Finite Group Databasebeta

← #34045915

Subgroups — #34045915

Order 19072.

306 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 69 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#23750206C211yesmaximal, characteristic
2C2×#18011839C212yesmaximal, complemented
3#23749624C212yesmaximal, complemented
4#23749394C211yesmaximal, characteristic, complemented
5#384×C149C211yesmaximal, characteristic, complemented
6C2×#14558736C2212yes—
7C2×#14558720C2212yes—
8#18011891—22no—
9#18011886—22no—
10#18011885—22no—
11#18011839—24no—
12#18011834—22no—
13#18011831—22no—
14C2×C4⋊C4×C149—22no—
15C2×C4⋊C4×C149C2211yescharacteristic
16C2×C4⋊C4×C149C2211yescharacteristic
17C2×C42×C149C2211yescharacteristic
18#14558736—22no—
19#14558736—22no—
20#14558736—22no—
21#14558736—22no—
22C2×Dic298D412yes—
23C2×D596—22no—
24C2×D596D412yes—
25C2×C22⋊D149—22no—
26C2×C4×D149—22no—
27#14558720—22no—
28#14558720—22no—
29C2×#11924746—22no—
30C4⋊Dic149—22no—
31#14558713—24no—
32C22×C4×C149—21no—
33C22×C4×C149—21no—
34C22×C4×C149D412yes—
35C22×C4×C149C2311yescharacteristic
36C4⋊C4×C149—22no—
37C4⋊C4×C149—22no—
38C4⋊C4×C149—44no—
39C42×C149—21no—
40C42×C149D412yescomplemented
41C22×D149—22no—
42Dic298—22no—
43Dic298—22no—
44D596—22no—
45D596—22no—
46D596—82no—
47C22⋊D149—42no—
48C22⋊D149—42no—
49C2×Dic149—22no—
50C4×D149—42no—
51C4×D149—42no—
52#11924746—42no—
53C23×C149C2×D411yescharacteristic
54C2×C4×C149—22no—
55C2×C4×C149—22no—
56C2×C4×C149—22no—
57C2×C4×C149—22no—
58C2×C4×C149—42no—
59C2×C4×C149—42no—
60C2×C4×C149—41no—
61C2×C4×C149C2×D412yes—
62C2×C4×C149C2×D411yescharacteristic
63C2×C4×C149#4111yescharacteristic
64C2×C4×C149#4112yes—
65C22×C149—21no—
66C22×C149—21no—
67C22×C149#12011yescharacteristic
68C22×C149#12111yescharacteristic
69C22×C149#12411yescharacteristic
70C2×D149—42no—
71C2×D149—42no—
72C2×D149—42no—
73C4×C149—24no—
74C4×C149—42no—
75C4×C149—81no—
76C4×C149#12112yes—
77C4×C149#12312yes—
78Dic149—42no—
79C2×C149—21no—
80C2×C149—21no—
81C2×C149#39411yescharacteristic
82C2×C149#45311yescharacteristic
83C2×C149#45611yescharacteristic
84D149—82no—
85C149#203911yescharacteristic, complemented, Sylow
86#2039—1491nomaximal, Sylow
87#537—1491no—
88C2×#104—1492no—
89#417—1492no—
90#384D14911yescharacteristic, complemented
91#343—1491no—
92C2×#41—1492no—
93C2×M16—1492no—
94C22⋊Q8—2982no—
95#121—2982no—
96#121—2982no—
97C2×C4⋊C4—22no—
98C2×C4⋊C4C2×D14911yescharacteristic
99C2×C4⋊C4C2×D14911yescharacteristic
100C2×C42C2×D14911yescharacteristic
101#104—2984no—
102#103—2982no—
103#102—2982no—
104#41—2982no—
105#41—2982no—
106#41—2982no—
107#41—2982no—
108C2×Q8—1492no—
109C2×D4—2982no—
110C2×D4—2982no—
111C2×D4—1492no—
112C22×C4—21no—
113C22×C4—21no—
114C22×C4—2982no—
115C22×C4C22⋊D14912yes—
116C22×C4C22×D14911yescharacteristic
117M16—2982no—
118M16—2982no—
119C2×C8—2982no—
120C4⋊C4—22no—
121C4⋊C4—22no—
122C4⋊C4—44no—
123C4⋊C4—2982no—
124C22⋊C4—2984no—
125C42—21no—
126C42D59612yescomplemented
127C23—2982no—
128C23C2×C22⋊D14911yescharacteristic
129Q8—2982no—
130Q8—2982no—
131D4—2982no—
132D4—2982no—
133D4—5962no—
134D4—5962no—
135D4—11922no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—42no—
141C2×C4—42no—
142C2×C4—41no—
143C2×C4—2982no—
144C2×C4—5962no—
145C2×C4—5962no—
146C2×C4D4×D14912yes—
147C2×C4C2×D59611yescharacteristic
148C2×C4#1455873611yescharacteristic
149C2×C4#1455873712yes—
150C8—5962no—
151C22—21no—
152C22—21no—
153C22—5962no—
154C22—5962no—
155C22—5962no—
156C22#1801187911yescharacteristic
157C22#1801188511yescharacteristic
158C22#1801190011yescharacteristic
159C4—24no—
160C4—42no—
161C4—81no—
162C4—5962no—
163C4#1801188612yes—
164C4#1801189612yes—
165C2—21no—
166C2—21no—
167C2—11922no—
168C2#2374954211yescharacteristic
169C2#2374979211yescharacteristic
170C2#2374980711yescharacteristic
subgroupG/H
centerC22#18011879
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting#384×C149C2
socleC22×C149#120
prime radical#23750206C2
hypercenter#384D149
hypocenterC149#2039
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #384

Complements

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

NH ≅ G/Ntype
2. C2×#18011839C2semidirect
3. #23749624C2semidirect
4. #23749394C2semidirect
5. #384×C149C2semidirect
40. C42×C149D4semidirect
85. C149#2039semidirect
90. #384D149semidirect
126. C42D596semidirect

Maximal subgroups

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

subgroupindex
#237502062
C2×#180118392
#237496242
#237493942
#384×C1492
#2039149