Finite Group Databasebeta

← #20256204

Subgroups — #20256204

Order 6016.

350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 123 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#15689858C211yesmaximal, characteristic
2Q8×Dic94C211yesmaximal, characteristic, complemented
3#15689483C212yesmaximal, complemented
4#15689470C211yesmaximal, characteristic
5#15689419C211yesmaximal, characteristic, complemented
6#15689404C212yesmaximal, complemented
7#15689346C212yesmaximal, complemented
8#15689324C211yesmaximal, characteristic
9#15689225C212yesmaximal, complemented
10C4×Dic188C211yesmaximal, characteristic, complemented
11C47×#446C211yesmaximal, characteristic, complemented
12C2×Dic188C2211yescharacteristic
13C2×#10625325C2212yes—
14#13094024C2212yes—
15#13094024C2211yescharacteristic
16#13094023—21no—
17#13094023—22no—
18#13094021C2211yescharacteristic
19#13094013—21no—
20#13094012C2212yes—
21#13094009—22no—
22Q8×Dic47—21no—
23C4×Dic94C2211yescharacteristic
24C4×Dic94C2211yescharacteristic
25C4×Dic94C2212yes—
26C4×D188C2212yes—
27#13093986—21no—
28#13093958C2211yescharacteristic
29#13093958C2212yes—
30#13093949C2211yescharacteristic
31#13093949C2211yescharacteristic
32#13093949C2212yes—
33#13093946C2212yes—
34#13093946C2212yes—
35#13093946C2212yes—
36C4×Q8×C47C2211yescharacteristic
37C4⋊C8×C47C2211yescharacteristic
38C4⋊C8×C47C2212yes—
39#97×C47C2212yes—
40C4×C8×C47C2211yescharacteristic
41C2×Q8×C47D411yescharacteristic
42C2×D188—21no—
43C2×D188—21no—
44C2×D188C2312yes—
45C2×C4×D47—22no—
46C2×Dic94—21no—
47C2×Dic94—22no—
48C2×Dic94C2311yescharacteristic
49C2×Dic94C2311yescharacteristic
50C2×C8×C47C2311yescharacteristic
51C2×C8×C47C2312yes—
52C2×C8×C47C2311yescharacteristic
53C4⋊C4×C47D411yescharacteristic
54C4⋊C4×C47D412yes—
55C42×C47C2312yes—
56C42×C47C2311yescharacteristic
57(C2×D47)⋊C4—22no—
58(C2×D47)⋊C4—22no—
59(C2×D47)⋊C4—22no—
60C4⋊Dic47—22no—
61C4⋊Dic47—21no—
62C4⋊Dic47C2312yes—
63C4⋊Dic47C2311yescharacteristic
64C4⋊Dic47C2311yescharacteristic
65Dic47⋊C4—21no—
66Dic47⋊C4—21no—
67Dic47⋊C4—22no—
68C4×Dic47—21no—
69C4×Dic47—22no—
70C4×Dic47—21no—
71Dic188—22no—
72#10625325—24no—
73C22×D47—22no—
74Q8×C47—22no—
75C2×C4×C47C2×D412yes—
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2×D412yes—
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2411yescharacteristic
80C2×Dic47—21no—
81C2×Dic47—22no—
82C2×Dic47—21no—
83C2×Dic47—21no—
84C2×Dic47—21no—
85D188—22no—
86D188—22no—
87D188—42no—
88D188—81no—
89C4×D47—82no—
90Dic94—21no—
91Dic94—21no—
92Dic94—21no—
93Dic94—82no—
94Dic94—81no—
95Dic94#4112yes—
96C8×C47—22no—
97C8×C47—21no—
98C8×C47—21no—
99C22×C47C22×D411yescharacteristic
100C2×D47—42no—
101C2×D47—42no—
102C2×D47—42no—
103C4×C47—22no—
104C4×C47—22no—
105C4×C47—21no—
106C4×C47#13712yes—
107C4×C47C2×#4111yescharacteristic
108C4×C472−1+411yescharacteristic
