Finite Group Databasebeta

← #26112813

Subgroups — #26112813

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#20254532C211yesmaximal, characteristic
2#20252331C211yesmaximal, characteristic
3#20244233C211yesmaximal, characteristic
4#20242076C211yesmaximal, characteristic
5#20241285C211yesmaximal, characteristic
6#20241238C211yesmaximal, characteristic
7C2×C47×#332C211yesmaximal, characteristic
8#15689680C2211yescharacteristic
9#15689519—21no—
10#15689475—21no—
11#15689453C414yes—
12#15689405—22no—
13#15689252—22no—
14#15689250—21no—
15#15689247—21no—
16#15689176C2211yescharacteristic
17#15689149—21no—
18#15689147C2211yescharacteristic
19C2×#13093943—21no—
20C2×#13093943—21no—
21#15689078—21no—
22C4×#10625329C2211yescharacteristic
23#15688871—21no—
24#15688870—21no—
25C2×C4⋊Q8×C47C2211yescharacteristic
26C2×C4⋊C8×C47C2211yescharacteristic
27C2×C4⋊C8×C47C2211yescharacteristic
28C47×#332—21no—
29C47×#332—21no—
30C2×#10625329—21no—
31C2×#10625329D411yescharacteristic
32C2×#10625329D411yescharacteristic
33#13094024D411yescharacteristic
34#13094024D411yescharacteristic
35#13094016—21no—
36#13094003—21no—
37#13094003C2×C412yes—
38C4×Dic94—21no—
39C4×Dic94D412yes—
40#13093983—21no—
41#13093955—24no—
42C4⋊(C47⋊C8)—21no—
43C4⋊(C47⋊C8)—21no—
44C4⋊(C47⋊C8)—21no—
45Dic47⋊C8—22no—
46Dic47⋊C8—22no—
47#13093947—24no—
48#13093943—42no—
49#13093943—42no—
50C22⋊(C47⋊C8)C2×C412yes—
51#13093935—21no—
52#13093934—22no—
53C4×C47⋊C8—21no—
54C4×C47⋊C8—21no—
55C8×Dic47—22no—
56C22×Q8×C47—21no—
57C22×C8×C47—21no—
58C22×C8×C47—21no—
59C4⋊Q8×C47—21no—
60C4⋊Q8×C47—21no—
61C4⋊Q8×C47—21no—
62C4⋊Q8×C47—21no—
63C2×C4⋊C4×C47—21no—
64C2×C4⋊C4×C47C2×C412yes—
65C2×C42×C47C2311yescharacteristic
66C4⋊C8×C47—21no—
67C4⋊C8×C47—21no—
68C4⋊C8×C47—21no—
69C4⋊C8×C47D411yescharacteristic
70C4⋊C8×C47D411yescharacteristic
71C2×Q8×C47—41no—
72C2×Q8×C47—41no—
73C2×Q8×C47—41no—
74C2×Q8×C47—41no—
75C2×Q8×C47—41no—
76C2×Q8×C47—41no—
77C22×C4×C47—22no—
78C22×C4×C47C22×C411yescharacteristic
79C22×C4×C47C2×D411yescharacteristic
80C22×C4×C47#4111yescharacteristic
81C2×Dic94—21no—
82C2×Dic94C22⋊C412yes—
83C2×C8×C47—21no—
84C2×C8×C47—21no—
85C2×C8×C47—41no—
86C2×C8×C47—41no—
87C2×C8×C47—41no—
88C2×C8×C47—81no—
89C4⋊C4×C47—22no—
90C4⋊C4×C47—22no—
91C4⋊C4×C47—41no—
92C4⋊C4×C47—41no—
93C42×C47C2×D411yescharacteristic
94C42×C47C2×D411yescharacteristic
95C42×C47C2×D411yescharacteristic
96C42×C47#4111yescharacteristic
97C22⋊Dic47—22no—
98C4⋊Dic47—21no—
99C4⋊Dic47—21no—
100C4⋊Dic47—21no—
101C4⋊Dic47C22⋊C412yes—
102Dic47⋊C4—22no—
103Dic47⋊C4—22no—
104C4×Dic47—22no—
105#10625329—21no—
106#10625329—21no—
107#10625329—21no—
108#10625329—41no—
109#10625329—41no—
110#10625329SD1612yes—
111C2×C47⋊C8—21no—
112C2×C47⋊C8—22no—
113C2×C47⋊C8—21no—
114C2×C47⋊C8—41no—
115C23×C47C4×D411yescharacteristic
116Q8×C47—81no—
117Q8×C47—81no—
118Q8×C47—81no—
119Q8×C47—81no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—41no—
123C2×C4×C47—42no—
124C2×C4×C47—42no—
125C2×C4×C47—42no—
126C2×C4×C47C2×C22⋊C411yescharacteristic
127C2×C4×C47C4×D411yescharacteristic
128C2×C4×C47#12011yescharacteristic
129C2×C4×C47#12111yescharacteristic
130C2×C4×C47#12111yescharacteristic
131C2×C4×C47#12311yescharacteristic
132C2×C4×C47C2×SD1611yescharacteristic
133C2×C4×C47#13511yescharacteristic
134C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C47#13711yescharacteristic
136C2×Dic47—22no—
137C2×Dic47—22no—
138Dic94—41no—
139Dic94—41no—
140Dic94—42no—
141C8×C47—41no—
142C8×C47—41no—
143C8×C47—81no—
144C47⋊C8—22no—
145C47⋊C8—42no—
146C47⋊C8—41no—
147C47⋊C8—81no—
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—82no—
158C4×C47#44811yescharacteristic
159C4×C47#44911yescharacteristic
160C4×C47#46011yescharacteristic
161C4×C47#46411yescharacteristic
162C4×C47#47111yescharacteristic
