Finite Group Databasebeta

← C2×#20241756 #26182254

Subgroups — C2×#20241756 #26182254

Order 12032.

1066 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094019C211yesmaximal, characteristic
2C2×#15689177C211yesmaximal, characteristic, complemented
3C2×#15689173C211yesmaximal, characteristic, complemented
4#20241756C218yesmaximal, direct product factor
5C2×#15688849C211yesmaximal, characteristic, complemented
6C2×#15688846C211yesmaximal, characteristic
7C2×#15688846C211yesmaximal, characteristic
8C2×C47×#324C211yesmaximal, characteristic, complemented
9C2×#13094019—21no—
10C2×#13094019—21no—
11C2×#13094019—21no—
12C2×#13094019—21no—
13C2×#13094019—22no—
14C2×#13094019—22no—
15C2×#13094019C414yes—
16C2×#13094019C2214yes—
17C22×C4⋊Dic47C411yescharacteristic
18C22×Dic47⋊C4C411yescharacteristic
19C22×(C2×D47)⋊C4C411yescharacteristic
20C22×(C2×D47)⋊C4C411yescharacteristic
21C22×(C2×D47)⋊C4C2211yescharacteristic
22C22×C4×Dic47C2211yescharacteristic
23#15689177—22no—
24#15689177C2214yescomplemented
25#15689173—22no—
26#15689173C2214yescomplemented
27C2×Dic47⋊C8—21no—
28C2×Dic47⋊C8—21no—
29C2×C22⋊(C47⋊C8)C2211yescharacteristic
30C2×C22⋊(C47⋊C8)C2211yescharacteristic
31C2×#13093934—21no—
32C2×C8×Dic47—21no—
33#15688849C2214yescomplemented
34#15688846C2214yes—
35#15688846C2214yes—
36C22×C4⋊C4×C47C2211yescharacteristic
37C2×C22⋊C8×C47C2211yescharacteristic
38C2×C22⋊C8×C47C2211yescharacteristic
39C47×#324C2214yescomplemented
40C24×D47C2×C411yescharacteristic
41C23×Dic47C2×C411yescharacteristic
42C23×Dic47C2×C411yescharacteristic
43C23×Dic47C2×C411yescharacteristic
44C22×C47⋊C8—21no—
45C22×C47⋊C8—21no—
46#13094019—24no—
47#13094019—24no—
48#13094019—24no—
49#13094019—24no—
50#13094019—24no—
51#13094019—24no—
52#13094019—24no—
53#13094019—24no—
54C2×C4⋊Dic47—21no—
55C2×C4⋊Dic47—21no—
56C2×C4⋊Dic47—22no—
57C2×C4⋊Dic47C2×C414yes—
58C2×Dic47⋊C4—22no—
59C2×Dic47⋊C4—21no—
60C2×Dic47⋊C4—21no—
61C2×Dic47⋊C4C2×C414yes—
62C2×(C2×D47)⋊C4—21no—
63C2×(C2×D47)⋊C4—21no—
64C2×(C2×D47)⋊C4—21no—
65C2×(C2×D47)⋊C4—21no—
66C2×(C2×D47)⋊C4—22no—
67C2×(C2×D47)⋊C4—21no—
68C2×(C2×D47)⋊C4—21no—
69C2×(C2×D47)⋊C4—21no—
70C2×(C2×D47)⋊C4—21no—
71C2×(C2×D47)⋊C4—22no—
72C2×(C2×D47)⋊C4C2×C414yes—
73C2×(C2×D47)⋊C4C2×C414yes—
74C2×(C2×D47)⋊C4C2×C412yes—
75C2×(C2×D47)⋊C4C2312yes—
76C2×C4×Dic47C2×C412yes—
77C2×C4×Dic47D411yescharacteristic
78C2×C4×Dic47D411yescharacteristic
79C2×C4×Dic47D411yescharacteristic
80C2×C4×Dic47D411yescharacteristic
81C2×C4×Dic47D412yes—
82C2×C4×Dic47D412yes—
