Finite Group Databasebeta

← #20253926

Subgroups — #20253926

Order 6016.

340 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 149 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#15689754C211yesmaximal, characteristic
2#15689751C211yesmaximal, characteristic
3#15689531C212yesmaximal, complemented
4#15689530C212yesmaximal, complemented
5#15689527C212yesmaximal, complemented
6#15689523C212yesmaximal, complemented
7#15689165C211yesmaximal, characteristic
8#15689159C211yesmaximal, characteristic
9C2×#13093957C211yesmaximal, characteristic
10#15689081C211yesmaximal, characteristic
11C47×#428C211yesmaximal, characteristic
12C22×C47⋊C8C2211yescharacteristic
13#13094024—21no—
14#13094023—21no—
15#13094023C2212yes—
16#13094023C2212yes—
17#13094016—21no—
18#13094015—21no—
19#13094015C2212yes—
20#13094015C2212yes—
21#13094003—22no—
22#13094001—22no—
23#13093983C2211yescharacteristic
24#13093983C2211yescharacteristic
25C2×C4⋊Dic47C2211yescharacteristic
26#13093958C2212yes—
27#13093957C2211yescharacteristic
28#13093957C2212yes—
29#13093957C2211yescharacteristic
30#13093957C2212yes—
31#13093956C2212yes—
32#13093955C2211yescharacteristic
33#13093955C2211yescharacteristic
34#13093934C2212yes—
35C8×Dic47C2212yes—
36C2×M16×C47C2211yescharacteristic
37#117×C47C2211yescharacteristic
38C2×C4⋊C4×C47C2211yescharacteristic
39#107×C47C2212yes—
40#106×C47C2212yes—
41C22×C4×C47—21no—
42C22×C4×C47C2311yescharacteristic
43C22×Dic47—21no—
44C2×Dic94—22no—
45C2×Dic94—22no—
46M16×C47Q814yescomplemented
47C2×C8×C47C2312yes—
48C4⋊C4×C47—21no—
49C4⋊C4×C47C2311yescharacteristic
50C4⋊C4×C47C2312yes—
51C4⋊C4×C47C2311yescharacteristic
52C22⋊C4×C47—21no—
53C42×C47—21no—
54C22⋊Dic47—21no—
55C22⋊Dic47D412yes—
56C4⋊Dic47—21no—
57C4⋊Dic47—22no—
58C4⋊Dic47—22no—
59C4⋊Dic47D411yescharacteristic
60C4⋊Dic47D411yescharacteristic
61C4⋊Dic47C2311yescharacteristic
62C4⋊Dic47C2311yescharacteristic
63C4⋊Dic47C2312yes—
64Dic47⋊C4—22no—
65Dic47⋊C4—22no—
66Dic47⋊C4—22no—
67Dic47⋊C4—22no—
68C4×Dic47—21no—
69C4×Dic47C2312yes—
70C2×C47⋊C8Q814yescomplemented
71C2×C47⋊C8C2311yescharacteristic
72C2×C47⋊C8C2311yescharacteristic
73C23×C47C2×D411yescharacteristic
74C2×C4×C47—21no—
75C2×C4×C47—22no—
76C2×C4×C47—21no—
77C2×C4×C47—81no—
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2×Q812yes—
80C2×C4×C47C2×Q812yes—
81C2×C4×C47C2411yescharacteristic
82C2×Dic47—21no—
83C2×Dic47—21no—
84C2×Dic47—22no—
85C2×Dic47—81no—
86C2×Dic47C2×D412yes—
87C2×Dic47C2×D412yes—
88Dic94—82no—
89Dic94—82no—
90C8×C47C2×Q814yes—
91C47⋊C8C2×Q812yes—
92C47⋊C8C2×Q812yes—
93C22×C47—21no—
94C22×C47—21no—
95C22×C47C4⋊Q812yes—
96C22×C47C22×D411yescharacteristic
97C4×C47—41no—
98C4×C47—42no—
99C4×C47—41no—
100C4×C47C4⋊Q812yes—
101C4×C47C22×Q811yescharacteristic
