Finite Group Databasebeta

← #34060084

Subgroups — #34060084

Order 19072.

228 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 58 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#23750561C211yesmaximal, characteristic
3#23750479C212yesmaximal
4#23750478C212yesmaximal
5#23750179C211yesmaximal, characteristic
6C2×C4×#10597010—21no—
7#18011978—21no—
8#18011968C2212yes—
9#18011966—21no—
10(C2×#10597010)⋊C4—21no—
11(C2×#10597010)⋊C4C2212yes—
12#18011910C411yescharacteristic, complemented
13#18011909C411yescharacteristic, complemented
14#18011901—21no—
15#18011891C2211yescharacteristic
16#18011889—21no—
17#18011887C2211yescharacteristic
18C4×Dic298—21no—
19C4×Dic298C411yescharacteristic, complemented
20#18011868—21no—
21C42×D149C2211yescharacteristic
22C4×Q8×C149C411yescharacteristic, complemented
23C22×#10597010—22no—
24C2×#11924753—22no—
25C4×#10597010—24no—
26C2×Dic298—21no—
27C2×Dic298C2×C411yescharacteristic
28C2×C4×D149D411yescharacteristic
29C2×C4×D149D411yescharacteristic
30C2×C4×D149C2311yescharacteristic
31C4⋊Dic149—21no—
32C4⋊Dic149C2×C411yescharacteristic
33#14558715—21no—
34#14558715—21no—
35#14558715—21no—
36#14558715—21no—
37#14558715—21no—
38#14558713—21no—
39#14558713—21no—
40C4×Dic149—21no—
41C4×Dic149C2×C411yescharacteristic
42C4×Dic149D411yescharacteristic
43C4×Dic149D411yescharacteristic
44C2×Q8×C149C2×C411yescharacteristic
45C4⋊C4×C149—21no—
46C4⋊C4×C149C2×C411yescharacteristic
47C42×C149—21no—
48C42×C149C2×C411yescharacteristic
49C2×#10597010—24no—
50C2×#10597010—42no—
51C2×#10597010—42no—
52#11924753—42no—
53C22×D149C2×D411yescharacteristic
54Dic298—42no—
55Dic298—41no—
56C2×Dic149—21no—
57C2×Dic149—21no—
58C2×Dic149C22⋊C411yescharacteristic
59C2×Dic149C22⋊C411yescharacteristic
60C2×Dic149C2×D411yescharacteristic
61C4×D149—22no—
62C4×D149—22no—
63C4×D149—41no—
64Q8×C149—41no—
65C2×C4×C149—21no—
66C2×C4×C149—21no—
67C2×C4×C149C22⋊C411yescharacteristic
68C2×C4×C149C22⋊C411yescharacteristic
69C2×C4×C149C22×C411yescharacteristic
70C22×C149C2×C22⋊C411yescharacteristic
71C2×D149—21no—
72C2×D149—21no—
73C2×D149#13712yes—
74#10597010—44no—
75C4×C149—21no—
76C4×C149—21no—
77C4×C149—21no—
78C4×C149—41no—
79C4×C149—41no—
80Dic149—21no—
81Dic149—21no—
82Dic149—41no—
83Dic149—41no—
84Dic149#10412yes—
85C2×C149#41011yescharacteristic
86C2×C149#41911yescharacteristic
87C2×C149C2×#10411yescharacteristic
88D149—22no—
89C149#150611yescharacteristic, complemented, Sylow
90#1506—1491nomaximal, Sylow
91#533—1491no—
92#432—1491no—
93#376—1491no—
94#328—1492no—
95#328—1492no—
96C4⋊Q8—1491no—
97C4⋊Q8—1491no—
98#125—2981no—
99C22⋊Q8—2981no—
100C22⋊Q8—1491no—
101C22⋊Q8—1491no—
102C4×Q8—2981no—
103C4×Q8—1491no—
104C4×Q8#1059701011yescharacteristic, complemented
105#117—2981no—
106C2×C42—2981no—
107C2×C42—1491no—
108C4⋊C8—2981no—
109C22⋊C8—1492no—
110#97—2981no—
111#95—2981no—
112#95—1492no—
113C2×Q8—2981no—
114C2×Q8—1491no—
115C2×Q8C2×#1059701011yescharacteristic
116C22×C4—2982no—
117C22×C4—1491no—
118C22×C4—1491no—
119C22×C4—1491no—
120C2×C8—2982no—
121C4⋊C4—21no—
122C4⋊C4—2981no—
123C4⋊C4—2981no—
124C4⋊C4—2981no—
125C4⋊C4—2981no—
126C4⋊C4—2981no—
127C4⋊C4—2981no—
128C4⋊C4—1491no—
129C4⋊C4C2×#1059701011yescharacteristic
130C22⋊C4—2981no—
131C22⋊C4—2981no—
132C42—21no—
133C42—2984no—
134C42—2981no—
135C42—1491no—
136C42—1491no—
137C42—1491no—
138C42C2×#1059701011yescharacteristic
139C23—1491no—
140Q8—41no—
141Q8—5961no—
142Q8—5962no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—2982no—
146C2×C4—2982no—
147C2×C4—2984no—
148C2×C4—2981no—
149C2×C4—2981no—
150C2×C4—5961no—
151C2×C4—5962no—
152C2×C4—5962no—
153C2×C4—1491no—
154C2×C4—1491no—
155C2×C4—1491no—
156C2×C4C22⋊#1059701011yescharacteristic
157C2×C4C22⋊#1059701011yescharacteristic
158C2×C4C22×#1059701011yescharacteristic
159C8—5962no—
160C22—2981no—
161C22—2981no—
162C22—1492no—
163C22C2×C22⋊#1059701011yescharacteristic
164C4—21no—
165C4—21no—
166C4—21no—
167C4—41no—
168C4—41no—
169C4—2981no—
170C4—2981no—
171C4—5964no—
172C4—5961no—
173C4—5961no—
174C4—1492no—
175C2—2982no—
176C2#2375060411yescharacteristic
177C2#2375061811yescharacteristic
178C2D149⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC4×Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC22×D149C2×D4
cosocleC2×C4×D149C23
hypercenterC4×Q8#10597010
hypocenterC149#1506
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
12. #18011910C4semidirect
13. #18011909C4semidirect
19. C4×Dic298C4semidirect
22. C4×Q8×C149C4semidirect
89. C149#1506semidirect
104. C4×Q8#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506482
#237505612
#237504792
#237504782
#237501792
#1506149