Finite Group Databasebeta

← C47×#10501 #26050199

Subgroups — C47×#10501 #26050199

Order 12032.

440 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3206C211yesmaximal, characteristic
2C47×#1997C211yesmaximal, characteristic, complemented
3C47×#1981C211yesmaximal, characteristic, complemented
4C47×#1980C211yesmaximal, characteristic
5C47×#1565C211yesmaximal, characteristic, complemented
6C47×#1547C211yesmaximal, characteristic
7C47×#1303C211yesmaximal, characteristic, complemented
8C47×#532C2211yescharacteristic
9C2×C4⋊Q8×C47C2211yescharacteristic
10C47×#492—21no—
11C47×#487—21no—
12C47×#461—21no—
13C47×#461—21no—
14C47×#448—22no—
15C47×#431C2211yescharacteristic
16C47×#423C2211yescharacteristic
17C2×C4⋊C8×C47C2211yescharacteristic
18C2×#104×C47—21no—
19C2×#104×C47—21no—
20C2×#103×C47—22no—
21C4×M16×C47C2211yescharacteristic
22C4×C4⋊C4×C47C2211yescharacteristic
23C47×#343—21no—
24C47×#343—21no—
25C47×#335—21no—
26C47×#334—21no—
27C47×#332—21no—
28C47×#331—21no—
29C2×#41×C47—21no—
30C22×Q8×C47D412yes—
31C2×SD16×C47—22no—
32C2×SD16×C47—22no—
33C2×M16×C47—21no—
34C2×M16×C47D411yescharacteristic
35C2×M16×C47D411yescharacteristic
36C22×C8×C47—21no—
37C4⋊Q8×C47—21no—
38C4⋊Q8×C47—21no—
39C4⋊Q8×C47—21no—
40C4⋊Q8×C47—21no—
41C4⋊Q8×C47D411yescharacteristic
42#127×C47D411yescharacteristic
43#124×C47—21no—
44#121×C47—21no—
45#121×C47—21no—
46C4×D4×C47—21no—
47C4×D4×C47—21no—
48C2×C4⋊C4×C47—21no—
49C2×C4⋊C4×C47—21no—
50C2×C4⋊C4×C47—21no—
51C2×C42×C47—21no—
52C2×C42×C47C2311yescharacteristic
53C4⋊C8×C47—21no—
54C4⋊C8×C47—21no—
55C4⋊C8×C47—21no—
56C4⋊C8×C47—21no—
57C4⋊C8×C47D411yescharacteristic
58C4⋊C8×C47D411yescharacteristic
59#104×C47—42no—
60#104×C47—42no—
61#103×C47—22no—
62#103×C47—22no—
63#103×C47—44no—
64C22⋊C8×C47—21no—
65#97×C47—21no—
66C4×C8×C47—21no—
67C4×C8×C47—21no—
68#95×C47—21no—
69#41×C47—41no—
70#41×C47—41no—
71#41×C47—41no—
72#41×C47—41no—
73C2×Q8×C47—22no—
74C2×Q8×C47—21no—
75C2×Q8×C47—22no—
76C2×Q8×C47—42no—
77C2×Q8×C47—42no—
78C2×D4×C47—21no—
79C2×D4×C47—21no—
80C2×D4×C47—21no—
81C2×D4×C47—41no—
82C22×C4×C47—22no—
83C22×C4×C47—41no—
84C22×C4×C47—41no—
85C22×C4×C47C2×D411yescharacteristic
86C22×C4×C47C2×D411yescharacteristic
87C22×C4×C47#4111yescharacteristic
88SD16×C47—82no—
89SD16×C47—82no—
90M16×C47—21no—
91M16×C47—21no—
92M16×C47—21no—
93M16×C47—41no—
94M16×C47—41no—
95M16×C47SD1612yescomplemented
96C2×C8×C47—21no—
97C2×C8×C47—21no—
98C2×C8×C47—21no—
99C2×C8×C47—21no—
100C2×C8×C47—42no—
101C2×C8×C47—41no—
102C2×C8×C47—41no—
103C4⋊C4×C47—22no—
104C4⋊C4×C47—21no—
105C4⋊C4×C47—21no—
106C4⋊C4×C47—41no—
107C4⋊C4×C47—41no—
108C4⋊C4×C47—41no—
109C4⋊C4×C47—41no—
110C4⋊C4×C47—41no—
111C22⋊C4×C47—41no—
112C22⋊C4×C47—41no—
113C42×C47—41no—
114C42×C47—41no—
115C42×C47C2×D411yescharacteristic
116C42×C47C2×D411yescharacteristic
117C42×C47#4111yescharacteristic
118C42×C47#4111yescharacteristic
119C23×C47—41no—
120C23×C47#12111yescharacteristic
