Finite Group Databasebeta

← #26109644

Subgroups — #26109644

Order 12032.

496 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20245786C211yesmaximal, characteristic
2C4×C22⋊(C47⋊C8)C211yesmaximal, characteristic
3#20241227C212yesmaximal, complemented
4#20241227C212yesmaximal, complemented
5C47×#1797C211yesmaximal, characteristic
6C2×C22⋊(C47⋊C8)—21no—
7C2×C4×C47⋊C8C2212yes—
8#15688991—21no—
9#15688989C411yescharacteristic
10#15688989C411yescharacteristic
11#15688986—21no—
12#15688983C411yescharacteristic
13#15688983C411yescharacteristic
14C4×C4⋊Dic47C2211yescharacteristic
15C4×C4⋊Dic47C2211yescharacteristic
16C4×C22⋊Dic47—21no—
17#15688969—21no—
18#15688878—21no—
19C22×C42×C47C2211yescharacteristic
20C2×C4⋊C8×C47C2212yes—
21C2×C22⋊C8×C47—21no—
22C47×#336—21no—
23C22×C47⋊C8—22no—
24C2×C4⋊Dic47C2×C411yescharacteristic
25C2×C4⋊Dic47C2×C411yescharacteristic
26C2×C4⋊Dic47C2×C411yescharacteristic
27C2×C4⋊Dic47C2×C411yescharacteristic
28C2×C22⋊Dic47—21no—
29C2×C22⋊Dic47—21no—
30C2×C4×Dic47—21no—
31C2×C4×Dic47—21no—
32C22⋊(C47⋊C8)—24no—
33C4×C47⋊C8—24no—
34C47⋊#95—21no—
35C47⋊#95—21no—
36C47⋊#95—21no—
37C47⋊#95—21no—
38C47⋊#95—21no—
39C47⋊#95—21no—
40C47⋊#95—21no—
41C47⋊#95—21no—
42C23×C4×C47C2×C411yescharacteristic
43C23×C4×C47D411yescharacteristic
44C23×C4×C47D411yescharacteristic
45C22×C8×C47—22no—
46C2×C42×C47—24no—
47C2×C42×C47C2×C411yescharacteristic
48C2×C42×C47D411yescharacteristic
49C2×C42×C47D411yescharacteristic
50C2×C42×C47C2311yescharacteristic
51C4⋊C8×C47—24no—
52C22⋊C8×C47—42no—
53C24×C47C22⋊C411yescharacteristic
54C22×C4×C47—22no—
55C22×C4×C47—22no—
56C22×C4×C47—22no—
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—41no—
64C22×C4×C47C22⋊C411yescharacteristic
65C22×C4×C47C22⋊C411yescharacteristic
66C22×C4×C47C22⋊C411yescharacteristic
67C22×C4×C47C22×C411yescharacteristic
68C22×C4×C47C2×D411yescharacteristic
69C22×C4×C47C2×D411yescharacteristic
70C22×Dic47—21no—
71C22×Dic47—21no—
72C22×Dic47—21no—
73C22×Dic47—21no—
74C2×C8×C47—42no—
75C2×C8×C47—42no—
76C2×C8×C47—42no—
77C42×C47—22no—
78C42×C47—22no—
79C42×C47—22no—
80C42×C47#4114yes—
81C22⋊Dic47—42no—
82C22⋊Dic47—42no—
83C4⋊Dic47—22no—
84C4⋊Dic47—22no—
85C4⋊Dic47—22no—
86C4⋊Dic47—22no—
87C4×Dic47—42no—
88C4×Dic47—41no—
89C4×Dic47—41no—
90C2×C47⋊C8—24no—
91C2×C47⋊C8—42no—
92C2×C47⋊C8—42no—
93C23×C47—21no—
94C23×C47—21no—
95C23×C47—21no—
96C23×C47—21no—
97C23×C47—21no—
98C23×C47—21no—
99C23×C47#10412yes—
100C23×C47C2×C22⋊C411yescharacteristic
101C2×C4×C47—21no—
102C2×C4×C47—21no—
103C2×C4×C47—21no—
104C2×C4×C47—21no—
105C2×C4×C47—21no—
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—21no—
109C2×C4×C47—21no—
110C2×C4×C47—21no—
111C2×C4×C47—21no—
112C2×C4×C47—44no—
113C2×C4×C47—44no—
114C2×C4×C47—42no—
115C2×C4×C47—42no—
116C2×C4×C47#11712yes—
117C2×C4×C47#12312yes—
118C2×C4×C47#12312yes—
119C2×C4×C47#13112yes—
120C2×C4×C47#13112yes—
121C2×C4×C47#13512yes—
122C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C47#13711yescharacteristic
124C2×Dic47—41no—
125C2×Dic47—41no—
126C2×Dic47—41no—
127C2×Dic47—41no—
128C2×Dic47—41no—
129C2×Dic47—41no—
130C2×Dic47—41no—
131C2×Dic47—41no—
132C2×Dic47—41no—
133C2×Dic47—41no—
134C2×Dic47—41no—
135C2×Dic47—41no—
136C8×C47—82no—
137C47⋊C8—44no—
138#8711—471nomaximal, Sylow
139C22×C47—22no—
140C22×C47—22no—
141C22×C47—22no—
142C22×C47—41no—
143C22×C47—41no—
144C22×C47—41no—
145C22×C47—41no—
146C22×C47#38111yescharacteristic
147C22×C47#40811yescharacteristic
148C22×C47#40811yescharacteristic
149C22×C47#41611yescharacteristic
150C22×C47#41711yescharacteristic
151C22×C47C2×#10411yescharacteristic
152C22×C47#42111yescharacteristic
153C4×C47—22no—
154C4×C47—41no—
155C4×C47—41no—
156C4×C47—41no—
157C4×C47#43314yes—
158C4×C47#48212yes—
159C4×C47#48512yes—
160Dic47—81no—
161Dic47—81no—
162Dic47—81no—
163Dic47—81no—
164#2283—471no—
165#1797D4711yescharacteristic
166C4×C22⋊C8—471no—
167#1279—472no—
168#1279—472no—
