Finite Group Databasebeta

← #34068420

Subgroups — #34068420

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#23752966C211yesmaximal, characteristic
2#23752618C211yesmaximal, characteristic, complemented
3#23752604C211yesmaximal, characteristic
4#23751954C211yesmaximal, characteristic, complemented
5#23751953C211yesmaximal, characteristic, complemented
6#23751951C211yesmaximal, characteristic
7#501×C151C211yesmaximal, characteristic, complemented
8C2×#14558994—21no—
9C2×#14558991—21no—
10#18012738—21no—
11#18012734—21no—
12#18012734—21no—
13#18012731C2211yescharacteristic
14#18012727C2211yescharacteristic
15#18012724—21no—
16#18012719—21no—
17#18012717—21no—
18#18012672—21no—
19#18012670—21no—
20#18012650C2211yescharacteristic
21#18012650C2211yescharacteristic
22C4⋊Q8×C151C2211yescharacteristic
23#125×C151C2211yescharacteristic
24#107×C151—21no—
25#106×C151—21no—
26#97×C151C2211yescharacteristic
27C2×Dic302—21no—
28C2×Dic302D411yescharacteristic
29C2×D604D411yescharacteristic
30C2×C4×D151—21no—
31#14558994—42no—
32#14558991—42no—
33C2×C151⋊C8—21no—
34C2×C151⋊C8—21no—
35C4⋊Dic151—21no—
36C4⋊Dic151D411yescharacteristic
37C4⋊Dic151D411yescharacteristic
38Dic151⋊C4—21no—
39Dic151⋊C4—21no—
40Dic151⋊C4—21no—
41(C2×D151)⋊C4—21no—
42(C2×D151)⋊C4—21no—
43(C2×D151)⋊C4—21no—
44(C2×D151)⋊C4—21no—
45(C2×D151)⋊C4—21no—
46C4×Dic151—21no—
47C2×Q8×C151—21no—
48C2×C8×C151—21no—
49C4⋊C4×C151—21no—
50C4⋊C4×C151—21no—
51C4⋊C4×C151—21no—
52C4⋊C4×C151—21no—
53C4⋊C4×C151D411yescharacteristic
54C4⋊C4×C151D411yescharacteristic
55C42×C151C2311yescharacteristic
56C22×D151—21no—
57Dic302—41no—
58Dic302—81no—
59D604—41no—
60C2×Dic151—21no—
61C2×Dic151—21no—
62C2×Dic151—21no—
63C4×D151—81no—
64C151⋊C8—22no—
65C151⋊C8—22no—
66Q8×C151—41no—
67Q8×C151—41no—
68C2×C4×C151—21no—
69C2×C4×C151—21no—
70C2×C4×C151—41no—
71C2×C4×C151C2×D411yescharacteristic
72C2×C4×C151C2×D411yescharacteristic
73C2×C4×C151C2×D411yescharacteristic
74C8×C151—22no—
75C22×C151#12011yescharacteristic
76C2×D151—41no—
77C2×D151—41no—
78C2×D151—41no—
79C4×C151—21no—
80C4×C151—21no—
81C4×C151—21no—
82C4×C151—41no—
83C4×C151—41no—
84C4×C151—81no—
85Dic151—41no—
86Dic151—41no—
87Dic151—41no—
88C2×C151#45311yescharacteristic
89C2×C151#45611yescharacteristic
90C2×C151#45611yescharacteristic
91D151—81no—
92C151#166011yescharacteristic, complemented, Sylow
93#1660—1511nomaximal, Sylow
94#563—1511no—
95#501—1511no—
96#501D15111yescharacteristic, complemented
97#497—1511no—
98#330—1511no—
99#330—1511no—
100#329—1511no—
101C2×Q16—3021no—
102C2×SD16—3021no—
103C4⋊Q8—3021no—
104C4⋊Q8C2×D15111yescharacteristic
105#126—3021no—
106#126—3021no—
107#125—1511no—
108#125C2×D15111yescharacteristic
109#124—1511no—
110#123—3021no—
111C22⋊Q8—3021no—
112C22⋊Q8—3021no—
113#107—21no—
114#107—3021no—
115#106—21no—
116#106—3021no—
117#97—1511no—
118#97—1511no—
119#97C2×D15111yescharacteristic
120C2×Q8—21no—
121C2×Q8—3021no—
122C2×Q8—1511no—
123C2×D4—1511no—
124C22×C4—3021no—
125Q16—6042no—
126SD16—6042no—
127C2×C8—21no—
128C2×C8—3021no—
129C2×C8—3021no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—3021no—
135C4⋊C4—3021no—
136C4⋊C4—3021no—
137C4⋊C4—3021no—
138C4⋊C4—1511no—
139C4⋊C4—1511no—
140C4⋊C4C22⋊D15111yescharacteristic
141C4⋊C4C22⋊D15111yescharacteristic
142C22⋊C4—3021no—
143C22⋊C4—3021no—
144C22⋊C4—3021no—
145C22⋊C4—3021no—
146C22⋊C4—3021no—
147C42—3021no—
148C42C22×D15111yescharacteristic
149C23—3021no—
150Q8—41no—
151Q8—41no—
152Q8—6041no—
153Q8—12081no—
154D4—6041no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—41no—
158C2×C4—3021no—
159C2×C4—3021no—
160C2×C4—3021no—
161C2×C4—12081no—
162C2×C4D4×D15111yescharacteristic
163C2×C4D4×D15111yescharacteristic
164C2×C4C2×C22⋊D15111yescharacteristic
165C8—22no—
166C8—3022no—
167C8—3022no—
168C22—6041no—
169C22—6041no—
170C22—6041no—
171C22#1801270711yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—81no—
178C4—6041no—
179C4—6041no—
180C4—6041no—
181C2—12081no—
182C2#2375237811yescharacteristic
183C2#2375239311yescharacteristic
184C2#2375239411yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#501×C151C2
socleC22×C151#120
prime radicalC2×D604D4
hypercenter#501D151
hypocenterC151#1660
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
2. #23752618C2semidirect
4. #23751954C2semidirect
5. #23751953C2semidirect
7. #501×C151C2semidirect
92. C151#1660semidirect
96. #501D151semidirect

Maximal subgroups

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

subgroupindex
#237529662
#237526182
#237526042
#237519542
#237519532
#237519512
#501×C1512
#1660151