Finite Group Databasebeta

← #26133198

Subgroups — #26133198

Order 12032.

466 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256490C211yesmaximal, characteristic, complemented
2#20252104C211yesmaximal, characteristic
3#20245016C211yesmaximal, characteristic, complemented
4#20245008C211yesmaximal, characteristic, complemented
5#20241467C211yesmaximal, characteristic, complemented
6#20241467C211yesmaximal, characteristic, complemented
7C47×#2117C211yesmaximal, characteristic, complemented
8C2×#13094030C2211yescharacteristic
9#15689669C411yescharacteristic
10#15689541—22no—
11#15689539—22no—
12C2×#13093964C2211yescharacteristic
13C2×#13093964C2211yescharacteristic
14M32×D47—22no—
15#15689194—22no—
16#15689192—22no—
17#15689146C411yescharacteristic
18#15689091C411yescharacteristic
19#15689090C411yescharacteristic
20C2×#13093934C2211yescharacteristic
21#15688907—22no—
22#15688904—22no—
23C2×#131×C47C2211yescharacteristic
24C2×M32×C47C2211yescharacteristic
25C2×M32×C47C2211yescharacteristic
26C47×#350—22no—
27C2×#10625350C2×C411yescharacteristic
28#13094030—21no—
29#13094030—21no—
30#13094030—21no—
31#13094030—21no—
32C2×#10625329C2×C411yescharacteristic
33C2×#10625324D412yes—
34C22×C47⋊C8C2×C411yescharacteristic
35C2×C8×D47D412yes—
36#13094022C811yescharacteristic
37#13094020C811yescharacteristic
38#13094013C811yescharacteristic
39#13094011C811yescharacteristic
40#13093996—22no—
41C4×C22⋊D47—22no—
42C2×C4×Dic47C2×C411yescharacteristic
43#13093964—21no—
44#13093964—21no—
45#13093964—21no—
46#13093964—21no—
47#13093963—24no—
48C2×C47⋊C16—21no—
49C2×C47⋊C16D412yescomplemented
50C16×D47—24no—
51Dic47⋊C8—22no—
52C22⋊(C47⋊C8)—22no—
53(C2×D47)⋊C8—22no—
54#13093934—21no—
55#13093934—21no—
56C2×#41×C47C2×C411yescharacteristic
57#131×C47—21no—
58#131×C47—21no—
59#131×C47—21no—
60#131×C47—21no—
61C2×M16×C47—21no—
62C2×M16×C47C2×C411yescharacteristic
63C22×C8×C47—21no—
64C22×C8×C47C2311yescharacteristic
65M32×C47—21no—
66M32×C47—21no—
67M32×C47—21no—
68M32×C47—21no—
69C2×C16×C47—21no—
70C2×C16×C47D412yescomplemented
71#41×C47—21no—
72#41×C47—21no—
73#41×C47—21no—
74#41×C47—21no—
75C2×Q8×C47C2×C811yescharacteristic
76C2×D4×C47—21no—
77C2×D4×C47C2×C811yescharacteristic
78C22×C4×C47—21no—
79C22×C4×C47C22×C411yescharacteristic
80C2×C22⋊D47—22no—
81C2×C22⋊D47M1612yes—
82C22×Dic47—21no—
83#10625350—21no—
84#10625350—21no—
85#10625350—21no—
86#10625350—21no—
87C2×D188C2×C811yescharacteristic
88C2×C4×D47C22⋊C412yes—
89C2×Dic94C2×C811yescharacteristic
90M16×C47—21no—
91M16×C47—21no—
92M16×C47—41no—
93M16×C47—41no—
94C2×C8×C47—21no—
95C2×C8×C47—41no—
96C2×C8×C47—41no—
97C2×C8×C47C2×D411yescharacteristic
98C2×C8×C47C2×D411yescharacteristic
99C2×C8×C47C2×D411yescharacteristic
100C2×C8×C47C2×D411yescharacteristic
101C2×C8×C47#4111yescharacteristic
102C2×C8×C47#4111yescharacteristic
103C22⋊Dic47—22no—
104(C2×D47)⋊C4—22no—
105Dic47⋊C4—22no—
106C4×Dic47—21no—
107C4×Dic47C2×C811yescharacteristic
108C4×Dic47C2×C811yescharacteristic
