Finite Group Databasebeta

← C2×#20241894 #26183421

Subgroups — C2×#20241894 #26183421

Order 12032.

1410 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689668C211yesmaximal, characteristic
2C2×#15689177C211yesmaximal, characteristic, complemented
3C2×#15688968C211yesmaximal, characteristic, complemented
4#20241894C218yesmaximal, 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×Dic47—21no—
23C22×C4×Dic47C2211yescharacteristic
24#15689177—22no—
25#15689177C2214yescomplemented
26C2×Dic47⋊C8—21no—
27C2×C22⋊(C47⋊C8)C2211yescharacteristic
28C2×#13093934—21no—
29#15688968—22no—
30#15688968C2214yescomplemented
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×Dic47—28no—
79C2×C4×Dic47—24no—
80C2×C4×Dic47C2×C411yescharacteristic
81C2×C4×Dic47C2×C411yescharacteristic
82C2×C4×Dic47C2×C412yes—
83C2×C4×Dic47D412yes—
84C2×C4×Dic47D411yescharacteristic
85C2×C4×Dic47D411yescharacteristic
86C2×C4×Dic47D412yes—
87C2×C4×Dic47C2312yes—
88Dic47⋊C8—24no—
89C22⋊(C47⋊C8)—21no—
90C22⋊(C47⋊C8)C2312yes—
91#13093934—24no—
92C47⋊#95—21no—
93C47⋊#95—24no—
94C47⋊#95C2312yes—
95C22×D4×C47—21no—
96C22×D4×C47C2×C411yescharacteristic
97C23×C4×C47—21no—
98C23×C4×C47C2311yescharacteristic
99C22×C8×C47—21no—
100#121×C47—21no—
101#121×C47—21no—
102#121×C47C2×C412yes—
103#121×C47C2312yes—
104C2×C4⋊C4×C47C2×C411yescharacteristic
105C2×C22⋊C4×C47—21no—
106C22⋊C8×C47—21no—
107C22⋊C8×C47C2312yes—
108#95×C47—21no—
109#95×C47C2312yes—
110C24×C47—21no—
111C24×C47C2×D411yescharacteristic
112C23×D47—21no—
113C2×D4×C47—22no—
114C2×D4×C47—22no—
115C2×D4×C47—21no—
116C2×D4×C47—42no—
117C2×D4×C47—42no—
118C2×D4×C47—42no—
119C2×D4×C47C22×C412yes—
120C22×C4×C47—24no—
121C22×C4×C47—21no—
122C22×C4×C47—22no—
123C22×C4×C47—42no—
124C22×C4×C47—42no—
125C22×C4×C47—42no—
126C22×C4×C47C22×C411yescharacteristic
127C22×C4×C47C22×C411yescharacteristic
128C22×C4×C47C2×D411yescharacteristic
129C22×C4×C47C2×D411yescharacteristic
130C22×C4×C47C2×D411yescharacteristic
131C22×C4×C47C2411yescharacteristic
132C2×C22⋊D47—22no—
133C2×C22⋊D47—22no—
134C2×C22⋊D47—24no—
135C2×C22⋊D47—24no—
136C2×C22⋊D47—44no—
137C2×C22⋊D47—42no—
138C2×C22⋊D47—42no—
139C2×C22⋊D47—44no—
140C22×Dic47—22no—
141C22×Dic47—22no—
142C22×Dic47—24no—
143C22×Dic47—24no—
144C22×Dic47—21no—
145C22×Dic47—22no—
146C22×Dic47—24no—
147C22×Dic47—44no—
148C22×Dic47—42no—
149C22×Dic47—42no—
150C22×Dic47C22⋊C411yescharacteristic
151C22×Dic47C22⋊C412yes—
152C22×Dic47C22⋊C411yescharacteristic
153C22×Dic47C22⋊C411yescharacteristic
154C22×Dic47C22⋊C412yes—
155C22×Dic47C22⋊C411yescharacteristic
156C22×Dic47C2×D412yes—
157C22×Dic47C2×D412yes—
158#10625352—48no—
159#10625352—48no—
160#10625352—416no—
161C2×D188—21no—
162C2×D188—42no—
163C2×D188C22×C412yes—
164C2×C4×D47—24no—
165C2×C4×D47—44no—
166C2×Dic94—24no—
167C2×Dic94—44no—
168C2×C8×C47—22no—
169C2×C8×C47—42no—
170C4⋊C4×C47—21no—
171C4⋊C4×C47C22×C412yes—
172C22⋊C4×C47—22no—
173C22⋊C4×C47—22no—
174C22⋊Dic47—24no—
175(C2×D47)⋊C4—22no—
