Finite Group Databasebeta

← C47×#10325 #26050023

Subgroups — C47×#10325 #26050023

Order 12032.

602 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3189C211yesmaximal, characteristic
2C47×#2855C212yesmaximal
3C47×#1817C211yesmaximal, characteristic
4C47×#1520C212yesmaximal
5C47×#1289C211yesmaximal, characteristic
6C2×C22⋊Q8×C47C2212yes—
7C22×C42×C47C2211yescharacteristic
8C47×#484—22no—
9C47×#467—22no—
10C47×#451—22no—
11C2×C22⋊C8×C47C2211yescharacteristic
12C2×C22⋊C8×C47C2211yescharacteristic
13C47×#391—22no—
14C47×#389—22no—
15C47×#387—24no—
16C47×#385—22no—
17C47×#381—22no—
18C47×#380C2212yes—
19C47×#336—22no—
20C47×#328—24no—
21C22×Q8×C47D412yes—
22C23×C4×C47D411yescharacteristic
23C23×C4×C47D411yescharacteristic
24C23×C4×C47C2311yescharacteristic
25C2×Q16×C47—22no—
26C22×C8×C47—21no—
27C22×C8×C47D412yes—
28C22⋊Q8×C47—22no—
29C22⋊Q8×C47—22no—
30C22⋊Q8×C47—22no—
31C22⋊Q8×C47—22no—
32C2×C4⋊C4×C47—24no—
33C2×C4⋊C4×C47—22no—
34C2×C4⋊C4×C47—22no—
35C2×C4⋊C4×C47D412yes—
36C2×C22⋊C4×C47—22no—
37C2×C22⋊C4×C47—22no—
38C2×C42×C47—21no—
39C2×C42×C47—22no—
40C2×C42×C47—22no—
41C2×C42×C47—21no—
42#107×C47—22no—
43#103×C47—24no—
44C22⋊C8×C47—22no—
45C22⋊C8×C47—22no—
46#95×C47—24no—
47#95×C47—24no—
48#95×C47—24no—
49#95×C47D414yes—
50C24×C47C2×D411yescharacteristic
51C2×Q8×C47—22no—
52C2×Q8×C47—22no—
53C2×Q8×C47—44no—
54C22×C4×C47—22no—
55C22×C4×C47—22no—
56C22×C4×C47—21no—
57C22×C4×C47—21no—
58C22×C4×C47—21no—
59C22×C4×C47—22no—
60C22×C4×C47—22no—
61C22×C4×C47—24no—
62C22×C4×C47—22no—
63C22×C4×C47—42no—
64C22×C4×C47—42no—
65C22×C4×C47Q1612yescomplemented
66C22×C4×C47C2×D412yes—
67C22×C4×C47C2×D411yescharacteristic
68C22×C4×C47C2×D412yes—
69C22×C4×C47#4111yescharacteristic
70Q16×C47—82no—
71C2×C8×C47—22no—
72C2×C8×C47—42no—
73C2×C8×C47—42no—
74C2×C8×C47—41no—
75C4⋊C4×C47—22no—
76C4⋊C4×C47—22no—
77C4⋊C4×C47—44no—
78C4⋊C4×C47—48no—
79C4⋊C4×C47—42no—
80C4⋊C4×C47—42no—
81C22⋊C4×C47—42no—
82C22⋊C4×C47—42no—
83C22⋊C4×C47—42no—
84C22⋊C4×C47—42no—
85C42×C47—41no—
86C42×C47—42no—
87C42×C47—41no—
88C23×C47—41no—
89C23×C47—41no—
90C23×C47#12012yes—
91C23×C47#12111yescharacteristic
92C23×C47C2×Q1611yescharacteristic
93C23×C47#13511yescharacteristic
94C23×C47#13712yes—
95Q8×C47—44no—
96Q8×C47—82no—
97C2×C4×C47—24no—
98C2×C4×C47—22no—
99C2×C4×C47—24no—
100C2×C4×C47—22no—
101C2×C4×C47—24no—
102C2×C4×C47—22no—
103C2×C4×C47—42no—
104C2×C4×C47—41no—
105C2×C4×C47—42no—
106C2×C4×C47—41no—
107C2×C4×C47—41no—
108C2×C4×C47—41no—
109C2×C4×C47—42no—
110C2×C4×C47—41no—
111C2×C4×C47—44no—
112C2×C4×C47—44no—
113C2×C4×C47—44no—
114C2×C4×C47—44no—
115C2×C4×C47—42no—
116C2×C4×C47—42no—
117C2×C4×C47—44no—
118C2×C4×C47#12011yescharacteristic
119C2×C4×C47#12112yes—
120C2×C4×C47#12711yescharacteristic
121C8×C47—42no—
122C8×C47—81no—
123#10325C4711yesmaximal, characteristic, direct product factor, Sylow
124C22×C47—22no—
125C22×C47—21no—
126C22×C47—22no—
127C22×C47—21no—
128C22×C47—41no—
129C22×C47—41no—
130C22×C47—42no—
131C22×C47#39211yescharacteristic
132C22×C47#45112yes—
133C22×C47#45212yes—
134C22×C47#46711yescharacteristic
135C22×C47#47011yescharacteristic
136C4×C47—21no—
137C4×C47—22no—
138C4×C47—42no—
139C4×C47—42no—
140C4×C47—84no—
141C4×C47—82no—
142C4×C47—82no—
143C4×C47#45812yes—
144#3189C2×C4711yescharacteristic
145#2855C2×C4712yes—
146#1817C2×C4711yescharacteristic
147#1520C2×C4712yes—
