Finite Group Databasebeta

← #26110596

Subgroups — #26110596

Order 12032.

392 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252056C211yesmaximal, characteristic
2#20243405C211yesmaximal, characteristic
3#20242164C211yesmaximal, characteristic, complemented
4#20241771C211yesmaximal, characteristic
5#20241289C211yesmaximal, characteristic, complemented
6#20241228C211yesmaximal, characteristic, complemented
7C47×#1566C211yesmaximal, characteristic, complemented
8C4×#10625350C2211yescharacteristic
9#15689183—22no—
10#15689179—21no—
11#15689176C2211yescharacteristic
12#15689175—21no—
13C2×C4⋊(C47⋊C8)C2211yescharacteristic
14C2×#13093950—21no—
15#15689091—21no—
16#15689081—21no—
17C4×C4⋊Dic47C2211yescharacteristic
18#15688884—21no—
19#15688875—21no—
20#15688875—21no—
21#15688855C411yescharacteristic, complemented
22#15688855C411yescharacteristic, complemented
23#15688852C411yescharacteristic, complemented
24#15688852C411yescharacteristic, complemented
25C47×#423C2211yescharacteristic
26C47×#423C2211yescharacteristic
27C2×C4×C8×C47C2211yescharacteristic
28C47×#334—22no—
29C2×#10625350D411yescharacteristic
30C22×C47⋊C8—21no—
31C4×Dic94C2×C411yescharacteristic
32C4×Dic94Q811yescharacteristic
33C4×D188C2×C411yescharacteristic
34C4×D188Q811yescharacteristic
35C4×C22⋊D47—21no—
36C4×C22⋊D47—21no—
37#13093983D411yescharacteristic
38#13093981—21no—
39C2×C4⋊Dic47—21no—
40C2×C4×Dic47—21no—
41C42×D47—21no—
42C4⋊(C47⋊C8)—21no—
43C4⋊(C47⋊C8)C2×C411yescharacteristic
44C4⋊(C47⋊C8)C2×C411yescharacteristic
45C4⋊(C47⋊C8)D411yescharacteristic
46C4⋊(C47⋊C8)D411yescharacteristic
47#13093950—42no—
48C22⋊(C47⋊C8)—21no—
49(C2×D47)⋊C8—22no—
50(C2×D47)⋊C8—22no—
51#13093934—22no—
52C4×C47⋊C8—21no—
53C8×Dic47—22no—
54C47⋊#95—21no—
55C2×M16×C47—21no—
56C2×M16×C47—21no—
57C22×C8×C47—21no—
58C2×C42×C47C2311yescharacteristic
59C4⋊C8×C47—21no—
60C4⋊C8×C47—21no—
61C4⋊C8×C47—21no—
62C4⋊C8×C47D412yes—
63C4×C8×C47—21no—
64C4×C8×C47C2×C411yescharacteristic
65C4×C8×C47C2×C411yescharacteristic
66C22×C4×C47C2×D411yescharacteristic
67C22×C4×C47#4111yescharacteristic
68C22×C4×C47#4111yescharacteristic
69C2×C22⋊D47—21no—
70C22×Dic47—41no—
71#10625350—21no—
72#10625350—21no—
73#10625350—21no—
74#10625350—21no—
75C2×D188C4⋊C411yescharacteristic
76C2×C4×D47—21no—
77C2×C4×D47—21no—
78C2×C4×D47—21no—
79C2×Dic94C4⋊C411yescharacteristic
80M16×C47—41no—
81M16×C47—41no—
82M16×C47—41no—
83M16×C47—41no—
84C2×C8×C47—21no—
85C2×C8×C47—21no—
86C2×C8×C47—22no—
87C2×C8×C47—42no—
88C2×C8×C47—41no—
89C42×C47C22×C411yescharacteristic
90C42×C47C2×D411yescharacteristic
91C42×C47C2×D411yescharacteristic
92C42×C47C2×Q811yescharacteristic
93C22⋊Dic47—21no—
94(C2×D47)⋊C4—21no—
95(C2×D47)⋊C4—21no—
96C4⋊Dic47—22no—
97C4⋊Dic47—41no—
98C4⋊Dic47C4⋊C411yescharacteristic
99C4⋊Dic47C4⋊C411yescharacteristic
100Dic47⋊C4—21no—
101Dic47⋊C4—21no—
102C4×Dic47—21no—
103C4×Dic47—21no—
104C4×Dic47—21no—
105C4×Dic47—41no—
106C4×Dic47—41no—
107C2×C47⋊C8—21no—
108C2×C47⋊C8—21no—
109C2×C47⋊C8—21no—
