Finite Group Databasebeta

← #99×Dic94 #26232826

Subgroups — #99×Dic94 #26232826

Order 12032.

1354 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic94C211yesmaximal, characteristic
2C22⋊C4×Dic94C212yesmaximal, complemented
3#20244373C212yesmaximal, complemented
4#20244371C214yesmaximal, complemented
5#20243376C211yesmaximal, characteristic
6#20243374C212yesmaximal
7#99×Dic47C212yesmaximal
8C4×#99×C47C211yesmaximal, characteristic
9C23×Dic94C411yescharacteristic, complemented
10C23×Dic94C2211yescharacteristic
11D4×Dic94—22no—
12D4×Dic94—24no—
13D4×Dic94—22no—
14C2×#13094024C411yescharacteristic, complemented
15C2×#13094023C412yescomplemented
16C2×#13094003C411yescharacteristic, complemented
17C2×#13094003C2211yescharacteristic
18C2×#13094001C412yescomplemented
19C2×#13094001C2212yes—
20C2×C4×Dic94—22no—
21C2×C4×Dic94C411yescharacteristic, complemented
22C2×D4×Dic47C2212yes—
23C2×#13093939C2212yes—
24#15689029—22no—
25#15689027—24no—
26#15688983C2212yes—
27#15688981C2214yes—
28C22⋊C4×Dic47C2214yes—
29#15688890C2212yes—
30#15688889C2214yes—
31#15688889C2214yes—
32C2×C4×D4×C47C2211yescharacteristic
33C2×#99×C47C2211yescharacteristic
34C2×#99×C47C2211yescharacteristic
35C4×C22⋊C4×C47C2212yes—
36C47×#342C2212yes—
37C22×Dic94—22no—
38C22×Dic94—21no—
39C22×Dic94—21no—
40C22×Dic94—44no—
41C22×Dic94—44no—
42C22×Dic94C2×C411yescharacteristic
43C22×Dic94C2×C412yes—
44C22×Dic94C2×C411yescharacteristic
45C22×Dic94C2×C412yes—
46C22×Dic94C2×C411yescharacteristic
47C22×Dic94D412yes—
48C22×Dic94D414yes—
49C22×Dic94D412yes—
50C23×Dic47C2×C412yes—
51C23×Dic47C2312yes—
52#13094024—22no—
53#13094024—22no—
54#13094023—24no—
55#13094023—24no—
56#13094003—22no—
57#13094003—22no—
58#13094003—22no—
59#13094003—22no—
60#13094001—24no—
61#13094001—24no—
62#13094001—24no—
63#13094001—24no—
64C4×Dic94—21no—
65C4×Dic94—22no—
66C4×Dic94—21no—
67C4×Dic94—48no—
68D4×Dic47—24no—
69D4×Dic47—24no—
70C2×C4⋊Dic47—22no—
71C2×C4⋊Dic47C2×C412yes—
72C2×C4⋊Dic47C2×C411yescharacteristic
73C2×C4⋊Dic47C2×C412yes—
74C2×Dic47⋊C4—24no—
75C2×Dic47⋊C4C2×C412yes—
76C2×Dic47⋊C4C2×C412yes—
77C2×Dic47⋊C4C2×C412yes—
78C2×C22⋊Dic47C2×C412yes—
79C2×C22⋊Dic47C2314yes—
80C2×C22⋊Dic47C2312yes—
81C2×C4×Dic47—24no—
82C2×C4×Dic47C2×C412yes—
83#13093939—24no—
84C47⋊#95—22no—
85C47⋊#95—24no—
86C47⋊#95—24no—
87C22×D4×C47C2311yescharacteristic
88C23×C4×C47C2×C411yescharacteristic
89C23×C4×C47C2311yescharacteristic
90C4×D4×C47—22no—
91C4×D4×C47—22no—
92C2×C4⋊C4×C47C2×C411yescharacteristic
93C2×C22⋊C4×C47C2×C411yescharacteristic
94C2×C22⋊C4×C47C2312yes—