169C2×C47—42no—
170C2×C47#148211yescharacteristic
171C2×C47#148311yescharacteristic
172C2×C47#149411yescharacteristic
173C2×C47#149511yescharacteristic
174C2×C47#181811yescharacteristic
175C2×C47#182511yescharacteristic
176C2×C47#182611yescharacteristic
177C22×C42C2×D4711yescharacteristic
178C2×C4⋊C8C2×D4712yes—
179C2×C22⋊C8—21no—
180C2×C22⋊C8—941no—
181C2×C4×C8—472no—
182#383—941no—
183#382—471no—
184#382—471no—
185#381—941no—
186#380—471no—
187#380—471no—
188C4×C4⋊C4—471no—
189C4×C4⋊C4—471no—
190C4×C22⋊C4—941no—
191#376—941no—
192#336—21no—
193#336—941no—
194C47#871111yescharacteristic, complemented, Sylow
195C23×C4C4×D4711yescharacteristic
196C23×C4D18811yescharacteristic
197C23×C4C22⋊D4711yescharacteristic
198C22×C8—22no—
199C22×C8—942no—
200C2×C4⋊C4—471no—
201C2×C4⋊C4—471no—
202C2×C4⋊C4—471no—
203C2×C4⋊C4—471no—
204C2×C22⋊C4—941no—
205C2×C22⋊C4—941no—
206C2×C42—24no—
207C2×C42—941no—
208C2×C42—941no—
209C2×C42C4×D4711yescharacteristic
210C2×C42D18811yescharacteristic
211C2×C42C22⋊D4711yescharacteristic
212C2×C42C22×D4711yescharacteristic
213C4⋊C8—24no—
214C22⋊C8—42no—
215C22⋊C8—944no—
216C4×C8—944no—
217#95—941no—
218#95—941no—
219#95—941no—
220#95—941no—
221#95—941no—
222#95—941no—
223#95—941no—
224#95—941no—
225C24(C2×D47)⋊C411yescharacteristic
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—41no—
236C22×C4—941no—
237C22×C4—941no—
238C22×C4—941no—
239C22×C4—941no—
240C22×C4(C2×D47)⋊C411yescharacteristic
241C22×C4(C2×D47)⋊C411yescharacteristic
242C22×C4(C2×D47)⋊C411yescharacteristic
243C22×C4C2×C4×D4711yescharacteristic
244C22×C4C2×D18811yescharacteristic
245C22×C4C2×C22⋊D4711yescharacteristic
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—42no—
249C2×C8—944no—
250C2×C8—1882no—
251C2×C8—1882no—
252C4⋊C4—942no—
253C4⋊C4—942no—
254C4⋊C4—942no—
255C4⋊C4—942no—
256C22⋊C4—1882no—
257C22⋊C4—1882no—
258C42—22no—
259C42—22no—
260C42—22no—
261C42—1882no—
262C42—1881no—
263C42—1881no—
264C42#1062535214yes—
265C23—21no—
266C23—21no—
267C23—21no—
268C23—21no—
269C23—21no—
270C23—21no—
271C23#1309395012yes—
272C23C2×(C2×D47)⋊C411yescharacteristic
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—44no—
285C2×C4—44no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—1881no—
289C2×C4—1881no—
290C2×C4—1881no—
291C2×C4—1881no—
292C2×C4—1881no—
293C2×C4—1881no—
294C2×C4—1881no—
295C2×C4—1881no—
296C2×C4—1881no—
297C2×C4—1881no—
298C2×C4—1881no—
299C2×C4—1881no—
300C2×C4#1309398012yes—
301C2×C4#1309400512yes—
302C2×C4#1309400812yes—
303C2×C4#1309403012yes—
304C2×C4#1309403212yes—
305C2×C4#1309404412yes—
306C2×C4#1309405011yescharacteristic
307C2×C4#1309405511yescharacteristic
308C8—82no—
309C8—1884no—
310C22—22no—
311C22—22no—
312C22—22no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22#1568898411yescharacteristic
318C22#1568908911yescharacteristic
319C22#1568909111yescharacteristic
320C22#1568911711yescharacteristic
321C22#1568912211yescharacteristic
322C22C2×#1309395011yescharacteristic
323C22#1568913911yescharacteristic
324C4—22no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—3761no—
329C4—3761no—
330C4—3761no—
331C4—3761no—
332C4#1568918114yes—
333C4#1568944412yes—
334C4#1568946112yes—
335C2—42no—
336C2#2024179411yescharacteristic
337C2#2024179911yescharacteristic
338C2#2024184611yescharacteristic
339C2#2024185111yescharacteristic
340C2#2024345711yescharacteristic
341C2#2024348011yescharacteristic
342C2#2024348511yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D47
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1797C2
socleC23×C47C2×C22⋊C4
prime radicalC24×C47C22⋊C4
cosocleC2×C42×C47C23
hypercenter#1797D47
hypocenterC47#8711
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
3. #20241227C2semidirect
4. #20241227C2semidirect
194. C47#8711semidirect

Maximal subgroups

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

subgroupindex
#202457862
C4×C22⋊(C47⋊C8)2
#202412272
C47×#17972
#871147