Finite Group Databasebeta

← #34067634

Subgroups — #34067634

Order 19328.

242 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 63 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#23752748C211yesmaximal, characteristic
2#23752266C211yesmaximal, characteristic, complemented
3#23752063C211yesmaximal, characteristic, complemented
4#23751949C211yesmaximal, characteristic, complemented
5#23751947C211yesmaximal, characteristic
6#23751945C211yesmaximal, characteristic
7#328×C151C211yesmaximal, characteristic, complemented
8#18012734—21no—
9#18012730C411yescharacteristic, complemented
10#18012728C411yescharacteristic, complemented
11#18012723—21no—
12#18012713C2211yescharacteristic
13Q8×Dic151C411yescharacteristic, complemented
14#18012701C411yescharacteristic, complemented
15(C22⋊D151)⋊C4—21no—
16#18012697—21no—
17C2×Dic151⋊C4—21no—
18C2×C4×Dic151—21no—
19C2×C4×Dic151C2211yescharacteristic
20Dic151⋊C8—21no—
21C22⋊(C151⋊C8)C2211yescharacteristic
22#18012649—21no—
23C151⋊#95C2211yescharacteristic
24C22⋊Q8×C151C2211yescharacteristic
25C22⋊C8×C151C2211yescharacteristic
26#95×C151C2211yescharacteristic
27C2×D604C2×C411yescharacteristic
28C2×C22⋊D151—21no—
29C22×Dic151—21no—
30C22×Dic151D411yescharacteristic
31C22×Dic151D411yescharacteristic
32C2×C4×D151—21no—
33C2×C151⋊C8—21no—
34C4⋊Dic151—21no—
35C4⋊Dic151—21no—
36C4⋊Dic151C2×C411yescharacteristic
37Dic151⋊C4—24no—
38Dic151⋊C4—21no—
39(C2×D151)⋊C4—21no—
40(C2×D151)⋊C4—21no—
41(C2×D151)⋊C4—21no—
42(C2×D151)⋊C4—21no—
43C4×Dic151—21no—
44C4×Dic151—42no—
45C4×Dic151C2×C411yescharacteristic
46C4×Dic151C2×C411yescharacteristic
47C4×Dic151D411yescharacteristic
48C4×Dic151D411yescharacteristic
49C2×Q8×C151C2×C411yescharacteristic
50C22×C4×C151—21no—
51C22×C4×C151C2311yescharacteristic
52C2×C8×C151—21no—
53C4⋊C4×C151—21no—
54C4⋊C4×C151C2×C411yescharacteristic
55C22⋊C4×C151—21no—
56C22×D151—21no—
57D604—41no—
58C22⋊D151—41no—
59C22⋊D151—41no—
60C2×Dic151—21no—
61C2×Dic151—21no—
62C2×Dic151—22no—
63C2×Dic151—22no—
64C2×Dic151—21no—
65C2×Dic151—41no—
66C2×Dic151—41no—
67C2×Dic151C22⋊C411yescharacteristic
68C2×Dic151C22⋊C411yescharacteristic
69C2×Dic151C22⋊C411yescharacteristic
70C2×Dic151C22⋊C411yescharacteristic
71C4×D151—42no—
72C151⋊C8—41no—
73C23×C151C2×D411yescharacteristic
74Q8×C151—41no—
75C2×C4×C151—22no—
76C2×C4×C151—21no—
77C2×C4×C151—21no—
78C2×C4×C151—41no—
79C2×C4×C151—41no—
80C2×C4×C151—41no—
81C2×C4×C151C22×C411yescharacteristic
82C2×C4×C151C2×D411yescharacteristic
83C8×C151—41no—
84C22×C151—21no—
85C22×C151—21no—
86C22×C151C2×C22⋊C411yescharacteristic
87C22×C151AGL(1,ℤ/8)11yescharacteristic
88C22×C151#13711yescharacteristic
89C2×D151—41no—
90C2×D151—41no—
91C2×D151—41no—
92C4×C151—21no—
93C4×C151—21no—
94C4×C151—42no—
95C4×C151—41no—
96C4×C151—41no—
97Dic151—21no—
98Dic151—21no—
99Dic151—21no—
100Dic151—42no—
101Dic151—41no—
102Dic151#10412yes—
103C2×C151—21no—
