Finite Group Databasebeta

← #34061168

Subgroups — #34061168

Order 19072.

512 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 162 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#23750574C218yesmaximal, complemented
2#23750568C212yesmaximal
3#23750567C212yesmaximal
4C4×C22⋊#10597010C212yesmaximal
5C2×C4⋊C4×D149C211yesmaximal, characteristic
6C2×C4⋊#10597010C2214yes—
7C2×C22⋊#10597010C2214yes—
8C2×C4×#10597010C2214yes—
9(C2×#10597010)⋊C4C2214yes—
10(C2×#10597010)⋊C4C2214yes—
11(C2×#10597010)⋊C4C2218yes—
12C22×C4×D149C2211yescharacteristic
13C22×C4×D149C2211yescharacteristic
14C22×C4×D149C2211yescharacteristic
15C2×C4⋊Dic149C411yescharacteristic, complemented
16C2×#14558715C411yescharacteristic, complemented
17C2×#14558715C411yescharacteristic, complemented
18C4⋊C4×D149C414yescomplemented
19C4⋊C4×D149C2214yes—
20C2×C4⋊C4×C149C411yescharacteristic, complemented
21C22×#10597010C2318yes—
22C4⋊#10597010—44no—
23C22⋊#10597010—28no—
24C4×#10597010—44no—
25C23×D149C2311yescharacteristic
26C22×Dic149C2×C411yescharacteristic
27C22×Dic149C2×C411yescharacteristic
28C22×Dic149C2×C411yescharacteristic
29C2×C4×D149—24no—
30C2×C4×D149—42no—
31C2×C4×D149—42no—
32C2×C4×D149C2×C412yes—
33C2×C4×D149C2×C412yes—
34C2×C4×D149C2×C412yes—
35C2×C4×D149C2312yes—
36C2×C4×D149C2312yes—
37C2×C4×D149C2312yes—
38C4⋊Dic149C2×C414yes—
39#14558715C2×C414yes—
40#14558715C2×C414yes—
41C22×C4×C149C2×C411yescharacteristic
42C22×C4×C149C2×C411yescharacteristic
43C22×C4×C149C2×C411yescharacteristic
44C4⋊C4×C149C2×C414yes—
45C2×#10597010—28no—
46C2×#10597010—28no—
47C2×#10597010—28no—
48C22×D149—22no—
49C22×D149—22no—
50C22×D149C22×C411yescharacteristic
51C22×D149#4114yes—
52C22×D149C2411yescharacteristic
53C2×Dic149—22no—
54C2×Dic149—41no—
55C2×Dic149—41no—
56C2×Dic149C22×C412yes—
57C2×Dic149C22×C412yes—
58C2×Dic149C22×C412yes—
59C4×D149—24no—
60C4×D149—24no—
61C4×D149—24no—
62C4×D149—24no—
63C4×D149—42no—
64C4×D149—42no—
65C23×C149C22×C411yescharacteristic
66C2×C4×C149—22no—
67C2×C4×C149—41no—
68C2×C4×C149—41no—
69C2×C4×C149C22×C412yes—
70C2×C4×C149C22×C412yes—
71C2×C4×C149C22×C412yes—
72C22×C149—21no—
73C22×C149—21no—
74C22×C149#11712yes—
75C22×C149C23×C411yescharacteristic
76C2×D149—21no—
77C2×D149—21no—
78C2×D149—28no—
79C2×D149#11712yes—
80C2×D149C2×#4112yes—
81C2×D149H(5,𝔽2)12yes—
82C2×D1492−1+412yes—
83#10597010—48no—
84C4×C149—22no—
85C4×C149—22no—
86C4×C149—22no—
87Dic149—22no—
88Dic149—22no—
89Dic149—22no—
90C2×C149—22no—
91C2×C149C2×#11711yescharacteristic
92C2×C149#51811yescharacteristic
93C2×C149#51911yescharacteristic
94D149—22no—
