Finite Group Databasebeta

← C2×#20241933 #26183536

Subgroups — C2×#20241933 #26183536

Order 12032.

1302 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689668C211yesmaximal, characteristic
2C2×#15689177C211yesmaximal, characteristic, complemented
3C2×#15688990C211yesmaximal, characteristic, complemented
4#20241933C218yesmaximal, direct product factor
5C2×#15688858C211yesmaximal, characteristic, complemented
6C2×#15688857C211yesmaximal, characteristic, complemented
7C2×#15688856C211yesmaximal, characteristic, complemented
8C2×C47×#327C211yesmaximal, characteristic, complemented
9C22×#10625352—21no—
10#15689668—22no—
11#15689668—22no—
12#15689668C414yescomplemented
13#15689668C2214yes—
14C2×#13094023C411yescharacteristic, complemented
15C2×#13094020C411yescharacteristic, complemented
16C2×#13094010—21no—
17C2×#13093998C2211yescharacteristic
18C2×#13093996—21no—
19C2×D4×Dic47C411yescharacteristic, complemented
20C2×#13093986C411yescharacteristic, complemented
21C2×(C22⋊D47)⋊C4—21no—
22C22×C4×Dic47C2211yescharacteristic
23#15689177—22no—
24#15689177C2214yescomplemented
25C2×Dic47⋊C8—21no—
26C2×C22⋊(C47⋊C8)C2211yescharacteristic
27C2×#13093934—21no—
28#15688990—22no—
29#15688990C2214yescomplemented
30C2×C47⋊#95—21no—
31C2×C47⋊#95—21no—
32C2×C47⋊#95C2211yescharacteristic
33#15688858C2214yescomplemented
34#15688857C2214yescomplemented
35#15688856C2214yescomplemented
36C2×#121×C47C2211yescharacteristic
37C2×C22⋊C8×C47C2211yescharacteristic
38C2×#95×C47C2211yescharacteristic
39C47×#327C2214yescomplemented
40C2×#10625352—24no—
41C2×#10625352—24no—
42C2×#10625352—44no—
43C2×#10625352—44no—
44C22×Dic94—21no—
45C22×D188C2×C411yescharacteristic
46C22×C22⋊D47—21no—
47C22×C22⋊D47—21no—
48C22×C22⋊D47—21no—
49C23×Dic47—21no—
50C23×Dic47—21no—
51C23×Dic47D411yescharacteristic
52C23×Dic47D411yescharacteristic
53C22×C4×D47—21no—
54C22×C47⋊C8—21no—
55#13094023—22no—
56#13094023C2×C414yescomplemented
57#13094020—22no—
58#13094020C2×C414yescomplemented
59#13094010—24no—
60#13094010—24no—
61#13093998—21no—
62#13093998—21no—
63#13093998C2×C412yes—
64#13093998C2312yes—
65#13093996—24no—
66#13093996—24no—
67D4×Dic47—22no—
68D4×Dic47C2×C414yescomplemented
69#13093986—22no—
70#13093986C2×C414yescomplemented
71(C22⋊D47)⋊C4—24no—
72(C22⋊D47)⋊C4—24no—
73C2×C4⋊Dic47C2×C411yescharacteristic
74C2×Dic47⋊C4—21no—
75C2×C22⋊Dic47—21no—
76C2×(C2×D47)⋊C4—21no—
77C2×(C2×D47)⋊C4—21no—
78C2×C4×Dic47C2×C411yescharacteristic
79C2×C4×Dic47C2×C411yescharacteristic
80C2×C4×Dic47C2×C412yes—
81C2×C4×Dic47D412yes—
82C2×C4×Dic47D411yescharacteristic
83C2×C4×Dic47D411yescharacteristic
84C2×C4×Dic47D412yes—
85C2×C4×Dic47C2312yes—
86Dic47⋊C8—24no—
87C22⋊(C47⋊C8)—21no—
88C22⋊(C47⋊C8)C2312yes—
89#13093934—24no—
