Finite Group Databasebeta

← #26133419

Subgroups — #26133419

Order 12032.

466 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256522C211yesmaximal, characteristic
2#20245137C211yesmaximal, characteristic, complemented
3#20245115C211yesmaximal, characteristic, complemented
4#20244281C211yesmaximal, characteristic, complemented
5#20241499C211yesmaximal, characteristic, complemented
6#20241472C211yesmaximal, characteristic, complemented
7C2×C47×#444C211yesmaximal, characteristic, complemented
8C2×#13094046C2211yescharacteristic
9#15689564—21no—
10#15689563C412yescomplemented
11#15689559—21no—
12#15689558C412yescomplemented
13#15689553—22no—
14C2×#13093964C2211yescharacteristic
15C2×#13093964C2211yescharacteristic
16C2×#13093960C2211yescharacteristic
17C2×#13093952—21no—
18#15689089—21no—
19#15688939—21no—
20#15688936—21no—
21#15688929—22no—
22C2×#135×C47C2211yescharacteristic
23C2×#131×C47—21no—
24C47×#444—22no—
25C47×#444—22no—
26C2×#108×C47C2211yescharacteristic
27C2×#104×C47—21no—
28C2×#97×C47C2211yescharacteristic
29C2×#10625350—21no—
30#13094046—21no—
31#13094046—21no—
32#13094046—21no—
33#13094046—21no—
34C2×Dic188C2×C411yescharacteristic
35C2×#10625325—21no—
36C2×D376C2×C411yescharacteristic
37C2×#10625329—21no—
38#13093970—22no—
39#13093968—22no—
40#13093967—22no—
41#13093965—22no—
42#13093964—21no—
43#13093964—21no—
44#13093964—21no—
45#13093964C2×C412yes—
46C2×C47⋊C16—21no—
47C2×C47⋊C16—21no—
48#13093960—21no—
49#13093960—21no—
50#13093952—42no—
51(C2×D47)⋊C8—42no—
52C2×#41×C47—21no—
53#135×C47—21no—
54#135×C47—21no—
55#135×C47C2×C412yes—
56#135×C47D412yes—
57C2×Q16×C47D411yescharacteristic
58C2×SD16×C47—21no—
59C2×D8×C47D411yescharacteristic
60#131×C47—24no—
61#131×C47—42no—
62C2×M16×C47—21no—
63C2×M16×C47—41no—
64C22×C8×C47—41no—
65C22×C8×C47D411yescharacteristic
66C22×C8×C47C2311yescharacteristic
67C2×C42×C47D411yescharacteristic
68#108×C47—21no—
69#108×C47D412yes—
70#104×C47—24no—
71#97×C47—21no—
72#97×C47—21no—
73#41×C47—22no—
74#41×C47—22no—
75#41×C47—41no—
76#41×C47—41no—
77C2×Q8×C47—21no—
78C2×D4×C47—21no—
79C2×D4×C47—41no—
80C22×C4×C47—21no—
81C22×C4×C47—41no—
82C22×C4×C47C2×D411yescharacteristic
83C2×C22⋊D47—41no—
84#10625350—41no—
85#10625350—41no—
86#10625350—41no—
87#10625350—41no—
88C2×D188—21no—
89C2×C4×D47—41no—
90C2×Dic94—21no—
91Q16×C47—21no—
92Q16×C47C22⋊C412yes—
93SD16×C47—22no—
94SD16×C47—22no—
95D8×C47—21no—
96D8×C47C22⋊C412yes—
97M16×C47—22no—
98M16×C47—44no—
99M16×C47—41no—
100C2×C8×C47—21no—
101C2×C8×C47—21no—
102C2×C8×C47—44no—
103C2×C8×C47—41no—
104C2×C8×C47D812yes—
105C2×C8×C47C22×C411yescharacteristic
106C2×C8×C47C2×D411yescharacteristic
107C2×C8×C47C2×D411yescharacteristic
108C2×C8×C47C2×D411yescharacteristic
109C2×C8×C47#4111yescharacteristic
110C2×C8×C47#4111yescharacteristic
111C42×C47—21no—
112C42×C47—21no—
113#10625329—41no—
114#10625329—41no—
115C2×C47⋊C8—41no—
