Finite Group Databasebeta

← #20256309

Subgroups — #20256309

Order 6016.

360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 133 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#15689851C211yesmaximal, characteristic, complemented
2#15689529C212yesmaximal, complemented
3#15689526C211yesmaximal, characteristic, complemented
4#15689423C212yesmaximal
5#15689415C212yesmaximal, complemented
6#15689405C211yesmaximal, characteristic, complemented
7#15689403C211yesmaximal, characteristic
8#15689254C211yesmaximal, characteristic, complemented
9#15689223C212yesmaximal
10C4×#10625335C211yesmaximal, characteristic
11D4×Q8×C47C211yesmaximal, characteristic
12C2×#10625335C2211yescharacteristic
13#13094024C2211yescharacteristic
14#13094022—21no—
15#13094016C2212yes—
16#13094014—22no—
17C4×Dic94C2212yes—
18C4×Dic94C2211yescharacteristic
19#13093989—21no—
20#13093957C2212yes—
21#13093957C2212yes—
22#13093957C2212yes—
23#13093955C2211yescharacteristic
24#13093955C2212yes—
25C4⋊(C47⋊C8)C2211yescharacteristic
26C4⋊(C47⋊C8)C2212yes—
27#13093947C2212yes—
28#13093947C2211yescharacteristic
29#13093945C2212yes—
30#13093945C2211yescharacteristic
31#13093935C2212yes—
32C4×C47⋊C8C2211yescharacteristic
33C22×Q8×C47—21no—
34C4⋊Q8×C47C2211yescharacteristic
35C4⋊Q8×C47C2212yes—
36C22⋊Q8×C47—21no—
37C22⋊Q8×C47—22no—
38C4×Q8×C47C2211yescharacteristic
39C4×D4×C47C2212yes—
40C4×D4×C47C2211yescharacteristic
41C2×Q8×C47—22no—
42C2×Q8×C47—21no—
43C2×Q8×C47—44no—
44C2×Q8×C47D411yescharacteristic
45C2×D4×C47C2311yescharacteristic
46C22×C4×C47—22no—
47C22×C4×C47—21no—
48C2×Dic94—21no—
49C2×Dic94C2311yescharacteristic
50C4⋊C4×C47—22no—
51C4⋊C4×C47—21no—
52C4⋊C4×C47D411yescharacteristic
53C4⋊C4×C47D412yes—
54C4⋊C4×C47C2312yes—
55C4⋊C4×C47C2311yescharacteristic
56C22⋊C4×C47—22no—
57C22⋊C4×C47—21no—
58C42×C47C2311yescharacteristic
59C42×C47C2312yes—
60#10625335Q814yescomplemented
61C4⋊Dic47—21no—
62C4⋊Dic47C2311yescharacteristic
63C4⋊Dic47C2312yes—
64Dic47⋊C4—22no—
65Dic47⋊C4—21no—
66Dic47⋊C4—22no—
67Dic47⋊C4—22no—
68C4×Dic47—22no—
69C4×Dic47—21no—
70C2×C47⋊C8C2311yescharacteristic
71C2×C47⋊C8C2312yes—
72C2×C47⋊C8C2311yescharacteristic
73C23×C47—21no—
74Q8×C47—22no—
75Q8×C47—44no—
76Q8×C47—42no—
77D4×C47—21no—
78D4×C47C2×Q812yes—
79C2×C4×C47—22no—
80C2×C4×C47—21no—
81C2×C4×C47—44no—
82C2×C4×C47—42no—
83C2×C4×C47C2×D412yes—
84C2×C4×C47C2×D412yes—
85C2×C4×C47C2×D411yescharacteristic
86C2×C4×C47C2×D411yescharacteristic
87C2×C4×C47C2411yescharacteristic
88C2×Dic47—21no—
89C2×Dic47—21no—
90C2×Dic47—22no—
91Dic94—21no—
92Dic94—42no—
93Dic94C2×Q812yescomplemented
94C47⋊C8—21no—
95C47⋊C8—22no—
96C47⋊C8C2×Q812yescomplemented
97C22×C47—22no—
98C22×C47—41no—
99C22×C47—41no—
100C22×C47C22×D411yescharacteristic
101C4×C47—22no—
102C4×C47—22no—
103C4×C47—21no—
104C4×C47—42no—
105C4×C47—41no—
106C4×C47AGL(1,ℤ/8)12yes—
107C4×C47C22×Q811yescharacteristic
108C4×C472−1+411yescharacteristic
