Finite Group Databasebeta

← #26133203

Subgroups — #26133203

Order 12032.

470 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
1#20256490C211yesmaximal, characteristic, complemented
2#20252091C211yesmaximal, characteristic
3#20245008C211yesmaximal, characteristic, complemented
4C2×#15688905C211yesmaximal, characteristic, complemented
5#20241475C211yesmaximal, characteristic, complemented
6#20241473C211yesmaximal, characteristic, complemented
7C2×C47×#349C211yesmaximal, characteristic, complemented
8C2×#13094030C2211yescharacteristic
9#15689634C411yescharacteristic
10#15689541—22no—
11#15689539—22no—
12C2×#13093964C2211yescharacteristic
13C2×#13093964C2211yescharacteristic
14M32×D47—22no—
15#15689199—22no—
16#15689192—22no—
17#15689149C411yescharacteristic
18#15689089C411yescharacteristic
19#15689087C411yescharacteristic
20#15689078C2211yescharacteristic
21#15688905—22no—
22#15688904—22no—
23C22×M16×C47C2211yescharacteristic
24C2×M32×C47C2211yescharacteristic
25C2×M32×C47C2211yescharacteristic
26C47×#349—22no—
27C2×#10625350C2×C411yescharacteristic
28#13094030—21no—
29#13094030—21no—
30#13094030—21no—
31#13094030—21no—
32C2×#10625329C2×C411yescharacteristic
33C2×#10625329C2×C411yescharacteristic
34C2×#10625324D412yes—
35C2×C8×D47D412yes—
36#13094007C812yes—
37#13094003—21no—
38#13093998—21no—
39#13093993C812yes—
40C4×C22⋊D47—22no—
41#13093983C2×C411yescharacteristic
42#13093964—21no—
43#13093964—21no—
44#13093964—21no—
45#13093964D412yescomplemented
46#13093963—24no—
47C2×C47⋊C16—21no—
48C2×C47⋊C16—21no—
49C16×D47—24no—
50Dic47⋊C8—22no—
51C22⋊(C47⋊C8)—22no—
52(C2×D47)⋊C8—22no—
53#13093934—21no—
54C8×Dic47—21no—
55C23×C4×C47C2×C411yescharacteristic
56C2×M16×C47—21no—
57C2×M16×C47—21no—
58C2×M16×C47—21no—
59C2×M16×C47—21no—
60C2×M16×C47—21no—
61C2×M16×C47—21no—
62C22×C8×C47C2×C411yescharacteristic
63C22×C8×C47C2311yescharacteristic
64M32×C47—21no—
65M32×C47—21no—
66M32×C47—21no—
67M32×C47D412yescomplemented
68C2×C16×C47—21no—
69C2×C16×C47—21no—
70C24×C47C2×C811yescharacteristic
71C22×C4×C47—21no—
72C22×C4×C47—21no—
73C22×C4×C47—21no—
74C22×C4×C47—21no—
75C22×C4×C47—21no—
76C22×C4×C47—21no—
77C22×C4×C47C2×C811yescharacteristic
78C22×C4×C47C22×C411yescharacteristic
79C2×C22⋊D47—22no—
80C2×C22⋊D47C2×C812yes—
81#10625350—21no—
82#10625350—21no—
83#10625350—21no—
84#10625350—21no—
85C2×D188M1611yescharacteristic
86C2×C4×D47C22⋊C412yes—
87C2×Dic94M1611yescharacteristic
88M16×C47—41no—
89M16×C47—41no—
90M16×C47—41no—
91M16×C47—41no—
92C2×C8×C47—21no—
93C2×C8×C47—21no—
94C2×C8×C47—21no—
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—
102C22⋊Dic47C2×C812yes—
103(C2×D47)⋊C4—22no—
104C4⋊Dic47—21no—
105Dic47⋊C4—22no—
106C4×Dic47—21no—
107#10625329—21no—
108#10625329—21no—
109#10625329—21no—
110#10625329—21no—
111C2×C47⋊C8—21no—
112C2×C47⋊C8C22⋊C412yes—
113#10625324—22no—
114#10625324—22no—