110C2×C47⋊C8—21no—
111C2×C47⋊C8—41no—
112C2×C47⋊C8—41no—
113C23×C47#12311yescharacteristic
114C22×D47—21no—
115C2×C4×C47—21no—
116C2×C4×C47—21no—
117C2×C4×C47—41no—
118C2×C4×C47C2×C4⋊C411yescharacteristic
119C2×C4×C47C4×D411yescharacteristic
120C2×C4×C47C4×D411yescharacteristic
121C2×C4×C47#12011yescharacteristic
122C2×C4×C47C22⋊Q811yescharacteristic
123C2×C4×C47C22⋊Q811yescharacteristic
124C2×C4×C47#13511yescharacteristic
125C2×C4×C47#13511yescharacteristic
126C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
127C2×C4×C47#13711yescharacteristic
128C22⋊D47—41no—
129C22⋊D47—41no—
130C2×Dic47—21no—
131C2×Dic47—21no—
132C2×Dic47—21no—
133C2×Dic47—42no—
134C2×Dic47—81no—
135C2×Dic47—81no—
136D188—21no—
137D188—21no—
138C4×D47—41no—
139C4×D47—41no—
140C4×D47—41no—
141C4×D47—41no—
142C4×D47—81no—
143Dic94—21no—
144Dic94—21no—
145C8×C47—22no—
146C8×C47—41no—
147C8×C47—42no—
148C8×C47—81no—
149C47⋊C8—41no—
150C47⋊C8—41no—
151C47⋊C8—41no—
152C47⋊C8—41no—
153#8905—471nomaximal, Sylow
154C22×C47—21no—
155C22×C47—21no—
156C22×C47#38511yescharacteristic
157C22×C47#48211yescharacteristic
158C22×C47#48511yescharacteristic
159C2×D47—41no—
160C2×D47—41no—
161C2×D47—41no—
162C4×C47—21no—
163C4×C47—21no—
164C4×C47—21no—
165C4×C47#42711yescharacteristic
166C4×C47#42811yescharacteristic
167C4×C47#44311yescharacteristic
168C4×C47#44411yescharacteristic
169C4×C47#44911yescharacteristic
170C4×C47#45211yescharacteristic
171Dic47—41no—
172Dic47—41no—
173Dic47—41no—
174Dic47—82no—
175#2925—471no—
176#1806—471no—
177#1571—471no—
178#1566D4711yescharacteristic, complemented
179#1476—471no—
180#1303—471no—
181#1279—471no—
182C2×C47—21no—
183C2×C47—21no—
184C2×C47#185411yescharacteristic
185C2×C47#186111yescharacteristic
186C2×C47#186611yescharacteristic
187D47—81no—
188C4×#41—471no—
189#433—942no—
190#432—941no—
191#431—471no—
192#431—941no—
193#423C2×D4711yescharacteristic
194#423C2×D4711yescharacteristic
195C2×C4⋊C8—471no—
196C2×#104—941no—
197#408—941no—
198#405—941no—
199C2×C4×C8C2×D4711yescharacteristic
200C4×C4⋊C4—471no—
201#339—941no—
202#335—941no—
203#335—941no—
204#334—22no—
205Q8⋊C8—471no—
206Q8⋊C8—471no—
207D4⋊C8—471no—
208D4⋊C8—471no—
209C47#890511yescharacteristic, complemented, Sylow
210C2×#41—471no—
211C2×M16—21no—
212C2×M16—21no—
213C22×C8—21no—
214C22×C8—941no—
215C4×Q8—471no—
216C4×Q8—471no—
217C4×D4—471no—
218C4×D4—471no—
219C4×D4—941no—
220C4×D4—941no—
221#117—471no—
222#117—941no—
223C2×C4⋊C4—941no—
224C2×C42—941no—
225C2×C42—941no—
226C2×C42C22×D4711yescharacteristic
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8—21no—
230C4⋊C8—471no—
231C4⋊C8—471no—
232C4⋊C8—471no—
233C4⋊C8—471no—
234C4⋊C8—941no—
235C4⋊C8C22⋊D4712yes—
236#104—1882no—
237C22⋊C8—942no—
238C22⋊C8—942no—
239C22⋊C8—941no—
240#97—942no—
241C4×C8—21no—
242C4×C8—942no—
243C4×C8—941no—
244C4×C8C4×D4711yescharacteristic
245C4×C8C4×D4711yescharacteristic
246#95—941no—
247#41—941no—
248#41—941no—
249#41—941no—
250#41—941no—
251C2×Q8—471no—
252C2×D4—471no—