104C2×C151—21no—
105C2×C151#41011yescharacteristic
106C2×C151#41711yescharacteristic
107C2×C151C2×#10411yescharacteristic
108D151—81no—
109C151#150911yescharacteristic, complemented, Sylow
110#1509—1511nomaximal, Sylow
111#529—1511no—
112#432—1511no—
113C4×C4⋊C4—1511no—
114#328—1511no—
115#328D15111yescharacteristic, complemented
116#327—1511no—
117#327—1511no—
118#126—3021no—
119#125—1511no—
120#124—1511no—
121#123—3021no—
122C22⋊Q8C2×D15111yescharacteristic
123#121—1511no—
124C4×Q8—1511no—
125C4×D4—3021no—
126C4×D4—1511no—
127#117—3021no—
128C2×C4⋊C4—3021no—
129C2×C42—3021no—
130C2×C42—1511no—
131C4⋊C8—3021no—
132C22⋊C8—1511no—
133C22⋊C8C2×D15111yescharacteristic
134#97—3021no—
135#95—1511no—
136#95C2×D15111yescharacteristic
137C2×Q8C4×D15111yescharacteristic
138C2×D4—3021no—
139C2×D4—1511no—
140C22×C4—21no—
141C22×C4—3021no—
142C22×C4—3021no—
143C22×C4—1511no—
144C22×C4—1511no—
145C22×C4C22×D15111yescharacteristic
146C2×C8—21no—
147C2×C8—3021no—
148C4⋊C4—21no—
149C4⋊C4—3024no—
150C4⋊C4—3021no—
151C4⋊C4—3021no—
152C4⋊C4—3021no—
153C4⋊C4—1511no—
154C4⋊C4C4×D15111yescharacteristic
155C22⋊C4—21no—
156C22⋊C4—3021no—
157C22⋊C4—3021no—
158C22⋊C4—3021no—
159C22⋊C4—3021no—
160C42—3021no—
161C42—6042no—
162C42—1511no—
163C42—1511no—
164C42—1511no—
165C42—1511no—
166C23—3021no—
167C23D4×D15111yescharacteristic
168Q8—41no—
169D4—6041no—
170D4—6041no—
171D4—6041no—
172C2×C4—22no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—3021no—
179C2×C4—3021no—
180C2×C4—3022no—
181C2×C4—3022no—
182C2×C4—3021no—
183C2×C4—6042no—
184C2×C4—6041no—
185C2×C4—6041no—
186C2×C4—1511no—
187C2×C4—1511no—
188C2×C4—1511no—
189C2×C4—1511no—
190C2×C4C2×C4×D15111yescharacteristic
191C2×C4D4×D15111yescharacteristic
192C8—41no—
193C8—6041no—
194C22—21no—
195C22—21no—
196C22—6041no—
197C22—6041no—
198C22—6041no—
199C22C22⋊C4×D15111yescharacteristic
200C22#1801276611yescharacteristic
201C22#1801277111yescharacteristic
202C4—21no—
203C4—21no—
204C4—42no—
205C4—41no—
206C4—41no—
207C4—3021no—
208C4—3021no—
209C4—3021no—
210C4—6042no—
211C4—6041no—
212C4—1512no—
213C2—21no—
214C2—21no—
215C2—12081no—
216C2#2375218411yescharacteristic
217C2#2375221211yescharacteristic
218C2#104×D15111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D151
commutatorC2×C4×C151C22×C4
FrattiniC22×C4C22×D151
Fitting#328×C151C2
socleC22×C151C2×C22⋊C4
prime radical#18012713C22
cosocleC22×C4×C151C23
hypercenter#328D151
hypocenterC151#1509
LCSG ▷ C2×C4×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #23752266C2semidirect
3. #23752063C2semidirect
4. #23751949C2semidirect
7. #328×C151C2semidirect
9. #18012730C4semidirect
10. #18012728C4semidirect
13. Q8×Dic151C4semidirect
14. #18012701C4semidirect
109. C151#1509semidirect
115. #328D151semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237527482
#237522662
#237520632
#237519492
#237519472
#237519452
#328×C1512
#1509151