Finite Group Databasebeta

← #34045238

Subgroups — #34045238

Order 19072.

340 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 89 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#23750189C211yesmaximal, characteristic
2#23749609C211yesmaximal, characteristic, complemented
3C2×#18011827C212yesmaximal, complemented
4#23749397C212yesmaximal, complemented
5#568×C149C211yesmaximal, characteristic, complemented
6C22×D596C2211yescharacteristic
7C2×#14558720C2212yes—
8#18011907—21no—
9#18011900—21no—
10#18011885—22no—
11#18011879C414yes—
12#18011870C2211yescharacteristic
13#18011830—21no—
14#18011828—21no—
15#18011827—24no—
16C2×#41×C149C2211yescharacteristic
17#131×C149—24no—
18C2×M16×C149—22no—
19C2×M16×C149C2212yes—
20C23×D149C2×C412yes—
21C2×D596—21no—
22C2×D596—22no—
23C2×D596—21no—
24C2×D596—22no—
25C2×C22⋊D149—24no—
26#14558720—22no—
27#14558720—22no—
28C2×#11924746—22no—
29C4⋊Dic149—21no—
30C22⋊Dic149C2×C412yes—
31#14558713—24no—
32C4×Dic149—21no—
33#41×C149—22no—
34#41×C149—22no—
35C2×Q8×C149D411yescharacteristic
36C2×D4×C149C2×C412yes—
37C2×D4×C149D411yescharacteristic
38C22×C4×C149D412yes—
39C22×C4×C149C2311yescharacteristic
40M16×C149—24no—
41M16×C149—22no—
42M16×C149D414yescomplemented
43C2×C8×C149—24no—
44C2×C8×C149—22no—
45C22×D149—22no—
46C22×D149—24no—
47C22×D149—82no—
48D596—41no—
49D596—42no—
50D596—41no—
51C22⋊D149—84no—
52C2×Dic149—22no—
53#11924746—42no—
54C23×C149C22⋊C412yes—
55C23×C149C22×C411yescharacteristic
56Q8×C149—22no—
57D4×C149—24no—
58D4×C149—22no—
59C2×C4×C149—22no—
60C2×C4×C149—22no—
61C2×C4×C149C22⋊C412yes—
62C2×C4×C149C2×D412yes—
63C2×C4×C149C2×D411yescharacteristic
64C2×C4×C149C2×D411yescharacteristic
65C2×C4×C149#4112yes—
66C8×C149—24no—
67C22×C149—22no—
68C22×C149—41no—
69C22×C149—42no—
70C22×C149C2×C22⋊C411yescharacteristic
71C22×C149C4×D412yes—
72C2×D149—44no—
73C2×D149—42no—
74C2×D149—84no—
75C4×C149—22no—
76C4×C149#12011yescharacteristic
77C4×C149#12112yes—
78C4×C149#12311yescharacteristic
79Dic149—42no—
80C2×C149—21no—
81C2×C149—22no—
82C2×C149—42no—
83C2×C149#38611yescharacteristic
84D149—82no—
85C149#191411yescharacteristic, complemented, Sylow
86#1914—1491nomaximal, Sylow
87#568D14911yescharacteristic, complemented
88#535—1491no—
89#413—1491no—
90C2×#100—1492no—
91#344—1492no—
92C2×#41C2×D14911yescharacteristic
93C22×D4—1491no—
94#131—24no—
95C2×M16—22no—
96C2×M16—1492no—
97C2×M16C2×D14912yes—
98#127—2981no—
99#124—2981no—
100#121—2982no—
101#120—1494no—
102#117—1491no—
103#101—2981no—
104#100—2981no—
105#100—2984no—
106C24—1492no—
107#41—22no—
108#41—22no—
109C2×Q8D59611yescharacteristic
110C2×D4—2984no—
111C2×D4—2982no—
112C2×D4—2981no—
113C2×D4—2981no—
114C2×D4—2982no—
115C2×D4C4×D14912yes—
116C2×D4D59611yescharacteristic
117C22×C4C22⋊D14912yes—
118C22×C4C22×D14911yescharacteristic
119M16—24no—
120M16—22no—
121M16—2982no—
122M16—2982no—
123M16C22⋊D14914yescomplemented
124C2×C8—24no—
125C2×C8—22no—
126C2×C8—2982no—
127C4⋊C4—2981no—
128C22⋊C4—2984no—
129C22⋊C4—1492no—
130C42—2981no—
131C23—2982no—
132C23—2984no—
133C23—11922no—
134C23#1455871312yes—
135C23C2×C4×D14911yescharacteristic
136Q8—22no—
137D4—24no—
138D4—22no—
139D4—5961no—
140D4—5962no—
141D4—5961no—
142D4—11924no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—2982no—
146C2×C4#1455871312yes—
147C2×C4C2×C22⋊D14912yes—
148C2×C4C2×C22⋊D14911yescharacteristic
149C2×C4C2×D59611yescharacteristic
150C2×C4#1455873612yes—
151C8—24no—
152C8—5962no—
153C22—22no—
154C22—41no—
155C22—42no—
156C22—5964no—
157C22—5962no—
158C22—11924no—
159C22C2×#1455871311yescharacteristic
160C22C4×C22⋊D14912yes—
161C4—22no—
162C4—5962no—
163C4#1801188011yescharacteristic
164C4#1801188512yes—
165C4#1801189411yescharacteristic
166C2—21no—
167C2—22no—
168C2—42no—
169C2—11922no—
170C2#2374950411yescharacteristic
subgroupG/H
centerC2#23749504
commutatorC23×C149C22×C4
FrattiniC22×C4C22×D149
Fitting#568×C149C2
socleC2×C149#386
prime radical#23750189C2
cosocleC22×C4×C149C23
hypercenter#568D149
hypocenterC149#1914
LCSG ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
2. #23749609C2semidirect
3. C2×#18011827C2semidirect
4. #23749397C2semidirect
5. #568×C149C2semidirect
42. M16×C149D4semidirect
85. C149#1914semidirect
87. #568D149semidirect
123. M16C22⋊D149semidirect

Maximal subgroups

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

subgroupindex
#237501892
#237496092
C2×#180118272
#237493972
#568×C1492
#1914149