C4×D43C22⋊C414yes—
337C2×C4×D43C22×C414yes—
338C2×Dic86—28no—
339C2×Dic86—28no—
340C2×Dic86—21no—
341C2×Dic86—21no—
342C2×Dic86—21no—
343C2×Dic86—21no—
344C2×Dic86—21no—
345C2×Dic86—21no—
346C2×Dic86—21no—
347C2×Dic86—28no—
348C2×Dic86C22⋊C412yes—
349C2×Dic86C22⋊C412yes—
350C2×Dic86C22⋊C412yes—
351C2×Dic86C22×C412yes—
352C2×Dic86C2×D412yes—
353M16×C43—22no—
354M16×C43—22no—
355M16×C43—41no—
356M16×C43—41no—
357C2×C8×C43—22no—
358C2×C8×C43—41no—
359C2×C8×C43—41no—
360C4⋊C4×C43—22no—
361C4⋊C4×C43—41no—
362C22⋊C4×C43—22no—
363C22⋊C4×C43—41no—
364C42×C43—22no—
365C42×C43—41no—
366C22⋊Dic43—22no—
367C22⋊Dic43—41no—
368C4⋊Dic43—22no—
369C4⋊Dic43—41no—
370C4×Dic43—22no—
371C4×Dic43—41no—
372#10621877—22no—
373#10621877—22no—
374#10621877—41no—
375#10621877—41no—
376C2×C43⋊C8—22no—
377C2×C43⋊C8—41no—
378C2×C43⋊C8—41no—
379C23×C43—42no—
380C23×C43C2×C22⋊C411yescharacteristic
381C23×C43C2×C22⋊C411yescharacteristic
382C23×C43#12011yescharacteristic
383C23×C43#12011yescharacteristic
384C23×C43#12011yescharacteristic
385C23×C43#12011yescharacteristic
386C23×C43C22×D411yescharacteristic
387C22×D43—22no—
388C22×D43—22no—
389C22×D43—22no—
390C22×D43—22no—
391C22×D43—22no—
392C22×D43—44no—
393C22×D43—44no—
394C22×D43C2×C22⋊C414yes—
395Q8×C43—24no—
396Q8×C43—24no—
397Q8×C43—24no—
398Q8×C43—24no—
399Q8×C43—24no—
400Q8×C43—24no—
401Q8×C43—24no—
402Q8×C43C2×C22⋊C418yes—
403C2×C4×C43—24no—
404C2×C4×C43—24no—
405C2×C4×C43—24no—
406C2×C4×C43—24no—
407C2×C4×C43—24no—
408C2×C4×C43—24no—
409C2×C4×C43—24no—
410C2×C4×C43—42no—
411C2×C4×C43—82no—
412C2×C4×C43C2×C22⋊C411yescharacteristic
413C2×C4×C43C2×C22⋊C411yescharacteristic
414C2×C4×C43C2×C22⋊C411yescharacteristic
415C2×C4×C43C2×C22⋊C411yescharacteristic
416C2×C4×C43C2×C22⋊C411yescharacteristic
417C2×C4×C43C2×C22⋊C411yescharacteristic
418C2×C4×C43C2×C22⋊C411yescharacteristic
419C2×C4×C43C2×C22⋊C411yescharacteristic
420C2×C4×C43C2×C22⋊C411yescharacteristic
421C2×C4×C43C2×C22⋊C411yescharacteristic
422C2×C4×C43#12011yescharacteristic
423C2×C4×C43#12011yescharacteristic
424C2×C4×C43#12011yescharacteristic
425C2×C4×C43#12011yescharacteristic
426C2×C4×C43#12011yescharacteristic
427C2×C4×C43#12011yescharacteristic
428C2×C4×C43#12011yescharacteristic
429C2×C4×C43#12011yescharacteristic
430C2×C4×C43#12011yescharacteristic
431C2×C4×C43#12011yescharacteristic
432C2×C4×C43#12011yescharacteristic
433C2×C4×C43#12011yescharacteristic
434C2×C4×C43C23×C411yescharacteristic
435C2×C4×C43C22×D411yescharacteristic
436C2×C4×C43C22×D411yescharacteristic
437C2×C4×C43C22×D411yescharacteristic
438C2×C4×C43C22×D411yescharacteristic