176(C2×D47)⋊C4—22no—
177(C2×D47)⋊C4—24no—
178C4⋊Dic47—21no—
179C4⋊Dic47C22×C412yes—
180Dic47⋊C4—24no—
181C4×Dic47—216no—
182C4×Dic47C22⋊C412yes—
183C4×Dic47C22⋊C412yes—
184C4×Dic47C22⋊C412yes—
185C4×Dic47C22⋊C412yes—
186C4×Dic47C22×C412yes—
187C4×Dic47C22×C412yes—
188C4×Dic47C2×D412yes—
189C4×Dic47C2×D412yes—
190C2×C47⋊C8—22no—
191C2×C47⋊C8—42no—
192C23×C47—22no—
193C23×C47—22no—
194C23×C47—22no—
195C23×C47—42no—
196C23×C47—42no—
197C23×C47—42no—
198C23×C47C2×C22⋊C411yescharacteristic
199C23×C47C2×C22⋊C411yescharacteristic
200C23×C47AGL(1,ℤ/8)12yes—
201C23×C47AGL(1,ℤ/8)12yes—
202C23×C47C22×D411yescharacteristic
203C22×D47—22no—
204C22×D47—42no—
205C22×D47—42no—
206C22×D47—42no—
207D4×C47—42no—
208D4×C47—42no—
209D4×C47—42no—
210D4×C47—42no—
211D4×C47—44no—
212C2×C4×C47—22no—
213C2×C4×C47—22no—
214C2×C4×C47—24no—
215C2×C4×C47—22no—
216C2×C4×C47—41no—
217C2×C4×C47—41no—
218C2×C4×C47—41no—
219C2×C4×C47—41no—
220C2×C4×C47—42no—
221C2×C4×C47—48no—
222C2×C4×C47—42no—
223C2×C4×C47—42no—
224C2×C4×C47C2×C22⋊C411yescharacteristic
225C2×C4×C47C2×C22⋊C411yescharacteristic
226C2×C4×C47C23×C411yescharacteristic
227C2×C4×C47C22×D411yescharacteristic
228C22⋊D47—48no—
229C22⋊D47—42no—
230C22⋊D47—42no—
231C22⋊D47—44no—
232C22⋊D47—48no—
233C2×Dic47—22no—
234C2×Dic47—22no—
235C2×Dic47—22no—
236C2×Dic47—22no—
237C2×Dic47—24no—
238C2×Dic47—22no—
239C2×Dic47—24no—
240C2×Dic47—24no—
241C2×Dic47—24no—
242C2×Dic47—22no—
243C2×Dic47—48no—
244C2×Dic47—42no—
245C2×Dic47—48no—
246C2×Dic47—42no—
247C2×Dic47—42no—
248C2×Dic47#10414yes—
249C2×Dic47C2×C22⋊C412yes—
250C2×Dic47C2×C22⋊C412yes—
251C2×Dic47C2×C22⋊C412yes—
252C2×Dic47C2×C22⋊C412yes—
253D188—42no—
254D188—42no—
255C4×D47—48no—
256Dic94—48no—
257C8×C47—42no—
258C47⋊C8—42no—
259C2×#1505—471nomaximal, Sylow
260C22×C47—21no—
261C22×C47—21no—
262C22×C47—21no—
263C22×C47—21no—
264C22×C47—24no—
265C22×C47—24no—
266C22×C47—42no—
267C22×C47—42no—
268C22×C47—42no—
269C22×C47—84no—
270C22×C47#41012yes—
271C22×C47#41812yes—
272C22×C47#41812yes—
273C22×C47C2×#10412yes—
274C22×C47C22×C22⋊C411yescharacteristic
275C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
276C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
277C2×D47—42no—
278C2×D47—42no—
279C2×D47—42no—
280C2×D47—84no—
281C4×C47—21no—
282C4×C47—21no—
283C4×C47—21no—
284C4×C47—21no—
285C4×C47—44no—
286C4×C47—42no—
287Dic47—22no—
288Dic47—22no—
289Dic47—22no—
290Dic47—44no—
291Dic47—42no—
292Dic47C2×#10414yes—
293C2×#532—471no—
294C2×#432—471no—
295C2×#376—471no—
296#1505—478no—
297C2×#327—471no—
298C2×#327—471no—
299C2×#327—471no—
300C2×#327D4711yescharacteristic, complemented
301C2×C47—21no—
302C2×C47—21no—
303C2×C47—22no—
304C2×C47—82no—
305C2×C47#150514yescomplemented
306C2×C47C2×#41011yescharacteristic
307C2×C47C2×#41811yescharacteristic
308C2×C47C22×#10411yescharacteristic
309D47—82no—
310C22×#41—941no—
311#532—474no—
312#532—474no—
313#532—942no—
314#532—942no—
315C2×C4⋊Q8—471no—
316C2×#127—471no—