109#10625329—21no—
110#10625329—21no—
111C2×C47⋊C8—21no—
112C2×C47⋊C8—21no—
113C2×C47⋊C8—21no—
114C2×C47⋊C8C22⋊C412yes—
115#10625324—22no—
116#10625324—22no—
117C8×D47—22no—
118C8×D47—22no—
119C16×C47—22no—
120C16×C47—41no—
121C47⋊C16—22no—
122C47⋊C16—41no—
123C23×C47—21no—
124C23×C47C2×M1611yescharacteristic
125C22×D47C22⋊C812yes—
126Q8×C47—21no—
127Q8×C47—21no—
128D4×C47—21no—
129D4×C47—21no—
130D4×C47—41no—
131D4×C47—41no—
132C2×C4×C47—21no—
133C2×C4×C47—41no—
134C2×C4×C47—41no—
135C2×C4×C47C2×C22⋊C411yescharacteristic
136C2×C4×C47C4×D411yescharacteristic
137C2×C4×C47C4×D411yescharacteristic
138C2×C4×C47C22×C811yescharacteristic
139C2×C4×C47#13111yescharacteristic
140C2×C4×C47#13111yescharacteristic
141C22⋊D47—22no—
142C22⋊D47—22no—
143C22⋊D47—82no—
144C2×Dic47—21no—
145C2×Dic47—21no—
146C2×Dic47—81no—
147C2×Dic47C22⋊C812yes—
148D188—21no—
149D188—21no—
150C4×D47—22no—
151C4×D47—22no—
152Dic94—21no—
153Dic94—21no—
154C8×C47—41no—
155C8×C47#12011yescharacteristic
156C8×C47#12111yescharacteristic
157C8×C47#12111yescharacteristic
158C8×C47#12311yescharacteristic
159C47⋊C8—22no—
160C47⋊C8—41no—
161#12988—471nomaximal, Sylow
162C22×C47—41no—
163C22×C47—42no—
164C22×C47—41no—
165C22×C47C2×C22⋊C811yescharacteristic
166C22×C47#43511yescharacteristic
167C22×C47#43511yescharacteristic
168C2×D47—22no—
169C2×D47—42no—
170C4×C47—41no—
171C4×C47#38611yescharacteristic
172C4×C47#40811yescharacteristic
173C4×C47C8×D411yescharacteristic
174C4×C47C8×D411yescharacteristic
175Dic47—22no—
176Dic47—41no—
177Dic47—41no—
178#3407—471no—
179#2932—471no—
180#2117—471no—
181#2117D4711yescharacteristic, complemented
182#2115—471no—
183#1375—471no—
184#1375—471no—
185C2×C47—21no—
186C2×C47—21no—
187C2×C47—21no—
188C2×C47—81no—
189C2×C47#186911yescharacteristic
190D47—42no—
191C2×#131—471no—
192C2×#131C2×D4711yescharacteristic
193#532—471no—
194#504—942no—
195#504—942no—
196C2×M32—471no—
197C2×M32—471no—
198C2×M32—942no—
199C2×M32C2×D4711yescharacteristic
200C2×M32C2×D4711yescharacteristic
201#435—942no—
202#435—942no—
203#423—471no—
204#408—471no—
205#408—471no—
206C2×#97—471no—
207#350—22no—
208#350—942no—
209#349—942no—
210C47#1298811yescharacteristic, complemented, Sylow
211C2×#41—471no—
212C2×#41C4×D4711yescharacteristic
213#131—21no—
214#131—21no—
215#131—21no—
216#131—21no—
217#131—941no—
218#131—941no—
219#131—941no—
220#131—941no—
221C2×M16—21no—
222C2×M16—471no—
223C2×M16—472no—
224C2×M16C4×D4711yescharacteristic
225C22×C8—21no—
226C22×C8—472no—
227C22×C8—471no—
228C22×C8C22×D4711yescharacteristic
229C4⋊Q8—471no—
230#127—471no—
231#124—471no—
232#124—471no—
233#121—942no—
234C4×D4—942no—
235C2×C42—471no—
236M32—21no—
237M32—21no—
238M32—21no—
239M32—21no—
240M32—944no—
241M32—941no—
242M32—941no—
243M32—941no—
244M32—941no—
245C2×C16—21no—
246C2×C16—472no—
247C2×C16—944no—
248C2×C16—941no—
249C2×C16C22⋊D4712yescomplemented
250C4⋊C8—942no—
251C22⋊C8—942no—
252C22⋊C8—942no—
253#97—941no—
254#97—941no—
255#41—21no—
256#41—21no—
