Finite Group Databasebeta

← #34060208

Subgroups — #34060208

Order 19072.

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

normal subgroups only

This group has 216 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#23750630C211yesmaximal, characteristic
2D149⋊(C4⋊C8)C211yesmaximal, characteristic
3#23750485C212yesmaximal, complemented
4#23750484C212yesmaximal, complemented
5#23750179C211yesmaximal, characteristic
6C2×#14558746—21no—
7C2×D149⋊C8—21no—
8#18011978—21no—
9#18011978C2212yes—
10#18011978C2212yes—
11C4⋊#11924753—21no—
12#18011910C2211yescharacteristic
13#18011909C2211yescharacteristic
14#18011901—21no—
15#18011891C411yescharacteristic
16#18011889—21no—
17#18011887C411yescharacteristic
18C4×Dic298—21no—
19C4×Dic298C411yescharacteristic
20#18011868—21no—
21C42×D149C2211yescharacteristic
22C4×Q8×C149C411yescharacteristic
23#14558746—42no—
24D149⋊C8—42no—
25C2×#11924753—22no—
26C2×#11924753—22no—
27C2×Dic298—21no—
28C2×Dic298C2×C411yescharacteristic
29C2×C4×D149C2×C411yescharacteristic
30C2×C4×D149D411yescharacteristic
31C2×C4×D149D411yescharacteristic
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×Dic149D411yescharacteristic
43C4×Dic149D411yescharacteristic
44C4×Dic149C2311yescharacteristic
45C2×Q8×C149C2×C411yescharacteristic
46C4⋊C4×C149—21no—
47C4⋊C4×C149C2×C411yescharacteristic
48C42×C149—21no—
49C42×C149C2×C411yescharacteristic
50#11924753—42no—
51#11924753—42no—
52C22×D149C22⋊C411yescharacteristic
53Dic298—41no—
54Dic298—41no—
55Dic298—41no—
56C2×Dic149—21no—
57C2×Dic149—21no—
58C2×Dic149C22⋊C411yescharacteristic
59C2×Dic149C2×D411yescharacteristic
60C2×Dic149C2×D411yescharacteristic
61C4×D149—21no—
62C4×D149—21no—
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×D149#10312yes—
76C4×C149—21no—
77C4×C149—21no—
78C4×C149—41no—
79C4×C149—41no—
80C4×C149#10312yes—
81Dic149—21no—
82Dic149—41no—
83Dic149—41no—
84Dic149C2×SD1611yescharacteristic
85Dic149C2×Q1611yescharacteristic
86Dic149AGL(1,ℤ/8)11yescharacteristic
87Dic149#13711yescharacteristic
88C2×C149#41311yescharacteristic
89C2×C149C2×#10311yescharacteristic
90C2×C149#41711yescharacteristic
91D149—22no—
92C149#155011yescharacteristic, complemented, Sylow
93#1550—1491nomaximal, Sylow
94#533—1491no—
95#423—1491no—
96C2×C4⋊C8—1491no—
97#333—1492no—
98#332—1492no—
99C2×M16—2981no—
100C22×C8—2981no—
101C4⋊Q8—1491no—
102C4⋊Q8—1491no—
103#125—2981no—
104C22⋊Q8—2981no—
105C22⋊Q8—1491no—
106C22⋊Q8—1491no—
107C4×Q8—2981no—
108C4×Q8—1491no—
109C4×Q8#1059701011yescharacteristic
110#117—2981no—
111C2×C42—1491no—
112C4⋊C8—2981no—
113C4⋊C8—2981no—
114C4⋊C8—1492no—
115C4⋊C8—1492no—
116C2×Q8—2981no—
117C2×Q8—1491no—
118C2×Q8C2×#1059701011yescharacteristic
119C22×C4—1491no—
120C22×C4—1491no—
121C22×C4—1491no—
122M16—5962no—
123C2×C8—2982no—
124C2×C8—2982no—
125C2×C8—5962no—
126C4⋊C4—21no—
127C4⋊C4—2981no—
128C4⋊C4—2981no—
129C4⋊C4—2981no—
130C4⋊C4—2981no—
131C4⋊C4—2981no—
132C4⋊C4—2981no—
133C4⋊C4—1491no—
134C4⋊C4C2×#1059701011yescharacteristic
135C22⋊C4—2981no—
136C22⋊C4—2981no—
137C42—21no—
138C42—2981no—
139C42—1491no—
140C42—1491no—
141C42—1491no—
142C42C2×#1059701011yescharacteristic
143C23—1491no—
144Q8—41no—
145Q8—5961no—
146Q8—5961no—
147Q8—5961no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—2981no—
151C2×C4—2981no—
152C2×C4—2981no—
153C2×C4—2981no—
154C2×C4—5961no—
155C2×C4—1491no—
156C2×C4—1491no—
157C2×C4—1491no—
158C2×C4—1492no—
159C2×C4—1492no—
160C2×C4C22⋊#1059701011yescharacteristic
161C2×C4C22⋊#1059701011yescharacteristic
162C2×C4C22×#1059701011yescharacteristic
163C8—5962no—
164C8—5962no—
165C22—2981no—
166C22—2981no—
167C22—1492no—
168C22C2×C22⋊#1059701011yescharacteristic
169C4—21no—
170C4—21no—
171C4—41no—
172C4—41no—
173C4—2981no—
174C4—5961no—
175C4—5961no—
176C4—1491no—
177C4—1491no—
178C4—1491no—
179C4—1491no—
180C4#1801197412yes—
181C2—2982no—
182C2#2375061111yescharacteristic
183C2C2×#1801197411yescharacteristic
184C2#2375061611yescharacteristic
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#1550
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. #23750485C2semidirect
4. #23750484C2semidirect
92. C149#1550semidirect

Maximal subgroups

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

subgroupindex
#237506302
D149⋊(C4⋊C8)2
#237504852
#237504842
#237501792
#1550149