Finite Group Databasebeta

← #34045004

Subgroups — #34045004

Order 19072.

360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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×#18011870C211yesmaximal, characteristic
2C2×#18011835C212yesmaximal, complemented
3C2×C22⋊#11924746C211yesmaximal, characteristic
4#23749387C212yesmaximal, complemented
5C2×C22⋊Q8×C149C211yesmaximal, characteristic
6C22×#11924746C2212yes—
7#18011870—24no—
8C2×C4⋊Dic149C2212yes—
9C2×C22⋊Dic149—21no—
10C2×C4×Dic149—21no—
11#18011835—24no—
12C22⋊#11924746—22no—
13C22×Q8×C149C2211yescharacteristic
14C23×C4×C149C2211yescharacteristic
15C22⋊Q8×C149—22no—
16C22⋊Q8×C149C414yescomplemented
17C2×C4⋊C4×C149—21no—
18C2×C4⋊C4×C149C2211yescharacteristic
19C2×C22⋊C4×C149—21no—
20C22×Dic149—22no—
21C2×#11924746—22no—
22C2×#11924746—22no—
23C2×#11924746—22no—
24C4⋊Dic149—22no—
25C4⋊Dic149D414yes—
26C22⋊Dic149—24no—
27C4×Dic149—24no—
28C24×C149D411yescharacteristic
29C2×Q8×C149—21no—
30C2×Q8×C149—22no—
31C2×Q8×C149—22no—
32C2×Q8×C149C2×C412yes—
33C22×C4×C149—22no—
34C22×C4×C149—22no—
35C22×C4×C149—21no—
36C22×C4×C149—21no—
37C22×C4×C149C2×C412yes—
38C22×C4×C149D411yescharacteristic
39C22×C4×C149D412yes—
40C22×C4×C149C2311yescharacteristic
41C4⋊C4×C149—24no—
42C4⋊C4×C149—21no—
43C4⋊C4×C149C2×C412yes—
44C22⋊C4×C149—24no—
45C2×Dic149—24no—
46C2×Dic149—42no—
47C2×Dic149—42no—
48#11924746—42no—
49C23×C149—21no—
50C23×C149—21no—
51C23×C149—22no—
52C23×C149—22no—
53C23×C149C22⋊C412yes—
54C23×C149C2×D411yescharacteristic
55Q8×C149—24no—
56Q8×C149—42no—
57C2×C4×C149—21no—
58C2×C4×C149—21no—
59C2×C4×C149—24no—
60C2×C4×C149—24no—
61C2×C4×C149—22no—
62C2×C4×C149—22no—
63C2×C4×C149—41no—
64C2×C4×C149—41no—
65C2×C4×C149—42no—
66C2×C4×C149C22⋊C412yes—
67C2×C4×C149C22×C411yescharacteristic
68C2×C4×C149C2×D412yes—
69C2×C4×C149C2×D411yescharacteristic
70C2×C4×C149#4112yes—
71C22×C149—22no—
72C22×C149—22no—
73C22×C149—22no—
74C22×C149—42no—
75C22×C149—42no—
76C22×C149C2×C22⋊C411yescharacteristic
77C22×C149#12011yescharacteristic
78C22×C149#12311yescharacteristic
79C22×C149#13512yes—
80C22×C149#13712yes—
81C4×C149—22no—
82C4×C149—42no—
83C4×C149—42no—
84C4×C149C4×D412yes—
85C4×C149#12112yes—
86Dic149—44no—
87C2×C149—42no—
88C2×C149#38611yescharacteristic
89C2×C149#41611yescharacteristic
90C2×C149#41911yescharacteristic
91C2×C149#45212yes—
92C2×C149#48512yes—
93C149#187311yescharacteristic, complemented, Sylow
94#1873—1491nomaximal, Sylow
95C2×C22⋊Q8D14911yescharacteristic
96C2×#117—1491no—
97C2×#103—1492no—
98C2×C22⋊C8—1491no—
99#340—1492no—
100C22×Q8C2×D14911yescharacteristic
101C23×C4C2×D14911yescharacteristic
102C22×C8—1492no—
103C22⋊Q8—22no—
104C22⋊Q8Dic14914yescomplemented
105#117—2984no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—1492no—
108C2×C4⋊C4C2×D14911yescharacteristic
109C2×C22⋊C4—21no—
110C2×C22⋊C4—2981no—
111C2×C42—2981no—
112#103—2984no—
113C22⋊C8—2982no—
114C24C22⋊D14911yescharacteristic
115C2×Q8—21no—
116C2×Q8—22no—
117C2×Q8—22no—
118C2×Q8C2×Dic14912yes—
119C22×C4—22no—
120C22×C4—22no—
121C22×C4—21no—
122C22×C4—21no—
123C22×C4—2982no—
124C22×C4C2×Dic14912yes—
125C22×C4C22⋊D14912yes—
126C22×C4C22⋊D14911yescharacteristic
127C22×C4C22×D14911yescharacteristic
128C2×C8—2982no—
129C2×C8—2982no—
130C2×C8—2982no—
131C4⋊C4—21no—
132C4⋊C4—24no—
133C4⋊C4—2982no—
134C4⋊C4—1494no—
135C4⋊C4C2×Dic14912yes—
136C22⋊C4—24no—
137C22⋊C4—2984no—
138C42—2984no—
139C23—22no—
140C23—22no—
141C23—21no—
142C23—21no—
143C23C22⋊Dic14912yes—
144C23C2×C22⋊D14911yescharacteristic
145Q8—24no—
146Q8—42no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—24no—
150C2×C4—24no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—42no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—2984no—
157C2×C4—5962no—
158C2×C4—5962no—
159C2×C4C22⋊Dic14912yes—
160C2×C4C22×Dic14911yescharacteristic
161C2×C4D4×D14912yes—
162C2×C4C2×C22⋊D14911yescharacteristic
163C2×C4#1455873512yes—
164C8—5962no—
165C22—22no—
166C22—22no—
167C22—22no—
168C22—42no—
169C22—42no—
170C22C2×C22⋊Dic14911yescharacteristic
171C22#1801187911yescharacteristic
172C22#1801189211yescharacteristic
173C22#1801193112yes—
174C22#1801194212yes—
175C4—22no—
176C4—42no—
177C4—42no—
178C4—5964no—
179C4D4×Dic14912yes—
180C4#1801188312yes—
181C2—42no—
182C2#2374950511yescharacteristic
183C2#2374962111yescharacteristic
184C2#2374963411yescharacteristic
185C2#2374978512yes—
186C2#2374996312yes—
subgroupG/H
centerC23C2×C22⋊D149
commutatorC2×C4×C149C22×C4
FrattiniC22×C4C22×D149
FittingC2×C22⋊Q8×C149C2
socleC23×C149C2×D4
prime radicalC24×C149D4
cosocleC22×C4×C149C23
hypercenterC2×C22⋊Q8D149
hypocenterC149#1873
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#18011835C2semidirect
4. #23749387C2semidirect
16. C22⋊Q8×C149C4semidirect
93. C149#1873semidirect
104. C22⋊Q8Dic149semidirect

Maximal subgroups

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

subgroupindex
C2×#180118702
C2×#180118352
C2×C22⋊#119247462
#237493872
C2×C22⋊Q8×C1492
#1873149