Finite Group Databasebeta

← #34060418

Subgroups — #34060418

Order 19072.

412 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 122 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×#18011968C212yesmaximal
2C2×#18011966C212yesmaximal, complemented
3#23750491C212yesmaximal, complemented
4C2×C42×D149C211yesmaximal, characteristic
5C22×#11924753C2214yes—
6#18011968C418yescomplemented
7#18011966—24no—
8C22×C4×D149C411yescharacteristic
9C22×C4×D149C411yescharacteristic
10C22×C4×D149C2211yescharacteristic
11C2×C4×Dic149C411yescharacteristic
12C2×C4×Dic149C2211yescharacteristic
13C2×C4×Dic149C2211yescharacteristic
14C42×D149—24no—
15C2×C42×C149C411yescharacteristic
16C2×#11924753—24no—
17C2×#11924753—24no—
18C2×#11924753C2×C418yescomplemented
19C23×D149C2×C411yescharacteristic
20C22×Dic149C2×C411yescharacteristic
21C22×Dic149C2×C411yescharacteristic
22C22×Dic149C2311yescharacteristic
23C2×C4×D149—22no—
24C2×C4×D149—22no—
25C2×C4×D149—22no—
26C2×C4×D149—22no—
27C2×C4×D149—22no—
28C2×C4×D149—22no—
29C2×C4×D149—22no—
30C2×C4×D149—22no—
31C2×C4×D149C2×C414yes—
32C4×Dic149—22no—
33C4×Dic149—22no—
34C4×Dic149D414yes—
35C22×C4×C149C2×C411yescharacteristic
36C22×C4×C149C2×C411yescharacteristic
37C22×C4×C149C2×C411yescharacteristic
38C42×C149—22no—
39#11924753—28no—
40C22×D149—21no—
41C22×D149—21no—
42C22×D149—21no—
43C22×D149—21no—
44C22×D149C4212yes—
45C22×D149M1612yes—
46C22×D149M1612yes—
47C2×Dic149—21no—
48C2×Dic149—21no—
49C2×Dic149—21no—
50C2×Dic149—21no—
51C2×Dic149C22⋊C412yes—
52C2×Dic149M1612yes—
53C2×Dic149C22×C412yes—
54C2×Dic149C2×D412yes—
55C2×Dic149#4112yes—
56C4×D149—28no—
57C4×D149—28no—
58C4×D149—28no—
59C23×C149C22×C411yescharacteristic
60C2×C4×C149—21no—
61C2×C4×C149—21no—
62C2×C4×C149—21no—
63C2×C4×C149—21no—
64C2×C4×C149—21no—
65C2×C4×C149—21no—
66C2×C4×C149C4212yes—
67C2×C4×C149C22⋊C412yes—
68C2×C4×C149M1612yes—
69C22×C149C2×C4211yescharacteristic
70C22×C149C2×C22⋊C411yescharacteristic
71C22×C149#11711yescharacteristic
72C22×C149C2×M1611yescharacteristic
73C22×C149C2×M1611yescharacteristic
74C22×C149C2×M1611yescharacteristic
75C22×C149C2×M1611yescharacteristic
76C2×D149—22no—
77C2×D149—22no—
78C2×D149—22no—
79C2×D149—22no—
80C2×D149—22no—
81C2×D149—22no—
82C2×D149#9714yescomplemented
83C4×C149—22no—
84C4×C149—22no—
85C4×C149—22no—
86Dic149—22no—
87Dic149—22no—
88Dic149C4×D414yes—
89C2×C149C4×C22⋊C411yescharacteristic
90C2×C149C2×#9711yescharacteristic
91C2×C149C4×M1611yescharacteristic
92C2×C149#40711yescharacteristic
93C2×C149#40711yescharacteristic
94C2×C149#43211yescharacteristic
95C2×C149#43211yescharacteristic
96D149—24no—
97C149#174911yescharacteristic, complemented, Sylow
98#1749—1491nomaximal, Sylow
99C22×C42—1491no—
100C2×C22⋊C8—1492no—
101C2×#97—1492no—
102#336—1492no—
103C23×C4—1491no—
104C23×C4—1491no—
105C23×C4—1491no—
106C22×C8—1494no—
107C2×C42—2984no—
108C2×C42—1491no—
109C2×C42—1491no—
110C2×C42—1491no—
111C2×C42#1059701011yescharacteristic
112C22⋊C8—1498no—
113#97—2984no—
114C24—1491no—
115C22×C4—2982no—
116C22×C4—2982no—
117C22×C4—2982no—
118C22×C4—2982no—
119C22×C4—2982no—
120C22×C4—2982no—
121C22×C4—2982no—
122C22×C4—2982no—
123C22×C4—1491no—
124C22×C4—1491no—
125C22×C4—1494no—
126C22×C4—1491no—
127C22×C4C2×#1059701011yescharacteristic
128C22×C4C2×#1059701011yescharacteristic
129C22×C4C2×#1059701011yescharacteristic
130C2×C8—2984no—
131C2×C8—2984no—
132C2×C8—1498no—
133C42—22no—
134C42—2982no—
135C42—2982no—
136C42—1494no—
137C23—2981no—
138C23—2981no—
139C23—2981no—
140C23—2981no—
141C23—1492no—
142C23—1492no—
143C23—1492no—
144C23C22×#1059701011yescharacteristic
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—2988no—
152C2×C4—2988no—
153C2×C4—2988no—
154C2×C4—2981no—
155C2×C4—2981no—
156C2×C4—2981no—
157C2×C4—2981no—
158C2×C4—1492no—
159C2×C4—1492no—
160C2×C4—1492no—
161C2×C4—1492no—
162C2×C4—1492no—
163C2×C4C4×#1059701012yes—
164C2×C4C22⋊#1059701012yes—
165C2×C4#1455874612yes—
166C8—2988no—
167C22—2982no—
168C22—2982no—
169C22—2982no—
170C22—2982no—
171C22—2982no—
172C22—2982no—
173C22—1494no—
174C22C2×C4×#1059701011yescharacteristic
175C22C2×C22⋊#1059701011yescharacteristic
176C22#1801199011yescharacteristic
177C22D149⋊M1611yescharacteristic
178C22D149⋊M1611yescharacteristic
179C22D149⋊M1611yescharacteristic
180C22C2×#1455874611yescharacteristic
181C4—22no—
182C4—22no—
183C4—22no—
184C4—2982no—
185C4—2982no—
186C4—1494no—
187C2—2984no—
188C2C4×C22⋊#1059701011yescharacteristic
189C2#2375058411yescharacteristic
190C2C4×#1455874611yescharacteristic
191C2#2375059611yescharacteristic
192C2#2375059711yescharacteristic
193C2#2375064711yescharacteristic
194C2#2375064811yescharacteristic
subgroupG/H
center, FrattiniC23C22×#10597010
commutatorC22×C149C2×C42
FittingC2×C42×C149C4
socleC23×C149C22×C4
prime radicalC23×D149C2×C4
cosocleC22×Dic149C23
hypercenterC2×C42#10597010
hypocenterC149#1749
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×#18011966C2semidirect
3. #23750491C2semidirect
6. #18011968C4semidirect
18. C2×#11924753C2×C4semidirect
82. C2×D149#97semidirect
97. C149#1749semidirect

Maximal subgroups

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

subgroupindex
C2×#180119682
C2×#180119662
#237504912
C2×C42×D1492
#1749149