109Dic47—22no—
110Dic47—42no—
111Dic47—41no—
112#3386—471nomaximal, Sylow
113C2×C47—42no—
114C2×C47D4×Q811yescharacteristic
115C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
116C2×C47#57811yescharacteristic
117#557—471no—
118D4×Q8D4711yescharacteristic
119#501—472no—
120#500—471no—
121#478—472no—
122#477—472no—
123#475—471no—
124#474—471no—
125#446—471no—
126#440—472no—
127C4×SD16—471no—
128C47#338611yescharacteristic, complemented, Sylow
129C22×Q8—21no—
130C2×SD16—471no—
131C4⋊Q8—471no—
132C4⋊Q8—941no—
133C4⋊Q8C2×D4711yescharacteristic
134C4⋊Q8C2×D4712yes—
135#125—472no—
136#125—942no—
137C22⋊Q8—21no—
138C22⋊Q8—22no—
139C4×Q8—471no—
140C4×Q8—472no—
141C4×Q8—941no—
142C4×Q8C2×D4711yescharacteristic
143C4×D4C2×D4711yescharacteristic
144C4×D4C2×D4712yes—
145#107—472no—
146#107—472no—
147#107—472no—
148#106—471no—
149#106—472no—
150C4⋊C8—471no—
151C4⋊C8—472no—
152#103—471no—
153#103—472no—
154#102—471no—
155#102—472no—
156#97—472no—
157C4×C8—471no—
158C2×Q8—22no—
159C2×Q8—21no—
160C2×Q8—44no—
161C2×Q8—471no—
162C2×Q8—941no—
163C2×Q8C22⋊D4711yescharacteristic
164C2×D4C22×D4711yescharacteristic
165C22×C4—22no—
166C22×C4—21no—
167SD16—474no—
168C2×C8—471no—
169C2×C8—471no—
170C2×C8—472no—
171C4⋊C4—22no—
172C4⋊C4—21no—
173C4⋊C4—471no—
174C4⋊C4—472no—
175C4⋊C4—941no—
176C4⋊C4—942no—
177C4⋊C4—942no—
178C4⋊C4—942no—
179C4⋊C4—941no—
180C4⋊C4C22⋊D4711yescharacteristic
181C4⋊C4C22⋊D4712yes—
182C4⋊C4C22×D4711yescharacteristic
183C4⋊C4C22×D4712yes—
184C22⋊C4—22no—
185C22⋊C4—21no—
186C42—942no—
187C42—941no—
188C42C22×D4711yescharacteristic
189C42C22×D4712yes—
190C23—21no—
191Q8—22no—
192Q8—44no—
193Q8—42no—
194Q8—472no—
195Q8—941no—
196Q8—1882no—
197D4—21no—
198D4Q8×D4712yes—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—44no—
202C2×C4—42no—
203C2×C4—941no—
204C2×C4—941no—
205C2×C4—942no—
206C2×C4C2×C22⋊D4712yes—
207C2×C4C2×C22⋊D4711yescharacteristic
208C2×C4C2×C22⋊D4712yes—
209C2×C4C2×C22⋊D4711yescharacteristic
210C2×C4C23×D4711yescharacteristic
211C8—472no—
212C8—941no—
213C8—942no—
214C22—22no—
215C22—41no—
216C22—41no—
217C22C22×C22⋊D4711yescharacteristic
218C4—22no—
219C4—22no—
220C4—21no—
221C4—42no—
222C4—41no—
223C4—942no—
224C4—1882no—
225C4—1881no—
226C4#1309405012yes—
227C4C2×Q8×D4711yescharacteristic
228C4#1309407211yescharacteristic
229C2—42no—
230C2Q8×C22⋊D4711yescharacteristic
231C2C2×#1309405011yescharacteristic
232C2#1568993811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingD4×Q8×C47C2
socleC22×C47C22×D4
hypercenterD4×Q8D47
hypocenterC47#3386
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×Q8 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. #15689851C2semidirect
2. #15689529C2semidirect
3. #15689526C2semidirect
5. #15689415C2semidirect
6. #15689405C2semidirect
8. #15689254C2semidirect
60. #10625335Q8semidirect
93. Dic94C2×Q8semidirect
96. C47⋊C8C2×Q8semidirect
128. C47#3386semidirect