Finite Group Databasebeta

← #34043347

Subgroups — #34043347

Order 19072.

212 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 73 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#23750180C211yesmaximal, characteristic
2#23749677C211yesmaximal, characteristic
3C4⋊C8×D149C211yesmaximal, characteristic
4#23749373C211yesmaximal, characteristic, complemented
5#23749373C211yesmaximal, characteristic, complemented
6#23749371C211yesmaximal, characteristic, complemented
7#332×C149C211yesmaximal, characteristic, complemented
8C2×C8×D149—21no—
9#18011911C2211yescharacteristic
10#18011902—21no—
11#18011891C412yes—
12#18011887—21no—
13Q8×Dic149—21no—
14#18011876C412yes—
15#18011869—21no—
16C42×D149C2211yescharacteristic
17C4⋊#11924746C2211yescharacteristic
18C4⋊#11924746C2211yescharacteristic
19#18011840—21no—
20#18011823—21no—
21C8×Dic149—21no—
22C4⋊Q8×C149C2211yescharacteristic
23C4⋊C8×C149C2211yescharacteristic
24C4⋊C8×C149C2211yescharacteristic
25C2×Dic298C2×C412yes—
26C2×C4×D149C2×C411yescharacteristic
27C2×C4×D149D411yescharacteristic
28C2×C4×D149D411yescharacteristic
29C2×#11924746—21no—
30C2×#11924746—21no—
31C8×D149—42no—
32C4⋊Dic149—22no—
33C4⋊Dic149—21no—
34C4⋊Dic149—21no—
35#14558715—22no—
36#14558713—22no—
37C4×Dic149—22no—
38C4×Dic149C2×C411yescharacteristic
39C4×Dic149D411yescharacteristic
40C4×Dic149D411yescharacteristic
41C2×Q8×C149—21no—
42C2×C8×C149—21no—
43C2×C8×C149—21no—
44C4⋊C4×C149—21no—
45C4⋊C4×C149C2×C412yes—
46C42×C149C2311yescharacteristic
47C22×D149C22⋊C411yescharacteristic
48Dic298—42no—
49C2×Dic149—22no—
50C2×Dic149C22⋊C411yescharacteristic
51C2×Dic149C22⋊C411yescharacteristic
52C2×Dic149C22⋊C411yescharacteristic
53C4×D149—21no—
54C4×D149—21no—
55C4×D149—41no—
56C4×D149SD1612yes—
57C4×D149Q1612yes—
58#11924746—41no—
59#11924746—41no—
60Q8×C149—41no—
61Q8×C149—41no—
62C2×C4×C149—22no—
63C2×C4×C149C22×C411yescharacteristic
64C2×C4×C149C2×D411yescharacteristic
65C2×C4×C149C2×D411yescharacteristic
66C8×C149—41no—
67C8×C149—41no—
68C22×C149C2×C22⋊C411yescharacteristic
69C2×D149—21no—
70C2×D149—21no—
71C2×D149#10312yes—
72C4×C149—21no—
73C4×C149—42no—
74C4×C149C2×SD1611yescharacteristic
75C4×C149C2×Q1611yescharacteristic
76C4×C149#13511yescharacteristic
77C4×C149#13511yescharacteristic
78Dic149—21no—
79Dic149—21no—
80Dic149—42no—
81Dic149#10312yes—
82C2×C149#41311yescharacteristic
83C2×C149C2×#10311yescharacteristic
84C2×C149#41611yescharacteristic
85D149—22no—
86C149#154211yescharacteristic, complemented, Sylow
87#1542—1491nomaximal, Sylow
88#533—1491no—
89#431—1491no—
90C2×C4⋊C8—1491no—
91#333—1491no—
92#333—1491no—
93#332—1491no—
94#332D14911yescharacteristic, complemented
95C22×C8—2981no—
96C4⋊Q8—1491no—
97C4⋊Q8C2×D14911yescharacteristic
98#125—2981no—
99C22⋊Q8—2981no—
100C22⋊Q8—1492no—
101C4×Q8—2981no—
102C4×Q8—1492no—
103#117—2981no—
104C2×C42—1491no—
105C4⋊C8—2981no—
106C4⋊C8—1491no—
107C4⋊C8—1491no—
108C4⋊C8C2×D14911yescharacteristic
109C4⋊C8C2×D14911yescharacteristic
110C22⋊C8—2981no—
111C4×C8—2981no—
112C2×Q8—21no—
113C2×Q8—1492no—
114C22×C4—1491no—
115C22×C4—1491no—
116C22×C4—1491no—
117C2×C8—21no—
118C2×C8—21no—
119C2×C8—2981no—
120C2×C8—2981no—
121C2×C8—5962no—
122C4⋊C4—21no—
123C4⋊C4—2982no—
124C4⋊C4—2982no—
125C4⋊C4—2981no—
126C4⋊C4—2981no—
127C4⋊C4C4×D14912yes—
128C22⋊C4—2982no—
129C42—2982no—
130C42—1491no—
131C42—1491no—
132C42—1491no—
133C42C22×D14911yescharacteristic
134C23—1491no—
135Q8—41no—
136Q8—41no—
137Q8—5962no—
138C2×C4—22no—
139C2×C4—2981no—
140C2×C4—2981no—
141C2×C4—2982no—
142C2×C4—5961no—
143C2×C4—1491no—
144C2×C4—1491no—
145C2×C4—1491no—
146C2×C4—1492no—
147C2×C4—1492no—
148C2×C4C2×C4×D14911yescharacteristic
149C2×C4D4×D14911yescharacteristic
150C2×C4D4×D14911yescharacteristic
151C8—41no—
152C8—41no—
153C8—5961no—
154C8—5961no—
155C22—2981no—
156C22—2981no—
157C22—1492no—
158C22C22⋊C4×D14911yescharacteristic
159C4—21no—
160C4—42no—
161C4—2981no—
162C4—2981no—
163C4—5962no—
164C4—1492no—
165C4SD16×D14911yescharacteristic
166C4Q16×D14911yescharacteristic
167C4#1801193011yescharacteristic
168C4#1801193211yescharacteristic
169C2—2982no—
170C2#2374960811yescharacteristic
171C2#103×D14911yescharacteristic
172C2#2374961811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D149
commutatorC2×C4×C149C22×C4
FrattiniC42C22×D149
Fitting#332×C149C2
socleC22×C149C2×C22⋊C4
prime radicalC22×D149C22⋊C4
cosocleC42×C149C23
hypercenter#332D149
hypocenterC149#1542
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
4. #23749373C2semidirect
5. #23749373C2semidirect
6. #23749371C2semidirect
7. #332×C149C2semidirect
86. C149#1542semidirect
94. #332D149semidirect

Maximal subgroups

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

subgroupindex
#237501802
#237496772
C4⋊C8×D1492
#237493732
#237493712
#332×C1492
#1542149