Finite Group Databasebeta

← #20256300

Subgroups — #20256300

Order 6016.

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

normal subgroups only

This group has 340 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, complemented
2#15689833C211yesmaximal, characteristic
3#15689532C212yesmaximal, complemented
4#15689528C211yesmaximal, characteristic, complemented
5#15689431C212yesmaximal, complemented
6#15689419C211yesmaximal, characteristic, complemented
7#15689414C211yesmaximal, characteristic
8#15689404C212yesmaximal
9#15689225C212yesmaximal
10C4×#10625325C211yesmaximal, characteristic
11C47×#446C211yesmaximal, characteristic, complemented
12C2×#10625325C2211yescharacteristic
13#13094024C2211yescharacteristic
14#13094024C2211yescharacteristic
15#13094024C2212yes—
16#13094023—21no—
17#13094023—22no—
18#13094016C2212yes—
19#13094002—22no—
20#13094000—21no—
21Q8×Dic47—21no—
22C4×Dic94C2212yes—
23C4×Dic94C2211yescharacteristic
24C4×D188C2212yes—
25C4×D188C2211yescharacteristic
26C4⋊C4×D47—21no—
27#13093958C2212yes—
28#13093958C2212yes—
29#13093958C2212yes—
30#13093956C2211yescharacteristic
31#13093956C2212yes—
32#13093949C2212yes—
33#13093949C2211yescharacteristic
34#13093946C2212yes—
35#13093946C2211yescharacteristic
36C4×Q8×C47C2211yescharacteristic
37C4⋊C8×C47C2212yes—
38C4⋊C8×C47C2211yescharacteristic
39#97×C47C2212yes—
40C4×C8×C47C2211yescharacteristic
41C2×Q8×C47D411yescharacteristic
42C2×D188C2311yescharacteristic
43C2×C4×D47—21no—
44C2×C4×D47—22no—
45C2×Dic94—21no—
46C2×Dic94—22no—
47C2×Dic94—21no—
48C2×Dic94C2311yescharacteristic
49C2×C8×C47C2312yes—
50C2×C8×C47C2311yescharacteristic
51C2×C8×C47C2311yescharacteristic
52C4⋊C4×C47D411yescharacteristic
53C4⋊C4×C47D412yes—
54C42×C47C2312yes—
55C42×C47C2311yescharacteristic
56(C2×D47)⋊C4—22no—
57(C2×D47)⋊C4—21no—
58C4⋊Dic47—21no—
59C4⋊Dic47—22no—
60C4⋊Dic47—21no—
61C4⋊Dic47C2312yes—
62C4⋊Dic47C2311yescharacteristic
63C4⋊Dic47C2311yescharacteristic
64C4⋊Dic47C2312yes—
65Dic47⋊C4—22no—
66Dic47⋊C4—22no—
67Dic47⋊C4—21no—
68Dic47⋊C4—22no—
69C4×Dic47—22no—
70C4×Dic47—21no—
71#10625325Q814yescomplemented
72C22×D47—21no—
73Q8×C47—22no—
74C2×C4×C47C2×D412yes—
75C2×C4×C47C2×D412yes—
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2×D411yescharacteristic
78C2×C4×C47C2411yescharacteristic
79C2×Dic47—21no—
80C2×Dic47—22no—
81C2×Dic47—21no—
82C2×Dic47—21no—
83C2×Dic47—22no—
84D188—21no—
85D188C2×Q812yes—
86C4×D47—42no—
87C4×D47—82no—
88Dic94—21no—
89Dic94—81no—
90Dic94—82no—
91Dic94—81no—
92Dic94C2×Q812yes—
93C8×C47—22no—
94C8×C47—21no—
95C8×C47C2×Q812yes—
96C22×C47C22×D411yescharacteristic
97C2×D47—22no—
98C2×D47—41no—
99C2×D47—41no—
100C4×C47—22no—
101C4×C47—21no—
102C4×C47—22no—
103C4×C47#13712yes—
104C4×C47C22×Q811yescharacteristic
105C4×C472−1+411yescharacteristic