83C2×C4×Dic47C2312yes—
84Dic47⋊C8—24no—
85Dic47⋊C8—24no—
86C22⋊(C47⋊C8)—21no—
87C22⋊(C47⋊C8)—21no—
88C22⋊(C47⋊C8)C2312yes—
89C22⋊(C47⋊C8)C2312yes—
90#13093934—24no—
91C8×Dic47—24no—
92C23×C4×C47C2×C411yescharacteristic
93C23×C4×C47C2×C411yescharacteristic
94C23×C4×C47C2311yescharacteristic
95C22×C8×C47—21no—
96C22×C8×C47—21no—
97C2×C4⋊C4×C47—21no—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47—21no—
100C2×C4⋊C4×C47—21no—
101C2×C4⋊C4×C47C2×C412yes—
102C2×C4⋊C4×C47C2312yes—
103C22⋊C8×C47—21no—
104C22⋊C8×C47—21no—
105C22⋊C8×C47C2312yes—
106C22⋊C8×C47C2312yes—
107C24×C47C22×C411yescharacteristic
108C23×D47—21no—
109C23×D47—21no—
110C23×D47—22no—
111C23×D47—22no—
112C23×D47—42no—
113C23×D47—42no—
114C23×D47C22×C412yes—
115C22×C4×C47—21no—
116C22×C4×C47—21no—
117C22×C4×C47—21no—
118C22×C4×C47—21no—
119C22×C4×C47—22no—
120C22×C4×C47—22no—
121C22×C4×C47—42no—
122C22×C4×C47—42no—
123C22×C4×C47C22×C412yes—
124C22×C4×C47C22×C412yes—
125C22×C4×C47C22×C411yescharacteristic
126C22×C4×C47C2×D411yescharacteristic
127C22×C4×C47C2×D411yescharacteristic
128C22×C4×C47C2×D411yescharacteristic
129C22×C4×C47C2×D411yescharacteristic
130C22×C4×C47C2411yescharacteristic
131C22×Dic47—22no—
132C22×Dic47—22no—
133C22×Dic47—21no—
134C22×Dic47—21no—
135C22×Dic47—42no—
136C22×Dic47—42no—
137C22×Dic47C22⋊C412yes—
138C22×Dic47C22⋊C411yescharacteristic
139C22×Dic47C22⋊C411yescharacteristic
140C22×Dic47C22⋊C411yescharacteristic
141C22×Dic47C22⋊C411yescharacteristic
142C22×Dic47C22⋊C412yes—
143C22×Dic47C22×C412yes—
144C22×Dic47C22×C412yes—
145C22×Dic47C22×C412yes—
146C2×C8×C47—22no—
147C2×C8×C47—22no—
148C2×C8×C47—42no—
149C2×C8×C47—42no—
150C4⋊C4×C47—22no—
151C4⋊C4×C47—22no—
152C4⋊C4×C47—22no—
153C4⋊C4×C47—22no—
154(C2×D47)⋊C4—22no—
155(C2×D47)⋊C4—22no—
156(C2×D47)⋊C4—22no—
157(C2×D47)⋊C4—22no—
158(C2×D47)⋊C4—24no—
159(C2×D47)⋊C4—24no—
160(C2×D47)⋊C4—24no—
161(C2×D47)⋊C4—24no—
162C4⋊Dic47—24no—
163C4⋊Dic47—24no—
164Dic47⋊C4—24no—
165Dic47⋊C4—24no—
166C4×Dic47C22⋊C412yes—
167C4×Dic47C22⋊C412yes—
168C4×Dic47C22⋊C412yes—
169C4×Dic47C22⋊C412yes—
170C4×Dic47C2×D412yes—
171C4×Dic47C2×D412yes—
172C4×Dic47C2×D412yes—
173C4×Dic47C2×D412yes—
174C2×C47⋊C8—22no—
175C2×C47⋊C8—22no—
176C2×C47⋊C8—42no—
177C2×C47⋊C8—42no—
178C23×C47—22no—
179C23×C47—22no—
180C23×C47C2×C22⋊C411yescharacteristic
181C23×C47C2×C22⋊C411yescharacteristic
182C23×C47#13112yes—
183C23×C47#13112yes—
184C23×C47C23×C411yescharacteristic
185C22×D47—22no—
186C22×D47—22no—
187C22×D47—22no—
188C22×D47—42no—
189C22×D47—42no—
190C22×D47—42no—
