Finite Group Databasebeta

← #20256064

Subgroups — #20256064

Order 6016.

336 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 125 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
1Q8×Dic94C211yesmaximal, characteristic
2#15689851C211yesmaximal, characteristic
3#15689474C211yesmaximal, characteristic
4#15689472C212yesmaximal
5#15689418C211yesmaximal, characteristic
6#15689417C212yesmaximal
7#15689333C211yesmaximal, characteristic
8#15689331C212yesmaximal
9C8×Dic94C211yesmaximal, characteristic
10#15689215C212yesmaximal
11C4×Q16×C47C211yesmaximal, characteristic
12C2×#10625337C2212yes—
13#13094024—21no—
14#13094024C2211yescharacteristic
15#13094024C2211yescharacteristic
16#13094023—22no—
17#13094023C2212yes—
18#13094022C2212yes—
19#13094016—21no—
20#13094014—22no—
21Q8×Dic47C2212yes—
22C4×Dic94—21no—
23C4×Dic94—21no—
24C4×Dic94C2211yescharacteristic
25#13093989C2212yes—
26#13093957C2212yes—
27C4⋊(C47⋊C8)C2211yescharacteristic
28Dic47⋊C8C2212yes—
29#13093949C2212yes—
30#13093949C2212yes—
31#13093948C2212yes—
32#13093947C2212yes—
33C8×Dic47C2212yes—
34C2×Q16×C47C2211yescharacteristic
35C4×Q8×C47C2211yescharacteristic
36C4×Q8×C47C2211yescharacteristic
37#107×C47C2211yescharacteristic
38#103×C47C2211yescharacteristic
39#103×C47C2211yescharacteristic
40C4×C8×C47C2211yescharacteristic
41C2×Q8×C47C2311yescharacteristic
42C2×Q8×C47C2311yescharacteristic
43C2×Dic94—21no—
44C2×Dic94—22no—
45C2×Dic94D411yescharacteristic
46C2×Dic94C2312yes—
47Q16×C47—22no—
48C2×C8×C47C2311yescharacteristic
49C2×C8×C47C2311yescharacteristic
50C4⋊C4×C47—21no—
51C4⋊C4×C47—21no—
52C4⋊C4×C47C2311yescharacteristic
53C4⋊C4×C47C2311yescharacteristic
54C42×C47—21no—
55C42×C47—21no—
56C42×C47C2311yescharacteristic
57#10625337—24no—
58C4⋊Dic47—21no—
59C4⋊Dic47—21no—
60C4⋊Dic47—21no—
61C4⋊Dic47—22no—
62C4⋊Dic47D411yescharacteristic
63C4⋊Dic47C2312yes—
64Dic47⋊C4—22no—
65Dic47⋊C4—22no—
66Dic47⋊C4—22no—
67Dic47⋊C4—22no—
68Dic47⋊C4D412yes—
69C4×Dic47—22no—
70C4×Dic47—22no—
71C4×Dic47C2312yes—
72C2×C47⋊C8C2312yes—
73Q8×C47—21no—
74Q8×C47—21no—
75Q8×C47—21no—
76Q8×C47#4112yes—
77C2×C4×C47—21no—
78C2×C4×C47—21no—
79C2×C4×C47—21no—
80C2×C4×C47—21no—
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47C2×D411yescharacteristic
83C2×C4×C47C2411yescharacteristic
84C2×Dic47—22no—
85C2×Dic47—22no—
86C2×Dic47C2×D412yes—
87C2×Dic47C2×D412yes—
88Dic94—22no—
89Dic94—22no—
90Dic94—82no—
91Dic94—81no—
92Dic94Q1614yescomplemented
93C8×C47—21no—
94C8×C47—21no—
95C47⋊C8—22no—
96C22×C47C22×D411yescharacteristic
97C4×C47—22no—
98C4×C47—21no—
99C4×C47—41no—
100C4×C47—41no—
101C4×C47—41no—
102C4×C47C2×Q1612yes—
103C4×C47C2×#4111yescharacteristic