106Dic47—22no—
107Dic47—41no—
108Dic47—42no—
109Dic47—41no—
110Dic47—42no—
111#3385—471nomaximal, Sylow
112C2×C47D4×Q811yescharacteristic
113C2×C47C2×#13711yescharacteristic
114C2×C47#57611yescharacteristic
115D47—42no—
116Q82—471no—
117#554—471no—
118#501—472no—
119#500—471no—
120#479—472no—
121#477—471no—
122#476—471no—
123#474—472no—
124#446D4711yescharacteristic, complemented
125#440—472no—
126C4×SD16—471no—
127C47#338511yescharacteristic, complemented, Sylow
128C2×SD16—471no—
129C4⋊Q8—471no—
130C4⋊Q8—472no—
131C4⋊Q8—471no—
132C4⋊Q8—941no—
133C4⋊Q8—942no—
134#125—472no—
135C22⋊Q8—941no—
136C22⋊Q8—942no—
137C4×Q8—471no—
138C4×Q8—472no—
139C4×Q8—941no—
140C4×Q8C2×D4711yescharacteristic
141C4×D4—471no—
142C4×D4—472no—
143C2×C4⋊C4—941no—
144#107—472no—
145#107—472no—
146#107—472no—
147#106—471no—
148#106—472no—
149C4⋊C8C2×D4712yes—
150C4⋊C8C2×D4711yescharacteristic
151#103—471no—
152#103—472no—
153#102—471no—
154#102—472no—
155#97C2×D4712yes—
156C4×C8C2×D4711yescharacteristic
157C2×Q8—471no—
158C2×Q8—941no—
159C2×Q8—941no—
160C2×Q8—942no—
161C2×Q8D18811yescharacteristic
162C2×D4—471no—
163C22×C4—942no—
164C22×C4—941no—
165SD16—474no—
166C2×C8C22×D4711yescharacteristic
167C2×C8C22×D4712yes—
168C2×C8C22×D4711yescharacteristic
169C4⋊C4—471no—
170C4⋊C4—472no—
171C4⋊C4—471no—
172C4⋊C4—472no—
173C4⋊C4—942no—
174C4⋊C4—941no—
175C4⋊C4—942no—
176C4⋊C4—942no—
177C4⋊C4—941no—
178C4⋊C4—942no—
179C4⋊C4—941no—
180C4⋊C4D18811yescharacteristic
181C4⋊C4D18812yes—
182C22⋊C4—941no—
183C22⋊C4—942no—
184C42—942no—
185C42—941no—
186C42C22×D4711yescharacteristic
187C42C22×D4712yes—
188C23—941no—
189Q8—22no—
190Q8—472no—
191Q8—941no—
192Q8—3762no—
193Q8—3761no—
194Q8—3761no—
195D4—472no—
196D4—941no—
197C2×C4—941no—
198C2×C4—942no—
199C2×C4—941no—
200C2×C4—941no—
201C2×C4—942no—
202C2×C4—3762no—
203C2×C4—1882no—
204C2×C4C2×D18812yes—
205C2×C4C2×D18811yescharacteristic
206C2×C4C2×D18812yes—
207C2×C4C2×D18811yescharacteristic
208C2×C4C23×D4711yescharacteristic
209C8—21no—
210C8—22no—
211C8Q8×D4712yes—
212C22—942no—
213C22—1881no—
214C22—1881no—
215C22C22×D18811yescharacteristic
216C4—22no—
217C4—22no—
218C4—21no—
219C4—942no—
220C4—1881no—
221C4—1882no—
222C4—1881no—
223C4—1882no—
224C4#1309405712yes—
225C4C2×Q8×D4711yescharacteristic
226C4#1309407111yescharacteristic
227C2—1882no—
228C2Q8×D18811yescharacteristic
229C2C2×#1309405711yescharacteristic
230C2#1568992811yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#446C2
socleC22×C47C22×D4
hypercenter#446D47
hypocenterC47#3385
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. Q8×Dic94C2semidirect
3. #15689532C2semidirect
4. #15689528C2semidirect
5. #15689431C2semidirect
6. #15689419C2semidirect
11. C47×#446C2semidirect
71. #10625325Q8semidirect
124. #446D47semidirect
127. C47#3385semidirect