Finite Group Databasebeta

← #34060200

Subgroups — #34060200

Order 19072.

240 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 72 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#23750642C211yesmaximal, characteristic
2#23750628C211yesmaximal, characteristic
3#23750484C214yesmaximal, complemented
4C2×#18011910C211yesmaximal, characteristic
5C2×#14558745—21no—
6#18011978C2212yes—
7#18011978C2212yes—
8C4⋊#11924753—21no—
9C22⋊#11924753—21no—
10C4×#11924753—21no—
11C22×Dic298—21no—
12#18011910—21no—
13#18011910—21no—
14#18011910C412yes—
15#18011910C2212yes—
16C2×C4⋊Dic149C411yescharacteristic
17C2×#14558715—21no—
18C2×C4×Dic149C2211yescharacteristic
19C2×C4⋊C4×C149C411yescharacteristic
20#14558745—42no—
21C2×#11924753—22no—
22C2×#11924753—22no—
23C2×Dic298—22no—
24C2×Dic298—22no—
25C2×Dic298—42no—
26C2×Dic298—42no—
27C22×Dic149—21no—
28C22×Dic149D411yescharacteristic
29C22×Dic149D411yescharacteristic
30C4⋊Dic149—21no—
31C4⋊Dic149C2×C412yes—
32#14558715—22no—
33#14558715—22no—
34C4×Dic149C2×C411yescharacteristic
35C4×Dic149D411yescharacteristic
36C4×Dic149D411yescharacteristic
37C4×Dic149C2311yescharacteristic
38C22×C4×C149—21no—
39C22×C4×C149C2×C411yescharacteristic
40C4⋊C4×C149—21no—
41C4⋊C4×C149C2×C412yes—
42#11924753—42no—
43#11924753—42no—
44Dic298—44no—
45Dic298—42no—
46Dic298—42no—
47C2×Dic149—22no—
48C2×Dic149—22no—
49C2×Dic149—42no—
50C2×Dic149C22⋊C411yescharacteristic
51C2×Dic149C22⋊C411yescharacteristic
52C2×Dic149D812yes—
53C2×Dic149SD1612yes—
54C2×Dic149C2×D411yescharacteristic
55C2×Dic149C2×D411yescharacteristic
56C23×C149C22⋊C411yescharacteristic
57C2×C4×C149—22no—
58C2×C4×C149—22no—
59C2×C4×C149—42no—
60C2×C4×C149C22⋊C411yescharacteristic
61C2×C4×C149C22×C411yescharacteristic
62C22×C149—21no—
63C22×C149—21no—
64C22×C149#10212yes—
65C22×C149C2×C22⋊C411yescharacteristic
66C4×C149—21no—
67C4×C149—42no—
68C4×C149#10112yes—
69Dic149—21no—
70Dic149—42no—
71Dic149#10212yes—
72Dic149C2×D811yescharacteristic
73Dic149C2×SD1611yescharacteristic
74Dic149#13712yes—
75C2×C149—22no—
76C2×C149C2×#10111yescharacteristic
77C2×C149C2×#10211yescharacteristic
78C2×C149#41911yescharacteristic
79C149#154611yescharacteristic, complemented, Sylow
80#1546—1491nomaximal, Sylow
81C2×C4⋊Q8—1491no—
82#431—1491no—
83#423—1491no—
84#332—1494no—
85C22×Q8—2981no—
86C2×M16—2981no—
87C4⋊Q8—2981no—
88C4⋊Q8—2981no—
89C4⋊Q8—1492no—
90C4⋊Q8—1492no—
91C2×C4⋊C4—2981no—
92C2×C4⋊C4—1491no—
93C2×C4⋊C4#1059701011yescharacteristic
94C2×C42—1491no—
95C4⋊C8—2981no—
96C4⋊C8—1492no—
97C4⋊C8—1492no—
98C22⋊C8—2981no—
99C4×C8—2981no—
100C2×Q8—2982no—
101C2×Q8—2982no—
102C2×Q8—5962no—
103C2×Q8—5962no—
104C22×C4—21no—
105C22×C4—2981no—
106C22×C4—1491no—
107C22×C4—1491no—
108C22×C4C2×#1059701011yescharacteristic
109M16—5962no—
110C2×C8—2982no—
111C2×C8—2982no—
112C4⋊C4—21no—
113C4⋊C4—2982no—
114C4⋊C4—2982no—
115C4⋊C4—2981no—
116C4⋊C4—1492no—
117C4⋊C4C2×#1059701012yes—
118C42—1491no—
119C42—1491no—
120C42—1491no—
121C42—1491no—
122C23C22⋊#1059701011yescharacteristic
123Q8—5962no—
124Q8—5964no—
125Q8—5962no—
126C2×C4—22no—
127C2×C4—22no—
128C2×C4—42no—
129C2×C4—2982no—
130C2×C4—2982no—
131C2×C4—5962no—
132C2×C4—1491no—
133C2×C4—1492no—
134C2×C4—1492no—
135C2×C4—1491no—
136C2×C4—1491no—
137C2×C4—1491no—
138C2×C4C22⋊#1059701011yescharacteristic
139C2×C4C22×#1059701011yescharacteristic
140C8—5962no—
141C8—5962no—
142C22—21no—
143C22—21no—
144C22#1801197312yes—
145C22C2×C22⋊#1059701011yescharacteristic
146C4—21no—
147C4—42no—
148C4—2981no—
149C4—5962no—
150C4—1491no—
151C4—1492no—
152C4—1491no—
153C4—1492no—
154C4#1801197212yes—
155C2—22no—
156C2C2×#1801197211yescharacteristic
157C2C2×#1801197311yescharacteristic
158C2#2375061811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC2×C4⋊C4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC23×C149C22⋊C4
cosocleC4×Dic149C23
hypercenterC2×C4⋊C4#10597010
hypocenterC149#1546
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #23750484C2semidirect
79. C149#1546semidirect

Maximal subgroups

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

subgroupindex
#237506422
#237506282
#237504842
C2×#180119102
#1546149