Finite Group Databasebeta

← C2×#20241803 #26182794

Subgroups — C2×#20241803 #26182794

Order 12032.

1354 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689670C211yesmaximal, characteristic
2C2×#15689175C211yesmaximal, characteristic, complemented
3C2×C4×#10625324C211yesmaximal, characteristic, complemented
4#20241803C218yesmaximal, direct product factor
5C2×#15688852C211yesmaximal, characteristic, complemented
6C2×D4⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
7C2×#15688850C211yesmaximal, characteristic, complemented
8C2×C47×D4⋊C8C211yesmaximal, characteristic, complemented
9C22×#10625350—21no—
10C22×#10625324—21no—
11#15689670—22no—
12#15689670—22no—
13#15689670C414yes—
14#15689670C2214yes—
15C2×#13094023C411yescharacteristic
16C2×#13094020C411yescharacteristic
17C2×#13094010—21no—
18C2×#13093999C411yescharacteristic
19C2×#13093997—21no—
20C2×#13093995C411yescharacteristic
21C2×C4×D188C2211yescharacteristic
22C2×C4×C22⋊D47—21no—
23C2×C42×D47C2211yescharacteristic
24#15689175—22no—
25#15689175C2214yescomplemented
26C2×C4⋊(C47⋊C8)C2211yescharacteristic
27C2×(C2×D47)⋊C8—21no—
28C4×#10625324—22no—
29C4×#10625324C2214yescomplemented
30C2×#13093934—21no—
31C2×C4×C47⋊C8C2211yescharacteristic
32C2×C8×Dic47—21no—
33#15688852C2214yescomplemented
34D4⋊(C47⋊C8)C2214yescomplemented
35#15688850C2214yescomplemented
36C2×C4×D4×C47C2211yescharacteristic
37C2×C4⋊C8×C47C2211yescharacteristic
38C2×C4×C8×C47C2211yescharacteristic
39C47×D4⋊C8C2214yescomplemented
40C2×#10625350—24no—
41C2×#10625350—24no—
42C2×#10625350—44no—
43C2×#10625350—44no—
44C22×Dic94—21no—
45C22×D188—21no—
46C22×D188C2×C411yescharacteristic
47C22×C22⋊D47—21no—
48C22×C22⋊D47—21no—
49C22×C22⋊D47—21no—
50C22×C4×D47—21no—
51C22×C4×D47C2×C411yescharacteristic
52C22×C4×D47D411yescharacteristic
53C22×C4×D47D411yescharacteristic
54C2×#10625324—28no—
55C2×#10625324—24no—
56C22×C47⋊C8—21no—
57C22×C47⋊C8—21no—
58#13094023—22no—
59#13094023C2×C414yes—
60#13094020—22no—
61#13094020C2×C414yes—
62#13094010—24no—
63#13094010—24no—
64#13093999—22no—
65#13093999C2×C414yes—
66#13093997—24no—
67#13093997—24no—
68#13093995—22no—
69#13093995C2×C414yes—
70C4×D188—21no—
71C4×D188—21no—
72C4×D188C2×C412yes—
73C4×D188C2312yes—
74C4×C22⋊D47—24no—
75C4×C22⋊D47—24no—
76C2×C4⋊Dic47C2×C411yescharacteristic
77C2×Dic47⋊C4—21no—
78C2×C22⋊Dic47—21no—
79C2×(C2×D47)⋊C4—21no—
80C2×(C2×D47)⋊C4—21no—
81C2×C4×Dic47C2×C411yescharacteristic
82C2×C4×Dic47D411yescharacteristic
83C2×C4×Dic47D411yescharacteristic
84C42×D47C2×C412yes—
85C42×D47D412yes—
86C42×D47D412yes—
87C42×D47C2312yes—
88C4⋊(C47⋊C8)—21no—
89C4⋊(C47⋊C8)C2312yes—
90(C2×D47)⋊C8—24no—
91#13093934—24no—
