Finite Group Databasebeta

← #26108097

Subgroups — #26108097

Order 12032.

868 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689754C211yesmaximal, characteristic
2#20243695C212yesmaximal
3C2×#15688859C212yesmaximal
4C2×#15688849C211yesmaximal, characteristic
5C47×#1441C211yesmaximal, characteristic
6#15689754—24no—
7#15689754—22no—
8#15689754C414yescomplemented
9C2×#13094023—22no—
10C2×#13094015—22no—
11C2×#13094003—21no—
12C2×#13094003C2212yes—
13C2×#13093983—21no—
14C2×#13093947—22no—
15C2×C22⋊(C47⋊C8)C2212yes—
16#15688885—22no—
17#15688859—24no—
18#15688849—22no—
19C22×C4⋊C4×C47C2211yescharacteristic
20C22×C4⋊C4×C47C2211yescharacteristic
21C2×#95×C47—21no—
22C2×#95×C47—21no—
23C2×#95×C47C2211yescharacteristic
24C22×Dic94—21no—
25C22×Dic94D412yes—
26C22×C47⋊C8—22no—
27#13094023—28no—
28#13094023—28no—
29#13094015—28no—
30#13094015—28no—
31#13094003—24no—
32#13094003—24no—
33#13094003—22no—
34#13094003—22no—
35#13094003C2×C414yes—
36#13094003D414yes—
37#13093983—24no—
38#13093983—24no—
39C2×C4⋊Dic47—21no—
40C2×C4⋊Dic47—21no—
41C2×C4⋊Dic47—21no—
42C2×C4⋊Dic47D412yes—
43C2×Dic47⋊C4—22no—
44C2×Dic47⋊C4—22no—
45C2×C22⋊Dic47—22no—
46C2×C4×Dic47—22no—
47#13093947—44no—
48C22⋊(C47⋊C8)—22no—
49C22⋊(C47⋊C8)—22no—
50C23×C4×C47—21no—
51C23×C4×C47—21no—
52C23×C4×C47D411yescharacteristic
53C23×C4×C47D411yescharacteristic
54C23×C4×C47C2311yescharacteristic
55C2×C4⋊C4×C47—22no—
56C2×C4⋊C4×C47—22no—
57C2×C4⋊C4×C47—22no—
58C2×C4⋊C4×C47—42no—
59C2×C4⋊C4×C47C2×C412yes—
60C2×C4⋊C4×C47D412yes—
61#95×C47—22no—
62#95×C47—42no—
63#95×C47—42no—
64C24×C47C2×D411yescharacteristic
65C22×C4×C47—21no—
66C22×C4×C47—21no—
67C22×C4×C47—21no—
68C22×C4×C47—21no—
69C22×C4×C47—21no—
70C22×C4×C47—21no—
71C22×C4×C47—22no—
72C22×C4×C47—22no—
73C22×C4×C47—41no—
74C22×C4×C47—41no—
75C22×C4×C47—41no—
76C22×C4×C47—41no—
77C22×C4×C47—41no—
78C22×C4×C47—41no—
79C22×C4×C47—41no—
80C22×C4×C47—41no—
81C22×C4×C47—41no—
82C22×C4×C47—41no—
83C22×C4×C47—41no—
84C22×C4×C47—41no—
85C22×C4×C47—41no—
86C22×C4×C47—41no—
87C22×C4×C47—41no—
88C22×C4×C47—41no—
89C22×C4×C47C22⋊C412yes—
90C22×C4×C47C22⋊C412yes—
91C22×C4×C47SD1612yes—
92C22×C4×C47Q1612yes—
93C22×C4×C47C22×C411yescharacteristic
94C22×C4×C47C2×D412yes—
95C22×C4×C47C2×D412yes—
96C22×C4×C47C2×D411yescharacteristic
97C22×Dic47—22no—
98C22×Dic47—22no—
99C2×Dic94—24no—
100C2×Dic94—22no—
101C2×Dic94—42no—
102C2×Dic94—42no—
103C2×Dic94—81no—
104C2×Dic94—81no—
105C2×Dic94C22⋊C414yes—
106C4⋊C4×C47—24no—
107C4⋊C4×C47—24no—
108C4⋊C4×C47—24no—
109C4⋊C4×C47—42no—
110C22⋊Dic47—24no—
111C22⋊Dic47—24no—
112C4⋊Dic47—24no—
113C4⋊Dic47—24no—
114C4⋊Dic47—24no—
115C4⋊Dic47—22no—
116C4⋊Dic47C22⋊C414yes—
117Dic47⋊C4—28no—
118Dic47⋊C4—24no—
119Dic47⋊C4—24no—
120C4×Dic47—28no—
121C2×C47⋊C8—42no—
122C2×C47⋊C8—42no—
123C2×C47⋊C8—42no—
124C23×C47—21no—
125C23×C47—21no—
126C23×C47—21no—
127C23×C47—21no—
128C23×C47C2×C22⋊C411yescharacteristic
129C23×C47#12011yescharacteristic
130C23×C47#12011yescharacteristic
131C23×C47C2×SD1611yescharacteristic
