Finite Group Databasebeta

← C2×#19134557 #25095917

Subgroups — C2×#19134557 #25095917

Order 11008.

3662 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583735C211yesmaximal, characteristic
2C2×#14582915C211yesmaximal, characteristic, complemented
3C2×#14582895C211yesmaximal, characteristic, complemented
4C2×#14582893C211yesmaximal, characteristic, complemented
5C2×#14582872C211yesmaximal, characteristic, complemented
6C2×#14582867C211yesmaximal, characteristic, complemented
7#19134557C218yesmaximal, direct product factor
8C2×C43×#421C211yesmaximal, characteristic, complemented
9#14583735—22no—
10#14583735—22no—
11#14583735—22no—
12#14583735—22no—
13#14583735—22no—
14#14583735—22no—
15#14583735C414yescomplemented
16#14583735C2214yes—
17C2×#13063373—21no—
18C2×#13063372—21no—
19C2×#13063372C412yescomplemented
20C2×#13063371—21no—
21C2×#13063371C412yescomplemented
22C2×#13063370—22no—
23C2×#13063370—21no—
24C22×#10621898—22no—
25C22×#10621898C2211yescharacteristic
26C22×#10621898C2211yescharacteristic
27C2×#41×D43—22no—
28C2×#41×D43—22no—
29C23×C43⋊C8C2211yescharacteristic, complemented
30C2×#13063284C2211yescharacteristic, complemented
31#14582915—22no—
32#14582915C2214yescomplemented
33C2×#13063251—22no—
34#14582895—22no—
35#14582895C2214yescomplemented
36#14582893—22no—
37#14582893C2214yescomplemented
38C2×#13063249—21no—
39C2×#13063248—21no—
40C2×#13063246—21no—
41C2×#13063245—21no—
42#14582872—22no—
43#14582872C2214yescomplemented
44C2×#13063239—22no—
45#14582867—22no—
46#14582867C2214yescomplemented
47C2×(C2×D43)⋊C8—22no—
48C22×#41×C43C2211yescharacteristic
49C22×M16×C43C2211yescharacteristic, complemented
50C2×#117×C43C2211yescharacteristic, complemented
51C43×#421—22no—
52C43×#421C2214yescomplemented
53C2×#104×C43—22no—
54#13063373—24no—
55#13063373—24no—
56#13063373—24no—
57#13063373—24no—
58#13063372—24no—
59#13063372—24no—
60#13063372—24no—
61#13063372—24no—
62#13063372—24no—
63#13063372—24no—
64#13063372—24no—
65#13063372C2×C418yescomplemented
66#13063371—24no—
67#13063371—24no—
68#13063371—24no—
69#13063371—24no—
70#13063371—24no—
71#13063371—24no—
72#13063371—24no—
73#13063371C2×C418yescomplemented
74#13063370—28no—
75#13063370—28no—
76#13063370—24no—
77#13063370—24no—
78#13063370—24no—
79#13063370—24no—
80#13063370—28no—
81#13063370—28no—
82C2×#10621902—22no—
83C2×#10621902—22no—
84C2×#10621898—24no—
85C2×#10621898—24no—
86C2×#10621898—28no—
87C2×#10621898—28no—
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—21no—
99C2×#10621898—21no—
100C2×#10621898—21no—
101C2×#10621898—21no—
102C2×#10621898—28no—
103C2×#10621898—28no—
104C2×#10621898—22no—
105C2×#10621898—22no—
106C2×#10621898C2×C412yes—
107C2×#10621898C2×C412yes—
108C2×#10621898C2×C412yes—
109C2×#10621898D412yes—
110C2×#10621898D412yes—
111C2×#10621898D412yes—
112C2×#10621898D412yes—
113C2×#10621898D412yes—
114C2×#10621898C2312yes—
115C2×#10621898C2312yes—
116C2×#10621900—24no—
117C2×#10621900—22no—
118C2×#10621900—22no—
119C2×#10621900—24no—
120#41×D43—28no—
121#41×D43—28no—
122#41×D43—28no—
123#41×D43—28no—
124#41×D43—28no—
125#41×D43—28no—
126#41×D43—28no—
127#41×D43—28no—
128C22×Dic86—22no—
129C22×Dic86C2×C411yescharacteristic
130C22×Dic86D411yescharacteristic
