Finite Group Databasebeta

← #26113077

Subgroups — #26113077

Order 12032.

518 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252429C211yesmaximal, characteristic, complemented
2#20243398C211yesmaximal, characteristic, complemented
3#20241948C211yesmaximal, characteristic, complemented
4#20241787C211yesmaximal, characteristic, complemented
5#20241283C211yesmaximal, characteristic, complemented
6#20241248C211yesmaximal, characteristic, complemented
7C47×#3036C211yesmaximal, characteristic
8#15689201—22no—
9#15689201—22no—
10#15689176C2211yescharacteristic
11#15689176C2211yescharacteristic
12C2×C4⋊(C47⋊C8)C2211yescharacteristic
13C2×#13093945—21no—
14#15689087—22no—
15#15688989C2211yescharacteristic
16#15688885—21no—
17#15688857—22no—
18D4⋊(C47⋊C8)—22no—
19C2×AGL(1,ℤ/8)×C47—21no—
20C47×#532C2211yescharacteristic
21C2×C4×D4×C47C2211yescharacteristic
22C47×#463—22no—
23C47×#461C412yescomplemented
24C47×#459C412yescomplemented
25C47×#423C2211yescharacteristic
26C47×#417—21no—
27C2×#10625329—24no—
28C22×C47⋊C8—21no—
29C2×C4⋊Dic47—21no—
30C4⋊(C47⋊C8)—21no—
31C4⋊(C47⋊C8)—21no—
32C4⋊(C47⋊C8)—21no—
33C4⋊(C47⋊C8)—21no—
34#13093945—42no—
35C22⋊(C47⋊C8)—24no—
36C22⋊(C47⋊C8)—21no—
37C22⋊(C47⋊C8)D412yes—
38C4×C47⋊C8—21no—
39C4×C47⋊C8D412yes—
40C47⋊#95—21no—
41C47⋊#95—21no—
42C2×#41×C47—21no—
43C22×D4×C47D411yescharacteristic
44C23×C4×C47—21no—
45AGL(1,ℤ/8)×C47—42no—
46AGL(1,ℤ/8)×C47—42no—
47C2×SD16×C47—22no—
48C2×D8×C47—22no—
49C2×M16×C47—21no—
50C4⋊Q8×C47C2×C411yescharacteristic
51#127×C47C2×C411yescharacteristic
52#124×C47—21no—
53#121×C47—21no—
54#121×C47—21no—
55C4×D4×C47—21no—
56C4×D4×C47—21no—
57C4×D4×C47—21no—
58C4×D4×C47—21no—
59C4×D4×C47C2×C412yes—
60C4×D4×C47D412yes—
61C2×C4⋊C4×C47D411yescharacteristic
62C2×C22⋊C4×C47—21no—
63C2×C42×C47C2311yescharacteristic
64C4⋊C8×C47—21no—
65C4⋊C8×C47C2×C412yes—
66#103×C47—22no—
67#102×C47—22no—
68C24×C47—21no—
69#41×C47—41no—
70#41×C47—41no—
71#41×C47—41no—
72#41×C47—41no—
73C2×Q8×C47—21no—
74C2×D4×C47—21no—
75C2×D4×C47—21no—
76C2×D4×C47—21no—
77C2×D4×C47—21no—
78C2×D4×C47—21no—
79C2×D4×C47—21no—
80C2×D4×C47—21no—
81C2×D4×C47—21no—
82C2×D4×C47—41no—
83C2×D4×C47C22⋊C412yes—
84C22×C4×C47—21no—
85C22×C4×C47—22no—
86C22×C4×C47—22no—
87C22×C4×C47—41no—
88C22×C4×C47—82no—
89C22×C4×C47C2×D411yescharacteristic
90C22×C4×C47C2×D411yescharacteristic
91C22×C4×C47#4111yescharacteristic
92C22×Dic47—41no—
93SD16×C47—44no—
94D8×C47—44no—
95M16×C47—41no—
96M16×C47—41no—
97C2×C8×C47—22no—
98C4⋊C4×C47—21no—
99C4⋊C4×C47—21no—
100C4⋊C4×C47—21no—
101C4⋊C4×C47C22⋊C412yes—
102C22⋊C4×C47—22no—
103C22⋊C4×C47—22no—
104C22⋊C4×C47—41no—
105C22⋊C4×C47—41no—
106C42×C47C22×C411yescharacteristic
107C42×C47C2×D411yescharacteristic
108C42×C47C2×D411yescharacteristic
109C42×C47#4111yescharacteristic
110C4⋊Dic47—41no—
111C4⋊Dic47—41no—
112#10625329—84no—
113C2×C47⋊C8—22no—
114C2×C47⋊C8—22no—
115C2×C47⋊C8—41no—
116C2×C47⋊C8—41no—
117C2×C47⋊C8—41no—
118C23×C47—22no—
119C23×C47—41no—
120C23×C47—41no—
121C23×C47—41no—
122C23×C47—81no—
123C23×C47—81no—