317C2×#124—941no—
318C2×#121—471no—
319C2×#121—941no—
320C2×#121C2×D4711yescharacteristic
321C2×C4×D4—471no—
322C2×C4×D4—471no—
323C2×C4×D4—941no—
324C22×C42—471no—
325C22×C42—941no—
326#432—474no—
327#432—942no—
328C2×C4⋊C8—941no—
329C2×C22⋊C8—471no—
330C2×C22⋊C8C2×D4711yescharacteristic
331C2×#97—941no—
332#376—474no—
333#376—942no—
334C2×#95—471no—
335C2×#95—941no—
336C2×#95C2×D4711yescharacteristic
337#327—474no—
338#327—474no—
339#327—474no—
340#327C2×D4714yescomplemented
341C47C2×#150511yescharacteristic, complemented, Sylow
342C2×#41—944no—
343C2×#41—944no—
344C2×#41—1884no—
345C2×#41—1884no—
346C22×Q8—941no—
347C22×D4—21no—
348C22×D4—471no—
349C22×D4—941no—
350C22×D4—941no—
351C22×D4—941no—
352C22×D4C4×D4711yescharacteristic
353C23×C4—21no—
354C23×C4—471no—
355C23×C4—471no—
356C23×C4—941no—
357C23×C4—941no—
358C23×C4—941no—
359C23×C4C22×D4711yescharacteristic
360C22×C8—21no—
361C22×C8—941no—
362C4⋊Q8—474no—
363C4⋊Q8—942no—
364#127—474no—
365#127—942no—
366#124—944no—
367#124—944no—
368#121—21no—
369#121—21no—
370#121—472no—
371#121—472no—
372#121—944no—
373#121—944no—
374#121—941no—
375#121—941no—
376#121C4×D4712yes—
377#121C22×D4712yes—
378C4×D4—474no—
379C4×D4—474no—
380C4×D4—944no—
381C4×D4—944no—
382C4×D4—942no—
383C4×D4—942no—
384C2×C4⋊C4—471no—
385C2×C4⋊C4—941no—
386C2×C4⋊C4C4×D4711yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—941no—
389C2×C22⋊C4—941no—
390C2×C22⋊C4—941no—
391C2×C42—471no—
392C2×C42—471no—
393C2×C42—472no—
394C2×C42—471no—
395C2×C42—471no—
396C2×C42—472no—
397C2×C42—472no—
398C2×C42—472no—
399C2×C42—944no—
400C2×C42—948no—
401C4⋊C8—944no—
402C22⋊C8—21no—
403C22⋊C8—472no—
404C22⋊C8—941no—
405C22⋊C8C22×D4712yes—
406#97—944no—
407#95—21no—
408#95—472no—
409#95—944no—
410#95—941no—
411#95C22×D4712yes—
412C24—21no—
413C24—941no—
414C24D4×D4711yescharacteristic
415#41—18816no—
416#41—1888no—
417#41—1888no—
418C2×Q8—944no—
419C2×Q8—1884no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—21no—
423C2×D4—42no—
424C2×D4—42no—
425C2×D4—42no—
426C2×D4—472no—
427C2×D4—944no—
428C2×D4—944no—
429C2×D4—942no—
430C2×D4—942no—
431C2×D4—941no—
432C2×D4—1882no—
433C2×D4—1884no—
434C2×D4—1884no—
435C2×D4—1882no—
436C2×D4—1882no—
437C2×D4C2×C4×D4712yes—
438C22×C4—24no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—471no—
445C22×C4—472no—
446C22×C4—472no—
447C22×C4—471no—
448C22×C4—471no—
449C22×C4—471no—
450C22×C4—472no—
451C22×C4—472no—
452C22×C4—944no—
453C22×C4—944no—
454C22×C4—944no—
455C22×C4—942no—
456C22×C4—942no—
457C22×C4—944no—
458C22×C4—941no—
459C22×C4—942no—
460C22×C4—1884no—
461C22×C4—1884no—
462C22×C4—1882no—
463C22×C4—1882no—
464C22×C4C2×C4×D4711yescharacteristic
465C22×C4C2×C4×D4711yescharacteristic
466C22×C4D4×D4711yescharacteristic
467C22×C4D4×D4711yescharacteristic
468C22×C4D4×D4711yescharacteristic
469C22×C4C23×D4711yescharacteristic
470C2×C8—22no—
471C2×C8—42no—
472C2×C8—942no—
473C2×C8—1882no—
474C4⋊C4—21no—
475C4⋊C4—472no—
476C4⋊C4—944no—