131C2×Q8×D43—22no—
132C2×Q8×D43—22no—
133C22×D172—22no—
134C22×D172C2×C411yescharacteristic
135C22×D172D411yescharacteristic
136C22×C22⋊D43—24no—
137C22×C22⋊D43—21no—
138C22×C22⋊D43D412yes—
139C2×D4×D43—24no—
140C2×D4×D43—22no—
141C2×D4×D43—24no—
142C2×D4×D43—22no—
143C22×C4×D43—24no—
144C22×C4×D43—21no—
145C22×C4×D43D412yes—
146C22×C43⋊C8—21no—
147C22×C43⋊C8—21no—
148C22×C43⋊C8—21no—
149C22×C43⋊C8—21no—
150C22×C43⋊C8—21no—
151C22×C43⋊C8—21no—
152C22×C43⋊C8C2312yescomplemented
153#13063284—21no—
154#13063284—21no—
155#13063284—21no—
156#13063284C2312yescomplemented
157C2×C4⋊Dic43—21no—
158C2×C22⋊Dic43—21no—
159C2×C4×Dic43—21no—
160#13063251—28no—
161#13063249—24no—
162#13063248—24no—
163#13063246—24no—
164#13063245—24no—
165#13063239—28no—
166(C2×D43)⋊C8—28no—
167C2×#41×C43—21no—
168C2×#41×C43—21no—
169C2×#41×C43—21no—
170C2×#41×C43—21no—
171C2×#41×C43—21no—
172C2×#41×C43—21no—
173C2×#41×C43C2×C412yes—
174C2×#41×C43C2×C412yes—
175C2×#41×C43D412yes—
176C2×#41×C43D412yes—
177C2×#41×C43D412yes—
178C2×#41×C43C2312yes—
179C22×Q8×C43D411yescharacteristic
180C22×D4×C43—21no—
181C22×D4×C43D411yescharacteristic
182C23×C4×C43—21no—
183C23×C4×C43C2311yescharacteristic
184C2×M16×C43—21no—
185C2×M16×C43—21no—
186C2×M16×C43—21no—
187C2×M16×C43—21no—
188C2×M16×C43—21no—
189C2×M16×C43C2312yescomplemented
190C22×C8×C43—21no—
191#117×C43—21no—
192#117×C43—21no—
193#117×C43—21no—
194#117×C43C2312yescomplemented
195C2×C4⋊C4×C43—21no—
196C2×C22⋊C4×C43—21no—
197C2×C42×C43—21no—
198#104×C43—28no—
199C24×C43—21no—
200C24×C43C2×D411yescharacteristic
201C23×D43—24no—
202C23×D43—21no—
203C23×D43C22⋊C412yes—
204#41×C43—22no—
205#41×C43—22no—
206#41×C43—22no—
207#41×C43—22no—
208#41×C43—22no—
209#41×C43—22no—
210#41×C43—22no—
211#41×C43—22no—
212#41×C43—22no—
213#41×C43—22no—
214#41×C43—22no—
215#41×C43—22no—
216#41×C43C22⋊C414yes—
217#41×C43C22⋊C414yes—
218#41×C43C22×C414yes—
219#41×C43C2×D414yes—
220C2×Q8×C43—21no—
221C2×Q8×C43—21no—
222C2×Q8×C43—21no—
223C2×Q8×C43C22⋊C412yes—
224C2×Q8×C43C22⋊C412yes—
225C2×Q8×C43C2×D412yes—
226C2×D4×C43—21no—
227C2×D4×C43—21no—
228C2×D4×C43—21no—
229C2×D4×C43—22no—
230C2×D4×C43—22no—
231C2×D4×C43—22no—
232C2×D4×C43—22no—
233C2×D4×C43—22no—
234C2×D4×C43—22no—
235C2×D4×C43C22⋊C412yes—
236C2×D4×C43C22⋊C412yes—
237C2×D4×C43C2×D412yes—
238C22×C4×C43—22no—
239C22×C4×C43—22no—
240C22×C4×C43—22no—
241C22×C4×C43—22no—
242C22×C4×C43—22no—
243C22×C4×C43—22no—
244C22×C4×C43—21no—
245C22×C4×C43—41no—
246C22×C4×C43C22×C411yescharacteristic
247C22×C4×C43C22×C411yescharacteristic
248C22×C4×C43C2×D411yescharacteristic
249C22×C4×C43C2×D411yescharacteristic
250C22×C4×C43C2×D411yescharacteristic
251C22×C4×C43C2×D411yescharacteristic
252C22×C4×C43C2×D411yescharacteristic
253C22×C4×C43C2×D411yescharacteristic
254C22×C4×C43C2×D411yescharacteristic
255C22×C4×C43C2×D411yescharacteristic
256C22×C4×C43C2×D411yescharacteristic
257C22×C4×C43C2×D411yescharacteristic
258C22×C4×C43C2×D411yescharacteristic
259C22×C4×C43C2411yescharacteristic
260C2×C22⋊D43—24no—
261C2×C22⋊D43—24no—
262C2×C22⋊D43—216no—
263C2×C22⋊D43—216no—
264C2×C22⋊D43—22no—
265C2×C22⋊D43—22no—
266C2×C22⋊D43—22no—
267C2×C22⋊D43—22no—
268C2×C22⋊D43—22no—
269C2×C22⋊D43—22no—
270C2×C22⋊D43—22no—
