Finite Group Databasebeta

← #26225729

Subgroups — #26225729

Order 12032.

1130 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689749C211yesmaximal, characteristic
2#20245986C211yesmaximal, characteristic
3#20244373C214yesmaximal, complemented
4#20244372C214yesmaximal, complemented
5#20243460C214yesmaximal
6C47×#2312C211yesmaximal, characteristic
7#15689749—24no—
8#15689749—24no—
9C2×#13094003C2212yes—
10C2×#13094003C2212yes—
11C2×#13094001C414yescomplemented
12C2×#13094001C414yescomplemented
13C22×C22⋊Dic47C2212yes—
14#15689016—24no—
15#15688983C2212yes—
16#15688979C2212yes—
17C4×C22⋊Dic47C2212yes—
18#15688889C22116yes—
19C22×C22⋊C4×C47C2211yescharacteristic
20C47×#388—24no—
21C47×#380C2212yes—
22C47×#379C2212yes—
23C4×C22⋊C4×C47C2212yes—
24C22×Dic94C2×C412yes—
25C22×Dic94C2×C412yes—
26C23×Dic47C2×C412yes—
27C23×Dic47C2×C412yes—
28#13094003—24no—
29#13094003—24no—
30#13094003—24no—
31#13094003—24no—
32#13094001—216no—
33#13094001—216no—
34C2×C4⋊Dic47—22no—
35C2×C4⋊Dic47C2×C412yes—
36C2×C4⋊Dic47C2×C412yes—
37C2×Dic47⋊C4C2×C414yes—
38C2×Dic47⋊C4C2×C414yes—
39C2×C22⋊Dic47—24no—
40C2×C22⋊Dic47—24no—
41C2×C22⋊Dic47—22no—
42C2×C22⋊Dic47—22no—
43C2×C22⋊Dic47C2×C414yes—
44C2×C22⋊Dic47C2314yes—
45C2×C22⋊Dic47C2314yes—
46C2×C4×Dic47—22no—
47C47⋊#95—22no—
48C47⋊#95—22no—
49C25×C47C2311yescharacteristic
50C23×C4×C47C2311yescharacteristic
51C23×C4×C47C2311yescharacteristic
52C2×C4⋊C4×C47—22no—
53C2×C22⋊C4×C47—22no—
54C2×C22⋊C4×C47—22no—
55C2×C22⋊C4×C47C2×C414yes—
56C2×C22⋊C4×C47D414yes—
57C2×C22⋊C4×C47D414yes—
58C2×C22⋊C4×C47C2314yes—
59C2×C42×C47—22no—
60#95×C47—22no—
61#95×C47—22no—
62C24×C47—24no—
63C24×C47—81no—
64C24×C47—81no—
65C24×C47C22×C412yes—
66C24×C47C2×D412yes—
67C24×C47C2×D412yes—
68C24×C47C2411yescharacteristic
69C22×C4×C47—24no—
70C22×C4×C47—81no—
71C22×C4×C47—81no—
72C22×C4×C47C22×C412yes—
73C22×C4×C47C22×C412yes—
74C22×C4×C47C2×D412yes—
75C22×C4×C47C2×D412yes—
76C22×C4×C47C2×D412yes—
77C22×C4×C47C2×D412yes—
78C22×Dic47—24no—
79C22×Dic47—24no—
80C22×Dic47—24no—
81C22×Dic47—82no—
82C22×Dic47—82no—
83C22×Dic47C22×C414yes—
84C22×Dic47C22×C414yes—
85C2×Dic94—24no—
86C2×Dic94—24no—
87C2×Dic94—82no—
88C2×Dic94—82no—
89C4⋊C4×C47—82no—
90C22⋊C4×C47—28no—
91C22⋊C4×C47—82no—
92C22⋊C4×C47—82no—
93C22⋊C4×C47C22⋊C4116yes—
94C42×C47—82no—
95C22⋊Dic47—28no—
96C22⋊Dic47—24no—
97C22⋊Dic47—24no—
98C22⋊Dic47—28no—
99C22⋊Dic47—82no—
100C22⋊Dic47—82no—
101C4⋊Dic47—24no—
102C4⋊Dic47—24no—
103C4⋊Dic47—82no—
104Dic47⋊C4—28no—
105Dic47⋊C4—28no—
106C4×Dic47—82no—
107C23×C47—24no—
108C23×C47—24no—
109C23×C47—24no—
110C23×C47—42no—
111C23×C47—42no—