115C8×D47—22no—
116C8×D47—22no—
117C16×C47—22no—
118C16×C47—41no—
119C47⋊C16—22no—
120C47⋊C16—41no—
121C23×C47—21no—
122C23×C47—21no—
123C23×C47—21no—
124C23×C47—81no—
125C23×C47C22×C811yescharacteristic
126C22×D47C22⋊C812yes—
127C2×C4×C47—21no—
128C2×C4×C47—21no—
129C2×C4×C47—21no—
130C2×C4×C47—41no—
131C2×C4×C47—41no—
132C2×C4×C47—41no—
133C2×C4×C47—41no—
134C2×C4×C47C2×C22⋊C411yescharacteristic
135C2×C4×C47C4×D411yescharacteristic
136C2×C4×C47C4×D411yescharacteristic
137C2×C4×C47C2×M1611yescharacteristic
138C2×C4×C47#13111yescharacteristic
139C2×C4×C47#13111yescharacteristic
140C22⋊D47—22no—
141C22⋊D47—22no—
142C22⋊D47—82no—
143C2×Dic47—22no—
144C2×Dic47C22⋊C812yes—
145D188—21no—
146D188—21no—
147C4×D47—22no—
148C4×D47—22no—
149Dic94—21no—
150Dic94—21no—
151C8×C47—41no—
152C8×C47#12011yescharacteristic
153C8×C47#12111yescharacteristic
154C8×C47#12111yescharacteristic
155C8×C47#12311yescharacteristic
156C47⋊C8—22no—
157C47⋊C8—41no—
158#12989—471nomaximal, Sylow
159C22×C47—41no—
160C22×C47—41no—
161C22×C47—41no—
162C22×C47—41no—
163C22×C47—81no—
164C22×C47—81no—
165C22×C47C2×C22⋊C811yescharacteristic
166C22×C47C8×D411yescharacteristic
167C22×C47C8×D411yescharacteristic
168C2×D47—22no—
169C2×D47—42no—
170C4×C47—41no—
171C4×C47#38611yescharacteristic
172C4×C47#40811yescharacteristic
173C4×C47#43511yescharacteristic
174C4×C47#43511yescharacteristic
175Dic47—22no—
176Dic47—42no—
177#3407—471no—
178#2930—471no—
179#2115—471no—
180C2×#349—471no—
181C2×#349D4711yescharacteristic, complemented
182#1378—471no—
183#1378—471no—
184C2×C47—21no—
185C2×C47—21no—
186C2×C47—21no—
187C2×C47—81no—
188C2×C47#186911yescharacteristic
189D47—42no—
190C2×#131—471no—
191C22×M16C2×D4711yescharacteristic
192#525—471no—
193#504—942no—
194#504—942no—
195C2×M32—471no—
196C2×M32—471no—
197C2×M32—942no—
198C2×M32C2×D4711yescharacteristic
199C2×M32C2×D4711yescharacteristic
200#436—942no—
201#435—942no—
202#424—471no—
203#408—471no—
204#407—471no—
205#405—471no—
206#349—22no—
207#349—942no—
208#349—942no—
209C47#1298911yescharacteristic, complemented, Sylow
210C2×#41—471no—
211C23×C4C4×D4711yescharacteristic
212#131—941no—
213#131—941no—
214#131—941no—
215#131—941no—
216C2×M16—21no—
217C2×M16—21no—
218C2×M16—21no—
219C2×M16—21no—
220C2×M16—21no—
221C2×M16—21no—
222C2×M16—471no—
223C2×M16—472no—
224C2×M16—471no—
225C22×C8—472no—
226C22×C8C4×D4711yescharacteristic
227C22×C8C22×D4711yescharacteristic
228#123—472no—
229C22⋊Q8—941no—
230#121—941no—
231#120—472no—
232C4×D4—942no—
233#117—471no—
234M32—21no—
235M32—21no—
236M32—21no—
237M32—472no—
238M32—944no—
239M32—941no—
240M32—941no—
241M32—941no—
242M32C22⋊D4712yescomplemented
243C2×C16—21no—
244C2×C16—21no—
245C2×C16—944no—
246C2×C16—941no—
247C2×C16—941no—
248C4⋊C8—942no—
249C22⋊C8—942no—
250C22⋊C8—942no—
251#97—941no—
252C4×C8—941no—
253C24C8×D4711yescharacteristic
254#41—941no—