90C47⋊#95—21no—
91C47⋊#95—24no—
92C47⋊#95—24no—
93C47⋊#95C2312yes—
94C22×D4×C47—21no—
95C22×D4×C47C2×C411yescharacteristic
96C23×C4×C47—21no—
97C23×C4×C47C2311yescharacteristic
98C22×C8×C47—21no—
99#121×C47—21no—
100#121×C47—21no—
101#121×C47C2×C412yes—
102#121×C47C2312yes—
103C2×C4⋊C4×C47C2×C411yescharacteristic
104C2×C22⋊C4×C47—21no—
105C22⋊C8×C47—21no—
106C22⋊C8×C47C2312yes—
107#95×C47—21no—
108#95×C47C2312yes—
109C24×C47—21no—
110C24×C47C2×D411yescharacteristic
111C23×D47—21no—
112C2×D4×C47—22no—
113C2×D4×C47—22no—
114C2×D4×C47—21no—
115C2×D4×C47—42no—
116C2×D4×C47—42no—
117C2×D4×C47—42no—
118C2×D4×C47C22×C412yes—
119C22×C4×C47—21no—
120C22×C4×C47—22no—
121C22×C4×C47—42no—
122C22×C4×C47—42no—
123C22×C4×C47—42no—
124C22×C4×C47—42no—
125C22×C4×C47C22×C411yescharacteristic
126C22×C4×C47C22×C411yescharacteristic
127C22×C4×C47C2×D411yescharacteristic
128C22×C4×C47C2×D411yescharacteristic
129C22×C4×C47C2×D411yescharacteristic
130C22×C4×C47C2411yescharacteristic
131C2×C22⋊D47—22no—
132C2×C22⋊D47—22no—
133C2×C22⋊D47—24no—
134C2×C22⋊D47—24no—
135C2×C22⋊D47—44no—
136C2×C22⋊D47—44no—
137C2×C22⋊D47—42no—
138C2×C22⋊D47—42no—
139C22×Dic47—22no—
140C22×Dic47—22no—
141C22×Dic47—21no—
142C22×Dic47—24no—
143C22×Dic47—22no—
144C22×Dic47—42no—
145C22×Dic47—44no—
146C22×Dic47—42no—
147C22×Dic47—42no—
148C22×Dic47—42no—
149C22×Dic47C22⋊C411yescharacteristic
150C22×Dic47C22⋊C411yescharacteristic
151C22×Dic47C22⋊C411yescharacteristic
152C22×Dic47C22⋊C411yescharacteristic
153C22×Dic47C22⋊C412yes—
154C22×Dic47C22⋊C412yes—
155C22×Dic47C2×D412yes—
156C22×Dic47C2×D412yes—
157#10625352—48no—
158#10625352—48no—
159#10625352—416no—
160C2×D188—21no—
161C2×D188—42no—
162C2×D188C22×C412yes—
163C2×C4×D47—24no—
164C2×C4×D47—44no—
165C2×Dic94—24no—
166C2×Dic94—44no—
167C2×C8×C47—22no—
168C2×C8×C47—42no—
169C4⋊C4×C47—21no—
170C4⋊C4×C47C22×C412yes—
171C22⋊C4×C47—22no—
172C22⋊C4×C47—22no—
173C22⋊Dic47—24no—
174(C2×D47)⋊C4—22no—
175(C2×D47)⋊C4—22no—
176(C2×D47)⋊C4—24no—
177C4⋊Dic47—21no—
178C4⋊Dic47C22×C412yes—
179Dic47⋊C4—24no—
180C4×Dic47C22⋊C412yes—
181C4×Dic47C22⋊C412yes—
182C4×Dic47C22⋊C412yes—
183C4×Dic47C22⋊C412yes—
184C4×Dic47C22×C412yes—
185C4×Dic47C22×C412yes—
186C4×Dic47C2×D412yes—
187C4×Dic47C2×D412yes—
188C2×C47⋊C8—22no—
189C2×C47⋊C8—42no—
190C23×C47—22no—
191C23×C47—22no—
192C23×C47—22no—
193C23×C47—42no—
194C23×C47—42no—
195C23×C47—42no—
196C23×C47C2×C22⋊C411yescharacteristic
197C23×C47C2×C22⋊C411yescharacteristic
198C23×C47AGL(1,ℤ/8)12yes—
199C23×C47AGL(1,ℤ/8)12yes—
200C23×C47C22×D411yescharacteristic
201C22×D47—22no—
202C22×D47—42no—
203C22×D47—42no—
204C22×D47—42no—
205D4×C47—42no—
206D4×C47—42no—
207D4×C47—42no—
208D4×C47—42no—
209D4×C47—44no—
210C2×C4×C47—22no—
211C2×C4×C47—22no—
