Finite Group Databasebeta

← #34059670

Subgroups — #34059670

Order 19072.

222 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 30 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#23750503C211yesmaximal, characteristic, complemented
2#23750469C211yesmaximal, characteristic, complemented
3#23749535C211yesmaximal, characteristic
4C2×C22⋊#10597010—21no—
5C22⋊#11924753—21no—
6C22×D596—21no—
7C22×D596C411yescharacteristic, complemented
8C2×#14558713—21no—
9C2×#14558713C2211yescharacteristic
10#95×C149C411yescharacteristic, complemented
11C22×#10597010—41no—
12C2×#11924753—41no—
13C22⋊#10597010—22no—
14C22⋊#10597010—41no—
15C23×D149—21no—
16C23×D149D411yescharacteristic
17C2×D596—42no—
18C2×D596—41no—
19C2×D596—42no—
20C2×D596—41no—
21C2×D596—41no—
22C2×D596—42no—
23C22×Dic149D411yescharacteristic
24#14558713—41no—
25#14558713—42no—
26C22×C4×C149—21no—
27C22×C4×C149C2×C411yescharacteristic
28C2×#10597010—42no—
29C2×#10597010—81no—
30C2×#10597010—81no—
31#11924753—81no—
32C22×D149—21no—
33C22×D149—21no—
34C22×D149—22no—
35C22×D149—41no—
36C22×D149—41no—
37C22×D149—41no—
38C22×D149—41no—
39C22×D149—41no—
40C22×D149—41no—
41C22×D149—41no—
42C22×D149—41no—
43C22×D149D811yescharacteristic
44C22×D149SD1611yescharacteristic
45D596—42no—
46D596—44no—
47D596—44no—
48D596—42no—
49C2×Dic149—21no—
50C2×Dic149—41no—
51C23×C149C22⋊C411yescharacteristic
52C2×C4×C149—22no—
53C2×C4×C149—21no—
54C2×C4×C149—41no—
55C2×C4×C149—41no—
56C2×C4×C149—41no—
57C22×C149—21no—
58C22×C149—21no—
59C22×C149#9911yescharacteristic
60C22×C149#10211yescharacteristic
61C22×C149#10411yescharacteristic
62C2×D149—21no—
63C2×D149—21no—
64C2×D149—41no—
65C2×D149—41no—
66C2×D149—41no—
67C2×D149—41no—
68C2×D149—42no—
69C2×D149—42no—
70C2×D149—42no—
71C2×D149—81no—
72C2×D149—81no—
73C2×D149—81no—
74C2×D149—81no—
75C2×D149—81no—
76#10597010—82no—
77C4×C149—42no—
78C4×C149—41no—
79Dic149—41no—
80C2×C149—21no—
81C2×C149—21no—
82C2×C149#32711yescharacteristic
83C2×C149AΣL(1,𝔽16)11yescharacteristic
84C2×C149#35311yescharacteristic
85D149—41no—
86D149—41no—
87D149—82no—
88C149#134311yescharacteristic, complemented, Sylow
89#1343—1491nomaximal, Sylow
90#392—1491no—
91#342—1491no—
92#323—1491no—
93C22×D4—2981no—
94C22×D4—1491no—
95C2×C22⋊C4—2981no—
96C2×C22⋊C4—2981no—
97C2×C22⋊C4—1491no—
98C22⋊C8—2981no—
99#95#1059701011yescharacteristic, complemented
100C24—2981no—
101C24—1491no—
102C2×D4—5961no—
103C2×D4—5962no—
104C2×D4—5962no—
105C2×D4—5961no—
106C2×D4—5961no—
107C2×D4—5962no—
108C22×C4—21no—
109C22×C4—5961no—
110C22×C4—1491no—
111C22×C4C2×#1059701011yescharacteristic
112C2×C8—5961no—
113C22⋊C4—2982no—
114C22⋊C4—5961no—
115C22⋊C4—5962no—
116C22⋊C4—5961no—
117C23—2982no—
118C23—2981no—
119C23—2981no—
120C23—5961no—
121C23—5961no—
122C23—5961no—
123C23—5961no—
124C23—5961no—
125C23—5961no—
126C23—5961no—
127C23—5961no—
128C23—1491no—
129C23—1491no—
130C23C22⋊#1059701011yescharacteristic
131D4—5962no—
132D4—5964no—
133D4—5964no—
134D4—5962no—
135C2×C4—22no—
136C2×C4—21no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—2981no—
141C2×C4—5961no—
142C2×C4—5962no—
143C2×C4—11921no—
144C2×C4—11921no—
145C8—11921no—
146C22—21no—
147C22—21no—
148C22—2981no—
149C22—2981no—
150C22—5961no—
151C22—5961no—
152C22—5962no—
153C22—5962no—
154C22—5961no—
155C22—5961no—
156C22—5962no—
157C22—11921no—
158C22—11921no—
159C22—11921no—
160C22—11921no—
161C22—11921no—
162C22#1801197011yescharacteristic
163C22#1801197311yescharacteristic
164C22#1801197611yescharacteristic
165C4—42no—
166C4—41no—
167C4—5961no—
168C4—11922no—
169C2—21no—
170C2—21no—
171C2—5961no—
172C2—5961no—
173C2—11922no—
174C2#2375047711yescharacteristic
175C2#2375052611yescharacteristic
176C2#2375053011yescharacteristic
subgroupG/H
centerC22#18011970
commutatorC22×C4×C149C2×C4
FrattiniC22×C4C2×#10597010
Fitting#95×C149C4
socleC22×C149#99
prime radical#23749535C2
cosocleC2×#14558713C22
hypercenter#95#10597010
hypocenterC149#1343
LCSG ▷ C22×C4×C149 ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
1. #23750503C2semidirect
2. #23750469C2semidirect
7. C22×D596C4semidirect
10. #95×C149C4semidirect
88. C149#1343semidirect
99. #95#10597010semidirect

Maximal subgroups

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

subgroupindex
#237505032
#237504692
#237495352
#1343149