Finite Group Databasebeta

← #26232430

Subgroups — #26232430

Order 12032.

1132 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689813C211yesmaximal, characteristic
2#20246255C212yesmaximal, complemented
3#20244373C212yesmaximal, complemented
4#20243843C214yesmaximal
5#20243464C212yesmaximal, complemented
6#20243376C211yesmaximal, characteristic
7#20243119C212yesmaximal, complemented
8C4×#99×C47C211yesmaximal, characteristic
9#15689813—22no—
10#15689813—24no—
11#15689813—22no—
12C2×#13094017C412yescomplemented
13C2×#13094016C411yescharacteristic, complemented
14C2×#13094014C412yescomplemented
15C2×#13094005C2212yes—
16C2×#13094003C411yescharacteristic, complemented
17C2×#13094003C2211yescharacteristic
18C2×C4×Dic94C411yescharacteristic, complemented
19C2×#13093983C411yescharacteristic, complemented
20C2×#13093980C2214yes—
21C2×#13093980C2212yes—
22C22×C4⋊Dic47C2211yescharacteristic
23C2×#13093939C2212yes—
24#15689021—22no—
25#15689008—24no—
26#15688984C2214yes—
27#15688983C2212yes—
28C4×C4⋊Dic47—22no—
29#15688890C2212yes—
30#15688889C2214yes—
31#15688889C2214yes—
32C2×C4×D4×C47C2211yescharacteristic
33C2×#99×C47C2212yes—
34C4×C22⋊C4×C47C2212yes—
35C47×#342C2211yescharacteristic
36C47×#342C2211yescharacteristic
37C22×Dic94C2×C411yescharacteristic
38C23×Dic47C2312yes—
39#13094017—24no—
40#13094017—24no—
41#13094016—22no—
42#13094016—22no—
43#13094014—24no—
44#13094014—24no—
45#13094005—24no—
46#13094005—24no—
47#13094003—22no—
48#13094003—22no—
49#13094003—22no—
50#13094003—22no—
51C4×Dic94—22no—
52C4×Dic94—21no—
53C4×Dic94—21no—
54#13093983—22no—
55#13093983—21no—
56#13093983—21no—
57#13093980—24no—
58#13093980—24no—
59#13093980—28no—
60#13093980—44no—
61C2×C4⋊Dic47—22no—
62C2×C4⋊Dic47C2×C411yescharacteristic
63C2×C4⋊Dic47C2×C411yescharacteristic
64C2×C4⋊Dic47C2×C411yescharacteristic
65C2×C4⋊Dic47C2×C412yes—
66C2×C4⋊Dic47D412yes—
67C2×C4⋊Dic47D414yes—
68C2×C4⋊Dic47D412yes—
69C2×Dic47⋊C4—24no—
70C2×Dic47⋊C4C2×C412yes—
71C2×Dic47⋊C4C2×C412yes—
72C2×Dic47⋊C4C2×C412yes—
73C2×Dic47⋊C4C2×C412yes—
74C2×Dic47⋊C4C2×C412yes—
75C2×C22⋊Dic47C2×C412yes—
76C2×C22⋊Dic47C2×C412yes—
77C2×C22⋊Dic47C2314yes—
78C2×C22⋊Dic47C2312yes—
79C2×C4×Dic47—24no—
80C2×C4×Dic47C2×C412yes—
81C2×C4×Dic47C2×C412yes—
82#13093939—42no—
83C47⋊#95—22no—
84C47⋊#95—24no—
85C47⋊#95—24no—
86C22×D4×C47C2311yescharacteristic
87C23×C4×C47C2×C411yescharacteristic
88C23×C4×C47C2311yescharacteristic
89C4×D4×C47—22no—
90C4×D4×C47—22no—
91C2×C4⋊C4×C47C2×C411yescharacteristic
92C2×C22⋊C4×C47C2×C411yescharacteristic
93C2×C22⋊C4×C47C2312yes—
94C2×C22⋊C4×C47C2311yescharacteristic
95C2×C22⋊C4×C47C2312yes—
96C2×C42×C47—22no—
97C2×C42×C47C2×C411yescharacteristic
98#99×C47—24no—
99#95×C47—22no—
100C24×C47C22×C411yescharacteristic
101C24×C47C2411yescharacteristic
102C2×D4×C47—22no—
103C2×D4×C47—22no—
104C2×D4×C47—21no—
105C2×D4×C47—21no—
106C22×C4×C47—22no—
