Finite Group Databasebeta

← #26112814

Subgroups — #26112814

Order 12032.

428 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20254529C211yesmaximal, characteristic
2#20252337C211yesmaximal, characteristic
3#20244231C211yesmaximal, characteristic
4C2×#15688868C211yesmaximal, characteristic
5#20241283C211yesmaximal, characteristic
6#20241238C211yesmaximal, characteristic
7C47×#1550C211yesmaximal, characteristic
8C2×#13094024C2211yescharacteristic
9#15689519—21no—
10#15689473—21no—
11#15689451C414yes—
12#15689408—22no—
13#15689254—21no—
14#15689254—22no—
15Q8×C47⋊C8—21no—
16#15689176C2211yescharacteristic
17#15689150—21no—
18C2×C4⋊(C47⋊C8)C2211yescharacteristic
19C2×#13093942—21no—
20C2×#13093942—21no—
21#15689079—21no—
22C4×#10625329C2211yescharacteristic
23#15688868—21no—
24#15688868—21no—
25C47×#533C2211yescharacteristic
26C47×#423C2211yescharacteristic
27C2×C4⋊C8×C47C2211yescharacteristic
28C47×#333—21no—
29C47×#332—21no—
30C22×Dic94—21no—
31C2×#10625329D411yescharacteristic
32C2×#10625329D411yescharacteristic
33C22×C47⋊C8—21no—
34#13094024—21no—
35#13094024—21no—
36#13094024—21no—
37#13094024—21no—
38C2×C4⋊Dic47—21no—
39C2×C4⋊Dic47C2×C412yes—
40#13093955—24no—
41C4⋊(C47⋊C8)—22no—
42C4⋊(C47⋊C8)—22no—
43C4⋊(C47⋊C8)—21no—
44C4⋊(C47⋊C8)—21no—
45C4⋊(C47⋊C8)D411yescharacteristic
46C4⋊(C47⋊C8)D411yescharacteristic
47#13093948—24no—
48#13093942—42no—
49#13093942—42no—
50C22⋊(C47⋊C8)C2×C412yes—
51#13093935—22no—
52#13093935—21no—
53C4×C47⋊C8—22no—
54C4×C47⋊C8—21no—
55C4×C47⋊C8—21no—
56C2×M16×C47—21no—
57C22×C8×C47—21no—
58C4⋊Q8×C47D411yescharacteristic
59C4⋊Q8×C47D411yescharacteristic
60#125×C47—21no—
61C22⋊Q8×C47—21no—
62C22⋊Q8×C47C2×C412yes—
63C4×Q8×C47—21no—
64C4×Q8×C47D412yes—
65#117×C47—21no—
66C2×C42×C47C2311yescharacteristic
67C4⋊C8×C47—21no—
68C4⋊C8×C47—21no—
69C4⋊C8×C47—21no—
70C4⋊C8×C47—21no—
71C2×Q8×C47—21no—
72C2×Q8×C47C22⋊C412yes—
73C22×C4×C47C22×C411yescharacteristic
74C22×C4×C47C2×D411yescharacteristic
75C22×C4×C47#4111yescharacteristic
76C22×Dic47—22no—
77C2×Dic94—41no—
78C2×Dic94—41no—
79C2×Dic94—41no—
80C2×Dic94—41no—
81C2×Dic94—41no—
82C2×Dic94—41no—
83M16×C47—41no—
84M16×C47—41no—
85C2×C8×C47—41no—
86C2×C8×C47—41no—
87C2×C8×C47—81no—
88C4⋊C4×C47—22no—
89C4⋊C4×C47—21no—
90C4⋊C4×C47—21no—
91C4⋊C4×C47—21no—
92C4⋊C4×C47—22no—
93C4⋊C4×C47C22⋊C412yes—
94C22⋊C4×C47—22no—
95C42×C47—22no—
96C42×C47C2×D411yescharacteristic
97C42×C47C2×D411yescharacteristic
98C42×C47C2×D411yescharacteristic
99C42×C47#4111yescharacteristic
100C4⋊Dic47—22no—
101C4⋊Dic47—22no—
102C4⋊Dic47—41no—
103C4⋊Dic47—41no—
104#10625329—21no—
105#10625329—21no—
106#10625329—21no—
107#10625329SD1612yes—
108C2×C47⋊C8—21no—
109C2×C47⋊C8—22no—
110C2×C47⋊C8—21no—