95C2×C22⋊C4×C47C2311yescharacteristic
96C2×C22⋊C4×C47C2312yes—
97C2×C42×C47—22no—
98C2×C42×C47C2×C411yescharacteristic
99#99×C47—22no—
100#99×C47Q814yescomplemented
101#95×C47—22no—
102C24×C47C22×C411yescharacteristic
103C24×C47C2411yescharacteristic
104C2×D4×C47—22no—
105C2×D4×C47—22no—
106C2×D4×C47C2×Q812yes—
107C2×D4×C47#4112yes—
108C22×C4×C47—22no—
109C22×C4×C47—21no—
110C22×C4×C47—21no—
111C22×C4×C47—22no—
112C22×C4×C47—42no—
113C22×C4×C47—42no—
114C22×C4×C47C22×C411yescharacteristic
115C22×C4×C47C22×C411yescharacteristic
116C22×C4×C47C22×C411yescharacteristic
117C22×C4×C47C22×C411yescharacteristic
118C22×C4×C47C22×C411yescharacteristic
119C22×C4×C47C2×D412yes—
120C22×C4×C47C2×D412yes—
121C22×Dic47—22no—
122C22×Dic47—22no—
123C22×Dic47—24no—
124C22×Dic47—44no—
125C22×Dic47—44no—
126C22×Dic47C22×C412yes—
127C22×Dic47C22×C412yes—
128C22×Dic47C22×C412yes—
129C22×Dic47C22×C412yes—
130C22×Dic47C2×D414yes—
131C22×Dic47C2×D414yes—
132C2×Dic94—28no—
133C2×Dic94—24no—
134C2×Dic94—21no—
135C2×Dic94—21no—
136C2×Dic94—22no—
137C2×Dic94—22no—
138C2×Dic94—44no—
139C2×Dic94—48no—
140C2×Dic94—42no—
141C2×Dic94—44no—
142C2×Dic94—44no—
143C2×Dic94—48no—
144C2×Dic94—44no—
145C2×Dic94—44no—
146C2×Dic94—42no—
147C2×Dic94C22⋊C411yescharacteristic
148C2×Dic94C22⋊C412yes—
149C2×Dic94C22⋊C414yes—
150C2×Dic94C22⋊C412yes—
151C2×Dic94C22⋊C414yes—
152C2×Dic94C22⋊C412yes—
153C2×Dic94C22⋊C411yescharacteristic
154C4⋊C4×C47—22no—
155C22⋊C4×C47—22no—
156C22⋊C4×C47—22no—
157C22⋊C4×C47—22no—
158C22⋊C4×C47—22no—
159C22⋊C4×C47—22no—
160C22⋊C4×C47C2×Q814yescomplemented
161C42×C47—21no—
162C42×C47—21no—
163C42×C47—44no—
164C22⋊Dic47—24no—
165C22⋊Dic47—24no—
166C22⋊Dic47—24no—
167C22⋊Dic47—24no—
168C4⋊Dic47—21no—
169C4⋊Dic47—21no—
170C4⋊Dic47—24no—
171C4⋊Dic47—24no—
172C4⋊Dic47—44no—
173Dic47⋊C4—24no—
174Dic47⋊C4—22no—
175Dic47⋊C4—22no—
176Dic47⋊C4—24no—
177Dic47⋊C4—48no—
178C4×Dic47—22no—
179C4×Dic47—22no—
180C4×Dic47—48no—
181C23×C47—21no—
182C23×C47—21no—
183C23×C47—41no—
184C23×C47—41no—
185C23×C47—41no—
186C23×C47—41no—
187C23×C47C4×Q812yescomplemented
188C23×C47C23×C411yescharacteristic
189C23×C47C22×D412yes—
190C23×C47C22×Q811yescharacteristic
191C23×C47C2×#4111yescharacteristic
192C23×C472−1+412yes—
193D4×C47—24no—
194D4×C47—24no—
195C2×C4×C47—21no—
196C2×C4×C47—21no—
197C2×C4×C47—24no—
198C2×C4×C47—22no—
199C2×C4×C47—21no—
200C2×C4×C47—21no—
201C2×C4×C47—24no—
202C2×C4×C47—41no—
203C2×C4×C47—42no—
204C2×C4×C47—42no—
205C2×C4×C47—42no—
206C2×C4×C47—42no—
207C2×C4×C47—42no—
208C2×C4×C47—41no—
209C2×C4×C47—41no—
