Finite Group Databasebeta

← #26133426

Subgroups — #26133426

Order 12032.

522 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689558C211yesmaximal, characteristic
2C2×#15688933C211yesmaximal, characteristic, complemented
3#20245103C211yesmaximal, characteristic, complemented
4#20244264C211yesmaximal, characteristic, complemented
5#20241493C211yesmaximal, characteristic, complemented
6#20241472C211yesmaximal, characteristic, complemented
7C47×#2943C211yesmaximal, characteristic, complemented
8C22×D376C2211yescharacteristic
9#15689558—22no—
10#15689558C414yescomplemented
11C2×#13093967—21no—
12C2×#13093965—21no—
13C2×#13093964C2211yescharacteristic
14C2×#13093964C2211yescharacteristic
15C2×#13093956C2211yescharacteristic
16C2×#13093946—21no—
17#15689025—21no—
18#15688933—22no—
19#15688923—22no—
20C2×#135×C47C2211yescharacteristic
21C4×#41×C47—21no—
22C47×#442—21no—
23C47×#441—21no—
24C47×#440—22no—
25C47×#427C2211yescharacteristic
26C47×#416—21no—
27C2×#97×C47C2211yescharacteristic
28C22×D188—21no—
29C2×D376—21no—
30C2×D376—21no—
31C2×D376—21no—
32C2×D376—21no—
33C2×D376—21no—
34C2×D376C2×C412yescomplemented
35C2×C4⋊Dic47—21no—
36C2×(C2×D47)⋊C4—42no—
37#13093967—24no—
38#13093965—24no—
39#13093964—21no—
40#13093964—21no—
41#13093964—21no—
42#13093964C2×C412yescomplemented
43C2×C47⋊C16—21no—
44C2×C47⋊C16—21no—
45#13093956—21no—
46#13093956—21no—
47#13093946—42no—
48C2×#41×C47—21no—
49#135×C47—21no—
50#135×C47—21no—
51#135×C47C2×C412yes—
52#135×C47D412yes—
53C2×Q16×C47D411yescharacteristic
54C2×SD16×C47—21no—
55C2×D8×C47D411yescharacteristic
56C22×C8×C47D411yescharacteristic
57C22×C8×C47C2311yescharacteristic
58C4×Q8×C47—22no—
59C4×D4×C47—22no—
60C4×D4×C47—42no—
61#117×C47—21no—
62#117×C47—41no—
63C2×C42×C47—41no—
64C2×C42×C47D411yescharacteristic
65#107×C47D412yes—
66#106×C47—21no—
67#103×C47—22no—
68#102×C47—22no—
69#97×C47—21no—
70#97×C47—21no—
71C23×D47—41no—
72#41×C47—22no—
73#41×C47—22no—
74#41×C47—41no—
75#41×C47—41no—
76C2×Q8×C47—21no—
77C2×D4×C47—21no—
78C2×D4×C47—41no—
79C22×C4×C47—42no—
80C22×C4×C47—41no—
81C22×C4×C47D812yes—
82C22×C4×C47C2×D411yescharacteristic
83C22×Dic47—41no—
84C2×D188—22no—
85C2×D188—41no—
86C2×D188—41no—
87C2×D188—41no—
88C2×D188—41no—
89C2×D188—41no—
90Q16×C47—21no—
91Q16×C47C22⋊C412yescomplemented
92SD16×C47—22no—
93SD16×C47—22no—
94D8×C47—21no—
95D8×C47C22⋊C412yescomplemented
96C2×C8×C47—21no—
97C2×C8×C47—21no—
98C2×C8×C47—21no—
99C2×C8×C47C22×C411yescharacteristic
100C2×C8×C47C2×D411yescharacteristic
101C2×C8×C47C2×D411yescharacteristic
102C2×C8×C47C2×D411yescharacteristic
103C2×C8×C47#4111yescharacteristic
104C2×C8×C47#4111yescharacteristic
105C4⋊C4×C47—22no—
106C4⋊C4×C47—42no—
107C22⋊C4×C47—42no—
108C22⋊C4×C47—41no—
109C42×C47—21no—
110C42×C47—21no—
111C42×C47—42no—
112C42×C47—41no—
113(C2×D47)⋊C4—84no—
114C4⋊Dic47—41no—
115C4⋊Dic47—41no—
116D376—22no—
117D376—22no—
118D376—41no—
119D376—41no—
120C47⋊C16—22no—
121C47⋊C16—41no—
