Finite Group Databasebeta

← #26106813

Subgroups — #26106813

Order 12032.

400 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
1C2×#15689185C211yesmaximal, characteristic
2#20241700C211yesmaximal, characteristic
3#20241700C211yesmaximal, characteristic
4#20241681C211yesmaximal, characteristic, complemented
5#20241672C211yesmaximal, characteristic, complemented
6#20241233C211yesmaximal, characteristic, complemented
7C47×#1281C211yesmaximal, characteristic, complemented
8C2×#13093981C2211yescharacteristic
9#15689185—21no—
10#15689185—21no—
11#15689185—21no—
12#15689185—21no—
13#15689176C2211yescharacteristic
14#15689176C2211yescharacteristic
15C2×Dic47⋊C8C411yescharacteristic
16C2×Dic47⋊C8C411yescharacteristic
17C2×(C2×D47)⋊C8C411yescharacteristic
18C2×(C2×D47)⋊C8C411yescharacteristic
19C2×C4×C47⋊C8C2211yescharacteristic
20#15688848C412yes—
21#15688848C412yes—
22#15688846C412yes—
23#15688846C412yes—
24#15688845—21no—
25#15688845—21no—
26#15688844—21no—
27C8×C47⋊C8—21no—
28C47×#431C2211yescharacteristic
29C47×#431C2211yescharacteristic
30C2×#97×C47C2211yescharacteristic
31C22×C4×D47C2×C411yescharacteristic
32C22×C47⋊C8C2×C411yescharacteristic
33C22×C47⋊C8C2×C411yescharacteristic
34#13093981—21no—
35#13093981—21no—
36#13093981—21no—
37#13093981—21no—
38C2×Dic47⋊C4C2×C411yescharacteristic
39C2×Dic47⋊C4C2×C411yescharacteristic
40C2×(C2×D47)⋊C4C2×C411yescharacteristic
41C2×(C2×D47)⋊C4C2×C411yescharacteristic
42C2×C4×Dic47C2×C411yescharacteristic
43C4⋊(C47⋊C8)—21no—
44C4⋊(C47⋊C8)—21no—
45Dic47⋊C8—21no—
46Dic47⋊C8—21no—
47Dic47⋊C8—21no—
48Dic47⋊C8—21no—
49C22⋊(C47⋊C8)C2×C412yes—
50C22⋊(C47⋊C8)C2×C412yes—
51(C2×D47)⋊C8—21no—
52(C2×D47)⋊C8—21no—
53(C2×D47)⋊C8—21no—
54(C2×D47)⋊C8—21no—
55C4×C47⋊C8—21no—
56C4×C47⋊C8—21no—
57C4×C47⋊C8D411yescharacteristic
58C4×C47⋊C8D411yescharacteristic
59C4×C47⋊C8D411yescharacteristic
60C4×C47⋊C8D411yescharacteristic
61C22×C8×C47C2×C411yescharacteristic
62C22×C8×C47C2×C411yescharacteristic
63C2×C42×C47C2311yescharacteristic
64C4⋊C8×C47—21no—
65C4⋊C8×C47—21no—
66C22⋊C8×C47C2×C412yes—
67C22⋊C8×C47C2×C412yes—
68#97×C47—21no—
69#97×C47—21no—
70C4×C8×C47—21no—
71C4×C8×C47—21no—
72C23×D47C4211yescharacteristic
73C22×C4×C47C22×C411yescharacteristic
74C22×C4×C47C22×C411yescharacteristic
75C22×C4×C47C22×C411yescharacteristic
76C22×Dic47C4211yescharacteristic
77C22×Dic47C4211yescharacteristic
78C22×Dic47C4211yescharacteristic
79C2×C4×D47—21no—
80C2×C4×D47—21no—
81C2×C4×D47—21no—
82C2×C4×D47—21no—
83C2×C4×D47—21no—
84C2×C4×D47—21no—
85C2×C8×C47—21no—
86C2×C8×C47—21no—
87C2×C8×C47—22no—
88C2×C8×C47—22no—
89C2×C8×C47—21no—
90C2×C8×C47—21no—
91C2×C8×C47—21no—
92C2×C8×C47—21no—
93C42×C47C2×D411yescharacteristic
94C42×C47C2×D411yescharacteristic
95C42×C47#4111yescharacteristic
96C42×C47#4111yescharacteristic
97(C2×D47)⋊C4—21no—
98(C2×D47)⋊C4—21no—
99(C2×D47)⋊C4—21no—
100(C2×D47)⋊C4—21no—
101Dic47⋊C4—21no—
102Dic47⋊C4—21no—
103Dic47⋊C4—21no—
104Dic47⋊C4—21no—
105C4×Dic47—21no—
106C4×Dic47—21no—
107C2×C47⋊C8—21no—
108C2×C47⋊C8—21no—
