Finite Group Databasebeta

← D47×#1356 #26127450

Subgroups — D47×#1356 #26127450

Order 12032.

314 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 71 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
1#491×D47C211yesmaximal, characteristic
2#347×D47C212yesmaximal
3#20241423C211yesmaximal, characteristic, complemented
4#20241422C212yesmaximal, complemented
5C47×#1356C211yesmaximal, characteristic, complemented
6C4⋊Q8×D47C411yescharacteristic
7#125×D47C411yescharacteristic
8M32×D47—22no—
9#15689493C411yescharacteristic
10#15689492C2211yescharacteristic
11#15689491C411yescharacteristic
12#15689490—22no—
13#103×D47—22no—
14#97×D47C2211yescharacteristic
15#15688901C2212yes—
16#15688900—22no—
17C47×#491C2211yescharacteristic
18C47×#347C2212yes—
19C2×Q8×D47—21no—
20C2×C8×D47D412yes—
21#13094024C2×C411yescharacteristic
22#13094023—41no—
23#13094022—21no—
24#13094016C2×C411yescharacteristic
25#13094015—21no—
26#13094014—41no—
27C4⋊C4×D47—21no—
28C4⋊C4×D47—41no—
29C4⋊C4×D47—41no—
30C42×D47C2×C411yescharacteristic
31#13093964—22no—
32#13093963—24no—
33C16×D47—24no—
34#13093949—22no—
35#13093948—22no—
36#13093947—22no—
37#13093935C2×C411yescharacteristic
38#13093934D412yes—
39C4⋊Q8×C47C2×C411yescharacteristic
40#125×C47C2×C411yescharacteristic
41M32×C47—22no—
42#103×C47—22no—
43#97×C47C2311yescharacteristic
44C2×Q8×C47—21no—
45Q8×D47—42no—
46Q8×D47—42no—
47C2×C4×D47—21no—
48C2×C4×D47—41no—
49C2×C4×D47—41no—
50C2×C4×D47C22⋊C411yescharacteristic
51C2×Dic94—21no—
52C2×Dic94—41no—
53C2×C8×C47C2×D412yes—
54C4⋊C4×C47—21no—
55C4⋊C4×C47—41no—
56C4⋊C4×C47—41no—
57C42×C47C22×C411yescharacteristic
58C4⋊Dic47—21no—
59C4⋊Dic47—41no—
60C4⋊Dic47—41no—
61Dic47⋊C4—41no—
62Dic47⋊C4—42no—
63Dic47⋊C4—41no—
64Dic47⋊C4—41no—
65C4×Dic47—21no—
66C4×Dic47C22⋊C411yescharacteristic
67C2×C47⋊C8C22⋊C412yes—
68C8×D47—22no—
69C8×D47—22no—
70C16×C47—24no—
71C47⋊C16—24no—
72C22×D47#10011yescharacteristic
73Q8×C47—42no—
74C2×C4×C47—21no—
75C2×C4×C47—41no—
76C2×C4×C47—41no—
77C2×C4×C47C2×C22⋊C411yescharacteristic
78C2×Dic47—21no—
79C2×Dic47—41no—
80C2×Dic47—41no—
81C2×Dic47#10011yescharacteristic
82C4×D47—42no—
83C4×D47—82no—
84C4×D47—81no—
85C4×D47—81no—
86C4×D47#10412yes—
87C4×D47#10412yes—
88Dic94—42no—
89Dic94—82no—
90C8×C47—22no—
91C47⋊C8—22no—
92C2×#1356—471nomaximal, Sylow
93C22×C47C2×#10011yescharacteristic
94C2×D47—22no—
95C2×D47#32911yescharacteristic
96C2×D47#32911yescharacteristic
97C4×C47—41no—
98C4×C47—81no—
99C4×C47—81no—
100C4×C47C2×#10412yes—
101Dic47—41no—
102Dic47—81no—
103Dic47—81no—
104Dic47#32912yes—
105C2×#491—471no—
106C2×#347—472no—
107#1356—471no—
108#1356—472no—
