Finite Group Databasebeta

← #20244606

Subgroups — #20244606

Order 6016.

278 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 69 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#15689697C211yesmaximal, characteristic
2#15689165C211yesmaximal, characteristic, complemented
3C2×#13093950C211yesmaximal, characteristic
4#15689125C211yesmaximal, characteristic
5#15689030C211yesmaximal, characteristic, complemented
6#15688884C211yesmaximal, characteristic, complemented
7C2×#101×C47C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9#13094022—21no—
10#13094013—21no—
11#13094007—22no—
12#13094000—21no—
13#13094000—21no—
14#13093983C2211yescharacteristic
15C2×C4⋊Dic47C2211yescharacteristic
16C2×C4×Dic47C2211yescharacteristic
17#13093958—21no—
18#13093956—21no—
19#13093950—22no—
20#13093949—21no—
21#13093946—21no—
22C47⋊#95—22no—
23C22×Q8×C47C2211yescharacteristic
24C2×M16×C47C2211yescharacteristic
25C2×M16×C47C2211yescharacteristic
26#101×C47—22no—
27C2×Q8×C47—21no—
28C2×Q8×C47—21no—
29C2×Q8×C47—21no—
30C2×Q8×C47—21no—
31C2×Q8×C47—21no—
32C2×Q8×C47—21no—
33C22×C4×C47D412yes—
34C22×C4×C47C2311yescharacteristic
35C2×C22⋊D47—21no—
36C22×Dic47—21no—
37C22×Dic47—21no—
38#10625350—21no—
39#10625350—21no—
40#10625350—21no—
41#10625350—21no—
42C2×D188D411yescharacteristic
43C2×C4×D47—21no—
44C2×Dic94D411yescharacteristic
45M16×C47—21no—
46M16×C47—21no—
47M16×C47—21no—
48M16×C47D412yes—
49C2×C8×C47—21no—
50C2×C8×C47—21no—
51C22⋊Dic47—21no—
52(C2×D47)⋊C4—22no—
53(C2×D47)⋊C4—22no—
54C4⋊Dic47—21no—
55C4⋊Dic47—21no—
56C4⋊Dic47D411yescharacteristic
57C4⋊Dic47D411yescharacteristic
58Dic47⋊C4—22no—
59Dic47⋊C4—22no—
60C4×Dic47—21no—
61C4×Dic47—21no—
62C4×Dic47—21no—
63C23×C47C2×D411yescharacteristic
64C22×D47—21no—
65Q8×C47—41no—
66Q8×C47—41no—
67Q8×C47—41no—
68Q8×C47—41no—
69C2×C4×C47—22no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47#4111yescharacteristic
76C2×C4×C47#4111yescharacteristic
77C2×C4×C47#4111yescharacteristic
78C22⋊D47—41no—
79C22⋊D47—41no—
80C2×Dic47—22no—
81C2×Dic47—21no—
82C2×Dic47—21no—
83C2×Dic47—21no—
84C2×Dic47—41no—
85C2×Dic47—41no—
86C2×Dic47—42no—
87C2×Dic47—41no—
88D188—21no—
89D188—21no—
90C4×D47—41no—
91C4×D47—41no—
92Dic94—21no—
93Dic94—21no—
94C8×C47—22no—
95C8×C47—41no—
96C22×C47—21no—
97C22×C47—21no—
98C22×C47#12011yescharacteristic
99C22×C47#12111yescharacteristic
100C22×C47#12311yescharacteristic
101C2×D47—41no—
102C2×D47—41no—
103C2×D47—41no—
104C4×C47—42no—
105C4×C47#12111yescharacteristic
106C4×C47#12111yescharacteristic
107C4×C47#12311yescharacteristic
108C4×C47#12411yescharacteristic
109Dic47—42no—
110Dic47—41no—
111Dic47—41no—
112Dic47—41no—
113Dic47—81no—
114#2038—471nomaximal, Sylow
115C2×C47—21no—
116C2×C47—21no—