109Dic47—22no—
110Dic47—41no—
111Dic47—41no—
112Dic47—42no—
113Dic47—41no—
114#3375—471nomaximal, Sylow
115C2×C47#54811yescharacteristic
116C2×C47C2×#13711yescharacteristic
117C2×C47#57611yescharacteristic
118D47—82no—
119#559—471no—
120Q82—471no—
121#489—472no—
122#486—471no—
123#477—471no—
124#474—472no—
125#464—472no—
126#460—471no—
127#446D4711yescharacteristic, complemented
128#440—472no—
129C4×Q16—471no—
130C47#337511yescharacteristic, complemented, Sylow
131C2×Q16—471no—
132C2×SD16—472no—
133C4⋊Q8—472no—
134C4⋊Q8—471no—
135C4⋊Q8—941no—
136C4⋊Q8—942no—
137#127—471no—
138#124—472no—
139#124—941no—
140#123—942no—
141C4×Q8—471no—
142C4×Q8—472no—
143C4×Q8—471no—
144C4×Q8—941no—
145C4×Q8C2×D4711yescharacteristic
146C4×D4—472no—
147C4×D4—941no—
148#107—471no—
149#107—472no—
150C4⋊C8C2×D4711yescharacteristic
151C4⋊C8C2×D4712yes—
152#103—471no—
153#103—471no—
154#103—472no—
155#102—472no—
156#102—472no—
157#102—472no—
158#97C2×D4712yes—
159C4×C8C2×D4711yescharacteristic
160C2×Q8—471no—
161C2×Q8—471no—
162C2×Q8—942no—
163C2×Q8—941no—
164C2×Q8D18811yescharacteristic
165C2×D4—472no—
166C2×D4—941no—
167C2×D4—941no—
168C22×C4—942no—
169Q16—942no—
170SD16—944no—
171C2×C8C22×D4711yescharacteristic
172C2×C8C22×D4711yescharacteristic
173C2×C8C22×D4712yes—
174C4⋊C4—472no—
175C4⋊C4—471no—
176C4⋊C4—471no—
177C4⋊C4—941no—
178C4⋊C4—942no—
179C4⋊C4—941no—
180C4⋊C4—942no—
181C4⋊C4—941no—
182C4⋊C4D18811yescharacteristic
183C4⋊C4D18812yes—
184C22⋊C4—942no—
185C22⋊C4—942no—
186C22⋊C4—942no—
187C42—941no—
188C42—942no—
189C42—941no—
190C42C22×D4711yescharacteristic
191C42C22×D4712yes—
192C23—942no—
193Q8—22no—
194Q8—472no—
195Q8—941no—
196Q8—941no—
197Q8—941no—
198Q8—3762no—
199Q8—3761no—
200D4—942no—
201D4—942no—
202D4—3761no—
203D4—1882no—
204C2×C4—941no—
205C2×C4—941no—
206C2×C4—941no—
207C2×C4—942no—
208C2×C4—941no—
209C2×C4—3762no—
210C2×C4C2×D18812yes—
211C2×C4C2×D18812yes—
212C2×C4C2×D18811yescharacteristic
213C2×C4C2×D18811yescharacteristic
214C2×C4C23×D4711yescharacteristic
215C8—22no—
216C8—21no—
217C8—21no—
218C22—1882no—
219C22—1882no—
220C22—1882no—
221C22C22×D18811yescharacteristic
222C4—22no—
223C4—22no—
224C4—21no—
225C4—942no—
226C4—1881no—
227C4—1881no—
228C4—1881no—
229C4—1882no—
230C4#1309405712yes—
231C4#41×D4711yescharacteristic
232C4#1309407211yescharacteristic
233C2—3762no—
234C2#1568978511yescharacteristic
235C2C2×#1309405711yescharacteristic
236C2#1568992811yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#446C2
socleC22×C47C22×D4
hypercenter#446D47
hypocenterC47#3375
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
2. Q8×Dic94C2semidirect
3. #15689483C2semidirect
5. #15689419C2semidirect
6. #15689404C2semidirect
7. #15689346C2semidirect
9. #15689225C2semidirect
10. C4×Dic188C2semidirect
11. C47×#446C2semidirect
127. #446D47semidirect
130. C47#3375semidirect