109#1356D4711yescharacteristic, direct product factor
110C2×C47—21no—
111C2×C47C2×#32911yescharacteristic
112D47—21no—
113D47#135612yesdirect product factor
114C2×C4⋊Q8—471no—
115C2×#125—471no—
116C2×M32—942no—
117#491—471no—
118#491—471no—
119#491—471no—
120#491—942no—
121#491C2×D4711yescharacteristic
122C2×#103—942no—
123C2×#97—471no—
124#347—472no—
125#347—942no—
126#347C2×D4712yes—
127C47C2×#135611yescharacteristic, complemented, Sylow
128C22×Q8—941no—
129C22×C8—472no—
130C4⋊Q8—471no—
131C4⋊Q8—941no—
132C4⋊Q8—1881no—
133C4⋊Q8C4×D4711yescharacteristic
134#125—471no—
135#125—941no—
136#125—1881no—
137#125C4×D4711yescharacteristic
138C2×C4⋊C4—941no—
139C2×C4⋊C4—1881no—
140C2×C4⋊C4—1881no—
141C2×C42—471no—
142M32—22no—
143M32—944no—
144M32—942no—
145C2×C16—944no—
146#103—22no—
147#103—942no—
148#103—942no—
149#103—942no—
150#97—472no—
151#97—471no—
152#97C22×D4711yescharacteristic
153C2×Q8—21no—
154C2×Q8—941no—
155C2×Q8—1881no—
156C2×Q8—1882no—
157C2×Q8—1882no—
158C22×C4—471no—
159C22×C4—941no—
160C22×C4—1881no—
161C22×C4—1881no—
162C2×C8—472no—
163C2×C8—942no—
164C2×C8—942no—
165C2×C8D4×D4712yes—
166C4⋊C4—21no—
167C4⋊C4—41no—
168C4⋊C4—41no—
169C4⋊C4—941no—
170C4⋊C4—1881no—
171C4⋊C4—1881no—
172C4⋊C4—1881no—
173C4⋊C4—1881no—
174C4⋊C4—1882no—
175C4⋊C4—1881no—
176C42—471no—
177C42—941no—
178C42C2×C4×D4711yescharacteristic
179C16—24no—
180C16—944no—
181C23—471no—
182Q8—42no—
183Q8—3762no—
184Q8—1882no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—471no—
189C2×C4—472no—
190C2×C4—472no—
191C2×C4—941no—
192C2×C4—3761no—
193C2×C4—3761no—
194C2×C4—3762no—
195C2×C4—1882no—
196C2×C4—1881no—
197C2×C4—1881no—
198C2×C4C22⋊C4×D4711yescharacteristic
199C8—22no—
200C8—942no—
201C22—471no—
202C22—471no—
203C22—942no—
204C22#100×D4711yescharacteristic
205C4—41no—
206C4—81no—
207C4—81no—
208C4—472no—
209C4—3761no—
210C4—3761no—
211C4—1881no—
212C4#104×D4712yes—
213C2—21no—
214C2—472no—
215C2—941no—
216C2#329×D4711yescharacteristic
subgroupG/H
centerC2#329×D47
commutatorC42×C47C22×C4
Frattini#97C22×D47
FittingC47×#1356C2
socleC2×C47C2×#329
prime radicalC22×D47#100
cosocle#97×C47C23
hypercenter#1356D47
hypocenterC47C2×#1356
LCSG ▷ C42×C47 ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #1356

Complements

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

NH ≅ G/Ntype
3. #20241423C2semidirect
4. #20241422C2semidirect
5. C47×#1356C2semidirect
109. #1356D47direct (N × H)
113. D47#1356direct (N × H)
127. C47C2×#1356semidirect

Maximal subgroups

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

subgroupindex
#491×D472
#347×D472
#202414232
#202414222
C47×#13562
C2×#135647