Finite Group Databasebeta

← #34045221

Subgroups — #34045221

Order 19072.

362 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 85 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#23750192C211yesmaximal, characteristic
2#23750100C211yesmaximal, characteristic, complemented
3#23749641C212yesmaximal, complemented
4#23749382C212yesmaximal, complemented
5C2×#100×C149C211yesmaximal, characteristic, complemented
6C2×#14558736C2211yescharacteristic
7#18011907C412yescomplemented
8#18011898C412yescomplemented
9#18011882—22no—
10#18011880—22no—
11D4×Dic149—24no—
12#18011870C2211yescharacteristic
13#18011870C2212yes—
14C2×C22⋊Dic149—22no—
15#18011837—24no—
16C22×D4×C149C2211yescharacteristic
17C2×M16×C149C2212yes—
18#100×C149—22no—
19#14558736—22no—
20#14558736—22no—
21C2×Dic298C2×C411yescharacteristic, complemented
22C2×D596C2×C411yescharacteristic, complemented
23C2×C22⋊D149—24no—
24C2×C22⋊D149—21no—
25C22×Dic149—24no—
26C2×C4×D149—21no—
27C4⋊Dic149—22no—
28C4⋊Dic149—21no—
29C22⋊Dic149—24no—
30C22⋊Dic149—24no—
31C22⋊Dic149—22no—
32C22⋊Dic149—21no—
33C4×Dic149C2×C412yescomplemented
34C4×Dic149D414yescomplemented
35C24×C149D412yes—
36C2×D4×C149—22no—
37C2×D4×C149—22no—
38C2×D4×C149C2×C412yes—
39C2×D4×C149D412yes—
40C22×C4×C149C2311yescharacteristic
41M16×C149—22no—
42M16×C149—22no—
43C2×C8×C149—22no—
44C22×D149—21no—
45Dic298—22no—
46D596—22no—
47C22⋊D149—41no—
48C22⋊D149—41no—
49C22⋊D149—84no—
50C2×Dic149—21no—
51C2×Dic149—22no—
52C2×Dic149—24no—
53C2×Dic149—84no—
54C4×D149—42no—
55C23×C149—22no—
56C23×C149—22no—
57C23×C149—82no—
58C23×C149C22⋊C414yes—
59C23×C149C2×D411yescharacteristic
60D4×C149—24no—
61D4×C149—24no—
62C2×C4×C149C22×C411yescharacteristic
63C2×C4×C149C2×D412yes—
64C2×C4×C149C2×D411yescharacteristic
65C2×C4×C149#4112yes—
66C8×C149—42no—
67C22×C149—24no—
68C22×C149—41no—
69C22×C149—44no—
70C22×C149—44no—
71C22×C149—82no—
72C22×C149C2×C22⋊C411yescharacteristic
73C22×C149#12011yescharacteristic
74C22×C149#12311yescharacteristic
75C2×D149—42no—
76C2×D149—41no—
77C4×C149C4×D412yes—
78C4×C149#12112yes—
79Dic149—44no—
80Dic149—42no—
81Dic149—41no—
82C2×C149—21no—
83C2×C149—21no—
84C2×C149—21no—
85C2×C149—44no—
86C2×C149#38611yescharacteristic
87D149—81no—
88C149#191111yescharacteristic, complemented, Sylow
89#1911—1491nomaximal, Sylow
90#535—1491no—
91#518—1491no—
92#421—1492no—
93C2×#100D14911yescharacteristic, complemented
94H(3,ℤ/4)—1492no—
95C2×#41—1491no—
96C22×D4C2×D14911yescharacteristic
97C2×M16C2×D14912yes—
98#127—1492no—
99#124—1492no—
100#121—2982no—
101#120—2982no—
102C4×D4—2984no—
103#117—1492no—
104#117—1491no—
105C2×C22⋊C4—2982no—
106#104—2984no—
107#100—22no—
108C24D59612yes—
109#41—2982no—
110#41—2982no—
111C2×Q8—1491no—
112C2×D4—22no—
113C2×D4—22no—
114C2×D4—2981no—
115C2×D4—2984no—
116C2×D4—1491no—
117C2×D4C4×D14912yes—
118C2×D4C22⋊D14912yes—
119C22×C4—2984no—
120C22×C4—2981no—
121C22×C4C22×D14911yescharacteristic
122M16—22no—
123M16—22no—
124C2×C8—22no—
125C4⋊C4—2982no—
126C4⋊C4—2981no—
127C22⋊C4—2984no—
128C22⋊C4—2982no—
129C22⋊C4—2981no—
130C22⋊C4—2984no—
131C42—1492no—
132C42—1494no—
133C23—22no—
134C23—22no—
135C23—82no—
136C23—2981no—
137C23#1455871314yes—
138C23C2×D59611yescharacteristic
139Q8—2982no—
140D4—24no—
141D4—24no—
142D4—2982no—
143D4—5961no—
144D4—5961no—
145D4—11924no—
146C2×C4—2982no—
147C2×C4—2981no—
148C2×C4—2984no—
149C2×C4—5962no—
150C2×C4—11924no—
151C2×C4C2×C4×D14911yescharacteristic
152C2×C4D4×D14912yes—
153C2×C4C2×C22⋊D14911yescharacteristic
154C2×C4#1455873512yes—
155C8—42no—
156C22—24no—
157C22—41no—
158C22—44no—
159C22—44no—
160C22—82no—
161C22—5962no—
162C22—5961no—
163C22C2×#1455871311yescharacteristic
164C22#1801188111yescharacteristic
165C22#1801189511yescharacteristic
166C4—5964no—
167C4—5962no—
168C4—5961no—
169C4#1801187112yes—
170C4#1801188312yes—
171C2—21no—
172C2—21no—
173C2—21no—
174C2—44no—
175C2—11921no—
176C2#2374950211yescharacteristic
subgroupG/H
centerC2#23749502
commutatorC2×C4×C149C22×C4
FrattiniC22×C4C22×D149
FittingC2×#100×C149C2
socleC2×C149#386
prime radical#23750192C2
cosocleC22×C4×C149C23
hypercenterC2×#100D149
hypocenterC149#1911
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
2. #23750100C2semidirect
3. #23749641C2semidirect
4. #23749382C2semidirect
5. C2×#100×C149C2semidirect
7. #18011907C4semidirect
8. #18011898C4semidirect
21. C2×Dic298C2×C4semidirect
22. C2×D596C2×C4semidirect
33. C4×Dic149C2×C4semidirect
34. C4×Dic149D4semidirect
88. C149#1911semidirect
93. C2×#100D149semidirect

Maximal subgroups

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

subgroupindex
#237501922
#237501002
#237496412
#237493822
C2×#100×C1492
#1911149