Finite Group Databasebeta

← #34060228

Subgroups — #34060228

Order 19072.

254 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 62 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#23750628C212yesmaximal, complemented
2#23750485C212yesmaximal, complemented
3#23750483C212yesmaximal, complemented
4#23750171C211yesmaximal, characteristic
5C2×#14558745—22no—
6#18011978C2214yes—
7C4⋊#11924753—22no—
8C2×#14558736C411yescharacteristic
9#18011909C2211yescharacteristic
10#18011907C2211yescharacteristic
11#18011900C411yescharacteristic
12#18011898C411yescharacteristic
13#18011883—22no—
14C4×C22⋊D149—22no—
15C2×C4×Dic149C2211yescharacteristic
16C2×#41×C149C411yescharacteristic
17#14558745—44no—
18C2×#11924753—24no—
19#14558736—42no—
20C2×Dic298C2×C411yescharacteristic
21C2×D596C2×C411yescharacteristic
22C2×C22⋊D149—22no—
23C2×C22⋊D149—21no—
24C22×Dic149D412yes—
25C2×C4×D149—21no—
26#14558715—22no—
27C22⋊Dic149—22no—
28#14558713—22no—
29C4×Dic149C2×C411yescharacteristic
30C4×Dic149D412yes—
31C4×Dic149C2311yescharacteristic
32#41×C149—42no—
33C2×Q8×C149C2×C411yescharacteristic
34C2×D4×C149—21no—
35C2×D4×C149C2×C411yescharacteristic
36C22×C4×C149—21no—
37C22×C4×C149C2×C411yescharacteristic
38#11924753—44no—
39C22×D149—21no—
40Dic298—41no—
41D596—41no—
42C22⋊D149—42no—
43C22⋊D149—42no—
44C22⋊D149—42no—
45C2×Dic149—22no—
46C2×Dic149—22no—
47C2×Dic149—21no—
48C2×Dic149C22⋊C412yes—
49C2×Dic149C2×D412yes—
50C4×D149—42no—
51C23×C149—21no—
52C23×C149C22⋊C411yescharacteristic
53Q8×C149—41no—
54D4×C149—41no—
55D4×C149—42no—
56C2×C4×C149—22no—
57C2×C4×C149—21no—
58C2×C4×C149—42no—
59C2×C4×C149C22⋊C411yescharacteristic
60C2×C4×C149C22×C411yescharacteristic
61C22×C149—21no—
62C22×C149—22no—
63C22×C149—41no—
64C22×C149—42no—
65C22×C149C2×C22⋊C411yescharacteristic
66C2×D149—41no—
67C2×D149—42no—
68C4×C149—21no—
69C4×C149—41no—
70C4×C149#10012yes—
71Dic149—22no—
72Dic149—41no—
73Dic149AGL(1,ℤ/8)12yes—
74Dic149#13712yes—
75C2×C149—41no—
76C2×C149—81no—
77C2×C149C2×#10011yescharacteristic
78C2×C149#41712yes—
79D149—81no—
80C149#156011yescharacteristic, complemented, Sylow
81#1560—1491nomaximal, Sylow
82#532—1491no—
83#423—1492no—
84#333—1492no—
85#331—1492no—
86C2×#41—1491no—
87C2×#41#1059701011yescharacteristic
88C2×M16—2982no—
89C4⋊Q8—1491no—
90#127—1491no—
91#124—1491no—
92#124—1491no—
93#121—2982no—
94C4×D4—2982no—
95C2×C42—1491no—
96C4⋊C8—2982no—
97C4⋊C8—1494no—
98#41—42no—
99#41—5962no—
100C2×Q8—1491no—
101C2×Q8C2×#1059701011yescharacteristic
102C2×D4—21no—
103C2×D4—2981no—
104C2×D4—2982no—
105C2×D4—1491no—
106C2×D4C2×#1059701011yescharacteristic
107C22×C4—21no—
108C22×C4—2981no—
109C22×C4—1492no—
110C22×C4C2×#1059701011yescharacteristic
111M16—5964no—
112C2×C8—2984no—
113C4⋊C4—2982no—
114C22⋊C4—2982no—
115C22⋊C4—2982no—
116C42—1492no—
117C42—1491no—
118C42—1491no—
119C23—21no—
120C23—2981no—
121C23C22⋊#1059701011yescharacteristic
122Q8—41no—
123Q8—5961no—
124D4—41no—
125D4—42no—
126D4—5961no—
127D4—5962no—
128D4—5962no—
129D4—5962no—
130C2×C4—22no—
131C2×C4—21no—
132C2×C4—42no—
133C2×C4—2982no—
134C2×C4—2982no—
135C2×C4—2981no—
136C2×C4—5962no—
137C2×C4—1492no—
138C2×C4—1492no—
139C2×C4C22⋊#1059701011yescharacteristic
140C2×C4C22×#1059701011yescharacteristic
141C8—5964no—
142C22—21no—
143C22—22no—
144C22—41no—
145C22—42no—
146C22—5961no—
147C22—5962no—
148C22C2×C22⋊#1059701011yescharacteristic
149C4—21no—
150C4—41no—
151C4—2982no—
152C4—5961no—
153C4—1492no—
154C4—1492no—
155C4#1801197112yes—
156C2—41no—
157C2—81no—
158C2—11921no—
159C2C2×#1801197111yescharacteristic
160C2#2375061612yes—
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC2×#41×C149C4
socleC22×C149C2×C22⋊C4
prime radical#23750171C2
cosocleC4×Dic149C23
hypercenterC2×#41#10597010
hypocenterC149#1560
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #23750628C2semidirect
2. #23750485C2semidirect
3. #23750483C2semidirect
80. C149#1560semidirect

Maximal subgroups

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

subgroupindex
#237506282
#237504852
#237504832
#237501712
#1560149