Finite Group Databasebeta

← C47×#13025 #26052723

Subgroups — C47×#13025 #26052723

Order 12032.

522 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#509C211yesmaximal, characteristic
2C47×#2943C211yesmaximal, characteristic, complemented
3C2×C47×#360C211yesmaximal, characteristic, complemented
4C47×#2140C211yesmaximal, characteristic, complemented
5C47×#1972C211yesmaximal, characteristic, complemented
6C47×#1386C211yesmaximal, characteristic, complemented
7C47×#1377C211yesmaximal, characteristic, complemented
8C2×#135×C47C2211yescharacteristic
9C22×D8×C47C2211yescharacteristic
10C4×#41×C47—21no—
11C47×#509—22no—
12C47×#509C414yescomplemented
13C2×SD32×C47—21no—
14C2×D16×C47—21no—
15C2×M32×C47C2211yescharacteristic
16C2×M32×C47C2211yescharacteristic
17C47×#442—21no—
18C47×#441—21no—
19C47×#440—22no—
20C47×#427C2211yescharacteristic
21C2×#106×C47C2211yescharacteristic
22C47×#416—21no—
23C2×#102×C47—21no—
24C2×#97×C47C2211yescharacteristic
25C47×#390—21no—
26C47×#360—22no—
27C47×#357—22no—
28C2×#41×C47—21no—
29C22×D4×C47—21no—
30#135×C47—21no—
31#135×C47—21no—
32#135×C47C2×C412yes—
33#135×C47D412yes—
34C2×Q16×C47D411yescharacteristic
35C2×SD16×C47—21no—
36C2×D8×C47—21no—
37C2×D8×C47—21no—
38C2×D8×C47—21no—
39C2×D8×C47—21no—
40C2×D8×C47—21no—
41C2×D8×C47C2×C412yescomplemented
42C2×D8×C47D411yescharacteristic
43C22×C8×C47D411yescharacteristic
44C22×C8×C47C2311yescharacteristic
45C4×Q8×C47—22no—
46C4×D4×C47—22no—
47C4×D4×C47—42no—
48#117×C47—21no—
49#117×C47—41no—
50C2×C4⋊C4×C47—21no—
51C2×C22⋊C4×C47—42no—
52C2×C42×C47—41no—
53C2×C42×C47D411yescharacteristic
54SD32×C47—24no—
55D16×C47—24no—
56M32×C47—21no—
57M32×C47—21no—
58M32×C47—21no—
59M32×C47C2×C412yescomplemented
60C2×C16×C47—21no—
61C2×C16×C47—21no—
62#107×C47D412yes—
63#106×C47—21no—
64#106×C47—21no—
65#106×C47—21no—
66#103×C47—22no—
67#102×C47—22no—
68#102×C47—42no—
69#97×C47—21no—
70#97×C47—21no—
71C24×C47—41no—
72#41×C47—22no—
73#41×C47—22no—
74#41×C47—41no—
75#41×C47—41no—
76C2×Q8×C47—21no—
77C2×D4×C47—22no—
78C2×D4×C47—21no—
79C2×D4×C47—41no—
80C2×D4×C47—41no—
81C2×D4×C47—41no—
82C2×D4×C47—41no—
83C2×D4×C47—41no—
84C2×D4×C47—41no—
85C22×C4×C47—42no—
86C22×C4×C47—41no—
87C22×C4×C47—41no—
88C22×C4×C47D812yes—
89C22×C4×C47C2×D411yescharacteristic
90Q16×C47—21no—
91Q16×C47C22⋊C412yescomplemented
92SD16×C47—22no—
93SD16×C47—22no—
94D8×C47—22no—
95D8×C47—22no—
96D8×C47—21no—
97D8×C47—41no—
98D8×C47—41no—
99D8×C47C22⋊C412yescomplemented
100C2×C8×C47—21no—
101C2×C8×C47—21no—
102C2×C8×C47—21no—
103C2×C8×C47C22×C411yescharacteristic
104C2×C8×C47C2×D411yescharacteristic
105C2×C8×C47C2×D411yescharacteristic
106C2×C8×C47C2×D411yescharacteristic
107C2×C8×C47#4111yescharacteristic
108C2×C8×C47#4111yescharacteristic
109C4⋊C4×C47—22no—
110C4⋊C4×C47—42no—
111C4⋊C4×C47—41no—
112C4⋊C4×C47—41no—
113C22⋊C4×C47—42no—
114C22⋊C4×C47—41no—
115C22⋊C4×C47—84no—
116C42×C47—21no—
117C42×C47—21no—
118C42×C47—42no—
119C42×C47—41no—
120C16×C47—22no—
121C16×C47—41no—
122C23×C47—41no—
123C23×C47—42no—
124C23×C47—82no—
125C23×C47—82no—
126C23×C47—81no—
127C23×C47—81no—
128C23×C47C2×D811yescharacteristic
