Finite Group Databasebeta

← C47×#8913 #26048611

Subgroups — C47×#8913 #26048611

Order 12032.

428 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 134 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×#2382C211yesmaximal, characteristic
2C47×#1992C211yesmaximal, characteristic
3C47×#1847C212yesmaximal
4C2×C47×#330C211yesmaximal, characteristic
5C47×#1295C212yesmaximal
6C2×#125×C47C2211yescharacteristic
7C2×#107×C47—22no—
8C2×#106×C47—22no—
9C2×#97×C47C2211yescharacteristic
10C2×#97×C47C2212yes—
11C47×#389—22no—
12C47×#387—22no—
13C47×#387—22no—
14C47×#384C2211yescharacteristic
15C47×#382C2212yes—
16C47×#340—22no—
17C47×#330C414yescomplemented
18C22×C8×C47—22no—
19C22×C8×C47—21no—
20#125×C47—22no—
21#125×C47C2×C412yes—
22#125×C47Q812yes—
23C2×C4⋊C4×C47—22no—
24C2×C4⋊C4×C47—21no—
25C2×C4⋊C4×C47—22no—
26C2×C4⋊C4×C47—22no—
27C2×C4⋊C4×C47D412yes—
28C2×C4⋊C4×C47D412yes—
29C2×C4⋊C4×C47D412yes—
30C2×C42×C47—22no—
31C2×C42×C47C2311yescharacteristic
32#107×C47—44no—
33#106×C47—44no—
34#97×C47—22no—
35#97×C47—22no—
36#97×C47C2×C414yes—
37#95×C47—22no—
38#95×C47—22no—
39#95×C47—22no—
40#95×C47—22no—
41C22×C4×C47—22no—
42C22×C4×C47—22no—
43C22×C4×C47—22no—
44C22×C4×C47—41no—
45C22×C4×C47C2×D411yescharacteristic
46C22×C4×C47C2×D412yes—
47C2×C8×C47—24no—
48C2×C8×C47—24no—
49C2×C8×C47—24no—
50C2×C8×C47—22no—
51C2×C8×C47—41no—
52C2×C8×C47—41no—
53C4⋊C4×C47—24no—
54C4⋊C4×C47—24no—
55C4⋊C4×C47—22no—
56C4⋊C4×C47—42no—
57C4⋊C4×C47—42no—
58C4⋊C4×C47—42no—
59C4⋊C4×C47—42no—
60C4⋊C4×C47—42no—
61C4⋊C4×C47—82no—
62C4⋊C4×C47C4⋊C414yes—
63C42×C47—82no—
64C42×C47C22×C411yescharacteristic
65C42×C47C2×Q811yescharacteristic
66C42×C47#4112yes—
67C23×C47#12011yescharacteristic
68C2×C4×C47—22no—
69C2×C4×C47—21no—
70C2×C4×C47—21no—
71C2×C4×C47—22no—
72C2×C4×C47—24no—
73C2×C4×C47—42no—
74C2×C4×C47—42no—
75C2×C4×C47—42no—
76C2×C4×C47—42no—
77C2×C4×C47—42no—
78C2×C4×C47—42no—
79C2×C4×C47—42no—
80C2×C4×C47—42no—
81C2×C4×C47—82no—
82C2×C4×C47—81no—
83C2×C4×C47C2×C4⋊C411yescharacteristic
84C2×C4×C47C4×D412yes—
85C2×C4×C47C22⋊Q812yes—
86C2×C4×C47#12311yescharacteristic
87C8×C47—28no—
88C8×C47—42no—
89#8913C4711yesmaximal, characteristic, direct product factor, Sylow
90C22×C47#38511yescharacteristic
91C22×C47#45312yes—
92C22×C47#45411yescharacteristic
93C22×C47#45611yescharacteristic
94C22×C47#45612yes—
95C4×C47—21no—
96C4×C47—21no—
97C4×C47—22no—
98C4×C47—22no—
99C4×C47—44no—
100C4×C47—82no—
101C4×C47—82no—
102C4×C47—161no—
103#2382C2×C4711yescharacteristic
104#1992C2×C4711yescharacteristic
105#1847C2×C4712yes—
106C2×#330C2×C4711yescharacteristic
