Finite Group Databasebeta

← #34068432

Subgroups — #34068432

Order 19328.

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

normal subgroups only

This group has 196 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#23752580C211yesmaximal, characteristic, complemented
3#23752574C211yesmaximal, characteristic, complemented
4#23751953C211yesmaximal, characteristic, complemented
5#23751952C211yesmaximal, characteristic, complemented
6#23751951C211yesmaximal, characteristic, complemented
7#489×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#18012663—21no—
17#18012663—21no—
18#18012662—21no—
19#18012659—21no—
20#18012650C2211yescharacteristic
21#18012650C2211yescharacteristic
22C4⋊Q8×C151C2211yescharacteristic
23#124×C151C2211yescharacteristic
24#103×C151—21no—
25#102×C151—21no—
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
48C2×C8×C151—21no—
49C4⋊C4×C151—21no—
50C4⋊C4×C151—21no—
51C22⋊C4×C151—21no—
52C22⋊C4×C151—21no—
53C42×C151C2311yescharacteristic
54C22×D151—21no—
55Dic302—41no—
56D604—41no—
57C22⋊D151—81no—
58C22⋊D151—81no—
59C2×Dic151—21no—
60C2×Dic151—21no—
61C2×Dic151—21no—
62C2×Dic151—81no—
63C4×D151—81no—
64C151⋊C8—41no—
65C151⋊C8—41no—
66C23×C151—21no—
67Q8×C151—41no—
68Q8×C151—42no—
69D4×C151—41no—
70C2×C4×C151—21no—
71C2×C4×C151—41no—
72C2×C4×C151C2×D411yescharacteristic
73C2×C4×C151C2×D411yescharacteristic
74C2×C4×C151C2×D411yescharacteristic
75C8×C151—41no—
76C22×C151—41no—
77C22×C151—41no—
78C22×C151—41no—
79C22×C151#12011yescharacteristic
80C2×D151—41no—
81C2×D151—41no—
82C2×D151—41no—
83C4×C151—21no—
84C4×C151—21no—
85C4×C151—21no—
86C4×C151—41no—
87C4×C151—81no—
88Dic151—41no—
89Dic151—41no—
90Dic151—41no—
91C2×C151—81no—
92C2×C151#45411yescharacteristic
93C2×C151#45511yescharacteristic
94C2×C151#45511yescharacteristic
95D151—81no—
96C151#166211yescharacteristic, complemented, Sylow
97#1662—1511nomaximal, Sylow
98#562—1511no—
99#491—1511no—
100#489—1511no—
101#489D15111yescharacteristic, complemented
102#330—1511no—
103#329—1511no—
104#329—1511no—
105C4⋊Q8C2×D15111yescharacteristic
106#125—1511no—
107#124—1511no—
108#124C2×D15111yescharacteristic
109#123—3021no—
110#123—3021no—
111C22⋊Q8—3021no—
112C22⋊Q8—3021no—
113#121—3021no—
114#121—3021no—
115#103—21no—
116#103—3021no—
117#103—3021no—
118#103—3021no—
119#102—21no—
120#102—3021no—
121#97—1511no—
122#97—1511no—
123#97C2×D15111yescharacteristic
124C2×Q8—21no—
125C2×Q8—1511no—
126C2×Q8C22⋊D15111yescharacteristic
127C2×D4—3021no—
128C2×D4—3021no—
129C2×D4—1511no—
130C2×D4C22⋊D15111yescharacteristic
131C22×C4—3021no—
132C22×C4—3021no—
133C2×C8—21no—
134C2×C8—3021no—
135C2×C8—3021no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—3021no—
139C4⋊C4—3021no—
140C4⋊C4—3021no—
141C4⋊C4—3021no—
142C4⋊C4—1511no—
143C4⋊C4—1511no—
144C22⋊C4—21no—
145C22⋊C4—21no—
146C22⋊C4—3021no—
147C22⋊C4—3021no—
148C22⋊C4—3021no—
149C22⋊C4—3021no—
150C42C22×D15111yescharacteristic
151C23—21no—
152C23—3021no—
153Q8—41no—
154Q8—42no—
155Q8—6041no—
156D4—41no—
157D4—6041no—
158D4—12081no—
159D4—12081no—
160C2×C4—21no—
161C2×C4—41no—
162C2×C4—3021no—
163C2×C4—3021no—
164C2×C4—3021no—
165C2×C4—12081no—
166C2×C4—12081no—
167C2×C4D4×D15111yescharacteristic
168C2×C4D4×D15111yescharacteristic
169C2×C4C2×C22⋊D15111yescharacteristic
170C8—41no—
171C8—6041no—
172C8—6041no—
173C22—41no—
174C22—41no—
175C22—41no—
176C22—6041no—
177C22—6041no—
178C22—6041no—
179C22#1801270711yescharacteristic
180C4—21no—
181C4—21no—
182C4—21no—
183C4—41no—
184C4—81no—
185C4—6041no—
186C4—6041no—
187C4—6041no—
188C2—81no—
189C2—12081no—
190C2#2375238311yescharacteristic
191C2#2375238811yescharacteristic
192C2#2375238911yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#489×C151C2
socleC22×C151#120
prime radical#23752956C2
hypercenter#489D151
hypocenterC151#1662
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
2. #23752580C2semidirect
3. #23752574C2semidirect
4. #23751953C2semidirect
5. #23751952C2semidirect
6. #23751951C2semidirect
7. #489×C151C2semidirect
96. C151#1662semidirect
101. #489D151semidirect

Maximal subgroups

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

subgroupindex
#237529562
#237525802
#237525742
#237519532
#237519522
#237519512
#489×C1512
#1662151