Finite Group Databasebeta

← #20241822

Subgroups — #20241822

Order 6016.

246 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 89 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#15689180C211yesmaximal, characteristic, complemented
2#15689176C211yesmaximal, characteristic, complemented
3Q8⋊(C47⋊C8)C212yesmaximal, complemented
4D4⋊(C47⋊C8)C212yesmaximal, complemented
5C4×#41×C47C211yesmaximal, characteristic
6C4⋊(C47⋊C8)—21no—
7C4⋊(C47⋊C8)C2212yes—
8C22⋊(C47⋊C8)—21no—
9C22⋊(C47⋊C8)—21no—
10#13093935—21no—
11C4×C47⋊C8C2212yes—
12C2×#41×C47C411yescharacteristic
13C4×Q8×C47C411yescharacteristic
14C4×Q8×C47C2211yescharacteristic
15C4×D4×C47—21no—
16C4×D4×C47—21no—
17C4×D4×C47C411yescharacteristic
18C4×D4×C47C2211yescharacteristic
19#117×C47—21no—
20#117×C47C411yescharacteristic
21C2×C42×C47—21no—
22C2×C42×C47C2211yescharacteristic
23#41×C47—22no—
24#41×C47—22no—
25C2×Q8×C47C2×C411yescharacteristic
26C2×D4×C47—21no—
27C2×D4×C47C2×C411yescharacteristic
28C22×C4×C47—21no—
29C22×C4×C47—21no—
30C22×C4×C47—21no—
31C22×C4×C47C2×C411yescharacteristic
32C22×C4×C47D411yescharacteristic
33C22×C4×C47D411yescharacteristic
34C4⋊C4×C47—21no—
35C4⋊C4×C47—21no—
36C4⋊C4×C47C2×C411yescharacteristic
37C4⋊C4×C47C2×C411yescharacteristic
38C22⋊C4×C47—21no—
39C22⋊C4×C47—21no—
40C22⋊C4×C47—21no—
41C42×C47—21no—
42C42×C47—21no—
43C42×C47—21no—
44C42×C47C2×C411yescharacteristic
45C42×C47D411yescharacteristic
46C42×C47D411yescharacteristic
47C42×C47C2311yescharacteristic
48C2×C47⋊C8—22no—
49C2×C47⋊C8—22no—
50C23×C47—21no—
51C23×C47C22⋊C411yescharacteristic
52Q8×C47—21no—
53Q8×C47M1612yes—
54D4×C47—24no—
55D4×C47—21no—
56D4×C47M1612yes—
57C2×C4×C47—24no—
58C2×C4×C47—21no—
59C2×C4×C47—21no—
60C2×C4×C47—21no—
61C2×C4×C47—22no—
62C2×C4×C47—21no—
63C2×C4×C47—21no—
64C2×C4×C47—41no—
65C2×C4×C47—42no—
66C2×C4×C47—42no—
67C2×C4×C47C22⋊C411yescharacteristic
68C2×C4×C47C22⋊C411yescharacteristic
69C2×C4×C47C22⋊C411yescharacteristic
70C2×C4×C47C22×C411yescharacteristic
71C2×C4×C47C2×D411yescharacteristic
72C2×C4×C47C2×D411yescharacteristic
73C47⋊C8—42no—
74C47⋊C8—42no—
75C22×C47—21no—
76C22×C47—22no—
77C22×C47—21no—
78C22×C47—21no—
79C22×C47—41no—
80C22×C47—41no—
81C22×C47C2×C22⋊C411yescharacteristic
82C4×C47—21no—
83C4×C47—22no—
84C4×C47—21no—
85C4×C47—21no—
86C4×C47—21no—
87C4×C47—41no—
88C4×C47—41no—
89C4×C47C2×M1611yescharacteristic
90C4×C47C2×M1611yescharacteristic
91C4×C47#13512yes—
92#1488—471nomaximal, Sylow
93C2×C47—41no—
94C2×C47—42no—
95C2×C47#40711yescharacteristic
96C2×C47#41611yescharacteristic
97C2×C47#42111yescharacteristic
98C4×#41D4711yescharacteristic
99#432—471no—
100#431—471no—
101Q8⋊C8—472no—
102D4⋊C8—472no—
103C47#148811yescharacteristic, complemented, Sylow
104C2×#41Dic4711yescharacteristic
105C4×Q8Dic4711yescharacteristic
106C4×Q8C2×D4711yescharacteristic
107C4×D4—21no—
108C4×D4—21no—
109C4×D4Dic4711yescharacteristic
110C4×D4C2×D4711yescharacteristic
111#117—21no—
112#117Dic4711yescharacteristic
113C2×C42—21no—
114C2×C42C2×D4711yescharacteristic
115C4⋊C8—472no—
116C4⋊C8—941no—
117C22⋊C8—941no—
118C22⋊C8—941no—
119#97—941no—
120C4×C8—472no—
121#41—22no—
122#41—22no—
123C2×Q8C2×Dic4711yescharacteristic
124C2×D4—21no—
125C2×D4C2×Dic4711yescharacteristic
126C22×C4—21no—
127C22×C4—21no—
128C22×C4—21no—
129C22×C4C2×Dic4711yescharacteristic
130C22×C4C22⋊D4711yescharacteristic
131C22×C4C22⋊D4711yescharacteristic
132C2×C8—942no—
133C2×C8—942no—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4C2×Dic4711yescharacteristic
137C4⋊C4C2×Dic4711yescharacteristic
138C22⋊C4—21no—
139C22⋊C4—21no—
140C22⋊C4—21no—
141C42—21no—
142C42—21no—
143C42—21no—
144C42C2×Dic4711yescharacteristic
145C42C22⋊D4711yescharacteristic
146C42C22⋊D4711yescharacteristic
147C42C22×D4711yescharacteristic
148C23—21no—
149C23C22⋊Dic4711yescharacteristic
150Q8—21no—
151Q8#1062532912yes—
152D4—24no—
153D4—21no—
154D4#1062532912yes—
155C2×C4—24no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4C22⋊Dic4711yescharacteristic
166C2×C4C22⋊Dic4711yescharacteristic
167C2×C4C22⋊Dic4711yescharacteristic
168C2×C4C22×Dic4711yescharacteristic
169C2×C4C2×C22⋊D4711yescharacteristic
170C2×C4C2×C22⋊D4711yescharacteristic
171C8—1882no—
172C8—1882no—
173C22—21no—
174C22—22no—
175C22—21no—
176C22—21no—
177C22—41no—
178C22—41no—
179C22C2×C22⋊Dic4711yescharacteristic
180C4—21no—
181C4—22no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—41no—
186C4—41no—
187C4C2×#1062532911yescharacteristic
188C4C2×#1062532911yescharacteristic
189C4#1309404412yes—
190C2—41no—
191C2—42no—
192C2#1568908711yescharacteristic
193C2#1568911911yescharacteristic
194C2#1568914011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D47
commutatorC2×C4×C47C22×C4
FrattiniC42C22×D47
FittingC4×#41×C47C2
socleC22×C47C2×C22⋊C4
hypercenterC4×#41D47
hypocenterC47#1488
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. #15689180C2semidirect
2. #15689176C2semidirect
3. Q8⋊(C47⋊C8)C2semidirect
4. D4⋊(C47⋊C8)C2semidirect
103. C47#1488semidirect