112C23×C47—41no—
113C23×C47—41no—
114C23×C47—42no—
115C23×C47—42no—
116C23×C47—42no—
117C23×C47—42no—
118C23×C47—88no—
119C23×C47C2×C22⋊C414yes—
120C23×C47C23×C411yescharacteristic
121C23×C47C22×D411yescharacteristic
122C23×C47C22×D411yescharacteristic
123C23×C472−1+414yes—
124C2×C4×C47—42no—
125C2×C4×C47—42no—
126C2×C4×C47—42no—
127C2×C4×C47—42no—
128C2×C4×C47—42no—
129C2×C4×C47—42no—
130C2×C4×C47—44no—
131C2×C4×C47—44no—
132C2×C4×C47—44no—
133C2×C4×C47C2×C22⋊C414yes—
134C2×C4×C47C2×C22⋊C414yes—
135C2×Dic47—24no—
136C2×Dic47—24no—
137C2×Dic47—44no—
138C2×Dic47—44no—
139C2×Dic47—44no—
140C2×Dic47—44no—
141C2×Dic47—44no—
142C2×Dic47—84no—
143C2×Dic47—84no—
144Dic94—84no—
145Dic94—84no—
146#21827—471nomaximal, Sylow
147C22×C47—21no—
148C22×C47—21no—
149C22×C47—21no—
150C22×C47—21no—
151C22×C47—21no—
152C22×C47—21no—
153C22×C47—24no—
154C22×C47—24no—
155C22×C47—24no—
156C22×C47—44no—
157C22×C47—48no—
158C22×C47—84no—
159C22×C47—84no—
160C22×C47C22×C22⋊C411yescharacteristic
161C22×C47#51912yes—
162C22×C47#53612yes—
163C22×C47#53612yes—
164C4×C47—24no—
165C4×C47—24no—
166C4×C47—84no—
167Dic47—44no—
168Dic47—44no—
169Dic47—84no—
170C2×#543—471no—
171#2312—471no—
172#2312D4711yescharacteristic
173#1996—474no—
174#1996—474no—
175#1819—474no—
176C2×C47—22no—
177C2×C47—22no—
178C2×C47—22no—
179C2×C47—44no—
180C2×C47#231011yescharacteristic
181C2×C47#288311yescharacteristic
182C2×C47#288311yescharacteristic
183#543—944no—
184#543—944no—
185C2×C22⋊Q8—472no—
186C2×C22⋊Q8—472no—
187C2×C22⋊Q8—474no—
188C2×C22⋊Q8—474no—
189C22×C22⋊C4—472no—
190C22×C22⋊C4C2×D4711yescharacteristic
191#388—24no—
192#388—944no—
193#380—472no—
194#380C2×D4712yes—
195#379—472no—
196#379C2×D4712yes—
197C4×C22⋊C4—472no—
198C4×C22⋊C4C2×D4712yes—
199#342—4716no—
200C47#2182711yescharacteristic, complemented, Sylow
201C25C22×D4711yescharacteristic
202C22×Q8—472no—
203C22×Q8—472no—
204C23×C4—472no—
205C23×C4—472no—
206C23×C4C22×D4711yescharacteristic
207C23×C4C22×D4711yescharacteristic
208C22⋊Q8—944no—
209C22⋊Q8—944no—
210C22⋊Q8—944no—
211C22⋊Q8—944no—
212C22⋊Q8—9416no—
213C22⋊Q8—9416no—
214C2×C4⋊C4—22no—
215C2×C4⋊C4—474no—
216C2×C4⋊C4—474no—
217C2×C4⋊C4—472no—
218C2×C4⋊C4—472no—
219C2×C4⋊C4—942no—
220C2×C22⋊C4—22no—
221C2×C22⋊C4—22no—
222C2×C22⋊C4—474no—
223C2×C22⋊C4—474no—
224C2×C22⋊C4—474no—
225C2×C22⋊C4—944no—
226C2×C22⋊C4—944no—
227C2×C22⋊C4—942no—
228C2×C22⋊C4—942no—
229C2×C22⋊C4C4×D4714yes—
230C2×C22⋊C4D18814yes—
231C2×C22⋊C4C22⋊D4714yes—
232C2×C22⋊C4C22×D4714yes—
233C2×C42—22no—
234C2×C42—942no—
235#95—22no—
236#95—22no—
237#95—942no—
238#95—942no—
239C24—24no—