439C2×C4×C43C22×D411yescharacteristic
440C22⋊D43—24no—
441C22⋊D43—24no—
442C22⋊D43—24no—
443C22⋊D43—24no—
444C22⋊D43—24no—
445C22⋊D43—24no—
446C22⋊D43—24no—
447C22⋊D43—24no—
448C2×Dic43—22no—
449C2×Dic43—22no—
450C2×Dic43—22no—
451C2×Dic43—22no—
452C2×Dic43—22no—
453C2×Dic43—42no—
454C2×Dic43—82no—
455C2×Dic43C2×C22⋊C414yes—
456D172—232no—
457D172—22no—
458D172—22no—
459D172—22no—
460D172—22no—
461D172—22no—
462D172—22no—
463D172—22no—
464D172C2×C22⋊C414yes—
465C4×D43—232no—
466C4×D43—232no—
467C4×D43—24no—
468C4×D43—24no—
469C4×D43—24no—
470C4×D43—24no—
471C4×D43—24no—
472C4×D43—24no—
473C4×D43—24no—
474C4×D43—24no—
475Dic86—232no—
476Dic86—22no—
477Dic86—22no—
478Dic86—22no—
479Dic86—22no—
480Dic86—22no—
481Dic86—22no—
482Dic86—22no—
483Dic86C2×C22⋊C414yes—
484C8×C43—42no—
485C43⋊C8—42no—
486C2×#1796—431nomaximal, Sylow
487C22×C43—22no—
488C22×C43—22no—
489C22×C43—22no—
490C22×C43—41no—
491C22×C43—41no—
492C22×C43—41no—
493C22×C43—41no—
494C22×C43#37911yescharacteristic
495C22×C43#37911yescharacteristic
496C22×C43#37911yescharacteristic
497C22×C43#37911yescharacteristic
498C22×C43C22×C22⋊C411yescharacteristic
499C22×C43C2×#12011yescharacteristic
500C22×C43C2×#12011yescharacteristic
501C2×D43—24no—
502C2×D43—24no—
503C2×D43—44no—
504C2×D43—44no—
505C2×D43—44no—
506C2×D43—44no—
507C2×D43—44no—
508C2×D43—44no—
509C4×C43—28no—
510C4×C43—82no—
511C4×C43#37911yescharacteristic
512C4×C43#37911yescharacteristic
513C4×C43#37911yescharacteristic
514C4×C43#37911yescharacteristic
515C4×C43C22×C22⋊C411yescharacteristic
516C4×C43C22×C22⋊C411yescharacteristic
517C4×C43C2×#12011yescharacteristic
518C4×C43C2×#12011yescharacteristic
519Dic43—24no—
520Dic43—24no—
521Dic43—82no—
522C22×2−1+4—431no—
523C2×#421—431no—
524C2×#421—431no—
525C2×#419—431no—
526C2×#419D4311yescharacteristic, complemented
527C2×#413—431no—
528C2×#410—431no—
529#1796—438no—
530C2×C43—21no—
531C2×C43—21no—
532C2×C43—21no—
533C2×C43—21no—
534C2×C43—21no—
535C2×C43—21no—
536C2×C43#179612yescomplemented
537C2×C43C2×#37911yescharacteristic
538D43—44no—
539D43—44no—
540C2×2−1+4—434no—
541C2×2−1+4—434no—
542C2×2−1+4—862no—
543C2×2−1+4—862no—
544C2×2−1+4—862no—
545C2×2−1+4—862no—
546C2×2−1+4—862no—
547C2×2−1+4—862no—
548C2×2−1+4—862no—
549C2×2−1+4—862no—
550C2×2−1+4—862no—
551C2×2−1+4—862no—
552C22×#41—431no—
553C22×#41—432no—
554C22×#41—431no—
555C22×#41—862no—
556C22×#41—861no—
557C23×Q8—432no—
558C23×Q8—861no—
559C23×Q8C2×D4311yescharacteristic
560C22×M16—431no—
561C22×M16C2×D4311yescharacteristic
562C2×#117—431no—
563C2×#117C2×D4311yescharacteristic
564#421—434no—