122C23×C47—41no—
123C23×C47C2×D811yescharacteristic
124C22×D47—42no—
125C22×D47—82no—
126C22×D47—82no—
127C22×D47—81no—
128C22×D47—81no—
129Q8×C47—22no—
130Q8×C47—41no—
131D4×C47—22no—
132D4×C47—42no—
133D4×C47—42no—
134D4×C47—41no—
135C2×C4×C47—22no—
136C2×C4×C47—41no—
137C2×C4×C47—42no—
138C2×C4×C47—42no—
139C2×C4×C47—42no—
140C2×C4×C47—42no—
141C2×C4×C47—84no—
142C2×C4×C47C4×D411yescharacteristic
143C2×C4×C47#12011yescharacteristic
144C2×C4×C47#12111yescharacteristic
145C2×C4×C47#13511yescharacteristic
146C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
148C2×Dic47—82no—
149C2×Dic47—81no—
150D188—42no—
151D188—42no—
152D188—81no—
153D188—81no—
154C8×C47—41no—
155C8×C47C2×C22⋊C411yescharacteristic
156C8×C47C4×D411yescharacteristic
157C8×C47#12111yescharacteristic
158C8×C47#12311yescharacteristic
159#13025—471nomaximal, Sylow
160C22×C47—22no—
161C22×C47—42no—
162C22×C47—82no—
163C22×C47C4×D811yescharacteristic
164C22×C47#44711yescharacteristic
165C22×C47#45911yescharacteristic
166C2×D47—84no—
167C2×D47—82no—
168C2×D47—161no—
169C2×D47—161no—
170C2×D47—162no—
171C4×C47—42no—
172C4×C47—42no—
173C4×C47—82no—
174C4×C47#38611yescharacteristic
175C4×C47#44211yescharacteristic
176C4×C47#44911yescharacteristic
177C4×C47#46311yescharacteristic
178Dic47—161no—
179C2×#509—471no—
180#2943D4711yescharacteristic, complemented
181C2×#360—471no—
182#2140—471no—
183#1972—471no—
184#1386—471no—
185#1377—471no—
186C2×C47—21no—
187C2×C47—21no—
188C2×C47—82no—
189C2×C47#187911yescharacteristic
190C2×C47#219012yes—
191D47—162no—
192C2×#135C2×D4711yescharacteristic
193C22×D8—471no—
194C4×#41—21no—
195#509—474no—
196#509—942no—
197C2×SD32—941no—
198C2×D16—941no—
199C2×M32—471no—
200C2×M32—471no—
201#442—21no—
202#441—21no—
203#440—22no—
204#427C2×D4711yescharacteristic
205C2×#106—471no—
206#416—21no—
207C2×#102—941no—
208C2×#97C2×D4711yescharacteristic
209#390—941no—
210#360—942no—
211#357—942no—
212C47#1302511yescharacteristic, complemented, Sylow
213C2×#41—21no—
214C22×D4—941no—
215#135—21no—
216#135—21no—
217#135C4×D4712yes—
218#135D18812yes—
219C2×Q16C22⋊D4711yescharacteristic
220C2×SD16—21no—
221C2×D8—472no—
222C2×D8—941no—
223C2×D8—941no—
224C2×D8—941no—
225C2×D8—941no—
226C2×D8—941no—
227C2×D8C22⋊D4711yescharacteristic
228C22×C8C22⋊D4711yescharacteristic
229C22×C8C22×D4711yescharacteristic
230C4×Q8—22no—
231C4×D4—22no—
232C4×D4—42no—
233#117—21no—
234#117—41no—
235C2×C4⋊C4—941no—
236C2×C22⋊C4—1882no—
237C2×C42—41no—
238C2×C42C22⋊D4711yescharacteristic
239SD32—944no—
240D16—944no—
241M32—472no—
242M32—941no—
243M32—941no—
244M32—941no—
245C2×C16—941no—
246C2×C16—941no—
247#107C22⋊D4712yes—
248#106—21no—
249#106—941no—
250#106—941no—
251#103—22no—
252#102—22no—
253#102—1882no—
254#97—21no—
255#97—21no—
256C24—1881no—
257#41—22no—
258#41—22no—
259#41—41no—
260#41—41no—
261C2×Q8—21no—
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—942no—
265C2×D4—1881no—
266C2×D4—1881no—
267C2×D4—1881no—