257#41—21no—
258#41—21no—
259#41—941no—
260#41—941no—
261#41—941no—
262#41—941no—
263C2×Q8—471no—
264C2×Q8C8×D4711yescharacteristic
265C2×D4—21no—
266C2×D4—472no—
267C2×D4—471no—
268C2×D4—942no—
269C2×D4C8×D4711yescharacteristic
270C22×C4—21no—
271C22×C4—472no—
272C22×C4—941no—
273C22×C4C2×C4×D4711yescharacteristic
274M16—21no—
275M16—21no—
276M16—41no—
277M16—41no—
278M16—941no—
279M16—941no—
280M16—942no—
281M16—942no—
282C2×C8—21no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—472no—
286C2×C8—942no—
287C2×C8—942no—
288C2×C8—941no—
289C2×C8—941no—
290C2×C8—941no—
291C2×C8#1062535011yescharacteristic
292C2×C8D4×D4711yescharacteristic
293C2×C8D4×D4711yescharacteristic
294C2×C8D4×D4711yescharacteristic
295C2×C8#1062535211yescharacteristic
296C2×C8C2×C22⋊D4711yescharacteristic
297C4⋊C4—942no—
298C22⋊C4—942no—
299C22⋊C4—942no—
300C42—471no—
301C42—471no—
302C42—941no—
303C16—22no—
304C16—41no—
305C16—942no—
306C16—1881no—
307C23—21no—
308C23—472no—
309C23M16×D4711yescharacteristic
310Q8—21no—
311Q8—21no—
312Q8—941no—
313Q8—941no—
314D4—21no—
315D4—21no—
316D4—41no—
317D4—41no—
318D4—942no—
319D4—942no—
320D4—941no—
321D4—941no—
322D4—3762no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—472no—
327C2×C4—942no—
328C2×C4—942no—
329C2×C4—941no—
330C2×C4—941no—
331C2×C4—3761no—
332C2×C4C22⋊C4×D4711yescharacteristic
333C2×C4(C22⋊D47)⋊C411yescharacteristic
334C2×C4C4×C22⋊D4711yescharacteristic
335C2×C4C2×C8×D4711yescharacteristic
336C2×C4#1309403011yescharacteristic
337C2×C4#1309403211yescharacteristic
338C8—41no—
339C8—942no—
340C8—1881no—
341C8#1309399211yescharacteristic
342C8#1309399511yescharacteristic
343C8#1309399711yescharacteristic
344C8#1309400611yescharacteristic
345C22—41no—
346C22—42no—
347C22—41no—
348C22—942no—
349C22—1882no—
350C22C22⋊C8×D4711yescharacteristic
351C22#1568919211yescharacteristic
352C22#1568919711yescharacteristic
353C4—41no—
354C4—942no—
355C4—1881no—
356C4—1881no—
357C4#1568899911yescharacteristic
358C4#1568908811yescharacteristic
359C4(C22⋊D47)⋊C811yescharacteristic
360C4C8×C22⋊D4711yescharacteristic
361C2—21no—
362C2—21no—
363C2—21no—
364C2—81no—
365C2—1882no—
366C2#2024367711yescharacteristic
subgroupG/H
centerC4#15688999
commutatorC2×C4×C47C22×C8
FrattiniC22×C8C22×D47
FittingC47×#2117C2
socleC2×C47#1869
prime radical#15689669C4
cosocleC22×C8×C47C23
hypercenter#2117D47
hypocenterC47#12988
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C8 ◁ #2117

Complements

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

NH ≅ G/Ntype
1. #20256490C2semidirect
3. #20245016C2semidirect
4. #20245008C2semidirect
5. #20241467C2semidirect
6. #20241467C2semidirect
7. C47×#2117C2semidirect
49. C2×C47⋊C16D4semidirect
70. C2×C16×C47D4semidirect
181. #2117D47semidirect
210. C47#12988semidirect
249. C2×C16C22⋊D47semidirect

Maximal subgroups

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

subgroupindex
#202564902
#202521042
#202450162
#202450082
#202414672
C47×#21172
#1298847