Finite Group Databasebeta

← #34067829

Subgroups — #34067829

Order 19328.

246 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 65 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#23752760C211yesmaximal, characteristic
2#23752268C211yesmaximal, characteristic, complemented
3#23752234C211yesmaximal, characteristic, complemented
4#23751959C211yesmaximal, characteristic, complemented
5#23751957C211yesmaximal, characteristic, complemented
6#23751956C211yesmaximal, characteristic, complemented
7#331×C151C211yesmaximal, characteristic, complemented
8C2×#14559003—21no—
9C2×#14558987—21no—
10#18012739C2211yescharacteristic
11#18012726—21no—
12#18012710—21no—
13#18012710C412yes—
14D4×Dic151—21no—
15D4×Dic151C412yes—
16C42×D151C2211yescharacteristic
17C4⋊(C151⋊C8)C2211yescharacteristic
18C4⋊(C151⋊C8)C2211yescharacteristic
19Dic151⋊C8—21no—
20(C2×D151)⋊C8—21no—
21#18012649—21no—
22#127×C151C2211yescharacteristic
23C4⋊C8×C151C2211yescharacteristic
24C4⋊C8×C151C2211yescharacteristic
25#14559003—42no—
26#14559003—42no—
27C2×Dic302—21no—
28C2×C22⋊D151—22no—
29C22×Dic151—22no—
30C2×C4×D151C2×C411yescharacteristic
31C2×C4×D151D411yescharacteristic
32C2×C4×D151D411yescharacteristic
33#14558987—42no—
34C2×C151⋊C8—21no—
35C2×C151⋊C8—21no—
36C4⋊Dic151—21no—
37C4⋊Dic151C2×C412yes—
38C22⋊Dic151—22no—
39C22⋊Dic151—22no—
40C4×Dic151C2×C411yescharacteristic
41C4×Dic151D411yescharacteristic
42C4×Dic151D411yescharacteristic
43C2×D4×C151—21no—
44C2×D4×C151—21no—
45C2×D4×C151C2×C412yes—
46C2×C8×C151—21no—
47C2×C8×C151—21no—
48C42×C151C2311yescharacteristic
49C22×D151C22⋊C411yescharacteristic
50Dic302—41no—
51Dic302—41no—
52C22⋊D151—44no—
53C2×Dic151—22no—
54C2×Dic151—44no—
55C2×Dic151C22⋊C411yescharacteristic
56C2×Dic151C22⋊C411yescharacteristic
57C2×Dic151C22⋊C411yescharacteristic
58C4×D151—21no—
59C4×D151—21no—
60C4×D151—21no—
61C4×D151—21no—
62C4×D151—41no—
63C151⋊C8—41no—
64C151⋊C8—41no—
65C23×C151—22no—
66D4×C151—42no—
67D4×C151—41no—
68D4×C151—41no—
69D4×C151—41no—
70D4×C151—41no—
71C2×C4×C151C22×C411yescharacteristic
72C2×C4×C151C2×D411yescharacteristic
73C2×C4×C151C2×D411yescharacteristic
74C8×C151—41no—
75C8×C151—41no—
76C22×C151—42no—
77C22×C151—42no—
78C22×C151—42no—
79C22×C151C2×C22⋊C411yescharacteristic
80C2×D151—21no—
81C2×D151—21no—
82C2×D151—21no—
83C4×C151—21no—
84C4×C151AGL(1,ℤ/8)11yescharacteristic
85C4×C151AGL(1,ℤ/8)11yescharacteristic
86C4×C151AGL(1,ℤ/8)11yescharacteristic
87C4×C151#13711yescharacteristic
88Dic151—21no—
89Dic151—21no—
90Dic151—21no—
91Dic151—42no—
92C2×C151—82no—
93C2×C151#41311yescharacteristic
94C2×C151#41711yescharacteristic
95C2×C151#41811yescharacteristic
96D151—41no—
97C151#155711yescharacteristic, complemented, Sylow
98#1557—1511nomaximal, Sylow
99#532—1511no—
100#432—1511no—
101#423—1511no—
102#332—1511no—
103#332—1511no—
104#331—1511no—
105#331D15111yescharacteristic, complemented
106C2×#41—3021no—
107C2×M16—3021no—
108C4⋊Q8—1511no—
109#127C2×D15111yescharacteristic
110#124—3021no—
111#121—3021no—
112#121—1512no—
113C4×D4—3021no—
114C4×D4—1512no—
115C2×C42—1511no—
116C4⋊C8—3021no—
117C4⋊C8—1511no—
118C4⋊C8—1511no—
119C4⋊C8C2×D15111yescharacteristic
120C4⋊C8C2×D15111yescharacteristic
121C22⋊C8—3021no—
122#97—3021no—
123#41—6042no—
124#41—6042no—
125C2×Q8—3021no—
126C2×D4—21no—
127C2×D4—21no—
128C2×D4—3022no—
129C2×D4C4×D15112yes—
130C22×C4—3022no—
131C22×C4—1511no—
132C22×C4—1511no—
133C22×C4—1511no—
134M16—6042no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—3021no—
138C2×C8—3021no—
139C4⋊C4—3021no—
140C4⋊C4—1512no—
141C22⋊C4—3022no—
142C22⋊C4—3022no—
143C42—1511no—
144C42—1511no—
145C42—1511no—
146C42C22×D15111yescharacteristic
147C23—22no—
148C23—1511no—
149Q8—6041no—
150Q8—6041no—
151D4—42no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—6044no—
157C2×C4—3021no—
158C2×C4—3021no—
159C2×C4—3021no—
160C2×C4—3021no—
161C2×C4—3022no—
162C2×C4—6041no—
163C2×C4—6044no—
164C2×C4—1511no—
165C2×C4—1511no—
166C2×C4—1511no—
167C2×C4C2×C4×D15111yescharacteristic
168C2×C4D4×D15111yescharacteristic
169C2×C4D4×D15111yescharacteristic
170C8—41no—
171C8—41no—
172C8—6041no—
173C8—6041no—
174C22—42no—
175C22—42no—
176C22—42no—
177C22—3021no—
178C22—3021no—
179C22—3021no—
180C22C22⋊C4×D15111yescharacteristic
181C4—21no—
182C4—3021no—
183C4—3021no—
184C4—3021no—
185C4—6042no—
186C4#1801276311yescharacteristic
187C4#1801276311yescharacteristic
188C4#1801276611yescharacteristic
189C4#1801276811yescharacteristic
190C2—82no—
191C2—6041no—
192C2#2375219311yescharacteristic
193C2#2375221011yescharacteristic
194C2#2375221511yescharacteristic
subgroupG/H
centerC22C22⋊C4×D151
commutatorC2×C4×C151C22×C4
FrattiniC42C22×D151
Fitting#331×C151C2
socleC22×C151C2×C22⋊C4
prime radical#23752760C2
cosocleC42×C151C23
hypercenter#331D151
hypocenterC151#1557
LCSG ▷ C2×C4×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #23752268C2semidirect
3. #23752234C2semidirect
4. #23751959C2semidirect
5. #23751957C2semidirect
6. #23751956C2semidirect
7. #331×C151C2semidirect
97. C151#1557semidirect
105. #331D151semidirect

Maximal subgroups

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

subgroupindex
#237527602
#237522682
#237522342
#237519592
#237519572
#237519562
#331×C1512
#1557151