Finite Group Databasebeta

← #34047260

Subgroups — #34047260

Order 19072.

588 conjugacy classes of subgroups; only the 237 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 237 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×#18011909C211yesmaximal, characteristic
2C2×Q8×Dic149C211yesmaximal, characteristic
3C2×#18011876C211yesmaximal, characteristic
4#23749531C211yesmaximal, characteristic
5#23749522C214yesmaximal
6#23749494C211yesmaximal, characteristic
7#23749476C214yesmaximal
8C42×Dic149C211yesmaximal, characteristic
9#391×C149C211yesmaximal, characteristic
10C22×Dic298C2211yescharacteristic
11#18011909C418yescomplemented
12Q8×Dic149—24no—
13#18011876—24no—
14C2×C4⋊Dic149C2211yescharacteristic
15C2×C4⋊Dic149C2212yes—
16C2×#14558715C2214yes—
17C2×#14558715C2212yes—
18C2×#14558715C2214yes—
19C2×C4×Dic149C2212yes—
20C2×C4×Dic149C2212yes—
21C2×C4×Dic149C2212yes—
22C2×C4×Dic149C2211yescharacteristic
23C2×C4×Dic149C2211yescharacteristic
24C2×C4×Dic149C2212yes—
25#18011818C2214yes—
26C22×Q8×C149C2211yescharacteristic
27C2×C4⋊C4×C149C2211yescharacteristic
28C2×C42×C149C2211yescharacteristic
29#95×C149C2214yes—
30C2×Dic298—22no—
31C2×Dic298—22no—
32C2×Dic298C2×C414yes—
33C22×Dic149C2312yes—
34C22×Dic149C2312yes—
35C22×Dic149C2311yescharacteristic
36C22×Dic149C2312yes—
37C22×Dic149C2311yescharacteristic
38C4⋊Dic149—24no—
39C4⋊Dic149—22no—
40#14558715—24no—
41#14558715—28no—
42#14558715C2×C4116yes—
43C4×Dic149—24no—
44C4×Dic149—24no—
45C4×Dic149—24no—
46C4×Dic149C2×C414yes—
47C4×Dic149D414yes—
48C4×Dic149Q818yescomplemented
49C2×Q8×C149—22no—
50C2×Q8×C149—22no—
51C2×Q8×C149C2×C414yes—
52C22×C4×C149C2312yes—
53C22×C4×C149C2312yes—
54C22×C4×C149C2312yes—
55C22×C4×C149C2311yescharacteristic
56C4⋊C4×C149—22no—
57C42×C149—22no—
58Dic298—28no—
59C2×Dic149—22no—
60C2×Dic149—22no—
61C2×Dic149—22no—
62C2×Dic149—22no—
63C2×Dic149—24no—
64C2×Dic149C22×C414yes—
65C2×Dic149C22×C414yes—
66C2×Dic149C2×D412yes—
67C2×Dic149C2×D412yes—
68C2×Dic149C2×Q814yes—
69C2×Dic149C2×Q814yes—
70C2×Dic149#4114yes—
71C23×C149C2411yescharacteristic
72Q8×C149—28no—
73C2×C4×C149—22no—
74C2×C4×C149—22no—
75C2×C4×C149—22no—
76C2×C4×C149—22no—
77C2×C4×C149—22no—
78C2×C4×C149—24no—
79C2×C4×C149C22×C414yes—
80C2×C4×C149C22×C412yes—
81C2×C4×C149C2×D412yes—
82C2×C4×C149C2×Q814yes—
83C2×C4×C149#4112yes—
84C22×C149C23×C411yescharacteristic
85C22×C149C22×D411yescharacteristic
86C22×C149C22×Q812yes—
87C22×C149C2×#4112yes—
88C22×C149C2×#4111yescharacteristic
89C4×C149—24no—
90C4×C149—24no—
91C4×C149—42no—
92C4×C149C4×D414yes—
93Dic149—24no—
94Dic149—22no—
95Dic149—42no—
96Dic149C4×Q818yescomplemented
97Dic149C4⋊Q814yescomplemented
98C2×C149C2×C4×D411yescharacteristic
