Finite Group Databasebeta

← #26134443

Subgroups — #26134443

Order 12032.

442 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#20252098C211yesmaximal, characteristic
2#20245143C211yesmaximal, characteristic, complemented
3C2×#15688908C211yesmaximal, characteristic, complemented
4C2×#15688907C211yesmaximal, characteristic, complemented
5C2×#15688906C211yesmaximal, characteristic, complemented
6C2×#15688898C211yesmaximal, characteristic, complemented
7C2×C47×#350C211yesmaximal, characteristic, complemented
8C2×#13094030C2211yescharacteristic
9#15689669C411yescharacteristic
10C2×#13093964C2211yescharacteristic
11C22×C47⋊C16C2211yescharacteristic
12#15689199—22no—
13C8×C22⋊D47—22no—
14#15689146C411yescharacteristic
15#15689091C411yescharacteristic
16#15689090C411yescharacteristic
17C2×C8×Dic47C2211yescharacteristic
18Dic47⋊C16—22no—
19#15688908—22no—
20#15688907—22no—
21#15688906—22no—
22#15688898—22no—
23C2×#131×C47C2211yescharacteristic
24C2×M32×C47C2211yescharacteristic
25C22×C16×C47C2211yescharacteristic
26C47×#350—22no—
27C2×#10625350C2×C411yescharacteristic
28#13094030—21no—
29#13094030—21no—
30#13094030—21no—
31#13094030—21no—
32C2×#10625329C2×C411yescharacteristic
33C2×#10625324—21no—
34C22×C47⋊C8C2×C411yescharacteristic
35C2×C8×D47—21no—
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—
45C2×C47⋊C16—21no—
46C2×C47⋊C16—21no—
47C2×C47⋊C16—21no—
48C2×C47⋊C16D412yescomplemented
49Dic47⋊C8—22no—
50C22⋊(C47⋊C8)—22no—
51(C2×D47)⋊C8—22no—
52C8×Dic47D412yes—
53C8×Dic47D412yes—
54C2×#41×C47C2×C411yescharacteristic
55#131×C47—21no—
56#131×C47—21no—
57#131×C47—21no—
58#131×C47—21no—
59C2×M16×C47—21no—
60C2×M16×C47C2×C411yescharacteristic
61C22×C8×C47—21no—
62C22×C8×C47C2311yescharacteristic
63M32×C47—21no—
64M32×C47—21no—
65C2×C16×C47—21no—
66C2×C16×C47—21no—
67C2×C16×C47—21no—
68C2×C16×C47D412yescomplemented
69#41×C47—21no—
70#41×C47—21no—
71#41×C47—21no—
72#41×C47—21no—
73C2×Q8×C47C2×C811yescharacteristic
74C2×D4×C47—21no—
75C2×D4×C47C2×C811yescharacteristic
76C22×C4×C47—21no—
77C22×C4×C47C22×C411yescharacteristic
78C2×C22⋊D47—21no—
79C2×C22⋊D47—22no—
80C22×Dic47M1612yes—
81#10625350—21no—
82#10625350—21no—
83#10625350—21no—
84#10625350—21no—
85C2×D188C2×C811yescharacteristic
86C2×C4×D47—21no—
87C2×Dic94C2×C811yescharacteristic
88M16×C47—21no—
89M16×C47—21no—
90M16×C47—41no—
91M16×C47—41no—
92C2×C8×C47—21no—
93C2×C8×C47—41no—
94C2×C8×C47—41no—
95C2×C8×C47C2×D411yescharacteristic
96C2×C8×C47C2×D411yescharacteristic
97C2×C8×C47C2×D411yescharacteristic
98C2×C8×C47C2×D411yescharacteristic
99C2×C8×C47#4111yescharacteristic
100C2×C8×C47#4111yescharacteristic
101C22⋊Dic47—22no—
102(C2×D47)⋊C4—22no—
103Dic47⋊C4—22no—
104C4×Dic47C22⋊C412yes—
105C4×Dic47C2×C811yescharacteristic
106C4×Dic47C2×C811yescharacteristic
107#10625329—21no—
108#10625329—21no—
109C2×C47⋊C8—21no—
110C2×C47⋊C8—21no—
111C2×C47⋊C8—21no—
112C2×C47⋊C8C22⋊C412yes—
113#10625324—41no—
114#10625324—41no—
