Finite Group Databasebeta

← #34060647

Subgroups — #34060647

Order 19072.

272 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 68 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
2#23750636C212yesmaximal
3(C2×#10597010)⋊Q8C211yesmaximal, characteristic
4#23750497C212yesmaximal
5#101×D149C211yesmaximal, characteristic
6Q8×#10597010—22no—
7Q8×#10597010—22no—
8#18011990—22no—
9#18011990C2212yes—
10C2×C4⋊#10597010C2211yescharacteristic
11C2×C4×#10597010C2211yescharacteristic
12#18011980—22no—
13#18011979—22no—
14(C2×#10597010)⋊C4—22no—
15C2×Q8×D149C2211yescharacteristic
16M16×D149C2212yes—
17#18011830C411yescharacteristic, complemented
18#18011829C412yescomplemented
19#101×C149C411yescharacteristic, complemented
20C22×#10597010—21no—
21C22×#10597010—21no—
22C4⋊#10597010—22no—
23C4⋊#10597010—22no—
24C4⋊#10597010—22no—
25C4⋊#10597010D412yes—
26C4⋊#10597010D412yes—
27C22⋊#10597010—22no—
28C4×#10597010—24no—
29C4×#10597010—22no—
30C4×#10597010—22no—
31C2×Dic298C2×C411yescharacteristic
32C2×Dic298Q812yes—
33Q8×D149—22no—
34Q8×D149—22no—
35C2×C4×D149D412yes—
36C2×C4×D149C2311yescharacteristic
37#14558720C2×C412yes—
38#14558719—22no—
39C8×D149—22no—
40C2×Q8×C149C2×C411yescharacteristic
41M16×C149C2×C412yes—
42C2×#10597010—22no—
43C2×#10597010—22no—
44C2×#10597010—22no—
45C2×#10597010—41no—
46C2×#10597010—41no—
47C2×#10597010—42no—
48C2×#10597010—41no—
49C22×D149C2×D411yescharacteristic
50Dic298—22no—
51Dic298—24no—
52C2×Dic149C4⋊C412yes—
53C2×Dic149C2×Q811yescharacteristic
54C4×D149—22no—
55C4×D149—22no—
56C4×D149C2×D412yes—
57C4×D149#4112yes—
58#11924746—22no—
59Q8×C149—22no—
60C2×C4×C149C4⋊C412yes—
61C2×C4×C149C22×C411yescharacteristic
62C8×C149—22no—
63C22×C149C2×C4⋊C411yescharacteristic
64C2×D149—21no—
65C2×D149—21no—
66C2×D149#12011yescharacteristic
67C2×D149#12311yescharacteristic
68#10597010—42no—
69#10597010—42no—
70#10597010—42no—
71#10597010—81no—
72C4×C149—22no—
73C4×C149C4×D412yes—
74Dic149—22no—
75Dic149C22⋊Q812yes—
76C2×C149—21no—
77C2×C149#38511yescharacteristic
78D149—21no—
79D149#45411yescharacteristic
80D149#45611yescharacteristic
81C149#185711yescharacteristic, complemented, Sylow
82#1857—1491nomaximal, Sylow
83#519—1491no—
84#428—1492no—
85C2×#101—1491no—
86#391—1491no—
87#339—1492no—
88C22×Q8—1491no—
89C2×M16—1492no—
90C4×Q8—2982no—
91C4×Q8—2982no—
92#117—2982no—
93#117—1492no—
94C2×C4⋊C4—1491no—
95C2×C42—1491no—
96#107—2982no—
97#106—2982no—
98#101—1491no—
99#101—1492no—
100#101#1059701011yescharacteristic, complemented
101#95—2982no—
102C2×Q8—2982no—
103C2×Q8—2982no—
104C2×Q8—1492no—
105C2×Q8—1491no—
106C2×Q8C2×#1059701011yescharacteristic
107C22×C4—2981no—
108C22×C4—2981no—
109C22×C4—1492no—
110C22×C4—1491no—
111M16—2982no—
112M16—1492no—
113M16C2×#1059701012yes—
114C2×C8—2982no—
115C4⋊C4—2982no—
116C4⋊C4—2982no—
117C4⋊C4—2982no—
118C4⋊C4—1492no—
119C4⋊C4—1492no—
120C22⋊C4—2982no—
121C42—2984no—
122C42—2982no—
123C42—2982no—
124C23—1491no—
125Q8—22no—
126Q8—2984no—
127Q8—2982no—
128C2×C4—2982no—
129C2×C4—2982no—
130C2×C4—2982no—
131C2×C4—2982no—
132C2×C4—2982no—
133C2×C4—5961no—
134C2×C4—5961no—
135C2×C4—5962no—
136C2×C4—5961no—
137C2×C4—1492no—
138C2×C4—1491no—
139C2×C4—1492no—
140C2×C4—1492no—
141C2×C4C4⋊#1059701012yes—
142C2×C4C22×#1059701011yescharacteristic
143C8—22no—
144C8—2982no—
145C22—2981no—
146C22—2981no—
147C22—1491no—
148C22—1491no—
149C22C2×C4⋊#1059701011yescharacteristic
150C4—22no—
151C4—2982no—
152C4—5962no—
153C4—5962no—
154C4—5962no—
155C4—1492no—
156C4—11921no—
157C4D4×#1059701012yes—
158C2—21no—
159C2—2981no—
160C2—1491no—
161C2—1491no—
162C2#2375057211yescharacteristic
subgroupG/H
centerC2#23750572
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#101×C149C4
socleC2×C149#385
prime radicalC22×D149C2×D4
cosocleC2×C4×D149C23
hypercenter#101#10597010
hypocenterC149#1857
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C2×C4 ◁ #101

Complements

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

NH ≅ G/Ntype
17. #18011830C4semidirect
18. #18011829C4semidirect
19. #101×C149C4semidirect
81. C149#1857semidirect
100. #101#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506932
#237506362
(C2×#10597010)⋊Q82
#237504972
#101×D1492
#1857149