Finite Group Databasebeta

← #34068238

Subgroups — #34068238

Order 19328.

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

normal subgroups only

This group has 256 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#23752584C211yesmaximal, characteristic, complemented
3#23752508C211yesmaximal, characteristic, complemented
4#23752503C211yesmaximal, characteristic, complemented
5#23751942C211yesmaximal, characteristic, complemented
6#23751939C211yesmaximal, characteristic, complemented
7#331×C151C211yesmaximal, characteristic, complemented
8C2×#14559003—21no—
9C2×#14558992—22no—
10#18012739C2211yescharacteristic
11#18012735—21no—
12#18012711—22no—
13#18012710—21no—
14C4×Dic302C2211yescharacteristic
15C4×D604C2211yescharacteristic
16D4×Dic151—21no—
17#18012673—21no—
18#18012671—21no—
19#18012664—21no—
20#18012661—21no—
21C4×C151⋊C8C2211yescharacteristic
22#127×C151C2211yescharacteristic
23C4⋊C8×C151C2211yescharacteristic
24C4⋊C8×C151C2211yescharacteristic
25#14559003—42no—
26#14559003—42no—
27C2×Dic302—21no—
28C2×Dic302D411yescharacteristic
29C2×D604D411yescharacteristic
30C2×C22⋊D151—22no—
31C2×C22⋊D151—22no—
32C22×Dic151—22no—
33C2×C4×D151—21no—
34#14558992—44no—
35C2×C151⋊C8—21no—
36C4⋊Dic151—21no—
37C4⋊Dic151—21no—
38C4⋊Dic151D411yescharacteristic
39C4⋊Dic151D411yescharacteristic
40Dic151⋊C4—21no—
41C22⋊Dic151—22no—
42(C2×D151)⋊C4—21no—
43C4×Dic151—21no—
44C2×D4×C151—21no—
45C2×D4×C151—21no—
46C2×D4×C151D412yes—
47C2×C8×C151—21no—
48C2×C8×C151—21no—
49C42×C151C2311yescharacteristic
50C22×D151—21no—
51Dic302—21no—
52Dic302—42no—
53Dic302SD1612yescomplemented
54D604—21no—
55D604—21no—
56C22⋊D151—44no—
57C22⋊D151—82no—
58C2×Dic151—21no—
59C2×Dic151—21no—
60C2×Dic151—21no—
61C2×Dic151—44no—
62C2×Dic151—41no—
63C4×D151—41no—
64C4×D151—41no—
65C151⋊C8—22no—
66C23×C151—22no—
67D4×C151—42no—
68D4×C151—41no—
69D4×C151—41no—
70D4×C151—41no—
71D4×C151—41no—
72C2×C4×C151C2×D411yescharacteristic
73C2×C4×C151C2×D411yescharacteristic
74C2×C4×C151C2×D411yescharacteristic
75C8×C151—41no—
76C8×C151—41no—
77C22×C151—42no—
78C22×C151—42no—
79C22×C151—42no—
80C22×C151#12011yescharacteristic
81C2×D151—41no—
82C2×D151—41no—
83C2×D151—41no—
84C4×C151—21no—
85C4×C151C2×SD1611yescharacteristic
86C4×C151#13511yescharacteristic
87C4×C151AGL(1,ℤ/8)11yescharacteristic
88C4×C151#13711yescharacteristic
89Dic151—22no—
90Dic151—41no—
91Dic151—41no—
92Dic151—81no—
93C2×C151—82no—
94C2×C151#45011yescharacteristic
95C2×C151#45211yescharacteristic
96C2×C151#45311yescharacteristic
97D151—81no—
98C151#163111yescharacteristic, complemented, Sylow
99#1631—1511nomaximal, Sylow
100#550—1511no—
101#492—1511no—
102#477—1511no—
103#476—1511no—
104#331D15111yescharacteristic, complemented
105Q8⋊C8—1511no—
106D4⋊C8—1511no—
107C2×#41—3021no—
108C2×SD16—3022no—
109C4⋊Q8—1511no—
110#127—3021no—
111#127C2×D15111yescharacteristic
112#121—3022no—
113#121—3021no—
114C4×Q8—1511no—
115C4×D4—3021no—
116C4×D4—1511no—
117#107—3021no—
118#106—3021no—
119C4⋊C8C2×D15111yescharacteristic
120C4⋊C8C2×D15111yescharacteristic
121#103—3021no—
122#102—3021no—
123C4×C8—1511no—
124#41—6042no—
125#41—6042no—
126C2×Q8—3021no—
127C2×Q8—1511no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—3022no—
131C2×D4—3022no—
132C2×D4—1511no—
133C2×D4D60412yes—
134C22×C4—3022no—
135C22×C4—3021no—
136SD16—6044no—
137C2×C8—21no—
138C2×C8—21no—
139C2×C8—3021no—
140C4⋊C4—3021no—
141C4⋊C4—3021no—
142C4⋊C4—3021no—
143C4⋊C4—1511no—
144C4⋊C4—1511no—
145C22⋊C4—3022no—
146C22⋊C4—3021no—
147C42—3021no—
148C42C22×D15111yescharacteristic
149C23—22no—
150C23—3021no—
151Q8—3021no—
152Q8—6042no—
153Q8—1512no—
154D4—42no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4—41no—
159D4—3021no—
160D4—3021no—
161D4—6044no—
162D4—12082no—
163C2×C4—3021no—
164C2×C4—3021no—
165C2×C4—3021no—
166C2×C4—6044no—
167C2×C4—6041no—
168C2×C4—6041no—
169C2×C4—6041no—
170C2×C4D4×D15111yescharacteristic
171C2×C4D4×D15111yescharacteristic
172C2×C4C2×D60411yescharacteristic
173C8—41no—
174C8—41no—
175C8—3022no—
176C22—42no—
177C22—42no—
178C22—42no—
179C22—6041no—
180C22—6041no—
181C22—6041no—
182C22#1801270911yescharacteristic
183C4—21no—
184C4—3022no—
185C4—6041no—
186C4—6041no—
187C4—12081no—
188C4SD16×D15111yescharacteristic
189C4#1801275811yescharacteristic
190C4#1801276311yescharacteristic
191C4#1801276811yescharacteristic
192C2—82no—
193C2—12081no—
194C2#2375236411yescharacteristic
195C2#2375237511yescharacteristic
196C2#2375238211yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#331×C151C2
socleC22×C151#120
prime radical#23752882C2
hypercenter#331D151
hypocenterC151#1631
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #23752584C2semidirect
3. #23752508C2semidirect
4. #23752503C2semidirect
5. #23751942C2semidirect
6. #23751939C2semidirect
7. #331×C151C2semidirect
53. Dic302SD16semidirect
98. C151#1631semidirect
104. #331D151semidirect

Maximal subgroups

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

subgroupindex
#237528822
#237525842
#237525082
#237525032
#237519422
#237519392
#331×C1512
#1631151