Finite Group Databasebeta

← #26135632

Subgroups — #26135632

Order 12032.

462 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689501C211yesmaximal, characteristic
2C2×#15688928C211yesmaximal, characteristic
3C2×#15688927C211yesmaximal, characteristic
4C2×#15688926C211yesmaximal, characteristic
5#20244119C211yesmaximal, characteristic
6#20241465C211yesmaximal, characteristic
7C2×C47×#358C211yesmaximal, characteristic
8C22×Dic188C2211yescharacteristic
9C22×#10625337—21no—
10C2×#13094022—21no—
11C22×C47⋊C16C2211yescharacteristic
12#15689501—22no—
13#15689501—22no—
14C2×#13093958C2211yescharacteristic
15C2×C8×Dic47C2211yescharacteristic
16#15689019—21no—
17#15688928—22no—
18#15688927—22no—
19#15688926—22no—
20#15688885—21no—
21C22×Q16×C47C2211yescharacteristic
22C22×C16×C47C2211yescharacteristic
23C2×#107×C47C2211yescharacteristic
24C47×#358—22no—
25C22×Dic94—21no—
26C2×Dic188—21no—
27C2×Dic188—21no—
28C2×Dic188—21no—
29C2×Dic188—21no—
30C2×Dic188—21no—
31C2×Dic188D412yes—
32C2×#10625337—24no—
33C2×#10625337—42no—
34C2×#10625337—42no—
35C22×C47⋊C8D411yescharacteristic
36#13094022—24no—
37#13094022—42no—
38C2×C4⋊Dic47—21no—
39C2×Dic47⋊C4—41no—
40C2×Dic47⋊C4—41no—
41C2×Dic47⋊C4—41no—
42C2×C4×Dic47D411yescharacteristic
43C2×C47⋊C16—21no—
44C2×C47⋊C16—21no—
45C2×C47⋊C16—21no—
46#13093958—21no—
47#13093958D412yes—
48C8×Dic47—21no—
49C8×Dic47—21no—
50C47⋊#95—41no—
51C22×Q8×C47—21no—
52C2×Q16×C47—21no—
53C2×Q16×C47—21no—
54C2×Q16×C47—21no—
55C2×Q16×C47—21no—
56C2×Q16×C47—21no—
57C2×Q16×C47D412yes—
58C22×C8×C47C2311yescharacteristic
59C2×C4⋊C4×C47—21no—
60C2×C16×C47—21no—
61C2×C16×C47—21no—
62C2×C16×C47—21no—
63#107×C47—21no—
64#107×C47—21no—
65C2×Q8×C47—22no—
66C2×Q8×C47—41no—
67C2×Q8×C47—41no—
68C2×Q8×C47—41no—
69C2×Q8×C47—41no—
70C2×Q8×C47—41no—
71C22×C4×C47—41no—
72C22×C4×C47—41no—
73C22×C4×C47C2×D411yescharacteristic
74C22×Dic47—41no—
75C22×Dic47—41no—
76C22×Dic47D811yescharacteristic
77C22×Dic47D811yescharacteristic
78C2×Dic94—22no—
79C2×Dic94—41no—
80C2×Dic94—41no—
81C2×Dic94—41no—
82C2×Dic94—41no—
83C2×Dic94—41no—
84Q16×C47—22no—
85Q16×C47—22no—
86Q16×C47—41no—
87Q16×C47—41no—
88C2×C8×C47C2×D411yescharacteristic
89C2×C8×C47C2×D411yescharacteristic
90C2×C8×C47C2×D411yescharacteristic
91C2×C8×C47#4111yescharacteristic
92C2×C8×C47#4111yescharacteristic
93C2×C8×C47#4111yescharacteristic
94C4⋊C4×C47—41no—
95C4⋊C4×C47—41no—
96#10625337—48no—
97C4⋊Dic47—22no—
98C4⋊Dic47—41no—
99Dic47⋊C4—44no—
100Dic47⋊C4—44no—
101Dic47⋊C4—82no—
102C4×Dic47—21no—
103C4×Dic47—21no—
104C2×C47⋊C8—21no—
105C2×C47⋊C8—21no—
106C2×C47⋊C8SD1612yes—
107Dic188—22no—
108Dic188—22no—
109Dic188—41no—
110Dic188—41no—
111C16×C47—41no—
112C47⋊C16—41no—
113C23×C47C2×D811yescharacteristic
114Q8×C47—42no—
115Q8×C47—42no—