102C4×C47C22×Q811yescharacteristic
103Dic47—22no—
104Dic47—22no—
105Dic47—41no—
106Dic47—42no—
107Dic47—41no—
108#3164—471nomaximal, Sylow
109C2×C47—22no—
110C2×C47C2×C4⋊Q811yescharacteristic
111C2×C47#57611yescharacteristic
112C2×C47#57811yescharacteristic
113#544—471no—
114#544—471no—
115#501—472no—
116#501—472no—
117#500—472no—
118#499—472no—
119#428—471no—
120#428D4711yescharacteristic
121#427—471no—
122C2×#107—471no—
123#405—471no—
124C47#316411yescharacteristic, complemented, Sylow
125C2×M16C2×D4711yescharacteristic
126C22×C8—471no—
127C4⋊Q8—472no—
128C4⋊Q8—472no—
129C4⋊Q8—941no—
130C4⋊Q8—941no—
131#125—472no—
132#125—472no—
133#125—941no—
134#125—941no—
135C22⋊Q8—942no—
136C22⋊Q8—942no—
137#117—471no—
138#117—471no—
139#117C2×D4711yescharacteristic
140C2×C4⋊C4—471no—
141C2×C4⋊C4C2×D4711yescharacteristic
142#107—472no—
143#107—472no—
144#107—472no—
145#107—471no—
146#107—471no—
147#107C2×D4712yes—
148#106—472no—
149#106—471no—
150#106—471no—
151#106C2×D4712yes—
152#97—472no—
153C4×C8—472no—
154C2×Q8—942no—
155C2×Q8—942no—
156C22×C4—21no—
157C22×C4—941no—
158C22×C4C22×D4711yescharacteristic
159M16Dic9414yescomplemented
160C2×C8—474no—
161C2×C8—471no—
162C2×C8—471no—
163C2×C8C22×D4712yes—
164C4⋊C4—21no—
165C4⋊C4—471no—
166C4⋊C4—471no—
167C4⋊C4—471no—
168C4⋊C4—472no—
169C4⋊C4—471no—
170C4⋊C4—942no—
171C4⋊C4—942no—
172C4⋊C4—942no—
173C4⋊C4—942no—
174C4⋊C4—942no—
175C4⋊C4—942no—
176C4⋊C4—941no—
177C4⋊C4C22×D4711yescharacteristic
178C4⋊C4C22×D4711yescharacteristic
179C4⋊C4C22×D4712yes—
180C22⋊C4—21no—
181C22⋊C4—472no—
182C22⋊C4—941no—
183C42—21no—
184C42—472no—
185C42—941no—
186C23D4×D4711yescharacteristic
187Q8—3762no—
188Q8—3762no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—81no—
193C2×C4—472no—
194C2×C4—472no—
195C2×C4—941no—
196C2×C4—941no—
197C2×C4—942no—
198C2×C4—3761no—
199C2×C4C2×Dic9412yes—
200C2×C4D4×D4711yescharacteristic
201C2×C4Q8×D4712yes—
202C2×C4C23×D4711yescharacteristic
203C8—472no—
204C8—472no—
205C8C2×Dic9414yes—
206C22—21no—
207C22—21no—
208C22#1309402312yes—
209C22C2×D4×D4711yescharacteristic
210C4—42no—
211C4—41no—
212C4—41no—
213C4—942no—
214C4—942no—
215C4—1882no—
216C4—1881no—
217C4—1881no—
218C4#1309402312yes—
219C4C2×Q8×D4711yescharacteristic
220C4C22×Dic9411yescharacteristic
221C2—22no—
222C2C2×#1309402311yescharacteristic
223C2#1568992711yescharacteristic
224C2#1568993911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#428C2
socleC22×C47C22×D4
hypercenter#428D47
hypocenterC47#3164
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
3. #15689531C2semidirect
4. #15689530C2semidirect
5. #15689527C2semidirect
6. #15689523C2semidirect
46. M16×C47Q8semidirect
70. C2×C47⋊C8Q8semidirect
124. C47#3164semidirect
159. M16Dic94semidirect