104C4×C472−1+411yescharacteristic
105Dic47—22no—
106Dic47—42no—
107Dic47—42no—
108Dic47C2×Q1614yes—
109#3363—471nomaximal, Sylow
110C2×C47#54811yescharacteristic
111C2×C47C22×Q1611yescharacteristic
112C2×C47#57711yescharacteristic
113Q82—471no—
114#557—471no—
115#487—472no—
116#487—471no—
117#477—471no—
118#477—472no—
119#462—472no—
120#462—471no—
121C8×Q8—471no—
122C4×Q16—472no—
123C4×Q16D4711yescharacteristic
124C47#336311yescharacteristic, complemented, Sylow
125C2×Q16—472no—
126C2×Q16C2×D4711yescharacteristic
127C4⋊Q8—472no—
128C4⋊Q8—472no—
129C4⋊Q8—471no—
130C4⋊Q8—471no—
131C4⋊Q8—941no—
132C4⋊Q8—942no—
133#125—941no—
134#125—942no—
135C4×Q8—471no—
136C4×Q8—472no—
137C4×Q8—472no—
138C4×Q8—941no—
139C4×Q8—941no—
140C4×Q8C2×D4711yescharacteristic
141C4×Q8C2×D4711yescharacteristic
142#107—472no—
143#107C2×D4711yescharacteristic
144C4⋊C8—472no—
145C4⋊C8—471no—
146#103—472no—
147#103—472no—
148#103—472no—
149#103—472no—
150#103C2×D4711yescharacteristic
151#103C2×D4711yescharacteristic
152C4×C8—472no—
153C4×C8C2×D4711yescharacteristic
154C2×Q8—471no—
155C2×Q8—472no—
156C2×Q8—942no—
157C2×Q8—941no—
158C2×Q8C22×D4711yescharacteristic
159C2×Q8C22×D4711yescharacteristic
160Q16—22no—
161Q16—944no—
162C2×C8—472no—
163C2×C8C22×D4711yescharacteristic
164C2×C8C22×D4711yescharacteristic
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—472no—
168C4⋊C4—471no—
169C4⋊C4—472no—
170C4⋊C4—942no—
171C4⋊C4—942no—
172C4⋊C4—942no—
173C4⋊C4—942no—
174C4⋊C4—942no—
175C4⋊C4—941no—
176C4⋊C4—941no—
177C4⋊C4—941no—
178C4⋊C4C22×D4711yescharacteristic
179C4⋊C4C22×D4711yescharacteristic
180C42—21no—
181C42—21no—
182C42—472no—
183C42—942no—
184C42—942no—
185C42C22×D4711yescharacteristic
186Q8—21no—
187Q8—21no—
188Q8—21no—
189Q8—474no—
190Q8—942no—
191Q8—942no—
192Q8—3761no—
193Q8—3762no—
194Q8#1062535012yes—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—472no—
200C2×C4—472no—
201C2×C4—942no—
202C2×C4—942no—
203C2×C4D4×D4711yescharacteristic
204C2×C4D4×D4711yescharacteristic
205C2×C4C23×D4711yescharacteristic
206C8—21no—
207C8—21no—
208C8—942no—
209C22C2×D4×D4711yescharacteristic
210C4—22no—
211C4—21no—
212C4—41no—
213C4—41no—
214C4—41no—
215C4—474no—
216C4—942no—
217C4—1882no—
218C4—1882no—
219C4Q16×D4712yes—
220C4C2×#1062535011yescharacteristic
221C4#1309407111yescharacteristic
222C2#1568978211yescharacteristic
223C2C2×Q16×D4711yescharacteristic
224C2#1568993011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC4×Q16×C47C2
socleC22×C47C22×D4
hypercenterC4×Q16D47
hypocenterC47#3363
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
92. Dic94Q16semidirect
124. C47#3363semidirect