Finite Group Databasebeta

← C47×#9173 #26048871

Subgroups — C47×#9173 #26048871

Order 12032.

562 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3038C211yesmaximal, characteristic
2C47×#2906C211yesmaximal, characteristic, complemented
3C47×#1545C211yesmaximal, characteristic, complemented
4C2×C47×#331C211yesmaximal, characteristic, complemented
5C47×#1477C211yesmaximal, characteristic, complemented
6C47×#1301C211yesmaximal, characteristic, complemented
7C47×#1292C211yesmaximal, characteristic, complemented
8C2×AGL(1,ℤ/8)×C47—21no—
9C2×#131×C47—21no—
10C2×#127×C47C2211yescharacteristic
11C4×#41×C47C2211yescharacteristic
12C47×#460—21no—
13C47×#460C412yes—
14C47×#459—21no—
15C47×#459C412yes—
16C47×#431C2211yescharacteristic
17C47×#424—21no—
18C47×#424—22no—
19C47×#423—21no—
20C47×#423C2211yescharacteristic
21C47×#423C2211yescharacteristic
22C2×C4⋊C8×C47—21no—
23C2×C4⋊C8×C47C2211yescharacteristic
24C2×C4⋊C8×C47C2211yescharacteristic
25C47×#418—21no—
26C47×#331—21no—
27C47×#331—21no—
28C47×#331—22no—
29C47×Q8⋊C8—21no—
30C47×D4⋊C8—21no—
31C2×#41×C47D411yescharacteristic
32C22×D4×C47—21no—
33C22×D4×C47—21no—
34C22×D4×C47—21no—
35AGL(1,ℤ/8)×C47—42no—
36AGL(1,ℤ/8)×C47—42no—
37C2×SD16×C47—22no—
38C2×D8×C47—22no—
39#131×C47—42no—
40#131×C47—42no—
41C2×M16×C47—22no—
42C2×M16×C47—21no—
43C2×M16×C47—21no—
44C22×C8×C47—22no—
45C22×C8×C47—21no—
46C22×C8×C47—21no—
47#127×C47—21no—
48#127×C47—21no—
49#127×C47—21no—
50#127×C47C2×C412yes—
51C4×Q8×C47C2×C411yescharacteristic
52C4×Q8×C47D411yescharacteristic
53C4×D4×C47—21no—
54C4×D4×C47—21no—
55C4×D4×C47C2×C411yescharacteristic
56C4×D4×C47D411yescharacteristic
57#117×C47—21no—
58#117×C47D411yescharacteristic
59C2×C42×C47—21no—
60C2×C42×C47C2311yescharacteristic
61C4⋊C8×C47—22no—
62C4⋊C8×C47—22no—
63C4⋊C8×C47—21no—
64C4⋊C8×C47—21no—
65C4⋊C8×C47—21no—
66C4⋊C8×C47—21no—
67C4⋊C8×C47—21no—
68C4⋊C8×C47—21no—
69C4⋊C8×C47C2×C412yes—
70C4⋊C8×C47D411yescharacteristic
71C4⋊C8×C47D411yescharacteristic
72C4⋊C8×C47D412yes—
73#102×C47—22no—
74#102×C47—22no—
75C22⋊C8×C47—21no—
76C4×C8×C47—21no—
77C24×C47—41no—
78#41×C47—21no—
79#41×C47—21no—
80#41×C47D812yes—
81#41×C47SD1612yes—
82C2×Q8×C47C22⋊C411yescharacteristic
83C2×D4×C47—21no—
84C2×D4×C47—22no—
85C2×D4×C47—22no—
86C2×D4×C47—22no—
87C2×D4×C47—41no—
88C2×D4×C47—41no—
89C2×D4×C47—41no—
90C2×D4×C47—41no—
91C2×D4×C47—41no—
92C2×D4×C47—41no—
93C2×D4×C47—41no—
94C2×D4×C47—81no—
95C2×D4×C47—81no—
96C2×D4×C47—82no—
97C2×D4×C47C22⋊C411yescharacteristic
98C22×C4×C47—21no—
99C22×C4×C47—21no—
100C22×C4×C47—21no—
101C22×C4×C47C2×D411yescharacteristic
102C22×C4×C47#4111yescharacteristic
103C22×C4×C47#4111yescharacteristic
104SD16×C47—44no—
105D8×C47—44no—
106M16×C47—44no—
107M16×C47—41no—
108M16×C47—41no—
109M16×C47—41no—
110M16×C47—41no—
111C2×C8×C47—22no—
112C2×C8×C47—21no—
113C2×C8×C47—22no—
114C2×C8×C47—21no—
115C2×C8×C47—44no—
116C2×C8×C47—41no—
117C2×C8×C47—41no—
118C2×C8×C47—41no—
119C2×C8×C47—41no—
120C2×C8×C47—81no—
121C4⋊C4×C47—21no—
122C4⋊C4×C47—21no—
123C4⋊C4×C47C22⋊C411yescharacteristic
124C4⋊C4×C47C22⋊C411yescharacteristic
125C22⋊C4×C47—21no—
126C22⋊C4×C47—21no—
127C22⋊C4×C47—21no—
128C42×C47—21no—
129C42×C47—21no—
130C42×C47—21no—
131C42×C47C22×C411yescharacteristic
132C42×C47C2×D411yescharacteristic
133C42×C47C2×D411yescharacteristic
134C42×C47C2×D411yescharacteristic
135C23×C47—21no—
136C23×C47—42no—
137C23×C47—82no—
138C23×C47—82no—
139C23×C47—81no—
140C23×C47—81no—
