Finite Group Databasebeta

← #26369742

Subgroups — #26369742

Order 12032.

632 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×#15689563C211yesmaximal, characteristic
2#20252305C211yesmaximal, characteristic
3#20252255C211yesmaximal, characteristic, complemented
4#20245276C218yesmaximal, complemented
5#20245160C211yesmaximal, characteristic, complemented
6C2×#15688940C211yesmaximal, characteristic, complemented
7#20244992C211yesmaximal, characteristic, complemented
8C47×#2145C211yesmaximal, characteristic
9C22×Dic188C2211yescharacteristic
10#15689890—21no—
11#15689600—21no—
12#15689563C414yescomplemented
13#15689563C2214yes—
14C2×#13093970C412yescomplemented
15C2×#13093968C412yescomplemented
16C2×#13093964C2211yescharacteristic
17#15689245C2214yes—
18#15689240—22no—
19#15689229C2214yescomplemented
20#15689217—22no—
21C2×#13093960C2211yescharacteristic
22#15689140—21no—
23#15689131—21no—
24#15689078C2211yescharacteristic
25#15688945C2214yescomplemented
26#15688940C2214yescomplemented
27#15688900C2214yescomplemented
28C2×#135×C47C2211yescharacteristic
29C2×M32×C47C2211yescharacteristic
30C47×#427C2211yescharacteristic
31C47×#360C2214yes—
32C22×Dic94—21no—
33C2×Dic188—21no—
34C2×Dic188—21no—
35C2×Dic188—21no—
36C2×Dic188C2×C412yes—
37C2×Dic188C2×C412yes—
38C2×Dic188C2312yes—
39#13094031—24no—
40#13094031—42no—
41C2×#10625329—21no—
42C2×#10625329—42no—
43C2×#10625329D411yescharacteristic
44C4×Dic94—42no—
45#13093989—24no—
46#13093983D411yescharacteristic
47#13093980—42no—
48#13093970C2×C418yes—
49#13093968C2×C418yes—
50#13093964C2×C412yes—
51#13093964C2312yes—
52C2×C47⋊C16C2×C412yes—
53#13093960—21no—
54#13093960C2312yes—
55#13093951—24no—
56#13093947—24no—
57#13093934C2312yes—
58C8×Dic47D412yes—
59C2×#41×C47—21no—
60#135×C47—21no—
61#135×C47—21no—
62#135×C47C2×C412yes—
63#135×C47C2312yes—
64C2×Q16×C47C2×C411yescharacteristic
65C2×SD16×C47—21no—
66C2×D8×C47C2×C411yescharacteristic
67C22×C8×C47C2311yescharacteristic
68#117×C47—21no—
69M32×C47—21no—
70M32×C47C2312yes—
71C2×C16×C47—21no—
72#107×C47—21no—
73#106×C47C2312yes—
74#41×C47—22no—
75#41×C47—22no—
76#41×C47—41no—
77#41×C47—41no—
78C2×Q8×C47—21no—
79C2×D4×C47—21no—
80C2×D4×C47—41no—
81C22×C4×C47—41no—
82C22×C4×C47C2×D411yescharacteristic
83C22×Dic47—41no—
84C2×Dic94—22no—
85C2×Dic94—22no—
86C2×Dic94—22no—
87C2×Dic94—41no—
88C2×Dic94—41no—
89C2×Dic94—41no—
90Q16×C47—21no—
91Q16×C47C22×C412yes—
92SD16×C47—22no—
93SD16×C47—22no—
94D8×C47—21no—
95D8×C47C22×C412yes—
96C2×C8×C47C22×C411yescharacteristic
97C2×C8×C47C22×C411yescharacteristic
98C2×C8×C47C2×D411yescharacteristic
99C2×C8×C47#4111yescharacteristic
100C2×C8×C47#4111yescharacteristic
101C2×C8×C47C2411yescharacteristic
102C4⋊C4×C47—22no—
103C22⋊C4×C47—41no—
104C42×C47—41no—
105C22⋊Dic47—21no—
106C4⋊Dic47—21no—
107Dic47⋊C4—44no—
108C4×Dic47—44no—
109C4×Dic47C2×D412yes—
110#10625329—21no—
111#10625329—21no—
