Finite Group Databasebeta

← #20256319

Subgroups — #20256319

Order 6016.

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

normal subgroups only

This group has 326 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#15689848C211yesmaximal, characteristic
3#15689530C212yesmaximal
4#15689519C211yesmaximal, characteristic
5#15689432C212yesmaximal
6#15689419C211yesmaximal, characteristic
7#15689407C212yesmaximal
8#15689250C211yesmaximal, characteristic
9#15689227C212yesmaximal
10C4×#10625337C211yesmaximal, characteristic
11C47×#475C211yesmaximal, characteristic
12C2×#10625337C2211yescharacteristic
13#13094024—21no—
14#13094024C2211yescharacteristic
15#13094023—22no—
16#13094023C2212yes—
17#13094022—21no—
18#13094015C2212yes—
19#13094014—22no—
20Q8×Dic47—21no—
21Q8×Dic47C2212yes—
22C4×Dic94—21no—
23C4×Dic94C2211yescharacteristic
24C4×Dic94C2211yescharacteristic
25#13093989C2212yes—
26#13093958C2212yes—
27#13093957C2211yescharacteristic
28#13093955C2212yes—
29#13093955C2212yes—
30Dic47⋊C8C2212yes—
31#13093949C2212yes—
32#13093948C2211yescharacteristic
33#13093947C2211yescharacteristic
34#13093934C2212yes—
35C4×C47⋊C8C2211yescharacteristic
36C4⋊Q8×C47C2211yescharacteristic
37C4×Q8×C47C2211yescharacteristic
38#106×C47C2212yes—
39C4⋊C8×C47C2211yescharacteristic
40#103×C47C2212yes—
41C2×Q8×C47—21no—
42C2×Q8×C47C2311yescharacteristic
43C2×Dic94—21no—
44C2×Dic94—22no—
45C2×Dic94D411yescharacteristic
46C2×Dic94C2311yescharacteristic
47C2×C8×C47C2312yes—
48C4⋊C4×C47—21no—
49C4⋊C4×C47—21no—
50C4⋊C4×C47C2312yes—
51C4⋊C4×C47C2311yescharacteristic
52C42×C47—21no—
53C42×C47C2311yescharacteristic
54#10625337Q814yescomplemented
55C4⋊Dic47—21no—
56C4⋊Dic47—22no—
57C4⋊Dic47—22no—
58C4⋊Dic47D411yescharacteristic
59C4⋊Dic47C2311yescharacteristic
60C4⋊Dic47C2312yes—
61Dic47⋊C4—21no—
62Dic47⋊C4—22no—
63Dic47⋊C4—22no—
64Dic47⋊C4—22no—
65Dic47⋊C4D412yes—
66C4×Dic47—21no—
67C4×Dic47—22no—
68C4×Dic47—22no—
69C4×Dic47C2312yes—
70C2×C47⋊C8C2311yescharacteristic
71C2×C47⋊C8C2311yescharacteristic
72Q8×C47—21no—
73Q8×C47—42no—
74Q8×C47C2×Q812yes—
75C2×C4×C47—21no—
76C2×C4×C47—22no—
77C2×C4×C47—21no—
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47C2411yescharacteristic
81C2×Dic47—21no—
82C2×Dic47—21no—
83C2×Dic47—22no—
84C2×Dic47C2×D412yes—
85C2×Dic47C2×D412yes—
86Dic94—22no—
87Dic94—21no—
88Dic94—82no—
89Dic94—81no—
90Dic94C2×Q812yes—
91C8×C47—22no—
92C47⋊C8—21no—
93C47⋊C8C2×Q812yes—
94C22×C47C22×D411yescharacteristic
95C4×C47—22no—
96C4×C47—21no—
97C4×C47—42no—
98C4×C47—41no—
99C4×C47#13712yes—
100C4×C47C22×Q811yescharacteristic
101C4×C472−1+411yescharacteristic
102Dic47—22no—
103Dic47—22no—
104Dic47—22no—
105Dic47—42no—
106Dic47—41no—
107#3387—471nomaximal, Sylow
108C2×C47D4×Q811yescharacteristic
109C2×C47C2×#13711yescharacteristic
110C2×C47#57711yescharacteristic
111Q82—471no—
112#557—471no—
113#501—472no—
114#498—471no—
115#479—472no—
116#477—471no—
117#475—472no—
118#475D4711yescharacteristic
119#446—471no—
120#441—472no—
121C4×Q16—471no—
122C47#338711yescharacteristic, complemented, Sylow
123C2×Q16—471no—
124C4⋊Q8—472no—
125C4⋊Q8—471no—
126C4⋊Q8—941no—
127C4⋊Q8—942no—
128C4⋊Q8—941no—
129C4⋊Q8C2×D4711yescharacteristic
130#125—472no—
131#125—942no—
132C4×Q8—471no—
133C4×Q8—472no—
134C4×Q8—472no—
135C4×Q8—471no—
136C4×Q8—941no—
137C4×Q8—941no—
138C4×Q8C2×D4711yescharacteristic
139#107—472no—
140#107—471no—
141#106—472no—
142#106—472no—
143#106C2×D4712yes—
144C4⋊C8—472no—
145C4⋊C8C2×D4711yescharacteristic
146#103—471no—
147#103—472no—
148#103—471no—
149#103C2×D4712yes—
150#97—472no—
151C4×C8—471no—
152C2×Q8—21no—
153C2×Q8—471no—
154C2×Q8—471no—
155C2×Q8—942no—
156C2×Q8—941no—
157C2×Q8C22×D4711yescharacteristic
158Q16—474no—
159C2×C8—471no—
160C2×C8—471no—
161C2×C8C22×D4712yes—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—472no—
165C4⋊C4—471no—
166C4⋊C4—472no—
167C4⋊C4—471no—
168C4⋊C4—942no—
169C4⋊C4—942no—
170C4⋊C4—942no—
171C4⋊C4—942no—
172C4⋊C4—942no—
173C4⋊C4—941no—
174C4⋊C4—941no—
175C4⋊C4C22×D4711yescharacteristic
176C4⋊C4C22×D4712yes—
177C42—21no—
178C42—472no—
179C42—942no—
180C42—942no—
181C42—941no—
182C42C22×D4711yescharacteristic
183Q8—21no—
184Q8—42no—
185Q8—472no—
186Q8—942no—
187Q8—941no—
188Q8—3761no—
189Q8—3762no—
190Q8Q8×D4712yes—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—472no—
195C2×C4—472no—
196C2×C4—941no—
197C2×C4—941no—
198C2×C4—942no—
199C2×C4D4×D4711yescharacteristic
200C2×C4D4×D4711yescharacteristic
201C2×C4C23×D4711yescharacteristic
202C8—22no—
203C8—472no—
204C8—941no—
205C22C2×D4×D4711yescharacteristic
206C4—22no—
207C4—21no—
208C4—42no—
209C4—41no—
210C4—942no—
211C4—942no—
212C4—942no—
213C4—1882no—
214C4—1881no—
215C4#1309405312yes—
216C4C2×Q8×D4711yescharacteristic
217C4#1309407111yescharacteristic
218C2#1568978611yescharacteristic
219C2C2×#1309405311yescharacteristic
220C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#475C2
socleC22×C47C22×D4
hypercenter#475D47
hypocenterC47#3387
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
54. #10625337Q8semidirect
122. C47#3387semidirect