Finite Group Databasebeta

← C47×#10158 #26049856

Subgroups — C47×#10158 #26049856

Order 12032.

514 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3226C211yesmaximal, characteristic
2C47×#3141C211yesmaximal, characteristic
3C2×C47×#487C211yesmaximal, characteristic, complemented
4C47×#1966C211yesmaximal, characteristic, complemented
5C47×#1549C211yesmaximal, characteristic, complemented
6C47×#1492C211yesmaximal, characteristic
7C47×#1278C211yesmaximal, characteristic, complemented
8C47×#532C2211yescharacteristic
9C2×C4⋊Q8×C47C2211yescharacteristic
10C2×C4⋊Q8×C47C2211yescharacteristic
11C47×#500—21no—
12C47×#489—22no—
13C47×#487—22no—
14C47×#487—22no—
15C47×#487—21no—
16C47×#486—21no—
17C47×#486—21no—
18C47×#480—22no—
19C47×#474—22no—
20C47×#431C2211yescharacteristic
21C47×#423C2211yescharacteristic
22C47×#417—22no—
23C2×#103×C47—22no—
24C2×#101×C47—22no—
25C4×M16×C47C2211yescharacteristic
26C2×C4×C8×C47C2211yescharacteristic
27C47×#332—22no—
28C47×D4⋊C8—22no—
29C2×#41×C47—21no—
30C22×Q8×C47—21no—
31C22×Q8×C47—21no—
32C2×M16×C47—21no—
33C2×M16×C47D412yes—
34C22×C8×C47—21no—
35C4⋊Q8×C47—21no—
36C4⋊Q8×C47—21no—
37C4⋊Q8×C47—21no—
38C4⋊Q8×C47—21no—
39C4⋊Q8×C47—21no—
40C4⋊Q8×C47—21no—
41C4⋊Q8×C47—21no—
42C4⋊Q8×C47D412yes—
43C4⋊Q8×C47D411yescharacteristic
44#127×C47D411yescharacteristic
45#124×C47—21no—
46#121×C47—21no—
47#121×C47—21no—
48C4×D4×C47—21no—
49C4×D4×C47—21no—
50C2×C4⋊C4×C47—21no—
51C2×C4⋊C4×C47—21no—
52C2×C4⋊C4×C47—21no—
53C2×C4⋊C4×C47D412yes—
54C2×C42×C47C2311yescharacteristic
55#107×C47—24no—
56C4⋊C8×C47—21no—
57C4⋊C8×C47—21no—
58C4⋊C8×C47D412yes—
59#103×C47—28no—
60#103×C47—24no—
61#102×C47—24no—
62#102×C47—24no—
63#101×C47—44no—
64C22⋊C8×C47—21no—
65#97×C47—21no—
66C4×C8×C47—21no—
67C4×C8×C47—21no—
68C4×C8×C47—21no—
69C4×C8×C47D412yes—
70#41×C47—42no—
71#41×C47—42no—
72C2×Q8×C47—21no—
73C2×Q8×C47—22no—
74C2×Q8×C47—44no—
75C2×Q8×C47—41no—
76C2×Q8×C47—41no—
77C2×Q8×C47—41no—
78C2×Q8×C47—42no—
79C2×Q8×C47—42no—
80C2×D4×C47—21no—
81C2×D4×C47—21no—
82C2×D4×C47—21no—
83C2×D4×C47—41no—
84C22×C4×C47—22no—
85C22×C4×C47—41no—
86C22×C4×C47—41no—
87C22×C4×C47C2×D411yescharacteristic
88C22×C4×C47C2×D411yescharacteristic
89C22×C4×C47#4111yescharacteristic
90M16×C47—22no—
91M16×C47—22no—
92M16×C47—42no—
93C2×C8×C47—22no—
94C2×C8×C47—22no—
95C2×C8×C47—22no—
96C2×C8×C47—42no—
97C2×C8×C47—41no—
98C4⋊C4×C47—22no—
99C4⋊C4×C47—22no—
100C4⋊C4×C47—21no—
101C4⋊C4×C47—22no—
102C4⋊C4×C47—22no—
103C4⋊C4×C47—21no—
104C4⋊C4×C47—41no—
105C4⋊C4×C47—41no—
106C4⋊C4×C47—41no—
107C4⋊C4×C47—41no—
108C22⋊C4×C47—41no—
109C22⋊C4×C47—41no—
110C42×C47C2×D411yescharacteristic
111C42×C47C2×D411yescharacteristic
112C42×C47C2×D411yescharacteristic
113C42×C47C2×D411yescharacteristic
114C23×C47—41no—
115C23×C47#12111yescharacteristic
116Q8×C47—44no—
117Q8×C47—42no—
118Q8×C47—82no—
119Q8×C47—82no—
120Q8×C47—81no—
121Q8×C47—81no—
122D4×C47—42no—
123D4×C47—42no—
124D4×C47—42no—
125D4×C47—82no—
126C2×C4×C47—22no—
127C2×C4×C47—22no—
128C2×C4×C47—41no—
129C2×C4×C47—42no—
130C2×C4×C47—42no—
131C2×C4×C47—44no—
132C2×C4×C47—82no—
133C2×C4×C47—81no—
134C2×C4×C47—81no—
135C2×C4×C47#12011yescharacteristic
136C2×C4×C47#12011yescharacteristic
137C2×C4×C47#12011yescharacteristic
138C2×C4×C47#12111yescharacteristic
139C2×C4×C47#12111yescharacteristic
140C2×C4×C47#12711yescharacteristic
141C2×C4×C47#13512yes—
142C2×C4×C47AGL(1,ℤ/8)12yes—
143C8×C47—42no—
144C8×C47—42no—
145C8×C47—42no—
146C8×C47—81no—
147#10158C4711yesmaximal, characteristic, direct product factor, Sylow
148C22×C47—21no—
149C22×C47—21no—
150C22×C47—81no—
151C22×C47—81no—
152C22×C47—81no—
153C22×C47#39211yescharacteristic
154C22×C47#46312yes—
155C4×C47—21no—
156C4×C47—21no—
157C4×C47—82no—
158C4×C47—82no—
159C4×C47—81no—
160C4×C47#44912yes—
161C4×C47#45412yes—
162C4×C47#47312yes—
163C4×C47#49511yescharacteristic
164C4×C47#49611yescharacteristic
165#3226C2×C4711yescharacteristic
