Finite Group Databasebeta

← C2×C47×#2212 #26073289

Subgroups — C2×C47×#2212 #26073289

Order 12032.

706 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#510C211yesmaximal, characteristic, complemented
2C2×C47×#509C211yesmaximal, characteristic
3C2×C47×#495C211yesmaximal, characteristic, complemented
4C2×C47×#443C211yesmaximal, characteristic, complemented
5C47×#2212C218yesmaximal, direct product factor
6C2×C47×#364C211yesmaximal, characteristic, complemented
7C2×C47×#362C211yesmaximal, characteristic, complemented
8C2×C47×#361C211yesmaximal, characteristic, complemented
9C2×#135×C47C2211yescharacteristic
10C22×Q16×C47C2211yescharacteristic
11C22×SD16×C47—21no—
12C22×D8×C47C2211yescharacteristic
13C2×#131×C47—21no—
14C2×#124×C47—21no—
15C47×#510—22no—
16C47×#510C2214yescomplemented
17C47×#509—22no—
18C47×#509C2214yes—
19C2×Q32×C47—21no—
20C2×SD32×C47—21no—
21C2×SD32×C47—21no—
22C2×D16×C47—21no—
23C2×M32×C47C2211yescharacteristic
24C2×M32×C47C2211yescharacteristic
25C47×#495—22no—
26C47×#495C2214yescomplemented
27C47×#443—22no—
28C47×#443C2214yescomplemented
29C2×#108×C47C2211yescharacteristic
30C2×#104×C47—21no—
31C2×C4×C8×C47C2211yescharacteristic
32C47×#364C2214yescomplemented
33C47×#362C2214yescomplemented
34C47×#361C2214yescomplemented
35C2×#41×C47—21no—
36C22×Q8×C47—21no—
37C22×D4×C47—21no—
38#135×C47—21no—
39#135×C47—21no—
40#135×C47D412yes—
41#135×C47C2312yes—
42C2×Q16×C47—21no—
43C2×Q16×C47—21no—
44C2×Q16×C47—21no—
45C2×Q16×C47—21no—
46C2×Q16×C47—21no—
47C2×Q16×C47D411yescharacteristic
48C2×Q16×C47C2312yes—
49C2×SD16×C47—24no—
50C2×SD16×C47—21no—
51C2×SD16×C47—41no—
52C2×SD16×C47—41no—
53C2×SD16×C47—42no—
54C2×D8×C47—21no—
55C2×D8×C47—21no—
56C2×D8×C47—21no—
57C2×D8×C47—21no—
58C2×D8×C47—21no—
59C2×D8×C47D411yescharacteristic
60C2×D8×C47C2312yes—
61#131×C47—24no—
62#131×C47—42no—
63C2×M16×C47—21no—
64C2×M16×C47—41no—
65C22×C8×C47—41no—
66C22×C8×C47D411yescharacteristic
67C22×C8×C47C2311yescharacteristic
68#124×C47—24no—
69#124×C47—42no—
70C2×C22⋊C4×C47—42no—
71C2×C42×C47D411yescharacteristic
72Q32×C47—24no—
73SD32×C47—24no—
74SD32×C47—24no—
75D16×C47—24no—
76M32×C47—21no—
77M32×C47—21no—
78M32×C47C2312yes—
79M32×C47C2312yes—
80C2×C16×C47—21no—
81C2×C16×C47—21no—
82#108×C47—21no—
83#108×C47C2312yes—
84#104×C47—24no—
85C4×C8×C47D412yes—
86C4×C8×C47C2312yes—
87C24×C47—41no—
88#41×C47—22no—
89#41×C47—22no—
90#41×C47—41no—
91#41×C47—41no—
92C2×Q8×C47—21no—
93C2×Q8×C47—22no—
94C2×Q8×C47—41no—
95C2×Q8×C47—41no—
96C2×Q8×C47—41no—
97C2×Q8×C47—41no—
98C2×Q8×C47—41no—
99C2×D4×C47—21no—
100C2×D4×C47—22no—
101C2×D4×C47—41no—
102C2×D4×C47—41no—
103C2×D4×C47—41no—
104C2×D4×C47—41no—
105C2×D4×C47—41no—
106C2×D4×C47—41no—
107C22×C4×C47—21no—
