Finite Group Databasebeta

← #34045975

Subgroups — #34045975

Order 19072.

266 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 67 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#23749648C211yesmaximal, characteristic, complemented
2C2×#18011838C212yesmaximal, complemented
3#23749609C212yesmaximal, complemented
4#23749383C211yesmaximal, characteristic, complemented
5#575×C149C211yesmaximal, characteristic
6C2×#14558720C2212yes—
7C2×#14558720C2211yescharacteristic
8C2×C4×Dic149C2211yescharacteristic
9#18011840—22no—
10#18011838—22no—
11#18011838—22no—
12#18011830—22no—
13#18011828—22no—
14C2×#41×C149C2212yes—
15#137×C149—22no—
16AGL(1,ℤ/8)×C149—22no—
17#135×C149—22no—
18C2×M16×C149C2211yescharacteristic
19C22×Dic149—21no—
20#14558720—22no—
21#14558720—22no—
22#14558720—22no—
23C2×#11924746—21no—
24C2×#11924746—22no—
25C4×Dic149—21no—
26C4×Dic149D411yescharacteristic
27C4×Dic149D411yescharacteristic
28#41×C149—22no—
29#41×C149—22no—
30#41×C149—22no—
31#41×C149—22no—
32C2×Q8×C149D412yes—
33C2×D4×C149—22no—
34C2×D4×C149D412yes—
35C22×C4×C149—22no—
36C22×C4×C149C2311yescharacteristic
37Q16×C149—22no—
38SD16×C149—24no—
39D8×C149—22no—
40M16×C149—22no—
41C2×C8×C149D412yes—
42C2×Dic149—21no—
43C2×Dic149—21no—
44C2×Dic149—42no—
45#11924746—41no—
46#11924746—42no—
47C23×C149—22no—
48C23×C149#4111yescharacteristic
49Q8×C149—22no—
50Q8×C149—22no—
51D4×C149—22no—
52D4×C149—22no—
53D4×C149—42no—
54D4×C149—42no—
55C2×C4×C149—22no—
56C2×C4×C149—42no—
57C2×C4×C149—42no—
58C2×C4×C149C2×D411yescharacteristic
59C2×C4×C149C2×D412yes—
60C2×C4×C149C2×D411yescharacteristic
61C2×C4×C149#4112yes—
62C8×C149—22no—
63C22×C149—41no—
64C22×C149—42no—
65C22×C149—82no—
66C22×C149#12111yescharacteristic
67C22×C149#12312yes—
68C4×C149—42no—
69C4×C149#12011yescharacteristic
70C4×C149#12112yes—
71C4×C149#12411yescharacteristic
72Dic149—22no—
73Dic149—41no—
74C2×C149—21no—
75C2×C149—22no—
76C2×C149—82no—
77C2×C149#39411yescharacteristic
78C149#205011yescharacteristic, complemented, Sylow
79#2050—1491nomaximal, Sylow
80#575D14911yescharacteristic
81#423—1491no—
82C2×#104—1492no—
83#413—1492no—
84#338—1491no—
85C2×#41C2×D14912yes—
86#137—22no—
87AGL(1,ℤ/8)—22no—
88#135—22no—
89C2×M16—1492no—
90C2×M16—1491no—
91C2×M16C2×D14911yescharacteristic
92C2×C42—1491no—
93C4⋊C8—2982no—
94#104—2982no—
95#104—2982no—
96#101—2982no—
97#100—2982no—
98#41—22no—
99#41—22no—
100#41—22no—
101#41—22no—
102C2×Q8C22⋊D14912yes—
103C2×D4—22no—
104C2×D4C22⋊D14912yes—
105C22×C4—22no—
106C22×C4—2981no—
107C22×C4C22×D14911yescharacteristic
108Q16—22no—
109SD16—24no—
110D8—22no—
111M16—22no—
112M16—2982no—
113M16—2982no—
114M16—2982no—
115C2×C8—2981no—
116C2×C8—2982no—
117C2×C8C22⋊D14912yes—
118C42—2981no—
119C42—1491no—
120C42—1491no—
121C23—22no—
122C23#1455873511yescharacteristic
123Q8—22no—
124Q8—22no—
125D4—22no—
126D4—22no—
127D4—42no—
128D4—42no—
129C2×C4—22no—
130C2×C4—42no—
131C2×C4—42no—
132C2×C4—2981no—
133C2×C4—2981no—
134C2×C4—5962no—
135C2×C4D4×D14911yescharacteristic
136C2×C4C2×C22⋊D14912yes—
137C2×C4C2×C22⋊D14911yescharacteristic
138C2×C4#1455873512yes—
139C8—22no—
140C8—5961no—
141C8—5962no—
142C22—41no—
143C22—42no—
144C22—82no—
145C22#1801188211yescharacteristic
146C22#1801189212yes—
147C4—42no—
148C4—2982no—
149C4—5961no—
150C4#1801188011yescharacteristic
151C4#1801188312yes—
152C4#1801189811yescharacteristic
153C2—21no—
154C2—22no—
155C2—82no—
156C2#2374953911yescharacteristic
subgroupG/H
centerC4#18011898
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting, prime radical#575×C149C2
socleC2×C149#394
hypercenter#575D149
hypocenterC149#2050
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #23749648C2semidirect
2. C2×#18011838C2semidirect
3. #23749609C2semidirect
4. #23749383C2semidirect
78. C149#2050semidirect

Maximal subgroups

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

subgroupindex
#237496482
C2×#180118382
#237496092
#237493832
#575×C1492
#2050149