255#41—941no—
256#41—941no—
257#41—941no—
258C2×Q8—471no—
259C2×D4—472no—
260C2×D4—471no—
261C2×D4—942no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—472no—
269C22×C4C8×D4711yescharacteristic
270C22×C4C2×C4×D4711yescharacteristic
271M16—41no—
272M16—41no—
273M16—41no—
274M16—41no—
275M16—941no—
276M16—941no—
277M16—942no—
278M16—942no—
279M16—941no—
280M16—941no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—472no—
285C2×C8—942no—
286C2×C8—942no—
287C2×C8—941no—
288C2×C8#1062535011yescharacteristic
289C2×C8D4×D4711yescharacteristic
290C2×C8D4×D4711yescharacteristic
291C2×C8D4×D4711yescharacteristic
292C2×C8#1062535211yescharacteristic
293C2×C8C2×C22⋊D4711yescharacteristic
294C4⋊C4—942no—
295C4⋊C4—941no—
296C22⋊C4—472no—
297C22⋊C4—942no—
298C22⋊C4—942no—
299C42—941no—
300C16—22no—
301C16—41no—
302C16—942no—
303C16—1881no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—81no—
308C23—472no—
309C23C2×C8×D4711yescharacteristic
310Q8—941no—
311Q8—941no—
312D4—942no—
313D4—942no—
314D4—941no—
315D4—941no—
316D4—3762no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—472no—
325C2×C4—942no—
326C2×C4—942no—
327C2×C4—942no—
328C2×C4C22⋊C4×D4711yescharacteristic
329C2×C4(C22⋊D47)⋊C411yescharacteristic
330C2×C4C4×C22⋊D4711yescharacteristic
331C2×C4M16×D4711yescharacteristic
332C2×C4#1309403011yescharacteristic
333C2×C4#1309403211yescharacteristic
334C8—41no—
335C8—942no—
336C8—1881no—
337C8#1309399211yescharacteristic
338C8#1309399511yescharacteristic
339C8#1309399711yescharacteristic
340C8#1309400611yescharacteristic
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—81no—
346C22—81no—
347C22—942no—
348C22—1882no—
349C22C22⋊C8×D4711yescharacteristic
350C22(C22⋊D47)⋊C811yescharacteristic
351C22C8×C22⋊D4711yescharacteristic
352C4—41no—
353C4—942no—
354C4—1882no—
355C4#1568899911yescharacteristic
356C4#1568908811yescharacteristic
357C4#1568919211yescharacteristic
358C4#1568919711yescharacteristic
359C2—21no—
360C2—21no—
361C2—21no—
362C2—81no—
363C2—1882no—
364C2#2024367711yescharacteristic
subgroupG/H
centerC4#15688999
commutatorC23×C47C22×C8
FrattiniC22×C8C22×D47
FittingC2×C47×#349C2
socleC2×C47#1869
prime radical#15689634C4
cosocleC22×C8×C47C23
hypercenterC2×#349D47
hypocenterC47#12989
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C8 ◁ C2×#349

Complements

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

NH ≅ G/Ntype
1. #20256490C2semidirect
3. #20245008C2semidirect
4. C2×#15688905C2semidirect
5. #20241475C2semidirect
6. #20241473C2semidirect
7. C2×C47×#349C2semidirect
45. #13093964D4semidirect
67. M32×C47D4semidirect
181. C2×#349D47semidirect
209. C47#12989semidirect
242. M32C22⋊D47semidirect

Maximal subgroups

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

subgroupindex
#202564902
#202520912
#202450082
C2×#156889052
#202414752
#202414732
C2×C47×#3492
#1298947