Finite Group Databasebeta

← #34060732

Subgroups — #34060732

Order 19072.

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

normal subgroups only

This group has 312 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#23750703C211yesmaximal, characteristic
2#23750618C212yesmaximal, complemented
3#23750605C211yesmaximal, characteristic
4#23750492C212yesmaximal, complemented
5#23750195C211yesmaximal, characteristic
6#18011998—24no—
7D149⋊M16C2212yes—
8C2×#14558745—22no—
9#18011990C2212yes—
10#18011974—24no—
11#18011969—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—24no—
23#14558745—22no—
24D149⋊C8D414yes—
25C2×#11924753—24no—
26C4⋊#10597010—22no—
27C22⋊#10597010—22no—
28C4×#10597010—22no—
29#14558735—22no—
30#14558735—22no—
31C2×Dic298—21no—
32C2×Dic298C2×C411yescharacteristic
33C2×Dic298C2×C411yescharacteristic
34Q8×D149—22no—
35Q8×D149—22no—
36C2×C22⋊D149D412yes—
37C22×Dic149D412yes—
38C2×C4×D149—21no—
39C2×C4×D149C2311yescharacteristic
40C4⋊Dic149—22no—
41#14558715—22no—
42#14558715—21no—
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—42no—
51#11924753—24no—
52C22×D149C2×D411yescharacteristic
53Dic298—22no—
54Dic298—22no—
55Dic298—41no—
56Dic298—41no—
57C22⋊D149—24no—
58C2×Dic149—22no—
59C2×Dic149—22no—
60C2×Dic149—21no—
61C2×Dic149—21no—
62C2×Dic149C22⋊C412yes—
63C2×Dic149C2×D411yescharacteristic
64C4×D149—42no—
65C4×D149C2×D412yes—
66C4×D149#4112yes—
67C23×C149C22⋊C412yes—
68Q8×C149—22no—
69D4×C149—22no—
70C2×C4×C149—21no—
71C2×C4×C149—21no—
72C2×C4×C149C22×C411yescharacteristic
73C22×C149—22no—
74C22×C149—42no—
75C22×C149C2×C22⋊C411yescharacteristic
76C2×D149—41no—
77C2×D149#12112yes—
78#10597010—82no—
79C4×C149—41no—
80C4×C149—41no—
81C4×C149C4×D412yes—
82Dic149—22no—
83Dic149—41no—
84Dic149—41no—
85Dic149#12011yescharacteristic
86Dic149#12311yescharacteristic
87C2×C149—21no—
88C2×C149—42no—
89C2×C149#38611yescharacteristic
90D149—22no—
91C149#190911yescharacteristic, complemented, Sylow
92#1909—1491nomaximal, Sylow
93#568—1491no—
94#536—1491no—
95#419—1492no—
96#410—1491no—
97H(3,ℤ/4)—1492no—
98C2×#41—1491no—
99C22×Q8—1491no—
100#131—2984no—
101C2×M16—2982no—
102C2×M16—1492no—
103C4⋊Q8—1491no—
104C4⋊Q8—1491no—
105#124—1491no—
106#124#1059701011yescharacteristic, complemented
107#123—2982no—
108C22⋊Q8—2982no—
109#117—1492no—
110#117—1491no—
111#103—2984no—
112#99—2982no—
113#41—2982no—
114#41—2982no—
115C2×Q8—2981no—
116C2×Q8—2982no—
117C2×Q8—2982no—
118C2×Q8—1491no—
119C2×Q8—1491no—
120C2×Q8C2×#1059701011yescharacteristic
121C2×D4—1492no—
122C2×D4C2×#1059701011yescharacteristic
123C22×C4—2981no—
124C22×C4—1492no—
125C22×C4—1491no—
126M16—2984no—
127M16—2982no—
128M16—2982no—
129C2×C8—2984no—
130C2×C8—1494no—
131C4⋊C4—2981no—
132C4⋊C4—2982no—
133C4⋊C4—2982no—
134C4⋊C4—2982no—
135C22⋊C4—22no—
136C22⋊C4—2981no—
137C22⋊C4—2982no—
138C22⋊C4—2982no—
139C42—2982no—
140C42—1491no—
141C42C2×#1059701011yescharacteristic
142C23—1491no—
143C23C22⋊#1059701012yes—
144Q8—22no—
145Q8—2982no—
146Q8—2982no—
147Q8—5961no—
148Q8—5961no—
149D4—22no—
150D4—2984no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—2982no—
154C2×C4—2982no—
155C2×C4—2981no—
156C2×C4—2981no—
157C2×C4—5962no—
158C2×C4—5962no—
159C2×C4—1492no—
160C2×C4—1491no—
161C2×C4—1492no—
162C2×C4—1492no—
163C2×C4C22×#1059701011yescharacteristic
164C8—2984no—
165C22—22no—
166C22—42no—
167C22—5961no—
168C22—1492no—
169C22C2×C22⋊#1059701011yescharacteristic
170C4—41no—
171C4—41no—
172C4—2982no—
173C4—5961no—
174C4—5961no—
175C4—1491no—
176C4—1491no—
177C4—11922no—
178C4D4×#1059701012yes—
179C2—21no—
180C2—42no—
181C2—2982no—
182C2#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#1909
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
2. #23750618C2semidirect
4. #23750492C2semidirect
14. #18011911C4semidirect
15. #18011909C4semidirect
16. #18011898C4semidirect
20. #124×C149C4semidirect
91. C149#1909semidirect
106. #124#10597010semidirect

Maximal subgroups

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

subgroupindex
#237507032
#237506182
#237506052
#237504922
#237501952
#1909149