116Dic188—21no—
117Dic188—21no—
118D376—21no—
119D376—21no—
120#10625325—41no—
121#10625325—41no—
122C47⋊C16—22no—
123C47⋊C16—41no—
124C23×C47—41no—
125C23×C47#13511yescharacteristic
126C22×D47—41no—
127Q8×C47—22no—
128Q8×C47—41no—
129D4×C47—22no—
130D4×C47—42no—
131D4×C47—42no—
132D4×C47—41no—
133C2×C4×C47—41no—
134C2×C4×C47—42no—
135C2×C4×C47—42no—
136C2×C4×C47—41no—
137C2×C4×C47—81no—
138C2×C4×C47C4×D411yescharacteristic
139C2×C4×C47#12011yescharacteristic
140C2×C4×C47#12111yescharacteristic
141C2×C4×C47C2×D811yescharacteristic
142C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
144C22⋊D47—81no—
145C22⋊D47—81no—
146C2×Dic47—41no—
147D188—41no—
148D188—41no—
149C4×D47—81no—
150C4×D47—81no—
151Dic94—41no—
152Dic94—41no—
153C8×C47—22no—
154C8×C47—42no—
155C8×C47C2×C22⋊C411yescharacteristic
156C8×C47C4×D411yescharacteristic
157C8×C47#12111yescharacteristic
158C8×C47#12311yescharacteristic
159C47⋊C8—81no—
160#13024—471nomaximal, Sylow
161C22×C47—41no—
162C22×C47—42no—
163C22×C47—82no—
164C22×C47C4×D811yescharacteristic
165C22×C47#44911yescharacteristic
166C22×C47#46311yescharacteristic
167C2×D47—82no—
168C2×D47—81no—
169C4×C47—42no—
170C4×C47—81no—
171C4×C47#38611yescharacteristic
172C4×C47#44211yescharacteristic
173C4×C47#44711yescharacteristic
174C4×C47#45911yescharacteristic
175Dic47—81no—
176#3414—471no—
177C2×#444D4711yescharacteristic, complemented
178#2148—471no—
179#2143—471no—
180#1975—471no—
181#1388—471no—
182#1377—471no—
183C2×C47—21no—
184C2×C47—21no—
185C2×C47—21no—
186C2×C47—82no—
187C2×C47#187911yescharacteristic
188D47—161no—
189C2×#135—471no—
190C2×#135C2×D4711yescharacteristic
191C2×#131—21no—
192#510—472no—
193#510—941no—
194#509—472no—
195#509—941no—
196#508—942no—
197C2×M32—471no—
198C2×M32—471no—
199#444—22no—
200#444—22no—
201C2×#108—471no—
202C2×#108C2×D4711yescharacteristic
203C2×#104—21no—
204C2×#104—941no—
205#408—941no—
206C2×#97C2×D4711yescharacteristic
207#362—941no—
208#361—941no—
209#359—942no—
210C47#1302411yescharacteristic, complemented, Sylow
211C2×#41—21no—
212C2×#41—941no—
213#135—21no—
214#135—21no—
215#135—941no—
216#135—941no—
217#135—941no—
218#135—941no—
219#135C4×D4712yes—
220#135C22⋊D4712yes—
221C2×Q16—471no—
222C2×Q16D18811yescharacteristic
223C2×SD16—21no—
224C2×SD16—941no—
225C2×D8—471no—
226C2×D8D18811yescharacteristic
227#131—24no—
228#131—42no—
229C2×M16—21no—
230C2×M16—41no—
231C2×M16—941no—
232C22×C8—41no—
233C22×C8C22⋊D4711yescharacteristic
234C22×C8C22×D4711yescharacteristic
235C2×C42C22⋊D4711yescharacteristic
236Q32—942no—
237SD32—942no—
238SD32—942no—
239D16—942no—
240M32—472no—
241M32—941no—
242M32—941no—
243M32—941no—
244C2×C16—941no—
245C2×C16—941no—
246#108—21no—
247#108—941no—
248#108—941no—
249#108C22⋊D4712yes—
250#104—24no—
251#104—1882no—
252C22⋊C8—1882no—
253#97—21no—
254#97—21no—
255#41—22no—
256#41—22no—
257#41—41no—
258#41—41no—
