Finite Group Databasebeta

← #34068339

Subgroups — #34068339

Order 19328.

212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 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#23752928C211yesmaximal, characteristic
2#23752562C211yesmaximal, characteristic, complemented
3#23752493C211yesmaximal, characteristic, complemented
4#23752418C211yesmaximal, characteristic, complemented
5#23751939C211yesmaximal, characteristic, complemented
6#23751939C211yesmaximal, characteristic, complemented
7#333×C151C211yesmaximal, characteristic, complemented
8C2×#14558993—21no—
9#18012739C2211yescharacteristic
10#18012728—22no—
11#18012714—21no—
12#18012714—21no—
13C4×D604C2211yescharacteristic
14C4×D604C2211yescharacteristic
15#18012697—21no—
16#18012697—21no—
17#18012673—21no—
18#18012664—21no—
19#18012663—22no—
20#18012661—21no—
21C4×C151⋊C8C2211yescharacteristic
22C4⋊Q8×C151C2211yescharacteristic
23C4⋊C8×C151C2211yescharacteristic
24C4⋊C8×C151C2211yescharacteristic
25C2×Dic302—21no—
26C2×D604—22no—
27C2×D604D411yescharacteristic
28C2×D604D411yescharacteristic
29C2×C4×D151—21no—
30C2×C4×D151—21no—
31#14558993—42no—
32C2×C151⋊C8—21no—
33C4⋊Dic151—21no—
34C4⋊Dic151—21no—
35C4⋊Dic151D411yescharacteristic
36C4⋊Dic151D411yescharacteristic
37(C2×D151)⋊C4—22no—
38(C2×D151)⋊C4—22no—
39(C2×D151)⋊C4—21no—
40(C2×D151)⋊C4—21no—
41C4×Dic151—22no—
42C2×Q8×C151D412yes—
43C2×C8×C151—21no—
44C2×C8×C151—21no—
45C4⋊C4×C151—21no—
46C4⋊C4×C151—21no—
47C42×C151C2311yescharacteristic
48C22×D151—21no—
49C22×D151—21no—
50Dic302—41no—
51Dic302—41no—
52D604—21no—
53D604—21no—
54D604—21no—
55D604—21no—
56D604—82no—
57C2×Dic151—21no—
58C2×Dic151—21no—
59C2×Dic151—41no—
60C4×D151—41no—
61C4×D151—41no—
62C4×D151—41no—
63C4×D151—41no—
64C151⋊C8—41no—
65Q8×C151—42no—
66C2×C4×C151—22no—
67C2×C4×C151C2×D411yescharacteristic
68C2×C4×C151C2×D411yescharacteristic
69C2×C4×C151C2×D411yescharacteristic
70C8×C151—41no—
71C8×C151—41no—
72C22×C151#12011yescharacteristic
73C2×D151—41no—
74C2×D151—41no—
75C2×D151—41no—
76C2×D151—41no—
77C2×D151—41no—
78C2×D151—41no—
79C4×C151—21no—
80C4×C151—42no—
81C4×C151#13511yescharacteristic
82C4×C151#13511yescharacteristic
83C4×C151AGL(1,ℤ/8)11yescharacteristic
84C4×C151#13711yescharacteristic
85Dic151—41no—
86Dic151—41no—
87Dic151—81no—
88C2×C151#44911yescharacteristic
89C2×C151#45211yescharacteristic
90C2×C151#45511yescharacteristic
91D151—81no—
92D151—81no—
93C151#164611yescharacteristic, complemented, Sylow
94#1646—1511nomaximal, Sylow
95#555—1511no—
96#487—1511no—
97#474—1511no—
98#461—1511no—
99#333D15111yescharacteristic, complemented
100D4⋊C8—1511no—
101D4⋊C8—1511no—
102C2×SD16—3021no—
103C4⋊Q8—1511no—
104C4⋊Q8C2×D15111yescharacteristic
105#124—3022no—
106#121—3021no—
107#121—3021no—
108C4×D4—1511no—
109C4×D4—1511no—
110#117—3021no—
111#117—3021no—
112#107—3021no—
113C4⋊C8C2×D15111yescharacteristic
114C4⋊C8C2×D15111yescharacteristic
115#103—3022no—
116#103—3021no—
117#102—3021no—
118C4×C8—1511no—
119C2×Q8—3021no—
120C2×Q8D60412yes—
121C2×D4—3022no—
122C2×D4—1511no—
123C2×D4—1511no—
124C22×C4—3021no—
125C22×C4—3021no—
126SD16—6042no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—3021no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—3021no—
133C4⋊C4—3021no—
134C4⋊C4—1511no—
135C4⋊C4—1511no—
136C22⋊C4—3022no—
137C22⋊C4—3022no—
138C22⋊C4—3021no—
139C22⋊C4—3021no—
140C42—3022no—
141C42C22×D15111yescharacteristic
142C23—3021no—
143C23—3021no—
144Q8—42no—
145Q8—6041no—
146Q8—6041no—
147D4—3021no—
148D4—3021no—
149D4—3021no—
150D4—3021no—
151D4—12082no—
152C2×C4—22no—
153C2×C4—3021no—
154C2×C4—3021no—
155C2×C4—6041no—
156C2×C4—6041no—
157C2×C4—6041no—
158C2×C4—6041no—
159C2×C4—6041no—
160C2×C4D4×D15111yescharacteristic
161C2×C4D4×D15111yescharacteristic
162C2×C4C2×D60411yescharacteristic
163C8—41no—
164C8—41no—
165C8—6041no—
166C22—6041no—
167C22—6041no—
168C22—6041no—
169C22—6041no—
170C22—6041no—
171C22—6041no—
172C22#1801270911yescharacteristic
173C4—21no—
174C4—42no—
175C4—6041no—
176C4—6041no—
177C4—12081no—
178C4#1801276011yescharacteristic
179C4#1801276211yescharacteristic
180C4#1801276611yescharacteristic
181C4#1801277111yescharacteristic
182C2—12081no—
183C2—12081no—
184C2#2375236011yescharacteristic
185C2#2375237711yescharacteristic
186C2#2375239211yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#333×C151C2
socleC22×C151#120
prime radical#23752928C2
hypercenter#333D151
hypocenterC151#1646
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #23752562C2semidirect
3. #23752493C2semidirect
4. #23752418C2semidirect
5. #23751939C2semidirect
6. #23751939C2semidirect
7. #333×C151C2semidirect
93. C151#1646semidirect
99. #333D151semidirect

Maximal subgroups

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

subgroupindex
#237529282
#237525622
#237524932
#237524182
#237519392
#333×C1512
#1646151