Finite Group Databasebeta

← #34060739

Subgroups — #34060739

Order 19072.

314 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 66 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#23750693C211yesmaximal, characteristic, complemented
2#23750623C212yesmaximal
3D149⋊#101C211yesmaximal, characteristic, complemented
4#23750492C212yesmaximal, complemented
5#23750195C211yesmaximal, characteristic
6D149⋊M16C2212yes—
7Q8×#10597010—24no—
8#18011990—22no—
9#18011990C2212yes—
10#18011975—24no—
11#18011972—22no—
12C2×#14558735C2211yescharacteristic
13C2×Q8×D149C2211yescharacteristic
14#18011911C411yescharacteristic, complemented
15#18011909C411yescharacteristic, complemented
16#18011898C411yescharacteristic, complemented
17#18011893—22no—
18#18011888—22no—
19#18011868C2211yescharacteristic
20#124×C149C411yescharacteristic, complemented
21#14558746—22no—
22#14558745—22no—
23D149⋊C8—22no—
24C4⋊#10597010—24no—
25C4⋊#10597010—22no—
26C22⋊#10597010—22no—
27C4×#10597010—24no—
28C4×#10597010D414yes—
29#14558735—22no—
30#14558735—22no—
31C2×Dic298C2×C411yescharacteristic
32C2×Dic298C2×C411yescharacteristic
33C2×Dic298D412yes—
34Q8×D149—22no—
35Q8×D149—22no—
36C2×C22⋊D149—21no—
37C22×Dic149—21no—
38C2×C4×D149D412yes—
39C2×C4×D149C2311yescharacteristic
40C4⋊Dic149—22no—
41#14558715—21no—
42#14558715—22no—
43C22⋊Dic149—22no—
44#14558713—21no—
45C4×Dic149C2×C411yescharacteristic
46C2×Q8×C149C2×C411yescharacteristic
47C2×D4×C149C2×C411yescharacteristic
48C22⋊C4×C149—22no—
49C42×C149C2×C411yescharacteristic
50C2×#10597010—24no—
51#11924753—42no—
52C22×D149C2×D411yescharacteristic
53Dic298—22no—
54Dic298—24no—
55Dic298—22no—
56C22⋊D149—41no—
57C22⋊D149—41no—
58C2×Dic149—21no—
59C2×Dic149—21no—
60C2×Dic149—42no—
61C2×Dic149C22⋊C412yes—
62C2×Dic149C2×D411yescharacteristic
63C4×D149—22no—
64C4×D149—22no—
65C4×D149C2×D412yes—
66C4×D149#4112yes—
67C23×C149—21no—
68Q8×C149—22no—
69D4×C149—22no—
70C2×C4×C149—21no—
71C2×C4×C149C22⋊C412yes—
72C2×C4×C149C22×C411yescharacteristic
73C22×C149—42no—
74C22×C149—41no—
75C22×C149C2×C22⋊C411yescharacteristic
76C2×D149—41no—
77C2×D149#12011yescharacteristic
78C2×D149#12311yescharacteristic
79#10597010—44no—
80C4×C149—22no—
81C4×C149—41no—
82C4×C149C4×D412yes—
83Dic149—22no—
84Dic149—41no—
85Dic149—41no—
86Dic149#12112yes—
87C2×C149—21no—
88C2×C149—81no—
89C2×C149#38611yescharacteristic
90D149—21no—
91D149—21no—
92C149#191211yescharacteristic, complemented, Sylow
93#1912—1491nomaximal, Sylow
94#536—1491no—
95#519—1491no—
96#421—1492no—
97C2×#101—1491no—
98H(3,ℤ/4)—1492no—
99C2×#41—1491no—
100C22×Q8—1491no—
101C2×M16—1492no—
102C4⋊Q8—1491no—
103C4⋊Q8—1491no—
104#124—1491no—
105#124#1059701011yescharacteristic, complemented
106#123—2982no—
107C22⋊Q8—2982no—
108C4×Q8—2984no—
109#117—2982no—
110#117—1492no—
111#117—1491no—
112#104—2984no—
113#101—2982no—
114#41—2982no—
115#41—2982no—
116C2×Q8—2982no—
117C2×Q8—2982no—
118C2×Q8—1491no—
119C2×Q8—1492no—
120C2×Q8—1491no—
121C2×Q8C2×#1059701011yescharacteristic
122C2×D4—2981no—
123C2×D4C2×#1059701011yescharacteristic
124C22×C4—2981no—
125C22×C4—1492no—
126C22×C4—1491no—
127M16—2982no—
128M16—2982no—
129C2×C8—2982no—
130C4⋊C4—2981no—
131C4⋊C4—2982no—
132C4⋊C4—2984no—
133C4⋊C4—2982no—
134C4⋊C4—2982no—
135C22⋊C4—22no—
136C22⋊C4—2981no—
137C22⋊C4—2982no—
138C22⋊C4—2982no—
139C42—2984no—
140C42—1494no—
141C42—1491no—
142C42C2×#1059701011yescharacteristic
143C23—21no—
144C23—1491no—
145Q8—22no—
146Q8—2984no—
147Q8—2982no—
148Q8—2982no—
149D4—22no—
150D4—5961no—
151D4—5961no—
152C2×C4—21no—
153C2×C4—2982no—
154C2×C4—2982no—
155C2×C4—2984no—
156C2×C4—2981no—
157C2×C4—2981no—
158C2×C4—5962no—
159C2×C4—1492no—
160C2×C4—1491no—
161C2×C4—1492no—
162C2×C4—1492no—
163C2×C4C22⋊#1059701012yes—
164C2×C4C22×#1059701011yescharacteristic
165C8—5962no—
166C22—42no—
167C22—41no—
168C22—5961no—
169C22—1491no—
170C22—1491no—
171C22C2×C22⋊#1059701011yescharacteristic
172C4—22no—
173C4—41no—
174C4—2982no—
175C4—5961no—
176C4—5964no—
177C4—5961no—
178C4—1492no—
179C4D4×#1059701012yes—
180C2—21no—
181C2—81no—
182C2—2981no—
183C2—2981no—
184C2#2375057311yescharacteristic
subgroupG/H
centerC2#23750573
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#124×C149C4
socleC2×C149#386
prime radicalC2×#14558735C22
cosocleC2×C4×D149C23
hypercenter#124#10597010
hypocenterC149#1912
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #23750693C2semidirect
3. D149⋊#101C2semidirect
4. #23750492C2semidirect
14. #18011911C4semidirect
15. #18011909C4semidirect
16. #18011898C4semidirect
20. #124×C149C4semidirect
92. C149#1912semidirect
105. #124#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506932
#237506232
D149⋊#1012
#237504922
#237501952
#1912149