Finite Group Databasebeta

← C47×#13318 #26053016

Subgroups — C47×#13318 #26053016

Order 12032.

532 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3414C211yesmaximal, characteristic, complemented
2C47×#3067C211yesmaximal, characteristic, complemented
3C47×#3060C211yesmaximal, characteristic, complemented
4C2×C47×#360C211yesmaximal, characteristic, complemented
5C47×#2143C211yesmaximal, characteristic, complemented
6C47×#2117C211yesmaximal, characteristic, complemented
7C47×#1383C211yesmaximal, characteristic, complemented
8C47×#575—21no—
9C2×#135×C47C2211yescharacteristic
10C2×#135×C47C2211yescharacteristic
11C2×#131×C47C2211yescharacteristic
12C47×#537—21no—
13C47×#510—21no—
14C47×#510—21no—
15C47×#509—21no—
16C47×#509—21no—
17C47×#508—22no—
18C2×M32×C47C2211yescharacteristic
19C2×M32×C47C2211yescharacteristic
20C47×#473—21no—
21C47×#472—21no—
22C47×#471—22no—
23C47×#470—21no—
24C47×#469—21no—
25C47×#465—22no—
26C2×#108×C47C2211yescharacteristic
27C2×#106×C47C2211yescharacteristic
28C47×#417—21no—
29C47×#413—21no—
30C47×#360—22no—
31C47×#359—22no—
32C47×#350—22no—
33C2×#41×C47—21no—
34C2×#41×C47—21no—
35C2×#41×C47D411yescharacteristic
36#137×C47—22no—
37#137×C47—41no—
38AGL(1,ℤ/8)×C47—22no—
39AGL(1,ℤ/8)×C47—41no—
40#135×C47—21no—
41#135×C47—21no—
42#135×C47—21no—
43#135×C47—21no—
44#135×C47—21no—
45#135×C47—21no—
46#135×C47—21no—
47#135×C47—21no—
48#135×C47—42no—
49C2×Q16×C47D411yescharacteristic
50C2×Q16×C47D411yescharacteristic, complemented
51C2×SD16×C47—21no—
52C2×SD16×C47—21no—
53C2×D8×C47D411yescharacteristic
54C2×D8×C47D411yescharacteristic, complemented
55#131×C47—21no—
56#131×C47—21no—
57#131×C47—21no—
58#131×C47—21no—
59C2×M16×C47—21no—
60C2×M16×C47—21no—
61C2×M16×C47D411yescharacteristic
62C22×C8×C47—21no—
63C22×C8×C47C2311yescharacteristic
64C22⋊Q8×C47—22no—
65C22⋊Q8×C47—41no—
66#121×C47—22no—
67#121×C47—42no—
68#121×C47—41no—
69C2×C4⋊C4×C47—21no—
70Q32×C47—22no—
71SD32×C47—22no—
72SD32×C47—22no—
73D16×C47—22no—
74M32×C47—21no—
75M32×C47—21no—
76M32×C47—21no—
77M32×C47—21no—
78C2×C16×C47—21no—
79C2×C16×C47D412yescomplemented
80#108×C47—21no—
81#108×C47D412yescomplemented
82#106×C47—21no—
83#106×C47D412yes—
84#103×C47—22no—
85#102×C47—22no—
86#101×C47—22no—
87#100×C47—22no—
88#41×C47—21no—
89#41×C47—21no—
90#41×C47—21no—
91#41×C47—21no—
92#41×C47—41no—
93#41×C47—41no—
94#41×C47—41no—
95#41×C47—41no—
96#41×C47—41no—
97#41×C47—41no—
98#41×C47—41no—
99#41×C47—41no—
100C2×Q8×C47—21no—
101C2×Q8×C47—21no—
102C2×Q8×C47D811yescharacteristic
103C2×D4×C47—21no—
104C2×D4×C47—21no—
105C2×D4×C47—21no—
106C2×D4×C47—41no—
107C2×D4×C47—41no—
108C2×D4×C47—42no—
109C2×D4×C47D811yescharacteristic
