Finite Group Databasebeta

← #20256318

Subgroups — #20256318

Order 6016.

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

normal subgroups only

This group has 326 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
1Q8×Dic94C211yesmaximal, characteristic
2#15689852C211yesmaximal, characteristic
3#15689531C212yesmaximal
4#15689521C211yesmaximal, characteristic
5#15689428C212yesmaximal
6#15689418C211yesmaximal, characteristic
7#15689408C211yesmaximal, characteristic
8#15689406C212yesmaximal
9#15689253C211yesmaximal, characteristic
10#15689230C212yesmaximal
11C4×Q16×C47C211yesmaximal, characteristic
12#13094024—21no—
13#13094024—21no—
14#13094024C2211yescharacteristic
15#13094024C2211yescharacteristic
16#13094023—22no—
17#13094023C2212yes—
18#13094015—22no—
19#13094015C2212yes—
20Q8×Dic47C2212yes—
21Q8×Dic47C2212yes—
22C4×Dic94—21no—
23C4×Dic94—21no—
24C4×Dic94C2211yescharacteristic
25#13093957C2212yes—
26#13093956C2212yes—
27#13093956C2212yes—
28#13093955C2212yes—
29C4⋊(C47⋊C8)C2211yescharacteristic
30Dic47⋊C8C2212yes—
31#13093948C2212yes—
32#13093948C2212yes—
33#13093934C2212yes—
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—21no—
45C2×Dic94—22no—
46C2×Dic94D411yescharacteristic
47Q16×C47Q814yescomplemented
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
57C4⋊Dic47—21no—
58C4⋊Dic47—21no—
59C4⋊Dic47—22no—
60C4⋊Dic47—22no—
61C4⋊Dic47—22no—
62C4⋊Dic47D411yescharacteristic
63C4⋊Dic47C2312yes—
64C4⋊Dic47C2312yes—
65Dic47⋊C4—22no—
66Dic47⋊C4—22no—
67Dic47⋊C4D412yes—
68C4×Dic47—22no—
69C4×Dic47—22no—
70C4×Dic47C2312yes—
71C2×C47⋊C8C2312yes—
72Q8×C47—21no—
73Q8×C47—21no—
74Q8×C47C2×Q812yes—
75Q8×C47C2×Q812yes—
76C2×C4×C47—21no—
77C2×C4×C47—21no—
78C2×C4×C47—21no—
79C2×C4×C47—21no—
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47C2411yescharacteristic
83C2×Dic47—22no—
84C2×Dic47—22no—
85C2×Dic47C2×D412yes—
86C2×Dic47C2×D412yes—
87Dic94—22no—
88Dic94—42no—
89Dic94—82no—
90Dic94—81no—
91C8×C47—21no—
92C8×C47C2×Q812yes—
93C47⋊C8—22no—
94C22×C47C22×D411yescharacteristic
95C4×C47—22no—
96C4×C47—22no—
97C4×C47—21no—
98C4×C47—41no—
99C4×C47—41no—
100C4×C47#13712yes—
101C4×C47C22×Q811yescharacteristic
102C4×C472−1+411yescharacteristic
103Dic47—22no—
104Dic47—22no—
105Dic47—42no—
106Dic47—42no—
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—471no—
118#475—472no—
119#446—471no—
120#441—472no—
121C4×Q16D4711yescharacteristic
122C47#338711yescharacteristic, complemented, Sylow
123C2×Q16C2×D4711yescharacteristic
124C4⋊Q8—472no—
125C4⋊Q8—471no—
126C4⋊Q8—471no—
127C4⋊Q8—941no—
128C4⋊Q8—941no—
129C4⋊Q8—942no—
130#125—472no—
131#125—942no—
132C4×Q8—471no—
133C4×Q8—472no—
134C4×Q8—472no—
135C4×Q8—941no—
136C4×Q8—941no—
137C4×Q8C2×D4711yescharacteristic
138C4×Q8C2×D4711yescharacteristic
139#107—472no—
140#107C2×D4711yescharacteristic
141#106—472no—
142#106—472no—
143#106—472no—
144C4⋊C8—472no—
145C4⋊C8—471no—
146#103—472no—
147#103—472no—
148#103C2×D4711yescharacteristic
149#103C2×D4711yescharacteristic
150#97—472no—
151C4×C8C2×D4711yescharacteristic
152C2×Q8—471no—
153C2×Q8—942no—
154C2×Q8—941no—
155C2×Q8—941no—
156C2×Q8C22×D4711yescharacteristic
157C2×Q8C22×D4711yescharacteristic
158Q16Dic9414yescomplemented
159C2×C8—472no—
160C2×C8C22×D4711yescharacteristic
161C2×C8C22×D4711yescharacteristic
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—472no—
165C4⋊C4—471no—
166C4⋊C4—472no—
167C4⋊C4—472no—
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×D4711yescharacteristic
177C42—21no—
178C42—21no—
179C42—472no—
180C42—942no—
181C42—942no—
182C42C22×D4711yescharacteristic
183Q8—21no—
184Q8—21no—
185Q8—942no—
186Q8—3761no—
187Q8—3762no—
188Q8—1882no—
189Q8C2×Dic9412yes—
190Q8C2×Dic9412yes—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—472no—
196C2×C4—472no—
197C2×C4—942no—
198C2×C4—942no—
199C2×C4D4×D4711yescharacteristic
200C2×C4D4×D4711yescharacteristic
201C2×C4C23×D4711yescharacteristic
202C8—21no—
203C8—942no—
204C8C2×Dic9412yes—
205C22C2×D4×D4711yescharacteristic
206C4—22no—
207C4—22no—
208C4—21no—
209C4—41no—
210C4—41no—
211C4—942no—
212C4—942no—
213C4—1882no—
214C4—1882no—
215C4#1309405612yes—
216C4C22×Dic9411yescharacteristic
217C4#1309407111yescharacteristic
218C2D4×Dic9411yescharacteristic
219C2C2×#1309405611yescharacteristic
220C2#1568993011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC4×Q16×C47C2
socleC22×C47C22×D4
hypercenterC4×Q16D47
hypocenterC47#3387
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
47. Q16×C47Q8semidirect
122. C47#3387semidirect
158. Q16Dic94semidirect