112#10625329—22no—
113#10625329—44no—
114#10625329—41no—
115C2×C47⋊C8—44no—
116C2×C47⋊C8—41no—
117C2×C47⋊C8C2×D412yes—
118Dic188—22no—
119Dic188—22no—
120Dic188—22no—
121Dic188C22×C414yes—
122C16×C47—22no—
123C47⋊C16C22×C414yes—
124C23×C47—41no—
125C23×C47AGL(1,ℤ/8)11yescharacteristic
126Q8×C47—22no—
127Q8×C47—41no—
128D4×C47—22no—
129D4×C47—42no—
130D4×C47—42no—
131D4×C47—41no—
132C2×C4×C47—41no—
133C2×C4×C47—42no—
134C2×C4×C47—42no—
135C2×C4×C47—42no—
136C2×C4×C47C4×D411yescharacteristic
137C2×C4×C47C4×D411yescharacteristic
138C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C47C22×D411yescharacteristic
142C2×Dic47—22no—
143C2×Dic47—42no—
144C2×Dic47—42no—
145C2×Dic47—42no—
146Dic94—24no—
147Dic94—42no—
148Dic94—42no—
149Dic94—42no—
150C8×C47C4×D411yescharacteristic
151C8×C47C4×D411yescharacteristic
152C8×C47C23×C411yescharacteristic
153C8×C47C2×#4111yescharacteristic
154C47⋊C8—22no—
155C47⋊C8—42no—
156#33470—471nomaximal, Sylow
157C22×C47—41no—
158C22×C47—42no—
159C22×C47—161no—
160C22×C47#44211yescharacteristic
161C22×C47#44211yescharacteristic
162C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
163C4×C47—42no—
164C4×C47—82no—
165C4×C47#44211yescharacteristic
166C4×C47#44211yescharacteristic
167C4×C47C2×C4×D411yescharacteristic
168C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
169Dic47—42no—
170Dic47—44no—
171C2×#510—471no—
172#2957—471no—
173#2950—471no—
174#2180—478no—
175#2155—471no—
176C2×#362—471no—
177#2145D4711yescharacteristic
178#2110—471no—
179C2×C47—21no—
180C2×C47—21no—
181C2×C47—21no—
182C2×C47—82no—
183C2×C47C2×#44211yescharacteristic
184C2×#135C2×D4711yescharacteristic
185C22×Q16—471no—
186#568—941no—
187#519—941no—
188#510—474no—
189#510—474no—
190C2×Q32—472no—
191C2×SD32—472no—
192C2×M32—471no—
193C2×M32C2×D4711yescharacteristic
194#444—474no—
195#443—942no—
196#441—474no—
197C4×Q16—942no—
198C2×#108—471no—
199#427C2×D4711yescharacteristic
200#421—941no—
201#419—941no—
202#405—471no—
203#365—474no—
204#362—474no—
205#360C2×D4714yes—
206#347—474no—
207C47#3347011yescharacteristic, complemented, Sylow
208C2×#41—21no—
209C22×Q8—941no—
210#135—21no—
211#135—21no—
212#135C4×D4712yes—
213#135C22×D4712yes—
214C2×Q16—472no—
215C2×Q16—472no—
216C2×Q16—472no—
217C2×Q16—941no—
218C2×Q16—941no—
219C2×Q16—941no—
220C2×Q16C4×D4711yescharacteristic
221C2×SD16—21no—
222C2×D8C4×D4711yescharacteristic
223#131—944no—
224#131—1882no—
225C2×M16—471no—
226C2×M16—941no—
227C2×M16—1882no—
228C22×C8C22×D4711yescharacteristic
229C4×Q8—944no—
230C4×Q8—1882no—
231#117—21no—
232#117—471no—
233#117—1882no—
234Q32—478no—
235SD32—478no—
236M32—21no—
237M32—472no—
238M32—472no—
239M32C22×D4712yes—
240C2×C16—21no—
241C2×C16—472no—
242#108—472no—
243#108—941no—
244#107—21no—
245#106C22×D4712yes—
246#104—944no—
247#103—944no—
248#97—472no—
249C4×C8—472no—
250#41—22no—
251#41—22no—
252#41—41no—