129Q8×C47—22no—
130Q8×C47—41no—
131D4×C47—22no—
132D4×C47—42no—
133D4×C47—42no—
134D4×C47—42no—
135D4×C47—42no—
136D4×C47—41no—
137D4×C47—81no—
138D4×C47—81no—
139C2×C4×C47—22no—
140C2×C4×C47—41no—
141C2×C4×C47—42no—
142C2×C4×C47—42no—
143C2×C4×C47—42no—
144C2×C4×C47—42no—
145C2×C4×C47—84no—
146C2×C4×C47—82no—
147C2×C4×C47—81no—
148C2×C4×C47C4×D411yescharacteristic
149C2×C4×C47#12011yescharacteristic
150C2×C4×C47#12111yescharacteristic
151C2×C4×C47#13511yescharacteristic
152C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
154C8×C47—41no—
155C8×C47C2×C22⋊C411yescharacteristic
156C8×C47C4×D411yescharacteristic
157C8×C47#12111yescharacteristic
158C8×C47#12311yescharacteristic
159#13025C4711yesmaximal, characteristic, direct product factor, Sylow
160C22×C47—22no—
161C22×C47—42no—
162C22×C47—84no—
163C22×C47—82no—
164C22×C47—82no—
165C22×C47—161no—
166C22×C47—161no—
167C22×C47—162no—
168C22×C47C4×D811yescharacteristic
169C22×C47#44711yescharacteristic
170C22×C47#45911yescharacteristic
171C4×C47—42no—
172C4×C47—42no—
173C4×C47—82no—
174C4×C47—161no—
175C4×C47#38611yescharacteristic
176C4×C47#44211yescharacteristic
177C4×C47#44911yescharacteristic
178C4×C47#46311yescharacteristic
179C2×#509C2×C4711yescharacteristic
180#2943C2×C4711yescharacteristic, complemented
181C2×#360C2×C4711yescharacteristic, complemented
182#2140C2×C4711yescharacteristic, complemented
183#1972C2×C4711yescharacteristic, complemented
184#1386C2×C4711yescharacteristic, complemented
185#1377C2×C4711yescharacteristic, complemented
186C2×C47—21no—
187C2×C47—21no—
188C2×C47—82no—
189C2×C47—162no—
190C2×C47#187911yescharacteristic
191C2×C47#219012yes—
192C2×#135C22×C4711yescharacteristic
193C22×D8C22×C4711yescharacteristic
194C4×#41—21no—
195#509—22no—
196#509C4×C4714yescomplemented
197C2×SD32—21no—
198C2×D16—21no—
199C2×M32C22×C4711yescharacteristic
200C2×M32C22×C4711yescharacteristic
201#442—21no—
202#441—21no—
203#440—22no—
204#427C22×C4711yescharacteristic
205C2×#106C22×C4711yescharacteristic
206#416—21no—
207C2×#102—21no—
208C2×#97C22×C4711yescharacteristic
209#390—21no—
210#360—22no—
211#357—22no—
212C47#1302511yescharacteristic, direct product factor, Sylow
213C2×#41—21no—
214C22×D4—21no—
215#135—21no—
216#135—21no—
217#135C2×C4×C4712yes—
218#135D4×C4712yes—
219C2×Q16D4×C4711yescharacteristic
220C2×SD16—21no—
221C2×D8—21no—
222C2×D8—21no—
223C2×D8—21no—
224C2×D8—21no—
225C2×D8—21no—
226C2×D8C2×C4×C4712yescomplemented
227C2×D8D4×C4711yescharacteristic
228C22×C8D4×C4711yescharacteristic
229C22×C8C23×C4711yescharacteristic
230C4×Q8—22no—
231C4×D4—22no—
232C4×D4—42no—
233#117—21no—
234#117—41no—
235C2×C4⋊C4—21no—
236C2×C22⋊C4—42no—
237C2×C42—41no—
238C2×C42D4×C4711yescharacteristic
239SD32—24no—
240D16—24no—
241M32—21no—
242M32—21no—
243M32—21no—
244M32C2×C4×C4712yescomplemented
245C2×C16—21no—
246C2×C16—21no—
247#107D4×C4712yes—
248#106—21no—
249#106—21no—
250#106—21no—
251#103—22no—
252#102—22no—
253#102—42no—
254#97—21no—
255#97—21no—
256C24—41no—
257#41—22no—
258#41—22no—
259#41—41no—
260#41—41no—
261C2×Q8—21no—
262C2×D4—22no—