111C2×C47⋊C8—21no—
112C2×C47⋊C8—21no—
113C2×C47⋊C8—41no—
114C2×C47⋊C8—41no—
115C23×C47C4×D411yescharacteristic
116Q8×C47—42no—
117Q8×C47—41no—
118Q8×C47—41no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—22no—
122C2×C4×C47—22no—
123C2×C4×C47—41no—
124C2×C4×C47C2×C22⋊C411yescharacteristic
125C2×C4×C47C4×D411yescharacteristic
126C2×C4×C47#12011yescharacteristic
127C2×C4×C47#12111yescharacteristic
128C2×C4×C47#12111yescharacteristic
129C2×C4×C47#12311yescharacteristic
130C2×C4×C47C2×SD1611yescharacteristic
131C2×C4×C47#13511yescharacteristic
132C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C47#13711yescharacteristic
134C2×Dic47—42no—
135C2×Dic47—42no—
136C2×Dic47—42no—
137Dic94—81no—
138Dic94—81no—
139Dic94—81no—
140Dic94—81no—
141C8×C47—81no—
142C8×C47—81no—
143C47⋊C8—22no—
144C47⋊C8—42no—
145C47⋊C8—41no—
146C47⋊C8—41no—
147C47⋊C8—41no—
148#9272—471nomaximal, Sylow
149C22×C47—21no—
150C22×C47—21no—
151C22×C47#38611yescharacteristic
152C22×C47C4×SD1611yescharacteristic
153C22×C47#44011yescharacteristic
154C4×C47—21no—
155C4×C47—21no—
156C4×C47—21no—
157C4×C47—42no—
158C4×C47—42no—
159C4×C47#44811yescharacteristic
160C4×C47#44911yescharacteristic
161C4×C47#46011yescharacteristic
162C4×C47#46411yescharacteristic
163C4×C47#47111yescharacteristic
164C4×C47#47311yescharacteristic
165Dic47—82no—
166#3229—471no—
167#2962—471no—
168#1966—471no—
169#1550D4711yescharacteristic
170C2×#332—471no—
171#1301—471no—
172#1283—471no—
173C2×C47—21no—
174C2×C47—21no—
175C2×C47#188011yescharacteristic
176C2×C47#190811yescharacteristic
177C2×C47#191511yescharacteristic
178#533C2×D4711yescharacteristic
179C2×C4⋊Q8—471no—
180#498—941no—
181#487—941no—
182#483—474no—
183#475—942no—
184#446—941no—
185#446—942no—
186C8×Q8—941no—
187#431—471no—
188#424—941no—
189#423C2×D4711yescharacteristic
190C2×C4⋊C8—471no—
191C2×C4⋊C8C2×D4711yescharacteristic
192C2×#101—941no—
193C2×#101—941no—
194#405—941no—
195C4×M16—471no—
196#333—21no—
197#332—21no—
198#332—941no—
199#332—941no—
200C47#927211yescharacteristic, complemented, Sylow
201C22×Q8—941no—
202C2×M16—21no—
203C2×M16—471no—
204C2×M16—471no—
205C22×C8—21no—
206C22×C8—941no—
207C4⋊Q8—941no—
208C4⋊Q8—941no—
209C4⋊Q8—941no—
210C4⋊Q8—941no—
211C4⋊Q8C22⋊D4711yescharacteristic
212C4⋊Q8C22⋊D4711yescharacteristic
213#125—21no—
214C22⋊Q8—21no—
215C22⋊Q8C4×D4712yes—
216C4×Q8—21no—
217C4×Q8D18812yes—
218#117—21no—
219C2×C4⋊C4—472no—
220C2×C4⋊C4—941no—
221C2×C42C22×D4711yescharacteristic
222#106—944no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8—471no—
228C4⋊C8—471no—
229C4⋊C8—942no—
230C4⋊C8—942no—
231C4⋊C8—941no—
232C4⋊C8—941no—
233#103—944no—
234#101—1882no—
235#101—1882no—
236C22⋊C8—472no—
237#97—942no—
