Finite Group Databasebeta

← #34060436

Subgroups — #34060436

Order 19072.

412 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 94 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
1C2×#18011970C212yesmaximal
2C4×C22⋊#10597010C212yesmaximal, complemented
3#23750503C212yesmaximal, complemented
4C2×#18011873C211yesmaximal, characteristic
5C2×C22⋊#10597010C2214yes—
6C2×C4×#10597010—22no—
7#18011970C418yescomplemented
8(C2×#10597010)⋊C4—22no—
9C22×D596C2211yescharacteristic
10C22×C4×D149C411yescharacteristic, complemented
11C22×C4×D149C2211yescharacteristic
12#18011873—22no—
13#18011873—22no—
14C2×#14558713C411yescharacteristic, complemented
15C2×#14558713C2211yescharacteristic
16C2×C4×Dic149C411yescharacteristic, complemented
17C2×C4⋊C4×C149C411yescharacteristic, complemented
18C22×#10597010—24no—
19C22⋊#10597010—24no—
20C22⋊#10597010C2×C418yescomplemented
21C4×#10597010—44no—
22C23×D149C2×C411yescharacteristic
23C23×D149C2311yescharacteristic
24C2×D596—22no—
25C2×D596—22no—
26C2×D596C2×C414yes—
27C22×Dic149C2×C411yescharacteristic
28C22×Dic149C2×C411yescharacteristic
29C2×C4×D149—21no—
30C2×C4×D149—21no—
31C2×C4×D149—42no—
32C2×C4×D149—42no—
33C2×C4×D149D412yes—
34C2×C4×D149D412yes—
35#14558713—22no—
36#14558713—22no—
37C4×Dic149—21no—
38C4×Dic149—21no—
39C22×C4×C149C2×C411yescharacteristic
40C22×C4×C149C2×C411yescharacteristic
41C22×C4×C149C2×C411yescharacteristic
42C4⋊C4×C149—22no—
43C2×#10597010—28no—
44C2×#10597010—44no—
45C2×#10597010—44no—
46C22×D149—21no—
47C22×D149—21no—
48C22×D149—41no—
49C22×D149—41no—
50C22×D149—41no—
51C22×D149—41no—
52C22×D149C4212yescomplemented
53C22×D149C22×C412yes—
54C22×D149C2×D412yes—
55C22×D149#4112yes—
56D596—28no—
57C2×Dic149—22no—
58C2×Dic149—21no—
59C2×Dic149—41no—
60C2×Dic149C22⋊C411yescharacteristic
61C2×Dic149C22⋊C411yescharacteristic
62C4×D149—24no—
63C4×D149—42no—
64C4×D149—42no—
65C4×D149—42no—
66C23×C149C22×C411yescharacteristic
67C2×C4×C149—21no—
68C2×C4×C149—21no—
69C2×C4×C149—21no—
70C2×C4×C149—41no—
71C2×C4×C149—41no—
72C2×C4×C149C4212yescomplemented
73C2×C4×C149C22⋊C412yes—
74C22×C149—21no—
75C22×C149—21no—
76C22×C149C2×C4211yescharacteristic
77C22×C149C2×C22⋊C411yescharacteristic
78C22×C149#11711yescharacteristic
79C2×D149—22no—
80C2×D149—22no—
81C2×D149—22no—
82C2×D149—42no—
83C2×D149—42no—
84C2×D149—42no—
85C2×D149—41no—
86C2×D149—41no—
87C2×D149—42no—
88C2×D149C4×D414yes—
89#10597010—48no—
90C4×C149—22no—
91C4×C149—22no—
92C4×C149—41no—
93Dic149—21no—
94Dic149—41no—
95Dic149#9912yescomplemented
96C2×C149—21no—
97C2×C149—21no—
98C2×C149C4×C22⋊C411yescharacteristic
99C2×C149C2×#9911yescharacteristic
100C2×C149#41011yescharacteristic
101D149—24no—
102D149—42no—
103C149C4×#9911yescharacteristic, complemented, Sylow
104C4×#99—1491nomaximal, Sylow