263C2×D4—21no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—41no—
270C22×C4—42no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4D8×C4712yes—
274C22×C4C2×D4×C4711yescharacteristic
275Q16—21no—
276Q16C22⋊C4×C4712yescomplemented
277SD16—22no—
278SD16—22no—
279D8—22no—
280D8—22no—
281D8—21no—
282D8—41no—
283D8—41no—
284D8C22⋊C4×C4712yescomplemented
285C2×C8—21no—
286C2×C8—21no—
287C2×C8—21no—
288C2×C8C22×C4×C4711yescharacteristic
289C2×C8C2×D4×C4711yescharacteristic
290C2×C8C2×D4×C4711yescharacteristic
291C2×C8C2×D4×C4711yescharacteristic
292C2×C8#41×C4711yescharacteristic
293C2×C8#41×C4711yescharacteristic
294C4⋊C4—22no—
295C4⋊C4—42no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C22⋊C4—42no—
299C22⋊C4—41no—
300C22⋊C4—84no—
301C42—21no—
302C42—21no—
303C42—42no—
304C42—41no—
305C16—22no—
306C16—41no—
307C23—41no—
308C23—42no—
309C23—82no—
310C23—82no—
311C23—81no—
312C23—81no—
313C23C2×D8×C4711yescharacteristic
314Q8—22no—
315Q8—41no—
316D4—22no—
317D4—42no—
318D4—42no—
319D4—41no—
320D4—42no—
321D4—42no—
322D4—81no—
323D4—81no—
324C2×C4—22no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—84no—
331C2×C4—82no—
332C2×C4—81no—
333C2×C4C4×D4×C4711yescharacteristic
334C2×C4#120×C4711yescharacteristic
335C2×C4#121×C4711yescharacteristic
336C2×C4#135×C4711yescharacteristic
337C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
338C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
339C8—41no—
340C8C2×C22⋊C4×C4711yescharacteristic
341C8C4×D4×C4711yescharacteristic
342C8#121×C4711yescharacteristic
343C8#123×C4711yescharacteristic
344C22—22no—
345C22—42no—
346C22—84no—
347C22—82no—
348C22—82no—
349C22—161no—
350C22—161no—
351C22—162no—
352C22C4×D8×C4711yescharacteristic
353C22C47×#44711yescharacteristic
354C22C47×#45911yescharacteristic
355C4—42no—
356C4—42no—
357C4—82no—
358C4—161no—
359C4C47×#38611yescharacteristic
360C4C47×#44211yescharacteristic
361C4C47×#44911yescharacteristic
362C4C47×#46311yescharacteristic
363C2—21no—
364C2—21no—
365C2—82no—
366C2—162no—
367C2C47×#187911yescharacteristic
368C2C47×#219012yes—
subgroupG/H
center, socleC22×C47#447
commutatorC2×C8C22×C4×C47
Frattini, cosocleC22×C8C23×C47
prime radicalC2×C47×#509C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C22×C4×C47 ◁ C2×#97×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2943C2semidirect
3. C2×C47×#360C2semidirect
4. C47×#2140C2semidirect
5. C47×#1972C2semidirect
6. C47×#1386C2semidirect
7. C47×#1377C2semidirect
12. C47×#509C4semidirect
41. C2×D8×C47C2×C4semidirect
59. M32×C47C2×C4semidirect
91. Q16×C47C22⋊C4semidirect
99. D8×C47C22⋊C4semidirect
159. #13025C47direct (N × H)
180. #2943C2×C47semidirect
181. C2×#360C2×C47semidirect
182. #2140C2×C47semidirect
183. #1972C2×C47semidirect
184. #1386C2×C47semidirect
185. #1377C2×C47semidirect
196. #509C4×C47semidirect
212. C47#13025direct (N × H)
226. C2×D8C2×C4×C47semidirect
244. M32C2×C4×C47semidirect
276. Q16C22⋊C4×C47semidirect
284. D8C22⋊C4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#5092
C47×#29432
C2×C47×#3602
C47×#21402
C47×#19722
C47×#13862
C47×#13772
#1302547