Finite Group Databasebeta

← #20244379

Subgroups — #20244379

Order 6016.

228 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#13094015C211yesmaximal, characteristic
2#15689146C211yesmaximal, characteristic
3M16×Dic47C211yesmaximal, characteristic
4#15688892C211yesmaximal, characteristic
5#15688891C211yesmaximal, characteristic
6#15688891C211yesmaximal, characteristic
7C47×#343C211yesmaximal, characteristic
8C2×#10625329C2211yescharacteristic
9C2×#10625329C2211yescharacteristic
10#13094015—21no—
11#13094015—21no—
12#13094015—21no—
13#13094015—21no—
14C2×C4⋊Dic47C412yes—
15C2×C4⋊Dic47C2211yescharacteristic
16C2×Dic47⋊C4C412yes—
17C2×C4×Dic47C2211yescharacteristic
18Dic47⋊C8—21no—
19Dic47⋊C8—21no—
20#13093934—21no—
21C8×Dic47—21no—
22C2×M16×C47C2211yescharacteristic
23C2×M16×C47C2211yescharacteristic
24C2×C4⋊C4×C47C2211yescharacteristic
25C22×C4×C47C2×C412yes—
26C22×C4×C47C2311yescharacteristic
27C22×Dic47C2×C412yes—
28C22×Dic47C2×C411yescharacteristic
29C22×Dic47C2×C411yescharacteristic
30M16×C47—21no—
31M16×C47—21no—
32M16×C47—21no—
33M16×C47Q812yes—
34C2×C8×C47—21no—
35C2×C8×C47—21no—
36C4⋊C4×C47—21no—
37C4⋊C4×C47—21no—
38C4⋊Dic47—21no—
39C4⋊Dic47—21no—
40C4⋊Dic47—22no—
41C4⋊Dic47—22no—
42Dic47⋊C4—22no—
43Dic47⋊C4—22no—
44C4×Dic47D411yescharacteristic
45C4×Dic47D411yescharacteristic
46C4×Dic47D411yescharacteristic
47C4×Dic47D411yescharacteristic
48#10625329—21no—
49#10625329—21no—
50#10625329—21no—
51#10625329Q812yes—
52C2×C47⋊C8—21no—
53C2×C47⋊C8—21no—
54C23×C47C22×C411yescharacteristic
55C2×C4×C47—22no—
56C2×C4×C47—42no—
57C2×C4×C47C2×D411yescharacteristic
58C2×C4×C47C2×D411yescharacteristic
59C2×C4×C47C2×Q811yescharacteristic
60C2×C4×C47C2×Q811yescharacteristic
61C2×C4×C47#4111yescharacteristic
62C2×C4×C47#4111yescharacteristic
63C2×Dic47—22no—
64C2×Dic47—41no—
65C2×Dic47—41no—
66C2×Dic47—42no—
67C2×Dic47C22⋊C411yescharacteristic
68C2×Dic47C22⋊C411yescharacteristic
69C2×Dic47C22⋊C411yescharacteristic
70C2×Dic47C22⋊C411yescharacteristic
71C8×C47—22no—
72C8×C47—41no—
73C47⋊C8—22no—
74C47⋊C8—41no—
75C22×C47—21no—
76C22×C47—21no—
77C22×C47C2×C22⋊C411yescharacteristic
78C22×C47C4×Q811yescharacteristic
79C22×C47C4×Q811yescharacteristic
80C4×C47—42no—
81C4×C47C22⋊Q811yescharacteristic
82C4×C47C22⋊Q811yescharacteristic
83C4×C47#12411yescharacteristic
84C4×C47C4⋊Q811yescharacteristic
85Dic47—21no—
86Dic47—21no—
87Dic47—21no—
88Dic47—21no—
89Dic47—42no—
90#1998—471nomaximal, Sylow
91C2×C47—21no—
92C2×C47—21no—
93C2×C47#39111yescharacteristic
94C2×C47#41311yescharacteristic
95C2×C47#41311yescharacteristic
96C2×#125—471no—
97#423—471no—
98C4×M16—471no—
99#343—471no—
100#343—471no—
101#343—471no—
102#343D4711yescharacteristic
103C47#199811yescharacteristic, complemented, Sylow
104C2×M16—471no—
105C2×M16—471no—
106C2×M16C2×D4711yescharacteristic
107C2×M16C2×D4711yescharacteristic
108#125—941no—
109#125—941no—
110#125—941no—
111#125—941no—
112C2×C4⋊C4—472no—
113C2×C4⋊C4—472no—
114C2×C4⋊C4—471no—
115C2×C4⋊C4C2×D4711yescharacteristic
116C2×C42—471no—
117C4⋊C8—941no—
118C4⋊C8—941no—
119#97—941no—
120C4×C8—941no—
121C22×C4—471no—
122C22×C4—471no—
123C22×C4—472no—
124C22×C4C4×D4712yes—
125C22×C4C22×D4711yescharacteristic
126M16—21no—
127M16—21no—
128M16—21no—
129M16—472no—
130M16—941no—
131M16—941no—
132M16—941no—
133M16Dic9412yes—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—941no—
137C2×C8—941no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—942no—
141C4⋊C4—942no—
142C4⋊C4—942no—
143C4⋊C4—942no—
144C4⋊C4—941no—
145C4⋊C4—941no—
146C42—471no—
147C42—471no—
148C42—471no—
149C42—471no—
150C23C2×C4×D4711yescharacteristic
151C2×C4—22no—
152C2×C4—42no—
153C2×C4—471no—
154C2×C4—471no—
155C2×C4—471no—
156C2×C4—471no—
157C2×C4—942no—
158C2×C4—1881no—
159C2×C4—1881no—
160C2×C4—1882no—
161C2×C4C2×Dic9411yescharacteristic
162C2×C4#1062535011yescharacteristic
163C2×C4D4×D4711yescharacteristic
164C2×C4D4×D4711yescharacteristic
165C2×C4#1062535211yescharacteristic
166C2×C4Q8×D4711yescharacteristic
167C8—22no—
168C8—41no—
169C8—942no—
170C8—1881no—
171C22—21no—
172C22—21no—
173C22C22⋊C4×D4711yescharacteristic
174C22#1309398911yescharacteristic
175C22C4×Dic9411yescharacteristic
176C4—42no—
177C4—941no—
178C4—941no—
179C4—941no—
180C4—941no—
181C4—1882no—
182C4#1309400111yescharacteristic
183C4#1309400211yescharacteristic
184C4#1309401011yescharacteristic
185C4#1309402311yescharacteristic
186C2—21no—
187C2—21no—
188C2#1568902711yescharacteristic
189C2#1568910411yescharacteristic
190C2#1568910611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D47
commutatorC23×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#343C2
socleC22×C47C2×C22⋊C4
hypercenter#343D47
hypocenterC47#1998
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
103. C47#1998semidirect