253C2×D4—941no—
254C22×C4—941no—
255C22×C4—941no—
256C22×C4—941no—
257C22×C4—1881no—
258C22×C4#1062535011yescharacteristic
259C22×C4D4×D4711yescharacteristic
260C22×C4#1062535411yescharacteristic
261M16—41no—
262M16—41no—
263M16—41no—
264M16—41no—
265C2×C8—21no—
266C2×C8—21no—
267C2×C8—22no—
268C2×C8—42no—
269C2×C8—41no—
270C2×C8—941no—
271C2×C8—941no—
272C2×C8—941no—
273C2×C8—941no—
274C2×C8—1881no—
275C2×C8—1881no—
276C4⋊C4—471no—
277C4⋊C4—471no—
278C4⋊C4—942no—
279C4⋊C4—941no—
280C4⋊C4—941no—
281C4⋊C4—1881no—
282C22⋊C4—941no—
283C22⋊C4—941no—
284C22⋊C4—941no—
285C42—941no—
286C42—941no—
287C42—941no—
288C42—1881no—
289C42—1881no—
290C42C2×C4×D4711yescharacteristic
291C42D4×D4711yescharacteristic
292C42Q8×D4711yescharacteristic
293C42C2×C22⋊D4711yescharacteristic
294C23—941no—
295C23#1309400911yescharacteristic
296Q8—941no—
297Q8—941no—
298D4—941no—
299D4—941no—
300D4—1881no—
301D4—1881no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—941no—
306C2×C4—941no—
307C2×C4—941no—
308C2×C4—3761no—
309C2×C4—3761no—
310C2×C4—3761no—
311C2×C4—1882no—
312C2×C4—1881no—
313C2×C4—1881no—
314C2×C4—1881no—
315C2×C4—1881no—
316C2×C4C4⋊C4×D4711yescharacteristic
317C2×C4C4×C22⋊D4711yescharacteristic
318C2×C4#1309398611yescharacteristic
319C2×C4#1309399211yescharacteristic
320C2×C4#1309400011yescharacteristic
321C2×C4#1309400211yescharacteristic
322C2×C4#1309404511yescharacteristic
323C2×C4#1309404511yescharacteristic
324C2×C4#1309405111yescharacteristic
325C2×C4#1309405311yescharacteristic
326C8—22no—
327C8—41no—
328C8—42no—
329C8—81no—
330C8—1881no—
331C8—1881no—
332C8—1881no—
333C8—1881no—
334C22—21no—
335C22—21no—
336C22—1881no—
337C22—1881no—
338C22—1881no—
339C22#1568899411yescharacteristic
340C22#1568944911yescharacteristic
341C22#1568946711yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—3762no—
346C4—1881no—
347C4—1881no—
348C4—1881no—
349C4#1568915811yescharacteristic
350C4#1568916211yescharacteristic
351C4#1568923911yescharacteristic
352C4#1568924411yescharacteristic
353C4#1568926711yescharacteristic
354C4#1568928211yescharacteristic
355C2—21no—
356C2—21no—
357C2—3761no—
358C2#2024358611yescharacteristic
359C2#2024362711yescharacteristic
360C2#2024366011yescharacteristic
subgroupG/H
centerC2×C4#13093992
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1566C2
socleC22×C47#385
prime radicalC2×#10625350D4
cosocleC2×C42×C47C23
hypercenter#1566D47
hypocenterC47#8905
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1566

Complements

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

NH ≅ G/Ntype
3. #20242164C2semidirect
5. #20241289C2semidirect
6. #20241228C2semidirect
7. C47×#1566C2semidirect
21. #15688855C4semidirect
22. #15688855C4semidirect
23. #15688852C4semidirect
24. #15688852C4semidirect
178. #1566D47semidirect
209. C47#8905semidirect

Maximal subgroups

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

subgroupindex
#202520562
#202434052
#202421642
#202417712
#202412892
#202412282
C47×#15662
#890547