Finite Group Databasebeta

← C2×C4×#13093939 #26213924

Subgroups — C2×C4×#13093939 #26213924

Order 12032.

2242 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093939C212yesmaximal
2C2×C4×C22⋊Dic47C212yesmaximal, complemented
3C4×#13093939C218yesmaximal, direct product factor
4C2×#15688890C212yesmaximal, complemented
5C22×C4×D4×C47C211yesmaximal, characteristic
6C22×C22⋊Dic47C2214yes—
7C22×C4×Dic47—22no—
8C2×#13093939C4116yesdirect product factor
9C2×#13093939C2218yes—
10C4×C22⋊Dic47—24no—
11C4×C22⋊Dic47C2218yescomplemented
12C2×C47⋊#95—22no—
13#15688890C2218yescomplemented
14C23×D4×C47C2211yescharacteristic
15C24×C4×C47C411yescharacteristic, complemented
16C24×C4×C47C2211yescharacteristic
17C2×C4×D4×C47—22no—
18C2×C4×D4×C47—22no—
19C2×C4×D4×C47—24no—
20C2×C4×D4×C47C414yescomplemented
21C2×C4×D4×C47C2214yes—
22C22×C4⋊C4×C47C411yescharacteristic, complemented
23C22×C22⋊C4×C47C411yescharacteristic, complemented
24C22×C22⋊C4×C47C2211yescharacteristic
25C22×C42×C47C411yescharacteristic, complemented
26C23×Dic47—24no—
27C2×C22⋊Dic47—24no—
28C2×C22⋊Dic47—28no—
29C2×C22⋊Dic47C2×C4116yescomplemented
30C2×C22⋊Dic47C2318yes—
31C2×C4×Dic47—28no—
32C2×C4×Dic47—48no—
33#13093939C2×C4132yesdirect product factor
34C47⋊#95—28no—
35C25×C47C2×C411yescharacteristic
36C25×C47C2311yescharacteristic
37C22×D4×C47—22no—
38C22×D4×C47—22no—
39C22×D4×C47—24no—
40C22×D4×C47C2×C418yes—
41C22×D4×C47C2×C412yes—
42C22×D4×C47C2312yes—
43C23×C4×C47—22no—
44C23×C4×C47—21no—
45C23×C4×C47—21no—
46C23×C4×C47—44no—
47C23×C4×C47—44no—
48C23×C4×C47C2×C411yescharacteristic
49C23×C4×C47C2×C411yescharacteristic
50C23×C4×C47C2×C411yescharacteristic
51C23×C4×C47C2×C411yescharacteristic
52C23×C4×C47C2×C411yescharacteristic
53C23×C4×C47C2×C412yes—
54C23×C4×C47C2×C414yescomplemented
55C23×C4×C47D412yes—
56C23×C4×C47D412yes—
57C23×C4×C47D414yes—
58C23×C4×C47C2312yes—
59C4×D4×C47—28no—
60C4×D4×C47—28no—
61C4×D4×C47—28no—
62C4×D4×C47—28no—
63C2×C4⋊C4×C47—22no—
64C2×C4⋊C4×C47—22no—
65C2×C4⋊C4×C47C2×C414yescomplemented
66C2×C22⋊C4×C47—22no—
67C2×C22⋊C4×C47—22no—
68C2×C22⋊C4×C47—22no—
69C2×C22⋊C4×C47—22no—
70C2×C22⋊C4×C47C2×C412yes—
71C2×C22⋊C4×C47C2×C414yescomplemented
72C2×C22⋊C4×C47C2312yes—
73C2×C42×C47—21no—
74C2×C42×C47—22no—
75C2×C42×C47—21no—
76C2×C42×C47C2×C414yescomplemented
77C24×C47—21no—
78C24×C47—21no—
79C24×C47—22no—
80C24×C47—42no—
81C24×C47—42no—
82C24×C47—42no—
83C24×C47—42no—
84C24×C47C4214yescomplemented
85C24×C47C22×C411yescharacteristic
86C24×C47C22×C412yes—
87C24×C47C22×C411yescharacteristic
88C24×C47C22×C414yes—
89C24×C47C2×D412yes—
90C24×C47C2×D412yes—
91C24×C47#4114yes—
92C24×C47C2411yescharacteristic
93C2×D4×C47—24no—
94C2×D4×C47—24no—
95C2×D4×C47—216no—
96C2×D4×C47—216no—
97C2×D4×C47—24no—
98C2×D4×C47—24no—