116Q8×C47—81no—
117Q8×C47—81no—
118C2×C4×C47—42no—
119C2×C4×C47—81no—
120C2×C4×C47—81no—
121C2×C4×C47—81no—
122C2×C4×C47—81no—
123C2×C4×C47—81no—
124C2×C4×C47#12011yescharacteristic
125C2×C4×C47#12111yescharacteristic
126C2×C4×C47#12411yescharacteristic
127C2×C4×C47C2×SD1611yescharacteristic
128C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—21no—
134C2×Dic47—42no—
135C2×Dic47—42no—
136C2×Dic47—81no—
137C2×Dic47—81no—
138C2×Dic47—81no—
139C2×Dic47—81no—
140C2×Dic47SD3212yes—
141C2×Dic47Q3212yes—
142Dic94—42no—
143Dic94—42no—
144Dic94—81no—
145Dic94—81no—
146C8×C47#12111yescharacteristic
147C8×C47#12111yescharacteristic
148C8×C47#12311yescharacteristic
149C8×C47#12311yescharacteristic
150C47⋊C8—22no—
151#13409—471nomaximal, Sylow
152C22×C47#44711yescharacteristic
153C22×C47#45911yescharacteristic
154C22×C47#48611yescharacteristic
155C22×C47C2×SD3211yescharacteristic
156C22×C47C2×Q3211yescharacteristic
157C22×C47#51011yescharacteristic
158C22×C47#51011yescharacteristic
159C4×C47—82no—
160C4×C47—161no—
161C4×C47#39411yescharacteristic
162C4×C47#45011yescharacteristic
163C4×C47#46011yescharacteristic
164C4×C47#49011yescharacteristic
165Dic47—22no—
166Dic47—22no—
167Dic47—82no—
168Dic47—82no—
169C2×#494—471no—
170C2×#358—471no—
171C2×#358—471no—
172C2×#358—471no—
173C2×#358D4711yescharacteristic
174#1942—471no—
175#1374—471no—
176C2×C47#204111yescharacteristic
177C2×C47#218511yescharacteristic
178C2×C47#218811yescharacteristic
179C2×C47#220811yescharacteristic
180C2×C47#220911yescharacteristic
181C2×C47#224111yescharacteristic
182C2×C47#224511yescharacteristic
183C22×Q16—471no—
184C22×Q16—941no—
185C22×Q16C2×D4711yescharacteristic
186C2×C4⋊Q8—941no—
187C22×C16—471no—
188C22×C16C2×D4711yescharacteristic
189#494—942no—
190#494—942no—
191C2×#107—471no—
192C2×#107C2×D4711yescharacteristic
193C2×C4×C8—471no—
194#389—941no—
195#358—22no—
196#358—942no—
197#358—942no—
198#358—942no—
199#340—941no—
200C47#1340911yescharacteristic, complemented, Sylow
201C22×Q8—21no—
202C22×Q8—941no—
203C2×Q16—21no—
204C2×Q16—21no—
205C2×Q16—21no—
206C2×Q16—21no—
207C2×Q16—21no—
208C2×Q16—472no—
209C2×Q16—944no—
210C2×Q16—941no—
211C2×Q16—941no—
212C2×Q16—941no—
213C2×Q16—941no—
214C2×Q16—941no—
215C2×Q16—1882no—
216C2×Q16—1882no—
217C2×Q16C22⋊D4712yes—
218C22×C8—471no—
219C22×C8C22×D4711yescharacteristic
220C4⋊Q8—944no—
221C4⋊Q8—1882no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—941no—
224C2×C4⋊C4—1881no—
225C2×C4⋊C4—1881no—
226C2×C4⋊C4—1881no—
227C2×C42—471no—
228C2×C16—21no—
229C2×C16—21no—
230C2×C16—21no—
231C2×C16—941no—
232C2×C16—941no—
233C2×C16—941no—
234#107—21no—
235#107—21no—
236#107—472no—
237#107—941no—
238C4×C8—941no—
239C4×C8—941no—
240#95—1881no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—942no—