121Q8×C47—44no—
122Q8×C47—42no—
123Q8×C47—42no—
124Q8×C47—41no—
125Q8×C47—41no—
126D4×C47—41no—
127D4×C47—41no—
128D4×C47—41no—
129D4×C47—41no—
130D4×C47—81no—
131D4×C47—81no—
132D4×C47—81no—
133C2×C4×C47—21no—
134C2×C4×C47—21no—
135C2×C4×C47—41no—
136C2×C4×C47—42no—
137C2×C4×C47—41no—
138C2×C4×C47—42no—
139C2×C4×C47—81no—
140C2×C4×C47—81no—
141C2×C4×C47—81no—
142C2×C4×C47—81no—
143C2×C4×C47—82no—
144C2×C4×C47#12011yescharacteristic
145C2×C4×C47#12111yescharacteristic
146C2×C4×C47#12111yescharacteristic
147C2×C4×C47#12311yescharacteristic
148C2×C4×C47#12311yescharacteristic
149C2×C4×C47#12411yescharacteristic
150C2×C4×C47C2×SD1611yescharacteristic
151C2×C4×C47#13511yescharacteristic
152C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C47#13711yescharacteristic
154C8×C47—22no—
155C8×C47—41no—
156C8×C47—41no—
157C8×C47—41no—
158C8×C47—81no—
159C8×C47—81no—
160#10501C4711yesmaximal, characteristic, direct product factor, Sylow
161C22×C47—21no—
162C22×C47—21no—
163C22×C47—81no—
164C22×C47—81no—
165C22×C47—81no—
166C22×C47#39411yescharacteristic
167C22×C47#46011yescharacteristic
168C22×C47#46411yescharacteristic
169C4×C47—21no—
170C4×C47—21no—
171C4×C47—21no—
172C4×C47—82no—
173C4×C47—81no—
174C4×C47—82no—
175C4×C47#45311yescharacteristic
176C4×C47#45511yescharacteristic
177C4×C47#46111yescharacteristic
178C4×C47#46311yescharacteristic
179C4×C47#46511yescharacteristic
180C4×C47#46811yescharacteristic
181#3206C2×C4711yescharacteristic
182#1997C2×C4711yescharacteristic, complemented
183#1981C2×C4711yescharacteristic, complemented
184#1980C2×C4711yescharacteristic
185#1565C2×C4711yescharacteristic, complemented
186#1547C2×C4711yescharacteristic
187#1303C2×C4711yescharacteristic, complemented
188C2×C47—21no—
189C2×C47—21no—
190C2×C47—161no—
191C2×C47#203711yescharacteristic
192C2×C47#204911yescharacteristic
193C2×C47#205511yescharacteristic
194#532C22×C4711yescharacteristic
195C2×C4⋊Q8C22×C4711yescharacteristic
196#492—21no—
197#487—21no—
198#461—21no—
199#461—21no—
200#448—22no—
201#431C22×C4711yescharacteristic
202#423C22×C4711yescharacteristic
203C2×C4⋊C8C22×C4711yescharacteristic
204C2×#104—21no—
205C2×#104—21no—
206C2×#103—22no—
207C4×M16C22×C4711yescharacteristic
208C4×C4⋊C4C22×C4711yescharacteristic
209#343—21no—
210#343—21no—
211#335—21no—
212#334—21no—
213#332—21no—
214#331—21no—
215C47#1050111yescharacteristic, direct product factor, Sylow
216C2×#41—21no—
217C22×Q8D4×C4712yes—
218C2×SD16—22no—
219C2×SD16—22no—
220C2×M16—21no—
221C2×M16D4×C4711yescharacteristic
222C2×M16D4×C4711yescharacteristic
223C22×C8—21no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226C4⋊Q8—21no—
227C4⋊Q8—21no—
228C4⋊Q8D4×C4711yescharacteristic
229#127D4×C4711yescharacteristic
230#124—21no—
231#121—21no—
232#121—21no—
233C4×D4—21no—
234C4×D4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C42—21no—
239C2×C42C23×C4711yescharacteristic