99C2×D4×C47C4218yescomplemented
100C2×D4×C47C22×C418yes—
101C22×C4×C47—21no—
102C22×C4×C47—21no—
103C22×C4×C47—22no—
104C22×C4×C47—24no—
105C22×C4×C47—28no—
106C22×C4×C47—21no—
107C22×C4×C47—21no—
108C22×C4×C47—21no—
109C22×C4×C47—21no—
110C22×C4×C47—24no—
111C22×C4×C47—24no—
112C22×C4×C47—44no—
113C22×C4×C47—48no—
114C22×C4×C47—44no—
115C22×C4×C47—42no—
116C22×C4×C47—44no—
117C22×C4×C47—44no—
118C22×C4×C47—48no—
119C22×C4×C47—48no—
120C22×C4×C47—44no—
121C22×C4×C47—42no—
122C22×C4×C47—42no—
123C22×C4×C47C4214yescomplemented
124C22×C4×C47C22⋊C411yescharacteristic
125C22×C4×C47C22⋊C412yes—
126C22×C4×C47C22⋊C412yes—
127C22×C4×C47C22⋊C414yes—
128C22×C4×C47C22⋊C412yes—
129C22×C4×C47C22⋊C414yes—
130C22×C4×C47C22⋊C411yescharacteristic
131C22×C4×C47C22×C412yes—
132C22×C4×C47C22×C412yes—
133C22×C4×C47C22×C412yes—
134C22×C4×C47C22×C412yes—
135C22×C4×C47C22×C412yes—
136C22×C4×C47C2×D414yes—
137C22×C4×C47C2×D414yes—
138C22×Dic47—216no—
139C22×Dic47—28no—
140C22×Dic47—48no—
141C22×Dic47—48no—
142C4⋊C4×C47—28no—
143C22⋊C4×C47—24no—
144C22⋊C4×C47—24no—
145C22⋊C4×C47—28no—
146C42×C47—24no—
147C42×C47—24no—
148C22⋊Dic47—216no—
149C22⋊Dic47—28no—
150C22⋊Dic47C22×C4116yescomplemented
151C4×Dic47—416no—
152C23×C47—24no—
153C23×C47—22no—
154C23×C47—24no—
155C23×C47—22no—
156C23×C47—22no—
157C23×C47—22no—
158C23×C47—24no—
159C23×C47—24no—
160C23×C47—41no—
161C23×C47—42no—
162C23×C47—41no—
163C23×C47—48no—
164C23×C47—41no—
165C23×C47—42no—
166C23×C47—48no—
167C23×C47—41no—
168C23×C47—42no—
169C23×C47—48no—
170C23×C47—42no—
171C23×C47—42no—
172C23×C47—42no—
173C23×C47—48no—
174C23×C47—42no—
175C23×C47—42no—
176C23×C47C2×C4212yes—
177C23×C47C2×C4212yes—
178C23×C47C2×C4214yescomplemented
179C23×C47C2×C22⋊C412yes—
180C23×C47C2×C22⋊C411yescharacteristic
181C23×C47C2×C22⋊C411yescharacteristic
182C23×C47#11712yes—
183C23×C47#11712yes—
184C23×C47C4×D418yes—
185C23×C47C4×D418yes—
186C23×C47C23×C412yes—
187C23×C47C23×C411yescharacteristic
188C23×C47C22×D412yes—
189C23×C47C2×#4112yes—
190D4×C47—216no—
191D4×C47—216no—
192C2×C4×C47—22no—
193C2×C4×C47—22no—
194C2×C4×C47—24no—
195C2×C4×C47—24no—
196C2×C4×C47—22no—
197C2×C4×C47—24no—
198C2×C4×C47—28no—
199C2×C4×C47—24no—
200C2×C4×C47—24no—
201C2×C4×C47—28no—
202C2×C4×C47—22no—
203C2×C4×C47—22no—
204C2×C4×C47—44no—
205C2×C4×C47—42no—
206C2×C4×C47—42no—
207C2×C4×C47—44no—
208C2×C4×C47—48no—
209C2×C4×C47—42no—
210C2×C4×C47—42no—
211C2×C4×C47—42no—
212C2×C4×C47—42no—
213C2×C4×C47—48no—
214C2×C4×C47—42no—
215C2×C4×C47—42no—
216C2×C4×C47#9914yescomplemented
217C2×C4×C47C2×C4214yescomplemented
218C2×C4×C47C2×C22⋊C412yes—
219C2×C4×C47C2×C22⋊C414yes—
220C2×C4×C47C2×C22⋊C412yes—
221C2×Dic47—216no—
222C2×Dic47—48no—
223C2×Dic47—48no—
224C2×Dic47—432no—
225C2×C4×#99—471nomaximal, Sylow
226C22×C47—22no—