108C22×C4×C47—41no—
109C22×C4×C47—41no—
110C22×C4×C47C2×D411yescharacteristic
111Q16×C47—21no—
112Q16×C47—22no—
113Q16×C47—22no—
114Q16×C47—41no—
115Q16×C47—41no—
116Q16×C47C2×D412yes—
117SD16×C47—22no—
118SD16×C47—22no—
119SD16×C47—44no—
120SD16×C47—44no—
121D8×C47—21no—
122D8×C47—22no—
123D8×C47—22no—
124D8×C47—41no—
125D8×C47—41no—
126D8×C47C2×D412yes—
127M16×C47—22no—
128M16×C47—41no—
129M16×C47—44no—
130C2×C8×C47—41no—
131C2×C8×C47—44no—
132C2×C8×C47D811yescharacteristic
133C2×C8×C47D811yescharacteristic
134C2×C8×C47D812yes—
135C2×C8×C47C2×D411yescharacteristic
136C2×C8×C47C2×D411yescharacteristic
137C2×C8×C47C2×D411yescharacteristic
138C2×C8×C47C2×D412yes—
139C2×C8×C47#4111yescharacteristic
140C2×C8×C47#4111yescharacteristic
141C2×C8×C47C2411yescharacteristic
142C22⋊C4×C47—48no—
143C42×C47—21no—
144C42×C47C2×D412yes—
145C16×C47—22no—
146C16×C47—22no—
147C23×C47—41no—
148C23×C47—42no—
149C23×C47—84no—
150C23×C47—81no—
151C23×C47—81no—
152C23×C47AGL(1,ℤ/8)11yescharacteristic
153Q8×C47—22no—
154Q8×C47—41no—
155Q8×C47—42no—
156Q8×C47—42no—
157Q8×C47—81no—
158Q8×C47—81no—
159D4×C47—22no—
160D4×C47—42no—
161D4×C47—42no—
162D4×C47—42no—
163D4×C47—42no—
164D4×C47—41no—
165D4×C47—81no—
166D4×C47—81no—
167C2×C4×C47—22no—
168C2×C4×C47—42no—
169C2×C4×C47—41no—
170C2×C4×C47—42no—
171C2×C4×C47—42no—
172C2×C4×C47—42no—
173C2×C4×C47—81no—
174C2×C4×C47—81no—
175C2×C4×C47#12111yescharacteristic
176C2×C4×C47#12111yescharacteristic
177C2×C4×C47C2×D811yescharacteristic
178C2×C4×C47C2×D811yescharacteristic
179C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
180C2×C4×C47C22×D411yescharacteristic
181C8×C47—42no—
182C8×C47#12111yescharacteristic
183C8×C47#12111yescharacteristic
184C8×C47C2×D812yes—
185C8×C47C2×D812yes—
186C8×C47C22×D411yescharacteristic
187C8×C47C2×#4111yescharacteristic
188C2×#2212C4711yesmaximal, characteristic, direct product factor, Sylow
189C22×C47—22no—
190C22×C47—42no—
191C22×C47—84no—
192C22×C47—82no—
193C22×C47—82no—
194C22×C47—162no—
195C22×C47—162no—
196C22×C47#45911yescharacteristic
197C22×C47#45911yescharacteristic
198C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
199C4×C47—42no—
200C4×C47—42no—
201C4×C47—82no—
202C4×C47#45911yescharacteristic
203C4×C47#45911yescharacteristic
204C4×C47C2×#12111yescharacteristic
205C4×C47C22×D811yescharacteristic
206C2×#510C2×C4711yescharacteristic, complemented
207C2×#509C2×C4711yescharacteristic
208C2×#495C2×C4711yescharacteristic, complemented
209C2×#443C2×C4711yescharacteristic, complemented
210#2212C2×C4718yesdirect product factor
211C2×#364C2×C4711yescharacteristic, complemented
212C2×#362C2×C4711yescharacteristic, complemented
213C2×#361C2×C4711yescharacteristic, complemented
