Finite Group Databasebeta

← #26104296

Subgroups — #26104296

Order 12032.

568 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20245871C211yesmaximal, characteristic
2C2×#15688878C211yesmaximal, characteristic
3#20241212C212yesmaximal, complemented
4#20241210C212yesmaximal, complemented
5C47×#1817C211yesmaximal, characteristic
6C23×C47⋊C8—21no—
7C2×#13093983C411yescharacteristic
8C2×#13093983C411yescharacteristic
9#15689021C411yescharacteristic
10#15689021C411yescharacteristic
11#15689021C2211yescharacteristic
12#15689021C2211yescharacteristic
13#15688996—21no—
14#15688996—21no—
15C4×Dic47⋊C4—21no—
16C4×Dic47⋊C4—21no—
17#15688878—21no—
18#15688878C2212yes—
19C22×C42×C47C2211yescharacteristic
20C2×C22⋊C8×C47—21no—
21C47×#336—21no—
22C47×#336C2212yes—
23C22×C47⋊C8—24no—
24C22×C47⋊C8—22no—
25C22×C47⋊C8—42no—
26C22×C47⋊C8—42no—
27#13093983—22no—
28#13093983—42no—
29#13093983C814yescomplemented
30C2×C4⋊Dic47C2×C411yescharacteristic
31C2×C4⋊Dic47C2×C411yescharacteristic
32C2×C4⋊Dic47C2×C411yescharacteristic
33C2×C4⋊Dic47C2×C411yescharacteristic
34C2×Dic47⋊C4—21no—
35C2×Dic47⋊C4—21no—
36C2×Dic47⋊C4—21no—
37C2×Dic47⋊C4—21no—
38C2×C22⋊Dic47—21no—
39C2×C22⋊Dic47—21no—
40C2×C4×Dic47—21no—
41C2×C4×Dic47—21no—
42C47⋊#95—21no—
43C47⋊#95—21no—
44C47⋊#95—21no—
45C47⋊#95—21no—
46C23×C4×C47C2×C411yescharacteristic
47C23×C4×C47D411yescharacteristic
48C23×C4×C47D411yescharacteristic
49C22×C8×C47—22no—
50C2×C42×C47—42no—
51C2×C42×C47C2×C411yescharacteristic
52C2×C42×C47D411yescharacteristic
53C2×C42×C47D411yescharacteristic
54C2×C42×C47C2311yescharacteristic
55C22⋊C8×C47—42no—
56C24×C47C22⋊C411yescharacteristic
57C22×C4×C47—22no—
58C22×C4×C47—22no—
59C22×C4×C47—22no—
60C22×C4×C47—22no—
61C22×C4×C47—21no—
62C22×C4×C47—21no—
63C22×C4×C47—22no—
64C22×C4×C47—22no—
65C22×C4×C47—41no—
66C22×C4×C47C22⋊C411yescharacteristic
67C22×C4×C47C22⋊C411yescharacteristic
68C22×C4×C47C22⋊C411yescharacteristic
69C22×C4×C47C2×C812yes—
70C22×C4×C47M1612yes—
71C22×C4×C47C22×C411yescharacteristic
72C22×C4×C47C2×D411yescharacteristic
73C22×C4×C47C2×D411yescharacteristic
74C22×Dic47—21no—
75C22×Dic47—21no—
76C22×Dic47—21no—
77C22×Dic47—21no—
78C2×C8×C47—42no—
79C2×C8×C47—42no—
80C2×C8×C47—42no—
81C42×C47—41no—
82C42×C47—41no—
83C42×C47—41no—
84C42×C47—41no—
85C22⋊Dic47—24no—
86C22⋊Dic47—42no—
87C4⋊Dic47—21no—
88C4⋊Dic47—21no—
89C4⋊Dic47—41no—
90C4⋊Dic47—41no—
91C4⋊Dic47C2×C812yescomplemented
92C4⋊Dic47C2×C812yescomplemented
93Dic47⋊C4—42no—
94Dic47⋊C4—42no—
95Dic47⋊C4—42no—
96Dic47⋊C4—41no—
97Dic47⋊C4—41no—
98C4×Dic47—24no—
99C4×Dic47—42no—
100C2×C47⋊C8—24no—
101C2×C47⋊C8—48no—
102C2×C47⋊C8—42no—
103C2×C47⋊C8—42no—
104C23×C47—21no—
105C23×C47—21no—
106C23×C47—21no—
107C23×C47—21no—
108C23×C47C22⋊C812yes—
109C23×C47#9912yes—
110C23×C47#10112yes—
111C23×C47C2×C22⋊C411yescharacteristic
112C2×C4×C47—24no—
113C2×C4×C47—24no—
114C2×C4×C47—24no—