117C2×C47#39411yescharacteristic
118C2×C47#45411yescharacteristic
119C2×C47#45611yescharacteristic
120D47—81no—
121#536—471no—
122#428—471no—
123C2×#104—471no—
124#417—471no—
125C2×#101D4711yescharacteristic, complemented
126#391—471no—
127#339—471no—
128C47#203811yescharacteristic, complemented, Sylow
129C2×#41—471no—
130C22×Q8C2×D4711yescharacteristic
131C2×M16C2×D4711yescharacteristic
132C2×M16C2×D4711yescharacteristic
133C4⋊Q8—941no—
134#124—941no—
135#123—942no—
136C22⋊Q8—941no—
137C22⋊Q8—941no—
138#117—471no—
139C2×C4⋊C4—471no—
140C2×C42—471no—
141#107—941no—
142#106—941no—
143#104—942no—
144#103—941no—
145#102—941no—
146#101—22no—
147#95—942no—
148#41—941no—
149#41—941no—
150#41—941no—
151#41—941no—
152C2×Q8—21no—
153C2×Q8—21no—
154C2×Q8—21no—
155C2×Q8—21no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—471no—
159C2×D4—471no—
160C2×D4—941no—
161C22×C4—941no—
162C22×C4—941no—
163C22×C4—941no—
164C22×C4D18812yes—
165C22×C4C22×D4711yescharacteristic
166M16—21no—
167M16—21no—
168M16—21no—
169M16C22⋊D4712yes—
170C2×C8—21no—
171C2×C8—21no—
172C4⋊C4—471no—
173C4⋊C4—471no—
174C4⋊C4—942no—
175C4⋊C4—942no—
176C4⋊C4—941no—
177C4⋊C4—941no—
178C22⋊C4—942no—
179C22⋊C4—942no—
180C22⋊C4—941no—
181C42—941no—
182C42—941no—
183C42—941no—
184C23—941no—
185C23C2×D18811yescharacteristic
186Q8—41no—
187Q8—41no—
188Q8—41no—
189Q8—41no—
190Q8—941no—
191Q8—941no—
192D4—941no—
193D4—941no—
194D4—1881no—
195D4—1881no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—942no—
200C2×C4—941no—
201C2×C4—941no—
202C2×C4—941no—
203C2×C4—1882no—
204C2×C4—1881no—
205C2×C4—1881no—
206C2×C4—1881no—
207C2×C4—1881no—
208C2×C4—1881no—
209C2×C4#1062535011yescharacteristic
210C2×C4D4×D4711yescharacteristic
211C2×C4D4×D4711yescharacteristic
212C2×C4#1062535211yescharacteristic
213C2×C4#1062535211yescharacteristic
214C2×C4C2×C22⋊D4711yescharacteristic
215C8—22no—
216C8—41no—
217C22—21no—
218C22—21no—
219C22—1881no—
220C22—1881no—
221C22—1881no—
222C22#1309399411yescharacteristic
223C22#1309399811yescharacteristic
224C22#1309400811yescharacteristic
225C4—42no—
226C4—3761no—
227C4—1882no—
228C4—1881no—
229C4—1881no—
230C4—1881no—
231C4#1309399511yescharacteristic
232C4#1309399611yescharacteristic
233C4#1309400611yescharacteristic
234C4#1309401011yescharacteristic
235C2—21no—
236C2—21no—
237C2—3761no—
238C2#1568903911yescharacteristic
239C2#1568929811yescharacteristic
240C2#1568930811yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC2×#101×C47C2
socleC22×C47#120
hypercenterC2×#101D47
hypocenterC47#2038
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. #15689165C2semidirect
5. #15689030C2semidirect
6. #15688884C2semidirect
7. C2×#101×C47C2semidirect
125. C2×#101D47semidirect
128. C47#2038semidirect