Finite Group Databasebeta

← #34046132

Subgroups — #34046132

Order 19072.

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

normal subgroups only

This group has 198 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#23749624C212yesmaximal
2#23749591C211yesmaximal, characteristic
3#23749394C212yesmaximal, complemented
4#23749390C211yesmaximal, characteristic, complemented
5C2×#107×C149C211yesmaximal, characteristic, complemented
6C2×#14558736C2211yescharacteristic
7C2×#14558720C2212yes—
8C2×#14558720C2211yescharacteristic
9#18011834—22no—
10#18011831—22no—
11#18011823—22no—
12C22×C8×C149C2211yescharacteristic
13C2×C4⋊C4×C149C2212yes—
14#107×C149—22no—
15#14558736—22no—
16#14558736—22no—
17C2×Dic298D411yescharacteristic
18C2×D596D411yescharacteristic
19C2×C22⋊D149—21no—
20C2×C4×D149—21no—
21#14558720—22no—
22#14558720—22no—
23#14558720—22no—
24C2×#11924746—21no—
25C2×#11924746—22no—
26C22×C4×C149—22no—
27C22×C4×C149C2311yescharacteristic
28C2×C8×C149—22no—
29C2×C8×C149D412yes—
30C4⋊C4×C149—22no—
31C4⋊C4×C149—22no—
32C22×D149—21no—
33Dic298—22no—
34D596—22no—
35C22⋊D149—42no—
36C2×Dic149—21no—
37C4×D149—41no—
38C4×D149—41no—
39#11924746—42no—
40#11924746—41no—
41C23×C149#4111yescharacteristic
42C2×C4×C149—42no—
43C2×C4×C149—82no—
44C2×C4×C149C2×D411yescharacteristic
45C2×C4×C149C2×D411yescharacteristic
46C2×C4×C149#4112yes—
47C2×C4×C149#4112yes—
48C8×C149—22no—
49C22×C149—21no—
50C22×C149—21no—
51C22×C149#12111yescharacteristic
52C22×C149#12612yes—
53C2×D149—41no—
54C2×D149—41no—
55C2×D149—41no—
56C4×C149—82no—
57C4×C149#12311yescharacteristic
58C4×C149#12312yes—
59C4×C149#12411yescharacteristic
60Dic149—41no—
61C2×C149—22no—
62C2×C149#39711yescharacteristic
63C2×C149#47211yescharacteristic
64C2×C149#47311yescharacteristic
65D149—81no—
66C149#207811yescharacteristic, complemented, Sylow
67#2078—1491nomaximal, Sylow
68C2×#107D14911yescharacteristic, complemented
69#417—1492no—
70#408—1491no—
71#343—1492no—
72#341—1491no—
73C2×#41—1491no—
74C2×M16—1492no—
75C2×M16—1491no—
76C22×C8C2×D14911yescharacteristic
77C2×C4⋊C4C2×D14912yes—
78#107—22no—
79#103—2982no—
80#102—2982no—
81C22⋊C8—2982no—
82#41—2982no—
83#41—2982no—
84C2×Q8—1491no—
85C2×D4—2981no—
86C2×D4—1491no—
87C22×C4—22no—
88C22×C4—2981no—
89C22×C4C22×D14911yescharacteristic
90M16—2982no—
91M16—2982no—
92M16—2982no—
93C2×C8—22no—
94C2×C8—2982no—
95C2×C8—2981no—
96C2×C8C22⋊D14912yes—
97C4⋊C4—22no—
98C4⋊C4—22no—
99C23—2981no—
100C23#1455873511yescharacteristic
101Q8—2982no—
102D4—2982no—
103D4—5962no—
104C2×C4—42no—
105C2×C4—82no—
106C2×C4—2981no—
107C2×C4—5961no—
108C2×C4—5961no—
109C2×C4D4×D14911yescharacteristic
110C2×C4C2×C22⋊D14911yescharacteristic
111C2×C4#1455873612yes—
112C2×C4#1455873712yes—
113C8—22no—
114C8—5962no—
115C8—5961no—
116C22—21no—
117C22—21no—
118C22—5961no—
119C22—5961no—
120C22—5961no—
121C22#1801188211yescharacteristic
122C22#1801190612yes—
123C4—82no—
124C4—5961no—
125C4#1801189411yescharacteristic
126C4#1801189612yes—
127C4#1801190011yescharacteristic
128C2—22no—
129C2—11921no—
130C2#2374955111yescharacteristic
131C2#2374989211yescharacteristic
132C2#2374989711yescharacteristic
subgroupG/H
centerC22#18011882
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
FittingC2×#107×C149C2
socleC22×C149#121
prime radicalC2×#14558736C22
hypercenterC2×#107D149
hypocenterC149#2078
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
3. #23749394C2semidirect
4. #23749390C2semidirect
5. C2×#107×C149C2semidirect
66. C149#2078semidirect
68. C2×#107D149semidirect

Maximal subgroups

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

subgroupindex
#237496242
#237495912
#237493942
#237493902
C2×#107×C1492
#2078149