271C2×C22⋊D43—22no—
272C2×C22⋊D43—22no—
273C2×C22⋊D43—22no—
274C2×C22⋊D43C22⋊C414yes—
275C2×C22⋊D43C2×D414yes—
276C22×Dic43—24no—
277C22×Dic43—21no—
278C22×Dic43—41no—
279C22×Dic43C22⋊C412yes—
280#10621902—28no—
281#10621902—28no—
282#10621902—28no—
283#10621902—28no—
284Q8×D43—28no—
285Q8×D43—28no—
286Q8×D43—28no—
287Q8×D43—28no—
288#10621900—216no—
289#10621900—216no—
290#10621900—216no—
291#10621900—28no—
292#10621900—28no—
293#10621900—28no—
294#10621900—28no—
295#10621900—216no—
296D4×D43—28no—
297D4×D43—28no—
298D4×D43—28no—
299D4×D43—216no—
300D4×D43—216no—
301D4×D43—216no—
302D4×D43—28no—
303D4×D43—216no—
304#10621898—216no—
305#10621898—216no—
306#10621898—216no—
307#10621898—216no—
308#10621898—28no—
309#10621898—28no—
310#10621898—22no—
311#10621898—22no—
312#10621898—22no—
313#10621898—22no—
314#10621898—22no—
315#10621898—22no—
316#10621898—22no—
317#10621898—22no—
318#10621898—22no—
319#10621898—22no—
320#10621898—22no—
321#10621898—22no—
322#10621898—22no—
323#10621898—22no—
324#10621898—22no—
325#10621898—22no—
326#10621898—22no—
327#10621898—22no—
328#10621898—22no—
329#10621898—22no—
330#10621898—22no—
331#10621898—22no—
332#10621898—22no—
333#10621898—22no—
334#10621898—22no—
335#10621898—22no—
336#10621898—22no—
337#10621898—22no—
338#10621898—28no—
339#10621898—28no—
340#10621898C22⋊C414yes—
341#10621898C22⋊C414yes—
342#10621898C22×C414yes—
343#10621898C2×D414yes—
344C2×D172—24no—
345C2×D172—28no—
346C2×D172—21no—
347C2×D172—21no—
348C2×D172—21no—
349C2×D172—21no—
350C2×D172—21no—
351C2×D172—21no—
352C2×D172—21no—
353C2×D172—28no—
354C2×D172C22⋊C412yes—
355C2×D172C22⋊C412yes—
356C2×D172C22⋊C412yes—
357C2×D172C22×C412yes—
358C2×D172C2×D412yes—
359C2×C4×D43—24no—
360C2×C4×D43—24no—
361C2×C4×D43—216no—
362C2×C4×D43—216no—
363C2×C4×D43—22no—
364C2×C4×D43—22no—
365C2×C4×D43—22no—
366C2×C4×D43—22no—
367C2×C4×D43—22no—
368C2×C4×D43—22no—
369C2×C4×D43—22no—
370C2×C4×D43—22no—
371C2×C4×D43—22no—
372C2×C4×D43—22no—
373C2×C4×D43C22⋊C414yes—
374C2×C4×D43C2×D414yes—
375C2×Dic86—24no—
376C2×Dic86—28no—
377C2×Dic86—21no—
378C2×Dic86—21no—
379C2×Dic86—21no—
380C2×Dic86—21no—
381C2×Dic86—21no—
382C2×Dic86—21no—
383C2×Dic86—21no—
384C2×Dic86—28no—
385C2×Dic86C22⋊C412yes—
386C2×Dic86C22⋊C412yes—
387C2×Dic86C22⋊C412yes—
388C2×Dic86C22×C412yes—
389C2×Dic86C2×D412yes—
390M16×C43—22no—
391M16×C43—22no—
392M16×C43—41no—
393M16×C43—41no—
394C2×C8×C43—22no—
395C2×C8×C43—41no—
396C2×C8×C43—41no—
397C4⋊C4×C43—22no—
398C4⋊C4×C43—41no—
399C22⋊C4×C43—22no—
400C22⋊C4×C43—41no—
401C42×C43—22no—
402C42×C43—41no—
403C22⋊Dic43—22no—
404C22⋊Dic43—41no—
405C4⋊Dic43—22no—
406C4⋊Dic43—41no—
407C4×Dic43—22no—
408C4×Dic43—41no—
409C2×C43⋊C8—22no—
410C2×C43⋊C8—22no—
411C2×C43⋊C8—22no—
412C2×C43⋊C8—41no—
413C2×C43⋊C8—41no—
414C2×C43⋊C8—41no—
415C2×C43⋊C8—41no—
416C23×C43—22no—
417C23×C43—22no—
418C23×C43—22no—
419C23×C43—42no—
420C23×C43—82no—
421C23×C43C2×C22⋊C411yescharacteristic
422C23×C43C2×C22⋊C411yescharacteristic
423C23×C43#12011yescharacteristic
424C23×C43#12011yescharacteristic
425C23×C43#12011yescharacteristic
426C23×C43#12011yescharacteristic
427C23×C43C22×D411yescharacteristic
428C22×D43—22no—
429C22×D43—22no—
430C22×D43—216no—
431C22×D43—22no—
432C22×D43—22no—
