Finite Group Databasebeta

← #34068372

Subgroups — #34068372

Order 19328.

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

normal subgroups only

This group has 234 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
1Q8×D604C211yesmaximal, characteristic
2#23752608C211yesmaximal, characteristic, complemented
3#23752414C211yesmaximal, characteristic
4#23751959C211yesmaximal, characteristic, complemented
5Q8⋊(C151⋊C8)C211yesmaximal, characteristic, complemented
6#23751939C211yesmaximal, characteristic
7#475×C151C211yesmaximal, characteristic, complemented
8C2×Q8×D151—21no—
9C2×#14558991—21no—
10#18012739—21no—
11#18012739C2211yescharacteristic
12#18012719—21no—
13#18012719—22no—
14C4×D604—21no—
15C4×D604C2211yescharacteristic
16#18012670—22no—
17C4⋊(C151⋊C8)C2211yescharacteristic
18#18012663—21no—
19C4×C151⋊C8C2211yescharacteristic
20C4⋊Q8×C151C2211yescharacteristic
21C4×Q8×C151C2211yescharacteristic
22#106×C151—21no—
23C4⋊C8×C151C2211yescharacteristic
24#103×C151—21no—
25C2×Dic302—22no—
26C2×Dic302—21no—
27Q8×D151—42no—
28Q8×D151—42no—
29C2×D604D411yescharacteristic
30C2×C4×D151—22no—
31C2×C4×D151—21no—
32#14558991—42no—
33C2×C151⋊C8—21no—
34C2×C151⋊C8—21no—
35C4⋊Dic151—22no—
36C4⋊Dic151—21no—
37C4⋊Dic151D411yescharacteristic
38C4⋊Dic151D412yes—
39(C2×D151)⋊C4—22no—
40(C2×D151)⋊C4—21no—
41C2×Q8×C151—21no—
42C2×Q8×C151D411yescharacteristic
43C2×C8×C151—21no—
44C4⋊C4×C151—21no—
45C4⋊C4×C151—21no—
46C4⋊C4×C151—21no—
47C4⋊C4×C151D411yescharacteristic
48C42×C151—21no—
49C42×C151C2311yescharacteristic
50C22×D151—21no—
51Dic302—44no—
52Dic302—41no—
53Dic302—41no—
54D604—21no—
55D604SD1612yes—
56C2×Dic151—22no—
57C2×Dic151—21no—
58C4×D151—44no—
59C4×D151—41no—
60C4×D151—41no—
61C151⋊C8—22no—
62C151⋊C8—41no—
63Q8×C151—21no—
64Q8×C151—41no—
65Q8×C151—41no—
66Q8×C151SD1612yescomplemented
67C2×C4×C151—21no—
68C2×C4×C151—21no—
69C2×C4×C151—41no—
70C2×C4×C151C2×D411yescharacteristic
71C2×C4×C151C2×D411yescharacteristic
72C2×C4×C151C2×D411yescharacteristic
73C8×C151—41no—
74C22×C151#12011yescharacteristic
75C2×D151—22no—
76C2×D151—41no—
77C2×D151—41no—
78C4×C151—22no—
79C4×C151—21no—
80C4×C151—41no—
81C4×C151—81no—
82C4×C151C2×SD1611yescharacteristic
83C4×C151C2×SD1611yescharacteristic
84C4×C151AGL(1,ℤ/8)11yescharacteristic
85C4×C151#13711yescharacteristic
86Dic151—42no—
87Dic151—41no—
88C2×C151#44811yescharacteristic
89C2×C151#45011yescharacteristic
90C2×C151#45611yescharacteristic
91D151—42no—
92C151#165111yescharacteristic, complemented, Sylow
93#1651—1511nomaximal, Sylow
94D4×Q8—1511no—
95#498—1511no—
96#475D15111yescharacteristic, complemented
97#461—1511no—
98#332—1511no—
99Q8⋊C8—1511no—
100D4⋊C8—1511no—
101C22×Q8—3021no—
102C2×SD16—3021no—
103C4⋊Q8—3021no—
104C4⋊Q8—1511no—
105C4⋊Q8C2×D15111yescharacteristic
106C22⋊Q8—3022no—
107C22⋊Q8—3021no—
108C4×Q8C2×D15111yescharacteristic
109C4×D4—3021no—
110C4×D4—1511no—
111#106—21no—
112#106—3022no—
113C4⋊C8—1511no—
114C4⋊C8C2×D15111yescharacteristic
115#103—21no—
116#103—3021no—
117C4×C8—1511no—
118C2×Q8—21no—
119C2×Q8—3022no—
120C2×Q8—3021no—
121C2×Q8—6042no—
122C2×Q8—6042no—
123C2×Q8C22⋊D15111yescharacteristic
124C2×D4—1511no—
125C22×C4—3022no—
126C22×C4—3021no—
127SD16—6042no—
128C2×C8—21no—
129C2×C8—3021no—
130C2×C8—3021no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—3022no—
135C4⋊C4—3021no—
136C4⋊C4—1511no—
137C4⋊C4—1512no—
138C4⋊C4C22⋊D15111yescharacteristic
139C22⋊C4—3022no—
140C22⋊C4—3021no—
141C42—21no—
142C42C22×D15111yescharacteristic
143C23—3021no—
144Q8—21no—
145Q8—41no—
146Q8—41no—
147Q8—6044no—
148Q8—6041no—
149Q8—6041no—
150Q8#1455899112yescomplemented
151D4—3021no—
152D4—1512no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—41no—
156C2×C4—3022no—
157C2×C4—3021no—
158C2×C4—6044no—
159C2×C4—6041no—
160C2×C4—6041no—
161C2×C4D4×D15111yescharacteristic
162C2×C4D4×D15111yescharacteristic
163C2×C4C2×C22⋊D15111yescharacteristic
164C8—41no—
165C8—3022no—
166C8—6041no—
167C22—3022no—
168C22—6041no—
169C22—6041no—
170C22#1801270711yescharacteristic
171C4—22no—
172C4—21no—
173C4—41no—
174C4—81no—
175C4—6042no—
176C4—6041no—
177C4SD16×D15111yescharacteristic
178C4C2×#1455899111yescharacteristic
179C4#1801276411yescharacteristic
180C4#1801276811yescharacteristic
181C2—6042no—
182C2#2375234911yescharacteristic
183C2#2375236211yescharacteristic
184C2#2375239311yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#475×C151C2
socleC22×C151#120
prime radicalC2×D604D4
hypercenter#475D151
hypocenterC151#1651
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
2. #23752608C2semidirect
4. #23751959C2semidirect
5. Q8⋊(C151⋊C8)C2semidirect
7. #475×C151C2semidirect
66. Q8×C151SD16semidirect
92. C151#1651semidirect
96. #475D151semidirect
150. Q8#14558991semidirect

Maximal subgroups

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

subgroupindex
Q8×D6042
#237526082
#237524142
#237519592
Q8⋊(C151⋊C8)2
#237519392
#475×C1512
#1651151