141C23×C47#12311yescharacteristic
142Q8×C47—21no—
143Q8×C47#10212yes—
144D4×C47—22no—
145D4×C47—22no—
146D4×C47—21no—
147D4×C47—42no—
148D4×C47—42no—
149D4×C47—82no—
150D4×C47—82no—
151D4×C47—82no—
152D4×C47—81no—
153D4×C47—81no—
154D4×C47—81no—
155D4×C47—81no—
156D4×C47#10212yes—
157C2×C4×C47—21no—
158C2×C4×C47—22no—
159C2×C4×C47—22no—
160C2×C4×C47—21no—
161C2×C4×C47—21no—
162C2×C4×C47—21no—
163C2×C4×C47—21no—
164C2×C4×C47—41no—
165C2×C4×C47—41no—
166C2×C4×C47—41no—
167C2×C4×C47—81no—
168C2×C4×C47C2×C22⋊C411yescharacteristic
169C2×C4×C47C4×D411yescharacteristic
170C2×C4×C47C4×D411yescharacteristic
171C2×C4×C47#12011yescharacteristic
172C2×C4×C47#12111yescharacteristic
173C2×C4×C47#12111yescharacteristic
174C2×C4×C47C2×D811yescharacteristic
175C2×C4×C47C2×SD1611yescharacteristic
176C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
177C2×C4×C47#13711yescharacteristic
178C8×C47—42no—
179C8×C47—41no—
180C8×C47—42no—
181C8×C47—41no—
182C8×C47—81no—
183C8×C47—81no—
184#9173C4711yesmaximal, characteristic, direct product factor, Sylow
185C22×C47—21no—
186C22×C47—21no—
187C22×C47—22no—
188C22×C47—41no—
189C22×C47—41no—
190C22×C47—82no—
191C22×C47—82no—
192C22×C47—82no—
193C22×C47—162no—
194C22×C47—162no—
195C22×C47#38611yescharacteristic
196C22×C47#48011yescharacteristic
197C22×C47#48111yescharacteristic
198C4×C47—22no—
199C4×C47—21no—
200C4×C47—21no—
201C4×C47—21no—
202C4×C47—41no—
203C4×C47—41no—
204C4×C47C2×#10211yescharacteristic
205C4×C47#41711yescharacteristic
206C4×C47#44711yescharacteristic
207C4×C47#44811yescharacteristic
208C4×C47#47111yescharacteristic
209C4×C47#47211yescharacteristic
210#3038C2×C4711yescharacteristic
211#2906C2×C4711yescharacteristic, complemented
212#1545C2×C4711yescharacteristic, complemented
213C2×#331C2×C4711yescharacteristic, complemented
214#1477C2×C4711yescharacteristic, complemented
215#1301C2×C4711yescharacteristic, complemented
216#1292C2×C4711yescharacteristic, complemented
217C2×C47—21no—
218C2×C47—21no—
219C2×C47—42no—
220C2×C47—162no—
221C2×C47#187411yescharacteristic
222C2×C47#190311yescharacteristic
223C2×C47#190711yescharacteristic
224C2×AGL(1,ℤ/8)—21no—
225C2×#131—21no—
226C2×#127C22×C4711yescharacteristic
227C4×#41C22×C4711yescharacteristic
228#460—21no—
229#460C4×C4712yes—
230#459—21no—
231#459C4×C4712yes—
232#431C22×C4711yescharacteristic
233#424—21no—
234#424—22no—
235#423—21no—
236#423C22×C4711yescharacteristic
237#423C22×C4711yescharacteristic
238C2×C4⋊C8—21no—
239C2×C4⋊C8C22×C4711yescharacteristic
240C2×C4⋊C8C22×C4711yescharacteristic
241#418—21no—
242#331—21no—
243#331—21no—
244#331—22no—
245Q8⋊C8—21no—
246D4⋊C8—21no—
247C47#917311yescharacteristic, direct product factor, Sylow
248C2×#41D4×C4711yescharacteristic
249C22×D4—21no—
250C22×D4—21no—
251C22×D4—21no—
252AGL(1,ℤ/8)—42no—
253AGL(1,ℤ/8)—42no—
254C2×SD16—22no—
255C2×D8—22no—
256#131—42no—
257#131—42no—
258C2×M16—22no—
259C2×M16—21no—
260C2×M16—21no—
261C22×C8—22no—
262C22×C8—21no—
263C22×C8—21no—
264#127—21no—
265#127—21no—
266#127—21no—
267#127C2×C4×C4712yes—
268C4×Q8C2×C4×C4711yescharacteristic
269C4×Q8D4×C4711yescharacteristic
270C4×D4—21no—
271C4×D4—21no—
272C4×D4C2×C4×C4711yescharacteristic
273C4×D4D4×C4711yescharacteristic
274#117—21no—
275#117D4×C4711yescharacteristic
276C2×C42—21no—
277C2×C42C23×C4711yescharacteristic
278C4⋊C8—22no—
279C4⋊C8—22no—
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8—21no—
283C4⋊C8—21no—
284C4⋊C8—21no—
285C4⋊C8—21no—