433C22×D43—22no—
434C22×D43—44no—
435C22×D43—82no—
436C22×D43—88no—
437C22×D43C2×C22⋊C414yes—
438Q8×C43—22no—
439Q8×C43—22no—
440Q8×C43—22no—
441Q8×C43C2×C22⋊C414yes—
442D4×C43—24no—
443D4×C43—24no—
444D4×C43—24no—
445D4×C43—24no—
446D4×C43—22no—
447D4×C43—22no—
448D4×C43—22no—
449D4×C43C2×C22⋊C414yes—
450C2×C4×C43—22no—
451C2×C4×C43—22no—
452C2×C4×C43—22no—
453C2×C4×C43—24no—
454C2×C4×C43—24no—
455C2×C4×C43—24no—
456C2×C4×C43—24no—
457C2×C4×C43—42no—
458C2×C4×C43—82no—
459C2×C4×C43C2×C22⋊C411yescharacteristic
460C2×C4×C43C2×C22⋊C411yescharacteristic
461C2×C4×C43C2×C22⋊C411yescharacteristic
462C2×C4×C43C2×C22⋊C411yescharacteristic
463C2×C4×C43C2×C22⋊C411yescharacteristic
464C2×C4×C43C2×C22⋊C411yescharacteristic
465C2×C4×C43C2×C22⋊C411yescharacteristic
466C2×C4×C43C2×C22⋊C411yescharacteristic
467C2×C4×C43C2×C22⋊C411yescharacteristic
468C2×C4×C43C2×C22⋊C411yescharacteristic
469C2×C4×C43#12011yescharacteristic
470C2×C4×C43#12011yescharacteristic
471C2×C4×C43#12011yescharacteristic
472C2×C4×C43#12011yescharacteristic
473C2×C4×C43#12011yescharacteristic
474C2×C4×C43#12011yescharacteristic
475C2×C4×C43#12011yescharacteristic
476C2×C4×C43#12011yescharacteristic
477C2×C4×C43#12011yescharacteristic
478C2×C4×C43#12011yescharacteristic
479C2×C4×C43#12011yescharacteristic
480C2×C4×C43#12011yescharacteristic
481C2×C4×C43C23×C411yescharacteristic
482C2×C4×C43C22×D411yescharacteristic
483C2×C4×C43C22×D411yescharacteristic
484C2×C4×C43C22×D411yescharacteristic
485C2×C4×C43C22×D411yescharacteristic
486C2×C4×C43C22×D411yescharacteristic
487C22⋊D43—216no—
488C22⋊D43—216no—
489C22⋊D43—24no—
490C22⋊D43—24no—
491C22⋊D43—24no—
492C22⋊D43—24no—
493C22⋊D43—24no—
494C22⋊D43—24no—
495C22⋊D43—24no—
496C22⋊D43—24no—
497C2×Dic43—216no—
498C2×Dic43—22no—
499C2×Dic43—22no—
500C2×Dic43—22no—
501C2×Dic43—22no—
502C2×Dic43—22no—
503C2×Dic43—42no—
504C2×Dic43—82no—
505C2×Dic43C2×C22⋊C414yes—
506D172—216no—
507D172—22no—
508D172—22no—
509D172—22no—
510D172—22no—
511D172—22no—
512D172—22no—
513D172—22no—
514D172C2×C22⋊C414yes—
515C4×D43—216no—
516C4×D43—216no—
517C4×D43—24no—
518C4×D43—24no—
519C4×D43—24no—
520C4×D43—24no—
521C4×D43—24no—
522C4×D43—24no—
523C4×D43—24no—
524C4×D43—24no—
525Dic86—216no—
526Dic86—22no—
527Dic86—22no—
528Dic86—22no—
529Dic86—22no—
530Dic86—22no—
531Dic86—22no—
532Dic86—22no—
533Dic86C2×C22⋊C414yes—
534C8×C43—42no—
535C43⋊C8—42no—
536C2×#1794—431nomaximal, Sylow
537C22×C43—22no—
538C22×C43—22no—
539C22×C43—22no—
540C22×C43—24no—
541C22×C43—41no—
542C22×C43—41no—
543C22×C43—41no—
544C22×C43—41no—
545C22×C43—44no—
546C22×C43—82no—
547C22×C43—82no—
548C22×C43#37911yescharacteristic
549C22×C43#37911yescharacteristic
550C22×C43#37911yescharacteristic
551C22×C43#37911yescharacteristic
552C22×C43C22×C22⋊C411yescharacteristic
553C22×C43C2×#12011yescharacteristic
554C22×C43C2×#12011yescharacteristic
555C2×D43—24no—
556C2×D43—24no—
557C2×D43—44no—
558C2×D43—44no—
559C2×D43—44no—
560C2×D43—82no—
561C2×D43—82no—
562C2×D43—82no—
563C2×D43—816no—
564C4×C43—24no—
565C4×C43—82no—
566C4×C43#37911yescharacteristic
567C4×C43#37911yescharacteristic
568C4×C43#37911yescharacteristic
569C4×C43#37911yescharacteristic
570C4×C43C22×C22⋊C411yescharacteristic
