Finite Group Databasebeta

← #34060950

Subgroups — #34060950

Order 19072.

266 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 54 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#23750611C211yesmaximal, characteristic, complemented
2#23750604C211yesmaximal, characteristic, complemented
3#23750525C214yesmaximal, complemented
4#23750192C211yesmaximal, characteristic
5D149⋊M16—21no—
6#18011990—21no—
7#18011972—21no—
8#18011971C2212yes—
9#18011970—21no—
10#18011969C2212yes—
11C2×#14558736C2211yescharacteristic
12#18011907—21no—
13#18011898—21no—
14#18011882—21no—
15#18011882—21no—
16#18011880C412yescomplemented
17#18011880C2212yes—
18#18011870C411yescharacteristic, complemented
19C22×D4×C149C411yescharacteristic, complemented
20#14558746—41no—
21#14558745—22no—
22D149⋊C8—41no—
23C4⋊#10597010—41no—
24C22⋊#10597010—22no—
25C4×#10597010—41no—
26#14558736—41no—
27#14558736—41no—
28C2×Dic298D411yescharacteristic
29C2×D596D411yescharacteristic
30C2×C22⋊D149—22no—
31C2×C22⋊D149—22no—
32C2×C22⋊D149C2×C411yescharacteristic
33C2×C22⋊D149C2311yescharacteristic
34C2×C4×D149D411yescharacteristic
35C2×C4×D149D411yescharacteristic
36C4⋊Dic149—21no—
37C22⋊Dic149—22no—
38C22⋊Dic149—22no—
39C22⋊Dic149C2×C412yes—
40C4×Dic149—21no—
41C24×C149C2×C412yes—
42C2×D4×C149—21no—
43C2×D4×C149—21no—
44C2×D4×C149—41no—
45C2×D4×C149—41no—
46C22×C4×C149C2×C411yescharacteristic
47C2×#10597010—42no—
48#11924753—42no—
49C22×D149C22⋊C411yescharacteristic
50C22×D149C2×D411yescharacteristic
51Dic298—41no—
52D596—41no—
53C22⋊D149—41no—
54C22⋊D149—41no—
55C22⋊D149—82no—
56C22⋊D149—82no—
57C2×Dic149—22no—
58C2×Dic149C22⋊C411yescharacteristic
59C2×Dic149C2×D411yescharacteristic
60C4×D149—21no—
61C4×D149—21no—
62C4×D149—21no—
63C4×D149—21no—
64C23×C149—22no—
65C23×C149—42no—
66C23×C149—82no—
67C23×C149C22×C411yescharacteristic
68D4×C149—42no—
69D4×C149—41no—
70D4×C149—41no—
71C2×C4×C149—21no—
72C2×C4×C149—21no—
73C2×C4×C149C22⋊C411yescharacteristic
74C2×C4×C149C22⋊C411yescharacteristic
75C22×C149—21no—
76C22×C149—41no—
77C22×C149—42no—
78C22×C149—42no—
79C22×C149—42no—
80C22×C149—84no—
81C22×C149C2×C22⋊C411yescharacteristic
82C2×D149—21no—
83C2×D149—21no—
84C2×D149—41no—
85C2×D149—41no—
86#10597010—82no—
87C4×C149—21no—
88C4×C149#9911yescharacteristic
89C4×C149#9911yescharacteristic
90Dic149—21no—
91Dic149—21no—
92Dic149—42no—
93C2×C149—21no—
94C2×C149—41no—
95C2×C149—82no—
96C2×C149C2×#9911yescharacteristic
97D149—41no—
98D149—41no—
99C149#212211yescharacteristic, complemented, Sylow
100#2122—1491nomaximal, Sylow
101#535—1491no—
102#413—1491no—
103#410—1491no—
104AΣL(1,𝔽16)—1494no—
105C2×#41—1491no—
106C22×D4#1059701011yescharacteristic, complemented
107C2×M16—2981no—
108#127—2981no—
109#124—2981no—
110#121—2981no—
111#121—2981no—
112#120—1492no—
113#120—1492no—
114#117—2981no—
115#117—1491no—
116#101—2981no—
117#100—1492no—
118#99—2981no—
119#99—1492no—
120C24C2×#1059701012yes—
121#41—5961no—
122#41—5961no—
123C2×Q8—1491no—
124C2×D4—21no—
125C2×D4—21no—
126C2×D4—41no—
127C2×D4—41no—
128C2×D4—2982no—
129C2×D4—2982no—
130C2×D4—1491no—
131C2×D4—1491no—
132C2×D4—1491no—
133C22×C4—1491no—
134C22×C4—1491no—
135C22×C4C2×#1059701011yescharacteristic
136M16—2982no—
137M16—5961no—
138C2×C8—5961no—
139C4⋊C4—2981no—
140C4⋊C4—5961no—
141C22⋊C4—2982no—
142C22⋊C4—2982no—
143C22⋊C4—2982no—
144C22⋊C4—1492no—
145C42—2981no—
146C42—5961no—
147C23—22no—
148C23—42no—
149C23—82no—
150C23—1491no—
151C23—1491no—
152C23C22×#1059701011yescharacteristic
153Q8—5961no—
154D4—42no—
155D4—41no—
156D4—41no—
157D4—5961no—
158D4—5961no—
159D4—5961no—
160D4—11922no—
161D4—11922no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—2981no—
165C2×C4—2981no—
166C2×C4—2981no—
167C2×C4—2981no—
168C2×C4—2982no—
169C2×C4—5962no—
170C2×C4—1491no—
171C2×C4—1491no—
172C2×C4C22⋊#1059701011yescharacteristic
173C2×C4C22⋊#1059701011yescharacteristic
174C8—5962no—
175C22—21no—
176C22—41no—
177C22—42no—
178C22—42no—
179C22—42no—
180C22—84no—
181C22—2981no—
182C22—2981no—
183C22—5961no—
184C22—5961no—
185C22C2×C22⋊#1059701011yescharacteristic
186C4—21no—
187C4—2981no—
188C4—2981no—
189C4—5962no—
190C4—11922no—
191C4#1801196911yescharacteristic
192C4#1801196911yescharacteristic
193C2—21no—
194C2—41no—
195C2—82no—
196C2—5961no—
197C2—5961no—
198C2C2×#1801196911yescharacteristic
subgroupG/H
centerC2C2×#18011969
commutatorC23×C149C22×C4
FrattiniC23C22×#10597010
FittingC22×D4×C149C4
socleC2×C149C2×#99
prime radical#23750192C2
cosocleC2×C22⋊D149C23
hypercenterC22×D4#10597010
hypocenterC149#2122
LCSG ▷ C23×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #23750611C2semidirect
2. #23750604C2semidirect
3. #23750525C2semidirect
16. #18011880C4semidirect
18. #18011870C4semidirect
19. C22×D4×C149C4semidirect
99. C149#2122semidirect
106. C22×D4#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506112
#237506042
#237505252
#237501922
#2122149