212C2×C4×C47—22no—
213C2×C4×C47—41no—
214C2×C4×C47—41no—
215C2×C4×C47—41no—
216C2×C4×C47—41no—
217C2×C4×C47—42no—
218C2×C4×C47—42no—
219C2×C4×C47—42no—
220C2×C4×C47—42no—
221C2×C4×C47—84no—
222C2×C4×C47C2×C22⋊C411yescharacteristic
223C2×C4×C47C2×C22⋊C411yescharacteristic
224C2×C4×C47C23×C411yescharacteristic
225C2×C4×C47C22×D411yescharacteristic
226C22⋊D47—48no—
227C22⋊D47—48no—
228C22⋊D47—42no—
229C22⋊D47—42no—
230C22⋊D47—44no—
231C2×Dic47—22no—
232C2×Dic47—22no—
233C2×Dic47—22no—
234C2×Dic47—22no—
235C2×Dic47—24no—
236C2×Dic47—22no—
237C2×Dic47—22no—
238C2×Dic47—22no—
239C2×Dic47—42no—
240C2×Dic47—42no—
241C2×Dic47—48no—
242C2×Dic47—42no—
243C2×Dic47—42no—
244C2×Dic47—42no—
245C2×Dic47—42no—
246C2×Dic47—84no—
247C2×Dic47C2×C22⋊C412yes—
248C2×Dic47C2×C22⋊C412yes—
249C2×Dic47C2×C22⋊C412yes—
250C2×Dic47C2×C22⋊C412yes—
251D188—42no—
252D188—42no—
253C4×D47—48no—
254Dic94—48no—
255C8×C47—42no—
256C47⋊C8—42no—
257C2×#1514—471nomaximal, Sylow
258C22×C47—21no—
259C22×C47—21no—
260C22×C47—21no—
261C22×C47—21no—
262C22×C47—24no—
263C22×C47—24no—
264C22×C47—42no—
265C22×C47—42no—
266C22×C47—42no—
267C22×C47—84no—
268C22×C47#41012yes—
269C22×C47#41812yes—
270C22×C47#41812yes—
271C22×C47#42112yes—
272C22×C47C22×C22⋊C411yescharacteristic
273C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
274C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
275C2×D47—42no—
276C2×D47—42no—
277C2×D47—42no—
278C2×D47—84no—
279C4×C47—21no—
280C4×C47—21no—
281C4×C47—21no—
282C4×C47—21no—
283C4×C47—42no—
284C4×C47—82no—
285Dic47—22no—
286Dic47—22no—
287Dic47—22no—
288Dic47—22no—
289Dic47—42no—
290Dic47—82no—
291C2×#532—471no—
292C2×#432—471no—
293C2×#383—471no—
294#1514—478no—
295C2×#327—471no—
296C2×#327—471no—
297C2×#327—471no—
298C2×#327D4711yescharacteristic, complemented
299C2×C47—21no—
300C2×C47—21no—
301C2×C47—22no—
302C2×C47—82no—
303C2×C47#151414yescomplemented
304C2×C47C2×#41011yescharacteristic
305C2×C47C2×#41811yescharacteristic
306C2×C47C2×#42111yescharacteristic
307D47—82no—
308C22×#41—941no—
309#532—474no—
310#532—474no—
311#532—942no—
312#532—942no—
313C2×C4⋊Q8—471no—
314C2×#127—471no—
315C2×#124—941no—
316C2×#121—471no—
317C2×#121—941no—
318C2×#121C2×D4711yescharacteristic
319C2×C4×D4—471no—
320C2×C4×D4—471no—
321C2×C4×D4—941no—
322C22×C42—471no—
323#432—474no—
324#432—942no—
325C2×C4⋊C8—941no—
326C2×C22⋊C8—471no—
327C2×C22⋊C8C2×D4711yescharacteristic
328C2×#97—941no—
329#383—474no—
330#383—942no—
331C2×#95—471no—
332C2×#95—941no—
333C2×#95—941no—
334C2×#95C2×D4711yescharacteristic
335#327—474no—
336#327—474no—
337#327—474no—
338#327C2×D4714yescomplemented
339C47C2×#151411yescharacteristic, complemented, Sylow
340C2×#41—944no—
341C2×#41—944no—
342C2×#41—1884no—
343C2×#41—1884no—
