Finite Group Databasebeta

← #20248592

Subgroups — #20248592

Order 6016.

500 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 171 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
1C2×#13094022C211yesmaximal, characteristic
2C2×#13093989C211yesmaximal, characteristic
3#15689044C211yesmaximal, characteristic
4#15689043C211yesmaximal, characteristic
5#15689042C211yesmaximal, characteristic
6#15689027C212yesmaximal
7#15689020C212yesmaximal
8#15689018C212yesmaximal
9#15688992C212yesmaximal
10#15688974C211yesmaximal, characteristic
11C47×#395C211yesmaximal, characteristic
12C22×Dic94C2211yescharacteristic
13C22×Dic94C2211yescharacteristic
14#13094022—24no—
15#13093989—24no—
16C2×C4⋊Dic47C2212yes—
17C2×Dic47⋊C4C2211yescharacteristic
18C2×Dic47⋊C4C2212yes—
19C2×Dic47⋊C4C2212yes—
20C2×Dic47⋊C4C2211yescharacteristic
21C2×Dic47⋊C4C2212yes—
22C2×Dic47⋊C4C2212yes—
23C2×Dic47⋊C4C2212yes—
24C2×C4×Dic47C2212yes—
25C2×C4×Dic47C2211yescharacteristic
26C2×C4×Dic47C2211yescharacteristic
27C2×C4×Dic47C2211yescharacteristic
28C47⋊#95C2211yescharacteristic
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C22×Q8×C47C2211yescharacteristic
33C2×C4⋊C4×C47C2211yescharacteristic
34C2×C4⋊C4×C47C2212yes—
35#95×C47C2211yescharacteristic
36#95×C47C2212yes—
37C2×Q8×C47—22no—
38C2×Q8×C47—42no—
39C22×C4×C47C2311yescharacteristic
40C22×C4×C47C2312yes—
41C22×C4×C47C2311yescharacteristic
42C22×C4×C47C2311yescharacteristic
43C22×C4×C47C2312yes—
44C22×Dic47C2312yes—
45C22×Dic47C2311yescharacteristic
46C22×Dic47C2311yescharacteristic
47C22×Dic47C2312yes—
48C22×Dic47C2311yescharacteristic
49C22×Dic47C2311yescharacteristic
50C2×Dic94—22no—
51C2×Dic94—22no—
52C2×Dic94—22no—
53C2×Dic94—42no—
54C2×Dic94Q814yescomplemented
55C4⋊C4×C47—22no—
56C4⋊C4×C47—42no—
57C4⋊Dic47—42no—
58Dic47⋊C4—22no—
59Dic47⋊C4—22no—
60Dic47⋊C4—24no—
61Dic47⋊C4—24no—
62Dic47⋊C4—42no—
63Dic47⋊C4—42no—
64Dic47⋊C4Q818yescomplemented
65C4×Dic47—22no—
66C4×Dic47—22no—
67C4×Dic47—24no—
68C4×Dic47D414yes—
69C23×C47C2411yescharacteristic
70Q8×C47—44no—
71C2×C4×C47—21no—
72C2×C4×C47—22no—
73C2×C4×C47—21no—
74C2×C4×C47—22no—
75C2×C4×C47—22no—
76C2×C4×C47—21no—
77C2×C4×C47—22no—
78C2×C4×C47—22no—
79C2×C4×C47—22no—
80C2×C4×C47—22no—
81C2×C4×C47C2×D412yes—
82C2×C4×C47C2×Q814yes—
83C2×C4×C47C2×Q812yes—
84C2×Dic47—21no—
85C2×Dic47—22no—
86C2×Dic47—21no—
87C2×Dic47—22no—
88C2×Dic47—21no—
89C2×Dic47—22no—
90C2×Dic47—22no—
91C2×Dic47—22no—
92C2×Dic47—22no—
93C2×Dic47C2×D412yes—
94C2×Dic47C2×D412yes—
95C2×Dic47C2×Q814yes—
96C2×Dic47C2×Q812yes—
97C2×Dic47C2×Q812yes—
98C2×Dic47C2×Q814yes—
99C2×Dic47#4112yes—
100Dic94—28no—
101Dic94—44no—
102C22×C47C22×D411yescharacteristic
103C22×C47C22×Q811yescharacteristic
104C22×C47C22×Q812yes—
105C22×C47C2×#4111yescharacteristic
106C22×C47H(5,𝔽2)12yes—
