Finite Group Databasebeta

← #34060982

Subgroups — #34060982

Order 19072.

250 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 54 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#23750611C212yesmaximal, complemented
2#23750535C212yesmaximal, complemented
3#23750533C212yesmaximal, complemented
4#23750171C211yesmaximal, characteristic
5D149⋊M16—22no—
6#18011972C2214yes—
7#18011971—22no—
8C2×#14558736C2211yescharacteristic
9#18011909C2211yescharacteristic
10#18011907C411yescharacteristic
11#18011900C411yescharacteristic
12#18011898C2211yescharacteristic
13#18011883—22no—
14C4×C22⋊D149—22no—
15C2×C4×Dic149C411yescharacteristic
16C2×#41×C149C411yescharacteristic
17#14558746—42no—
18#14558745—24no—
19D149⋊C8—42no—
20#14558736—41no—
21#14558736—41no—
22C2×Dic298C2311yescharacteristic
23C2×D596C2×C411yescharacteristic
24C2×C22⋊D149—22no—
25C2×C22⋊D149D412yes—
26C22×Dic149—21no—
27C2×C4×D149D412yes—
28#14558715—22no—
29C22⋊Dic149—22no—
30#14558713—22no—
31C4×Dic149—21no—
32C4×Dic149C2×C411yescharacteristic
33C4×Dic149C2×C411yescharacteristic
34#41×C149—41no—
35#41×C149—41no—
36C2×Q8×C149C2×C411yescharacteristic
37C2×D4×C149—21no—
38C2×D4×C149C2×C411yescharacteristic
39C22×C4×C149—21no—
40C22×C4×C149C2×C411yescharacteristic
41#11924753—44no—
42C22×D149C22⋊C412yes—
43Dic298—41no—
44D596—41no—
45C22⋊D149—42no—
46C22⋊D149—44no—
47C2×Dic149—21no—
48C2×Dic149—21no—
49C2×Dic149—42no—
50C2×Dic149C2×D412yes—
51C4×D149—22no—
52C4×D149—22no—
53C23×C149—21no—
54C23×C149C22⋊C411yescharacteristic
55Q8×C149—41no—
56D4×C149—41no—
57D4×C149—42no—
58C2×C4×C149—21no—
59C2×C4×C149—21no—
60C2×C4×C149—21no—
61C2×C4×C149—41no—
62C2×C4×C149—41no—
63C2×C4×C149C22⋊C411yescharacteristic
64C2×C4×C149C22×C411yescharacteristic
65C22×C149—21no—
66C22×C149—41no—
67C22×C149—42no—
68C22×C149—41no—
69C22×C149C2×C22⋊C411yescharacteristic
70C2×D149—22no—
71C2×D149—42no—
72C4×C149—21no—
73C4×C149—41no—
74C4×C149#9911yescharacteristic
75C4×C149#9911yescharacteristic
76Dic149—22no—
77Dic149—22no—
78Dic149—41no—
79C2×C149—21no—
80C2×C149—41no—
81C2×C149—81no—
82C2×C149C2×#9911yescharacteristic
83D149—42no—
84C149#213211yescharacteristic, complemented, Sylow
85#2132—1491nomaximal, Sylow
86#532—1491no—
87#413—1492no—
88#356—1492no—
89#355—1492no—
90C2×#41—1491no—
91C2×#41#1059701011yescharacteristic
92C2×M16—2982no—
93C4⋊Q8—1491no—
94#127—1491no—
95#124—1491no—
96#124—1491no—
97#121—2982no—
98C4×D4—2982no—
99C2×C42—1491no—
100#101—1494no—
101#100—2982no—
102#41—41no—
103#41—41no—
104#41—5961no—
105#41—5961no—
106C2×Q8—1491no—
107C2×Q8C2×#1059701011yescharacteristic
108C2×D4—21no—
109C2×D4—2982no—
110C2×D4—1492no—
111C2×D4—1491no—
112C2×D4C2×#1059701011yescharacteristic
113C22×C4—21no—
114C22×C4—2981no—
115C22×C4—1492no—
116C22×C4C2×#1059701011yescharacteristic
117M16—2984no—
118M16—5962no—
119C2×C8—5962no—
120C4⋊C4—2982no—
121C22⋊C4—2982no—
122C22⋊C4—2982no—
123C42—2981no—
124C42—1491no—
125C42—1491no—
126C23—21no—
127C23—1492no—
128C23C22⋊#1059701011yescharacteristic
129Q8—41no—
130Q8—5961no—
131D4—41no—
132D4—42no—
133D4—5961no—
134D4—5962no—
135D4—5964no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—2981no—
142C2×C4—2982no—
143C2×C4—2982no—
144C2×C4—2981no—
145C2×C4—5962no—
146C2×C4—1492no—
147C2×C4C22⋊#1059701011yescharacteristic
148C2×C4C22×#1059701011yescharacteristic
149C8—5964no—
150C22—21no—
151C22—41no—
152C22—42no—
153C22—41no—
154C22—2982no—
155C22—5962no—
156C22C2×C22⋊#1059701011yescharacteristic
157C4—21no—
158C4—41no—
159C4—2982no—
160C4—2982no—
161C4—5961no—
162C4#1801196911yescharacteristic
163C4#1801196911yescharacteristic
164C2—21no—
165C2—41no—
166C2—81no—
167C2—5962no—
168C2C2×#1801196911yescharacteristic
subgroupG/H
centerC4#18011969
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC2×#41×C149C4
socleC2×C149C2×#99
prime radical#23750171C2
cosocleC2×Dic298C23
hypercenterC2×#41#10597010
hypocenterC149#2132
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #23750611C2semidirect
2. #23750535C2semidirect
3. #23750533C2semidirect
84. C149#2132semidirect

Maximal subgroups

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

subgroupindex
#237506112
#237505352
#237505332
#237501712
#2132149