Finite Group Databasebeta

← C2×#23749680 #34053310

Subgroups — C2×#23749680 #34053310

Order 19072.

488 conjugacy classes of subgroups; only the 205 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 205 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×C42×D149C211yesmaximal, characteristic
2#23749680C218yesmaximal, direct product factor
3C2×#18011840C212yesmaximal, complemented
4C2×#18011823C212yesmaximal
5C2×#18011822C211yesmaximal, characteristic, complemented
6C2×#97×C149C211yesmaximal, characteristic, complemented
7C22×C4×D149C411yescharacteristic
8C22×C4×D149C411yescharacteristic
9C22×C4×D149C2211yescharacteristic
10C22×#11924746C2212yes—
11C2×C4×Dic149C411yescharacteristic
12C2×C4×Dic149C411yescharacteristic
13C2×C4×Dic149C2211yescharacteristic
14C42×D149C414yes—
15C42×D149C2214yes—
16#18011840C2218yescomplemented
17#18011823C2218yes—
18#18011822C2214yescomplemented
19C22×C8×C149C2212yes—
20C2×C42×C149C2211yescharacteristic
21#97×C149C2214yescomplemented
22C23×D149C2×C411yescharacteristic
23C22×Dic149C2×C411yescharacteristic
24C22×Dic149C2×C411yescharacteristic
25C22×Dic149C2×C411yescharacteristic
26C2×C4×D149—24no—
27C2×C4×D149—24no—
28C2×C4×D149—24no—
29C2×C4×D149C2×C414yes—
30C2×C4×D149C2×C414yes—
31C2×C4×D149C2×C412yes—
32C2×C4×D149C2312yes—
33C2×#11924746—24no—
34C2×#11924746C2314yes—
35C4×Dic149C2×C412yes—
36C4×Dic149C2×C414yes—
37C4×Dic149C2×C414yes—
38C4×Dic149C2312yes—
39C22×C4×C149C2×C411yescharacteristic
40C22×C4×C149C2×C411yescharacteristic
41C22×C4×C149C2311yescharacteristic
42C2×C8×C149—24no—
43C2×C8×C149C2314yes—
44C42×C149C2×C412yes—
45C42×C149C2312yes—
46C22×D149—22no—
47C22×D149—22no—
48C22×D149M1614yes—
49C22×D149C22×C412yes—
50C2×Dic149—22no—
51C2×Dic149—22no—
52C2×Dic149M1614yes—
53C2×Dic149C22×C412yes—
54C2×Dic149C22×C412yes—
55C2×Dic149C22×C412yes—
56C4×D149—28no—
57C4×D149—24no—
58C4×D149—24no—
59C4×D149—28no—
60#11924746—24no—
61C23×C149C22×C411yescharacteristic
62C2×C4×C149—22no—
63C2×C4×C149—22no—
64C2×C4×C149C22×C412yes—
65C2×C4×C149C22×C412yes—
66C2×C4×C149C22×C411yescharacteristic
67C2×C4×C149#4114yes—
68C2×C4×C149C2411yescharacteristic
69C8×C149—24no—
70C22×C149#11712yes—
71C22×C149C2×M1612yes—
72C22×C149C2×M1612yes—
73C22×C149C23×C411yescharacteristic
74C2×D149—22no—
75C2×D149—22no—
76C2×D149—28no—
77C2×D149C2×M1614yes—
78C4×C149—22no—
79C4×C149—22no—
80C4×C149#11712yes—
81C4×C149C2×#4112yes—
82Dic149—22no—
83Dic149—22no—
84Dic149C2×M1614yes—
85C2×C149#43214yescomplemented
86C2×C149C2×#11711yescharacteristic
87C2×C149C22×M1611yescharacteristic
88C2×C149C22×M1611yescharacteristic
89D149—24no—
90C149C2×#43211yescharacteristic, complemented, Sylow
91C2×#432—1491nomaximal, Sylow
92C22×C42—1491no—
93#432—1498no—
94C2×C4⋊C8—1492no—
95C2×C22⋊C8—1492no—
96C2×#97—1491no—
97C2×#97D14911yescharacteristic, complemented
98C23×C4—1491no—
99C23×C4—1491no—
100C23×C4—1491no—
101C22×C8—1492no—
102C22×C8C2×D14912yes—
103C2×C42—1491no—
104C2×C42—1491no—
105C2×C42—1491no—
106C2×C42—1494no—
107C2×C42—1494no—
108C2×C42C2×D14911yescharacteristic
109C4⋊C8—1498no—
110C22⋊C8—1498no—
111#97—1494no—
112#97C2×D14914yescomplemented
113C24—1491no—
114C22×C4—2984no—
115C22×C4—2984no—
116C22×C4—2984no—
117C22×C4—1491no—
118C22×C4—1491no—
119C22×C4—1494no—
120C22×C4—1494no—
121C22×C4—1492no—
122C22×C4—1492no—
123C22×C4—1491no—
124C22×C4C4×D14911yescharacteristic
125C22×C4C4×D14911yescharacteristic
126C22×C4C22×D14911yescharacteristic
127C2×C8—24no—
128C2×C8—2984no—
129C2×C8—1494no—
130C2×C8C22×D14914yes—
131C42—1494no—
132C42—1494no—
133C42—1492no—
134C42—1492no—
135C42C4×D14912yes—
136C42C22×D14912yes—
137C23—2982no—
138C23—2982no—
139C23—1494no—
140C23—1492no—
141C23C2×C4×D14911yescharacteristic
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—2988no—
145C2×C4—2988no—
146C2×C4—2982no—
147C2×C4—2982no—
148C2×C4—2984no—
149C2×C4—2984no—
150C2×C4—1492no—
151C2×C4—1492no—
152C2×C4—1494no—
153C2×C4—1492no—
154C2×C4C2×C4×D14912yes—
155C2×C4C2×C4×D14912yes—
156C2×C4C2×C4×D14911yescharacteristic
157C2×C4#1455873614yes—
158C2×C4C23×D14911yescharacteristic
159C8—24no—
160C8—2984no—
161C22—2988no—
162C22—2982no—
163C22—2982no—
164C22—1494no—
165C22#1801186812yes—
166C22M16×D14912yes—
167C22M16×D14912yes—
168C22C22×C4×D14911yescharacteristic
169C4—22no—
170C4—22no—
171C4—2982no—
172C4—2982no—
173C4—1494no—
174C4#1801186812yes—
175C4C2×#1455873612yes—
176C2—2984no—
177C2#2374968014yesdirect product factor
178C2C2×#1801186811yescharacteristic
179C2C2×M16×D14911yescharacteristic
180C2C2×M16×D14911yescharacteristic
subgroupG/H
centerC22×C4C22×D149
commutatorC22×C149C23×C4
FrattiniC2×C4C23×D149
FittingC2×#97×C149C2
socleC23×C149C22×C4
prime radicalC23×D149C2×C4
cosocleC2×C4×C149C24
hypercenterC2×#97D149
hypocenterC149C2×#432
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C22×C4 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
2. #23749680C2direct (N × H)
3. C2×#18011840C2semidirect
5. C2×#18011822C2semidirect
6. C2×#97×C149C2semidirect
16. #18011840C22semidirect
18. #18011822C22semidirect
21. #97×C149C22semidirect
85. C2×C149#432semidirect
90. C149C2×#432semidirect
97. C2×#97D149semidirect
112. #97C2×D149semidirect
177. C2#23749680direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C42×D1492
#237496802
C2×#180118402
C2×#180118232
C2×#180118222
C2×#97×C1492
C2×#432149