565#421—434no—
566#421—862no—
567#421—862no—
568C2×#104—862no—
569C2×#104—862no—
570#419—22no—
571#419—434no—
572#419—862no—
573#419C2×D4314yescomplemented
574C2×#103—22no—
575C2×#103—862no—
576#413—434no—
577#413—862no—
578C2×#101—861no—
579C2×#100—861no—
580#410—434no—
581#410—862no—
582C2×#99—862no—
583C43C2×#179611yescharacteristic, complemented, Sylow
5842−1+4—868no—
5852−1+4—868no—
5862−1+4—868no—
5872−1+4—868no—
5882−1+4—868no—
5892−1+4—868no—
5902−1+4—868no—
5912−1+4—868no—
5922−1+4—868no—
5932−1+4—868no—
5942−1+4—868no—
5952−1+4—868no—
5962−1+4—868no—
5972−1+4—868no—
5982−1+4—868no—
5992−1+4—868no—
600C2×#41—432no—
601C2×#41—432no—
602C2×#41—432no—
603C2×#41—432no—
604C2×#41—438no—
605C2×#41—432no—
606C2×#41—432no—
607C2×#41—432no—
608C2×#41—432no—
609C2×#41—432no—
610C2×#41—432no—
611C2×#41—868no—
612C2×#41—868no—
613C2×#41—868no—
614C2×#41—868no—
615C2×#41—868no—
616C2×#41—868no—
617C2×#41—864no—
618C2×#41—864no—
619C2×#41—864no—
620C2×#41—864no—
621C2×#41—864no—
622C2×#41—864no—
623C2×#41—864no—
624C2×#41—864no—
625C2×#41—864no—
626C2×#41—864no—
627C2×#41—864no—
628C2×#41—861no—
629C2×#41—861no—
630C2×#41—861no—
631C2×#41—861no—
632C2×#41—861no—
633C2×#41—861no—
634C2×#41—861no—
635C2×#41—861no—
636C2×#41—861no—
637C2×#41—861no—
638C2×#41—861no—
639C2×#41—861no—
640C2×#41—861no—
641C2×#41—861no—
642C22×Q8—21no—
643C22×Q8—21no—
644C22×Q8—21no—
645C22×Q8—21no—
646C22×Q8—21no—
647C22×Q8—21no—
648C22×Q8—21no—
649C22×Q8—431no—
650C22×Q8—438no—
651C22×Q8—431no—
652C22×Q8—862no—
653C22×Q8—864no—
654C22×Q8—864no—
655C22×Q8—864no—
656C22×Q8—864no—
657C22×Q8—864no—
658C22×Q8—864no—
659C22×Q8—864no—
660C22×Q8—864no—
661C22×Q8—864no—
662C22×Q8—864no—
663C22×Q8—864no—
664C22×Q8C4×D4312yes—
665C22×Q8C4×D4312yes—
666C22×Q8D17212yes—
667C22×Q8D17212yes—
668C22×Q8C22⋊D4312yes—
669C22×Q8C22⋊D4312yes—
670C22×Q8C22×D4312yes—
671C22×D4—432no—
672C22×D4—431no—
673C22×D4—431no—
674C22×D4—862no—
675C22×D4—861no—
676C23×C4—21no—
677C23×C4—432no—
678C23×C4—862no—
679C23×C4—862no—
680C23×C4—861no—
681C23×C4C22×D4311yescharacteristic
682C2×M16—21no—
683C2×M16—21no—
684C2×M16—21no—
685C2×M16—21no—
686C2×M16—21no—
687C2×M16—432no—
688C2×M16—861no—
689C2×M16—861no—
690C2×M16—861no—
691C2×M16—861no—
692C2×M16—861no—
693C2×M16C22×D4312yes—
694C22×C8—21no—
695C22×C8—861no—
696#117—21no—
697#117—21no—
698#117—21no—
699#117—432no—
700#117—861no—
701#117—861no—
702#117—861no—
703#117C22×D4312yes—
704C2×C4⋊C4—21no—
705C2×C4⋊C4—861no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—861no—
708C2×C42—21no—
709C2×C42—861no—
710#104—868no—
711#104—868no—