105C2×C4×D4—1491no—
106C2×#99—1492no—
107C4×C22⋊C4—1492no—
108#342—1492no—
109C22×D4—1491no—
110C23×C4—1491no—
111C23×C4—1491no—
112C4×D4—2982no—
113C4×D4—2982no—
114C2×C4⋊C4#1059701011yescharacteristic, complemented
115C2×C22⋊C4—1491no—
116C2×C22⋊C4—1491no—
117C2×C22⋊C4—1494no—
118C2×C42—2982no—
119C2×C42—1491no—
120#99—1498no—
121#95—2982no—
122C24—1491no—
123C24—1491no—
124C2×D4—2982no—
125C2×D4—2982no—
126C2×D4—1494no—
127C22×C4—2981no—
128C22×C4—2981no—
129C22×C4—2984no—
130C22×C4—5962no—
131C22×C4—5962no—
132C22×C4—1491no—
133C22×C4—1492no—
134C22×C4—1491no—
135C22×C4—1492no—
136C22×C4C2×#1059701011yescharacteristic
137C22×C4C2×#1059701011yescharacteristic
138C22×C4C2×#1059701011yescharacteristic
139C4⋊C4—22no—
140C22⋊C4—2982no—
141C22⋊C4—2984no—
142C22⋊C4—2982no—
143C22⋊C4—1498no—
144C42—2981no—
145C42—2981no—
146C42—5964no—
147C23—2981no—
148C23—2981no—
149C23—5961no—
150C23—5961no—
151C23—5961no—
152C23—5961no—
153C23—1492no—
154C23—1492no—
155C23—1492no—
156C23—1492no—
157C23C22×#1059701011yescharacteristic
158D4—2988no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—2984no—
165C2×C4—2982no—
166C2×C4—2988no—
167C2×C4—2981no—
168C2×C4—5962no—
169C2×C4—5962no—
170C2×C4—5962no—
171C2×C4—5964no—
172C2×C4—5964no—
173C2×C4—5961no—
174C2×C4—1491no—
175C2×C4—1491no—
176C2×C4C4×#1059701012yescomplemented
177C2×C4C22⋊#1059701012yes—
178C22—21no—
179C22—21no—
180C22—2982no—
181C22—2982no—
182C22—2982no—
183C22—5962no—
184C22—5962no—
185C22—5962no—
186C22—5962no—
187C22—5961no—
188C22—5961no—
189C22—1494no—
190C22C2×C4×#1059701011yescharacteristic
191C22C2×C22⋊#1059701011yescharacteristic
192C22#1801199011yescharacteristic
193C4—22no—
194C4—22no—
195C4—41no—
196C4—2981no—
197C4—5968no—
198C4—5961no—
199C4—1492no—
200C2—21no—
201C2—21no—
202C2—2984no—
203C2—5962no—
204C2C4×C22⋊#1059701011yescharacteristic
205C2D149⋊#9911yescharacteristic
206C2#2375060611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC22×C149C2×C42
FrattiniC23C22×#10597010
FittingC2×C4⋊C4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC22×D596C22
cosocleC23×D149C23
hypercenterC2×C4⋊C4#10597010
hypocenterC149C4×#99
LCSG ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C4×C22⋊#10597010C2semidirect
3. #23750503C2semidirect
7. #18011970C4semidirect
10. C22×C4×D149C4semidirect
14. C2×#14558713C4semidirect
16. C2×C4×Dic149C4semidirect
17. C2×C4⋊C4×C149C4semidirect
20. C22⋊#10597010C2×C4semidirect
52. C22×D149C42semidirect
72. C2×C4×C149C42semidirect
95. Dic149#99semidirect
103. C149C4×#99semidirect
114. C2×C4⋊C4#10597010semidirect
176. C2×C4C4×#10597010semidirect

Maximal subgroups

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

subgroupindex
C2×#180119702
C4×C22⋊#105970102
#237505032
C2×#180118732
C4×#99149