Finite Group Databasebeta

← #34068424

Subgroups — #34068424

Order 19328.

208 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 45 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#23752956C211yesmaximal, characteristic
2#23752618C211yesmaximal, characteristic, complemented
3#23752574C211yesmaximal, characteristic, complemented
4#23751953C211yesmaximal, characteristic, complemented
5#23751952C211yesmaximal, characteristic, complemented
6#23751951C211yesmaximal, characteristic, complemented
7#497×C151C211yesmaximal, characteristic, complemented
8#18012731C2211yescharacteristic
9#18012727C2211yescharacteristic
10#18012723—21no—
11#18012721—21no—
12#18012716—21no—
13#18012715—21no—
14#18012712—21no—
15#18012711—21no—
16#18012672—21no—
17#18012670—21no—
18#18012662—21no—
19#18012659—21no—
20#18012650C2211yescharacteristic
21#18012650C2211yescharacteristic
22C2×Q16×C151—21no—
23C2×SD16×C151—21no—
24C4⋊Q8×C151C2211yescharacteristic
25#124×C151C2211yescharacteristic
26#97×C151C2211yescharacteristic
27C2×Dic302D411yescharacteristic
28C2×D604D411yescharacteristic
29C2×C22⋊D151—21no—
30C2×C22⋊D151—21no—
31C22×Dic151—21no—
32C2×C4×D151—21no—
33C2×C151⋊C8—21no—
34C2×C151⋊C8—21no—
35C4⋊Dic151—21no—
36C4⋊Dic151D411yescharacteristic
37C4⋊Dic151D411yescharacteristic
38Dic151⋊C4—21no—
39Dic151⋊C4—21no—
40Dic151⋊C4—21no—
41C22⋊Dic151—21no—
42(C2×D151)⋊C4—21no—
43(C2×D151)⋊C4—21no—
44(C2×D151)⋊C4—21no—
45C2×Q8×C151—21no—
46C2×Q8×C151D411yescharacteristic
47C2×D4×C151D411yescharacteristic
48Q16×C151—42no—
49SD16×C151—42no—
50C2×C8×C151—21no—
51C4⋊C4×C151—21no—
52C4⋊C4×C151—21no—
53C22⋊C4×C151—21no—
54C22⋊C4×C151—21no—
55C42×C151C2311yescharacteristic
56C22×D151—21no—
57Dic302—41no—
58D604—41no—
59C22⋊D151—81no—
60C22⋊D151—81no—
61C2×Dic151—21no—
62C2×Dic151—21no—
63C2×Dic151—21no—
64C2×Dic151—81no—
65C4×D151—81no—
66C151⋊C8—22no—
67C151⋊C8—41no—
68C23×C151—21no—
69Q8×C151—41no—
70Q8×C151—41no—
71Q8×C151—41no—
72D4×C151—41no—
73C2×C4×C151—21no—
74C2×C4×C151—41no—
75C2×C4×C151C2×D411yescharacteristic
76C2×C4×C151C2×D411yescharacteristic
77C2×C4×C151C2×D411yescharacteristic
78C8×C151—22no—
79C22×C151—41no—
80C22×C151—41no—
81C22×C151—41no—
82C22×C151#12011yescharacteristic
83C2×D151—41no—
84C2×D151—41no—
85C2×D151—41no—
86C4×C151—21no—
87C4×C151—21no—
88C4×C151—21no—
89C4×C151—41no—
90C4×C151—81no—
91Dic151—41no—
92Dic151—41no—
93Dic151—41no—
94C2×C151—81no—
95C2×C151#45311yescharacteristic
96C2×C151#45511yescharacteristic
97C2×C151#45611yescharacteristic
98D151—81no—
99C151#166111yescharacteristic, complemented, Sylow
100#1661—1511nomaximal, Sylow
101#562—1511no—
102#501—1511no—
103#497D15111yescharacteristic, complemented
104#489—1511no—
105#330—1511no—
106#329—1511no—
107#329—1511no—
108C2×Q16—21no—
109C2×SD16—21no—
110C4⋊Q8C2×D15111yescharacteristic
111#125—1511no—
112#124—1511no—
113#124C2×D15111yescharacteristic
114#123—3021no—
115#123—3021no—
116C22⋊Q8—3021no—
117C22⋊Q8—3021no—
118#121—3021no—
119#121—3021no—
120#107—3021no—
121#106—3021no—
122#103—3021no—
123#102—3021no—
124#97—1511no—
125#97—1511no—
126#97C2×D15111yescharacteristic
127C2×Q8—21no—
128C2×Q8—1511no—
129C2×Q8C22⋊D15111yescharacteristic
130C2×D4—3021no—
131C2×D4—3021no—
132C2×D4—1511no—
133C2×D4C22⋊D15111yescharacteristic
134C22×C4—3021no—
135C22×C4—3021no—
136Q16—42no—
137SD16—42no—
138C2×C8—21no—
139C2×C8—3021no—
140C2×C8—3021no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—3021no—
144C4⋊C4—3021no—
145C4⋊C4—3021no—
146C4⋊C4—3021no—
147C4⋊C4—1511no—
148C4⋊C4—1511no—
149C22⋊C4—21no—
150C22⋊C4—21no—
151C22⋊C4—3021no—
152C22⋊C4—3021no—
153C22⋊C4—3021no—
154C22⋊C4—3021no—
155C42C22×D15111yescharacteristic
156C23—21no—
157C23—3021no—
158Q8—41no—
159Q8—41no—
160Q8—41no—
161Q8—6041no—
162D4—41no—
163D4—6041no—
164D4—12081no—
165D4—12081no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—3021no—
169C2×C4—3021no—
170C2×C4—3021no—
171C2×C4—12081no—
172C2×C4—12081no—
173C2×C4D4×D15111yescharacteristic
174C2×C4D4×D15111yescharacteristic
175C2×C4C2×C22⋊D15111yescharacteristic
176C8—22no—
177C8—3022no—
178C8—6041no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—6041no—
183C22—6041no—
184C22—6041no—
185C22#1801270711yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—41no—
190C4—81no—
191C4—6041no—
192C4—6041no—
193C4—6041no—
194C2—81no—
195C2—12081no—
196C2#2375237911yescharacteristic
197C2#2375238811yescharacteristic
198C2#2375239311yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#497×C151C2
socleC22×C151#120
prime radical#23752956C2
hypercenter#497D151
hypocenterC151#1661
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
2. #23752618C2semidirect
3. #23752574C2semidirect
4. #23751953C2semidirect
5. #23751952C2semidirect
6. #23751951C2semidirect
7. #497×C151C2semidirect
99. C151#1661semidirect
103. #497D151semidirect

Maximal subgroups

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

subgroupindex
#237529562
#237526182
#237525742
#237519532
#237519522
#237519512
#497×C1512
#1661151