Finite Group Databasebeta

← #34060962

Subgroups — #34060962

Order 19072.

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

normal subgroups only

This group has 258 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#23750604C212yesmaximal, complemented
2#23750531C212yesmaximal, complemented
3#23750529C212yesmaximal, complemented
4#23750171C211yesmaximal, characteristic
5#18011990—22no—
6#18011970C2214yes—
7#18011969—22no—
8C2×#14558736C2211yescharacteristic
9#18011909C411yescharacteristic, complemented
10#18011907C2211yescharacteristic
11#18011900C2211yescharacteristic
12#18011898C411yescharacteristic, complemented
13#18011883—22no—
14C4×C22⋊D149—22no—
15C2×C4×Dic149C411yescharacteristic, complemented
16C2×#41×C149C411yescharacteristic, complemented
17C4⋊#10597010—42no—
18C22⋊#10597010—24no—
19C4×#10597010—42no—
20#14558736—41no—
21#14558736—41no—
22C2×Dic298C2×C411yescharacteristic
23C2×D596C2311yescharacteristic
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
41C2×#10597010—44no—
42C22×D149C2×D412yes—
43Dic298—41no—
44D596—41no—
45C22⋊D149—42no—
46C22⋊D149—44no—
47C2×Dic149—21no—
48C2×Dic149—21no—
49C2×Dic149—42no—
50C2×Dic149C22⋊C412yes—
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—
72#10597010—84no—
73C4×C149—21no—
74C4×C149—41no—
75C4×C149#9911yescharacteristic
76C4×C149#9911yescharacteristic
77Dic149—22no—
78Dic149—22no—
79Dic149—41no—
80C2×C149—21no—
81C2×C149—41no—
82C2×C149—81no—
83C2×C149C2×#9911yescharacteristic
84D149—42no—
85C149#212611yescharacteristic, complemented, Sylow
86#2126—1491nomaximal, Sylow
87#532—1491no—
88#410—1492no—
89#354—1492no—
90#353—1492no—
91C2×#41—1491no—
92C2×#41#1059701011yescharacteristic, complemented
93C4⋊Q8—1491no—
94#127—1491no—
95#124—1491no—
96#124—1491no—
97#121—2982no—
98C4×D4—2982no—
99#117—2982no—
100C2×C42—1491no—
101#99—2982no—
102#99—1494no—
103#41—41no—
104#41—41no—
105#41—5961no—
106#41—5961no—
107C2×Q8—1491no—
108C2×Q8C2×#1059701011yescharacteristic
109C2×D4—21no—
110C2×D4—2982no—
111C2×D4—1492no—
112C2×D4—1491no—
113C2×D4C2×#1059701011yescharacteristic
114C22×C4—21no—
115C22×C4—2981no—
116C22×C4—1492no—
117C22×C4C2×#1059701011yescharacteristic
118C4⋊C4—2982no—
119C4⋊C4—5962no—
120C22⋊C4—2982no—
121C22⋊C4—2982no—
122C22⋊C4—2984no—
123C42—2981no—
124C42—5962no—
125C42—1491no—
126C42—1491no—
127C23—21no—
128C23—1492no—
129C23C22⋊#1059701011yescharacteristic
130Q8—41no—
131Q8—5961no—
132D4—41no—
133D4—42no—
134D4—5961no—
135D4—5962no—
136D4—5964no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—2981no—
143C2×C4—2982no—
144C2×C4—2982no—
145C2×C4—2981no—
146C2×C4—5962no—
147C2×C4—5964no—
148C2×C4—1492no—
149C2×C4C22⋊#1059701011yescharacteristic
150C2×C4C22×#1059701011yescharacteristic
151C22—21no—
152C22—41no—
153C22—42no—
154C22—41no—
155C22—2982no—
156C22—5962no—
157C22C2×C22⋊#1059701011yescharacteristic
158C4—21no—
159C4—41no—
160C4—2982no—
161C4—2982no—
162C4—5961no—
163C4—11924no—
164C4#1801196911yescharacteristic
165C4#1801196911yescharacteristic
166C2—21no—
167C2—41no—
168C2—81no—
169C2—5962no—
170C2C2×#1801196911yescharacteristic
subgroupG/H
centerC4#18011969
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC2×#41×C149C4
socleC2×C149C2×#99
prime radical#23750171C2
cosocleC2×D596C23
hypercenterC2×#41#10597010
hypocenterC149#2126
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. #23750604C2semidirect
2. #23750531C2semidirect
3. #23750529C2semidirect
9. #18011909C4semidirect
12. #18011898C4semidirect
15. C2×C4×Dic149C4semidirect
16. C2×#41×C149C4semidirect
85. C149#2126semidirect
92. C2×#41#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506042
#237505312
#237505292
#237501712
#2126149