240C24—81no—
241C24—81no—
242C24C2×C4×D4712yes—
243C24C2×D18812yes—
244C24C2×C22⋊D4712yes—
245C24C23×D4711yescharacteristic
246C2×Q8—944no—
247C2×Q8—944no—
248C2×Q8—3762no—
249C2×Q8—3762no—
250C22×C4—24no—
251C22×C4—81no—
252C22×C4—81no—
253C22×C4—474no—
254C22×C4—474no—
255C22×C4—944no—
256C22×C4—944no—
257C22×C4—944no—
258C22×C4—3762no—
259C22×C4—3762no—
260C22×C4C2×C4×D4712yes—
261C22×C4C2×C4×D4712yes—
262C22×C4C2×D18812yes—
263C22×C4C2×D18812yes—
264C22×C4C2×C22⋊D4712yes—
265C22×C4C2×C22⋊D4712yes—
266C4⋊C4—82no—
267C4⋊C4—948no—
268C4⋊C4—948no—
269C4⋊C4—944no—
270C4⋊C4—944no—
271C4⋊C4—3762no—
272C22⋊C4—28no—
273C22⋊C4—82no—
274C22⋊C4—82no—
275C22⋊C4—948no—
276C22⋊C4—944no—
277C22⋊C4—944no—
278C22⋊C4—948no—
279C22⋊C4—3762no—
280C22⋊C4—3762no—
281C22⋊C4(C2×D47)⋊C4116yes—
282C42—82no—
283C42—3762no—
284C23—24no—
285C23—24no—
286C23—24no—
287C23—41no—
288C23—41no—
289C23—42no—
290C23—42no—
291C23—42no—
292C23—42no—
293C23—42no—
294C23—42no—
295C23—88no—
296C23C2×(C2×D47)⋊C414yes—
297C23C22×C4×D4711yescharacteristic
298C23C22×C22⋊D4711yescharacteristic
299C23C22×D18811yescharacteristic
300C23#1309407114yes—
301Q8—3764no—
302Q8—3764no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—44no—
310C2×C4—44no—
311C2×C4—44no—
312C2×C4—944no—
313C2×C4—944no—
314C2×C4—3764no—
315C2×C4—3764no—
316C2×C4—1884no—
317C2×C4—1884no—
318C2×C4—1884no—
319C2×C4—1884no—
320C2×C4—1884no—
321C2×C4C2×(C2×D47)⋊C414yes—
322C2×C4C2×(C2×D47)⋊C414yes—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—24no—
330C22—24no—
331C22—24no—
332C22—44no—
333C22—48no—
334C22—84no—
335C22—84no—
336C22C22×(C2×D47)⋊C411yescharacteristic
337C22#1568960012yes—
338C22#1568969412yes—
339C22#1568969912yes—
340C4—24no—
341C4—24no—
342C4—84no—
343C4—3764no—
344C4—1884no—
345C4—1884no—
346C2—22no—
347C2—22no—
348C2—22no—
349C2—44no—
350C2#2024597211yescharacteristic
351C2#2025184811yescharacteristic
352C2#2025184811yescharacteristic
subgroupG/H
centerC22C22×(C2×D47)⋊C4
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC47×#2312C2
socleC22×C47C22×C22⋊C4
prime radicalC25×C47C23
cosocleC24×C47C24
hypercenter#2312D47
hypocenterC47#21827
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C22⋊C4 ◁ #2312

Complements

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

NH ≅ G/Ntype
3. #20244373C2semidirect
4. #20244372C2semidirect
11. C2×#13094001C4semidirect
12. C2×#13094001C4semidirect
200. C47#21827semidirect

Maximal subgroups

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

subgroupindex
C2×#156897492
#202459862
#202443732
#202443722
#202434602
C47×#23122
#2182747