248C2×Q8—1881no—
249C2×Q8—1881no—
250C2×Q8—1881no—
251C2×Q8—1881no—
252C2×Q8—1881no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—471no—
256C22×C4—471no—
257C22×C4—1881no—
258C22×C4—1881no—
259C22×C4D4×D4711yescharacteristic
260Q16—22no—
261Q16—22no—
262Q16—41no—
263Q16—41no—
264Q16—942no—
265Q16—942no—
266Q16—1888no—
267Q16—1881no—
268Q16—1881no—
269C2×C8—472no—
270C2×C8—941no—
271C2×C8—941no—
272C2×C8#1062535011yescharacteristic
273C2×C8#1062535011yescharacteristic
274C2×C8D4×D4711yescharacteristic
275C2×C8D4×D4711yescharacteristic
276C2×C8#1062535211yescharacteristic
277C2×C8C2×C22⋊D4711yescharacteristic
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—942no—
281C4⋊C4—3762no—
282C4⋊C4—1884no—
283C4⋊C4—1884no—
284C4⋊C4—1881no—
285C42—941no—
286C42—941no—
287C16—41no—
288C16—1881no—
289C23D8×D4711yescharacteristic
290Q8—42no—
291Q8—42no—
292Q8—81no—
293Q8—81no—
294Q8—3761no—
295Q8—3761no—
296Q8—1882no—
297Q8—1882no—
298C2×C4—42no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—472no—
305C2×C4—472no—
306C2×C4—941no—
307C2×C4—941no—
308C2×C4—941no—
309C2×C4—941no—
310C2×C4—3761no—
311C2×C4—3761no—
312C2×C4—3761no—
313C2×C4—3761no—
314C2×C4—1882no—
315C2×C4—1882no—
316C2×C4#1309399211yescharacteristic
317C2×C4#1309399711yescharacteristic
318C2×C4#1309401011yescharacteristic
319C2×C4SD16×D4711yescharacteristic
320C2×C4#1309404811yescharacteristic
321C2×C4#1309405111yescharacteristic
322C8—942no—
323C8#1309399611yescharacteristic
324C8#1309399711yescharacteristic
325C8#1309400611yescharacteristic
326C8#1309400711yescharacteristic
327C22#1568925511yescharacteristic
328C22#1568931711yescharacteristic
329C22#1568946811yescharacteristic
330C22SD32×D4711yescharacteristic
331C22Q32×D4711yescharacteristic
332C22#1568956211yescharacteristic
333C22#1568956511yescharacteristic
334C4—82no—
335C4—161no—
336C4—942no—
337C4—942no—
338C4—3762no—
339C4—3762no—
340C4#1568903811yescharacteristic
341C4#1568927211yescharacteristic
342C4#1568932211yescharacteristic
343C4#1568948611yescharacteristic
344C2#2024462011yescharacteristic
345C2#2024530311yescharacteristic
346C2#2024532011yescharacteristic
347C2#2024543211yescharacteristic
348C2#2024543711yescharacteristic
349C2#2024561411yescharacteristic
350C2#2024563211yescharacteristic
subgroupG/H
centerC23D8×D47
commutator, cosocleC22×C8×C47C23
FrattiniC22×C8C22×D47
FittingC2×C47×#358C2
socle, prime radicalC23×C47C2×D8
hypercenterC2×#358D47
hypocenterC47#13409
LCSG ▷ C22×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
200. C47#13409semidirect

Maximal subgroups

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

subgroupindex
C2×#156895012
C2×#156889282
C2×#156889272
C2×#156889262
#202441192
#202414652
C2×C47×#3582
#1340947