Finite Group Databasebeta

← #34060644

Subgroups — #34060644

Order 19072.

278 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C22×#14558746C211yesmaximal, characteristic
2C2×#18011981C212yesmaximal, complemented
3#23750596C211yesmaximal, characteristic
4#23750501C212yesmaximal, complemented
5C22⋊C8×D149C211yesmaximal, characteristic
6C2×#14558746—24no—
7C2×#14558746—21no—
8C2×#14558746C2211yescharacteristic
9C2×#14558746C2211yescharacteristic
10C2×#14558746C2212yes—
11C22×#11924753—21no—
12#18011981—24no—
13#18011968—21no—
14C22⋊#11924753—21no—
15C22×C4×D149C2211yescharacteristic
16C2×C8×D149C2212yes—
17C22⋊#11924746C411yescharacteristic
18#18011823C412yes—
19C22⋊C8×C149C411yescharacteristic
20#14558746—24no—
21#14558746—22no—
22#14558746—22no—
23#14558746—22no—
24#14558746D414yes—
25C2×#11924753—24no—
26C2×#11924753—22no—
27C2×#11924753—21no—
28C2×#11924753—21no—
29C23×D149Q811yescharacteristic
30C22×Dic149D411yescharacteristic
31C2×C4×D149—22no—
32C2×C4×D149—22no—
33C2×C4×D149C2×C411yescharacteristic
34C2×C4×D149D411yescharacteristic
35C2×C4×D149Q811yescharacteristic
36C2×C4×D149C2311yescharacteristic
37C2×#11924746C2×C412yes—
38C8×D149—22no—
39C8×D149—22no—
40C22×C4×C149C2×C411yescharacteristic
41C2×C8×C149C2×C412yes—
42#11924753—24no—
43#11924753—41no—
44#11924753—41no—
45C22×D149—22no—
46C22×D149—22no—
47C22×D149—41no—
48C22×D149C4⋊C411yescharacteristic
49C22×D149C2×Q811yescharacteristic
50C2×Dic149—21no—
51C2×Dic149—21no—
52C2×Dic149C4⋊C411yescharacteristic
53C2×Dic149C2×D411yescharacteristic
54C4×D149—22no—
55C4×D149—22no—
56C4×D149—21no—
57C4×D149—21no—
58C4×D149C2×D412yes—
59C4×D149#4112yes—
60#11924746—22no—
61C23×C149C4⋊C411yescharacteristic
62C2×C4×C149—22no—
63C2×C4×C149C4⋊C411yescharacteristic
64C2×C4×C149C22×C411yescharacteristic
65C8×C149—22no—
66C22×C149—21no—
67C22×C149—21no—
68C22×C149#10812yescomplemented
69C22×C149C2×C4⋊C411yescharacteristic
70C2×D149—21no—
71C2×D149—21no—
72C2×D149—21no—
73C2×D149—21no—
74C2×D149—21no—
75C2×D149—44no—
76C2×D149C22⋊Q812yes—
77C4×C149—21no—
78C4×C149C4×D412yes—
79Dic149—21no—
80Dic149#12011yescharacteristic
81Dic149#12311yescharacteristic
82C2×C149—22no—
83C2×C149#38511yescharacteristic
84C2×C149C2×#10811yescharacteristic
85C2×C149#43011yescharacteristic
86D149—22no—
87D149—41no—
88C149#185511yescharacteristic, complemented, Sylow
89#1855—1491nomaximal, Sylow
90C22×M16—1491no—
91C2×#108—1492no—
92#407—1491no—
93C2×C22⋊C8—1491no—
94#341—1492no—
95C23×C4—1491no—
96C2×M16—2981no—
97C2×M16—2984no—
98C2×M16—1491no—
99C2×M16—1491no—
100C2×M16—1492no—
101C22×C8—2981no—
102C22×C8—1492no—
103#108—2984no—
104C22⋊C8—2981no—
105C22⋊C8—2981no—
106C22⋊C8—1491no—
107C22⋊C8—1492no—
108C22⋊C8#1059701011yescharacteristic
109C24—1491no—
110C22×C4—2982no—
111C22×C4—2982no—
112C22×C4—1491no—
113C22×C4—1491no—
114C22×C4—1491no—
115C22×C4—1491no—
116C22×C4—1491no—
117C22×C4C2×#1059701011yescharacteristic
118M16—2984no—
119M16—2982no—
120M16—2982no—
121M16—2982no—
122M16—1494no—
123C2×C8—2982no—
124C2×C8—2982no—
125C2×C8—2984no—
126C2×C8—2982no—
127C2×C8—2981no—
128C2×C8—2981no—
129C2×C8—1492no—
130C2×C8C2×#1059701012yes—
131C23—2982no—
132C23—2982no—
133C23—5961no—
134C23—1491no—
135C23—1491no—
136C23C4⋊#1059701011yescharacteristic
137C2×C4—22no—
138C2×C4—2982no—
139C2×C4—2981no—
140C2×C4—2981no—
141C2×C4—2981no—
142C2×C4—2981no—
143C2×C4—2982no—
144C2×C4—1491no—
145C2×C4—1491no—
146C2×C4—1492no—
147C2×C4—1492no—
148C2×C4C4⋊#1059701011yescharacteristic
149C2×C4C22×#1059701011yescharacteristic
150C8—22no—
151C8—2984no—
152C8—2982no—
153C8—5961no—
154C8—5961no—
155C22—21no—
156C22—21no—
157C22—2981no—
158C22—2981no—
159C22—2981no—
160C22—2981no—
161C22—2981no—
162C22—5964no—
163C22—1492no—
164C22#1801198112yescomplemented
165C22C2×C4⋊#1059701011yescharacteristic
166C4—21no—
167C4—2981no—
168C4—1491no—
169C4—1491no—
170C4D4×#1059701012yes—
171C2—22no—
172C2—2982no—
173C2—5961no—
174C2#2375057211yescharacteristic
175C2C2×#1801198111yescharacteristic
176C2#2375064011yescharacteristic
subgroupG/H
centerC22C2×C4⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC22⋊C8×C149C4
socleC22×C149C2×C4⋊C4
prime radicalC23×D149Q8
cosocleC2×C4×D149C23
hypercenterC22⋊C8#10597010
hypocenterC149#1855
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#18011981C2semidirect
4. #23750501C2semidirect
68. C22×C149#108semidirect
88. C149#1855semidirect
164. C22#18011981semidirect

Maximal subgroups

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

subgroupindex
C22×#145587462
C2×#180119812
#237505962
#237505012
C22⋊C8×D1492
#1855149