Finite Group Databasebeta

← #34060221

Subgroups — #34060221

Order 19072.

228 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 60 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#23750648C211yesmaximal, characteristic
2#23750648C211yesmaximal, characteristic
3#23750484C214yesmaximal, complemented
4C4⋊Q8×D149C211yesmaximal, characteristic
5#18011978C2212yes—
6#18011978C2212yes—
7#18011968—21no—
8#18011968—21no—
9#18011966—21no—
10#18011966—21no—
11C2×Q8×D149—21no—
12#18011911C411yescharacteristic
13#18011910—21no—
14#18011910C2212yes—
15#18011909—21no—
16C4⋊C4×D149—21no—
17C4⋊C4×D149C412yes—
18C42×D149C2211yescharacteristic
19C4⋊Q8×C149C411yescharacteristic
20C2×#11924753—22no—
21C2×#11924753—22no—
22C2×Dic298—22no—
23C2×Dic298—21no—
24Q8×D149—44no—
25C2×C4×D149—22no—
26C2×C4×D149C2×C411yescharacteristic
27C2×C4×D149D411yescharacteristic
28C2×C4×D149D411yescharacteristic
29C4⋊Dic149—21no—
30C4⋊Dic149C2×C412yes—
31#14558715—22no—
32#14558715—22no—
33C4×Dic149D411yescharacteristic
34C4×Dic149D411yescharacteristic
35C4×Dic149C2311yescharacteristic
36C2×Q8×C149—21no—
37C4⋊C4×C149—21no—
38C4⋊C4×C149C2×C412yes—
39C42×C149C2×C411yescharacteristic
40#11924753—42no—
41#11924753—42no—
42C22×D149C22⋊C411yescharacteristic
43Dic298—42no—
44Dic298—44no—
45C2×Dic149—22no—
46C2×Dic149C22⋊C411yescharacteristic
47C2×Dic149C2×D411yescharacteristic
48C2×Dic149C2×D411yescharacteristic
49C4×D149—22no—
50C4×D149—22no—
51C4×D149—22no—
52C4×D149—44no—
53Q8×C149—42no—
54C2×C4×C149—22no—
55C2×C4×C149C22⋊C411yescharacteristic
56C2×C4×C149C22⋊C411yescharacteristic
57C2×C4×C149C22×C411yescharacteristic
58C22×C149C2×C22⋊C411yescharacteristic
59C2×D149—21no—
60C2×D149—21no—
61C2×D149#10112yes—
62C4×C149—21no—
63C4×C149—21no—
64C4×C149—21no—
65C4×C149—42no—
66Dic149—21no—
67Dic149—42no—
68Dic149AGL(1,ℤ/8)12yes—
69Dic149#13712yes—
70C2×C149C2×#10111yescharacteristic
71C2×C149#41811yescharacteristic
72C2×C149#41911yescharacteristic
73D149—22no—
74C149#155611yescharacteristic, complemented, Sylow
75#1556—1491nomaximal, Sylow
76C2×C4⋊Q8—1491no—
77#432—1491no—
78#432—1491no—
79#332—1494no—
80C22×Q8—2981no—
81C4⋊Q8—2981no—
82C4⋊Q8—2981no—
83C4⋊Q8—1492no—
84C4⋊Q8—1491no—
85C4⋊Q8#1059701011yescharacteristic
86C2×C4⋊C4—2981no—
87C2×C4⋊C4—1492no—
88C2×C42—1491no—
89C4⋊C8—1492no—
90C4⋊C8—1492no—
91C22⋊C8—2981no—
92C22⋊C8—2981no—
93#97—2981no—
94#97—2981no—
95C2×Q8—21no—
96C2×Q8—2982no—
97C2×Q8—2981no—
98C2×Q8—5964no—
99C22×C4—2982no—
100C22×C4—1491no—
101C22×C4—1491no—
102C22×C4—1491no—
103C2×C8—2982no—
104C2×C8—2982no—
105C4⋊C4—21no—
106C4⋊C4—2982no—
107C4⋊C4—2982no—
108C4⋊C4—2981no—
109C4⋊C4—1492no—
110C4⋊C4C2×#1059701012yes—
111C42—1491no—
112C42—1491no—
113C42—1491no—
114C42C2×#1059701011yescharacteristic
115C23—1491no—
116Q8—42no—
117Q8—5962no—
118Q8—5964no—
119C2×C4—22no—
120C2×C4—2982no—
121C2×C4—2982no—
122C2×C4—2982no—
123C2×C4—2982no—
124C2×C4—5964no—
125C2×C4—1491no—
126C2×C4—1491no—
127C2×C4—1491no—
128C2×C4C22⋊#1059701011yescharacteristic
129C2×C4C22⋊#1059701011yescharacteristic
130C2×C4C22×#1059701011yescharacteristic
131C8—5962no—
132C8—5962no—
133C22—2981no—
134C22—2981no—
135C22—1492no—
136C22C2×C22⋊#1059701011yescharacteristic
137C4—21no—
138C4—21no—
139C4—21no—
140C4—42no—
141C4—2981no—
142C4—5962no—
143C4—1492no—
144C4—1492no—
145C2—2982no—
146C2D149⋊#10111yescharacteristic
147C2#2375061711yescharacteristic
148C2#2375061811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC4⋊Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC22×D149C22⋊C4
cosocleC4×Dic149C23
hypercenterC4⋊Q8#10597010
hypocenterC149#1556
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #23750484C2semidirect
74. C149#1556semidirect

Maximal subgroups

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

subgroupindex
#237506482
#237504842
C4⋊Q8×D1492
#1556149