191C22×D47—42no—
192C22×D47—42no—
193C22×D47—42no—
194C22×D47—42no—
195C22×D47—42no—
196C22×D47—84no—
197C22×D47—84no—
198C2×C4×C47—22no—
199C2×C4×C47—22no—
200C2×C4×C47—22no—
201C2×C4×C47—22no—
202C2×C4×C47—22no—
203C2×C4×C47—22no—
204C2×C4×C47—41no—
205C2×C4×C47—41no—
206C2×C4×C47—41no—
207C2×C4×C47—41no—
208C2×C4×C47—42no—
209C2×C4×C47—42no—
210C2×C4×C47—42no—
211C2×C4×C47—42no—
212C2×C4×C47—42no—
213C2×C4×C47C2×C22⋊C411yescharacteristic
214C2×C4×C47C2×C22⋊C411yescharacteristic
215C2×C4×C47C22×D411yescharacteristic
216C2×C4×C47C22×D411yescharacteristic
217C2×Dic47—22no—
218C2×Dic47—22no—
219C2×Dic47—24no—
220C2×Dic47—22no—
221C2×Dic47—22no—
222C2×Dic47—22no—
223C2×Dic47—22no—
224C2×Dic47—22no—
225C2×Dic47—42no—
226C2×Dic47—42no—
227C2×Dic47—42no—
228C2×Dic47—42no—
229C2×Dic47—42no—
230C2×Dic47C2×C22⋊C412yes—
231C2×Dic47C2×C22⋊C412yes—
232C2×Dic47C2×C22⋊C412yes—
233C2×Dic47C2×C22⋊C412yes—
234C8×C47—42no—
235C8×C47—42no—
236C47⋊C8—42no—
237C47⋊C8—42no—
238C2×#1473—471nomaximal, Sylow
239C22×C47—21no—
240C22×C47—21no—
241C22×C47—21no—
242C22×C47—21no—
243C22×C47—24no—
244C22×C47—24no—
245C22×C47#40812yes—
246C22×C47#40812yes—
247C22×C47#41012yes—
248C22×C47#41312yes—
249C22×C47C22×C22⋊C411yescharacteristic
250C22×C47C2×#13111yescharacteristic
251C22×C47C2×#13111yescharacteristic
252C2×D47—42no—
253C2×D47—42no—
254C2×D47—42no—
255C2×D47—84no—
256C2×D47—84no—
257C2×D47—82no—
258C2×D47—82no—
259C4×C47—21no—
260C4×C47—21no—
261C4×C47—21no—
262C4×C47—21no—
263C4×C47—42no—
264C4×C47—42no—
265Dic47—22no—
266Dic47—22no—
267Dic47—22no—
268Dic47—22no—
269Dic47—42no—
270C22×#126—471no—
271C2×#432—471no—
272C2×#431—471no—
273#1473—478no—
274C2×#324—471no—
275C2×#324D4711yescharacteristic, complemented
276C2×#323—471no—
277C2×#323—471no—
278C2×C47—21no—
279C2×C47—21no—
280C2×C47—22no—
281C2×C47#147314yescomplemented
282C2×C47C2×#40811yescharacteristic
283C2×C47C2×#41011yescharacteristic
284C2×C47C2×#41311yescharacteristic
285D47—82no—
286C2×#126—474no—
287C2×#126—474no—
288C2×#126—941no—
289C2×#126—941no—
290C2×#126—941no—
291C2×#126—941no—
292C2×#126—942no—
293C2×#126—942no—
294C22×C4⋊C4—471no—
295C22×C4⋊C4—471no—
296C22×C4⋊C4C2×D4711yescharacteristic
297C22×C22⋊C4—471no—
298C22×C22⋊C4—471no—
299C22×C22⋊C4—471no—
300C22×C42—471no—
301#432—474no—
302#432—942no—
303#431—474no—
304#431—942no—
305C2×C4⋊C8—941no—
306C2×C4⋊C8—941no—
307C2×C22⋊C8—471no—
308C2×C22⋊C8—471no—
309C2×C22⋊C8C2×D4711yescharacteristic
310C2×C22⋊C8C2×D4711yescharacteristic
311C2×#97—941no—