344C22×Q8—941no—
345C22×D4—21no—
346C22×D4—471no—
347C22×D4—941no—
348C22×D4—941no—
349C22×D4—941no—
350C22×D4C4×D4711yescharacteristic
351C23×C4—21no—
352C23×C4—471no—
353C23×C4—471no—
354C23×C4—941no—
355C23×C4—941no—
356C23×C4—941no—
357C23×C4C22×D4711yescharacteristic
358C22×C8—21no—
359C22×C8—941no—
360C4⋊Q8—474no—
361C4⋊Q8—942no—
362#127—474no—
363#127—942no—
364#124—944no—
365#124—944no—
366#121—21no—
367#121—21no—
368#121—472no—
369#121—472no—
370#121—944no—
371#121—944no—
372#121—941no—
373#121—941no—
374#121C4×D4712yes—
375#121C22×D4712yes—
376C4×D4—474no—
377C4×D4—474no—
378C4×D4—944no—
379C4×D4—944no—
380C4×D4—942no—
381C4×D4—942no—
382C2×C4⋊C4—471no—
383C2×C4⋊C4—941no—
384C2×C4⋊C4C4×D4711yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—941no—
387C2×C22⋊C4—941no—
388C2×C22⋊C4—941no—
389C2×C42—471no—
390C2×C42—471no—
391C2×C42—472no—
392C2×C42—471no—
393C2×C42—471no—
394C2×C42—472no—
395C2×C42—472no—
396C2×C42—472no—
397C4⋊C8—944no—
398C22⋊C8—21no—
399C22⋊C8—472no—
400C22⋊C8—941no—
401C22⋊C8C22×D4712yes—
402#97—944no—
403#95—21no—
404#95—472no—
405#95—944no—
406#95—944no—
407#95—941no—
408#95C22×D4712yes—
409C24—21no—
410C24—941no—
411C24D4×D4711yescharacteristic
412#41—18816no—
413#41—1888no—
414#41—1888no—
415C2×Q8—944no—
416C2×Q8—1884no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—21no—
420C2×D4—42no—
421C2×D4—42no—
422C2×D4—42no—
423C2×D4—472no—
424C2×D4—944no—
425C2×D4—944no—
426C2×D4—942no—
427C2×D4—942no—
428C2×D4—941no—
429C2×D4—1882no—
430C2×D4—1884no—
431C2×D4—1884no—
432C2×D4—1882no—
433C2×D4—1882no—
434C2×D4C2×C4×D4712yes—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—472no—
442C22×C4—471no—
443C22×C4—471no—
444C22×C4—471no—
445C22×C4—471no—
446C22×C4—472no—
447C22×C4—472no—
448C22×C4—472no—
449C22×C4—944no—
450C22×C4—944no—
451C22×C4—942no—
452C22×C4—942no—
453C22×C4—941no—
454C22×C4—942no—
455C22×C4—1884no—
456C22×C4—1882no—
457C22×C4—1884no—
458C22×C4—1882no—
459C22×C4—1882no—
460C22×C4—1882no—
461C22×C4C2×C4×D4711yescharacteristic
462C22×C4C2×C4×D4711yescharacteristic
463C22×C4D4×D4711yescharacteristic
464C22×C4D4×D4711yescharacteristic
465C22×C4D4×D4711yescharacteristic
466C22×C4C23×D4711yescharacteristic
467C2×C8—22no—
468C2×C8—42no—
469C2×C8—942no—
470C2×C8—1882no—
471C4⋊C4—21no—
472C4⋊C4—472no—
473C4⋊C4—944no—
474C4⋊C4—941no—
475C4⋊C4C2×C4×D4712yes—
476C22⋊C4—22no—
477C22⋊C4—22no—
478C22⋊C4—944no—
479C22⋊C4—944no—
480C22⋊C4—942no—
481C22⋊C4—942no—
482C42—472no—
483C42—472no—
484C42—472no—
485C42—472no—
486C42—472no—
487C42—472no—
488C42—472no—
489C42—472no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—942no—
497C23—1882no—
498C23—1882no—
499C23—1882no—
500C23C22⋊C4×D4711yescharacteristic