286C4⋊C8C2×C4×C4712yes—
287C4⋊C8D4×C4711yescharacteristic
288C4⋊C8D4×C4711yescharacteristic
289C4⋊C8D4×C4712yes—
290#102—22no—
291#102—22no—
292C22⋊C8—21no—
293C4×C8—21no—
294C24—41no—
295#41—21no—
296#41—21no—
297#41D8×C4712yes—
298#41SD16×C4712yes—
299C2×Q8C22⋊C4×C4711yescharacteristic
300C2×D4—21no—
301C2×D4—22no—
302C2×D4—22no—
303C2×D4—22no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—41no—
308C2×D4—41no—
309C2×D4—41no—
310C2×D4—41no—
311C2×D4—81no—
312C2×D4—81no—
313C2×D4—82no—
314C2×D4C22⋊C4×C4711yescharacteristic
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4C2×D4×C4711yescharacteristic
319C22×C4#41×C4711yescharacteristic
320C22×C4#41×C4711yescharacteristic
321SD16—44no—
322D8—44no—
323M16—44no—
324M16—41no—
325M16—41no—
326M16—41no—
327M16—41no—
328C2×C8—22no—
329C2×C8—21no—
330C2×C8—22no—
331C2×C8—21no—
332C2×C8—44no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—41no—
336C2×C8—41no—
337C2×C8—81no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4C22⋊C4×C4711yescharacteristic
341C4⋊C4C22⋊C4×C4711yescharacteristic
342C22⋊C4—21no—
343C22⋊C4—21no—
344C22⋊C4—21no—
345C42—21no—
346C42—21no—
347C42—21no—
348C42C22×C4×C4711yescharacteristic
349C42C2×D4×C4711yescharacteristic
350C42C2×D4×C4711yescharacteristic
351C42C2×D4×C4711yescharacteristic
352C23—21no—
353C23—42no—
354C23—82no—
355C23—82no—
356C23—81no—
357C23—81no—
358C23#123×C4711yescharacteristic
359Q8—21no—
360Q8#102×C4712yes—
361D4—22no—
362D4—22no—
363D4—21no—
364D4—42no—
365D4—42no—
366D4—82no—
367D4—82no—
368D4—82no—
369D4—81no—
370D4—81no—
371D4—81no—
372D4—81no—
373D4#102×C4712yes—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—81no—
385C2×C4C2×C22⋊C4×C4711yescharacteristic
386C2×C4C4×D4×C4711yescharacteristic
387C2×C4C4×D4×C4711yescharacteristic
388C2×C4#120×C4711yescharacteristic
389C2×C4#121×C4711yescharacteristic
390C2×C4#121×C4711yescharacteristic
391C2×C4C2×D8×C4711yescharacteristic
392C2×C4C2×SD16×C4711yescharacteristic
393C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
394C2×C4#137×C4711yescharacteristic
395C8—42no—
396C8—41no—
397C8—42no—
398C8—41no—
399C8—81no—
400C8—81no—
401C22—21no—
402C22—21no—
403C22—22no—
404C22—41no—
405C22—41no—
406C22—82no—
407C22—82no—
408C22—82no—
409C22—162no—
410C22—162no—
411C22C47×#38611yescharacteristic
412C22C47×#48011yescharacteristic
413C22C47×#48111yescharacteristic
414C4—22no—
415C4—21no—
416C4—21no—
417C4—21no—
418C4—41no—
419C4—41no—
420C4C2×#102×C4711yescharacteristic
421C4C47×#41711yescharacteristic
422C4C47×#44711yescharacteristic
423C4C47×#44811yescharacteristic
424C4C47×#47111yescharacteristic
425C4C47×#47211yescharacteristic
426C2—21no—
427C2—21no—
428C2—42no—
429C2—162no—
430C2C47×#187411yescharacteristic
431C2C47×#190311yescharacteristic
432C2C47×#190711yescharacteristic
subgroupG/H
center, socleC22×C47#386
commutatorC42C22×C4×C47
Frattini, cosocleC2×C42C23×C47
prime radicalC47×#3038C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2906C2semidirect
3. C47×#1545C2semidirect
4. C2×C47×#331C2semidirect
5. C47×#1477C2semidirect
6. C47×#1301C2semidirect
7. C47×#1292C2semidirect
184. #9173C47direct (N × H)
211. #2906C2×C47semidirect
212. #1545C2×C47semidirect
213. C2×#331C2×C47semidirect
214. #1477C2×C47semidirect
215. #1301C2×C47semidirect
216. #1292C2×C47semidirect
247. C47#9173direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#30382
C47×#29062
C47×#15452
C2×C47×#3312
C47×#14772
C47×#13012
C47×#12922
#917347