312C2×C4×C8—941no—
313#324—474no—
314#324C2×D4714yescomplemented
315#323—474no—
316#323—474no—
317C47C2×#147311yescharacteristic, complemented, Sylow
318C25—471no—
319C23×C4—471no—
320C23×C4—471no—
321C23×C4—471no—
322C23×C4C4×D4711yescharacteristic
323C23×C4C4×D4711yescharacteristic
324C23×C4C22×D4711yescharacteristic
325C22×C8—21no—
326C22×C8—21no—
327C22×C8—941no—
328C22×C8—941no—
329#126—944no—
330#126—944no—
331#126—944no—
332#126—944no—
333#126—944no—
334#126—944no—
335#126—944no—
336#126—944no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—474no—
342C2×C4⋊C4—474no—
343C2×C4⋊C4—942no—
344C2×C4⋊C4—941no—
345C2×C4⋊C4—941no—
346C2×C4⋊C4—942no—
347C2×C4⋊C4—941no—
348C2×C4⋊C4—941no—
349C2×C4⋊C4C4×D4712yes—
350C2×C4⋊C4C22×D4712yes—
351C2×C22⋊C4—474no—
352C2×C22⋊C4—474no—
353C2×C22⋊C4—472no—
354C2×C22⋊C4—472no—
355C2×C22⋊C4—942no—
356C2×C22⋊C4—942no—
357C2×C22⋊C4—941no—
358C2×C22⋊C4—941no—
359C2×C22⋊C4—941no—
360C2×C22⋊C4—941no—
361C2×C22⋊C4—941no—
362C2×C22⋊C4—941no—
363C2×C22⋊C4—941no—
364C2×C22⋊C4—941no—
365C2×C42—472no—
366C2×C42—471no—
367C2×C42—471no—
368C2×C42—471no—
369C2×C42—471no—
370C2×C42—472no—
371C2×C42—472no—
372C2×C42—472no—
373C4⋊C8—944no—
374C4⋊C8—944no—
375C22⋊C8—21no—
376C22⋊C8—21no—
377C22⋊C8—472no—
378C22⋊C8—472no—
379C22⋊C8—941no—
380C22⋊C8—941no—
381C22⋊C8C22×D4712yes—
382C22⋊C8C22×D4712yes—
383#97—944no—
384C4×C8—944no—
385C24—472no—
386C24—942no—
387C24—942no—
388C24—941no—
389C24—941no—
390C24—1882no—
391C24—1882no—
392C24C2×C4×D4711yescharacteristic
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—42no—
400C22×C4—42no—
401C22×C4—472no—
402C22×C4—471no—
403C22×C4—471no—
404C22×C4—471no—
405C22×C4—471no—
406C22×C4—472no—
407C22×C4—472no—
408C22×C4—472no—
409C22×C4—472no—
410C22×C4—942no—
411C22×C4—942no—
412C22×C4—941no—
413C22×C4—941no—
414C22×C4—1882no—
415C22×C4—1882no—
416C22×C4C2×C4×D4712yes—
417C22×C4C2×C4×D4712yes—
418C22×C4C2×C4×D4711yescharacteristic
419C22×C4D4×D4711yescharacteristic
420C22×C4D4×D4711yescharacteristic
421C22×C4D4×D4711yescharacteristic
422C22×C4D4×D4711yescharacteristic
423C22×C4C23×D4711yescharacteristic
424C2×C8—22no—
425C2×C8—22no—
426C2×C8—42no—
427C2×C8—42no—
428C2×C8—942no—
429C2×C8—942no—
430C2×C8—1882no—
431C2×C8—1882no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—944no—
437C4⋊C4—944no—
438C4⋊C4—944no—
439C4⋊C4—944no—
440C22⋊C4—944no—
441C22⋊C4—944no—
442C22⋊C4—944no—
443C22⋊C4—944no—
444C22⋊C4—942no—
445C22⋊C4—942no—
446C22⋊C4—942no—
447C22⋊C4—942no—
448C42—472no—
449C42—472no—