92C4×C47⋊C8—21no—
93C4×C47⋊C8C2312yes—
94C8×Dic47—24no—
95C22×D4×C47C2×C411yescharacteristic
96C23×C4×C47—21no—
97C22×C8×C47—21no—
98C22×C8×C47—21no—
99C4×D4×C47—21no—
100C4×D4×C47—21no—
101C4×D4×C47C2×C412yes—
102C4×D4×C47C2312yes—
103C2×C4⋊C4×C47C2×C411yescharacteristic
104C2×C22⋊C4×C47—21no—
105C2×C42×C47C2311yescharacteristic
106C4⋊C8×C47—21no—
107C4⋊C8×C47C2312yes—
108C4×C8×C47—21no—
109C4×C8×C47C2312yes—
110C24×C47—21no—
111C23×D47—21no—
112C23×D47C22⋊C411yescharacteristic
113C2×D4×C47—21no—
114C2×D4×C47—22no—
115C2×D4×C47—22no—
116C2×D4×C47C22×C412yes—
117C22×C4×C47—21no—
118C22×C4×C47—22no—
119C22×C4×C47—22no—
120C22×C4×C47—42no—
121C22×C4×C47—42no—
122C22×C4×C47C22×C411yescharacteristic
123C22×C4×C47C2×D411yescharacteristic
124C22×C4×C47C2×D411yescharacteristic
125C2×C22⋊D47—24no—
126C2×C22⋊D47—24no—
127C2×C22⋊D47—24no—
128C2×C22⋊D47—44no—
129C2×C22⋊D47—44no—
130C2×C22⋊D47—44no—
131C22×Dic47—21no—
132C22×Dic47C22⋊C411yescharacteristic
133C22×Dic47C22⋊C411yescharacteristic
134C22×Dic47C22⋊C411yescharacteristic
135#10625350—48no—
136#10625350—48no—
137#10625350—416no—
138C2×D188—22no—
139C2×D188—22no—
140C2×D188—24no—
141C2×D188—21no—
142C2×D188—44no—
143C2×D188C22×C412yes—
144C2×C4×D47—22no—
145C2×C4×D47—22no—
146C2×C4×D47—22no—
147C2×C4×D47—22no—
148C2×C4×D47—24no—
149C2×C4×D47—22no—
150C2×C4×D47—22no—
151C2×C4×D47—42no—
152C2×C4×D47—42no—
153C2×C4×D47C22⋊C412yes—
154C2×C4×D47C22⋊C412yes—
155C2×C4×D47C22⋊C412yes—
156C2×C4×D47C22×C412yes—
157C2×C4×D47C2×D412yes—
158C2×C4×D47C2×D412yes—
159C2×Dic94—24no—
160C2×Dic94—44no—
161C2×C8×C47—24no—
162C2×C8×C47—22no—
163C2×C8×C47—22no—
164C2×C8×C47—42no—
165C4⋊C4×C47—21no—
166C4⋊C4×C47C22×C412yes—
167C22⋊C4×C47—22no—
168C22⋊C4×C47—22no—
169C42×C47C22×C411yescharacteristic
170C42×C47C2×D411yescharacteristic
171C42×C47C2×D411yescharacteristic
172C42×C47C2411yescharacteristic
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×Dic47C2×D412yes—
185C4×Dic47C2×D412yes—
186C2×C47⋊C8—24no—
187C2×C47⋊C8—22no—
188C2×C47⋊C8—22no—
189C2×C47⋊C8—42no—
190#10625324—216no—
191C23×C47—22no—
192C23×C47—42no—
193C23×C47—42no—
194C23×C47—42no—
195C23×C47C2×C22⋊C411yescharacteristic
196C22×D47—22no—
197C22×D47—22no—
198C22×D47—22no—
199C22×D47—22no—
200C22×D47—42no—
201C22×D47—42no—
202C22×D47—42no—
203C22×D47C2×C22⋊C412yes—
204D4×C47—22no—
205D4×C47—22no—
206D4×C47—42no—
207C2×C4×C47—22no—
208C2×C4×C47—22no—
209C2×C4×C47—42no—
210C2×C4×C47—42no—
211C2×C4×C47—42no—
212C2×C4×C47—44no—
213C2×C4×C47C2×C22⋊C411yescharacteristic
214C2×C4×C47C2×C22⋊C411yescharacteristic
215C2×C4×C47C2×C22⋊C411yescharacteristic
216C2×C4×C47#13112yes—
217C2×C4×C47#13112yes—
