Finite Group Databasebeta

← #34060594

Subgroups — #34060594

Order 19072.

344 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 84 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
1D149⋊(C22⋊C8)C211yesmaximal, characteristic
2#23750567C211yesmaximal, characteristic
3#23750498C214yesmaximal, complemented
4C2×C4⋊C4×D149C211yesmaximal, characteristic
5C2×D149⋊C8C2212yes—
6C2×C4⋊#10597010C2212yes—
7C2×C22⋊#10597010—21no—
8#18011968—21no—
9C22⋊#11924753—21no—
10(C2×#10597010)⋊C4—21no—
11C22×C4×D149—21no—
12C22×C4×D149C2211yescharacteristic
13C2×C4⋊Dic149C411yescharacteristic, complemented
14C2×#14558715—21no—
15C4⋊C4×D149—21no—
16C4⋊C4×D149—21no—
17C4⋊C4×D149C412yescomplemented
18C4⋊C4×D149C2212yes—
19C2×C4⋊C4×C149C411yescharacteristic, complemented
20C22×#10597010—22no—
21D149⋊C8—24no—
22C2×#11924753—22no—
23C4⋊#10597010—24no—
24C22⋊#10597010—42no—
25C23×D149D411yescharacteristic
26C22×Dic149—21no—
27C22×Dic149D411yescharacteristic
28C2×C4×D149—24no—
29C2×C4×D149—22no—
30C2×C4×D149—22no—
31C2×C4×D149—42no—
32C2×C4×D149—42no—
33C2×C4×D149C2×C411yescharacteristic
34C2×C4×D149D411yescharacteristic
35C2×C4×D149D411yescharacteristic
36C2×C4×D149C2311yescharacteristic
37C4⋊Dic149—21no—
38C4⋊Dic149C2×C412yes—
39#14558715—22no—
40#14558715—22no—
41C22×C4×C149—21no—
42C22×C4×C149C2×C411yescharacteristic
43C4⋊C4×C149—21no—
44C4⋊C4×C149C2×C412yes—
45C2×#10597010—42no—
46C2×#10597010—42no—
47C2×#10597010—42no—
48#11924753—42no—
49C22×D149—22no—
50C22×D149—22no—
51C22×D149C22⋊C411yescharacteristic
52C22×D149D812yes—
53C22×D149SD1612yes—
54C22×D149C2×D411yescharacteristic
55C2×Dic149—22no—
56C2×Dic149—22no—
57C2×Dic149—42no—
58C2×Dic149C22⋊C411yescharacteristic
59C2×Dic149C2×D411yescharacteristic
60C4×D149—22no—
61C4×D149—22no—
62C4×D149—22no—
63C4×D149—44no—
64C4×D149—42no—
65C4×D149—42no—
66C4×D149#4114yes—
67C23×C149C22⋊C411yescharacteristic
68C2×C4×C149—22no—
69C2×C4×C149—22no—
70C2×C4×C149—42no—
71C2×C4×C149C22⋊C411yescharacteristic
72C2×C4×C149C22×C411yescharacteristic
73C22×C149—21no—
74C22×C149—21no—
75C22×C149#10212yes—
76C22×C149C2×C22⋊C411yescharacteristic
77C2×D149—21no—
78C2×D149—21no—
79C2×D149—24no—
80C2×D149—24no—
81C2×D149#10212yes—
82C2×D149#12312yes—
83C2×D149C2×D811yescharacteristic
84C2×D149C2×SD1611yescharacteristic
85C2×D149#13712yes—
86#10597010—82no—
87C4×C149—21no—
88C4×C149—42no—
89C4×C149#11712yes—
90Dic149—21no—
91Dic149—42no—
92Dic149#12312yes—
93C2×C149—22no—
94C2×C149#38111yescharacteristic
95C2×C149C2×#10211yescharacteristic
96C2×C149#41911yescharacteristic
97D149—22no—
98D149#48012yes—
99D149#48312yes—
100C149#182311yescharacteristic, complemented, Sylow
101#1823—1491nomaximal, Sylow
102C22×C4⋊C4—1491no—
103C2×C22⋊C8—1491no—
104#380—1491no—
105#340—1494no—
106C23×C4—2981no—
107C23×C4—1491no—
108C22×C8—1492no—
109C2×C4⋊C4—2981no—
110C2×C4⋊C4—2981no—
111C2×C4⋊C4—2981no—
112C2×C4⋊C4—1492no—
113C2×C4⋊C4—1491no—
114C2×C4⋊C4—1492no—
115C2×C4⋊C4—1492no—
116C2×C4⋊C4#1059701011yescharacteristic, complemented
117C2×C22⋊C4—2981no—
118C22⋊C8—2981no—
119C22⋊C8—2981no—
120#95—2981no—
121C24—1491no—
122C22×C4—21no—
123C22×C4—2984no—
124C22×C4—2982no—
125C22×C4—2982no—
126C22×C4—2981no—
127C22×C4—2982no—
128C22×C4—5962no—
129C22×C4—5962no—
130C22×C4—1491no—
131C22×C4—1491no—
132C22×C4—1491no—
133C22×C4—1491no—
134C22×C4—1491no—
135C22×C4C2×#1059701011yescharacteristic
136C2×C8—2982no—
137C2×C8—2984no—
138C4⋊C4—21no—
139C4⋊C4—2982no—
140C4⋊C4—2982no—
141C4⋊C4—2981no—
142C4⋊C4—2984no—
143C4⋊C4—1492no—
144C4⋊C4C2×#1059701012yes—
145C22⋊C4—5962no—
146C23—2982no—
147C23—2982no—
148C23—1492no—
149C23—1492no—
150C23—1491no—
151C23—1491no—
152C23C22⋊#1059701011yescharacteristic
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—42no—
156C2×C4—2982no—
157C2×C4—2982no—
158C2×C4—2982no—
159C2×C4—2982no—
160C2×C4—2982no—
161C2×C4—5964no—
162C2×C4—5962no—
163C2×C4—5962no—
164C2×C4—5962no—
165C2×C4—5962no—
166C2×C4—5962no—
167C2×C4—5962no—
168C2×C4—1491no—
169C2×C4—1491no—
170C2×C4—1494no—
171C2×C4C22⋊#1059701011yescharacteristic
172C2×C4C22×#1059701011yescharacteristic
173C8—5962no—
174C22—21no—
175C22—21no—
176C22—2984no—
177C22—2984no—
178C22—2981no—
179C22—2981no—
180C22—1492no—
181C22—1492no—
182C22—1491no—
183C22—1491no—
184C22—1492no—
185C22#1801197312yes—
186C22C2×C22⋊#1059701011yescharacteristic
187C4—21no—
188C4—42no—
189C4—2981no—
190C4—5962no—
191C4—1492no—
192C4—11922no—
193C4#1801199012yes—
194C2—22no—
195C2—2982no—
196C2—1492no—
197C2—1492no—
198C2#2375056811yescharacteristic
199C2C2×#1801197311yescharacteristic
200C2#2375061811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC2×C4⋊C4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC23×D149D4
cosocleC2×C4×D149C23
hypercenterC2×C4⋊C4#10597010
hypocenterC149#1823
LCSG ▷ C2×C4×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
3. #23750498C2semidirect
13. C2×C4⋊Dic149C4semidirect
17. C4⋊C4×D149C4semidirect
19. C2×C4⋊C4×C149C4semidirect
100. C149#1823semidirect
116. C2×C4⋊C4#10597010semidirect

Maximal subgroups

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

subgroupindex
D149⋊(C22⋊C8)2
#237505672
#237504982
C2×C4⋊C4×D1492
#1823149