571C4×C43C22×C22⋊C411yescharacteristic
572C4×C43C2×#12011yescharacteristic
573C4×C43C2×#12011yescharacteristic
574Dic43—24no—
575Dic43—24no—
576Dic43—82no—
577C2×#585—431no—
578C2×#421—431no—
579C2×#421D4311yescharacteristic, complemented
580C2×#416—431no—
581C2×#416—431no—
582C2×#410—431no—
583C2×#408—431no—
584#1794—438no—
585C2×C43—21no—
586C2×C43—21no—
587C2×C43—21no—
588C2×C43—21no—
589C2×C43—21no—
590C2×C43—21no—
591C2×C43—44no—
592C2×C43#179412yescomplemented
593C2×C43C2×#37911yescharacteristic
594D43—44no—
595D43—44no—
596#585—434no—
597#585—434no—
598#585—862no—
599#585—862no—
600#585—862no—
601#585—862no—
602#585—862no—
603#585—862no—
604C2×2−1+4—432no—
605C2×2−1+4—861no—
606C2×2−1+4—861no—
607C2×H(5,𝔽2)—432no—
608C2×H(5,𝔽2)—862no—
609C2×H(5,𝔽2)—861no—
610C2×H(5,𝔽2)—861no—
611C22×#41—431no—
612C22×#41—431no—
613C22×#41—862no—
614C22×#41—862no—
615C22×#41—862no—
616C22×#41C2×D4311yescharacteristic
617C22×M16C2×D4311yescharacteristic, complemented
618C23×C8—431no—
619C2×#117—431no—
620C2×#117C2×D4311yescharacteristic, complemented
621#421—22no—
622#421—434no—
623#421—862no—
624#421C2×D4314yescomplemented
625C2×#104—22no—
626C2×#104—862no—
627#416—434no—
628#416—434no—
629#416—862no—
630#416—862no—
631C2×#103—861no—
632C2×#103—861no—
633C2×#102—861no—
634C2×#102—861no—
635#410—434no—
636#410—862no—
637C2×#99—862no—
638#408—434no—
639#408—862no—
640C2×C22⋊C8—862no—
641C43C2×#179411yescharacteristic, complemented, Sylow
6422−1+4—438no—
6432−1+4—864no—
6442−1+4—864no—
6452−1+4—864no—
6462−1+4—864no—
6472−1+4—864no—
6482−1+4—864no—
6492−1+4—864no—
6502−1+4—864no—
6512−1+4—864no—
6522−1+4—864no—
6532−1+4—864no—
654H(5,𝔽2)—438no—
655H(5,𝔽2)—868no—
656H(5,𝔽2)—868no—
657H(5,𝔽2)—868no—
658H(5,𝔽2)—868no—
659H(5,𝔽2)—864no—
660H(5,𝔽2)—864no—
661H(5,𝔽2)—864no—
662H(5,𝔽2)—864no—
663H(5,𝔽2)—864no—
664H(5,𝔽2)—864no—
665H(5,𝔽2)—864no—
666H(5,𝔽2)—864no—
667H(5,𝔽2)—864no—
668H(5,𝔽2)—864no—
669H(5,𝔽2)—864no—
670C2×#41—21no—
671C2×#41—21no—
672C2×#41—21no—
673C2×#41—21no—
674C2×#41—21no—
675C2×#41—21no—
676C2×#41—432no—
677C2×#41—432no—
678C2×#41—432no—
679C2×#41—432no—
680C2×#41—432no—
681C2×#41—432no—
682C2×#41—432no—
683C2×#41—432no—
684C2×#41—432no—
685C2×#41—432no—
686C2×#41—862no—
687C2×#41—862no—
688C2×#41—868no—
689C2×#41—868no—
690C2×#41—864no—
691C2×#41—864no—
692C2×#41—868no—
693C2×#41—868no—
694C2×#41—864no—
695C2×#41—868no—
696C2×#41—868no—
697C2×#41—864no—
698C2×#41—862no—
699C2×#41—862no—
700C2×#41—868no—
701C2×#41—868no—
702C2×#41—868no—
703C2×#41—868no—
704C2×#41—868no—
705C2×#41—868no—
706C2×#41—862no—
707C2×#41—862no—
708C2×#41—861no—
709C2×#41—861no—
710C2×#41—861no—
711C2×#41—861no—
712C2×#41—861no—
713C2×#41—861no—
714C2×#41—861no—
715C2×#41—861no—
716C2×#41—861no—
717C2×#41—861no—
718C2×#41—861no—
719C2×#41—861no—
720C2×#41—861no—
721C2×#41—861no—
722C2×#41C4×D4312yes—
723C2×#41C4×D4312yes—
724C2×#41D17212yes—
725C2×#41C22⋊D4312yes—
726C2×#41C22⋊D4312yes—
727C2×#41C22×D4312yes—
728C22×Q8—431no—
729C22×Q8—431no—
730C22×Q8—862no—
731C22×Q8—862no—
732C22×Q8—862no—
733C22×Q8D17211yescharacteristic
734C22×D4—21no—
735C22×D4—432no—
736C22×D4—431no—
737C22×D4—431no—
738C22×D4—862no—
739C22×D4—864no—
740C22×D4—864no—
741C22×D4—862no—
742C22×D4—864no—
