Finite Group Databasebeta

← #20243604

Subgroups — #20243604

Order 6016.

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

normal subgroups only

This group has 272 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
1#15689600C211yesmaximal, characteristic
2#15689166C211yesmaximal, characteristic
3#15689165C211yesmaximal, characteristic
4C2×#13093942C211yesmaximal, characteristic
5#15689029C211yesmaximal, characteristic
6#15688883C211yesmaximal, characteristic
7C47×#339C211yesmaximal, characteristic
8C22×Dic94C2211yescharacteristic
9C2×#10625329C2211yescharacteristic
10C4×Dic94—21no—
11C4×Dic94—21no—
12#13093989—21no—
13#13093989—21no—
14#13093983C2211yescharacteristic
15#13093980—22no—
16C2×C4⋊Dic47C2211yescharacteristic
17#13093958—21no—
18#13093957—21no—
19#13093956—21no—
20#13093955—21no—
21#13093942C414yescomplemented
22C47⋊#95—22no—
23C2×M16×C47C2211yescharacteristic
24#117×C47C2211yescharacteristic
25C2×C42×C47C2211yescharacteristic
26C22×C4×C47—21no—
27C22×C4×C47C2311yescharacteristic
28C22×Dic47—21no—
29C22×Dic47D412yes—
30C2×Dic94—21no—
31C2×Dic94—21no—
32C2×Dic94—21no—
33C2×Dic94—21no—
34C2×Dic94C2×C412yes—
35C2×Dic94Q812yes—
36M16×C47—21no—
37M16×C47C2×C412yes—
38C2×C8×C47—21no—
39C4⋊C4×C47D411yescharacteristic
40C4⋊C4×C47D411yescharacteristic
41C22⋊C4×C47—21no—
42C42×C47—21no—
43C42×C47—21no—
44C42×C47—21no—
45C22⋊Dic47—21no—
46C4⋊Dic47—21no—
47C4⋊Dic47—21no—
48C4⋊Dic47D411yescharacteristic
49C4⋊Dic47D411yescharacteristic
50Dic47⋊C4—22no—
51Dic47⋊C4—22no—
52C4×Dic47—22no—
53C4×Dic47—22no—
54C4×Dic47—21no—
55#10625329—21no—
56#10625329C2×C412yes—
57C2×C47⋊C8—21no—
58C23×C47C2×D411yescharacteristic
59C2×C4×C47—22no—
60C2×C4×C47—21no—
61C2×C4×C47—21no—
62C2×C4×C47—41no—
63C2×C4×C47—41no—
64C2×C4×C47C22×C411yescharacteristic
65C2×C4×C47C2×D411yescharacteristic
66C2×C4×C47C2×D411yescharacteristic
67C2×C4×C47C2×Q811yescharacteristic
68C2×C4×C47#4111yescharacteristic
69C2×C4×C47#4111yescharacteristic
70C2×Dic47—22no—
71C2×Dic47—22no—
72C2×Dic47—21no—
73C2×Dic47—21no—
74C2×Dic47—42no—
75C2×Dic47—41no—
76C2×Dic47C4⋊C414yes—
77Dic94—22no—
78Dic94—22no—
79Dic94—22no—
80Dic94—22no—
81C8×C47—22no—
82C47⋊C8—22no—
83C22×C47—21no—
84C22×C47—21no—
85C22×C47C2×C4⋊C411yescharacteristic
86C22×C47#12011yescharacteristic
87C22×C47#12311yescharacteristic
88C4×C47—42no—
89C4×C47—41no—
90C4×C47—41no—
91C4×C47C4×D411yescharacteristic
92C4×C47C4×D411yescharacteristic
93C4×C47C22⋊Q811yescharacteristic
94C4×C47C22⋊Q811yescharacteristic
95Dic47—24no—
96Dic47—41no—
97Dic47—41no—
98Dic47—81no—
99#1857—471nomaximal, Sylow
100C2×C47—21no—
101C2×C47—21no—
102C2×C47#38511yescharacteristic
103C2×C47#45411yescharacteristic
104C2×C47#45611yescharacteristic
105#519—471no—
106#428—471no—
107#428—471no—
108C2×#101—471no—
109#391—471no—
110#339—471no—
111#339D4711yescharacteristic
112C47#185711yescharacteristic, complemented, Sylow
113C22×Q8—471no—
114C2×M16—471no—
115C2×M16C2×D4711yescharacteristic
116C4×Q8—941no—
117C4×Q8—941no—
118C4×Q8—941no—
119C4×Q8—941no—
120#117—471no—
121#117—942no—
122#117C2×D4711yescharacteristic
123C2×C4⋊C4—471no—
124C2×C42C2×D4711yescharacteristic
125#107—941no—
126#107—941no—
127#106—941no—
128#106—941no—
129#101—474no—
130#95—942no—
131C2×Q8—472no—
132C2×Q8—472no—
133C2×Q8—941no—
134C2×Q8—941no—
135C2×Q8—941no—
136C2×Q8—941no—
137C22×C4—21no—
138C22×C4—472no—
139C22×C4—941no—
140C22×C4C22×D4711yescharacteristic
141M16—21no—
142M16—472no—
143M16—941no—
144M16C4×D4712yes—
145C2×C8—21no—
146C2×C8—941no—
147C4⋊C4—471no—
148C4⋊C4—471no—
149C4⋊C4—942no—
150C4⋊C4—942no—
151C4⋊C4—941no—
152C4⋊C4—941no—
153C4⋊C4D18811yescharacteristic
154C4⋊C4D18811yescharacteristic
155C22⋊C4—21no—
156C22⋊C4—941no—
157C42—21no—
158C42—21no—
159C42—21no—
160C42—942no—
161C42—942no—
162C42—941no—
163C23D4×D4711yescharacteristic
164Q8—942no—
165Q8—942no—
166Q8—942no—
167Q8—942no—
168C2×C4—22no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—474no—
174C2×C4—942no—
175C2×C4—942no—
176C2×C4—941no—
177C2×C4—941no—
178C2×C4—1882no—
179C2×C4—1881no—
180C2×C4C2×C4×D4711yescharacteristic
181C2×C4C2×D18811yescharacteristic
182C2×C4#1062535011yescharacteristic
183C2×C4D4×D4711yescharacteristic
184C2×C4#1062535211yescharacteristic
185C2×C4Q8×D4711yescharacteristic
186C8—22no—
187C8—942no—
188C22—21no—
189C22—21no—
190C22C4⋊C4×D4711yescharacteristic
191C22#1309399411yescharacteristic
192C22#1309400611yescharacteristic
193C4—42no—
194C4—41no—
195C4—41no—
196C4—944no—
197C4—3761no—
198C4—1881no—
199C4—1881no—
200C4(C22⋊D47)⋊C411yescharacteristic
201C4C4×D18811yescharacteristic
202C4#1309400211yescharacteristic
203C4#1309400411yescharacteristic
204C2—21no—
205C2—21no—
206C2#1568899711yescharacteristic
207C2#1568929711yescharacteristic
208C2#1568930711yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#339C2
socleC22×C47#120
hypercenter#339D47
hypocenterC47#1857
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
21. #13093942C4semidirect
112. C47#1857semidirect