Finite Group Databasebeta

← #34069556

Subgroups — #34069556

Order 19328.

358 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 89 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#23752723C211yesmaximal, characteristic
2C2×#18012698C211yesmaximal, characteristic, complemented
3C2×#18012665C212yesmaximal, complemented
4#23751973C212yesmaximal, complemented
5#407×C151C211yesmaximal, characteristic, complemented
6C2×#14559004C2211yescharacteristic
7#18012722—21no—
8#18012718C412yescomplemented
9#18012713C412yescomplemented
10#18012708—21no—
11C4×C22⋊D151—22no—
12#18012698—24no—
13#18012698C2211yescharacteristic
14C2×C4⋊Dic151—21no—
15C2×C22⋊Dic151—21no—
16C2×C4×Dic151C2212yes—
17#18012665—24no—
18C23×C4×C151C2211yescharacteristic
19C2×M16×C151C2212yes—
20C22⋊C8×C151—22no—
21#14559004—22no—
22#14559004—22no—
23C2×Dic302C2×C411yescharacteristic
24C2×D604C2×C411yescharacteristic
25C2×C22⋊D151—22no—
26C2×C22⋊D151—21no—
27C22×Dic151—22no—
28C2×C4×D151—21no—
29C4⋊Dic151—24no—
30C4⋊Dic151C2×C412yes—
31Dic151⋊C4—22no—
32C22⋊Dic151—24no—
33C22⋊Dic151—22no—
34C22⋊Dic151—21no—
35(C2×D151)⋊C4—22no—
36C4×Dic151—22no—
37C4×Dic151—21no—
38C4×Dic151D414yescomplemented
39C24×C151D411yescharacteristic
40C22×C4×C151—22no—
41C22×C4×C151—22no—
42C22×C4×C151C2×C412yes—
43C22×C4×C151D412yes—
44C22×C4×C151D411yescharacteristic
45C22×C4×C151C2311yescharacteristic
46M16×C151—22no—
47M16×C151—22no—
48C2×C8×C151—22no—
49C22×D151—21no—
50Dic302—22no—
51D604—22no—
52C22⋊D151—44no—
53C22⋊D151—41no—
54C22⋊D151—41no—
55C2×Dic151—22no—
56C2×Dic151—21no—
57C2×Dic151—24no—
58C2×Dic151—44no—
59C4×D151—42no—
60C23×C151—21no—
61C23×C151—21no—
62C23×C151—42no—
63C23×C151C22⋊C412yes—
64C23×C151C2×D411yescharacteristic
65C2×C4×C151—21no—
66C2×C4×C151—21no—
67C2×C4×C151—24no—
68C2×C4×C151—24no—
69C2×C4×C151C22⋊C412yes—
70C2×C4×C151C22×C411yescharacteristic
71C2×C4×C151C2×D412yes—
72C2×C4×C151C2×D411yescharacteristic
73C2×C4×C151#4112yes—
74C8×C151—42no—
75C22×C151—22no—
76C22×C151—22no—
77C22×C151—22no—
78C22×C151—22no—
79C22×C151—42no—
80C22×C151—42no—
81C22×C151C2×C22⋊C411yescharacteristic
82C22×C151#12011yescharacteristic
83C22×C151#12311yescharacteristic
84C2×D151—41no—
85C2×D151—42no—
86C4×C151—22no—
87C4×C151C4×D412yes—
88C4×C151#12112yes—
89Dic151—44no—
90Dic151—41no—
91Dic151—42no—
92C2×C151—21no—
93C2×C151—21no—
94C2×C151—42no—
95C2×C151#38611yescharacteristic
96C2×C151#42112yes—
97D151—81no—
98C151#189711yescharacteristic, complemented, Sylow
99#1897—1511nomaximal, Sylow
100#525—1511no—
101C2×#117—1511no—
102C2×#104—1512no—
103#407D15111yescharacteristic, complemented
104#339—1512no—
105C2×#41—1511no—
106C23×C4C2×D15111yescharacteristic
107C2×M16C2×D15112yes—
108#123—3021no—
109C22⋊Q8—1512no—
110#121—1512no—
111#120—3021no—
112C4×D4—3022no—
113#117—3024no—
114#117—1511no—
115C2×C4⋊C4—3021no—
116C2×C22⋊C4—3021no—
117C2×C42—1512no—
118#104—3024no—
119C22⋊C8—22no—
120C24D60411yescharacteristic
121#41—3022no—
122#41—3022no—
123C2×Q8—1511no—
124C2×D4—3022no—
125C2×D4—3021no—
126C2×D4—1511no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—3022no—
130C22×C4—3021no—
131C22×C4C4×D15112yes—
132C22×C4C22⋊D15112yes—
133C22×C4D60411yescharacteristic
134C22×C4C22×D15111yescharacteristic
135M16—22no—
136M16—22no—
137C2×C8—22no—
138C4⋊C4—3024no—
139C4⋊C4—3022no—
140C4⋊C4—1512no—
141C22⋊C4—3024no—
142C22⋊C4—3022no—
143C22⋊C4—3021no—
144C22⋊C4—3022no—
145C42—3022no—
146C42—3021no—
147C42—1514no—
148C23—21no—
149C23—21no—
150C23—42no—
151C23—3021no—
152C23(C2×D151)⋊C412yes—
153C23C2×D60411yescharacteristic
154Q8—3022no—
155D4—3022no—
156D4—6044no—
157D4—6041no—
158D4—6041no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—3022no—
164C2×C4—3021no—
165C2×C4—3024no—
166C2×C4—6044no—
167C2×C4—6042no—
168C2×C4(C2×D151)⋊C412yes—
169C2×C4C2×C4×D15111yescharacteristic
170C2×C4D4×D15112yes—
171C2×C4C2×C22⋊D15111yescharacteristic
172C2×C4#1455900312yes—
173C8—42no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—6042no—
181C22—6041no—
182C22C2×(C2×D151)⋊C411yescharacteristic
183C22#1801270911yescharacteristic
184C22#1801272311yescharacteristic
185C4—22no—
186C4—6044no—
187C4—6042no—
188C4—6041no—
189C4(C22⋊D151)⋊C412yes—
190C4#1801271112yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—12081no—
195C2#2375208911yescharacteristic
196C2#2375222812yes—
subgroupG/H
centerC2×C4C2×C22⋊D151
commutatorC2×C4×C151C22×C4
FrattiniC22×C4C22×D151
Fitting#407×C151C2
socleC22×C151C2×C22⋊C4
prime radical#23752723C2
cosocleC22×C4×C151C23
hypercenter#407D151
hypocenterC151#1897
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×#18012698C2semidirect
3. C2×#18012665C2semidirect
4. #23751973C2semidirect
5. #407×C151C2semidirect
8. #18012718C4semidirect
9. #18012713C4semidirect
38. C4×Dic151D4semidirect
98. C151#1897semidirect
103. #407D151semidirect

Maximal subgroups

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

subgroupindex
#237527232
C2×#180126982
C2×#180126652
#237519732
#407×C1512
#1897151