268C2×D4—1881no—
269C2×D4—1881no—
270C22×C4—42no—
271C22×C4—41no—
272C22×C4—1881no—
273C22×C4#1062533412yes—
274C22×C4C2×C22⋊D4711yescharacteristic
275Q16—21no—
276Q16(C2×D47)⋊C412yescomplemented
277SD16—22no—
278SD16—22no—
279D8—21no—
280D8—942no—
281D8—942no—
282D8—1881no—
283D8—1881no—
284D8(C2×D47)⋊C412yescomplemented
285C2×C8—21no—
286C2×C8—21no—
287C2×C8—21no—
288C2×C8C2×C4×D4711yescharacteristic
289C2×C8C2×D18811yescharacteristic
290C2×C8#1062535011yescharacteristic
291C2×C8#1062535011yescharacteristic
292C2×C8C2×C22⋊D4711yescharacteristic
293C2×C8C2×C22⋊D4711yescharacteristic
294C4⋊C4—22no—
295C4⋊C4—42no—
296C4⋊C4—1881no—
297C4⋊C4—1881no—
298C22⋊C4—42no—
299C22⋊C4—41no—
300C22⋊C4—3764no—
301C42—21no—
302C42—21no—
303C42—42no—
304C42—41no—
305C16—942no—
306C16—1881no—
307C23—41no—
308C23—3762no—
309C23—3762no—
310C23—3761no—
311C23—3761no—
312C23—1882no—
313C23C2×#1062533411yescharacteristic
314Q8—22no—
315Q8—41no—
316D4—22no—
317D4—42no—
318D4—42no—
319D4—41no—
320D4—3761no—
321D4—3761no—
322D4—1882no—
323D4—1882no—
324C2×C4—22no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—84no—
331C2×C4—3762no—
332C2×C4—3761no—
333C2×C4C4×C22⋊D4711yescharacteristic
334C2×C4#1309399311yescharacteristic
335C2×C4#1309399811yescharacteristic
336C2×C4#1309404411yescharacteristic
337C2×C4#1309404911yescharacteristic
338C2×C4#1309405011yescharacteristic
339C8—41no—
340C8C2×(C2×D47)⋊C411yescharacteristic
341C8C4×C22⋊D4711yescharacteristic
342C8#1309399811yescharacteristic
343C8#1309400711yescharacteristic
344C22—22no—
345C22—42no—
346C22—82no—
347C22—3764no—
348C22—3762no—
349C22—7521no—
350C22—7521no—
351C22—7522no—
352C22C4×#1062533411yescharacteristic
353C22#1568925711yescharacteristic
354C22#1568931811yescharacteristic
355C4—42no—
356C4—42no—
357C4—82no—
358C4—7521no—
359C4#1568900211yescharacteristic
360C4#1568923311yescharacteristic
361C4#1568926811yescharacteristic
362C4#1568933811yescharacteristic
363C2—21no—
364C2—21no—
365C2—82no—
366C2—7522no—
367C2#2024373611yescharacteristic
368C2#2024533412yes—
subgroupG/H
centerC22#15689257
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
FittingC47×#2943C2
socleC22×C47#447
prime radicalC2×#15689558C2
cosocleC22×C8×C47C23
hypercenter#2943D47
hypocenterC47#13025
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#97 ◁ #2943

Complements

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

NH ≅ G/Ntype
2. C2×#15688933C2semidirect
3. #20245103C2semidirect
4. #20244264C2semidirect
5. #20241493C2semidirect
6. #20241472C2semidirect
7. C47×#2943C2semidirect
10. #15689558C4semidirect
34. C2×D376C2×C4semidirect
42. #13093964C2×C4semidirect
91. Q16×C47C22⋊C4semidirect
95. D8×C47C22⋊C4semidirect
180. #2943D47semidirect
212. C47#13025semidirect
276. Q16(C2×D47)⋊C4semidirect
284. D8(C2×D47)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#156895582
C2×#156889332
#202451032
#202442642
#202414932
#202414722
C47×#29432
#1302547