712#103—28no—
713#103—868no—
714#101—864no—
715#100—864no—
716#99—868no—
717C24—432no—
718C24—861no—
719C24D4×D4311yescharacteristic
720#41—434no—
721#41—434no—
722#41—434no—
723#41—434no—
724#41—8632no—
725#41—8632no—
726#41—8632no—
727#41—8632no—
728#41—8616no—
729#41—8616no—
730#41—8616no—
731#41—8616no—
732#41—8616no—
733#41—8616no—
734#41—8616no—
735#41—8616no—
736#41—862no—
737#41—862no—
738#41—862no—
739#41—862no—
740#41—862no—
741#41—862no—
742#41—862no—
743#41—862no—
744#41—862no—
745#41—862no—
746#41—862no—
747#41—862no—
748#41—862no—
749#41—862no—
750#41—862no—
751#41—862no—
752#41—862no—
753#41—862no—
754#41—862no—
755#41—862no—
756#41—862no—
757#41—862no—
758#41—862no—
759#41—862no—
760#41—862no—
761#41—862no—
762#41—862no—
763#41—862no—
764C2×Q8—22no—
765C2×Q8—22no—
766C2×Q8—22no—
767C2×Q8—22no—
768C2×Q8—22no—
769C2×Q8—22no—
770C2×Q8—22no—
771C2×Q8—22no—
772C2×Q8—22no—
773C2×Q8—22no—
774C2×Q8—22no—
775C2×Q8—22no—
776C2×Q8—22no—
777C2×Q8—22no—
778C2×Q8—22no—
779C2×Q8—22no—
780C2×Q8—22no—
781C2×Q8—22no—
782C2×Q8—22no—
783C2×Q8—22no—
784C2×Q8—22no—
785C2×Q8—432no—
786C2×Q8—432no—
787C2×Q8—432no—
788C2×Q8—432no—
789C2×Q8—432no—
790C2×Q8—868no—
791C2×Q8—868no—
792C2×Q8—868no—
793C2×Q8—8616no—
794C2×Q8—8616no—
795C2×Q8—8616no—
796C2×Q8—8616no—
797C2×Q8—8616no—
798C2×Q8—8616no—
799C2×Q8—8616no—
800C2×Q8—8616no—
801C2×Q8—861no—
802C2×Q8—861no—
803C2×Q8—861no—
804C2×Q8—861no—
805C2×Q8—861no—
806C2×Q8—861no—
807C2×Q8—861no—
808C2×Q8(C2×D43)⋊C414yes—
809C2×Q8(C2×D43)⋊C414yes—
810C2×Q8(C2×D43)⋊C414yes—
811C2×Q8(C2×D43)⋊C414yes—
812C2×Q8C2×C4×D4314yes—
813C2×Q8C2×D17214yes—
814C2×Q8C2×C22⋊D4314yes—
815C2×D4—434no—
816C2×D4—434no—
817C2×D4—432no—
818C2×D4—432no—
819C2×D4—432no—
820C2×D4—432no—
821C2×D4—432no—
822C2×D4—868no—
823C2×D4—868no—
824C2×D4—868no—
825C2×D4—862no—
826C2×D4—862no—
827C2×D4—862no—
828C2×D4—862no—
829C2×D4—862no—
830C2×D4—862no—
831C2×D4—862no—
832C2×D4—862no—
833C2×D4—862no—
834C2×D4—862no—
835C2×D4—861no—
836C2×D4—861no—
837C2×D4—861no—
838C2×D4—861no—
839C2×D4—861no—
840C2×D4—861no—
841C2×D4—861no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—41no—
850C22×C4—432no—
851C22×C4—434no—
852C22×C4—434no—
853C22×C4—868no—
854C22×C4—868no—
855C22×C4—868no—
856C22×C4—868no—
857C22×C4—868no—
858C22×C4—868no—
859C22×C4—861no—
860C22×C4—862no—
861C22×C4—862no—
862C22×C4—862no—
863C22×C4—862no—
864C22×C4—862no—
865C22×C4—862no—
866C22×C4—862no—
867C22×C4—862no—
868C22×C4—862no—
869C22×C4—862no—
870C22×C4—1721no—
871C22×C4C2×C4×D4311yescharacteristic
872C22×C4C2×C4×D4311yescharacteristic
