Finite Group Databasebeta

← #20244287

Subgroups — #20244287

Order 6016.

284 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 93 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#15689161C211yesmaximal, characteristic, complemented
2#15689140C212yesmaximal, complemented
3#15689097C212yesmaximal, complemented
4#15689078C211yesmaximal, characteristic, complemented
5C2×#135×C47C211yesmaximal, characteristic
6C2×#10625329C2211yescharacteristic
7#13093983C2212yes—
8#13093983C2211yescharacteristic
9#13093958—21no—
10#13093956—21no—
11#13093951—24no—
12#13093939—24no—
13#13093934—21no—
14C8×Dic47—21no—
15C2×#41×C47C2212yes—
16#135×C47—21no—
17#135×C47—21no—
18#135×C47—21no—
19#135×C47—21no—
20C2×Q16×C47C411yescharacteristic, complemented
21C2×SD16×C47C412yescomplemented
22C2×D8×C47C411yescharacteristic, complemented
23C22×C8×C47C2211yescharacteristic
24#41×C47—22no—
25#41×C47—22no—
26#41×C47—22no—
27#41×C47—22no—
28C2×Q8×C47C2×C412yes—
29C2×D4×C47—22no—
30C2×D4×C47C2×C412yes—
31C22×C4×C47—22no—
32C22×C4×C47C2311yescharacteristic
33Q16×C47—21no—
34Q16×C47—21no—
35SD16×C47—22no—
36SD16×C47—22no—
37D8×C47—21no—
38D8×C47—21no—
39C2×C8×C47C2×C411yescharacteristic
40C2×C8×C47C2×C411yescharacteristic
41C2×C8×C47D411yescharacteristic
42C2×C8×C47D411yescharacteristic
43C2×C8×C47D411yescharacteristic
44C2×C8×C47D411yescharacteristic
45C22⋊Dic47—22no—
46C22⋊Dic47D412yes—
47C4⋊Dic47—21no—
48C4⋊Dic47—22no—
49C4×Dic47—21no—
50C4×Dic47—22no—
51#10625329—21no—
52#10625329D412yes—
53C2×C47⋊C8—21no—
54C23×C47—22no—
55C23×C47C2×D411yescharacteristic
56Q8×C47—22no—
57Q8×C47—22no—
58D4×C47—22no—
59D4×C47—22no—
60D4×C47—42no—
61D4×C47—42no—
62C2×C4×C47—22no—
63C2×C4×C47—42no—
64C2×C4×C47—42no—
65C2×C4×C47C22×C411yescharacteristic
66C2×C4×C47C2×D411yescharacteristic
67C2×C4×C47C2×D411yescharacteristic
68C2×C4×C47C2×D411yescharacteristic
69C2×C4×C47#4111yescharacteristic
70C2×C4×C47#4111yescharacteristic
71C2×Dic47—22no—
72C2×Dic47—42no—
73C8×C47C22⋊C411yescharacteristic
74C8×C47C22⋊C411yescharacteristic
75C8×C47C22⋊C411yescharacteristic
76C8×C47C22⋊C411yescharacteristic
77C47⋊C8—22no—
78C22×C47—41no—
79C22×C47—42no—
80C22×C47—82no—
81C22×C47C4×D411yescharacteristic
82C22×C47#12111yescharacteristic
83C22×C47#12711yescharacteristic
84C4×C47—42no—
85C4×C47C2×C22⋊C411yescharacteristic
86C4×C47C4×D411yescharacteristic
87C4×C47#12111yescharacteristic
88C4×C47#12411yescharacteristic
89Dic47—42no—
90Dic47—82no—
91#1976—471nomaximal, Sylow
92C2×C47—21no—
93C2×C47—21no—
94C2×C47—21no—
95C2×C47—82no—
96C2×C47#39011yescharacteristic
97C2×#135D4711yescharacteristic
98#427—471no—
99#421—472no—
100#410—472no—
101#405—471no—
102C47#197611yescharacteristic, complemented, Sylow
103C2×#41C2×D4712yes—
104#135—21no—
105#135—21no—
106#135—21no—
107#135—21no—
108C2×Q16Dic4711yescharacteristic, complemented
109C2×SD16Dic4712yescomplemented
110C2×D8Dic4711yescharacteristic, complemented
111C2×M16—471no—
112C22×C8C2×D4711yescharacteristic
113#117—471no—
114#117—472no—
115#107—941no—
116#106—941no—
117#104—944no—
118#99—944no—
119#97—941no—
120C4×C8—941no—
121#41—22no—
122#41—22no—
123#41—22no—
124#41—22no—
125C2×Q8C2×Dic4712yes—
126C2×D4—22no—
127C2×D4C2×Dic4712yes—
128C22×C4—22no—
129C22×C4C22×D4711yescharacteristic
130Q16—21no—
131Q16—21no—
132SD16—22no—
133SD16—22no—
134D8—21no—
135D8—21no—
136M16—472no—
137M16—941no—
138C2×C8—941no—
139C2×C8C2×Dic4711yescharacteristic
140C2×C8C2×Dic4711yescharacteristic
141C2×C8C22⋊D4711yescharacteristic
142C2×C8C22⋊D4711yescharacteristic
143C2×C8C22⋊D4711yescharacteristic
144C2×C8C22⋊D4711yescharacteristic
145C4⋊C4—941no—
146C4⋊C4—942no—
147C22⋊C4—472no—
148C22⋊C4—942no—
149C42—941no—
150C42—942no—
151C23—22no—
152C23D4×D4711yescharacteristic
153Q8—22no—
154Q8—22no—
155D4—22no—
156D4—22no—
157D4—42no—
158D4—42no—
159C2×C4—22no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—942no—
163C2×C4—1882no—
164C2×C4D4×D4711yescharacteristic
165C2×C4#1062535211yescharacteristic
166C2×C4#1062535211yescharacteristic
167C2×C4C22×Dic4711yescharacteristic
168C2×C4C2×C22⋊D4711yescharacteristic
169C2×C4C2×C22⋊D4711yescharacteristic
170C8—942no—
171C8C22⋊Dic4711yescharacteristic
172C8C22⋊Dic4711yescharacteristic
173C8C22⋊Dic4711yescharacteristic
174C8C22⋊Dic4711yescharacteristic
175C22—41no—
176C22—42no—
177C22—82no—
178C22D4×Dic4711yescharacteristic
179C22#1309399511yescharacteristic
180C22#1309402011yescharacteristic
181C4—42no—
182C4—3762no—
183C4—1882no—
184C4C2×C22⋊Dic4711yescharacteristic
185C4D4×Dic4711yescharacteristic
186C4#1309399511yescharacteristic
187C4#1309401111yescharacteristic
188C2—21no—
189C2—21no—
190C2—21no—
191C2—82no—
192C2#1568902611yescharacteristic
subgroupG/H
centerC4#13093995
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#135×C47C2
socleC2×C47#390
hypercenterC2×#135D47
hypocenterC47#1976
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. #15689161C2semidirect
2. #15689140C2semidirect
3. #15689097C2semidirect
4. #15689078C2semidirect
20. C2×Q16×C47C4semidirect
21. C2×SD16×C47C4semidirect
22. C2×D8×C47C4semidirect
102. C47#1976semidirect
108. C2×Q16Dic47semidirect
109. C2×SD16Dic47semidirect
110. C2×D8Dic47semidirect