218C2×C4×C47AGL(1,ℤ/8)12yes—
219C2×C4×C47AGL(1,ℤ/8)12yes—
220C2×C4×C47C23×C411yescharacteristic
221C2×C4×C47C22×D411yescharacteristic
222C2×C4×C47C22×D411yescharacteristic
223C22⋊D47—48no—
224C22⋊D47—48no—
225C22⋊D47—48no—
226C2×Dic47—22no—
227C2×Dic47—22no—
228C2×Dic47—22no—
229C2×Dic47—42no—
230C2×Dic47#10414yes—
231C2×Dic47C2×C22⋊C412yes—
232C2×Dic47C2×C22⋊C412yes—
233C2×Dic47C2×C22⋊C412yes—
234D188—22no—
235D188—22no—
236D188—48no—
237D188—42no—
238C4×D47—22no—
239C4×D47—22no—
240C4×D47—22no—
241C4×D47—22no—
242C4×D47—24no—
243C4×D47—24no—
244C4×D47—24no—
245C4×D47—24no—
246C4×D47—42no—
247C4×D47—42no—
248C4×D47—44no—
249Dic94—48no—
250C8×C47—24no—
251C8×C47—42no—
252C47⋊C8—24no—
253C47⋊C8—42no—
254C2×#1484—471nomaximal, Sylow
255C22×C47—42no—
256C22×C47—42no—
257C22×C47—42no—
258C22×C47—84no—
259C22×C47#40812yes—
260C22×C47#41812yes—
261C22×C47C2×#10412yes—
262C22×C47C22×C22⋊C411yescharacteristic
263C2×D47—22no—
264C2×D47—22no—
265C2×D47—22no—
266C2×D47—44no—
267C2×D47—42no—
268C2×D47—42no—
269C2×D47—42no—
270C2×D47—84no—
271C4×C47—21no—
272C4×C47—21no—
273C4×C47—42no—
274C4×C47#40812yes—
275C4×C47#41812yes—
276C4×C47C2×#13111yescharacteristic
277C4×C47C2×#13111yescharacteristic
278C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
279C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
280Dic47—22no—
281Dic47—22no—
282Dic47—42no—
283Dic47C2×#10414yes—
284C2×#532—471no—
285C2×#431—471no—
286C2×C4×M16—471no—
287#1484—478no—
288C2×D4⋊C8—471no—
289C2×D4⋊C8—471no—
290C2×D4⋊C8—471no—
291C2×D4⋊C8D4711yescharacteristic, complemented
292C2×C47—82no—
293C2×C47#148414yescomplemented
294C2×C47C2×#40811yescharacteristic
295C2×C47C2×#41811yescharacteristic
296C2×C47C22×#10411yescharacteristic
297D47—42no—
298D47—82no—
299C22×#41—941no—
300C22×M16—941no—
301#532—474no—
302#532—474no—
303#532—942no—
304#532—942no—
305C2×C4⋊Q8—471no—
306C2×#127—471no—
307C2×#124—941no—
308C2×#121—471no—
309C2×#121—471no—
310C2×#121—941no—
311C2×C4×D4—471no—
312C2×C4×D4—941no—
313C2×C4×D4C2×D4711yescharacteristic
314C22×C42—471no—
315#431—474no—
316#431—942no—
317C2×C4⋊C8—471no—
318C2×C4⋊C8C2×D4711yescharacteristic
319C2×C22⋊C8—941no—
320C4×M16—474no—
321C4×M16—942no—
322C2×#97—941no—
323C2×C4×C8—471no—
324C2×C4×C8—941no—
325C2×C4×C8C2×D4711yescharacteristic
326D4⋊C8—474no—
327D4⋊C8—474no—
328D4⋊C8—474no—
329D4⋊C8C2×D4714yescomplemented
330C47C2×#148411yescharacteristic, complemented, Sylow
331C2×#41—944no—
332C2×#41—944no—
333C2×#41—1884no—
334C2×#41—1884no—
335C22×Q8—941no—
336C22×D4—471no—
337C22×D4—941no—
338C22×D4—941no—
339C22×D4—941no—
340C22×D4—941no—
341C22×D4C4×D4711yescharacteristic
342C23×C4—21no—