95D149#53914yes—
96C149#231311yescharacteristic, complemented, Sylow
97#2313—1491nomaximal, Sylow
98C22×C4⋊C4—1491no—
99#387—1498no—
100#381—1492no—
101#380—1492no—
102C4×C22⋊C4—1492no—
103C23×C4—1491no—
104C23×C4—1491no—
105C23×C4—1491no—
106C2×C4⋊C4—1494no—
107C2×C4⋊C4—1491no—
108C2×C4⋊C4—1491no—
109C2×C4⋊C4—1491no—
110C2×C4⋊C4—1494no—
111C2×C4⋊C4—1494no—
112C2×C4⋊C4#1059701011yescharacteristic, complemented
113C2×C22⋊C4—1494no—
114C2×C42—1494no—
115#95—1494no—
116#95—1494no—
117#95—1498no—
118C24—1491no—
119C22×C4—2984no—
120C22×C4—5962no—
121C22×C4—5962no—
122C22×C4—1498no—
123C22×C4—1491no—
124C22×C4—1492no—
125C22×C4—1492no—
126C22×C4—1492no—
127C22×C4—1492no—
128C22×C4—1491no—
129C22×C4—1491no—
130C22×C4—1492no—
131C22×C4—1492no—
132C22×C4C2×#1059701011yescharacteristic
133C22×C4C2×#1059701011yescharacteristic
134C22×C4C2×#1059701011yescharacteristic
135C4⋊C4—5964no—
136C4⋊C4—1494no—
137C4⋊C4—1494no—
138C4⋊C4—1494no—
139C4⋊C4C2×#1059701014yes—
140C22⋊C4—2988no—
141C42—5964no—
142C23—2982no—
143C23—2982no—
144C23—1494no—
145C23—1491no—
146C23—1491no—
147C23C22×#1059701011yescharacteristic
148C2×C4—22no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—2984no—
152C2×C4—2984no—
153C2×C4—2984no—
154C2×C4—2984no—
155C2×C4—2982no—
156C2×C4—2988no—
157C2×C4—2988no—
158C2×C4—2988no—
159C2×C4—5962no—
160C2×C4—5962no—
161C2×C4—5961no—
162C2×C4—5961no—
163C2×C4—1492no—
164C2×C4—1492no—
165C2×C4—1492no—
166C2×C4C22×#1059701012yes—
167C2×C4C22×#1059701012yes—
168C2×C4C22×#1059701012yes—
169C22—21no—
170C22—21no—
171C22—2988no—
172C22—2981no—
173C22—2981no—
174C22—1492no—
175C22—1492no—
176C22—1492no—
177C22—1492no—
178C22#1801199012yes—
179C22C23×#1059701011yescharacteristic
180C4—22no—
181C4—22no—
182C4—22no—
183C4—2982no—
184C4—2982no—
185C4—2982no—
186C4—5968no—
187C2—22no—
188C2—2982no—
189C2—1494no—
190C2C2×#1801199011yescharacteristic
191C2#2375069211yescharacteristic
192C2#2375069311yescharacteristic
subgroupG/H
center, FrattiniC22C23×#10597010
commutator, socleC22×C149C23×C4
FittingC2×C4⋊C4×C149C4
prime radicalC23×D149C23
cosocleC22×D149C24
hypercenterC2×C4⋊C4#10597010
hypocenterC149#2313
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #23750574C2semidirect
15. C2×C4⋊Dic149C4semidirect
16. C2×#14558715C4semidirect
17. C2×#14558715C4semidirect
18. C4⋊C4×D149C4semidirect
20. C2×C4⋊C4×C149C4semidirect
96. C149#2313semidirect
112. C2×C4⋊C4#10597010semidirect

Maximal subgroups

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

subgroupindex
#237505742
#237505682
#237505672
C4×C22⋊#105970102
C2×C4⋊C4×D1492
#2313149