Finite Group Databasebeta

← #20241984

Subgroups — #20241984

Order 6016.

264 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 61 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#124×D47C211yesmaximal, characteristic
2#15689178C211yesmaximal, characteristic, complemented
3#15689075C211yesmaximal, characteristic, complemented
4#15688863C211yesmaximal, characteristic, complemented
5#15688862C211yesmaximal, characteristic, complemented
6#15688862C211yesmaximal, characteristic, complemented
7C47×#329C211yesmaximal, characteristic, complemented
8C2×Q8×D47C411yescharacteristic
9C2×D4×D47C411yescharacteristic
10C2×#10625324—21no—
11#13094013C411yescharacteristic
12#13094012C2211yescharacteristic
13#13094011C411yescharacteristic
14#13094010—21no—
15#13094010—21no—
16C22⋊C4×D47—21no—
17C22⋊C4×D47—21no—
18C42×D47C2211yescharacteristic
19Dic47⋊C8—21no—
20(C2×D47)⋊C8—21no—
21#13093935C2211yescharacteristic, complemented
22#13093935C2211yescharacteristic, complemented
23C8×Dic47—21no—
24#124×C47C2211yescharacteristic
25#97×C47C2211yescharacteristic, complemented
26#97×C47C2211yescharacteristic, complemented
27C23×D47—21no—
28C2×Q8×C47C2×C411yescharacteristic
29C2×D4×C47C2×C411yescharacteristic
30C2×C22⋊D47—21no—
31Q8×D47—42no—
32D4×D47—42no—
33C2×D188C2×C411yescharacteristic
34C2×C4×D47—21no—
35C2×C4×D47C2×C411yescharacteristic
36C2×C4×D47D411yescharacteristic
37C2×C4×D47D411yescharacteristic
38C2×Dic94—21no—
39C2×Dic94C2×C411yescharacteristic
40C2×C8×C47—21no—
41C2×C8×C47—21no—
42C22⋊C4×C47—21no—
43C22⋊C4×C47—21no—
44C42×C47C2311yescharacteristic
45C22⋊Dic47—21no—
46C22⋊Dic47—21no—
47(C2×D47)⋊C4—21no—
48(C2×D47)⋊C4—21no—
49(C2×D47)⋊C4—21no—
50(C2×D47)⋊C4—21no—
51C4×Dic47C2×C411yescharacteristic
52C4×Dic47D411yescharacteristic
53C4×Dic47D411yescharacteristic
54C2×C47⋊C8—21no—
55C2×C47⋊C8—21no—
56#10625324—24no—
57C23×C47—21no—
58C22×D47—21no—
59C22×D47—42no—
60C22×D47—42no—
61C22×D47—42no—
62C22×D47C22⋊C411yescharacteristic
63Q8×C47—41no—
64D4×C47—41no—
65C2×C4×C47—21no—
66C2×C4×C47C22×C411yescharacteristic
67C2×C4×C47C2×D411yescharacteristic
68C2×C4×C47C2×D411yescharacteristic
69C22⋊D47—42no—
70C2×Dic47—21no—
71C2×Dic47C22⋊C411yescharacteristic
72C2×Dic47C22⋊C411yescharacteristic
73C2×Dic47C22⋊C411yescharacteristic
74D188—41no—
75C4×D47—22no—
76C4×D47—22no—
77C4×D47—41no—
78C4×D47—42no—
79Dic94—42no—
80Dic94—41no—
81C8×C47—22no—
82C8×C47—41no—
83C47⋊C8—22no—
84C47⋊C8—41no—
85C22×C47—41no—
86C22×C47—41no—
87C22×C47—41no—
88C22×C47C2×C22⋊C411yescharacteristic
89C2×D47—21no—
90C2×D47—21no—
91C2×D47—41no—
92C2×D47—41no—
93C2×D47—41no—
94C2×D47—84no—
95C2×D47#10412yes—
96C4×C47—21no—
97C4×C47—21no—
98C4×C47—21no—
99C4×C47—41no—
100Dic47—21no—
101Dic47—21no—
102Dic47—41no—
103Dic47#10012yes—