743C22×D4—861no—
744C22×D4—862no—
745C22×D4D17211yescharacteristic
746C23×C4—21no—
747C23×C4—432no—
748C23×C4—864no—
749C23×C4—861no—
750C23×C4C22×D4311yescharacteristic
751C2×M16—21no—
752C2×M16—21no—
753C2×M16—21no—
754C2×M16—21no—
755C2×M16—21no—
756C2×M16C22×D4312yescomplemented
757C22×C8—21no—
758C22×C8—432no—
759C22×C8—861no—
760C22×C8—861no—
761C22×C8—861no—
762C22×C8—861no—
763C22×C8—861no—
764C22×C8—861no—
765#117—21no—
766#117—21no—
767#117—21no—
768#117—432no—
769#117—861no—
770#117—861no—
771#117—861no—
772#117C22×D4312yescomplemented
773C2×C4⋊C4—21no—
774C2×C4⋊C4—861no—
775C2×C22⋊C4—21no—
776C2×C22⋊C4—861no—
777C2×C42—21no—
778C2×C42—861no—
779#104—28no—
780#104—868no—
781#103—864no—
782#103—864no—
783#102—864no—
784#102—864no—
785#99—868no—
786C22⋊C8—868no—
787C24—21no—
788C24—432no—
789C24—864no—
790C24—861no—
791C24D4×D4311yescharacteristic
792#41—22no—
793#41—22no—
794#41—22no—
795#41—22no—
796#41—22no—
797#41—22no—
798#41—22no—
799#41—22no—
800#41—22no—
801#41—22no—
802#41—22no—
803#41—22no—
804#41—434no—
805#41—434no—
806#41—434no—
807#41—434no—
808#41—868no—
809#41—868no—
810#41—8616no—
811#41—8616no—
812#41—8616no—
813#41—8616no—
814#41—868no—
815#41—868no—
816#41—8616no—
817#41—8616no—
818#41—8616no—
819#41—8616no—
820#41—868no—
821#41—868no—
822#41—868no—
823#41—868no—
824#41—868no—
825#41—868no—
826#41—868no—
827#41—868no—
828#41—862no—
829#41—862no—
830#41—862no—
831#41—862no—
832#41—862no—
833#41—862no—
834#41—862no—
835#41—862no—
836#41—862no—
837#41—862no—
838#41—862no—
839#41—862no—
840#41—862no—
841#41—862no—
842#41—862no—
843#41—862no—
844#41—862no—
845#41—862no—
846#41—862no—
847#41—862no—
848#41—862no—
849#41—862no—
850#41—862no—
851#41—862no—
852#41—862no—
853#41—862no—
854#41—862no—
855#41—862no—
856#41(C2×D43)⋊C414yes—
857#41(C2×D43)⋊C414yes—
858#41C2×C4×D4314yes—
859#41C2×C22⋊D4314yes—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—432no—
864C2×Q8—432no—
865C2×Q8—432no—
866C2×Q8—432no—
867C2×Q8—432no—
868C2×Q8—868no—
869C2×Q8—864no—
870C2×Q8—868no—
871C2×Q8—868no—
872C2×Q8—868no—
873C2×Q8—868no—
874C2×Q8—868no—
875C2×Q8—861no—
876C2×Q8—861no—
877C2×Q8—861no—
878C2×Q8—861no—
879C2×Q8—861no—
880C2×Q8—861no—
881C2×Q8—861no—
882C2×Q8(C2×D43)⋊C412yes—
883C2×Q8(C2×D43)⋊C412yes—
884C2×Q8C2×D17212yes—
885C2×D4—22no—
886C2×D4—22no—
887C2×D4—22no—
888C2×D4—22no—
889C2×D4—22no—
890C2×D4—22no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—434no—
895C2×D4—434no—
896C2×D4—432no—
897C2×D4—432no—
898C2×D4—432no—
899C2×D4—432no—
900C2×D4—432no—
901C2×D4—868no—
902C2×D4—864no—
903C2×D4—868no—
904C2×D4—8616no—
905C2×D4—8616no—
906C2×D4—8616no—
907C2×D4—8616no—
908C2×D4—868no—
909C2×D4—868no—
910C2×D4—868no—
911C2×D4—864no—
912C2×D4—864no—
913C2×D4—8616no—
914C2×D4—8616no—
915C2×D4—862no—
916C2×D4—862no—
917C2×D4—862no—
918C2×D4—862no—
919C2×D4—862no—
920C2×D4—862no—
921C2×D4—862no—
922C2×D4—862no—
923C2×D4—862no—
924C2×D4—862no—
925C2×D4—868no—
926C2×D4—861no—
927C2×D4—861no—
928C2×D4—861no—
929C2×D4—861no—
930C2×D4—861no—
931C2×D4—861no—
932C2×D4—861no—
933C2×D4(C2×D43)⋊C412yes—
934C2×D4(C2×D43)⋊C412yes—
935C2×D4C2×D17212yes—
936C22×C4—21no—
937C22×C4—22no—
938C22×C4—22no—
939C22×C4—22no—
940C22×C4—22no—