210C2×C4×C47—42no—
211C2×C4×C47—42no—
212C2×C4×C47—42no—
213C2×C4×C47C2×C22⋊C412yes—
214C2×C4×C47C2×C22⋊C411yescharacteristic
215C2×C4×C47C2×C22⋊C411yescharacteristic
216C2×C4×C47C4×Q812yescomplemented
217C2×Dic47—28no—
218C2×Dic47—24no—
219C2×Dic47—22no—
220C2×Dic47—22no—
221C2×Dic47—42no—
222C2×Dic47—44no—
223C2×Dic47—44no—
224C2×Dic47—44no—
225C2×Dic47—42no—
226C2×Dic47—42no—
227C2×Dic47—44no—
228C2×Dic47—44no—
229C2×Dic47—44no—
230C2×Dic47C2×C22⋊C412yes—
231C2×Dic47C2×C22⋊C414yes—
232C2×Dic47C2×C22⋊C412yes—
233Dic94—22no—
234Dic94—24no—
235Dic94—24no—
236Dic94—28no—
237Dic94—44no—
238Dic94—42no—
239Dic94—44no—
240Dic94—42no—
241Dic94—42no—
242Dic94—44no—
243Dic94#9914yesdirect product factor
244Q8×#99—471nomaximal, Sylow
245C22×C47—22no—
246C22×C47—21no—
247C22×C47—22no—
248C22×C47—21no—
249C22×C47—22no—
250C22×C47—41no—
251C22×C47—41no—
252C22×C47—42no—
253C22×C47—42no—
254C22×C47—42no—
255C22×C47—41no—
256C22×C47—41no—
257C22×C47C22×C22⋊C411yescharacteristic
258C22×C47C2×C4×Q811yescharacteristic
259C22×C47#51911yescharacteristic
260C22×C47#54812yes—
261C22×C47D4×Q812yes—
262C4×C47—22no—
263C4×C47—21no—
264C4×C47—22no—
265C4×C47—44no—
266C4×C47—41no—
267C4×C47—41no—
268C4×C47—82no—
269C4×C47C2×#9912yes—
270Dic47—22no—
271Dic47—24no—
272Dic47—42no—
273Dic47—42no—
274Dic47—84no—
275Dic47C2×#9914yes—
276C2×D4×Q8—471no—
277Q8×C22⋊C4—472no—
278#1996—472no—
279#1996—474no—
280#1799—472no—
281#1799—471no—
282C4×#99—472no—
283C4×#99D4711yescharacteristic
284C2×C47—22no—
285C2×C47—22no—
286C2×C47—21no—
287C2×C47—21no—
288C2×C47—42no—
289C2×C47Q8×C22⋊C411yescharacteristic
290C2×C47C22×#9911yescharacteristic
291C2×C47#288411yescharacteristic
292C23×Q8—471no—
293C23×Q8—471no—
294D4×Q8—942no—
295D4×Q8—942no—
296D4×Q8—944no—
297C2×C4⋊Q8—472no—
298C2×C4⋊Q8—471no—
299C2×C22⋊Q8—471no—
300C2×C22⋊Q8—471no—
301C2×C22⋊Q8—472no—
302C2×C22⋊Q8—472no—
303C2×C4×Q8—471no—
304C2×C4×Q8—942no—
305C2×C4×D4—472no—
306C2×C4×D4C2×D4711yescharacteristic
307C2×#99—472no—
308C2×#99C2×D4711yescharacteristic
309C2×#99C2×D4711yescharacteristic
310#391—944no—
311#391—942no—
312#380—472no—
313#380—474no—
314C4×C22⋊C4—474no—
315C4×C22⋊C4C2×D4712yes—
316#342—474no—
317#342—472no—
318#342—474no—
319#342C2×D4712yes—
320C47Q8×#9911yescharacteristic, complemented, Sylow
321C22×Q8—471no—
322C22×Q8—472no—
323C22×Q8—471no—
324C22×Q8—472no—
325C22×Q8—471no—
326C22×Q8—472no—
327C22×Q8—474no—
328C22×Q8—472no—
329C22×Q8—941no—
330C22×Q8—942no—
331C22×Q8—941no—
332C22×Q8—1884no—
333C22×Q8—1884no—
334C22×D4C22×D4711yescharacteristic
