Finite Group Databasebeta

← #34067743

Subgroups — #34067743

Order 19328.

238 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 59 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#23752761C211yesmaximal, characteristic
2#23752267C212yesmaximal, complemented
3#23751952C211yesmaximal, characteristic, complemented
4#23751951C212yesmaximal, complemented
5#329×C151C211yesmaximal, characteristic, complemented
6C2×#14559005C411yescharacteristic
7C2×#14559003C411yescharacteristic
8#18012737C411yescharacteristic
9#18012735C411yescharacteristic
10#18012727C2211yescharacteristic
11#18012712—22no—
12(C22⋊D151)⋊C4—22no—
13C42×D151C2211yescharacteristic
14Dic151⋊C8—22no—
15(C2×D151)⋊C8—22no—
16#18012650C2212yes—
17#124×C151C2211yescharacteristic
18#97×C151C2212yes—
19#14559005—42no—
20#14559003—42no—
21C2×Dic302C2×C411yescharacteristic
22C2×D604—21no—
23C2×D604C2×C411yescharacteristic
24C2×C22⋊D151—21no—
25C2×C22⋊D151—22no—
26C22×Dic151—21no—
27C2×C4×D151—21no—
28C2×C4×D151C2×C411yescharacteristic
29C2×C4×D151D412yes—
30C2×C151⋊C8—22no—
31Dic151⋊C4—22no—
32(C2×D151)⋊C4—22no—
33C4×Dic151C2×C411yescharacteristic
34C4×Dic151D412yes—
35C2×Q8×C151C2×C411yescharacteristic
36C2×D4×C151C2×C411yescharacteristic
37C2×C8×C151—22no—
38C22⋊C4×C151—22no—
39C42×C151C2311yescharacteristic
40C22×D151—21no—
41C22×D151C22⋊C411yescharacteristic
42Dic302—41no—
43D604—41no—
44D604—42no—
45C22⋊D151—44no—
46C22⋊D151—42no—
47C2×Dic151—21no—
48C2×Dic151—42no—
49C2×Dic151C22⋊C412yes—
50C2×Dic151C22⋊C411yescharacteristic
51C4×D151—22no—
52C4×D151—42no—
53C4×D151—42no—
54C151⋊C8—42no—
55C23×C151—21no—
56Q8×C151—41no—
57D4×C151—41no—
58C2×C4×C151—21no—
59C2×C4×C151C22×C411yescharacteristic
60C2×C4×C151C2×D412yes—
61C8×C151—42no—
62C22×C151—41no—
63C22×C151—42no—
64C22×C151C2×C22⋊C411yescharacteristic
65C2×D151—21no—
66C2×D151—22no—
67C2×D151—41no—
68C2×D151—42no—
69C4×C151—21no—
70C4×C151—22no—
71C4×C151—41no—
72Dic151—22no—
73Dic151—41no—
74Dic151#10012yes—
75C2×C151—81no—
76C2×C151C2×#10011yescharacteristic
77C2×C151#42112yes—
78D151—41no—
79D151—81no—
80C151#153611yescharacteristic, complemented, Sylow
81#1536—1511nomaximal, Sylow
82#532—1511no—
83#432—1512no—
84#329—1511no—
85#329—1512no—
86#329D15111yescharacteristic, complemented
87C2×#41—1511no—
88C2×#41—1511no—
89C4⋊Q8—1511no—
90#127—1511no—
91#124—1511no—
92#124C2×D15111yescharacteristic
93#121—3022no—
94C4×D4—3022no—
95C2×C42—1511no—
96C4⋊C8—3022no—
97C22⋊C8—3022no—
98#97—1512no—
99#97C2×D15112yes—
100#41—6042no—
101#41—6042no—
102C2×Q8—1511no—
103C2×Q8C4×D15111yescharacteristic
104C2×D4—3021no—
105C2×D4—3021no—
106C2×D4—3022no—
107C2×D4—1511no—
108C2×D4C4×D15111yescharacteristic
109C22×C4—3021no—
110C22×C4—3021no—
111C22×C4—1511no—
112C22×C4—1512no—
113C2×C8—22no—
114C2×C8—3022no—
115C4⋊C4—3022no—
116C22⋊C4—22no—
117C22⋊C4—3022no—
118C42—1511no—
119C42—1512no—
120C42C22×D15111yescharacteristic
121C23—21no—
122C23—3021no—
123C23—1511no—
124Q8—41no—
125Q8—6041no—
126D4—41no—
127D4—6041no—
128D4—6042no—
129D4—6044no—
130D4—6042no—
131C2×C4—21no—
132C2×C4—3022no—
133C2×C4—3021no—
134C2×C4—6042no—
135C2×C4—6042no—
136C2×C4—6042no—
137C2×C4—1512no—
138C2×C4—1511no—
139C2×C4C2×C4×D15111yescharacteristic
140C2×C4D4×D15112yes—
141C8—42no—
142C8—6042no—
143C22—42no—
144C22—41no—
145C22—3022no—
146C22—3021no—
147C22—6042no—
148C22—6041no—
149C22C22⋊C4×D15111yescharacteristic
150C4—22no—
151C4—21no—
152C4—41no—
153C4—3022no—
154C4—6041no—
155C4—1512no—
156C2—81no—
157C2—6041no—
158C2—12081no—
159C2#100×D15111yescharacteristic
160C2#2375222712yes—
subgroupG/H
centerC22C22⋊C4×D151
commutatorC2×C4×C151C22×C4
FrattiniC42C22×D151
Fitting#329×C151C2
socleC22×C151C2×C22⋊C4
prime radical#23752761C2
cosocleC42×C151C23
hypercenter#329D151
hypocenterC151#1536
LCSG ▷ C2×C4×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #23752267C2semidirect
3. #23751952C2semidirect
4. #23751951C2semidirect
5. #329×C151C2semidirect
80. C151#1536semidirect
86. #329D151semidirect

Maximal subgroups

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

subgroupindex
#237527612
#237522672
#237519522
#237519512
#329×C1512
#1536151