110C22×C4×C47—21no—
111C22×C4×C47—41no—
112C22×C4×C47—41no—
113C22×C4×C47—41no—
114C22×C4×C47C2×D411yescharacteristic
115Q16×C47—21no—
116Q16×C47—21no—
117Q16×C47—21no—
118Q16×C47—21no—
119Q16×C47—42no—
120SD16×C47—42no—
121SD16×C47—42no—
122SD16×C47—41no—
123SD16×C47—41no—
124SD16×C47—41no—
125SD16×C47—41no—
126D8×C47—21no—
127D8×C47—21no—
128D8×C47—21no—
129D8×C47—21no—
130D8×C47—42no—
131M16×C47—22no—
132M16×C47—21no—
133M16×C47—21no—
134M16×C47—41no—
135M16×C47—41no—
136M16×C47—41no—
137C2×C8×C47—21no—
138C2×C8×C47—41no—
139C2×C8×C47—41no—
140C2×C8×C47—41no—
141C2×C8×C47C2×D411yescharacteristic
142C2×C8×C47C2×D411yescharacteristic
143C2×C8×C47C2×D411yescharacteristic
144C2×C8×C47C2×D411yescharacteristic
145C2×C8×C47C2×D411yescharacteristic
146C2×C8×C47#4111yescharacteristic
147C4⋊C4×C47—22no—
148C4⋊C4×C47—42no—
149C4⋊C4×C47—41no—
150C22⋊C4×C47—42no—
151C22⋊C4×C47—42no—
152C16×C47—22no—
153C16×C47—41no—
154C23×C47—21no—
155C23×C47—41no—
156C23×C47—41no—
157C23×C47AGL(1,ℤ/8)11yescharacteristic
158Q8×C47—21no—
159Q8×C47—21no—
160Q8×C47—41no—
161Q8×C47—41no—
162Q8×C47—41no—
163Q8×C47—41no—
164D4×C47—21no—
165D4×C47—21no—
166D4×C47—41no—
167D4×C47—41no—
168D4×C47—41no—
169D4×C47—41no—
170D4×C47—41no—
171D4×C47—41no—
172D4×C47—81no—
173D4×C47—81no—
174D4×C47—81no—
175D4×C47—81no—
176D4×C47—162no—
177C2×C4×C47—21no—
178C2×C4×C47—41no—
179C2×C4×C47—41no—
180C2×C4×C47—42no—
181C2×C4×C47—41no—
182C2×C4×C47—41no—
183C2×C4×C47—81no—
184C2×C4×C47—81no—
185C2×C4×C47—81no—
186C2×C4×C47—81no—
187C2×C4×C47—161no—
188C2×C4×C47#12011yescharacteristic
189C2×C4×C47#12011yescharacteristic
190C2×C4×C47#12111yescharacteristic
191C2×C4×C47C2×D811yescharacteristic
192C2×C4×C47#13511yescharacteristic
193C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
194C8×C47—41no—
195C8×C47—42no—
196C8×C47#12011yescharacteristic
197C8×C47#12111yescharacteristic
198C8×C47#12111yescharacteristic
199C8×C47#12711yescharacteristic
200#13318C4711yesmaximal, characteristic, direct product factor, Sylow
201C22×C47—41no—
202C22×C47—42no—
203C22×C47—41no—
204C22×C47—81no—
205C22×C47—81no—
206C22×C47—81no—
207C22×C47—81no—
208C22×C47—161no—
209C22×C47#44711yescharacteristic
210C22×C47#44911yescharacteristic
211C22×C47#46911yescharacteristic
212C4×C47—41no—
213C4×C47—82no—
214C4×C47—81no—
215C4×C47—81no—
216C4×C47#39211yescharacteristic
217C4×C47#44711yescharacteristic
218C4×C47#44911yescharacteristic
219C4×C47#46611yescharacteristic
220#3414C2×C4711yescharacteristic, complemented
221#3067C2×C4711yescharacteristic, complemented
222#3060C2×C4711yescharacteristic, complemented
223C2×#360C2×C4711yescharacteristic, complemented