477C4⋊C4—941no—
478C4⋊C4C2×C4×D4712yes—
479C22⋊C4—22no—
480C22⋊C4—22no—
481C22⋊C4—944no—
482C22⋊C4—944no—
483C22⋊C4—942no—
484C22⋊C4—942no—
485C42—472no—
486C42—472no—
487C42—472no—
488C42—472no—
489C42—472no—
490C42—472no—
491C42—472no—
492C42—472no—
493C42—9416no—
494C23—22no—
495C23—22no—
496C23—22no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—942no—
501C23—1882no—
502C23—1882no—
503C23—1882no—
504C23C22⋊C4×D4711yescharacteristic
505C23C22⋊C4×D4711yescharacteristic
506C23#1309404812yes—
507C23#1309405112yes—
508C23C2×D4×D4711yescharacteristic
509Q8—1888no—
510D4—42no—
511D4—42no—
512D4—44no—
513D4—42no—
514D4—42no—
515D4—1882no—
516D4—1882no—
517D4—1888no—
518D4—1888no—
519D4—1884no—
520D4—1882no—
521D4—1882no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—24no—
525C2×C4—22no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—48no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—472no—
535C2×C4—474no—
536C2×C4—472no—
537C2×C4—472no—
538C2×C4—472no—
539C2×C4—944no—
540C2×C4—944no—
541C2×C4—942no—
542C2×C4—942no—
543C2×C4—944no—
544C2×C4—942no—
545C2×C4—942no—
546C2×C4—942no—
547C2×C4—944no—
548C2×C4—942no—
549C2×C4—1888no—
550C2×C4—1888no—
551C2×C4—1882no—
552C2×C4—1888no—
553C2×C4—1882no—
554C2×C4—1882no—
555C2×C4C22⋊C4×D4711yescharacteristic
556C2×C4C22⋊C4×D4711yescharacteristic
557C2×C4C22×C4×D4711yescharacteristic
558C2×C4C2×D4×D4711yescharacteristic
559C8—42no—
560C8—1882no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—21no—
565C22—24no—
566C22—24no—
567C22—42no—
568C22—42no—
569C22—42no—
570C22—84no—
571C22—3764no—
572C22—1882no—
573C22—1882no—
574C22—1882no—
575C22#1568909512yes—
576C22#1568912612yes—
577C22#1568912612yes—
578C22#104×D4712yes—
579C22C2×C22⋊C4×D4711yescharacteristic
580C22C2×#1309404811yescharacteristic
581C22C2×#1309405111yescharacteristic
582C4—21no—
583C4—21no—
584C4—21no—
585C4—21no—
586C4—44no—
587C4—42no—
588C4—474no—
589C4—942no—
590C4—942no—
591C4—942no—
592C4—1884no—
593C4—1882no—
594C2—21no—
595C2—21no—
596C2—22no—
597C2—82no—
598C2—3762no—
599C2#2024189414yesdirect product factor
600C2C2×#1568909511yescharacteristic
601C2C2×#1568912611yescharacteristic
602C2C2×#104×D4711yescharacteristic
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×#1505
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×#15688968C2semidirect
4. #20241894C2direct (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
25. #15689177C22semidirect
30. #15688968C22semidirect
33. #15688858C22semidirect
34. #15688857C22semidirect
35. #15688856C22semidirect
39. C47×#327C22semidirect
56. #13094023C2×C4semidirect
58. #13094020C2×C4semidirect
68. D4×Dic47C2×C4semidirect
70. #13093986C2×C4semidirect
300. C2×#327D47semidirect
305. C2×C47#1505semidirect
340. #327C2×D47semidirect
341. C47C2×#1505semidirect
599. C2#20241894direct (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×#156889682
#202418942
C2×#156888582
C2×#156888572
C2×#156888562
C2×C47×#3272
C2×#150547