Finite Group Databasebeta

← #34068300

Subgroups — #34068300

Order 19328.

250 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 55 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#23752882C211yesmaximal, characteristic
2#23752489C211yesmaximal, characteristic, complemented
3#23752419C211yesmaximal, characteristic, complemented
4#23751956C211yesmaximal, characteristic, complemented
5#23751944C211yesmaximal, characteristic, complemented
6#23751941C211yesmaximal, characteristic, complemented
7#486×C151C211yesmaximal, characteristic, complemented
8C2×#14559003—21no—
9C2×#14558994—21no—
10#18012735—21no—
11#18012711—22no—
12#18012710—21no—
13C4×Dic302C2211yescharacteristic
14C4×D604C2211yescharacteristic
15D4×Dic151—21no—
16#18012672—21no—
17C4⋊(C151⋊C8)C2211yescharacteristic
18C4⋊(C151⋊C8)C2211yescharacteristic
19#18012663—21no—
20#18012659—21no—
21C4⋊Q8×C151C2211yescharacteristic
22#127×C151C2211yescharacteristic
23#102×C151—22no—
24C4×C8×C151C2211yescharacteristic
25#14559003—42no—
26#14559003—42no—
27C2×Dic302D411yescharacteristic
28C2×D604D411yescharacteristic
29C2×C22⋊D151—22no—
30C2×C22⋊D151—22no—
31C22×Dic151—22no—
32C2×C4×D151—21no—
33#14558994—42no—
34C2×C151⋊C8—21no—
35C2×C151⋊C8—21no—
36C4⋊Dic151D411yescharacteristic
37C4⋊Dic151D411yescharacteristic
38Dic151⋊C4—21no—
39C22⋊Dic151—22no—
40(C2×D151)⋊C4—21no—
41C4×Dic151—21no—
42C2×Q8×C151—21no—
43C2×D4×C151—21no—
44C2×D4×C151—21no—
45C2×D4×C151D412yes—
46C2×C8×C151—21no—
47C4⋊C4×C151—21no—
48C4⋊C4×C151—21no—
49C42×C151C2311yescharacteristic
50C22×D151—21no—
51Dic302—21no—
52Dic302D812yes—
53D604—21no—
54D604—21no—
55C22⋊D151—44no—
56C22⋊D151—82no—
57C2×Dic151—21no—
58C2×Dic151—21no—
59C2×Dic151—21no—
60C2×Dic151—44no—
61C4×D151—41no—
62C4×D151—41no—
63C151⋊C8—41no—
64C151⋊C8—41no—
65C23×C151—22no—
66Q8×C151—41no—
67Q8×C151—41no—
68D4×C151—42no—
69D4×C151—41no—
70D4×C151—41no—
71D4×C151—41no—
72D4×C151—41no—
73C2×C4×C151—41no—
74C2×C4×C151C2×D411yescharacteristic
75C2×C4×C151C2×D411yescharacteristic
76C2×C4×C151C2×D411yescharacteristic
77C8×C151—41no—
78C22×C151—42no—
79C22×C151—42no—
80C22×C151—42no—
81C22×C151#12011yescharacteristic
82C2×D151—41no—
83C2×D151—41no—
84C2×D151—41no—
85C4×C151—21no—
86C4×C151—81no—
87C4×C151C2×D811yescharacteristic
88C4×C151#13511yescharacteristic
89C4×C151AGL(1,ℤ/8)11yescharacteristic
90C4×C151#13711yescharacteristic
91Dic151—22no—
92Dic151—41no—
93Dic151—41no—
94C2×C151—82no—
95C2×C151#44711yescharacteristic
96C2×C151#45211yescharacteristic
97C2×C151#45511yescharacteristic
98D151—81no—
99C151#164111yescharacteristic, complemented, Sylow
100#1641—1511nomaximal, Sylow
101#550—1511no—
102#486D15111yescharacteristic, complemented
103#474—1511no—
104#462—1511no—
105#331—1511no—
106Q8⋊C8—1511no—
107D4⋊C8—1511no—
108C2×#41—3021no—
109C2×Q16—3021no—
110C4⋊Q8C2×D15111yescharacteristic
111#127—3021no—
112#127C2×D15111yescharacteristic
113#121—3022no—
114#121—3021no—
115C4×Q8—1511no—
116C4×D4—3021no—
117C4×D4—1511no—
118#107—3021no—
119C4⋊C8—1511no—
120C4⋊C8—1511no—
121#103—3021no—
122#102—22no—
123#102—3021no—
124C4×C8C2×D15111yescharacteristic
125#41—6042no—
126#41—6042no—
127C2×Q8—21no—
128C2×Q8—1511no—
129C2×D4—21no—
130C2×D4—21no—
131C2×D4—3022no—
132C2×D4—3022no—
133C2×D4—1511no—
134C2×D4C22⋊D15112yes—
135C22×C4—3022no—
136C22×C4—3021no—
137Q16—6042no—
138C2×C8—21no—
139C2×C8—3021no—
140C2×C8—3021no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—3021no—
144C4⋊C4—1511no—
145C4⋊C4—1511no—
146C22⋊C4—3022no—
147C22⋊C4—3021no—
148C42—3021no—
149C42C22×D15111yescharacteristic
150C23—22no—
151C23—3021no—
152Q8—41no—
153Q8—41no—
154Q8—3021no—
155Q8—1512no—
156D4—42no—
157D4—41no—
158D4—41no—
159D4—41no—
160D4—41no—
161D4—3021no—
162D4—3021no—
163D4—6044no—
164D4—12082no—
165C2×C4—41no—
166C2×C4—3021no—
167C2×C4—3021no—
168C2×C4—3021no—
169C2×C4—6044no—
170C2×C4—6041no—
171C2×C4—6041no—
172C2×C4D4×D15111yescharacteristic
173C2×C4D4×D15111yescharacteristic
174C2×C4C2×C22⋊D15111yescharacteristic
175C8—41no—
176C8—6041no—
177C8—6041no—
178C22—42no—
179C22—42no—
180C22—42no—
181C22—6041no—
182C22—6041no—
183C22—6041no—
184C22#1801270711yescharacteristic
185C4—21no—
186C4—81no—
187C4—3022no—
188C4—6041no—
189C4—6041no—
190C4D8×D15111yescharacteristic
191C4#1801276011yescharacteristic
192C4#1801276311yescharacteristic
193C4#1801276811yescharacteristic
194C2—82no—
195C2—12081no—
196C2#2375234411yescharacteristic
197C2#2375237111yescharacteristic
198C2#2375238911yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#486×C151C2
socleC22×C151#120
prime radical#23752882C2
hypercenter#486D151
hypocenterC151#1641
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. #23752489C2semidirect
3. #23752419C2semidirect
4. #23751956C2semidirect
5. #23751944C2semidirect
6. #23751941C2semidirect
7. #486×C151C2semidirect
99. C151#1641semidirect
102. #486D151semidirect

Maximal subgroups

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

subgroupindex
#237528822
#237524892
#237524192
#237519562
#237519442
#237519412
#486×C1512
#1641151