343C23×C4—471no—
344C23×C4—471no—
345C23×C4—471no—
346C23×C4—941no—
347C2×M16—944no—
348C2×M16—948no—
349C22×C8—21no—
350C22×C8—21no—
351C22×C8—941no—
352C22×C8—941no—
353C4⋊Q8—474no—
354C4⋊Q8—942no—
355#127—474no—
356#127—942no—
357#124—944no—
358#124—944no—
359#121—474no—
360#121—474no—
361#121—944no—
362#121—944no—
363#121—942no—
364#121—942no—
365C4×D4—21no—
366C4×D4—21no—
367C4×D4—472no—
368C4×D4—472no—
369C4×D4—944no—
370C4×D4—944no—
371C4×D4—941no—
372C4×D4—941no—
373C4×D4C4×D4712yes—
374C4×D4C22×D4712yes—
375C2×C4⋊C4—471no—
376C2×C4⋊C4—941no—
377C2×C4⋊C4C4×D4711yescharacteristic
378C2×C22⋊C4—21no—
379C2×C22⋊C4—941no—
380C2×C22⋊C4—941no—
381C2×C22⋊C4—941no—
382C2×C42—471no—
383C2×C42—471no—
384C2×C42—471no—
385C2×C42—472no—
386C2×C42—472no—
387C2×C42—472no—
388C2×C42—472no—
389C2×C42C22×D4711yescharacteristic
390C4⋊C8—21no—
391C4⋊C8—472no—
392C4⋊C8—941no—
393C4⋊C8C22×D4712yes—
394C22⋊C8—944no—
395#97—944no—
396C4×C8—21no—
397C4×C8—472no—
398C4×C8—944no—
399C4×C8—941no—
400C4×C8C22×D4712yes—
401C24—21no—
402C24—471no—
403C24—941no—
404#41—18816no—
405#41—1888no—
406#41—1888no—
407C2×Q8—944no—
408C2×Q8—1884no—
409C2×D4—21no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—472no—
413C2×D4—944no—
414C2×D4—944no—
415C2×D4—944no—
416C2×D4—944no—
417C2×D4—941no—
418C2×D4—942no—
419C2×D4—942no—
420C2×D4—1884no—
421C2×D4—1884no—
422C2×D4—1884no—
423C2×D4—1884no—
424C2×D4C2×C4×D4712yes—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4—471no—
431C22×C4—471no—
432C22×C4—471no—
433C22×C4—472no—
434C22×C4—472no—
435C22×C4—472no—
436C22×C4—472no—
437C22×C4—472no—
438C22×C4—472no—
439C22×C4—944no—
440C22×C4—942no—
441C22×C4—942no—
442C22×C4—942no—
443C22×C4—942no—
444C22×C4—941no—
445C22×C4—942no—
446C22×C4—942no—
447C22×C4—1882no—
448C22×C4—1882no—
449C22×C4C2×C4×D4711yescharacteristic
450C22×C4D4×D4711yescharacteristic
451C22×C4D4×D4711yescharacteristic
452M16—9416no—
453C2×C8—24no—
454C2×C8—22no—
455C2×C8—22no—
456C2×C8—42no—
457C2×C8—944no—
458C2×C8—942no—
459C2×C8—942no—
460C2×C8—1882no—
461C4⋊C4—21no—
462C4⋊C4—472no—
463C4⋊C4—944no—
464C4⋊C4—941no—
465C4⋊C4C2×C4×D4712yes—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—944no—
469C22⋊C4—944no—
470C22⋊C4—942no—
471C22⋊C4—942no—
472C42—472no—
473C42—472no—
474C42—472no—
475C42—472no—
476C42—472no—
477C42—472no—
478C42C2×C4×D4711yescharacteristic
479C42D4×D4711yescharacteristic
480C42D4×D4711yescharacteristic
481C42C23×D4711yescharacteristic
482C23—22no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—472no—
487C23—942no—
488C23—942no—
489C23—942no—
490C23—942no—
491C23—1882no—
492C23—1882no—
493C23—1882no—