941C22×C4—22no—
942C22×C4—22no—
943C22×C4—41no—
944C22×C4—432no—
945C22×C4—434no—
946C22×C4—434no—
947C22×C4—864no—
948C22×C4—864no—
949C22×C4—8616no—
950C22×C4—8616no—
951C22×C4—864no—
952C22×C4—861no—
953C22×C4—862no—
954C22×C4—862no—
955C22×C4—862no—
956C22×C4—862no—
957C22×C4—862no—
958C22×C4—862no—
959C22×C4—862no—
960C22×C4—862no—
961C22×C4—862no—
962C22×C4—862no—
963C22×C4—1721no—
964C22×C4C2×C4×D4311yescharacteristic
965C22×C4C2×C4×D4311yescharacteristic
966C22×C4C2×D17211yescharacteristic
967C22×C4C2×D17211yescharacteristic
968C22×C4D4×D4311yescharacteristic
969C22×C4D4×D4311yescharacteristic
970C22×C4D4×D4311yescharacteristic
971C22×C4D4×D4311yescharacteristic
972C22×C4D4×D4311yescharacteristic
973C22×C4D4×D4311yescharacteristic
974C22×C4D4×D4311yescharacteristic
975C22×C4C2×C22⋊D4311yescharacteristic
976C22×C4C2×C22⋊D4311yescharacteristic
977C22×C4C23×D4311yescharacteristic
978M16—22no—
979M16—22no—
980M16—41no—
981M16—41no—
982C2×C8—22no—
983C2×C8—41no—
984C2×C8—41no—
985C2×C8—862no—
986C2×C8—862no—
987C2×C8—862no—
988C2×C8—1721no—
989C2×C8—1721no—
990C2×C8—1721no—
991C2×C8—1721no—
992C4⋊C4—22no—
993C4⋊C4—41no—
994C4⋊C4—862no—
995C4⋊C4—1721no—
996C22⋊C4—22no—
997C22⋊C4—41no—
998C22⋊C4—862no—
999C22⋊C4—1721no—
1000C42—22no—
1001C42—41no—
1002C42—862no—
1003C42—1721no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—42no—
1008C23—82no—
1009C23—434no—
1010C23—8616no—
1011C23—862no—
1012C23—862no—
1013C23—862no—
1014C23—862no—
1015C23—862no—
1016C23—3442no—
1017C23—3448no—
1018C23—1724no—
1019C23C22⋊C4×D4311yescharacteristic
1020C23C22⋊C4×D4311yescharacteristic
1021C23#1306329311yescharacteristic
1022C23#1306329311yescharacteristic
1023C23#1306329511yescharacteristic
1024C23#1306329511yescharacteristic
1025C23C2×D4×D4311yescharacteristic
1026Q8—22no—
1027Q8—22no—
1028Q8—22no—
1029Q8—434no—
1030Q8—8616no—
1031Q8—862no—
1032Q8—862no—
1033Q8—862no—
1034Q8—862no—
1035Q8—862no—
1036Q8—862no—
1037Q8—862no—
1038Q8C2×(C2×D43)⋊C414yes—
1039D4—24no—
1040D4—24no—
1041D4—24no—
1042D4—24no—
1043D4—22no—
1044D4—22no—
1045D4—22no—
1046D4—434no—
1047D4—8616no—
1048D4—8616no—
1049D4—8616no—
1050D4—864no—
1051D4—864no—
1052D4—864no—
1053D4—864no—
1054D4—864no—
1055D4—864no—
1056D4—864no—
1057D4—864no—
1058D4—862no—
1059D4—862no—
1060D4—862no—
1061D4—862no—
1062D4—862no—
1063D4—862no—
1064D4—862no—
1065D4C2×(C2×D43)⋊C414yes—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—24no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—42no—
1074C2×C4—82no—
1075C2×C4—434no—
1076C2×C4—8616no—
1077C2×C4—8616no—
1078C2×C4—8616no—
1079C2×C4—862no—
1080C2×C4—862no—
1081C2×C4—862no—
1082C2×C4—862no—
1083C2×C4—862no—
1084C2×C4—864no—
1085C2×C4—864no—
1086C2×C4—864no—
1087C2×C4—864no—
1088C2×C4—864no—
1089C2×C4—864no—
1090C2×C4—864no—
1091C2×C4—864no—
1092C2×C4—3442no—
1093C2×C4—1722no—
1094C2×C4C22⋊C4×D4311yescharacteristic
1095C2×C4C22⋊C4×D4311yescharacteristic
1096C2×C4C22⋊C4×D4311yescharacteristic
1097C2×C4C22⋊C4×D4311yescharacteristic
1098C2×C4C22⋊C4×D4311yescharacteristic
1099C2×C4C22⋊C4×D4311yescharacteristic
1100C2×C4C2×(C2×D43)⋊C411yescharacteristic
1101C2×C4C2×(C2×D43)⋊C411yescharacteristic
1102C2×C4C2×(C2×D43)⋊C411yescharacteristic
1103C2×C4C2×(C2×D43)⋊C411yescharacteristic
