Finite Group Databasebeta

← #26133363

Subgroups — #26133363

Order 12032.

462 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689553C211yesmaximal, characteristic
2#20245124C211yesmaximal, characteristic, complemented
3#20245115C211yesmaximal, characteristic, complemented
4#20244286C211yesmaximal, characteristic, complemented
5#20241485C211yesmaximal, characteristic, complemented
6#20241477C211yesmaximal, characteristic, complemented
7C47×#2957C211yesmaximal, characteristic, complemented
8C2×#13094046C2211yescharacteristic
9#15689553—22no—
10#15689553—22no—
11C2×#13093970C411yescharacteristic, complemented
12C2×#13093968C411yescharacteristic, complemented
13C2×#13093967C411yescharacteristic, complemented
14C2×#13093965C411yescharacteristic, complemented
15C2×#13093964C2211yescharacteristic
16C22×C47⋊C16C2211yescharacteristic
17#15689161C2211yescharacteristic
18#15689139—21no—
19#15689096—21no—
20#15688933—22no—
21#15688929—22no—
22C2×#135×C47C2211yescharacteristic
23C47×#568—21no—
24C47×#444—22no—
25C47×#443—22no—
26C2×#108×C47C2211yescharacteristic
27C47×#421—21no—
28C47×#405C2211yescharacteristic
29C2×#10625350—21no—
30#13094046—21no—
31#13094046—21no—
32#13094046—21no—
33#13094046—21no—
34C2×Dic188C2×C411yescharacteristic
35C2×#10625325—21no—
36C2×D376C2×C411yescharacteristic
37#13093983—21no—
38#13093970—22no—
39#13093968—22no—
40#13093967—22no—
41#13093965—22no—
42#13093964—21no—
43#13093964—21no—
44C2×C47⋊C16—21no—
45C2×C47⋊C16—21no—
46C2×C47⋊C16—21no—
47C2×C47⋊C16C2×C411yescharacteristic
48C2×C47⋊C16C2×C411yescharacteristic
49#13093958—21no—
50#13093956—21no—
51#13093950—42no—
52#13093938—42no—
53C2×#41×C47—21no—
54#135×C47—21no—
55#135×C47—21no—
56#135×C47D412yes—
57#135×C47D412yes—
58C2×Q16×C47C2×C411yescharacteristic
59C2×SD16×C47—21no—
60C2×D8×C47C2×C411yescharacteristic
61#131×C47—24no—
62#131×C47—42no—
63C2×M16×C47—21no—
64C2×M16×C47—42no—
65C2×M16×C47D411yescharacteristic
66C22×C8×C47C2311yescharacteristic
67#117×C47D411yescharacteristic
68#108×C47—21no—
69#108×C47D412yes—
70#104×C47—24no—
71#97×C47—21no—
72C4×C8×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—41no—
81C22×C4×C47C2×D411yescharacteristic
82C2×C22⋊D47—41no—
83#10625350—41no—
84#10625350—41no—
85#10625350—41no—
86#10625350—41no—
87C2×D188—21no—
88C2×C4×D47—41no—
89C2×Dic94—21no—
90Q16×C47—21no—
91Q16×C47C22⋊C412yes—
92SD16×C47—22no—
93SD16×C47—22no—
94D8×C47—21no—
95D8×C47C22⋊C412yes—
96M16×C47—21no—
97M16×C47—22no—
98M16×C47—44no—
99M16×C47—41no—
100M16×C47D812yes—
101C2×C8×C47—21no—
102C2×C8×C47—44no—
103C2×C8×C47—41no—
104C2×C8×C47C22×C411yescharacteristic
105C2×C8×C47C2×D411yescharacteristic
106C2×C8×C47C2×D411yescharacteristic
107C2×C8×C47C2×D411yescharacteristic
108C2×C8×C47#4111yescharacteristic
109C2×C8×C47#4111yescharacteristic
110C4⋊C4×C47—21no—
111C22⋊C4×C47—21no—
112C42×C47—21no—