104#1527—471nomaximal, Sylow
105C2×C47—81no—
106C2×C47C2×#10011yescharacteristic
107C2×C47C2×#10411yescharacteristic
108C2×C47#42111yescharacteristic
109D47—22no—
110D47—81no—
111C2×#124—471no—
112#432—471no—
113C4×M16—471no—
114#329—471no—
115#329—471no—
116#329—471no—
117#329D4711yescharacteristic, complemented
118C47#152711yescharacteristic, complemented, Sylow
119C22×Q8—471no—
120C22×D4—471no—
121C2×M16—941no—
122#124—471no—
123#124—471no—
124#124—471no—
125#124—941no—
126#124—941no—
127#124C2×D4711yescharacteristic
128C2×C22⋊C4—941no—
129C2×C22⋊C4—941no—
130C2×C42—471no—
131C4⋊C8—941no—
132C22⋊C8—941no—
133#97—471no—
134#97—471no—
135#97C2×D4711yescharacteristic, complemented
136#97C2×D4711yescharacteristic, complemented
137C4×C8—941no—
138C24—941no—
139C2×Q8—471no—
140C2×Q8—941no—
141C2×Q8—1882no—
142C2×Q8C4×D4711yescharacteristic
143C2×D4—471no—
144C2×D4—941no—
145C2×D4—1882no—
146C2×D4C4×D4711yescharacteristic
147C22×C4—471no—
148C22×C4—471no—
149C22×C4—471no—
150C22×C4—941no—
151M16—944no—
152C2×C8—21no—
153C2×C8—21no—
154C2×C8—941no—
155C2×C8—941no—
156C22⋊C4—21no—
157C22⋊C4—21no—
158C22⋊C4—941no—
159C22⋊C4—941no—
160C22⋊C4—941no—
161C22⋊C4—941no—
162C22⋊C4—941no—
163C22⋊C4—941no—
164C42—471no—
165C42—471no—
166C42—471no—
167C42C22×D4711yescharacteristic
168C23—21no—
169C23—471no—
170C23—941no—
171C23—1882no—
172C23—1882no—
173C23—1882no—
174Q8—41no—
175Q8—1881no—
176Q8—1882no—
177D4—41no—
178D4—1881no—
179D4—1882no—
180C2×C4—21no—
181C2×C4—471no—
182C2×C4—471no—
183C2×C4—471no—
184C2×C4—942no—
185C2×C4—942no—
186C2×C4—941no—
187C2×C4—1881no—
188C2×C4—1882no—
189C2×C4C2×C4×D4711yescharacteristic
190C2×C4D4×D4711yescharacteristic
191C2×C4D4×D4711yescharacteristic
192C8—22no—
193C8—41no—
194C8—942no—
195C8—1881no—
196C22—41no—
197C22—41no—
198C22—41no—
199C22—472no—
200C22—941no—
201C22—941no—
202C22—3764no—
203C22—1881no—
204C22—1881no—
205C22—1881no—
206C22C22⋊C4×D4711yescharacteristic
207C4—21no—
208C4—21no—
209C4—21no—
210C4—41no—
211C4—472no—
212C4—941no—
213C4—941no—
214C4—1881no—
215C2—81no—
216C2—942no—
217C2—3761no—
218C2#100×D4711yescharacteristic
219C2#104×D4711yescharacteristic
220C2#1568913811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D47
commutatorC2×C4×C47C22×C4
FrattiniC42C22×D47
FittingC47×#329C2
socleC22×C47C2×C22⋊C4
hypercenter#329D47
hypocenterC47#1527
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #15689178C2semidirect
3. #15689075C2semidirect
4. #15688863C2semidirect
5. #15688862C2semidirect
6. #15688862C2semidirect
7. C47×#329C2semidirect
21. #13093935C22semidirect
22. #13093935C22semidirect
25. #97×C47C22semidirect
26. #97×C47C22semidirect
117. #329D47semidirect
118. C47#1527semidirect
135. #97C2×D47semidirect
136. #97C2×D47semidirect