253#41—41no—
254C2×Q8—21no—
255C2×Q8—942no—
256C2×Q8—942no—
257C2×Q8—942no—
258C2×Q8—1881no—
259C2×Q8—1881no—
260C2×Q8—1881no—
261C2×D4—21no—
262C2×D4—41no—
263C22×C4—41no—
264C22×C4—1881no—
265C22×C4D4×D4711yescharacteristic
266Q16—21no—
267Q16—474no—
268Q16—942no—
269Q16—942no—
270Q16—942no—
271Q16C2×C4×D4712yes—
272SD16—22no—
273SD16—22no—
274D8—21no—
275D8C2×C4×D4712yes—
276M16—941no—
277M16—941no—
278M16—942no—
279M16—1884no—
280M16—1881no—
281C2×C8—472no—
282C2×C8—1884no—
283C2×C8—1881no—
284C2×C8C2×C4×D4711yescharacteristic
285C2×C8C2×C4×D4711yescharacteristic
286C2×C8D4×D4711yescharacteristic
287C2×C8#1062535211yescharacteristic
288C2×C8#1062535211yescharacteristic
289C2×C8C23×D4711yescharacteristic
290C4⋊C4—22no—
291C4⋊C4—941no—
292C4⋊C4—1884no—
293C22⋊C4—41no—
294C22⋊C4—941no—
295C42—41no—
296C42—472no—
297C42—1884no—
298C16—22no—
299C16—474no—
300C23—41no—
301C23#1309404811yescharacteristic
302Q8—22no—
303Q8—41no—
304Q8—944no—
305Q8—1882no—
306Q8—1882no—
307Q8—1882no—
308D4—22no—
309D4—42no—
310D4—42no—
311D4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—942no—
317C2×C4—1882no—
318C2×C4—1882no—
319C2×C4—1882no—
320C2×C4(C22⋊D47)⋊C411yescharacteristic
321C2×C4(C22⋊D47)⋊C411yescharacteristic
322C2×C4#1309404811yescharacteristic
323C2×C4#1309405111yescharacteristic
324C2×C4#1309405111yescharacteristic
325C2×C4C2×D4×D4711yescharacteristic
326C8—942no—
327C8—1882no—
328C8(C22⋊D47)⋊C411yescharacteristic
329C8(C22⋊D47)⋊C411yescharacteristic
330C8C22×C4×D4711yescharacteristic
331C8C2×#1062535211yescharacteristic
332C22—41no—
333C22—42no—
334C22—161no—
335C22#1568923211yescharacteristic
336C22#1568923211yescharacteristic
337C22C2×#1309404811yescharacteristic
338C4—42no—
339C4—82no—
340C4—1882no—
341C4—1884no—
342C4#1568923211yescharacteristic
343C4#1568923211yescharacteristic
344C4C2×(C22⋊D47)⋊C411yescharacteristic
345C4C2×#1309405111yescharacteristic
346C2—21no—
347C2—21no—
348C2—21no—
349C2—82no—
350C2C2×#1568923211yescharacteristic
subgroupG/H
centerC2C2×#15689232
commutatorC8×C47C23×C4
FrattiniC2×C8C23×D47
FittingC47×#2145C2
socleC2×C47C2×#442
prime radicalC2×#135×C47C22
cosocleC2×C8×C47C24
hypercenter#2145D47
hypocenterC47#33470
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ #2145

Complements

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

NH ≅ G/Ntype
3. #20252255C2semidirect
4. #20245276C2semidirect
5. #20245160C2semidirect
6. C2×#15688940C2semidirect
7. #20244992C2semidirect
12. #15689563C4semidirect
14. C2×#13093970C4semidirect
15. C2×#13093968C4semidirect
19. #15689229C22semidirect
25. #15688945C22semidirect
26. #15688940C22semidirect
27. #15688900C22semidirect
207. C47#33470semidirect

Maximal subgroups

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

subgroupindex
C2×#156895632
#202523052
#202522552
#202452762
#202451602
C2×#156889402
#202449922
C47×#21452
#3347047