Finite Group Databasebeta

← #34060073

Subgroups — #34060073

Order 19072.

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

normal subgroups only

This group has 240 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#23750643C211yesmaximal, characteristic
2C4×C4⋊#10597010C211yesmaximal, characteristic
3#23750479C212yesmaximal
4#23750478C212yesmaximal
5#23750179C211yesmaximal, characteristic
6C2×C4⋊#10597010—21no—
7C2×C4×#10597010—21no—
8#18011978—21no—
9#18011968C2212yes—
10C4×#11924753—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—
26C4×#10597010—42no—
27C2×Dic298—21no—
28C2×Dic298C2×C411yescharacteristic
29C2×C4×D149D411yescharacteristic
30C2×C4×D149D411yescharacteristic
31C2×C4×D149C2311yescharacteristic
32C4⋊Dic149—21no—
33C4⋊Dic149C2×C411yescharacteristic
34#14558715—21no—
35#14558715—21no—
36#14558715—21no—
37#14558715—21no—
38#14558715—21no—
39#14558713—21no—
40#14558713—21no—
41C4×Dic149—21no—
42C4×Dic149C2×C411yescharacteristic
43C4×Dic149D411yescharacteristic
44C4×Dic149D411yescharacteristic
45C2×Q8×C149C2×C411yescharacteristic
46C4⋊C4×C149—21no—
47C4⋊C4×C149C2×C411yescharacteristic
48C42×C149—21no—
49C42×C149C2×C411yescharacteristic
50C2×#10597010—24no—
51C2×#10597010—42no—
52C2×#10597010—42no—
53#11924753—42no—
54C22×D149C2×D411yescharacteristic
55Dic298—42no—
56Dic298—41no—
57C2×Dic149—21no—
58C2×Dic149—21no—
59C2×Dic149C22⋊C411yescharacteristic
60C2×Dic149C22⋊C411yescharacteristic
61C2×Dic149C2×D411yescharacteristic
62C4×D149—22no—
63C4×D149—41no—
64C4×D149SD1612yes—
65C4×D149Q1612yes—
66Q8×C149—41no—
67C2×C4×C149—21no—
68C2×C4×C149—21no—
69C2×C4×C149C22⋊C411yescharacteristic
70C2×C4×C149C22⋊C411yescharacteristic
71C2×C4×C149C22×C411yescharacteristic
72C22×C149C2×C22⋊C411yescharacteristic
73C2×D149—21no—
74C2×D149—21no—
75C2×D149C2×SD1611yescharacteristic
76C2×D149C2×Q1611yescharacteristic
77#10597010—44no—
78C4×C149—21no—
79C4×C149—21no—
80C4×C149—41no—
81C4×C149—41no—
82C4×C149#10312yes—
83Dic149—21no—
84Dic149—41no—
85Dic149—41no—
86Dic149#10312yes—
87Dic149#10412yes—
88C2×C149#41011yescharacteristic
89C2×C149C2×#10311yescharacteristic
90C2×C149C2×#10411yescharacteristic
91D149—21no—
92D149—21no—
93C149#150311yescharacteristic, complemented, Sylow
94#1503—1491nomaximal, Sylow
95#533—1491no—
96#431—1491no—
97C4×C4⋊C4—1491no—
98#328—1492no—
99#328—1492no—
100C4⋊Q8—1491no—
101C4⋊Q8—1491no—
102#125—2981no—
103C22⋊Q8—2981no—
104C22⋊Q8—1491no—
105C22⋊Q8—1491no—
106C4×Q8—2981no—
107C4×Q8—1491no—
108C4×Q8#1059701011yescharacteristic, complemented
109#117—2981no—
110C2×C4⋊C4—2981no—
111C2×C42—2981no—
112C2×C42—1491no—
113C4⋊C8—2981no—
114C22⋊C8—1492no—
115C4×C8—2981no—
116#95—1492no—
117C2×Q8—2981no—
118C2×Q8—1491no—
119C2×Q8C2×#1059701011yescharacteristic
120C22×C4—2982no—
121C22×C4—1491no—
122C22×C4—1491no—
123C22×C4—1491no—
124C2×C8—2982no—
125C4⋊C4—21no—
126C4⋊C4—2981no—
127C4⋊C4—2981no—
128C4⋊C4—2981no—
129C4⋊C4—2981no—
130C4⋊C4—2981no—
131C4⋊C4—2984no—
132C4⋊C4—2981no—
133C4⋊C4—1491no—
134C4⋊C4C2×#1059701011yescharacteristic
135C22⋊C4—2981no—
136C22⋊C4—2981no—
137C42—21no—
138C42—2981no—
139C42—5962no—
140C42—1491no—
141C42—1491no—
142C42—1491no—
143C42C2×#1059701011yescharacteristic
144C23—1491no—
145Q8—41no—
146Q8—5961no—
147Q8—5962no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—2982no—
151C2×C4—2984no—
152C2×C4—2981no—
153C2×C4—2981no—
154C2×C4—5961no—
155C2×C4—5962no—
156C2×C4—5962no—
157C2×C4—1491no—
158C2×C4—1491no—
159C2×C4—1491no—
160C2×C4—1492no—
161C2×C4—1492no—
162C2×C4C22⋊#1059701011yescharacteristic
163C2×C4C22⋊#1059701011yescharacteristic
164C2×C4C22×#1059701011yescharacteristic
165C8—5962no—
166C22—2981no—
167C22—2981no—
168C22—1491no—
169C22—1491no—
170C22C2×C22⋊#1059701011yescharacteristic
171C4—21no—
172C4—21no—
173C4—41no—
174C4—41no—
175C4—2981no—
176C4—5964no—
177C4—5961no—
178C4—5961no—
179C4—1492no—
180C4—1492no—
181C4#1801197412yes—
182C2—2981no—
183C2—2981no—
184C2#2375060411yescharacteristic
185C2C2×#1801197411yescharacteristic
186C2D149⋊#10411yescharacteristic
subgroupG/H
centerC2×C4C22⋊#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#1503
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C2×C4 ◁ 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
93. C149#1503semidirect
108. C4×Q8#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506432
C4×C4⋊#105970102
#237504792
#237504782
#237501792
#1503149