124C23×C47#12111yescharacteristic
125Q8×C47—41no—
126Q8×C47—41no—
127D4×C47—22no—
128D4×C47—22no—
129D4×C47—42no—
130D4×C47—41no—
131D4×C47—41no—
132D4×C47—41no—
133D4×C47—41no—
134D4×C47—81no—
135D4×C47—81no—
136D4×C47—81no—
137C2×C4×C47—22no—
138C2×C4×C47—41no—
139C2×C4×C47—41no—
140C2×C4×C47—44no—
141C2×C4×C47—41no—
142C2×C4×C47—82no—
143C2×C4×C47—81no—
144C2×C4×C47—81no—
145C2×C4×C47—81no—
146C2×C4×C47C2×C22⋊C411yescharacteristic
147C2×C4×C47C4×D411yescharacteristic
148C2×C4×C47C4×D411yescharacteristic
149C2×C4×C47#12011yescharacteristic
150C2×C4×C47#12111yescharacteristic
151C2×C4×C47#12311yescharacteristic
152C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C47#13711yescharacteristic
156C2×Dic47—81no—
157C2×Dic47—81no—
158C2×Dic47—81no—
159C8×C47—42no—
160C47⋊C8—42no—
161C47⋊C8—42no—
162C47⋊C8—81no—
163#9309—471nomaximal, Sylow
164C22×C47—21no—
165C22×C47—21no—
166C22×C47—42no—
167C22×C47—42no—
168C22×C47—42no—
169C22×C47—82no—
170C22×C47—82no—
171C22×C47—81no—
172C22×C47—81no—
173C22×C47—81no—
174C22×C47#38611yescharacteristic
175C22×C47#46811yescharacteristic
176C22×C47#46911yescharacteristic
177C4×C47—21no—
178C4×C47—21no—
179C4×C47—21no—
180C4×C47—21no—
181C4×C47—42no—
182C4×C47—81no—
183C4×C47#41711yescharacteristic
184C4×C47#41811yescharacteristic
185C4×C47#46811yescharacteristic
186C4×C47#46911yescharacteristic
187Dic47—161no—
188#3036D4711yescharacteristic
189#2975—471no—
190#1804—471no—
191#1517—471no—
192#1480—471no—
193#1301—471no—
194#1286—471no—
195C2×C47—21no—
196C2×C47—21no—
197C2×C47—82no—
198C2×C47—161no—
199C2×C47#188111yescharacteristic
200C2×C47#189511yescharacteristic
201C2×C47#190411yescharacteristic
202C2×AGL(1,ℤ/8)—21no—
203#532C2×D4711yescharacteristic
204C2×C4×D4C2×D4711yescharacteristic
205#463—22no—
206#461Dic4712yescomplemented
207#459Dic4712yescomplemented
208#436—942no—
209#436—942no—
210#431—471no—
211#431—471no—
212#423C2×D4711yescharacteristic
213C2×C4⋊C8—471no—
214#417—21no—
215C2×#102—941no—
216#407—942no—
217#382—471no—
218#340—941no—
219#327—942no—
220D4⋊C8—942no—
221C47#930911yescharacteristic, complemented, Sylow
222C2×#41—21no—
223C22×D4C22⋊D4711yescharacteristic
224C23×C4—21no—
225AGL(1,ℤ/8)—42no—
226AGL(1,ℤ/8)—42no—
227C2×SD16—22no—
228C2×D8—22no—
229C2×M16—21no—
230C2×M16—944no—
231C22×C8—941no—
232C4⋊Q8C2×Dic4711yescharacteristic
233#127C2×Dic4711yescharacteristic
234#124—21no—
235#121—21no—
236#121—21no—
237C4×D4—21no—
238C4×D4—21no—
239C4×D4—21no—
240C4×D4—21no—
241C4×D4C2×Dic4712yes—
242C4×D4C22⋊D4712yes—
243C2×C4⋊C4—941no—
244C2×C4⋊C4C22⋊D4711yescharacteristic
245C2×C22⋊C4—21no—
246C2×C42C22×D4711yescharacteristic
247C4⋊C8—21no—
248C4⋊C8—941no—
249C4⋊C8—941no—
250C4⋊C8—941no—
251C4⋊C8—941no—
252C4⋊C8C2×Dic4712yes—
253#103—22no—
254#102—22no—
255#102—1882no—
256C22⋊C8—472no—
257C22⋊C8—944no—
258C22⋊C8—941no—
259C4×C8—472no—
260C4×C8—941no—
261#95—941no—
262#95—941no—
263C24—21no—
264#41—41no—
265#41—41no—
266#41—41no—
267#41—41no—
268C2×Q8—21no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—41no—
