Finite Group Databasebeta

← #34045137

Subgroups — #34045137

Order 19072.

358 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 89 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#23750136C211yesmaximal, characteristic
2C2×#18011870C211yesmaximal, characteristic, complemented
3C2×#18011837C212yesmaximal, complemented
4#23749386C212yesmaximal, complemented
5#407×C149C211yesmaximal, characteristic, complemented
6C2×#14558736C2211yescharacteristic
7#18011894—21no—
8#18011890C412yescomplemented
9#18011885C412yescomplemented
10#18011880—21no—
11C4×C22⋊D149—22no—
12#18011870—24no—
13#18011870C2211yescharacteristic
14C2×C4⋊Dic149—21no—
15C2×C22⋊Dic149—21no—
16C2×C4×Dic149C2212yes—
17#18011837—24no—
18C23×C4×C149C2211yescharacteristic
19C2×M16×C149C2212yes—
20C22⋊C8×C149—22no—
21#14558736—22no—
22#14558736—22no—
23C2×Dic298C2×C411yescharacteristic
24C2×D596C2×C411yescharacteristic
25C2×C22⋊D149—22no—
26C2×C22⋊D149—21no—
27C22×Dic149—22no—
28C2×C4×D149—21no—
29C4⋊Dic149—24no—
30C4⋊Dic149C2×C412yes—
31#14558715—22no—
32C22⋊Dic149—24no—
33C22⋊Dic149—22no—
34C22⋊Dic149—21no—
35#14558713—22no—
36C4×Dic149—22no—
37C4×Dic149—21no—
38C4×Dic149D414yescomplemented
39C24×C149D411yescharacteristic
40C22×C4×C149—22no—
41C22×C4×C149—22no—
42C22×C4×C149C2×C412yes—
43C22×C4×C149D411yescharacteristic
44C22×C4×C149D412yes—
45C22×C4×C149C2311yescharacteristic
46M16×C149—22no—
47M16×C149—22no—
48C2×C8×C149—22no—
49C22×D149—21no—
50Dic298—22no—
51D596—22no—
52C22⋊D149—44no—
53C22⋊D149—41no—
54C22⋊D149—41no—
55C2×Dic149—21no—
56C2×Dic149—22no—
57C2×Dic149—24no—
58C2×Dic149—44no—
59C4×D149—42no—
60C23×C149—21no—
61C23×C149—21no—
62C23×C149—42no—
63C23×C149C22⋊C412yes—
64C23×C149C2×D411yescharacteristic
65C2×C4×C149—21no—
66C2×C4×C149—21no—
67C2×C4×C149—24no—
68C2×C4×C149—24no—
69C2×C4×C149C22⋊C412yes—
70C2×C4×C149C22×C411yescharacteristic
71C2×C4×C149C2×D412yes—
72C2×C4×C149C2×D411yescharacteristic
73C2×C4×C149#4112yes—
74C8×C149—42no—
75C22×C149—22no—
76C22×C149—22no—
77C22×C149—22no—
78C22×C149—22no—
79C22×C149—42no—
80C22×C149—42no—
81C22×C149C2×C22⋊C411yescharacteristic
82C22×C149#12011yescharacteristic
83C22×C149#12311yescharacteristic
84C2×D149—41no—
85C2×D149—42no—
86C4×C149—22no—
87C4×C149C4×D412yes—
88C4×C149#12112yes—
89Dic149—44no—
90Dic149—41no—
91Dic149—42no—
92C2×C149—21no—
93C2×C149—21no—
94C2×C149—42no—
95C2×C149#38611yescharacteristic
96C2×C149#42112yes—
97D149—81no—
98C149#189711yescharacteristic, complemented, Sylow
99#1897—1491nomaximal, Sylow
100#525—1491no—
101C2×#117—1491no—
102C2×#104—1492no—
103#407D14911yescharacteristic, complemented
104#339—1492no—
105C2×#41—1491no—
106C23×C4C2×D14911yescharacteristic
107C2×M16C2×D14912yes—
108#123—2981no—
109C22⋊Q8—1492no—
110#121—1492no—
111#120—2981no—
112C4×D4—2982no—
113#117—2984no—
114#117—1491no—
115C2×C4⋊C4—2981no—
116C2×C22⋊C4—2981no—
117C2×C42—1492no—
118#104—2984no—
119C22⋊C8—22no—
120C24D59611yescharacteristic
121#41—2982no—
122#41—2982no—
123C2×Q8—1491no—
124C2×D4—2981no—
125C2×D4—2982no—
126C2×D4—1491no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—2982no—
130C22×C4—2981no—
131C22×C4C4×D14912yes—
132C22×C4C22⋊D14912yes—
133C22×C4D59611yescharacteristic
134C22×C4C22×D14911yescharacteristic
135M16—22no—
136M16—22no—
137C2×C8—22no—
138C4⋊C4—2984no—
139C4⋊C4—2982no—
140C4⋊C4—1492no—
141C22⋊C4—2984no—
142C22⋊C4—2981no—
143C22⋊C4—2982no—
144C22⋊C4—2982no—
145C42—2982no—
146C42—2981no—
147C42—1494no—
148C23—21no—
149C23—21no—
150C23—42no—
151C23—2981no—
152C23#1455871312yes—
153C23C2×D59611yescharacteristic
154Q8—2982no—
155D4—2982no—
156D4—5964no—
157D4—5961no—
158D4—5961no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—2982no—
164C2×C4—2981no—
165C2×C4—2984no—
166C2×C4—5964no—
167C2×C4—5962no—
168C2×C4#1455871312yes—
169C2×C4C2×C4×D14911yescharacteristic
170C2×C4D4×D14912yes—
171C2×C4C2×C22⋊D14911yescharacteristic
172C2×C4#1455873512yes—
173C8—42no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—5962no—
181C22—5961no—
182C22C2×#1455871311yescharacteristic
183C22#1801188111yescharacteristic
184C22#1801189511yescharacteristic
185C4—22no—
186C4—5964no—
187C4—5962no—
188C4—5961no—
189C4#1801187112yes—
190C4#1801188312yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—11921no—
195C2#2374950211yescharacteristic
196C2#2374964112yes—
subgroupG/H
centerC2×C4C2×C22⋊D149
commutatorC2×C4×C149C22×C4
FrattiniC22×C4C22×D149
Fitting#407×C149C2
socleC22×C149C2×C22⋊C4
prime radical#23750136C2
cosocleC22×C4×C149C23
hypercenter#407D149
hypocenterC149#1897
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×#18011870C2semidirect
3. C2×#18011837C2semidirect
4. #23749386C2semidirect
5. #407×C149C2semidirect
8. #18011890C4semidirect
9. #18011885C4semidirect
38. C4×Dic149D4semidirect
98. C149#1897semidirect
103. #407D149semidirect

Maximal subgroups

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

subgroupindex
#237501362
C2×#180118702
C2×#180118372
#237493862
#407×C1492
#1897149