214C2×C47—21no—
215C2×C47—21no—
216C2×C47—82no—
217C2×C47—162no—
218C2×C47#221212yesdirect product factor
219C2×C47C2×#45911yescharacteristic
220C2×#135C22×C4711yescharacteristic
221C22×Q16C22×C4711yescharacteristic
222C22×SD16—21no—
223C22×D8C22×C4711yescharacteristic
224C2×#131—21no—
225C2×#124—21no—
226#510—22no—
227#510C22×C4714yescomplemented
228#509—22no—
229#509C22×C4714yes—
230C2×Q32—21no—
231C2×SD32—21no—
232C2×SD32—21no—
233C2×D16—21no—
234C2×M32C22×C4711yescharacteristic
235C2×M32C22×C4711yescharacteristic
236#495—22no—
237#495C22×C4714yescomplemented
238#443—22no—
239#443C22×C4714yescomplemented
240C2×#108C22×C4711yescharacteristic
241C2×#104—21no—
242C2×C4×C8C22×C4711yescharacteristic
243#364C22×C4714yescomplemented
244#362C22×C4714yescomplemented
245#361C22×C4714yescomplemented
246C47C2×#221211yescharacteristic, direct product factor, Sylow
247C2×#41—21no—
248C22×Q8—21no—
249C22×D4—21no—
250#135—21no—
251#135—21no—
252#135D4×C4712yes—
253#135C23×C4712yes—
254C2×Q16—21no—
255C2×Q16—21no—
256C2×Q16—21no—
257C2×Q16—21no—
258C2×Q16—21no—
259C2×Q16D4×C4711yescharacteristic
260C2×Q16C23×C4712yes—
261C2×SD16—24no—
262C2×SD16—21no—
263C2×SD16—41no—
264C2×SD16—41no—
265C2×SD16—42no—
266C2×D8—21no—
267C2×D8—21no—
268C2×D8—21no—
269C2×D8—21no—
270C2×D8—21no—
271C2×D8D4×C4711yescharacteristic
272C2×D8C23×C4712yes—
273#131—24no—
274#131—42no—
275C2×M16—21no—
276C2×M16—41no—
277C22×C8—41no—
278C22×C8D4×C4711yescharacteristic
279C22×C8C23×C4711yescharacteristic
280#124—24no—
281#124—42no—
282C2×C22⋊C4—42no—
283C2×C42D4×C4711yescharacteristic
284Q32—24no—
285SD32—24no—
286SD32—24no—
287D16—24no—
288M32—21no—
289M32—21no—
290M32C23×C4712yes—
291M32C23×C4712yes—
292C2×C16—21no—
293C2×C16—21no—
294#108—21no—
295#108C23×C4712yes—
296#104—24no—
297C4×C8D4×C4712yes—
298C4×C8C23×C4712yes—
299C24—41no—
300#41—22no—
301#41—22no—
302#41—41no—
303#41—41no—
304C2×Q8—21no—
305C2×Q8—22no—
306C2×Q8—41no—
307C2×Q8—41no—
308C2×Q8—41no—
309C2×Q8—41no—
310C2×Q8—41no—
311C2×D4—21no—
312C2×D4—22no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C22×C4—21no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4C2×D4×C4711yescharacteristic
323Q16—21no—
324Q16—22no—
325Q16—22no—
326Q16—41no—
327Q16—41no—
328Q16C2×D4×C4712yes—
329SD16—22no—
330SD16—22no—
331SD16—44no—
332SD16—44no—
333D8—21no—
334D8—22no—
335D8—22no—
336D8—41no—
337D8—41no—
338D8C2×D4×C4712yes—
339M16—22no—
340M16—41no—
341M16—44no—
342C2×C8—41no—
343C2×C8—44no—
344C2×C8D8×C4711yescharacteristic
345C2×C8D8×C4711yescharacteristic
346C2×C8D8×C4712yes—
347C2×C8C2×D4×C4711yescharacteristic
348C2×C8C2×D4×C4711yescharacteristic
349C2×C8C2×D4×C4711yescharacteristic
350C2×C8C2×D4×C4712yes—