450C42—472no—
451C42—472no—
452C42—472no—
453C42—472no—
454C42—472no—
455C42—472no—
456C23—22no—
457C23—22no—
458C23—942no—
459C23—942no—
460C23—942no—
461C23—3764no—
462C23—3764no—
463C23—1882no—
464C23—1882no—
465C23—1882no—
466C23—1882no—
467C23—1882no—
468C23—1882no—
469C23—1882no—
470C23—1882no—
471C23C22⋊C4×D4711yescharacteristic
472C23C22⋊C4×D4711yescharacteristic
473C23#1309403012yes—
474C23#1309403212yes—
475C23C22×C4×D4711yescharacteristic
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—472no—
492C2×C4—472no—
493C2×C4—472no—
494C2×C4—472no—
495C2×C4—944no—
496C2×C4—942no—
497C2×C4—942no—
498C2×C4—942no—
499C2×C4—942no—
500C2×C4—942no—
501C2×C4—942no—
502C2×C4—942no—
503C2×C4—1882no—
504C2×C4—1882no—
505C2×C4—1882no—
506C2×C4—1882no—
507C2×C4—1882no—
508C2×C4C22⋊C4×D4711yescharacteristic
509C2×C4C22⋊C4×D4711yescharacteristic
510C2×C4C2×D4×D4711yescharacteristic
511C2×C4C2×D4×D4711yescharacteristic
512C8—42no—
513C8—42no—
514C8—1882no—
515C8—1882no—
516C22—24no—
517C22—24no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—3762no—
523C22—3762no—
524C22—3764no—
525C22—3764no—
526C22—1882no—
527C22—1882no—
528C22—1882no—
529C22#1568908812yes—
530C22#1568908812yes—
531C22#1568909512yes—
532C22#1568910612yes—
533C22C2×C22⋊C4×D4711yescharacteristic
534C22C2×#1309403011yescharacteristic
535C22C2×#1309403211yescharacteristic
536C4—21no—
537C4—21no—
538C4—21no—
539C4—21no—
540C4—42no—
541C4—42no—
542C4—942no—
543C4—942no—
544C4—942no—
545C4—942no—
546C4—1882no—
547C2—22no—
548C2—21no—
549C2—21no—
550C2—3762no—
551C2#2024175614yesdirect product factor
552C2C2×#1568908811yescharacteristic
553C2C2×#1568909511yescharacteristic
554C2C2×#1568910611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D47
commutatorC23×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#324C2
socleC23×C47C2×C22⋊C4
prime radicalC24×D47C2×C4
cosocleC22×C4×C47C24
hypercenterC2×#324D47
hypocenterC47C2×#1473
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
2. C2×#15689177C2semidirect
3. C2×#15689173C2semidirect
4. #20241756C2direct (N × H)
5. C2×#15688849C2semidirect
8. C2×C47×#324C2semidirect
24. #15689177C22semidirect
26. #15689173C22semidirect
33. #15688849C22semidirect
39. C47×#324C22semidirect
275. C2×#324D47semidirect
281. C2×C47#1473semidirect
314. #324C2×D47semidirect
317. C47C2×#1473semidirect
551. C2#20241756direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940192
C2×#156891772
C2×#156891732
#202417562
C2×#156888492
C2×#156888462
C2×C47×#3242
C2×#147347