148#1289C2×C4711yescharacteristic
149C2×C47—22no—
150C2×C47—22no—
151C2×C47—21no—
152C2×C47—21no—
153C2×C47#200111yescharacteristic
154C2×C47#201011yescharacteristic
155C2×C47#202211yescharacteristic
156C2×C22⋊Q8C22×C4712yes—
157C22×C42C22×C4711yescharacteristic
158#484—22no—
159#467—22no—
160#451—22no—
161C2×C22⋊C8C22×C4711yescharacteristic
162C2×C22⋊C8C22×C4711yescharacteristic
163#391—22no—
164#389—22no—
165#387—24no—
166#385—22no—
167#381—22no—
168#380C22×C4712yes—
169#336—22no—
170#328—24no—
171C47#1032511yescharacteristic, direct product factor, Sylow
172C22×Q8D4×C4712yes—
173C23×C4D4×C4711yescharacteristic
174C23×C4D4×C4711yescharacteristic
175C23×C4C23×C4711yescharacteristic
176C2×Q16—22no—
177C22×C8—21no—
178C22×C8D4×C4712yes—
179C22⋊Q8—22no—
180C22⋊Q8—22no—
181C22⋊Q8—22no—
182C22⋊Q8—22no—
183C2×C4⋊C4—24no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4—22no—
186C2×C4⋊C4D4×C4712yes—
187C2×C22⋊C4—22no—
188C2×C22⋊C4—22no—
189C2×C42—21no—
190C2×C42—22no—
191C2×C42—22no—
192C2×C42—21no—
193#107—22no—
194#103—24no—
195C22⋊C8—22no—
196C22⋊C8—22no—
197#95—24no—
198#95—24no—
199#95—24no—
200#95D4×C4714yes—
201C24C2×D4×C4711yescharacteristic
202C2×Q8—22no—
203C2×Q8—22no—
204C2×Q8—44no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—24no—
213C22×C4—22no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4Q16×C4712yescomplemented
217C22×C4C2×D4×C4712yes—
218C22×C4C2×D4×C4711yescharacteristic
219C22×C4C2×D4×C4712yes—
220C22×C4#41×C4711yescharacteristic
221Q16—82no—
222C2×C8—22no—
223C2×C8—42no—
224C2×C8—42no—
225C2×C8—41no—
226C4⋊C4—22no—
227C4⋊C4—22no—
228C4⋊C4—44no—
229C4⋊C4—48no—
230C4⋊C4—42no—
231C4⋊C4—42no—
232C22⋊C4—42no—
233C22⋊C4—42no—
234C22⋊C4—42no—
235C22⋊C4—42no—
236C42—41no—
237C42—42no—
238C42—41no—
239C23—41no—
240C23—41no—
241C23#120×C4712yes—
242C23#121×C4711yescharacteristic
243C23C2×Q16×C4711yescharacteristic
244C23#135×C4711yescharacteristic
245C23#137×C4712yes—
246Q8—44no—
247Q8—82no—
248C2×C4—24no—
249C2×C4—22no—
250C2×C4—24no—
251C2×C4—22no—
252C2×C4—24no—
253C2×C4—22no—
254C2×C4—42no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—44no—
263C2×C4—44no—
264C2×C4—44no—
265C2×C4—44no—
266C2×C4—44no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4#120×C4711yescharacteristic
270C2×C4#121×C4712yes—
271C2×C4#127×C4711yescharacteristic
272C8—42no—
273C8—81no—
274C22—22no—
275C22—21no—
276C22—22no—
277C22—21no—
278C22—41no—
279C22—41no—
280C22—42no—
281C22C47×#39211yescharacteristic
282C22C47×#45112yes—
283C22C47×#45212yes—
284C22C47×#46711yescharacteristic
285C22C47×#47011yescharacteristic
286C4—21no—
287C4—22no—
288C4—42no—
289C4—42no—
290C4—84no—
291C4—82no—
292C4—82no—
293C4C47×#45812yes—
294C2—22no—
295C2—22no—
296C2—21no—
297C2—21no—
298C2C47×#200111yescharacteristic
299C2C47×#201011yescharacteristic
300C2C47×#202211yescharacteristic
subgroupG/H
center, socleC22×C47#392
commutator, Frattini, cosocleC23×C4C23×C47
prime radicalC24×C47C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C47 ◁ C23×C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
65. C22×C4×C47Q16semidirect
123. #10325C47direct (N × H)
171. C47#10325direct (N × H)
216. C22×C4Q16×C47semidirect

Maximal subgroups

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

subgroupindex
C47×#31892
C47×#28552
C47×#18172
C47×#15202
C47×#12892
#1032547