107#1295C2×C4712yes—
108C2×C47#165611yescharacteristic
109C2×C47#166012yes—
110C2×C47#166311yescharacteristic
111C2×C47#185711yescharacteristic
112C2×C47#185912yes—
113C2×#125C22×C4711yescharacteristic
114C2×#107—22no—
115C2×#106—22no—
116C2×#97C22×C4711yescharacteristic
117C2×#97C22×C4712yes—
118#389—22no—
119#387—22no—
120#387—22no—
121#384C22×C4711yescharacteristic
122#382C22×C4712yes—
123#340—22no—
124#330C4×C4714yescomplemented
125C47#891311yescharacteristic, direct product factor, Sylow
126C22×C8—22no—
127C22×C8—21no—
128#125—22no—
129#125C2×C4×C4712yes—
130#125Q8×C4712yes—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—21no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4D4×C4712yes—
136C2×C4⋊C4D4×C4712yes—
137C2×C4⋊C4D4×C4712yes—
138C2×C42—22no—
139C2×C42C23×C4711yescharacteristic
140#107—44no—
141#106—44no—
142#97—22no—
143#97—22no—
144#97C2×C4×C4714yes—
145#95—22no—
146#95—22no—
147#95—22no—
148#95—22no—
149C22×C4—22no—
150C22×C4—22no—
151C22×C4—22no—
152C22×C4—41no—
153C22×C4C2×D4×C4711yescharacteristic
154C22×C4C2×D4×C4712yes—
155C2×C8—24no—
156C2×C8—24no—
157C2×C8—24no—
158C2×C8—22no—
159C2×C8—41no—
160C2×C8—41no—
161C4⋊C4—24no—
162C4⋊C4—24no—
163C4⋊C4—22no—
164C4⋊C4—42no—
165C4⋊C4—42no—
166C4⋊C4—42no—
167C4⋊C4—42no—
168C4⋊C4—42no—
169C4⋊C4—82no—
170C4⋊C4C4⋊C4×C4714yes—
171C42—82no—
172C42C22×C4×C4711yescharacteristic
173C42C2×Q8×C4711yescharacteristic
174C42#41×C4712yes—
175C23#120×C4711yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—24no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—82no—
190C2×C4—81no—
191C2×C4C2×C4⋊C4×C4711yescharacteristic
192C2×C4C4×D4×C4712yes—
193C2×C4C22⋊Q8×C4712yes—
194C2×C4#123×C4711yescharacteristic
195C8—28no—
196C8—42no—
197C22C47×#38511yescharacteristic
198C22C47×#45312yes—
199C22C47×#45411yescharacteristic
200C22C47×#45611yescharacteristic
201C22C47×#45612yes—
202C4—21no—
203C4—21no—
204C4—22no—
205C4—22no—
206C4—44no—
207C4—82no—
208C4—82no—
209C4—161no—
210C2C47×#165611yescharacteristic
211C2C47×#166012yes—
212C2C47×#166311yescharacteristic
213C2C47×#185711yescharacteristic
214C2C47×#185912yes—
subgroupG/H
center, socle, prime radicalC23×C47#120
commutatorC42C22×C4×C47
Frattini, cosocleC2×C42C23×C47
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C47 ◁ C2×C42×C47 ◁ G

Complements

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

NH ≅ G/Ntype
17. C47×#330C4semidirect
89. #8913C47direct (N × H)
124. #330C4×C47semidirect
125. C47#8913direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#23822
C47×#19922
C47×#18472
C2×C47×#3302
C47×#12952
#891347