227C22×C47—21no—
228C22×C47—21no—
229C22×C47—22no—
230C22×C47—22no—
231C22×C47—21no—
232C22×C47—21no—
233C22×C47—22no—
234C22×C47—216no—
235C22×C47—24no—
236C22×C47—24no—
237C22×C47—24no—
238C22×C47—42no—
239C22×C47—42no—
240C22×C47—48no—
241C22×C47—42no—
242C22×C47—42no—
243C22×C47—44no—
244C22×C47—44no—
245C22×C47—48no—
246C22×C47—42no—
247C22×C47—42no—
248C22×C47—48no—
249C22×C47C4×C22⋊C412yes—
250C22×C47C4×C22⋊C414yes—
251C22×C47C4×C22⋊C412yes—
252C22×C47C2×#9912yes—
253C22×C47#41012yes—
254C22×C47C22×C4211yescharacteristic
255C22×C47C22×C22⋊C411yescharacteristic
256C22×C47C2×#11711yescharacteristic
257C22×C47C2×C4×D414yes—
258C4×C47—22no—
259C4×C47—24no—
260C4×C47—24no—
261C4×C47—42no—
262C4×C47—42no—
263C4×C47C2×#9914yescomplemented
264Dic47—416no—
265C22×C4×D4D4711yescharacteristic
266C22×#99—472no—
267C2×C4×C22⋊C4—472no—
268C4×#99—478no—
269C2×#342—472no—
270C2×C47—24no—
271C2×C47—21no—
272C2×C47—22no—
273C2×C47—21no—
274C2×C47—24no—
275C2×C47—44no—
276C2×C47C4×#9914yescomplemented
277C2×C47C2×C4×C22⋊C411yescharacteristic
278C2×C47C22×#9911yescharacteristic
279C2×C47C2×#41011yescharacteristic
280C23×D4C2×D4711yescharacteristic
281C24×C4Dic4711yescharacteristic, complemented
282C24×C4C2×D4711yescharacteristic
283C2×C4×D4—22no—
284C2×C4×D4—24no—
285C2×C4×D4—22no—
286C2×C4×D4Dic4714yescomplemented
287C2×C4×D4C2×D4714yes—
288C22×C4⋊C4Dic4711yescharacteristic, complemented
289C22×C22⋊C4—474no—
290C22×C22⋊C4Dic4711yescharacteristic, complemented
291C22×C22⋊C4C2×D4711yescharacteristic
292C22×C42—942no—
293C22×C42Dic4711yescharacteristic, complemented
294C2×#99—4716no—
295C2×#99—478no—
296C4×C22⋊C4—478no—
297C4×C22⋊C4—944no—
298C2×#95—942no—
299#342—478no—
300C47C2×C4×#9911yescharacteristic, complemented, Sylow
301C25C2×Dic4711yescharacteristic
302C25C22×D4711yescharacteristic
303C22×D4—24no—
304C22×D4—22no—
305C22×D4—22no—
306C22×D4C4×D4718yes—
307C22×D4C2×Dic4712yes—
308C22×D4C22×D4712yes—
309C23×C4—22no—
310C23×C4—21no—
311C23×C4—21no—
312C23×C4—44no—
313C23×C4—44no—
314C23×C4—944no—
315C23×C4C2×Dic4711yescharacteristic
316C23×C4C2×Dic4711yescharacteristic
317C23×C4C2×Dic4711yescharacteristic
318C23×C4C2×Dic4711yescharacteristic
319C23×C4C2×Dic4711yescharacteristic
320C23×C4C2×Dic4712yes—
321C23×C4C2×Dic4714yescomplemented
322C23×C4C22⋊D4712yes—
323C23×C4C22⋊D4712yes—
324C23×C4C22⋊D4714yes—
325C23×C4C22×D4712yes—
326C4×D4—28no—
327C4×D4—28no—
328C4×D4—28no—
329C4×D4—28no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4C2×Dic4714yescomplemented
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—4716no—
338C2×C22⋊C4—478no—
339C2×C22⋊C4—948no—
340C2×C22⋊C4—944no—
341C2×C22⋊C4C2×Dic4712yes—
342C2×C22⋊C4C2×Dic4714yescomplemented
343C2×C22⋊C4C22×D4712yes—
344C2×C42—21no—
345C2×C42—22no—
346C2×C42—21no—