166#3141C2×C4711yescharacteristic
167C2×#487C2×C4711yescharacteristic, complemented
168#1966C2×C4711yescharacteristic, complemented
169#1549C2×C4711yescharacteristic, complemented
170#1492C2×C4711yescharacteristic
171#1278C2×C4711yescharacteristic, complemented
172C2×C47—22no—
173C2×C47—161no—
174C2×C47#200311yescharacteristic
175C2×C47#201211yescharacteristic
176C2×C47#202011yescharacteristic
177#532C22×C4711yescharacteristic
178C2×C4⋊Q8C22×C4711yescharacteristic
179C2×C4⋊Q8C22×C4711yescharacteristic
180#500—21no—
181#489—22no—
182#487—22no—
183#487—21no—
184#487—22no—
185#486—21no—
186#486—21no—
187#480—22no—
188#474—22no—
189#431C22×C4711yescharacteristic
190#423C22×C4711yescharacteristic
191#417—22no—
192C2×#103—22no—
193C2×#101—22no—
194C4×M16C22×C4711yescharacteristic
195C2×C4×C8C22×C4711yescharacteristic
196#332—22no—
197D4⋊C8—22no—
198C47#1015811yescharacteristic, direct product factor, Sylow
199C2×#41—21no—
200C22×Q8—21no—
201C22×Q8—21no—
202C2×M16—21no—
203C2×M16D4×C4712yes—
204C22×C8—21no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8D4×C4712yes—
213C4⋊Q8D4×C4711yescharacteristic
214#127D4×C4711yescharacteristic
215#124—21no—
216#121—21no—
217#121—21no—
218C4×D4—21no—
219C4×D4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4D4×C4712yes—
224C2×C42C23×C4711yescharacteristic
225#107—24no—
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8D4×C4712yes—
229#103—28no—
230#103—24no—
231#102—24no—
232#102—24no—
233#101—44no—
234C22⋊C8—21no—
235#97—21no—
236C4×C8—21no—
237C4×C8—21no—
238C4×C8—21no—
239C4×C8D4×C4712yes—
240#41—42no—
241#41—42no—
242C2×Q8—21no—
243C2×Q8—22no—
244C2×Q8—44no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—42no—
249C2×Q8—42no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—41no—
254C22×C4—22no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4C2×D4×C4711yescharacteristic
258C22×C4C2×D4×C4711yescharacteristic
259C22×C4#41×C4711yescharacteristic
260M16—22no—
261M16—22no—
262M16—42no—
263C2×C8—22no—
264C2×C8—22no—
265C2×C8—22no—
266C2×C8—42no—
267C2×C8—41no—
268C4⋊C4—22no—
269C4⋊C4—22no—
270C4⋊C4—22no—
271C4⋊C4—21no—
272C4⋊C4—22no—
273C4⋊C4—21no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C42C2×D4×C4711yescharacteristic
281C42C2×D4×C4711yescharacteristic
282C42C2×D4×C4711yescharacteristic
283C42C2×D4×C4711yescharacteristic
284C23—41no—
285C23#121×C4711yescharacteristic
286Q8—44no—
287Q8—42no—
288Q8—82no—
289Q8—82no—
290Q8—81no—
291Q8—81no—
292D4—42no—
293D4—42no—
294D4—42no—
295D4—82no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—44no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—82no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4#120×C4711yescharacteristic
306C2×C4#120×C4711yescharacteristic
307C2×C4#120×C4711yescharacteristic
308C2×C4#121×C4711yescharacteristic
309C2×C4#121×C4711yescharacteristic
310C2×C4#127×C4711yescharacteristic
311C2×C4#135×C4712yes—
312C2×C4AGL(1,ℤ/8)×C4712yes—
313C8—42no—
314C8—42no—
315C8—42no—
316C8—81no—
317C22—21no—
318C22—21no—
319C22—81no—
320C22—81no—
321C22—81no—
322C22C47×#39211yescharacteristic
323C22C47×#46312yes—
324C4—21no—
325C4—21no—
326C4—82no—
327C4—81no—
328C4—82no—
329C4C47×#44912yes—
330C4C47×#45412yes—
331C4C47×#47312yes—
332C4C47×#49511yescharacteristic
333C4C47×#49611yescharacteristic
334C2—22no—
335C2—161no—
336C2C47×#200311yescharacteristic
337C2C47×#201211yescharacteristic
338C2C47×#202011yescharacteristic
subgroupG/H
center, socleC22×C47#392
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
3. C2×C47×#487C2semidirect
4. C47×#1966C2semidirect
5. C47×#1549C2semidirect
7. C47×#1278C2semidirect
147. #10158C47direct (N × H)
167. C2×#487C2×C47semidirect
168. #1966C2×C47semidirect
169. #1549C2×C47semidirect
171. #1278C2×C47semidirect
198. C47#10158direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#32262
C47×#31412
C2×C47×#4872
C47×#19662
C47×#15492
C47×#14922
C47×#12782
#1015847