Finite Group Databasebeta

← #34044879

Subgroups — #34044879

Order 19072.

360 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 125 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×#18011844C212yesmaximal, complemented
2C2×C22⋊#11924746C211yesmaximal, characteristic
3#23749485C211yesmaximal, characteristic
4#23749387C212yesmaximal, complemented
5C22×C4⋊C4×C149C211yesmaximal, characteristic
6C22×#11924746C2212yes—
7C2×C4⋊Dic149C2211yescharacteristic
8C2×C4⋊Dic149C2211yescharacteristic
9C2×C22⋊Dic149—21no—
10#18011844—24no—
11C22⋊#11924746C414yescomplemented
12#18011818—21no—
13C23×C4×C149—21no—
14C23×C4×C149C2211yescharacteristic
15C2×C4⋊C4×C149—21no—
16C2×C4⋊C4×C149—24no—
17C2×C4⋊C4×C149C2212yes—
18C22×Dic149—21no—
19C22×Dic149—21no—
20C2×#11924746—22no—
21C2×#11924746—22no—
22C2×#11924746C2×C414yescomplemented
23C4⋊Dic149—22no—
24C4⋊Dic149—22no—
25C22⋊Dic149—42no—
26C24×C149D411yescharacteristic
27C22×C4×C149—22no—
28C22×C4×C149—22no—
29C22×C4×C149—24no—
30C22×C4×C149—22no—
31C22×C4×C149—42no—
32C22×C4×C149—42no—
33C22×C4×C149C2×C412yes—
34C22×C4×C149D411yescharacteristic
35C22×C4×C149Q812yes—
36C22×C4×C149C2311yescharacteristic
37C4⋊C4×C149—24no—
38C4⋊C4×C149—22no—
39C4⋊C4×C149D414yes—
40C2×Dic149—41no—
41C2×Dic149—41no—
42C2×Dic149—41no—
43C2×Dic149—41no—
44C2×Dic149—41no—
45C2×Dic149—41no—
46#11924746—24no—
47C23×C149—21no—
48C23×C149—21no—
49C23×C149—21no—
50C23×C149—21no—
51C23×C149C4⋊C412yes—
52C23×C149D812yes—
53C23×C149Q1612yes—
54C23×C149C2×D411yescharacteristic
55C2×C4×C149—21no—
56C2×C4×C149—21no—
57C2×C4×C149—24no—
58C2×C4×C149—24no—
59C2×C4×C149—24no—
60C2×C4×C149—48no—
61C2×C4×C149—42no—
62C2×C4×C149—42no—
63C2×C4×C149C4⋊C412yes—
64C2×C4×C149C22×C411yescharacteristic
65C2×C4×C149C2×D412yes—
66C2×C4×C149C2×Q811yescharacteristic
67C2×C4×C149#4112yes—
68C22×C149—22no—
69C22×C149—22no—
70C22×C149—22no—
71C22×C149—22no—
72C22×C149—22no—
73C22×C149—22no—
74C22×C149#10714yescomplemented
75C22×C149C2×C4⋊C411yescharacteristic
76C22×C149#12011yescharacteristic
77C22×C149#12311yescharacteristic
78C22×C149C2×D811yescharacteristic
79C22×C149C2×Q1611yescharacteristic
80C22×C149AGL(1,ℤ/8)11yescharacteristic
81C22×C149#13711yescharacteristic
82C4×C149—22no—
83C4×C149—44no—
84C4×C149C4×D412yes—
85C4×C149C22⋊Q812yes—
86Dic149—81no—
87Dic149—81no—
88C2×C149—24no—
89C2×C149#38511yescharacteristic
90C2×C149C2×#10711yescharacteristic
91C2×C149#42811yescharacteristic
92C2×C149#44711yescharacteristic
93C2×C149#45111yescharacteristic
94C2×C149#48011yescharacteristic
95C2×C149#48411yescharacteristic
96C149#185211yescharacteristic, complemented, Sylow
97#1852—1491nomaximal, Sylow
98C22×C4⋊C4D14911yescharacteristic