224#2143C2×C4711yescharacteristic, complemented
225#2117C2×C4711yescharacteristic, complemented
226#1383C2×C4711yescharacteristic, complemented
227C2×C47—21no—
228C2×C47—21no—
229C2×C47—21no—
230C2×C47—81no—
231C2×C47—161no—
232C2×C47—161no—
233C2×C47#199911yescharacteristic
234#575—21no—
235C2×#135C22×C4711yescharacteristic
236C2×#135C22×C4711yescharacteristic
237C2×#131C22×C4711yescharacteristic
238#537—21no—
239#510—21no—
240#510—21no—
241#509—21no—
242#509—21no—
243#508—22no—
244C2×M32C22×C4711yescharacteristic
245C2×M32C22×C4711yescharacteristic
246#473—21no—
247#472—21no—
248#471—22no—
249#470—21no—
250#469—21no—
251#465—22no—
252C2×#108C22×C4711yescharacteristic
253C2×#106C22×C4711yescharacteristic
254#417—21no—
255#413—21no—
256#360—22no—
257#359—22no—
258#350—22no—
259C47#1331811yescharacteristic, direct product factor, Sylow
260C2×#41—21no—
261C2×#41—21no—
262C2×#41D4×C4711yescharacteristic
263#137—22no—
264#137—41no—
265AGL(1,ℤ/8)—22no—
266AGL(1,ℤ/8)—41no—
267#135—21no—
268#135—21no—
269#135—21no—
270#135—21no—
271#135—21no—
272#135—21no—
273#135—21no—
274#135—21no—
275#135—42no—
276C2×Q16D4×C4711yescharacteristic
277C2×Q16D4×C4711yescharacteristic, complemented
278C2×SD16—21no—
279C2×SD16—21no—
280C2×D8D4×C4711yescharacteristic
281C2×D8D4×C4711yescharacteristic, complemented
282#131—21no—
283#131—21no—
284#131—21no—
285#131—21no—
286C2×M16—21no—
287C2×M16—21no—
288C2×M16D4×C4711yescharacteristic
289C22×C8—21no—
290C22×C8C23×C4711yescharacteristic
291C22⋊Q8—22no—
292C22⋊Q8—41no—
293#121—22no—
294#121—42no—
295#121—41no—
296C2×C4⋊C4—21no—
297Q32—22no—
298SD32—22no—
299SD32—22no—
300D16—22no—
301M32—21no—
302M32—21no—
303M32—21no—
304M32—21no—
305C2×C16—21no—
306C2×C16D4×C4712yescomplemented
307#108—21no—
308#108D4×C4712yescomplemented
309#106—21no—
310#106D4×C4712yes—
311#103—22no—
312#102—22no—
313#101—22no—
314#100—22no—
315#41—21no—
316#41—21no—
317#41—21no—
318#41—21no—
319#41—41no—
320#41—41no—
321#41—41no—
322#41—41no—
323#41—41no—
324#41—41no—
325#41—41no—
326#41—41no—
327C2×Q8—21no—
328C2×Q8—21no—
329C2×Q8D8×C4711yescharacteristic
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4—41no—
334C2×D4—41no—
335C2×D4—42no—
336C2×D4D8×C4711yescharacteristic
337C22×C4—21no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4C2×D4×C4711yescharacteristic
342Q16—21no—
343Q16—21no—
344Q16—21no—
345Q16—21no—
346Q16—42no—
347SD16—42no—
348SD16—42no—
349SD16—41no—
350SD16—41no—
351SD16—41no—
352SD16—41no—
353D8—21no—
354D8—21no—
355D8—21no—
356D8—21no—
357D8—42no—
358M16—21no—
359M16—22no—
360M16—21no—
361M16—41no—
362M16—41no—
363M16—41no—
364C2×C8—21no—
365C2×C8—41no—
366C2×C8—41no—
