Finite Group Databasebeta

← #34059968

Subgroups — #34059968

Order 19072.

322 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 64 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#23750596C211yesmaximal, characteristic, complemented
2D149⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
3#23750469C214yesmaximal, complemented
4C2×#18011886C211yesmaximal, characteristic
5C2×#14558746—21no—
6C2×D149⋊C8—21no—
7#18011968—21no—
8#18011968—21no—
9C22⋊#11924753C2212yes—
10C22⋊#11924753C2212yes—
11C22×D596C412yes—
12C22×D596C411yescharacteristic
13C22×C4×D149C2211yescharacteristic
14#18011886—21no—
15#18011886—21no—
16#18011886—21no—
17#18011886—21no—
18C2×#14558713C2212yes—
19C2×C4⋊C4×C149C411yescharacteristic
20#14558746—42no—
21D149⋊C8—42no—
22C2×#11924753—22no—
23C2×#11924753—22no—
24C23×D149C2×C411yescharacteristic
25C23×D149C2×C412yes—
26C2×D596—22no—
27C2×D596—22no—
28C2×D596—21no—
29C2×D596—21no—
30C2×D596—42no—
31C2×D596—44no—
32C22×Dic149C2311yescharacteristic
33C2×C4×D149—42no—
34C2×C4×D149D411yescharacteristic
35C2×C4×D149D411yescharacteristic
36C2×C4×D149D411yescharacteristic
37C2×C4×D149D411yescharacteristic
38#14558713—22no—
39#14558713—22no—
40C22×C4×C149C2×C411yescharacteristic
41C22×C4×C149C2×C412yes—
42C4⋊C4×C149—21no—
43C4⋊C4×C149—21no—
44#11924753—42no—
45#11924753—42no—
46C22×D149—22no—
47C22×D149—22no—
48C22×D149—22no—
49C22×D149—24no—
50C22×D149—41no—
51C22×D149—42no—
52C22×D149—42no—
53C22×D149C22⋊C411yescharacteristic
54C22×D149C22⋊C411yescharacteristic
55D596—42no—
56D596—44no—
57D596—44no—
58D596—42no—
59C2×Dic149—41no—
60C2×Dic149C2×D411yescharacteristic
61C2×Dic149C2×D411yescharacteristic
62C4×D149—22no—
63C4×D149—22no—
64C4×D149—41no—
65C4×D149—41no—
66C23×C149C22×C411yescharacteristic
67C2×C4×C149—22no—
68C2×C4×C149—22no—
69C2×C4×C149—42no—
70C2×C4×C149C22⋊C411yescharacteristic
71C2×C4×C149C22⋊C411yescharacteristic
72C22×C149—21no—
73C22×C149—21no—
74C22×C149C2×C22⋊C411yescharacteristic
75C22×C149#13112yes—
76C2×D149—21no—
77C2×D149—21no—
78C2×D149—21no—
79C2×D149—21no—
80C2×D149—21no—
81C2×D149—44no—
82C2×D149—42no—
83C2×D149—42no—
84C2×D149—42no—
85C2×D149—84no—
86C2×D149#10012yes—
87C4×C149—21no—
88C4×C149—42no—
89C4×C149#9912yes—
90Dic149—21no—
91Dic149—21no—
92C2×C149—22no—
93C2×C149#40811yescharacteristic
94C2×C149C2×#9911yescharacteristic
95C2×C149C2×#10011yescharacteristic
96D149—22no—
97D149—41no—
98D149—82no—
99C149#147111yescharacteristic, complemented, Sylow
100#1471—1491nomaximal, Sylow
101C2×#121—1491no—
102#407—1491no—
103C2×C22⋊C8—1491no—
104#323—1494no—
105C22×D4—1492no—
106C22×D4—1491no—
107C23×C4—1491no—
108C2×M16—2981no—
109C22×C8—2981no—
110#121—2981no—
111#121—2981no—
112#121—2981no—
113#121—2981no—
114C2×C4⋊C4#1059701011yescharacteristic
115C2×C22⋊C4—1492no—
116C22⋊C8—2981no—
117C22⋊C8—2981no—
118C22⋊C8—1492no—
119C22⋊C8—1492no—
120C24—1491no—
121C24—1492no—
122C2×D4—2982no—
123C2×D4—2982no—
124C2×D4—2981no—
125C2×D4—2981no—
126C2×D4—5962no—
127C2×D4—5964no—
128C22×C4—5962no—
129C22×C4—1491no—
130C22×C4—1491no—
131C22×C4—1491no—
132C22×C4—1491no—
133C22×C4—1491no—
134C22×C4C2×#1059701012yes—
135C22×C4C2×#1059701011yescharacteristic
136M16—5962no—
137C2×C8—2982no—
138C2×C8—2982no—
139C2×C8—5962no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C22⋊C4—2982no—
143C22⋊C4—2982no—
144C23—2982no—
145C23—2982no—
146C23—2982no—
147C23—2984no—
148C23—5961no—
149C23—5962no—
150C23—5962no—
151C23—1491no—
152C23—1491no—
153C23C22×#1059701011yescharacteristic
154D4—5962no—
155D4—5964no—
156D4—5964no—
157D4—5962no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—42no—
161C2×C4—2982no—
162C2×C4—2982no—
163C2×C4—5961no—
164C2×C4—5961no—
165C2×C4—5961no—
166C2×C4—1491no—
167C2×C4—1491no—
168C2×C4C22⋊#1059701011yescharacteristic
169C2×C4C22⋊#1059701011yescharacteristic
170C8—5962no—
171C8—5962no—
172C22—21no—
173C22—21no—
174C22—2981no—
175C22—2981no—
176C22—2981no—
177C22—2981no—
178C22—2981no—
179C22—5964no—
180C22—5962no—
181C22—5962no—
182C22—5962no—
183C22—1492no—
184C22—11924no—
185C22C2×C22⋊#1059701011yescharacteristic
186C22#1801199912yes—
187C4—21no—
188C4—42no—
189C4—2981no—
190C4—2981no—
191C4#1801197012yes—
192C2—22no—
193C2—2982no—
194C2—5961no—
195C2—11922no—
196C2#2375060011yescharacteristic
197C2C2×#1801197011yescharacteristic
198C2D149⋊#10011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC23×C149C22×C4
FrattiniC23C22×#10597010
FittingC2×C4⋊C4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC2×#18011886C2
cosocleC22×Dic149C23
hypercenterC2×C4⋊C4#10597010
hypocenterC149#1471
LCSG ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #23750596C2semidirect
2. D149⋊(C22⋊C8)C2semidirect
3. #23750469C2semidirect
99. C149#1471semidirect

Maximal subgroups

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

subgroupindex
#237505962
D149⋊(C22⋊C8)2
#237504692
C2×#180118862
#1471149