Finite Group Databasebeta

← #34060441

Subgroups — #34060441

Order 19072.

360 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 94 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
1C2×#18011971C212yesmaximal
2C4×#14558745C212yesmaximal, complemented
3#23750505C212yesmaximal, complemented
4C2×#18011871C211yesmaximal, characteristic
5C2×#14558745C2214yes—
6#18011971C418yescomplemented
7#18011966—22no—
8C4×#11924753—22no—
9C22×C22⋊D149C2211yescharacteristic
10C23×Dic149C411yescharacteristic
11C22×C4×D149C411yescharacteristic
12#18011871—22no—
13#18011871—22no—
14C2×#14558715C2211yescharacteristic
15C2×#14558713C411yescharacteristic
16C2×C4×Dic149C2211yescharacteristic
17C2×C22⋊C4×C149C411yescharacteristic
18#14558745—24no—
19#14558745C2×C418yescomplemented
20C2×#11924753—24no—
21C23×D149C2×C411yescharacteristic
22C2×C22⋊D149—22no—
23C2×C22⋊D149—22no—
24C2×C22⋊D149C2×C414yes—
25C22×Dic149—21no—
26C22×Dic149—21no—
27C22×Dic149—42no—
28C22×Dic149C2×C411yescharacteristic
29C22×Dic149C2×C411yescharacteristic
30C22×Dic149C2311yescharacteristic
31C2×C4×D149—21no—
32C2×C4×D149—21no—
33C2×C4×D149—42no—
34#14558715—22no—
35#14558713—22no—
36C4×Dic149D412yes—
37C4×Dic149D412yes—
38C24×C149C2×C411yescharacteristic
39C22×C4×C149C2×C411yescharacteristic
40C22×C4×C149C2×C411yescharacteristic
41C22⋊C4×C149—22no—
42#11924753—28no—
43C22×D149—21no—
44C22×D149—21no—
45C22×D149—41no—
46C22×D149—41no—
47C22×D149C4212yes—
48C22⋊D149—28no—
49C2×Dic149—22no—
50C2×Dic149—21no—
51C2×Dic149—42no—
52C2×Dic149—42no—
53C2×Dic149—41no—
54C2×Dic149C22⋊C411yescharacteristic
55C2×Dic149C22⋊C411yescharacteristic
56C2×Dic149C22×C412yes—
57C2×Dic149C2×D412yes—
58C2×Dic149#4112yes—
59C4×D149—42no—
60C4×D149—42no—
61C23×C149—21no—
62C23×C149—21no—
63C23×C149—41no—
64C23×C149—41no—
65C23×C149C4212yes—
66C23×C149C22×C411yescharacteristic
67C2×C4×C149—21no—
68C2×C4×C149—41no—
69C2×C4×C149—41no—
70C2×C4×C149C22⋊C412yes—
71C22×C149—21no—
72C22×C149—21no—
73C22×C149—22no—
74C22×C149—42no—
75C22×C149—42no—
76C22×C149—41no—
77C22×C149—41no—
78C22×C149C2×C4211yescharacteristic
79C22×C149C2×C22⋊C411yescharacteristic
80C22×C149#11711yescharacteristic
81C2×D149—22no—
82C2×D149—42no—
83C2×D149—41no—
84C2×D149—41no—
85C2×D149—42no—
86C4×C149—22no—
87C4×C149—41no—
88Dic149—21no—
89Dic149—41no—
90Dic149#10012yescomplemented
91Dic149C4×D414yes—
92C2×C149—21no—
93C2×C149—21no—
94C2×C149—42no—
95C2×C149C4×C22⋊C411yescharacteristic
96C2×C149C2×#10011yescharacteristic
97C2×C149#41311yescharacteristic
98D149—42no—
99C149C4×#10011yescharacteristic, complemented, Sylow
100C4×#100—1491nomaximal, Sylow
101C2×C4×D4—1491no—
102C2×#100—1492no—
103C4×M16—1492no—
104#343—1492no—
105C22×D4—1491no—
106C23×C4—1491no—
107C23×C4—1491no—
108C2×M16—1494no—
109C4×D4—2982no—
110C4×D4—2982no—
111C2×C4⋊C4—1491no—
112C2×C22⋊C4—1491no—
113C2×C22⋊C4#1059701011yescharacteristic
114C2×C42—1491no—
115#100—1498no—
116#97—2982no—
117C4×C8—2982no—
118C24—1491no—
119C24C2×#1059701011yescharacteristic
120C2×D4—2982no—
121C2×D4—2982no—
122C2×D4—1494no—
123C22×C4—2981no—
124C22×C4—2981no—
125C22×C4—2981no—
126C22×C4—2981no—
127C22×C4—5962no—
128C22×C4—5962no—
129C22×C4—1491no—
130C22×C4—1491no—
131C22×C4—1491no—
132C22×C4C2×#1059701011yescharacteristic
133C22×C4C2×#1059701011yescharacteristic
134M16—2984no—
135M16—1498no—
136C2×C8—2984no—
137C4⋊C4—2982no—
138C22⋊C4—22no—
139C22⋊C4—2982no—
140C42—1492no—
141C42—1492no—
142C23—21no—
143C23—21no—
144C23—41no—
145C23—41no—
146C23—2981no—
147C23—2981no—
148C23—5961no—
149C23—5961no—
150C23—1492no—
151C23C4×#1059701012yes—
152C23C22×#1059701011yescharacteristic
153D4—2988no—
154C2×C4—21no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—2982no—
158C2×C4—2981no—
159C2×C4—5962no—
160C2×C4—5962no—
161C2×C4—5962no—
162C2×C4—5962no—
163C2×C4—5961no—
164C2×C4—1491no—
165C2×C4—1492no—
166C2×C4—1491no—
167C2×C4—1492no—
168C2×C4—1492no—
169C2×C4C22⋊#1059701012yes—
170C8—2988no—
171C22—21no—
172C22—21no—
173C22—22no—
174C22—42no—
175C22—42no—
176C22—41no—
177C22—41no—
178C22—2982no—
179C22—5962no—
180C22—5962no—
181C22—5961no—
182C22—5961no—
183C22C2×C4×#1059701011yescharacteristic
184C22C2×C22⋊#1059701011yescharacteristic
185C22#1801199011yescharacteristic
186C4—22no—
187C4—41no—
188C4—2981no—
189C4—5961no—
190C4—1494no—
191C4—1492no—
192C2—21no—
193C2—21no—
194C2—42no—
195C2—5962no—
196C2C4×C22⋊#1059701011yescharacteristic
197C2D149⋊#10011yescharacteristic
198C2#2375061211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC22×C149C2×C42
FrattiniC23C22×#10597010
FittingC2×C22⋊C4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC22×C22⋊D149C22
cosocleC22×Dic149C23
hypercenterC2×C22⋊C4#10597010
hypocenterC149C4×#100
LCSG ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C4×#14558745C2semidirect
3. #23750505C2semidirect
6. #18011971C4semidirect
19. #14558745C2×C4semidirect
90. Dic149#100semidirect
99. C149C4×#100semidirect

Maximal subgroups

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

subgroupindex
C2×#180119712
C4×#145587452
#237505052
C2×#180118712
C4×#100149