238#97—941no—
239C4×C8—942no—
240C4×C8—941no—
241C4×C8—941no—
242C2×Q8—21no—
243C2×Q8—1881no—
244C2×Q8—1881no—
245C2×Q8—1881no—
246C2×Q8—1881no—
247C2×Q8—1881no—
248C2×Q8—1881no—
249C2×Q8(C2×D47)⋊C412yes—
250C22×C4—942no—
251C22×C4C2×C4×D4711yescharacteristic
252C22×C4D4×D4711yescharacteristic
253C22×C4#1062535211yescharacteristic
254M16—41no—
255M16—41no—
256M16—472no—
257M16—941no—
258M16—941no—
259M16—941no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—81no—
263C2×C8—941no—
264C2×C8—942no—
265C2×C8—941no—
266C2×C8—941no—
267C2×C8—941no—
268C2×C8—1881no—
269C2×C8—1881no—
270C4⋊C4—22no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—22no—
275C4⋊C4—942no—
276C4⋊C4—942no—
277C4⋊C4—1881no—
278C4⋊C4—1881no—
279C4⋊C4(C2×D47)⋊C412yes—
280C22⋊C4—22no—
281C42—22no—
282C42C2×D18811yescharacteristic
283C42D4×D4711yescharacteristic
284C42#1062535211yescharacteristic
285C42C2×C22⋊D4711yescharacteristic
286C23(C22⋊D47)⋊C411yescharacteristic
287Q8—42no—
288Q8—41no—
289Q8—41no—
290Q8—3761no—
291Q8—3761no—
292Q8—3761no—
293Q8—3761no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—41no—
299C2×C4—1882no—
300C2×C4—1882no—
301C2×C4—1882no—
302C2×C4C2×(C2×D47)⋊C411yescharacteristic
303C2×C4(C22⋊D47)⋊C411yescharacteristic
304C2×C4#1309399411yescharacteristic
305C2×C4#1309399611yescharacteristic
306C2×C4#1309399611yescharacteristic
307C2×C4#1309400811yescharacteristic
308C2×C4SD16×D4711yescharacteristic
309C2×C4#1309404711yescharacteristic
310C2×C4#1309405111yescharacteristic
311C2×C4#1309405611yescharacteristic
312C8—81no—
313C8—81no—
314C8—942no—
315C8—1882no—
316C8—1881no—
317C8—1881no—
318C8—1881no—
319C22—21no—
320C22—21no—
321C22#1568900011yescharacteristic
322C22#1568920811yescharacteristic
323C22#1568922611yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—42no—
328C4—42no—
329C4—3762no—
330C4#1568926311yescharacteristic
331C4#1568927111yescharacteristic
332C4#1568932111yescharacteristic
333C4#1568934711yescharacteristic
334C4#1568938411yescharacteristic
335C4#1568939611yescharacteristic
336C2—21no—
337C2—21no—
338C2#2024374111yescharacteristic
339C2#2024390111yescharacteristic
340C2#2024393811yescharacteristic
subgroupG/H
centerC22#15689000
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1550C2
socleC22×C47#386
prime radicalC23×C47C4×D4
cosocleC2×C42×C47C23
hypercenter#1550D47
hypocenterC47#9272
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1550

Complements

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

NH ≅ G/Ntype
200. C47#9272semidirect

Maximal subgroups

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

subgroupindex
#202545292
#202523372
#202442312
C2×#156888682
#202412832
#202412382
C47×#15502
#927247