335C23×C4—472no—
336C23×C4—472no—
337C23×C4C4×D4711yescharacteristic
338C23×C4C22×D4711yescharacteristic
339C4⋊Q8—942no—
340C4⋊Q8—942no—
341C4⋊Q8—944no—
342C4⋊Q8—944no—
343C22⋊Q8—944no—
344C22⋊Q8—944no—
345C22⋊Q8—944no—
346C22⋊Q8—944no—
347C22⋊Q8—942no—
348C22⋊Q8—942no—
349C22⋊Q8—942no—
350C22⋊Q8—942no—
351C4×Q8—941no—
352C4×Q8—942no—
353C4×Q8—941no—
354C4×Q8—1888no—
355C4×D4—22no—
356C4×D4—22no—
357C4×D4—944no—
358C4×D4—944no—
359C2×C4⋊C4—472no—
360C2×C4⋊C4—472no—
361C2×C4⋊C4—471no—
362C2×C4⋊C4—472no—
363C2×C4⋊C4—472no—
364C2×C4⋊C4—472no—
365C2×C4⋊C4—944no—
366C2×C4⋊C4—942no—
367C2×C4⋊C4C4×D4711yescharacteristic
368C2×C22⋊C4—472no—
369C2×C22⋊C4—472no—
370C2×C22⋊C4—474no—
371C2×C22⋊C4C4×D4711yescharacteristic
372C2×C22⋊C4C22×D4712yes—
373C2×C22⋊C4C22×D4711yescharacteristic
374C2×C22⋊C4C22×D4712yes—
375C2×C42—22no—
376C2×C42—472no—
377C2×C42—944no—
378C2×C42C4×D4711yescharacteristic
379#99—22no—
380#99—944no—
381#99Dic9414yesdirect product factor
382#95—22no—
383#95—944no—
384#95—944no—
385#95—942no—
386C24C2×C4×D4711yescharacteristic
387C24C23×D4711yescharacteristic
388C2×Q8—471no—
389C2×Q8—472no—
390C2×Q8—471no—
391C2×Q8—474no—
392C2×Q8—472no—
393C2×Q8—474no—
394C2×Q8—472no—
395C2×Q8—942no—
396C2×Q8—942no—
397C2×Q8—948no—
398C2×Q8—944no—
399C2×Q8—941no—
400C2×Q8—941no—
401C2×Q8—1884no—
402C2×Q8—1882no—
403C2×Q8—1882no—
404C2×Q8—1884no—
405C2×Q8—1888no—
406C2×Q8—1884no—
407C2×Q8—1884no—
408C2×Q8—1888no—
409C2×Q8—1884no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4C2×Dic9412yes—
413C2×D4#1062535012yes—
414C22×C4—22no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—472no—
421C22×C4—474no—
422C22×C4—472no—
423C22×C4—474no—
424C22×C4—472no—
425C22×C4—472no—
426C22×C4—942no—
427C22×C4—942no—
428C22×C4—944no—
429C22×C4—1884no—
430C22×C4—1884no—
431C22×C4C2×C4×D4711yescharacteristic
432C22×C4C2×C4×D4711yescharacteristic
433C22×C4C2×C4×D4711yescharacteristic
434C22×C4C2×C4×D4711yescharacteristic
435C22×C4C2×C4×D4711yescharacteristic
436C22×C4D4×D4712yes—
437C22×C4D4×D4712yes—
438C4⋊C4—22no—
439C4⋊C4—942no—
440C4⋊C4—942no—
441C4⋊C4—944no—
442C4⋊C4—944no—
443C4⋊C4—944no—
444C4⋊C4—944no—
445C4⋊C4—941no—
446C4⋊C4—941no—
447C4⋊C4—1884no—
448C4⋊C4—1888no—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C22⋊C4—944no—
455C22⋊C4—944no—
456C22⋊C4—944no—
457C22⋊C4—944no—
458C22⋊C4C2×Dic9414yescomplemented
459C42—21no—
460C42—21no—
461C42—44no—
462C42—942no—
463C42—942no—
464C42—1888no—
465C23—21no—
466C23—21no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23C4×Dic9412yescomplemented