347C2×C42—948no—
348C2×C42—1888no—
349C2×C42C2×Dic4714yescomplemented
350#99—4732no—
351#95—948no—
352C24—21no—
353C24—21no—
354C24—22no—
355C24—42no—
356C24—42no—
357C24—42no—
358C24—42no—
359C24C4×Dic4714yescomplemented
360C24C2×C4×D4714yes—
361C24#1062535014yes—
362C24C22×Dic4711yescharacteristic
363C24C22×Dic4712yes—
364C24C22×Dic4711yescharacteristic
365C24C2×C22⋊D4712yes—
366C24C2×C22⋊D4712yes—
367C24C23×D4711yescharacteristic
368C2×D4—24no—
369C2×D4—24no—
370C2×D4—216no—
371C2×D4—216no—
372C2×D4—24no—
373C2×D4—24no—
374C2×D4C4×Dic4718yescomplemented
375C2×D4C2×C4×D4718yes—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—28no—
380C22×C4—24no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—24no—
386C22×C4—24no—
387C22×C4—44no—
388C22×C4—48no—
389C22×C4—44no—
390C22×C4—42no—
391C22×C4—44no—
392C22×C4—44no—
393C22×C4—48no—
394C22×C4—48no—
395C22×C4—44no—
396C22×C4—42no—
397C22×C4—42no—
398C22×C4—9416no—
399C22×C4—948no—
400C22×C4—1888no—
401C22×C4—1888no—
402C22×C4C4×Dic4714yescomplemented
403C22×C4C22⋊Dic4711yescharacteristic
404C22×C4C22⋊Dic4712yes—
405C22×C4C22⋊Dic4712yes—
406C22×C4C22⋊Dic4714yes—
407C22×C4C22⋊Dic4712yes—
408C22×C4C22⋊Dic4714yes—
409C22×C4C22⋊Dic4711yescharacteristic
410C22×C4C22×Dic4712yes—
411C22×C4C22×Dic4712yes—
412C22×C4C22×Dic4712yes—
413C22×C4C22×Dic4712yes—
414C22×C4C22×Dic4712yes—
415C22×C4C2×C22⋊D4714yes—
416C22×C4C2×C22⋊D4714yes—
417C4⋊C4—28no—
418C22⋊C4—24no—
419C22⋊C4—24no—
420C22⋊C4—28no—
421C22⋊C4—4716no—
422C22⋊C4—9416no—
423C22⋊C4—948no—
424C42—24no—
425C42—24no—
426C42—18816no—
427C23—22no—
428C23—24no—
429C23—22no—
430C23—24no—
431C23—24no—
432C23—24no—
433C23—22no—
434C23—22no—
435C23—41no—
436C23—42no—
437C23—41no—
438C23—48no—
439C23—48no—
440C23—41no—
441C23—42no—
442C23—41no—
443C23—42no—
444C23—48no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23—48no—
449C23—42no—
450C23—42no—
451C23C2×C4×Dic4712yes—
452C23C2×C4×Dic4712yes—
453C23C2×C4×Dic4714yescomplemented
454C23C2×C22⋊Dic4712yes—
455C23C2×C22⋊Dic4711yescharacteristic
456C23C2×C22⋊Dic4711yescharacteristic
457C23#1309398312yes—
458C23#1309398312yes—
459C23C4×C22⋊D4718yes—
460C23C4×C22⋊D4718yes—
461C23C22×C4×D4712yes—
462C23C23×Dic4711yescharacteristic
463C23C22×C22⋊D4712yes—
464C23C2×#1062535012yes—
465D4—216no—
466D4—216no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—24no—
473C2×C4—28no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—28no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—44no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—44no—
483C2×C4—48no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—48no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—9416no—
492C2×C4—1888no—
493C2×C4—1888no—
494C2×C4—18832no—
495C2×C4#1309393914yesdirect product factor
