Finite Group Databasebeta

← #20243395

Subgroups — #20243395

Order 6016.

356 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 109 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×C4×D188C211yesmaximal, characteristic
2C2×C4⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
3C2×#13093944C212yesmaximal
4#15688885C212yesmaximal, complemented
5C47×#382C211yesmaximal, characteristic, complemented
6C22×D188C2211yescharacteristic
7C22×C4×D47—21no—
8C22×C47⋊C8C2212yes—
9C4×D188—22no—
10C4×D188C414yescomplemented
11C2×C4⋊Dic47C2211yescharacteristic
12C2×(C2×D47)⋊C4—21no—
13C4⋊(C47⋊C8)—22no—
14#13093944—24no—
15C2×C4⋊C4×C47C2212yes—
16C2×C42×C47C2211yescharacteristic
17#95×C47—21no—
18#95×C47—21no—
19C23×D47—21no—
20C22×C4×C47—22no—
21C22×C4×C47D411yescharacteristic
22C22×C4×C47D411yescharacteristic
23C22×C4×C47C2311yescharacteristic
24C22×Dic47—21no—
25C2×D188—21no—
26C2×D188—21no—
27C2×D188—21no—
28C2×D188C2×C412yes—
29C2×D188D412yes—
30C2×D188Q812yes—
31C2×C4×D47—24no—
32C2×C4×D47—44no—
33C4⋊C4×C47—22no—
34C4⋊C4×C47—22no—
35C42×C47C2×C412yes—
36C42×C47D412yes—
37(C2×D47)⋊C4—24no—
38C4⋊Dic47—21no—
39C4⋊Dic47C2×C412yes—
40C2×C47⋊C8—22no—
41C2×C47⋊C8—22no—
42C2×C47⋊C8—22no—
43C23×C47C2×D411yescharacteristic
44C22×D47—22no—
45C22×D47—22no—
46C22×D47—22no—
47C22×D47—42no—
48C22×D47—42no—
49C2×C4×C47—22no—
50C2×C4×C47—22no—
51C2×C4×C47—42no—
52C2×C4×C47—42no—
53C2×C4×C47—42no—
54C2×C4×C47C22⋊C412yes—
55C2×C4×C47C22⋊C412yes—
56C2×C4×C47C22×C411yescharacteristic
57C2×C4×C47C2×D411yescharacteristic
58C2×C4×C47C2×D411yescharacteristic
59C2×C4×C47C2×Q811yescharacteristic
60C2×C4×C47#4111yescharacteristic
61C2×C4×C47#4111yescharacteristic
62C2×Dic47—22no—
63C2×Dic47—42no—
64D188—22no—
65D188—22no—
66D188—22no—
67D188C4⋊C414yes—
68C4×D47—48no—
69C47⋊C8—42no—
70C22×C47C2×C22⋊C411yescharacteristic
71C22×C47#12111yescharacteristic
72C22×C47C22⋊Q811yescharacteristic
73C22×C47#13512yes—
74C22×C47AGL(1,ℤ/8)12yes—
75C2×D47—24no—
76C2×D47—42no—
77C2×D47—42no—
78C2×D47—44no—
79C2×D47—44no—
80C4×C47—22no—
81C4×C47—22no—
82C4×C47—82no—
83C4×C47C2×C4⋊C411yescharacteristic
84C4×C47#11711yescharacteristic
85C4×C47#12111yescharacteristic
86C4×C47C22⋊Q811yescharacteristic
87Dic47—42no—
88#1804—471nomaximal, Sylow
89C2×C47#38011yescharacteristic
90C2×C47#41611yescharacteristic
91C2×C47#41811yescharacteristic
92C2×C47#46312yes—
93C2×C47#47812yes—
94D47—44no—
95C2×C4×D4—471no—
96C2×C4⋊C8—471no—
97C2×#102—472no—
98#382D4711yescharacteristic, complemented
99#340—472no—
100C47#180411yescharacteristic, complemented, Sylow
101C22×D4—471no—
102C23×C4—941no—
103C22×C8—472no—
104C4×D4—474no—
105C4×D4—942no—
106C2×C4⋊C4—471no—
107C2×C4⋊C4C2×D4712yes—
108C2×C22⋊C4—941no—
109C2×C42C2×D4711yescharacteristic
110C4⋊C8—942no—
111#102—944no—
112#95—21no—
113#95—21no—
114C24—941no—
115C2×D4—472no—
116C2×D4—472no—
117C2×D4—472no—
118C2×D4—941no—
119C2×D4—941no—
120C2×D4—941no—
121C22×C4—22no—
122C22×C4—941no—
123C22×C4—944no—
124C22×C4—1884no—
125C22×C4C22⋊D4711yescharacteristic
126C22×C4C22⋊D4711yescharacteristic
127C22×C4C22×D4711yescharacteristic
128C2×C8—942no—
129C2×C8—942no—
130C2×C8—942no—
131C4⋊C4—22no—
132C4⋊C4—22no—
133C4⋊C4—472no—
134C4⋊C4—941no—
135C22⋊C4—944no—
136C42C4×D4712yes—
137C42D18812yes—
138C23—942no—
139C23—942no—
140C23—942no—
141C23—1882no—
142C23—1882no—
143C23C2×C22⋊D4711yescharacteristic
144D4—474no—
145D4—942no—
146D4—942no—
147D4—942no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—42no—
151C2×C4—42no—
152C2×C4—42no—
153C2×C4—942no—
154C2×C4—1888no—
155C2×C4—1882no—
156C2×C4(C2×D47)⋊C412yes—
157C2×C4(C2×D47)⋊C412yes—
158C2×C4C2×C4×D4711yescharacteristic
159C2×C4C2×D18811yescharacteristic
160C2×C4D4×D4711yescharacteristic
161C2×C4#1062535211yescharacteristic
162C2×C4Q8×D4711yescharacteristic
163C2×C4#1062535411yescharacteristic
164C8—1882no—
165C22—944no—
166C22—1884no—
167C22—1882no—
168C22—1882no—
169C22—1884no—
170C22C2×(C2×D47)⋊C411yescharacteristic
171C22#1309399511yescharacteristic
172C22#1309400011yescharacteristic
173C22#1309404412yes—
174C22#1309404912yes—
175C4—22no—
176C4—22no—
177C4—82no—
178C4—1882no—
179C4C4⋊C4×D4711yescharacteristic
180C4#1309398211yescharacteristic
181C4#1309399911yescharacteristic
182C4#1309400411yescharacteristic
183C2—1884no—
184C2#1568898011yescharacteristic
185C2#1568911711yescharacteristic
186C2#1568912711yescharacteristic
187C2#1568933512yes—
188C2#1568942012yes—
subgroupG/H
centerC23C2×C22⋊D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#382C2
socleC23×C47C2×D4
hypercenter#382D47
hypocenterC47#1804
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊(C47⋊C8)C2semidirect
4. #15688885C2semidirect
5. C47×#382C2semidirect
10. C4×D188C4semidirect
98. #382D47semidirect
100. C47#1804semidirect