278C2×D4C22⋊Dic4712yes—
279C22×C4—21no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—41no—
283C22×C4—82no—
284C22×C4—1881no—
285C22×C4D4×D4711yescharacteristic
286C22×C4#1062535211yescharacteristic
287C22×C4C2×C22⋊D4711yescharacteristic
288SD16—44no—
289D8—44no—
290M16—41no—
291M16—41no—
292M16—3764no—
293C2×C8—22no—
294C2×C8—942no—
295C2×C8—942no—
296C2×C8—1881no—
297C2×C8—1881no—
298C2×C8—1881no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—1881no—
303C4⋊C4—1881no—
304C4⋊C4C22⋊Dic4712yes—
305C22⋊C4—22no—
306C22⋊C4—22no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C42D4×D4711yescharacteristic
310C42#1062535211yescharacteristic
311C42C22×Dic4711yescharacteristic
312C42C2×C22⋊D4711yescharacteristic
313C23—22no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—81no—
318C23—81no—
319C23#1309399611yescharacteristic
320Q8—41no—
321Q8—41no—
322D4—22no—
323D4—22no—
324D4—42no—
325D4—41no—
326D4—41no—
327D4—41no—
328D4—41no—
329D4—81no—
330D4—81no—
331D4—81no—
332C2×C4—22no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—44no—
336C2×C4—41no—
337C2×C4—82no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—3761no—
342C2×C4—3761no—
343C2×C4—3761no—
344C2×C4C2×C22⋊Dic4711yescharacteristic
345C2×C4D4×Dic4711yescharacteristic
346C2×C4D4×Dic4711yescharacteristic
347C2×C4#1309399211yescharacteristic
348C2×C4#1309399611yescharacteristic
349C2×C4#1309400511yescharacteristic
350C2×C4#1309404911yescharacteristic
351C2×C4#1309405011yescharacteristic
352C2×C4#1309405011yescharacteristic
353C2×C4#1309405411yescharacteristic
354C8—42no—
355C8—3761no—
356C8—1882no—
357C8—1882no—
358C22—21no—
359C22—21no—
360C22—42no—
361C22—42no—
362C22—42no—
363C22—82no—
364C22—82no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22#1568900311yescharacteristic
369C22#1568936711yescharacteristic
370C22#1568937411yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—42no—
376C4—81no—
377C4—7521no—
378C4#1568912411yescharacteristic
379C4#1568912811yescharacteristic
380C4#1568936711yescharacteristic
381C4#1568937411yescharacteristic
382C2—21no—
383C2—21no—
384C2—82no—
385C2—161no—
386C2#2024375211yescharacteristic
387C2#2024382711yescharacteristic
388C2#2024387711yescharacteristic
subgroupG/H
centerC22#15689003
commutatorC42×C47C22×C4
FrattiniC2×C42C22×D47
Fitting, prime radicalC47×#3036C2
socleC22×C47#386
cosocleC2×C42×C47C23
hypercenter#3036D47
hypocenterC47#9309
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3036

Complements

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

NH ≅ G/Ntype
1. #20252429C2semidirect
2. #20243398C2semidirect
3. #20241948C2semidirect
4. #20241787C2semidirect
5. #20241283C2semidirect
6. #20241248C2semidirect
23. C47×#461C4semidirect
24. C47×#459C4semidirect
206. #461Dic47semidirect
207. #459Dic47semidirect
221. C47#9309semidirect

Maximal subgroups

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

subgroupindex
#202524292
#202433982
#202419482
#202417872
#202412832
#202412482
C47×#30362
#930947