115C2×C4×C47—24no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—21no—
120C2×C4×C47—21no—
121C2×C4×C47—21no—
122C2×C4×C47—21no—
123C2×C4×C47—21no—
124C2×C4×C47—21no—
125C2×C4×C47—21no—
126C2×C4×C47—21no—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—44no—
130C2×C4×C47C22⋊C812yes—
131C2×C4×C47#10412yes—
132C2×C4×C47C22×C811yescharacteristic
133C2×C4×C47C2×M1611yescharacteristic
134C2×C4×C47#13512yes—
135C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C47#13711yescharacteristic
137C2×Dic47—22no—
138C2×Dic47—22no—
139C2×Dic47—41no—
140C2×Dic47—41no—
141C2×Dic47—41no—
142C2×Dic47—41no—
143C2×Dic47—41no—
144C2×Dic47—41no—
145C2×Dic47—41no—
146C2×Dic47—41no—
147C2×Dic47—41no—
148C2×Dic47—41no—
149C8×C47—82no—
150C47⋊C8—44no—
151#7579—471nomaximal, Sylow
152C22×C47—22no—
153C22×C47—22no—
154C22×C47—22no—
155C22×C47—22no—
156C22×C47—22no—
157C22×C47—22no—
158C22×C47#32414yes—
159C22×C47C2×C22⋊C811yescharacteristic
160C22×C47C2×#9911yescharacteristic
161C22×C47C2×#10111yescharacteristic
162C22×C47#41611yescharacteristic
163C22×C47#41711yescharacteristic
164C22×C47C2×#10411yescharacteristic
165C22×C47#42111yescharacteristic
166C4×C47—22no—
167C4×C47—21no—
168C4×C47—21no—
169C4×C47—21no—
170C4×C47—22no—
171C4×C47—21no—
172C4×C47—22no—
173C4×C47—41no—
174Dic47—42no—
175Dic47—42no—
176Dic47—81no—
177Dic47—81no—
178#2296—471no—
179#1817D4711yescharacteristic
180C2×#336—471no—
181#1271—472no—
182#1271—472no—
183C2×C47—24no—
184C2×C47C2×#32411yescharacteristic
185C2×C47#147611yescharacteristic
186C2×C47#147711yescharacteristic
187C2×C47#150411yescharacteristic
188C2×C47#151611yescharacteristic
189C2×C47#153111yescharacteristic
190C2×C47#155211yescharacteristic
191C23×C8—941no—
192C2×#117—471no—
193C2×#117—471no—
194C22×C42C2×D4711yescharacteristic
195C2×C22⋊C8—21no—
196#389—471no—
197#389—471no—
198#389—471no—
199#389—471no—
200#385—941no—
201#385—941no—
202C4×C4⋊C4—941no—
203C4×C4⋊C4—941no—
204#336—21no—
205#336—472no—
206#336—941no—
207#336C2×D4712yes—
208C47#757911yescharacteristic, complemented, Sylow
209C23×C4C4×D4711yescharacteristic
210C23×C4D18811yescharacteristic
211C23×C4C22⋊D4711yescharacteristic
212C22×C8—22no—
213C22×C8—944no—
214C22×C8—942no—
215C22×C8—1882no—
216C22×C8—1882no—
217#117—474no—
218#117—942no—
219#117—1882no—
220C2×C4⋊C4—471no—
221C2×C4⋊C4—471no—
222C2×C4⋊C4—471no—
223C2×C4⋊C4—471no—
224C2×C4⋊C4—941no—
225C2×C4⋊C4—941no—
226C2×C4⋊C4—941no—
227C2×C4⋊C4—941no—
228C2×C22⋊C4—941no—
229C2×C22⋊C4—941no—
230C2×C42—42no—
231C2×C42—941no—
232C2×C42—941no—
233C2×C42C4×D4711yescharacteristic
234C2×C42D18811yescharacteristic
235C2×C42C22⋊D4711yescharacteristic
236C2×C42C22×D4711yescharacteristic
237C22⋊C8—42no—
238#95—941no—
239#95—941no—
240#95—941no—
241#95—941no—
242C24(C2×D47)⋊C411yescharacteristic
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—41no—
252C22×C4—941no—
253C22×C4—941no—
254C22×C4—941no—
255C22×C4—941no—