107C4×C47—22no—
108C4×C47—22no—
109C4×C47—24no—
110C4×C47—41no—
111C4×C47—42no—
112Dic47—22no—
113Dic47—24no—
114Dic47—42no—
115Dic47—41no—
116Dic47C22⋊Q814yes—
117Dic47C4⋊Q814yes—
118#2567—471nomaximal, Sylow
119C2×C47C2×C22⋊Q811yescharacteristic
120C2×C47C2×C4⋊Q811yescharacteristic
121C2×C47#53511yescharacteristic
122C2×C47#55412yes—
123C2×C47Q8212yes—
124C2×C4⋊Q8—471no—
125C2×C4×Q8—471no—
126#395—471no—
127#395—471no—
128#395—471no—
129#395D4711yescharacteristic
130#391—472no—
131#389—472no—
132#389—472no—
133#384—472no—
134C4×C4⋊C4—471no—
135C47#256711yescharacteristic, complemented, Sylow
136C22×Q8—471no—
137C22×Q8—471no—
138C22×Q8C2×D4711yescharacteristic
139C4⋊Q8—944no—
140C4×Q8—944no—
141C2×C4⋊C4—472no—
142C2×C4⋊C4—471no—
143C2×C4⋊C4—471no—
144C2×C4⋊C4—472no—
145C2×C4⋊C4—472no—
146C2×C4⋊C4—472no—
147C2×C4⋊C4—472no—
148C2×C4⋊C4—472no—
149C2×C4⋊C4C2×D4711yescharacteristic
150C2×C4⋊C4C2×D4712yes—
151C2×C42—471no—
152C2×C42—471no—
153C2×C42—471no—
154C2×C42—472no—
155#95—471no—
156#95—472no—
157#95—472no—
158#95—472no—
159#95C2×D4711yescharacteristic
160#95C2×D4712yes—
161C2×Q8—22no—
162C2×Q8—42no—
163C2×Q8—474no—
164C2×Q8—942no—
165C2×Q8—942no—
166C2×Q8—942no—
167C2×Q8—1882no—
168C22×C4—471no—
169C22×C4—471no—
170C22×C4—471no—
171C22×C4—472no—
172C22×C4—472no—
173C22×C4—471no—
174C22×C4C22×D4712yes—
175C22×C4C22×D4711yescharacteristic
176C22×C4C22×D4711yescharacteristic
177C22×C4C22×D4711yescharacteristic
178C22×C4C22×D4712yes—
179C4⋊C4—22no—
180C4⋊C4—42no—
181C4⋊C4—478no—
182C4⋊C4—942no—
183C4⋊C4—944no—
184C4⋊C4—944no—
185C4⋊C4—942no—
186C4⋊C4—1882no—
187C4⋊C4—1882no—
188C4⋊C4—1882no—
189C42—474no—
190C42—944no—
191C42—942no—
192C42—942no—
193C23C23×D4711yescharacteristic
194Q8—44no—
195Q8—948no—
196Q8—1884no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—472no—
208C2×C4—472no—
209C2×C4—474no—
210C2×C4—472no—
211C2×C4—472no—
212C2×C4—474no—
213C2×C4—472no—
214C2×C4—941no—
215C2×C4—942no—
216C2×C4—941no—
217C2×C4—942no—
218C2×C4—941no—
219C2×C4—942no—
220C2×C4—942no—
221C2×C4—942no—
222C2×C4—942no—
223C2×C4D4×D4712yes—
224C2×C4Q8×D4714yes—
225C2×C4Q8×D4712yes—
226C22C2×D4×D4711yescharacteristic
227C22C2×Q8×D4712yes—
228C22C2×Q8×D4711yescharacteristic
229C22#41×D4711yescharacteristic
230C22#1309406912yes—
231C4—24no—
232C4—22no—
233C4—22no—
234C4—42no—
235C4—41no—
236C4—474no—
237C4—474no—
238C4—944no—
239C4—942no—
240C4—1882no—
241C4—1881no—
242C2C22⋊Q8×D4711yescharacteristic
243C2C4⋊Q8×D4711yescharacteristic
244C2#1568968811yescharacteristic
245C2#1568982712yes—
246C2#1568985312yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#395C2
hypercenter#395D47
hypocenterC47#2567
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
54. C2×Dic94Q8semidirect
64. Dic47⋊C4Q8semidirect
135. C47#2567semidirect