494C23C22⋊C4×D4711yescharacteristic
495Q8—1888no—
496D4—22no—
497D4—22no—
498D4—42no—
499D4—942no—
500D4—942no—
501D4—1888no—
502D4—1888no—
503D4—1888no—
504D4—1888no—
505D4—1882no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—42no—
509C2×C4—44no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—472no—
513C2×C4—474no—
514C2×C4—472no—
515C2×C4—472no—
516C2×C4—944no—
517C2×C4—944no—
518C2×C4—942no—
519C2×C4—942no—
520C2×C4—944no—
521C2×C4—942no—
522C2×C4—942no—
523C2×C4—944no—
524C2×C4—942no—
525C2×C4—942no—
526C2×C4—942no—
527C2×C4—1882no—
528C2×C4—1884no—
529C2×C4—1882no—
530C2×C4—1882no—
531C2×C4C22⋊C4×D4711yescharacteristic
532C2×C4C22⋊C4×D4711yescharacteristic
533C2×C4C22⋊C4×D4711yescharacteristic
534C2×C4#1309403012yes—
535C2×C4#1309403212yes—
536C2×C4#1309404812yes—
537C2×C4#1309405112yes—
538C2×C4C22×C4×D4711yescharacteristic
539C2×C4C2×D4×D4711yescharacteristic
540C2×C4C2×D4×D4711yescharacteristic
541C8—24no—
542C8—42no—
543C8—944no—
544C8—1882no—
545C22—42no—
546C22—42no—
547C22—42no—
548C22—84no—
549C22—942no—
550C22—942no—
551C22—942no—
552C22—3764no—
553C22—1882no—
554C22—1882no—
555C22—1882no—
556C22—1884no—
557C22#1568908812yes—
558C22#1568912612yes—
559C22#104×D4712yes—
560C22C2×C22⋊C4×D4711yescharacteristic
561C4—21no—
562C4—21no—
563C4—42no—
564C4—474no—
565C4—942no—
566C4—942no—
567C4—1882no—
568C4#1568908812yes—
569C4#1568912612yes—
570C4C2×#1309403011yescharacteristic
571C4C2×#1309403211yescharacteristic
572C4C2×#1309404811yescharacteristic
573C4C2×#1309405111yescharacteristic
574C2—82no—
575C2—3762no—
576C2—1882no—
577C2#2024180314yesdirect product factor
578C2C2×#1568908811yescharacteristic
579C2C2×#1568912611yescharacteristic
580C2C2×#104×D4711yescharacteristic
subgroupG/H
centerC22×C4D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC2×C47×D4⋊C8C2
socleC23×C47C2×C22⋊C4
prime radicalC2×#15689670C2
cosocleC42×C47C24
hypercenterC2×D4⋊C8D47
hypocenterC47C2×#1484
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#15689175C2semidirect
3. C2×C4×#10625324C2semidirect
4. #20241803C2direct (N × H)
5. C2×#15688852C2semidirect
6. C2×D4⋊(C47⋊C8)C2semidirect
7. C2×#15688850C2semidirect
8. C2×C47×D4⋊C8C2semidirect
25. #15689175C22semidirect
29. C4×#10625324C22semidirect
33. #15688852C22semidirect
34. D4⋊(C47⋊C8)C22semidirect
35. #15688850C22semidirect
39. C47×D4⋊C8C22semidirect
291. C2×D4⋊C8D47semidirect
293. C2×C47#1484semidirect
329. D4⋊C8C2×D47semidirect
330. C47C2×#1484semidirect
577. C2#20241803direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896702
C2×#156891752
C2×C4×#106253242
#202418032
C2×#156888522
C2×D4⋊(C47⋊C8)2
C2×#156888502
C2×C47×D4⋊C82
C2×#148447