107C22×C4×C47—21no—
108C22×C4×C47—21no—
109C22×C4×C47—22no—
110C22×C4×C47—42no—
111C22×C4×C47—42no—
112C22×C4×C47C22×C411yescharacteristic
113C22×C4×C47C22×C411yescharacteristic
114C22×C4×C47C22×C411yescharacteristic
115C22×C4×C47C22×C411yescharacteristic
116C22×C4×C47C22×C411yescharacteristic
117C22×C4×C47C2×D412yes—
118C22×C4×C47C2×D412yes—
119C22×Dic47—24no—
120C22×Dic47—22no—
121C22×Dic47—22no—
122C22×Dic47—24no—
123C22×Dic47C22×C412yes—
124C22×Dic47C22×C412yes—
125C22×Dic47C22×C412yes—
126C22×Dic47C22×C412yes—
127C22×Dic47C2×D414yes—
128C22×Dic47C2×D414yes—
129C2×Dic94—21no—
130C2×Dic94—21no—
131C2×Dic94—42no—
132C4⋊C4×C47—22no—
133C22⋊C4×C47—22no—
134C22⋊C4×C47—22no—
135C22⋊C4×C47—22no—
136C22⋊C4×C47—22no—
137C22⋊C4×C47—22no—
138C22⋊C4×C47#4114yes—
139C42×C47—21no—
140C42×C47—21no—
141C42×C47—44no—
142C22⋊Dic47—24no—
143C22⋊Dic47—22no—
144C22⋊Dic47—22no—
145C22⋊Dic47—24no—
146C22⋊Dic47—24no—
147C22⋊Dic47—24no—
148C4⋊Dic47—21no—
149C4⋊Dic47—21no—
150C4⋊Dic47—44no—
151C4⋊Dic47C22⋊C412yes—
152C4⋊Dic47C22⋊C411yescharacteristic
153C4⋊Dic47C22⋊C411yescharacteristic
154C4⋊Dic47C22⋊C412yes—
155C4⋊Dic47C22⋊C412yes—
156C4⋊Dic47C22⋊C414yes—
157C4⋊Dic47C22⋊C414yes—
158Dic47⋊C4—24no—
159Dic47⋊C4—24no—
160Dic47⋊C4—24no—
161Dic47⋊C4—22no—
162Dic47⋊C4—22no—
163Dic47⋊C4—24no—
164Dic47⋊C4—48no—
165C4×Dic47—22no—
166C4×Dic47—22no—
167C4×Dic47—22no—
168C4×Dic47—22no—
169C4×Dic47—48no—
170C23×C47—21no—
171C23×C47—21no—
172C23×C47—21no—
173C23×C47—41no—
174C23×C47—41no—
175C23×C47—41no—
176C23×C47—41no—
177C23×C47C23×C411yescharacteristic
178C23×C47C22×D412yes—
179C23×C47C2×#4112yes—
180C23×C47H(5,𝔽2)11yescharacteristic
181C23×C472−1+411yescharacteristic
182D4×C47—42no—
183D4×C47—42no—
184C2×C4×C47—24no—
185C2×C4×C47—22no—
186C2×C4×C47—21no—
187C2×C4×C47—21no—
188C2×C4×C47—21no—
189C2×C4×C47—21no—
190C2×C4×C47—21no—
191C2×C4×C47—24no—
192C2×C4×C47—41no—
193C2×C4×C47—42no—
194C2×C4×C47—42no—
195C2×C4×C47—42no—
196C2×C4×C47—42no—
197C2×C4×C47—42no—
198C2×C4×C47—41no—
199C2×C4×C47—41no—
200C2×C4×C47—42no—
201C2×C4×C47—42no—
202C2×C4×C47—42no—
203C2×C4×C47C2×C22⋊C412yes—
204C2×C4×C47C2×C22⋊C411yescharacteristic
205C2×C4×C47C2×C22⋊C411yescharacteristic
206C2×Dic47—22no—
207C2×Dic47—22no—
208C2×Dic47—22no—
209C2×Dic47—22no—
210C2×Dic47—24no—
211C2×Dic47—24no—
212C2×Dic47—24no—
213C2×Dic47—24no—
214C2×Dic47—22no—
215C2×Dic47—22no—
216C2×Dic47—42no—
217C2×Dic47—42no—
218C2×Dic47—44no—
219C2×Dic47—44no—
220C2×Dic47—44no—
221C2×Dic47C2×C22⋊C412yes—
222C2×Dic47C2×C22⋊C412yes—
223C2×Dic47C2×C22⋊C414yes—
224Dic94—42no—
225Dic94—42no—
226#22478—471nomaximal, Sylow
227C22×C47—22no—
228C22×C47—21no—
229C22×C47—22no—
230C22×C47—21no—
231C22×C47—42no—
232C22×C47—41no—
233C22×C47—41no—
234C22×C47—41no—
235C22×C47—41no—
236C22×C47—41no—
237C22×C47—81no—
238C22×C47—81no—
239C22×C47C22×C22⋊C411yescharacteristic
240C22×C47C4×#4111yescharacteristic