873C22×C4C2×D17211yescharacteristic
874C22×C4C2×D17211yescharacteristic
875C22×C4D4×D4311yescharacteristic
876C22×C4D4×D4311yescharacteristic
877C22×C4D4×D4311yescharacteristic
878C22×C4D4×D4311yescharacteristic
879C22×C4D4×D4311yescharacteristic
880C22×C4D4×D4311yescharacteristic
881C22×C4D4×D4311yescharacteristic
882C22×C4C2×C22⋊D4311yescharacteristic
883C22×C4C2×C22⋊D4311yescharacteristic
884C22×C4C23×D4311yescharacteristic
885M16—22no—
886M16—22no—
887M16—41no—
888M16—41no—
889M16—862no—
890M16—862no—
891M16—1721no—
892M16—1721no—
893C2×C8—22no—
894C2×C8—41no—
895C2×C8—41no—
896C2×C8—862no—
897C2×C8—1721no—
898C2×C8—1721no—
899C4⋊C4—22no—
900C4⋊C4—41no—
901C4⋊C4—862no—
902C4⋊C4—1721no—
903C22⋊C4—22no—
904C22⋊C4—41no—
905C22⋊C4—862no—
906C22⋊C4—1721no—
907C42—22no—
908C42—41no—
909C42—862no—
910C42—1721no—
911C23—42no—
912C23—434no—
913C23—862no—
914C23—862no—
915C23—862no—
916C23—862no—
917C23—862no—
918C23—1724no—
919C23—1724no—
920C23C22⋊C4×D4311yescharacteristic
921C23C22⋊C4×D4311yescharacteristic
922C23#1306329311yescharacteristic
923C23#1306329311yescharacteristic
924C23#1306329511yescharacteristic
925C23#1306329511yescharacteristic
926C23C2×D4×D4311yescharacteristic
927Q8—24no—
928Q8—24no—
929Q8—24no—
930Q8—24no—
931Q8—24no—
932Q8—24no—
933Q8—24no—
934Q8—434no—
935Q8—8632no—
936Q8—862no—
937Q8—862no—
938Q8—862no—
939Q8—862no—
940Q8—862no—
941Q8—862no—
942Q8—862no—
943Q8C2×(C2×D43)⋊C418yes—
944D4—434no—
945D4—8632no—
946D4—864no—
947D4—864no—
948D4—864no—
949D4—864no—
950D4—864no—
951D4—864no—
952D4—864no—
953D4—864no—
954D4—862no—
955D4—862no—
956D4—862no—
957D4—862no—
958D4—862no—
959D4—862no—
960D4—862no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—42no—
969C2×C4—82no—
970C2×C4—434no—
971C2×C4—8632no—
972C2×C4—8632no—
973C2×C4—862no—
974C2×C4—862no—
975C2×C4—862no—
976C2×C4—862no—
977C2×C4—862no—
978C2×C4—864no—
979C2×C4—864no—
980C2×C4—864no—
981C2×C4—864no—
982C2×C4—864no—
983C2×C4—864no—
984C2×C4—864no—
985C2×C4—864no—
986C2×C4—3442no—
987C2×C4—1722no—
988C2×C4C22⋊C4×D4311yescharacteristic
989C2×C4C22⋊C4×D4311yescharacteristic
990C2×C4C22⋊C4×D4311yescharacteristic
991C2×C4C22⋊C4×D4311yescharacteristic
992C2×C4C22⋊C4×D4311yescharacteristic
993C2×C4C22⋊C4×D4311yescharacteristic
994C2×C4C2×(C2×D43)⋊C411yescharacteristic
995C2×C4C2×(C2×D43)⋊C411yescharacteristic
996C2×C4C2×(C2×D43)⋊C411yescharacteristic
997C2×C4C2×(C2×D43)⋊C411yescharacteristic
998C2×C4#1306329311yescharacteristic
999C2×C4#1306329311yescharacteristic
1000C2×C4#1306329311yescharacteristic
1001C2×C4#1306329311yescharacteristic
1002C2×C4#1306329311yescharacteristic