132C23×C47C2×Q1611yescharacteristic
133C23×C47#13711yescharacteristic
134C23×C47#13711yescharacteristic
135C2×C4×C47—22no—
136C2×C4×C47—22no—
137C2×C4×C47—22no—
138C2×C4×C47—22no—
139C2×C4×C47—22no—
140C2×C4×C47—22no—
141C2×C4×C47—22no—
142C2×C4×C47—22no—
143C2×C4×C47—22no—
144C2×C4×C47—41no—
145C2×C4×C47—41no—
146C2×C4×C47—42no—
147C2×C4×C47—41no—
148C2×C4×C47—41no—
149C2×C4×C47—42no—
150C2×C4×C47—42no—
151C2×C4×C47—42no—
152C2×C4×C47—42no—
153C2×C4×C47—42no—
154C2×C4×C47—42no—
155C2×C4×C47—42no—
156C2×C4×C47—81no—
157C2×C4×C47—81no—
158C2×C4×C47—81no—
159C2×C4×C47—81no—
160C2×C4×C47—81no—
161C2×C4×C47—81no—
162C2×C4×C47—81no—
163C2×C4×C47—81no—
164C2×C4×C47—81no—
165C2×C4×C47#10314yescomplemented
166C2×C4×C47C2×C22⋊C412yes—
167C2×C4×C47#12012yes—
168C2×Dic47—24no—
169C2×Dic47—24no—
170C2×Dic47—42no—
171C2×Dic47—42no—
172C2×Dic47—42no—
173C2×Dic47—42no—
174Dic94—44no—
175Dic94—82no—
176Dic94—84no—
177C47⋊C8—82no—
178#8406—471nomaximal, Sylow
179C22×C47—21no—
180C22×C47—21no—
181C22×C47—21no—
182C22×C47—21no—
183C22×C47—21no—
184C22×C47—21no—
185C22×C47—21no—
186C22×C47—21no—
187C22×C47—21no—
188C22×C47—21no—
189C22×C47—21no—
190C22×C47—21no—
191C22×C47#37911yescharacteristic
192C22×C47C2×#10311yescharacteristic
193C22×C47#41911yescharacteristic
194C22×C47#44811yescharacteristic
195C22×C47#44811yescharacteristic
196C22×C47#45111yescharacteristic
197C22×C47#45111yescharacteristic
198C22×C47#45411yescharacteristic
199C22×C47#45611yescharacteristic
200C22×C47B(4,𝔽2)11yescharacteristic
201C22×C47#45811yescharacteristic
202C4×C47—24no—
203C4×C47—22no—
204C4×C47—22no—
205C4×C47—42no—
206C4×C47—82no—
207C4×C47—82no—
208Dic47—44no—
209Dic47—44no—
210C2×#544—471no—
211#1872—472no—
212C2×#328—472no—
213C2×#324—471no—
214#1441D4711yescharacteristic
215C2×C47—21no—
216C2×C47—21no—
217C2×C47—21no—
218C2×C47—21no—
219C2×C47#159911yescharacteristic
220C2×C47#160511yescharacteristic
221C2×C47#161111yescharacteristic
222C2×C47#161711yescharacteristic
223C2×C47#178711yescharacteristic
224C2×C47#179011yescharacteristic
225C2×C47#179311yescharacteristic
226#544—474no—
227#544—944no—
228#544—942no—
229C2×C4⋊Q8—942no—
230C2×#125—942no—
231C2×C22⋊Q8—472no—
232C2×C22⋊Q8—941no—
233C2×#117—941no—
234C22×C4⋊C4C2×D4711yescharacteristic
235C22×C4⋊C4C2×D4711yescharacteristic
236C2×#103—942no—
237C2×C22⋊C8—472no—
238C2×#95—21no—
239C2×#95—21no—
240C2×#95C2×D4711yescharacteristic
241#340—942no—
242#328—944no—
243#324—942no—
244C47#840611yescharacteristic, complemented, Sylow
245C22×Q8—472no—
246C22×Q8—941no—
247C23×C4—21no—
248C23×C4—21no—
249C23×C4C22⋊D4711yescharacteristic
250C23×C4C22⋊D4711yescharacteristic
251C23×C4C22×D4711yescharacteristic
252C22×C8—942no—
253C4⋊Q8—948no—
254C4⋊Q8—948no—
255#125—948no—
256#125—948no—
257C22⋊Q8—474no—
258C22⋊Q8—474no—
259C22⋊Q8—944no—
260C22⋊Q8—944no—
261C22⋊Q8—942no—
262C22⋊Q8—942no—
263#117—944no—
264#117—944no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—42no—
269C2×C4⋊C4—472no—
270C2×C4⋊C4—941no—
271C2×C4⋊C4—941no—