367C2×C8—41no—
368C2×C8C2×D4×C4711yescharacteristic
369C2×C8C2×D4×C4711yescharacteristic
370C2×C8C2×D4×C4711yescharacteristic
371C2×C8C2×D4×C4711yescharacteristic
372C2×C8C2×D4×C4711yescharacteristic
373C2×C8#41×C4711yescharacteristic
374C4⋊C4—22no—
375C4⋊C4—42no—
376C4⋊C4—41no—
377C22⋊C4—42no—
378C22⋊C4—42no—
379C16—22no—
380C16—41no—
381C23—21no—
382C23—41no—
383C23—41no—
384C23AGL(1,ℤ/8)×C4711yescharacteristic
385Q8—21no—
386Q8—21no—
387Q8—41no—
388Q8—41no—
389Q8—41no—
390Q8—41no—
391D4—21no—
392D4—21no—
393D4—41no—
394D4—41no—
395D4—41no—
396D4—41no—
397D4—41no—
398D4—41no—
399D4—81no—
400D4—81no—
401D4—81no—
402D4—81no—
403D4—162no—
404C2×C4—21no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—81no—
411C2×C4—81no—
412C2×C4—81no—
413C2×C4—81no—
414C2×C4—161no—
415C2×C4#120×C4711yescharacteristic
416C2×C4#120×C4711yescharacteristic
417C2×C4#121×C4711yescharacteristic
418C2×C4C2×D8×C4711yescharacteristic
419C2×C4#135×C4711yescharacteristic
420C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
421C8—41no—
422C8—42no—
423C8#120×C4711yescharacteristic
424C8#121×C4711yescharacteristic
425C8#121×C4711yescharacteristic
426C8#127×C4711yescharacteristic
427C22—41no—
428C22—42no—
429C22—41no—
430C22—81no—
431C22—81no—
432C22—81no—
433C22—81no—
434C22—161no—
435C22C47×#44711yescharacteristic
436C22C47×#44911yescharacteristic
437C22C47×#46911yescharacteristic
438C4—41no—
439C4—82no—
440C4—81no—
441C4—81no—
442C4C47×#39211yescharacteristic
443C4C47×#44711yescharacteristic
444C4C47×#44911yescharacteristic
445C4C47×#46611yescharacteristic
446C2—21no—
447C2—21no—
448C2—21no—
449C2—81no—
450C2—161no—
451C2—161no—
452C2C47×#199911yescharacteristic
subgroupG/H
center, socleC2×C47#1999
commutator, Frattini, cosocleC22×C8C23×C47
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C47 ◁ C22×C4×C47 ◁ C2×#131×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3414C2semidirect
2. C47×#3067C2semidirect
3. C47×#3060C2semidirect
4. C2×C47×#360C2semidirect
5. C47×#2143C2semidirect
6. C47×#2117C2semidirect
7. C47×#1383C2semidirect
50. C2×Q16×C47D4semidirect
54. C2×D8×C47D4semidirect
79. C2×C16×C47D4semidirect
81. #108×C47D4semidirect
200. #13318C47direct (N × H)
220. #3414C2×C47semidirect
221. #3067C2×C47semidirect
222. #3060C2×C47semidirect
223. C2×#360C2×C47semidirect
224. #2143C2×C47semidirect
225. #2117C2×C47semidirect
226. #1383C2×C47semidirect
259. C47#13318direct (N × H)
277. C2×Q16D4×C47semidirect
281. C2×D8D4×C47semidirect
306. C2×C16D4×C47semidirect
308. #108D4×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#34142
C47×#30672
C47×#30602
C2×C47×#3602
C47×#21432
C47×#21172
C47×#13832
#1331847