163C4×C47#47311yescharacteristic
164Dic47—42no—
165Dic47—42no—
166#3229—471no—
167#2962—471no—
168#1966—471no—
169#1550—471no—
170C2×#332D4711yescharacteristic
171#1301—471no—
172#1283—471no—
173C2×C47—21no—
174C2×C47—21no—
175C2×C47#188011yescharacteristic
176C2×C47#190811yescharacteristic
177C2×C47#191511yescharacteristic
178#533—471no—
179C2×C4⋊Q8C2×D4711yescharacteristic
180#498—941no—
181#487—941no—
182#483—474no—
183#475—942no—
184#446—942no—
185#446—941no—
186C8×Q8—941no—
187#431—471no—
188#424—941no—
189#423—471no—
190C2×C4⋊C8C2×D4711yescharacteristic
191C2×C4⋊C8C2×D4711yescharacteristic
192C2×#101—941no—
193C2×#101—941no—
194#405—941no—
195C4×M16—471no—
196#333—941no—
197#332—21no—
198#332—21no—
199#332—941no—
200C47#927211yescharacteristic, complemented, Sylow
201C22×Q8—21no—
202C2×M16—471no—
203C2×M16—471no—
204C2×M16—941no—
205C22×C8—21no—
206C22×C8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—471no—
212C4⋊Q8—471no—
213#125—941no—
214C22⋊Q8—472no—
215C22⋊Q8—941no—
216C4×Q8—472no—
217C4×Q8—941no—
218#117—941no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4C4×D4712yes—
221C2×C42C22×D4711yescharacteristic
222#106—944no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—942no—
227C4⋊C8—942no—
228C4⋊C8—941no—
229C4⋊C8—941no—
230C4⋊C8—941no—
231C4⋊C8C22⋊D4711yescharacteristic
232C4⋊C8C22⋊D4711yescharacteristic
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—41no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—472no—
249C2×Q8—941no—
250C22×C4—22no—
251C22×C4C2×C4×D4711yescharacteristic
252C22×C4D4×D4711yescharacteristic
253C22×C4#1062535211yescharacteristic
254M16—472no—
255M16—941no—
256M16—941no—
257M16—941no—
258M16—1881no—
259M16—1881no—
260C2×C8—21no—
261C2×C8—21no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—41no—
265C2×C8—81no—
266C2×C8—941no—
267C2×C8—942no—
268C2×C8—941no—
269C2×C8—1881no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—472no—
275C4⋊C4—942no—
276C4⋊C4—941no—
277C4⋊C4—941no—
278C4⋊C4—941no—
279C4⋊C4—942no—
280C22⋊C4—942no—
281C42—942no—
282C42#1062535011yescharacteristic
283C42D4×D4711yescharacteristic
284C42D4×D4711yescharacteristic
285C42C2×C22⋊D4711yescharacteristic
286C23(C22⋊D47)⋊C411yescharacteristic
287Q8—81no—
288Q8—81no—
289Q8—81no—
290Q8—81no—
291Q8—1882no—
292Q8—1881no—
293Q8—1881no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—942no—
301C2×C4—942no—
302C2×C4C22⋊C4×D4711yescharacteristic
303C2×C4C4×C22⋊D4711yescharacteristic
304C2×C4#1309399211yescharacteristic
305C2×C4#1309399511yescharacteristic
306C2×C4#1309399711yescharacteristic
307C2×C4#1309400611yescharacteristic
308C2×C4SD16×D4711yescharacteristic
309C2×C4#1309404311yescharacteristic
310C2×C4#1309404811yescharacteristic
311C2×C4#1309405311yescharacteristic
312C8—41no—
313C8—41no—
314C8—81no—
315C8—942no—
316C8—3761no—
317C8—1882no—
318C8—1881no—
319C22—21no—
320C22—21no—
321C22#1568899911yescharacteristic
322C22#1568921411yescharacteristic
323C22#1568922011yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—82no—
328C4—1882no—
329C4—1882no—
330C4#1568926011yescharacteristic
331C4#1568926511yescharacteristic
332C4#1568932211yescharacteristic
333C4#1568934411yescharacteristic
334C4#1568938311yescharacteristic
335C4#1568939511yescharacteristic
336C2—21no—
337C2—21no—
338C2#2024374011yescharacteristic
339C2#2024390611yescharacteristic
340C2#2024393711yescharacteristic
subgroupG/H
centerC22#15688999
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC2×C47×#332C2
socleC22×C47#386
prime radicalC23×C47C4×D4
cosocleC2×C42×C47C23
hypercenterC2×#332D47
hypocenterC47#9272
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#332

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
#202545322
#202523312
#202442332
#202420762
#202412852
#202412382
C2×C47×#3322
#927247