256C22×C4C8×D4712yes—
257C22×C4#1062532412yes—
258C22×C4(C2×D47)⋊C411yescharacteristic
259C22×C4(C2×D47)⋊C411yescharacteristic
260C22×C4(C2×D47)⋊C411yescharacteristic
261C22×C4C2×C4×D4711yescharacteristic
262C22×C4C2×D18811yescharacteristic
263C22×C4C2×C22⋊D4711yescharacteristic
264C2×C8—42no—
265C2×C8—42no—
266C2×C8—42no—
267C2×C8—944no—
268C2×C8—1888no—
269C2×C8—1882no—
270C2×C8—1882no—
271C4⋊C4—472no—
272C4⋊C4—472no—
273C4⋊C4—941no—
274C4⋊C4—941no—
275C4⋊C4—1881no—
276C4⋊C4—1881no—
277C4⋊C4—1882no—
278C4⋊C4—1882no—
279C4⋊C4—1882no—
280C4⋊C4—1881no—
281C4⋊C4—1881no—
282C22⋊C4—944no—
283C22⋊C4—1882no—
284C42—41no—
285C42—41no—
286C42—41no—
287C42—41no—
288C42—944no—
289C42—1882no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23(C2×D47)⋊C812yes—
295C23#1309393812yes—
296C23#1309394212yes—
297C23C2×(C2×D47)⋊C411yescharacteristic
298C2×C4—24no—
299C2×C4—24no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—24no—
308C2×C4—24no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—44no—
316C2×C4—942no—
317C2×C4—942no—
318C2×C4—1881no—
319C2×C4—1881no—
320C2×C4—1881no—
321C2×C4—1881no—
322C2×C4—1881no—
323C2×C4—1881no—
324C2×C4—1881no—
325C2×C4—1881no—
326C2×C4—1881no—
327C2×C4—1881no—
328C2×C4(C2×D47)⋊C812yes—
329C2×C4#1309395012yes—
330C2×C4C2×C8×D4711yescharacteristic
331C2×C4C2×#1062532411yescharacteristic
332C2×C4#1309404412yes—
333C2×C4#1309405211yescharacteristic
334C2×C4#1309405711yescharacteristic
335C8—82no—
336C8—1884no—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—22no—
341C22—22no—
342C22—22no—
343C22#1568884814yes—
344C22C2×(C2×D47)⋊C811yescharacteristic
345C22C2×#1309393811yescharacteristic
346C22C2×#1309394211yescharacteristic
347C22#1568911711yescharacteristic
348C22#1568912511yescharacteristic
349C22C2×#1309395011yescharacteristic
350C22#1568914111yescharacteristic
351C4—22no—
352C4—22no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—22no—
357C4—21no—
358C4—41no—
359C4—3761no—
360C4—3761no—
361C4—1882no—
362C4—1882no—
363C2—24no—
364C2C2×#1568884811yescharacteristic
365C2#2024176811yescharacteristic
366C2#2024177611yescharacteristic
367C2#2024189311yescharacteristic
368C2#2024194211yescharacteristic
369C2#2024200411yescharacteristic
370C2#2024208911yescharacteristic
subgroupG/H
centerC23C2×(C2×D47)⋊C4
commutatorC2×C4×C47C22×C8
FrattiniC2×C42C22×D47
FittingC47×#1817C2
socleC23×C47C2×C22⋊C4
prime radicalC24×C47C22⋊C4
cosocleC2×C42×C47C23
hypercenter#1817D47
hypocenterC47#7579
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

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

NH ≅ G/Ntype
3. #20241212C2semidirect
4. #20241210C2semidirect
29. #13093983C8semidirect
91. C4⋊Dic47C2×C8semidirect
92. C4⋊Dic47C2×C8semidirect
208. C47#7579semidirect

Maximal subgroups

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

subgroupindex
#202458712
C2×#156888782
#202412122
#202412102
C47×#18172
#757947