472C23C22×C4×D4711yescharacteristic
473C23C2×D4×D4712yes—
474C23C22×Dic9411yescharacteristic
475C23C2×#1062535011yescharacteristic
476C23#1309407112yes—
477Q8—474no—
478Q8—948no—
479Q8—944no—
480Q8—944no—
481Q8—942no—
482Q8—1882no—
483Q8—1884no—
484Q8—1882no—
485Q8—1884no—
486Q8—1884no—
487Q8—1882no—
488D4—24no—
489D4—24no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—24no—
493C2×C4—22no—
494C2×C4—24no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—41no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—472no—
509C2×C4—472no—
510C2×C4—474no—
511C2×C4—948no—
512C2×C4—944no—
513C2×C4—942no—
514C2×C4—942no—
515C2×C4—1884no—
516C2×C4—1884no—
517C2×C4—1882no—
518C2×C4—1884no—
519C2×C4—1884no—
520C2×C4—1884no—
521C2×C4—1884no—
522C2×C4—1882no—
523C2×C4—1882no—
524C2×C4C22⋊C4×D4711yescharacteristic
525C2×C4C22⋊C4×D4712yes—
526C2×C4C22⋊C4×D4711yescharacteristic
527C2×C4C4×Dic9412yescomplemented
528C22—22no—
529C22—21no—
530C22—22no—
531C22—21no—
532C22—22no—
533C22—41no—
534C22—41no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—41no—
539C22—41no—
540C22C2×C22⋊C4×D4711yescharacteristic
541C22C2×C4×Dic9411yescharacteristic
542C22#1568960011yescharacteristic
543C22#1568978212yes—
544C22D4×Dic9412yes—
545C4—21no—
546C4—22no—
547C4—22no—
548C4—44no—
549C4—41no—
550C4—41no—
551C4—82no—
552C4—474no—
553C4—942no—
554C4—944no—
555C4—3764no—
556C4—1882no—
557C4—1882no—
558C4#99×D4712yes—
559C2—22no—
560C2—22no—
561C2—21no—
562C2—21no—
563C2—42no—
564C2C22⋊C4×Dic9411yescharacteristic
565C2C2×#99×D4711yescharacteristic
566C2#2025185011yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D47
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC4×#99×C47C2
socleC22×C47C22×C22⋊C4
prime radicalC22×D4×C47C23
cosocleC24×C47C24
hypercenterC4×#99D47
hypocenterC47Q8×#99
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. C22⋊C4×Dic94C2semidirect
3. #20244373C2semidirect
4. #20244371C2semidirect
9. C23×Dic94C4semidirect
14. C2×#13094024C4semidirect
15. C2×#13094023C4semidirect
16. C2×#13094003C4semidirect
18. C2×#13094001C4semidirect
21. C2×C4×Dic94C4semidirect
100. #99×C47Q8semidirect
160. C22⋊C4×C47C2×Q8semidirect
187. C23×C47C4×Q8semidirect
216. C2×C4×C47C4×Q8semidirect
243. Dic94#99direct (N × H)
320. C47Q8×#99semidirect
381. #99Dic94direct (N × H)
458. C22⋊C4C2×Dic94semidirect
471. C23C4×Dic94semidirect
527. C2×C4C4×Dic94semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic942
C22⋊C4×Dic942
#202443732
#202443712
#202433762
#202433742
#99×Dic472
C4×#99×C472
Q8×#9947