99C2×#107—1492no—
100C2×C22⋊C8—1491no—
101#380—1491no—
102#340—1492no—
103C23×C4—21no—
104C23×C4C2×D14911yescharacteristic
105C22×C8—1492no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—24no—
108C2×C4⋊C4—1491no—
109C2×C4⋊C4—1491no—
110C2×C4⋊C4C2×D14912yes—
111C2×C22⋊C4—2981no—
112#107—2984no—
113C22⋊C8—1494no—
114#95—2981no—
115C24C22⋊D14911yescharacteristic
116C22×C4—22no—
117C22×C4—22no—
118C22×C4—24no—
119C22×C4—22no—
120C22×C4—42no—
121C22×C4—42no—
122C22×C4—2981no—
123C22×C4—2981no—
124C22×C4C4×D14912yes—
125C22×C4C22⋊D14911yescharacteristic
126C22×C4Dic29812yes—
127C22×C4C22×D14911yescharacteristic
128C2×C8—2982no—
129C2×C8—2982no—
130C2×C8—1494no—
131C4⋊C4—24no—
132C4⋊C4—22no—
133C4⋊C4—2982no—
134C4⋊C4—2982no—
135C4⋊C4C22⋊D14914yes—
136C22⋊C4—5962no—
137C23—21no—
138C23—21no—
139C23—21no—
140C23—21no—
141C23#1455871512yes—
142C23#1455872112yes—
143C23#1455872612yes—
144C23C2×C22⋊D14911yescharacteristic
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—24no—
148C2×C4—24no—
149C2×C4—24no—
150C2×C4—48no—
151C2×C4—42no—
152C2×C4—42no—
153C2×C4—5961no—
154C2×C4—5961no—
155C2×C4—5961no—
156C2×C4—5961no—
157C2×C4—5961no—
158C2×C4—5961no—
159C2×C4#1455871512yes—
160C2×C4C2×C4×D14911yescharacteristic
161C2×C4C2×C22⋊D14912yes—
162C2×C4C2×Dic29811yescharacteristic
163C2×C4#1455873612yes—
164C8—2984no—
165C22—22no—
166C22—22no—
167C22—22no—
168C22—22no—
169C22—22no—
170C22—22no—
171C22#1801184414yescomplemented
172C22C2×#1455871511yescharacteristic
173C22#1801188011yescharacteristic
174C22#1801189411yescharacteristic
175C22C2×#1455872111yescharacteristic
176C22C2×#1455872611yescharacteristic
177C22#1801193711yescharacteristic
178C22#1801194211yescharacteristic
179C4—22no—
180C4—44no—
181C4—11921no—
182C4—11921no—
183C4C4×C22⋊D14912yes—
184C4#1801189012yes—
185C2—24no—
186C2#2374949811yescharacteristic
187C2C2×#1801184411yescharacteristic
188C2#2374966511yescharacteristic
189C2#2374975911yescharacteristic
190C2#2374978111yescharacteristic
191C2#2374993811yescharacteristic
192C2#2374996011yescharacteristic
subgroupG/H
centerC23C2×C22⋊D149
commutatorC2×C4×C149C22×C4
FrattiniC22×C4C22×D149
FittingC22×C4⋊C4×C149C2
socleC23×C149C2×D4
prime radicalC24×C149D4
cosocleC22×C4×C149C23
hypercenterC22×C4⋊C4D149
hypocenterC149#1852
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#18011844C2semidirect
4. #23749387C2semidirect
11. C22⋊#11924746C4semidirect
22. C2×#11924746C2×C4semidirect
74. C22×C149#107semidirect
96. C149#1852semidirect
171. C22#18011844semidirect

Maximal subgroups

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

subgroupindex
C2×#180118442
C2×C22⋊#119247462
#237494852
#237493872
C22×C4⋊C4×C1492
#1852149