99C2×C149C2×C4×Q812yes—
100C2×C149C2×C4⋊Q811yescharacteristic
101C2×C149#53211yescharacteristic
102C2×C149#53312yes—
103C149C4×C4⋊Q811yescharacteristic, complemented, Sylow
104C4×C4⋊Q8—1491nomaximal, Sylow
105C2×C4⋊Q8—1491no—
106C2×C4×Q8—1491no—
107C2×C4×Q8—1491no—
108#391—1491no—
109#391D14911yescharacteristic
110#389—1494no—
111#384—1491no—
112C4×C4⋊C4—1494no—
113C43—1491no—
114C22×Q8—1491no—
115C22×Q8C2×D14911yescharacteristic
116C4⋊Q8—1498no—
117C4×Q8—2984no—
118C4×Q8—2984no—
119C2×C4⋊C4—1491no—
120C2×C4⋊C4—1492no—
121C2×C4⋊C4—1492no—
122C2×C4⋊C4—1494no—
123C2×C4⋊C4—1494no—
124C2×C4⋊C4C2×D14911yescharacteristic
125C2×C42—1492no—
126C2×C42—1492no—
127C2×C42—1492no—
128C2×C42—1491no—
129C2×C42—1491no—
130C2×C42—1492no—
131C2×C42C2×D14911yescharacteristic
132#95—1494no—
133#95C2×D14914yes—
134C2×Q8—22no—
135C2×Q8—22no—
136C2×Q8—2982no—
137C2×Q8—2982no—
138C2×Q8—1494no—
139C2×Q8C4×D14914yes—
140C22×C4—1492no—
141C22×C4—1492no—
142C22×C4—1491no—
143C22×C4—1491no—
144C22×C4—1492no—
145C22×C4C22×D14912yes—
146C22×C4C22×D14912yes—
147C22×C4C22×D14912yes—
148C22×C4C22×D14911yescharacteristic
149C4⋊C4—22no—
150C4⋊C4—2984no—
151C4⋊C4—2984no—
152C4⋊C4—2988no—
153C4⋊C4—2982no—
154C4⋊C4—14916no—
155C42—22no—
156C42—2984no—
157C42—2984no—
158C42—2984no—
159C42—1494no—
160C42—1494no—
161C42—1498no—
162C23C23×D14911yescharacteristic
163Q8—28no—
164Q8—2988no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—24no—
171C2×C4—2982no—
172C2×C4—2982no—
173C2×C4—2982no—
174C2×C4—2982no—
175C2×C4—2984no—
176C2×C4—1494no—
177C2×C4—1492no—
178C2×C4—1494no—
179C2×C4—1492no—
180C2×C4—1494no—
181C2×C4—1494no—
182C2×C4—1494no—
183C2×C4C2×C4×D14914yes—
184C2×C4C2×C4×D14912yes—
185C2×C4D4×D14912yes—
186C2×C4Q8×D14914yes—
187C2×C4#1455873512yes—
188C22C22×C4×D14911yescharacteristic
189C22C2×D4×D14911yescharacteristic
190C22C2×Q8×D14912yes—
191C22#41×D14912yes—
192C22C2×#1455873511yescharacteristic
193C4—24no—
194C4—24no—
195C4—42no—
196C4—2982no—
197C4—2984no—
198C4—5962no—
199C4—1494no—
200C4—1498no—
201C4#1801187114yes—
202C2C2×#1801187111yescharacteristic
203C2C4×Q8×D14912yes—
204C2C4⋊Q8×D14911yescharacteristic
205C2#2375017411yescharacteristic
206C2#2375017712yes—
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
Fitting#391×C149C2
socle, prime radical, cosocleC23×C149C24
hypercenter#391D149
hypocenterC149C4×C4⋊Q8
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
11. #18011909C4semidirect
48. C4×Dic149Q8semidirect
96. Dic149C4×Q8semidirect
97. Dic149C4⋊Q8semidirect
103. C149C4×C4⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#180119092
C2×Q8×Dic1492
C2×#180118762
#237495312
#237495222
#237494942
#237494762
C42×Dic1492
#391×C1492
C4×C4⋊Q8149