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8D4×C4711yescharacteristic
245C4⋊C8D4×C4711yescharacteristic
246#104—42no—
247#104—42no—
248#103—22no—
249#103—22no—
250#103—44no—
251C22⋊C8—21no—
252#97—21no—
253C4×C8—21no—
254C4×C8—21no—
255#95—21no—
256#41—41no—
257#41—41no—
258#41—41no—
259#41—41no—
260C2×Q8—22no—
261C2×Q8—21no—
262C2×Q8—22no—
263C2×Q8—42no—
264C2×Q8—42no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—41no—
269C22×C4—22no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4C2×D4×C4711yescharacteristic
273C22×C4C2×D4×C4711yescharacteristic
274C22×C4#41×C4711yescharacteristic
275SD16—82no—
276SD16—82no—
277M16—21no—
278M16—21no—
279M16—21no—
280M16—41no—
281M16—41no—
282M16SD16×C4712yescomplemented
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—21no—
287C2×C8—42no—
288C2×C8—41no—
289C2×C8—41no—
290C4⋊C4—22no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C42—41no—
301C42—41no—
302C42C2×D4×C4711yescharacteristic
303C42C2×D4×C4711yescharacteristic
304C42#41×C4711yescharacteristic
305C42#41×C4711yescharacteristic
306C23—41no—
307C23#121×C4711yescharacteristic
308Q8—44no—
309Q8—42no—
310Q8—42no—
311Q8—41no—
312Q8—41no—
313D4—41no—
314D4—41no—
315D4—41no—
316D4—41no—
317D4—81no—
318D4—81no—
319D4—81no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—82no—
331C2×C4#120×C4711yescharacteristic
332C2×C4#121×C4711yescharacteristic
333C2×C4#121×C4711yescharacteristic
334C2×C4#123×C4711yescharacteristic
335C2×C4#123×C4711yescharacteristic
336C2×C4#124×C4711yescharacteristic
337C2×C4C2×SD16×C4711yescharacteristic
338C2×C4#135×C4711yescharacteristic
339C2×C4AGL(1,ℤ/8)×C4711yescharacteristic
340C2×C4#137×C4711yescharacteristic
341C8—22no—
342C8—41no—
343C8—41no—
344C8—41no—
345C8—81no—
346C8—81no—
347C22—21no—
348C22—21no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22C47×#39411yescharacteristic
353C22C47×#46011yescharacteristic
354C22C47×#46411yescharacteristic
355C4—21no—
356C4—21no—
357C4—21no—
358C4—82no—
359C4—82no—
360C4—81no—
361C4C47×#45311yescharacteristic
362C4C47×#45511yescharacteristic
363C4C47×#46111yescharacteristic
364C4C47×#46311yescharacteristic
365C4C47×#46511yescharacteristic
366C4C47×#46811yescharacteristic
367C2—21no—
368C2—21no—
369C2—161no—
370C2C47×#203711yescharacteristic
371C2C47×#204911yescharacteristic
372C2C47×#205511yescharacteristic
subgroupG/H
center, socleC22×C47#394
commutator, Frattini, cosocleC2×C42C23×C47
prime radicalC47×#532C22
LCSG ▷ C2×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×#1997C2semidirect
3. C47×#1981C2semidirect
5. C47×#1565C2semidirect
7. C47×#1303C2semidirect
95. M16×C47SD16semidirect
160. #10501C47direct (N × H)
182. #1997C2×C47semidirect
183. #1981C2×C47semidirect
185. #1565C2×C47semidirect
187. #1303C2×C47semidirect
215. C47#10501direct (N × H)
282. M16SD16×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#32062
C47×#19972
C47×#19812
C47×#19802
C47×#15652
C47×#15472
C47×#13032
#1050147