241C22×C47#52011yescharacteristic
242C22×C47#54612yes—
243C22×C47#54712yes—
244C4×C47—21no—
245C4×C47—22no—
246C4×C47—44no—
247C4×C47—41no—
248C4×C47—41no—
249C4×C47—41no—
250C4×C47—82no—
251C4×C47#41012yes—
252Dic47—22no—
253Dic47—24no—
254Dic47—22no—
255Dic47—42no—
256Dic47—42no—
257Dic47—84no—
258C2×#552—471no—
259#2344—472no—
260#1996—472no—
261#1899—474no—
262#1820—472no—
263#1799—471no—
264C4×#99D4711yescharacteristic
265#1740—472no—
266C2×C47—22no—
267C2×C47—22no—
268C2×C47—21no—
269C2×C47—21no—
270C2×C47—81no—
271C2×C47#233911yescharacteristic
272C2×C47C2×#41011yescharacteristic
273C2×C47#288411yescharacteristic
274#552—942no—
275#552—944no—
276#552—942no—
277C2×#126—472no—
278C2×#125—472no—
279C2×#125—471no—
280C2×#123—472no—
281C2×C22⋊Q8—471no—
282C2×C22⋊Q8—471no—
283C2×C4×Q8—471no—
284C2×C4×D4C2×D4711yescharacteristic
285C2×#117—471no—
286C2×#117—472no—
287C2×#117—474no—
288C22×C4⋊C4—471no—
289C2×#99—472no—
290C2×#99C2×D4712yes—
291#389—942no—
292#387—944no—
293#381—474no—
294#380—472no—
295C4×C4⋊C4—942no—
296C4×C22⋊C4C2×D4712yes—
297#342—472no—
298#342—474no—
299#342—474no—
300#342C2×D4711yescharacteristic
301#342C2×D4711yescharacteristic
302C47#2247811yescharacteristic, complemented, Sylow
303C22×Q8—471no—
304C22×D4C22×D4711yescharacteristic
305C23×C4—472no—
306C23×C4C4×D4711yescharacteristic
307C23×C4C22×D4711yescharacteristic
308#126—944no—
309#126—944no—
310#125—942no—
311#125—942no—
312#125—944no—
313#125—944no—
314#123—944no—
315#123—944no—
316C22⋊Q8—942no—
317C22⋊Q8—942no—
318C22⋊Q8—942no—
319C22⋊Q8—942no—
320C4×Q8—942no—
321C4×Q8—941no—
322C4×Q8—941no—
323C4×D4—22no—
324C4×D4—22no—
325#117—944no—
326#117—944no—
327#117—942no—
328#117—941no—
329#117—941no—
330#117—948no—
331#117—1884no—
332C2×C4⋊C4—471no—
333C2×C4⋊C4—471no—
334C2×C4⋊C4—472no—
335C2×C4⋊C4—472no—
336C2×C4⋊C4—474no—
337C2×C4⋊C4—472no—
338C2×C4⋊C4—472no—
339C2×C4⋊C4—471no—
340C2×C4⋊C4—472no—
341C2×C4⋊C4—472no—
342C2×C4⋊C4—472no—
343C2×C4⋊C4—472no—
344C2×C4⋊C4—944no—
345C2×C4⋊C4—942no—
346C2×C4⋊C4C4×D4711yescharacteristic
347C2×C22⋊C4—472no—
348C2×C22⋊C4—472no—
349C2×C22⋊C4—472no—
350C2×C22⋊C4—474no—
351C2×C22⋊C4C4×D4711yescharacteristic
352C2×C22⋊C4C22×D4712yes—
353C2×C22⋊C4C22×D4711yescharacteristic
354C2×C22⋊C4C22×D4712yes—
355C2×C42—22no—
356C2×C42—472no—
357C2×C42—472no—
358C2×C42—944no—
359C2×C42C4×D4711yescharacteristic
360#99—24no—
361#99—1882no—
362#95—22no—
363#95—944no—
364#95—944no—
365#95—942no—
366C24C2×C4×D4711yescharacteristic
367C24C23×D4711yescharacteristic
368C2×Q8—941no—
369C2×Q8—941no—
370C2×Q8—1882no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—21no—
374C2×D4—21no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—42no—
380C22×C4—42no—
381C22×C4—472no—
382C22×C4—472no—
383C22×C4—474no—
384C22×C4—474no—
385C22×C4—472no—
386C22×C4—472no—
387C22×C4—944no—
388C22×C4—942no—
389C22×C4—942no—
390C22×C4—944no—