259#41—1881no—
260#41—1881no—
261#41—1881no—
262#41—1881no—
263C2×Q8—21no—
264C2×Q8—941no—
265C2×D4—21no—
266C2×D4—41no—
267C2×D4—941no—
268C2×D4—1881no—
269C22×C4—21no—
270C22×C4—41no—
271C22×C4—1881no—
272C22×C4C2×C22⋊D4711yescharacteristic
273Q16—21no—
274Q16—941no—
275Q16—941no—
276Q16(C2×D47)⋊C412yes—
277SD16—22no—
278SD16—22no—
279SD16—1881no—
280SD16—1881no—
281D8—21no—
282D8—941no—
283D8—941no—
284D8(C2×D47)⋊C412yes—
285M16—22no—
286M16—44no—
287M16—41no—
288M16—1881no—
289M16—1881no—
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—44no—
293C2×C8—41no—
294C2×C8—1881no—
295C2×C8#1062533412yes—
296C2×C8C2×C4×D4711yescharacteristic
297C2×C8C2×D18811yescharacteristic
298C2×C8#1062535011yescharacteristic
299C2×C8#1062535011yescharacteristic
300C2×C8C2×C22⋊D4711yescharacteristic
301C2×C8C2×C22⋊D4711yescharacteristic
302C42—21no—
303C42—21no—
304C16—942no—
305C16—1881no—
306C23—41no—
307C23—1881no—
308C23#1309404411yescharacteristic
309Q8—22no—
310Q8—41no—
311Q8—1881no—
312Q8—1881no—
313D4—22no—
314D4—42no—
315D4—42no—
316D4—41no—
317D4—3761no—
318D4—3761no—
319D4—1881no—
320D4—1881no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—81no—
326C2×C4—3761no—
327C2×C4—3761no—
328C2×C4—1881no—
329C2×C4C4×C22⋊D4711yescharacteristic
330C2×C4#1309399311yescharacteristic
331C2×C4#1309399811yescharacteristic
332C2×C4C2×#1062533411yescharacteristic
333C2×C4#1309404911yescharacteristic
334C2×C4#1309405011yescharacteristic
335C8—22no—
336C8—42no—
337C8—3761no—
338C8C2×(C2×D47)⋊C411yescharacteristic
339C8C4×C22⋊D4711yescharacteristic
340C8#1309399811yescharacteristic
341C8#1309400711yescharacteristic
342C22—41no—
343C22—42no—
344C22—82no—
345C22—3762no—
346C22—3761no—
347C22C4×#1062533411yescharacteristic
348C22#1568926811yescharacteristic
349C22#1568933811yescharacteristic
350C4—42no—
351C4—81no—
352C4—3761no—
353C4#1568900211yescharacteristic
354C4#1568923311yescharacteristic
355C4#1568925711yescharacteristic
356C4#1568931811yescharacteristic
357C2—21no—
358C2—21no—
359C2—21no—
360C2—82no—
361C2—7521no—
362C2#2024373611yescharacteristic
subgroupG/H
centerC4#15689257
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
FittingC2×C47×#444C2
socleC2×C47#1879
prime radical#20256522C2
cosocleC22×C8×C47C23
hypercenterC2×#444D47
hypocenterC47#13024
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#97 ◁ C2×#444

Complements

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

NH ≅ G/Ntype
2. #20245137C2semidirect
3. #20245115C2semidirect
4. #20244281C2semidirect
5. #20241499C2semidirect
6. #20241472C2semidirect
7. C2×C47×#444C2semidirect
10. #15689563C4semidirect
12. #15689558C4semidirect
177. C2×#444D47semidirect
210. C47#13024semidirect

Maximal subgroups

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

subgroupindex
#202565222
#202451372
#202451152
#202442812
#202414992
#202414722
C2×C47×#4442
#1302447