113C22⋊Dic47—41no—
114C4⋊Dic47—41no—
115C4×Dic47—41no—
116Dic188—21no—
117Dic188—21no—
118D376—21no—
119D376—21no—
120#10625325—41no—
121#10625325—41no—
122C47⋊C16—21no—
123C47⋊C16—21no—
124C47⋊C16—41no—
125C23×C47—41no—
126C23×C47AGL(1,ℤ/8)11yescharacteristic
127C22×D47—41no—
128Q8×C47—22no—
129Q8×C47—41no—
130D4×C47—22no—
131D4×C47—42no—
132D4×C47—42no—
133D4×C47—41no—
134C2×C4×C47—41no—
135C2×C4×C47—42no—
136C2×C4×C47—42no—
137C2×C4×C47—41no—
138C2×C4×C47C4×D411yescharacteristic
139C2×C4×C47#12011yescharacteristic
140C2×C4×C47#12111yescharacteristic
141C2×C4×C47C2×D811yescharacteristic
142C2×C4×C47#13511yescharacteristic
143C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
144C22⋊D47—81no—
145C22⋊D47—81no—
146C2×Dic47—41no—
147C2×Dic47—81no—
148D188—41no—
149D188—41no—
150C4×D47—81no—
151C4×D47—81no—
152Dic94—41no—
153Dic94—41no—
154C8×C47—22no—
155C8×C47—42no—
156C8×C47C2×C22⋊C411yescharacteristic
157C8×C47C4×D411yescharacteristic
158C8×C47#12111yescharacteristic
159C8×C47#12311yescharacteristic
160#13016—471nomaximal, Sylow
161C22×C47—41no—
162C22×C47—42no—
163C22×C47—161no—
164C22×C47#44211yescharacteristic
165C22×C47#44911yescharacteristic
166C22×C47#45911yescharacteristic
167C2×D47—81no—
168C2×D47—161no—
169C4×C47—42no—
170C4×C47—81no—
171C4×C47#38611yescharacteristic
172C4×C47C4×D811yescharacteristic
173C4×C47#44711yescharacteristic
174C4×C47#46311yescharacteristic
175Dic47—81no—
176Dic47—161no—
177C2×#508—471no—
178#2957D4711yescharacteristic, complemented
179#2145—471no—
180#2143—471no—
181#1976—471no—
182#1382—471no—
183#1379—471no—
184C2×C47—21no—
185C2×C47—21no—
186C2×C47—21no—
187C2×C47—82no—
188C2×C47#187911yescharacteristic
189D47—161no—
190C2×#135—471no—
191C2×#135C2×D4711yescharacteristic
192#568—21no—
193#508—942no—
194#508—942no—
195C2×Q32—471no—
196C2×SD32—471no—
197C2×SD32—471no—
198C2×D16—471no—
199C2×M32—471no—
200C22×C16—471no—
201#444—22no—
202#443—22no—
203C2×#108C2×D4711yescharacteristic
204#427—471no—
205#421—21no—
206#421—941no—
207#410—941no—
208#405C2×D4711yescharacteristic
209#360—942no—
210#359—942no—
211C47#1301611yescharacteristic, complemented, Sylow
212C2×#41—21no—
213C2×#41—941no—
214#135—21no—
215#135—21no—
216#135—941no—
217#135—941no—
218#135—941no—
219#135—941no—
220#135D18812yes—
221#135C22⋊D4712yes—
222C2×Q16—471no—
223C2×Q16C4×D4711yescharacteristic
224C2×SD16—21no—
225C2×SD16—941no—
226C2×D8—471no—
227C2×D8C4×D4711yescharacteristic
228#131—24no—
229#131—42no—
230C2×M16—21no—
231C2×M16—42no—
232C2×M16C22⋊D4711yescharacteristic
233C22×C8C22×D4711yescharacteristic
234#117—941no—
235#117C22⋊D4711yescharacteristic
236Q32—942no—
237SD32—942no—
238SD32—942no—
239D16—942no—
240M32—941no—
241M32—941no—
242C2×C16—471no—
243C2×C16—471no—
244C2×C16—941no—
245C2×C16—941no—
246C2×C16—941no—
247#108—21no—
248#108C22⋊D4712yes—
249#107—941no—
250#106—941no—