115C8×D47—41no—
116C8×D47—41no—
117C16×C47—22no—
118C16×C47—41no—
119C47⋊C16—22no—
120C47⋊C16—41no—
121C23×C47—21no—
122C23×C47C2×M1611yescharacteristic
123C22×D47—21no—
124Q8×C47—21no—
125Q8×C47—21no—
126D4×C47—21no—
127D4×C47—21no—
128D4×C47—41no—
129D4×C47—41no—
130C2×C4×C47—21no—
131C2×C4×C47—41no—
132C2×C4×C47—41no—
133C2×C4×C47C2×C22⋊C411yescharacteristic
134C2×C4×C47C4×D411yescharacteristic
135C2×C4×C47C4×D411yescharacteristic
136C2×C4×C47C22×C811yescharacteristic
137C2×C4×C47#13111yescharacteristic
138C2×C4×C47#13111yescharacteristic
139C22⋊D47—44no—
140C22⋊D47—41no—
141C22⋊D47—41no—
142C2×Dic47—21no—
143C2×Dic47—42no—
144C2×Dic47C22⋊C812yes—
145C2×Dic47C22⋊C812yes—
146D188—21no—
147D188—21no—
148C4×D47—41no—
149C4×D47—41no—
150Dic94—21no—
151Dic94—21no—
152C8×C47—41no—
153C8×C47#12111yescharacteristic
154C8×C47#12111yescharacteristic
155C8×C47#12411yescharacteristic
156C8×C47#12711yescharacteristic
157C47⋊C8—22no—
158C47⋊C8—41no—
159#13192—471nomaximal, Sylow
160C22×C47—22no—
161C22×C47—42no—
162C22×C47—41no—
163C22×C47C2×C22⋊C811yescharacteristic
164C22×C47#43611yescharacteristic
165C22×C47#43611yescharacteristic
166C2×D47—42no—
167C2×D47—41no—
168C4×C47—41no—
169C4×C47#39011yescharacteristic
170C4×C47#40811yescharacteristic
171C4×C47C8×D411yescharacteristic
172C4×C47C8×D411yescharacteristic
173Dic47—22no—
174Dic47—22no—
175Dic47—41no—
176#2931—471no—
177#2150—471no—
178C2×#350—471no—
179C2×#350—471no—
180C2×#350—471no—
181C2×#350D4711yescharacteristic, complemented
182C2×#346—471no—
183C2×C47—21no—
184C2×C47—21no—
185C2×C47—81no—
186C2×C47#195411yescharacteristic
187C2×C47#211712yes—
188D47—81no—
189C2×#131—471no—
190C2×#131C2×D4711yescharacteristic
191#532—471no—
192C2×M32—471no—
193C2×M32C2×D4711yescharacteristic
194C22×C16—471no—
195C22×C16C2×D4711yescharacteristic
196#436—942no—
197C8×D4—942no—
198#423—471no—
199#408—471no—
200#408—471no—
201C2×C4×C8—471no—
202C4⋊C16—942no—
203#350—22no—
204#350—942no—
205#350—942no—
206#350—942no—
207#346—942no—
208C47#1319211yescharacteristic, complemented, Sylow
209C2×#41—471no—
210C2×#41C4×D4711yescharacteristic
211#131—21no—
212#131—21no—
213#131—21no—
214#131—21no—
215#131—941no—
216#131—941no—
217#131—941no—
218#131—941no—
219C2×M16—21no—
220C2×M16—471no—
221C2×M16—941no—
222C2×M16C4×D4711yescharacteristic
223C22×C8—21no—
224C22×C8—471no—
225C22×C8—941no—
226C22×C8C22×D4711yescharacteristic
227C4⋊Q8—471no—
228#127—471no—
229#124—471no—
230#124—471no—
231#121—942no—
232C4×D4—942no—
233C2×C42—471no—
234M32—21no—
235M32—21no—
236M32—941no—
237M32—941no—
238C2×C16—21no—
239C2×C16—21no—
240C2×C16—21no—
241C2×C16—472no—
242C2×C16—941no—
243C2×C16—941no—
244C2×C16—941no—
245C2×C16C22⋊D4712yescomplemented
246C4⋊C8—942no—
247C22⋊C8—942no—
248C22⋊C8—942no—
249C4×C8—472no—
250C4×C8—472no—
251#41—21no—
252#41—21no—
253#41—21no—
254#41—21no—
255#41—941no—
256#41—941no—
257#41—941no—
258#41—941no—
259C2×Q8—471no—