1003C2×C4#1306329311yescharacteristic
1004C2×C4#1306329511yescharacteristic
1005C2×C4#1306329511yescharacteristic
1006C2×C4#1306329511yescharacteristic
1007C2×C4#1306329511yescharacteristic
1008C2×C4#1306329511yescharacteristic
1009C2×C4#1306329511yescharacteristic
1010C2×C4C22×C4×D4311yescharacteristic
1011C2×C4C2×D4×D4311yescharacteristic
1012C2×C4C2×D4×D4311yescharacteristic
1013C2×C4C2×D4×D4311yescharacteristic
1014C2×C4C22×C22⋊D4311yescharacteristic
1015C2×C4C22×D17211yescharacteristic
1016C8—42no—
1017C8—1722no—
1018C22—22no—
1019C22—22no—
1020C22—22no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—864no—
1026C22—864no—
1027C22—1724no—
1028C22—1724no—
1029C22—1724no—
1030C22—1724no—
1031C22—1724no—
1032C22—1724no—
1033C22#1458275411yescharacteristic
1034C22#1458275411yescharacteristic
1035C22#1458275411yescharacteristic
1036C22#1458275411yescharacteristic
1037C22C2×C22⋊C4×D4311yescharacteristic
1038C22C2×#1306329311yescharacteristic
1039C22C2×#1306329511yescharacteristic
1040C4—28no—
1041C4—82no—
1042C4—864no—
1043C4—864no—
1044C4—3442no—
1045C4#1458275411yescharacteristic
1046C4#1458275411yescharacteristic
1047C4#1458275411yescharacteristic
1048C4#1458275411yescharacteristic
1049C4C2×C22⋊C4×D4311yescharacteristic
1050C4C22×(C2×D43)⋊C411yescharacteristic
1051C4C2×#1306329311yescharacteristic
1052C4C2×#1306329511yescharacteristic
1053C2—21no—
1054C2—21no—
1055C2—21no—
1056C2—21no—
1057C2—21no—
1058C2—21no—
1059C2—1724no—
1060C2—1724no—
1061C2#1913456712yesdirect product factor
1062C2C2×#1458275411yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#419C2
socleC22×C43#379
prime radicalC22×#13063373C2
cosocleC22×C4×C43C24
hypercenterC2×#419D43
hypocenterC43C2×#1796
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
2. C2×#14582917C2semidirect
3. C2×#14582915C2semidirect
4. C2×#14582908C2semidirect
5. C2×#14582881C2semidirect
6. C2×#14582872C2semidirect
7. #19134567C2direct (N × H)
8. C2×C43×#419C2semidirect
19. C2×#13063373C4semidirect
22. C22×#10621902C4semidirect
27. C22×Q8×D43C4semidirect
31. #14582917C22semidirect
33. #14582915C22semidirect
37. #14582908C22semidirect
40. #14582881C22semidirect
44. #14582872C22semidirect
50. C43×#419C22semidirect
79. C2×#10621902C2×C4semidirect
124. C2×Q8×D43C2×C4semidirect
526. C2×#419D43semidirect
536. C2×C43#1796semidirect
573. #419C2×D43semidirect
583. C43C2×#1796semidirect
1061. C2#19134567direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633732
C2×#145829172
C2×#145829152
C2×#145829082
C2×#145828812
C2×#145828722
#191345672
C2×C43×#4192
C2×#179643