109C2×C47⋊C8—21no—
110C2×C47⋊C8—21no—
111C2×C47⋊C8—22no—
112C2×C47⋊C8—22no—
113C2×C47⋊C8C22⋊C411yescharacteristic
114C2×C47⋊C8C22⋊C411yescharacteristic
115C2×C47⋊C8C22⋊C411yescharacteristic
116C2×C47⋊C8C22⋊C411yescharacteristic
117C23×C47C2×C4211yescharacteristic
118C22×D47—21no—
119C22×D47—21no—
120C22×D47—21no—
121C22×D47—41no—
122C22×D47—41no—
123C2×C4×C47—41no—
124C2×C4×C47—41no—
125C2×C4×C47C2×C22⋊C411yescharacteristic
126C2×C4×C47#11711yescharacteristic
127C2×C4×C47C4×D411yescharacteristic
128C2×C4×C47C4×D411yescharacteristic
129C2×C4×C47C4×D411yescharacteristic
130C2×C4×C47C4×D411yescharacteristic
131C2×C4×C47#13111yescharacteristic
132C2×C4×C47#13111yescharacteristic
133C2×C4×C47#13111yescharacteristic
134C2×C4×C47#13111yescharacteristic
135C2×Dic47—21no—
136C2×Dic47—21no—
137C2×Dic47—21no—
138C2×Dic47—21no—
139C2×Dic47—21no—
140C2×Dic47—41no—
141C2×Dic47—41no—
142C4×D47—41no—
143C4×D47—41no—
144C4×D47—41no—
145C4×D47—41no—
146C8×C47—42no—
147C8×C47—42no—
148C8×C47—41no—
149C8×C47—41no—
150C47⋊C8—21no—
151C47⋊C8—21no—
152C47⋊C8—21no—
153C47⋊C8—21no—
154C47⋊C8—42no—
155C47⋊C8—42no—
156#8158—471nomaximal, Sylow
157C22×C47—21no—
158C22×C47—21no—
159C22×C47C4×C22⋊C411yescharacteristic
160C22×C47#40511yescharacteristic
161C22×C47#40511yescharacteristic
162C2×D47—41no—
163C2×D47—41no—
164C2×D47—41no—
165C2×D47—81no—
166C2×D47—81no—
167C4×C47—21no—
168C4×C47—21no—
169C4×C47—21no—
170C4×C47—21no—
171C4×C47#40811yescharacteristic
172C4×C47#40811yescharacteristic
173C4×C47#43311yescharacteristic
174C4×C47#43311yescharacteristic
175Dic47—41no—
176Dic47—41no—
177Dic47—41no—
178C2×#433—471no—
179#1458—471no—
180#1458—471no—
181#1452—471no—
182#1450—471no—
183#1281—471no—
184#1281D4711yescharacteristic, complemented
185C2×C47—21no—
186C2×C47—21no—
187C2×C47#175011yescharacteristic
188C2×C47#175711yescharacteristic
189C2×C47#175711yescharacteristic
190D47—81no—
191C2×#117—471no—
192#433—941no—
193#433—941no—
194#433—941no—
195#433—941no—
196#431—471no—
197#431—471no—
198#431C2×D4711yescharacteristic
199#431C2×D4711yescharacteristic
200C2×C4⋊C8—471no—
201C2×C4⋊C8—471no—
202C2×C22⋊C8—471no—
203C2×C22⋊C8—471no—
204C2×#97C2×D4711yescharacteristic
205C2×C4×C8—471no—
206#324—472no—
207#324—472no—
208#323—472no—
209#323—472no—
210#322—941no—
211#322—941no—
212#322—941no—
213C82—941no—
214C47#815811yescharacteristic, complemented, Sylow
215C23×C4—471no—
216C22×C8—471no—
217C22×C8—471no—
218C22×C8C4×D4711yescharacteristic
219C22×C8C4×D4711yescharacteristic
220#117—941no—
221#117—941no—
222#117—941no—
223#117—941no—
224C2×C4⋊C4—471no—
225C2×C4⋊C4—471no—
226C2×C22⋊C4—471no—
227C2×C22⋊C4—471no—
228C2×C42—471no—
229C2×C42C22×D4711yescharacteristic
230C4⋊C8—21no—
231C4⋊C8—21no—
232C4⋊C8—941no—
233C4⋊C8—941no—
234C4⋊C8—941no—
235C4⋊C8—941no—
236C4⋊C8—941no—
237C4⋊C8—941no—
238C22⋊C8—472no—
239C22⋊C8—472no—
240C22⋊C8—941no—
241C22⋊C8—941no—
242C22⋊C8—941no—
243C22⋊C8—941no—
244C22⋊C8C4×D4712yes—
245C22⋊C8C4×D4712yes—
246#97—21no—
247#97—21no—
248C4×C8—21no—
249C4×C8—21no—