351C2×C8#41×C4711yescharacteristic
352C2×C8#41×C4711yescharacteristic
353C2×C8C24×C4711yescharacteristic
354C22⋊C4—48no—
355C42—21no—
356C42C2×D4×C4712yes—
357C16—22no—
358C16—22no—
359C23—41no—
360C23—42no—
361C23—84no—
362C23—81no—
363C23—81no—
364C23AGL(1,ℤ/8)×C4711yescharacteristic
365Q8—22no—
366Q8—41no—
367Q8—42no—
368Q8—42no—
369Q8—81no—
370Q8—81no—
371D4—22no—
372D4—42no—
373D4—42no—
374D4—41no—
375D4—42no—
376D4—42no—
377D4—81no—
378D4—81no—
379C2×C4—22no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4#121×C4711yescharacteristic
388C2×C4#121×C4711yescharacteristic
389C2×C4C2×D8×C4711yescharacteristic
390C2×C4C2×D8×C4711yescharacteristic
391C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
392C2×C4C22×D4×C4711yescharacteristic
393C8—42no—
394C8#121×C4711yescharacteristic
395C8#121×C4711yescharacteristic
396C8C2×D8×C4712yes—
397C8C2×D8×C4712yes—
398C8C22×D4×C4711yescharacteristic
399C8C2×#41×C4711yescharacteristic
400C22—22no—
401C22—42no—
402C22—84no—
403C22—82no—
404C22—82no—
405C22—162no—
406C22—162no—
407C22C47×#45911yescharacteristic
408C22C47×#45911yescharacteristic
409C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
410C4—42no—
411C4—42no—
412C4—82no—
413C4C47×#45911yescharacteristic
414C4C47×#45911yescharacteristic
415C4C2×#121×C4711yescharacteristic
416C4C22×D8×C4711yescharacteristic
417C2—21no—
418C2—21no—
419C2—82no—
420C2—162no—
421C2C47×#221212yesdirect product factor
422C2C2×C47×#45911yescharacteristic
subgroupG/H
center, socleC22×C47#459
commutator, Frattini, cosocleC2×C8C24×C47
prime radicalC2×C47×#509C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C22×C4×C47 ◁ C2×C4×C8×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#510C2semidirect
3. C2×C47×#495C2semidirect
4. C2×C47×#443C2semidirect
5. C47×#2212C2direct (N × H)
6. C2×C47×#364C2semidirect
7. C2×C47×#362C2semidirect
8. C2×C47×#361C2semidirect
16. C47×#510C22semidirect
26. C47×#495C22semidirect
28. C47×#443C22semidirect
32. C47×#364C22semidirect
33. C47×#362C22semidirect
34. C47×#361C22semidirect
188. C2×#2212C47direct (N × H)
206. C2×#510C2×C47semidirect
208. C2×#495C2×C47semidirect
209. C2×#443C2×C47semidirect
210. #2212C2×C47direct (N × H)
211. C2×#364C2×C47semidirect
212. C2×#362C2×C47semidirect
213. C2×#361C2×C47semidirect
218. C2×C47#2212direct (N × H)
227. #510C22×C47semidirect
237. #495C22×C47semidirect
239. #443C22×C47semidirect
243. #364C22×C47semidirect
244. #362C22×C47semidirect
245. #361C22×C47semidirect
246. C47C2×#2212direct (N × H)
421. C2C47×#2212direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C47×#5102
C2×C47×#5092
C2×C47×#4952
C2×C47×#4432
C47×#22122
C2×C47×#3642
C2×C47×#3622
C2×C47×#3612
C2×#221247