272C2×C4⋊C4—941no—
273C2×C4⋊C4—942no—
274C2×C4⋊C4—942no—
275C2×C4⋊C4C4×D4712yes—
276C2×C4⋊C4D18812yes—
277C2×C22⋊C4—942no—
278C2×C42—942no—
279#103—1884no—
280C22⋊C8—942no—
281C22⋊C8—942no—
282#95—22no—
283#95—42no—
284#95—42no—
285C24C2×C22⋊D4711yescharacteristic
286C2×Q8—474no—
287C2×Q8—944no—
288C2×Q8—942no—
289C2×Q8—3761no—
290C2×Q8—3761no—
291C2×Q8—1882no—
292C2×Q8—1882no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—942no—
318C22×C4—942no—
319C22×C4(C2×D47)⋊C412yes—
320C22×C4(C2×D47)⋊C412yes—
321C22×C4#1062533512yes—
322C22×C4#1062533712yes—
323C22×C4C2×C4×D4711yescharacteristic
324C22×C4C2×D18811yescharacteristic
325C22×C4D4×D4712yes—
326C22×C4D4×D4712yes—
327C2×C8—1882no—
328C2×C8—1882no—
329C2×C8—1882no—
330C4⋊C4—24no—
331C4⋊C4—24no—
332C4⋊C4—24no—
333C4⋊C4—42no—
334C4⋊C4—474no—
335C4⋊C4—948no—
336C4⋊C4—944no—
337C4⋊C4—944no—
338C4⋊C4—944no—
339C4⋊C4—944no—
340C4⋊C4—944no—
341C4⋊C4—942no—
342C22⋊C4—944no—
343C22⋊C4—944no—
344C42—948no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23C2×(C2×D47)⋊C411yescharacteristic
350C23#1309399211yescharacteristic
351C23#1309399211yescharacteristic
352C23C2×#1062533511yescharacteristic
353C23C2×#1062533711yescharacteristic
354C23#1309405411yescharacteristic
355C23#1309405411yescharacteristic
356Q8—3762no—
357Q8—3764no—
358Q8—1884no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—944no—
390C2×C4—944no—
391C2×C4—1882no—
392C2×C4—1882no—
393C2×C4—1882no—
394C2×C4—1882no—
395C2×C4#1309394714yescomplemented
396C2×C4C22⋊C4×D4712yes—
397C2×C4#1309399412yes—
398C8—3762no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22#1568897811yescharacteristic
412C22C2×#1309394711yescharacteristic
413C22#1568913111yescharacteristic
414C22#1568926111yescharacteristic
415C22#1568926111yescharacteristic
416C22#1568927811yescharacteristic
417C22#1568927811yescharacteristic
418C22#1568929511yescharacteristic
419C22#1568930511yescharacteristic
420C22#1568930911yescharacteristic
421C22#1568931211yescharacteristic
422C4—24no—
423C4—22no—
424C4—22no—
425C4—42no—
426C4—82no—
427C4—82no—
428C4—1884no—
429C4—1884no—
430C2—21no—
431C2—21no—
432C2—21no—
433C2—21no—
434C2#2024232711yescharacteristic
435C2#2024236111yescharacteristic
436C2#2024239511yescharacteristic
437C2#2024242911yescharacteristic
438C2#2024332211yescharacteristic
439C2#2024333511yescharacteristic
440C2#2024334611yescharacteristic
subgroupG/H
centerC23#13093992
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC47×#1441C2
socleC23×C47#120
prime radicalC24×C47C2×D4
cosocleC23×C4×C47C23
hypercenter#1441D47
hypocenterC47#8406
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1441

Complements

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

NH ≅ G/Ntype
8. #15689754C4semidirect
165. C2×C4×C47#103semidirect
244. C47#8406semidirect
395. C2×C4#13093947semidirect

Maximal subgroups

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

subgroupindex
C2×#156897542
#202436952
C2×#156888592
C2×#156888492
C47×#14412
#840647