501C23C22⋊C4×D4711yescharacteristic
502C23#1309404812yes—
503C23#1309405112yes—
504C23C2×D4×D4711yescharacteristic
505Q8—1888no—
506D4—42no—
507D4—42no—
508D4—44no—
509D4—42no—
510D4—42no—
511D4—1882no—
512D4—1882no—
513D4—1888no—
514D4—1888no—
515D4—1884no—
516D4—1882no—
517D4—1882no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—84no—
530C2×C4—472no—
531C2×C4—472no—
532C2×C4—472no—
533C2×C4—472no—
534C2×C4—942no—
535C2×C4—942no—
536C2×C4—944no—
537C2×C4—942no—
538C2×C4—942no—
539C2×C4—942no—
540C2×C4—942no—
541C2×C4—942no—
542C2×C4—3764no—
543C2×C4—1888no—
544C2×C4—1882no—
545C2×C4—1882no—
546C2×C4—1888no—
547C2×C4—1882no—
548C2×C4—1882no—
549C2×C4—1882no—
550C2×C4—1882no—
551C2×C4C22⋊C4×D4711yescharacteristic
552C2×C4C22⋊C4×D4711yescharacteristic
553C2×C4C22×C4×D4711yescharacteristic
554C2×C4C2×D4×D4711yescharacteristic
555C8—42no—
556C8—1882no—
557C22—24no—
558C22—24no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—42no—
564C22—42no—
565C22—42no—
566C22—84no—
567C22—3764no—
568C22—1882no—
569C22—1882no—
570C22—1882no—
571C22#1568909512yes—
572C22#1568912612yes—
573C22#1568912612yes—
574C22#1568913812yes—
575C22C2×C22⋊C4×D4711yescharacteristic
576C22C2×#1309404811yescharacteristic
577C22C2×#1309405111yescharacteristic
578C4—21no—
579C4—21no—
580C4—21no—
581C4—21no—
582C4—42no—
583C4—82no—
584C4—942no—
585C4—942no—
586C4—942no—
587C4—942no—
588C4—3762no—
589C4—1882no—
590C2—21no—
591C2—21no—
592C2—22no—
593C2—82no—
594C2—3762no—
595C2#2024193314yesdirect product factor
596C2C2×#1568909511yescharacteristic
597C2C2×#1568912611yescharacteristic
598C2C2×#1568913811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#327C2
socleC23×C47C2×C22⋊C4
prime radicalC2×#15689668C2
cosocleC22×C4×C47C24
hypercenterC2×#327D47
hypocenterC47C2×#1514
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. C2×#15689177C2semidirect
3. C2×#15688990C2semidirect
4. #20241933C2direct (N × H)
5. C2×#15688858C2semidirect
6. C2×#15688857C2semidirect
7. C2×#15688856C2semidirect
8. C2×C47×#327C2semidirect
12. #15689668C4semidirect
14. C2×#13094023C4semidirect
15. C2×#13094020C4semidirect
19. C2×D4×Dic47C4semidirect
20. C2×#13093986C4semidirect
24. #15689177C22semidirect
29. #15688990C22semidirect
33. #15688858C22semidirect
34. #15688857C22semidirect
35. #15688856C22semidirect
39. C47×#327C22semidirect
56. #13094023C2×C4semidirect
58. #13094020C2×C4semidirect
68. D4×Dic47C2×C4semidirect
70. #13093986C2×C4semidirect
298. C2×#327D47semidirect
303. C2×C47#1514semidirect
338. #327C2×D47semidirect
339. C47C2×#1514semidirect
595. C2#20241933direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896682
C2×#156891772
C2×#156889902
#202419332
C2×#156888582
C2×#156888572
C2×#156888562
C2×C47×#3272
C2×#151447