391C22×C4C2×C4×D4711yescharacteristic
392C22×C4C2×C4×D4711yescharacteristic
393C22×C4C2×C4×D4711yescharacteristic
394C22×C4C2×C4×D4711yescharacteristic
395C22×C4C2×C4×D4711yescharacteristic
396C22×C4D4×D4712yes—
397C22×C4D4×D4712yes—
398C4⋊C4—22no—
399C4⋊C4—472no—
400C4⋊C4—471no—
401C4⋊C4—471no—
402C4⋊C4—472no—
403C4⋊C4—472no—
404C4⋊C4—474no—
405C4⋊C4—474no—
406C4⋊C4—944no—
407C4⋊C4—944no—
408C4⋊C4—942no—
409C4⋊C4—942no—
410C4⋊C4—944no—
411C4⋊C4—944no—
412C4⋊C4—941no—
413C4⋊C4—941no—
414C4⋊C4—1888no—
415C4⋊C4—1884no—
416C22⋊C4—22no—
417C22⋊C4—22no—
418C22⋊C4—22no—
419C22⋊C4—22no—
420C22⋊C4—22no—
421C22⋊C4—942no—
422C22⋊C4—942no—
423C22⋊C4—944no—
424C22⋊C4—944no—
425C22⋊C4—944no—
426C22⋊C4—944no—
427C22⋊C4#1062535014yes—
428C42—21no—
429C42—21no—
430C42—44no—
431C42—942no—
432C42—942no—
433C42—942no—
434C42—942no—
435C42—1888no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—41no—
440C23—41no—
441C23—41no—
442C23—41no—
443C23C22×C4×D4711yescharacteristic
444C23C2×D4×D4712yes—
445C23C2×#1062535012yes—
446C23#1309407011yescharacteristic
447C23#1309407111yescharacteristic
448Q8—1882no—
449Q8—1882no—
450D4—42no—
451D4—42no—
452C2×C4—24no—
453C2×C4—22no—
454C2×C4—24no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—472no—
472C2×C4—472no—
473C2×C4—474no—
474C2×C4—944no—
475C2×C4—944no—
476C2×C4—944no—
477C2×C4—944no—
478C2×C4—942no—
479C2×C4—942no—
480C2×C4—942no—
481C2×C4—942no—
482C2×C4—942no—
483C2×C4—942no—
484C2×C4—1884no—
485C2×C4—1884no—
486C2×C4—1884no—
487C2×C4—1882no—
488C2×C4—1882no—
489C2×C4C22⋊C4×D4711yescharacteristic
490C2×C4C22⋊C4×D4712yes—
491C2×C4C22⋊C4×D4711yescharacteristic
492C22—22no—
493C22—21no—
494C22—22no—
495C22—21no—
496C22—42no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—81no—
503C22—81no—
504C22C2×C22⋊C4×D4711yescharacteristic
505C22C4×#1062535011yescharacteristic
506C22#1568960311yescharacteristic
507C22#1568976912yes—
508C22#1568977812yes—
509C4—21no—
510C4—22no—
511C4—44no—
512C4—41no—
513C4—41no—
514C4—41no—
515C4—82no—
516C4—942no—
517C4—942no—
518C4—944no—
519C4—3764no—
520C4—1882no—
521C4—1882no—
522C4#1568909512yes—
523C2—22no—
524C2—22no—
525C2—21no—
526C2—21no—
527C2—81no—
528C2#2024621911yescharacteristic
529C2C2×#1568909511yescharacteristic
530C2#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
hypocenterC47#22478
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. #20246255C2semidirect
3. #20244373C2semidirect
5. #20243464C2semidirect
7. #20243119C2semidirect
12. C2×#13094017C4semidirect
13. C2×#13094016C4semidirect
14. C2×#13094014C4semidirect
16. C2×#13094003C4semidirect
18. C2×C4×Dic94C4semidirect
19. C2×#13093983C4semidirect
302. C47#22478semidirect

Maximal subgroups

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

subgroupindex
C2×#156898132
#202462552
#202443732
#202438432
#202434642
#202433762
#202431192
C4×#99×C472
#2247847