260C2×Q8C8×D4711yescharacteristic
261C2×D4—21no—
262C2×D4—471no—
263C2×D4—942no—
264C2×D4—941no—
265C2×D4C8×D4711yescharacteristic
266C22×C4—21no—
267C22×C4—472no—
268C22×C4—941no—
269C22×C4C2×C4×D4711yescharacteristic
270M16—21no—
271M16—21no—
272M16—41no—
273M16—41no—
274M16—941no—
275M16—941no—
276M16—1881no—
277M16—1881no—
278C2×C8—21no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—472no—
282C2×C8—941no—
283C2×C8—941no—
284C2×C8—941no—
285C2×C8—1881no—
286C2×C8—1881no—
287C2×C8#1062535011yescharacteristic
288C2×C8D4×D4711yescharacteristic
289C2×C8D4×D4711yescharacteristic
290C2×C8D4×D4711yescharacteristic
291C2×C8#1062535211yescharacteristic
292C2×C8C2×C22⋊D4711yescharacteristic
293C4⋊C4—942no—
294C22⋊C4—942no—
295C22⋊C4—942no—
296C42—472no—
297C42—471no—
298C42—471no—
299C16—22no—
300C16—41no—
301C16—942no—
302C16—1881no—
303C23—21no—
304C23—941no—
305C23M16×D4711yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—941no—
309Q8—941no—
310D4—21no—
311D4—21no—
312D4—41no—
313D4—41no—
314D4—941no—
315D4—941no—
316D4—1884no—
317D4—1881no—
318D4—1881no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—472no—
323C2×C4—472no—
324C2×C4—941no—
325C2×C4—1882no—
326C2×C4—1881no—
327C2×C4—1881no—
328C2×C4C22⋊C4×D4711yescharacteristic
329C2×C4(C22⋊D47)⋊C411yescharacteristic
330C2×C4C4×C22⋊D4711yescharacteristic
331C2×C4C2×C8×D4711yescharacteristic
332C2×C4#1309403011yescharacteristic
333C2×C4#1309403211yescharacteristic
334C8—41no—
335C8—942no—
336C8—1881no—
337C8#1309399611yescharacteristic
338C8#1309399711yescharacteristic
339C8#1309401011yescharacteristic
340C8#1309402011yescharacteristic
341C22—22no—
342C22—42no—
343C22—41no—
344C22—1882no—
345C22—1881no—
346C22C22⋊C8×D4711yescharacteristic
347C22#1568919811yescharacteristic
348C22#1568919911yescharacteristic
349C4—41no—
350C4—942no—
351C4—942no—
352C4—1881no—
353C4#1568902311yescharacteristic
354C4#1568908811yescharacteristic
355C4(C22⋊D47)⋊C811yescharacteristic
356C4C8×C22⋊D4711yescharacteristic
357C2—21no—
358C2—21no—
359C2—81no—
360C2—3761no—
361C2#2024418011yescharacteristic
362C2#2024501412yes—
subgroupG/H
centerC2×C8D4×D47
commutatorC2×C4×C47C22×C8
FrattiniC22×C8C22×D47
FittingC2×C47×#350C2
socleC22×C47C2×C22⋊C8
prime radical#15689669C4
cosocleC22×C8×C47C23
hypercenterC2×#350D47
hypocenterC47#13192
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#350

Complements

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

NH ≅ G/Ntype
2. #20245143C2semidirect
3. C2×#15688908C2semidirect
4. C2×#15688907C2semidirect
5. C2×#15688906C2semidirect
6. C2×#15688898C2semidirect
7. C2×C47×#350C2semidirect
48. C2×C47⋊C16D4semidirect
68. C2×C16×C47D4semidirect
181. C2×#350D47semidirect
208. C47#13192semidirect
245. C2×C16C22⋊D47semidirect

Maximal subgroups

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

subgroupindex
#202520982
#202451432
C2×#156889082
C2×#156889072
C2×#156889062
C2×#156888982
C2×C47×#3502
#1319247