251#104—24no—
252#104—1882no—
253#99—1882no—
254#97—21no—
255C4×C8—21no—
256#41—22no—
257#41—22no—
258#41—41no—
259#41—41no—
260#41—1881no—
261#41—1881no—
262#41—1881no—
263#41—1881no—
264C2×Q8—21no—
265C2×Q8—941no—
266C2×D4—21no—
267C2×D4—41no—
268C2×D4—941no—
269C2×D4—1881no—
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—21no—
286M16—22no—
287M16—44no—
288M16—41no—
289M16#1062533412yes—
290C2×C8—21no—
291C2×C8—44no—
292C2×C8—41no—
293C2×C8C2×C4×D4711yescharacteristic
294C2×C8C2×D18811yescharacteristic
295C2×C8#1062535011yescharacteristic
296C2×C8#1062535011yescharacteristic
297C2×C8C2×C22⋊D4711yescharacteristic
298C2×C8C2×C22⋊D4711yescharacteristic
299C4⋊C4—21no—
300C4⋊C4—1881no—
301C22⋊C4—21no—
302C22⋊C4—1881no—
303C42—21no—
304C42—1881no—
305C16—941no—
306C16—941no—
307C16—1881no—
308C23—41no—
309C23—1881no—
310C23#1309404911yescharacteristic
311Q8—22no—
312Q8—41no—
313Q8—1881no—
314Q8—1881no—
315D4—22no—
316D4—42no—
317D4—42no—
318D4—41no—
319D4—3761no—
320D4—3761no—
321D4—1881no—
322D4—1881no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—3761no—
328C2×C4—3761no—
329C2×C4—3761no—
330C2×C4—1881no—
331C2×C4C4×C22⋊D4711yescharacteristic
332C2×C4#1309399311yescharacteristic
333C2×C4#1309399811yescharacteristic
334C2×C4C2×#1062533411yescharacteristic
335C2×C4#1309404411yescharacteristic
336C2×C4#1309405011yescharacteristic
337C8—22no—
338C8—42no—
339C8C2×(C2×D47)⋊C411yescharacteristic
340C8C4×C22⋊D4711yescharacteristic
341C8#1309399811yescharacteristic
342C8#1309400711yescharacteristic
343C22—41no—
344C22—42no—
345C22—161no—
346C22—3761no—
347C22—7521no—
348C22#1568923311yescharacteristic
349C22#1568926811yescharacteristic
350C22#1568931811yescharacteristic
351C4—42no—
352C4—81no—
353C4—3761no—
354C4—7521no—
355C4#1568900211yescharacteristic
356C4C4×#1062533411yescharacteristic
357C4#1568925711yescharacteristic
358C4#1568933811yescharacteristic
359C2—21no—
360C2—21no—
361C2—21no—
362C2—82no—
363C2—7521no—
364C2#2024373611yescharacteristic
subgroupG/H
centerC4#15689257
commutatorC2×C8×C47C22×C4
FrattiniC22×C8C22×D47
FittingC47×#2957C2
socleC2×C47#1879
prime radicalC2×#15689553C2
cosocleC22×C8×C47C23
hypercenter#2957D47
hypocenterC47#13016
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ #405 ◁ #2957

Complements

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

NH ≅ G/Ntype
2. #20245124C2semidirect
3. #20245115C2semidirect
4. #20244286C2semidirect
5. #20241485C2semidirect
6. #20241477C2semidirect
7. C47×#2957C2semidirect
11. C2×#13093970C4semidirect
12. C2×#13093968C4semidirect
13. C2×#13093967C4semidirect
14. C2×#13093965C4semidirect
178. #2957D47semidirect
211. C47#13016semidirect

Maximal subgroups

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

subgroupindex
C2×#156895532
#202451242
#202451152
#202442862
#202414852
#202414772
C47×#29572
#1301647