1104C2×C4#1306329311yescharacteristic
1105C2×C4#1306329311yescharacteristic
1106C2×C4#1306329311yescharacteristic
1107C2×C4#1306329311yescharacteristic
1108C2×C4#1306329311yescharacteristic
1109C2×C4#1306329311yescharacteristic
1110C2×C4#1306329511yescharacteristic
1111C2×C4#1306329511yescharacteristic
1112C2×C4#1306329511yescharacteristic
1113C2×C4#1306329511yescharacteristic
1114C2×C4#1306329511yescharacteristic
1115C2×C4#1306329511yescharacteristic
1116C2×C4C22×C4×D4311yescharacteristic
1117C2×C4C2×D4×D4311yescharacteristic
1118C2×C4C2×D4×D4311yescharacteristic
1119C2×C4C2×D4×D4311yescharacteristic
1120C2×C4C22×C22⋊D4311yescharacteristic
1121C2×C4C22×D17211yescharacteristic
1122C8—42no—
1123C8—1722no—
1124C22—22no—
1125C22—22no—
1126C22—22no—
1127C22—24no—
1128C22—41no—
1129C22—41no—
1130C22—41no—
1131C22—41no—
1132C22—44no—
1133C22—82no—
1134C22—82no—
1135C22—864no—
1136C22—864no—
1137C22—3442no—
1138C22—3442no—
1139C22—3442no—
1140C22—34416no—
1141C22—1724no—
1142C22—1724no—
1143C22—1724no—
1144C22#1458275411yescharacteristic
1145C22#1458275411yescharacteristic
1146C22#1458275411yescharacteristic
1147C22#1458275411yescharacteristic
1148C22C2×C22⋊C4×D4311yescharacteristic
1149C22C2×#1306329311yescharacteristic
1150C22C2×#1306329511yescharacteristic
1151C4—24no—
1152C4—82no—
1153C4—864no—
1154C4—864no—
1155C4—3442no—
1156C4#1458275411yescharacteristic
1157C4#1458275411yescharacteristic
1158C4#1458275411yescharacteristic
1159C4#1458275411yescharacteristic
1160C4C2×C22⋊C4×D4311yescharacteristic
1161C4C22×(C2×D43)⋊C411yescharacteristic
1162C4C2×#1306329311yescharacteristic
1163C4C2×#1306329511yescharacteristic
1164C2—21no—
1165C2—21no—
1166C2—21no—
1167C2—21no—
1168C2—21no—
1169C2—21no—
1170C2—44no—
1171C2—1724no—
1172C2—1724no—
1173C2#1913455712yesdirect product factor
1174C2C2×#1458275411yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#421C2
socleC22×C43#379
prime radicalC2×#14583735C2
cosocleC22×C4×C43C24
hypercenterC2×#421D43
hypocenterC43C2×#1794
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. C2×#14582915C2semidirect
3. C2×#14582895C2semidirect
4. C2×#14582893C2semidirect
5. C2×#14582872C2semidirect
6. C2×#14582867C2semidirect
7. #19134557C2direct (N × H)
8. C2×C43×#421C2semidirect
15. #14583735C4semidirect
19. C2×#13063372C4semidirect
21. C2×#13063371C4semidirect
29. C23×C43⋊C8C22semidirect
30. C2×#13063284C22semidirect
32. #14582915C22semidirect
35. #14582895C22semidirect
37. #14582893C22semidirect
43. #14582872C22semidirect
46. #14582867C22semidirect
49. C22×M16×C43C22semidirect
50. C2×#117×C43C22semidirect
52. C43×#421C22semidirect
65. #13063372C2×C4semidirect
73. #13063371C2×C4semidirect
152. C22×C43⋊C8C23semidirect
156. #13063284C23semidirect
189. C2×M16×C43C23semidirect
194. #117×C43C23semidirect
579. C2×#421D43semidirect
592. C2×C43#1794semidirect
617. C22×M16C2×D43semidirect
620. C2×#117C2×D43semidirect
624. #421C2×D43semidirect
641. C43C2×#1794semidirect
756. C2×M16C22×D43semidirect
772. #117C22×D43semidirect
1173. C2#19134557direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145837352
C2×#145829152
C2×#145828952
C2×#145828932
C2×#145828722
C2×#145828672
#191345572
C2×C43×#4212
C2×#179443