496C2×C4C2×C4×Dic4714yescomplemented
497C2×C4C2×C22⋊Dic4712yes—
498C2×C4C2×C22⋊Dic4714yes—
499C2×C4C2×C22⋊Dic4712yes—
500C22—21no—
501C22—21no—
502C22—22no—
503C22—22no—
504C22—21no—
505C22—21no—
506C22—22no—
507C22—22no—
508C22—216no—
509C22—24no—
510C22—24no—
511C22—24no—
512C22—42no—
513C22—42no—
514C22—48no—
515C22—42no—
516C22—42no—
517C22—44no—
518C22—48no—
519C22—44no—
520C22—42no—
521C22—42no—
522C22—48no—
523C22C4×C22⋊Dic4712yes—
524C22C4×C22⋊Dic4714yes—
525C22C4×C22⋊Dic4712yes—
526C22C2×#1309393912yes—
527C22#1568909712yes—
528C22C22×C4×Dic4711yescharacteristic
529C22C22×C22⋊Dic4711yescharacteristic
530C22C2×#1309398311yescharacteristic
531C22C2×C4×C22⋊D4714yes—
532C4—22no—
533C4—24no—
534C4—24no—
535C4—42no—
536C4—42no—
537C4—18816no—
538C4C2×#1309393914yesdirect product factor
539C2—24no—
540C2—22no—
541C2—21no—
542C2—21no—
543C2—24no—
544C2—44no—
545C2C4×#1309393914yesdirect product factor
546C2C2×C4×C22⋊Dic4711yescharacteristic
547C2C22×#1309393911yescharacteristic
548C2C2×#1568909711yescharacteristic
subgroupG/H
centerC22×C4C22⋊Dic47
commutatorC22×C47C22×C42
FrattiniC24C23×D47
FittingC22×C4×D4×C47C2
socleC23×C47C2×C22⋊C4
prime radicalC23×D4×C47C22
cosocleC24×C47C24
hypercenterC22×C4×D4D47
hypocenterC47C2×C4×#99
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊Dic47C2semidirect
3. C4×#13093939C2direct (N × H)
4. C2×#15688890C2semidirect
8. C2×#13093939C4direct (N × H)
11. C4×C22⋊Dic47C22semidirect
13. #15688890C22semidirect
15. C24×C4×C47C4semidirect
20. C2×C4×D4×C47C4semidirect
22. C22×C4⋊C4×C47C4semidirect
23. C22×C22⋊C4×C47C4semidirect
25. C22×C42×C47C4semidirect
29. C2×C22⋊Dic47C2×C4semidirect
33. #13093939C2×C4direct (N × H)
54. C23×C4×C47C2×C4semidirect
65. C2×C4⋊C4×C47C2×C4semidirect
71. C2×C22⋊C4×C47C2×C4semidirect
76. C2×C42×C47C2×C4semidirect
84. C24×C47C42semidirect
99. C2×D4×C47C42semidirect
123. C22×C4×C47C42semidirect
150. C22⋊Dic47C22×C4semidirect
178. C23×C47C2×C42semidirect
216. C2×C4×C47#99semidirect
217. C2×C4×C47C2×C42semidirect
263. C4×C47C2×#99semidirect
276. C2×C47C4×#99semidirect
281. C24×C4Dic47semidirect
286. C2×C4×D4Dic47semidirect
288. C22×C4⋊C4Dic47semidirect
290. C22×C22⋊C4Dic47semidirect
293. C22×C42Dic47semidirect
300. C47C2×C4×#99semidirect
321. C23×C4C2×Dic47semidirect
332. C2×C4⋊C4C2×Dic47semidirect
342. C2×C22⋊C4C2×Dic47semidirect
349. C2×C42C2×Dic47semidirect
359. C24C4×Dic47semidirect
374. C2×D4C4×Dic47semidirect
402. C22×C4C4×Dic47semidirect
453. C23C2×C4×Dic47semidirect
495. C2×C4#13093939direct (N × H)
496. C2×C4C2×C4×Dic47semidirect
538. C4C2×#13093939direct (N × H)
545. C2C4×#13093939direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130939392
C2×C4×C22⋊Dic472
C4×#130939392
C2×#156888902
C22×C4×D4×C472
C2×C4×#9947