250C4×C8—471no—
251C4×C8—471no—
252C4×C8—471no—
253C4×C8—471no—
254C4×C8—941no—
255C4×C8—941no—
256C24—471no—
257C22×C4—471no—
258C22×C4—471no—
259C22×C4—471no—
260C22×C4—941no—
261C22×C4—941no—
262C22×C4—941no—
263C22×C4—941no—
264C22×C4—941no—
265C22×C4—941no—
266C22×C4C2×C4×D4711yescharacteristic
267C22×C4C2×C4×D4711yescharacteristic
268C22×C4C2×C4×D4711yescharacteristic
269C2×C8—21no—
270C2×C8—21no—
271C2×C8—22no—
272C2×C8—22no—
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—471no—
278C2×C8—471no—
279C2×C8—471no—
280C2×C8—471no—
281C2×C8—941no—
282C2×C8—941no—
283C2×C8—941no—
284C2×C8—941no—
285C2×C8—942no—
286C2×C8—942no—
287C4⋊C4—941no—
288C4⋊C4—941no—
289C4⋊C4—941no—
290C4⋊C4—941no—
291C22⋊C4—941no—
292C22⋊C4—941no—
293C22⋊C4—941no—
294C22⋊C4—941no—
295C42—941no—
296C42—941no—
297C42D4×D4711yescharacteristic
298C42D4×D4711yescharacteristic
299C42#1062535211yescharacteristic
300C42#1062535411yescharacteristic
301C23—941no—
302C23—941no—
303C23—941no—
304C23—1881no—
305C23—1881no—
306C23C42×D4711yescharacteristic
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—941no—
310C2×C4—941no—
311C2×C4—941no—
312C2×C4—941no—
313C2×C4—941no—
314C2×C4—1881no—
315C2×C4—1881no—
316C2×C4—1881no—
317C2×C4—1881no—
318C2×C4—1881no—
319C2×C4—1881no—
320C2×C4C22⋊C4×D4711yescharacteristic
321C2×C4#1309398211yescharacteristic
322C2×C4(C22⋊D47)⋊C411yescharacteristic
323C2×C4(C22⋊D47)⋊C411yescharacteristic
324C2×C4#1309398611yescharacteristic
325C2×C4#1309398611yescharacteristic
326C2×C4#1309403011yescharacteristic
327C2×C4#1309403011yescharacteristic
328C2×C4#1309403211yescharacteristic
329C2×C4#1309403211yescharacteristic
330C8—42no—
331C8—42no—
332C8—41no—
333C8—41no—
334C8—941no—
335C8—941no—
336C8—941no—
337C8—941no—
338C8—1882no—
339C8—1882no—
340C22—21no—
341C22—21no—
342C22—3761no—
343C22—3761no—
344C22—1881no—
345C22—1881no—
346C22—1881no—
347C22#1568897011yescharacteristic
348C22#1568907711yescharacteristic
349C22#1568908011yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—1881no—
355C4—1881no—
356C4—1881no—
357C4#1568908811yescharacteristic
358C4#1568908811yescharacteristic
359C4#1568918311yescharacteristic
360C4#1568918311yescharacteristic
361C2—21no—
362C2—21no—
363C2—3761no—
364C2#2024315311yescharacteristic
365C2#2024318711yescharacteristic
366C2#2024318711yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D47
commutatorC23×C47C2×C42
FrattiniC2×C42C22×D47
FittingC47×#1281C2
socleC22×C47C4×C22⋊C4
prime radicalC23×D47C42
cosocleC2×C42×C47C23
hypercenter#1281D47
hypocenterC47#8158
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1281

Complements

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

NH ≅ G/Ntype
4. #20241681C2semidirect
5. #20241672C2semidirect
6. #20241233C2semidirect
7. C47×#1281C2semidirect
184. #1281D47semidirect
214. C47#8158semidirect

Maximal subgroups

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

subgroupindex
C2×#156891852
#202417002
#202416812
#202416722
#202412332
C47×#12812
#815847