Finite Group Databasebeta

← #34045979

Subgroups — #34045979

Order 19072.

266 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 63 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#23750425C211yesmaximal, characteristic
2#23749648C211yesmaximal, characteristic, complemented
3C2×#18011837C212yesmaximal, complemented
4#23749607C212yesmaximal, complemented
5#338×C149C211yesmaximal, characteristic, complemented
6C2×#14558736C2212yes—
7#18011944—22no—
8#18011939—22no—
9#18011933—22no—
10C2×#14558720C2211yescharacteristic
11C2×C4×Dic149C2211yescharacteristic
12#18011840—22no—
13#18011837—22no—
14#18011837—22no—
15#18011829—22no—
16#18011827—22no—
17C2×M16×C149C2212yes—
18C2×M16×C149C2211yescharacteristic
19#14558736—22no—
20#14558736—22no—
21#14558736—22no—
22#14558736—22no—
23C2×Dic298D412yes—
24C2×D596D412yes—
25C2×C22⋊D149—22no—
26C22×Dic149—21no—
27C2×C4×D149—22no—
28Dic596—22no—
29#14558725—24no—
30D1192—22no—
31#14558720—22no—
32C2×#11924746—21no—
33C4×Dic149—21no—
34C4×Dic149D411yescharacteristic
35C4×Dic149D411yescharacteristic
36C22×C4×C149C2311yescharacteristic
37M16×C149—22no—
38M16×C149—22no—
39M16×C149—22no—
40C2×C8×C149—22no—
41C2×C8×C149D412yes—
42C22×D149—22no—
43Dic298—22no—
44Dic298—22no—
45D596—22no—
46D596—22no—
47C22⋊D149—42no—
48C22⋊D149—42no—
49C2×Dic149—21no—
50C2×Dic149—21no—
51C2×Dic149—22no—
52C2×Dic149—42no—
53C4×D149—42no—
54C4×D149—42no—
55#11924746—41no—
56C23×C149#4111yescharacteristic
57C2×C4×C149C2×D412yes—
58C2×C4×C149C2×D411yescharacteristic
59C2×C4×C149C2×D411yescharacteristic
60C2×C4×C149#4112yes—
61C8×C149—22no—
62C8×C149—42no—
63C22×C149—41no—
64C22×C149#12111yescharacteristic
65C22×C149#12312yes—
66C2×D149—42no—
67C2×D149—82no—
68C4×C149#12011yescharacteristic
69C4×C149#12112yes—
70C4×C149#12411yescharacteristic
71Dic149—22no—
72Dic149—41no—
73Dic149—42no—
74C2×C149—21no—
75C2×C149—22no—
76C2×C149#39411yescharacteristic
77D149—82no—
78C149#205011yescharacteristic, complemented, Sylow
79#2050—1491nomaximal, Sylow
80#575—1491no—
81#423—1491no—
82C2×#104—1492no—
83#413—1492no—
84#338D14911yescharacteristic, complemented
85C2×#41—1492no—
86#137—2982no—
87AGL(1,ℤ/8)—2982no—
88#135—2982no—
89C2×M16—1491no—
90C2×M16C2×D14912yes—
91C2×M16C2×D14911yescharacteristic
92C2×C42—1491no—
93C4⋊C8—2982no—
94#104—2982no—
95#104—2982no—
96#101—2982no—
97#100—2982no—
98#41—2982no—
99#41—2982no—
100#41—2982no—
101#41—2982no—
102C2×Q8—1492no—
103C2×D4—2982no—
104C2×D4—1492no—
105C22×C4—2981no—
106C22×C4—2982no—
107C22×C4C22×D14911yescharacteristic
108Q16—2982no—
109SD16—2984no—
110D8—2982no—
111M16—22no—
112M16—22no—
113M16—22no—
114M16—2982no—
115C2×C8—22no—
116C2×C8—2981no—
117C2×C8D59612yes—
118C42—2981no—
119C42—1491no—
120C42—1491no—
121C23—2982no—
122C23#1455873711yescharacteristic
123Q8—2982no—
124Q8—2982no—
125D4—2982no—
126D4—2982no—
127D4—5962no—
128D4—5962no—
129C2×C4—2981no—
130C2×C4—2981no—
131C2×C4—2982no—
132C2×C4—5962no—
133C2×C4—5962no—
134C2×C4—5962no—
135C2×C4D4×D14912yes—
136C2×C4D4×D14911yescharacteristic
137C2×C4C2×D59611yescharacteristic
138C2×C4#1455873612yes—
139C8—22no—
140C8—42no—
141C8—5961no—
142C22—41no—
143C22—5962no—
144C22—11922no—
145C22#1801188611yescharacteristic
146C22#1801189612yes—
147C4—2982no—
148C4—5961no—
149C4—5962no—
150C4#1801188111yescharacteristic
151C4#1801188412yes—
152C4#1801189911yescharacteristic
153C2—21no—
154C2—22no—
155C2—11922no—
156C2#2374954311yescharacteristic
subgroupG/H
centerC4#18011899
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting#338×C149C2
socleC2×C149#394
prime radical#23750425C2
hypercenter#338D149
hypocenterC149#2050
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C4 ◁ C22×C4 ◁ #338

Complements

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

NH ≅ G/Ntype
2. #23749648C2semidirect
3. C2×#18011837C2semidirect
4. #23749607C2semidirect
5. #338×C149C2semidirect
78. C149#2050semidirect
84. #338D149semidirect

Maximal subgroups

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

subgroupindex
#237504252
#237496482
C2×#180118372
#237496072
#338×C1492
#2050149