Finite Group Databasebeta

← #34047409

Subgroups — #34047409

Order 19072.

516 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 197 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#23749512C214yesmaximal
6#23749507C214yesmaximal
7#23749490C211yesmaximal, characteristic
8#23749471C211yesmaximal, characteristic
9#391×C149C211yesmaximal, characteristic
10C22×Dic298C2211yescharacteristic
11#18011909C418yescomplemented
12Q8×Dic149—24no—
13#18011876—24no—
14C2×C4⋊Dic149C2211yescharacteristic
15C2×C4⋊Dic149C2212yes—
16C2×#14558715C2212yes—
17C2×#14558715C2214yes—
18C2×C4×Dic149C2212yes—
19C2×C4×Dic149C2212yes—
20C2×C4×Dic149C2211yescharacteristic
21C2×C4×Dic149C2211yescharacteristic
22#18011818C2212yes—
23#18011818C2212yes—
24#18011818C2214yes—
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×Dic149C2312yes—
36C22×Dic149C2311yescharacteristic
37C22×Dic149C2311yescharacteristic
38C4⋊Dic149—24no—
39C4⋊Dic149—22no—
40#14558715—24no—
41#14558715C2×C4116yes—
42C4×Dic149—24no—
43C4×Dic149—24no—
44C4×Dic149C2×C414yes—
45C4×Dic149D414yes—
46C2×Q8×C149—22no—
47C2×Q8×C149—22no—
48C2×Q8×C149C2×C414yes—
49C22×C4×C149C2312yes—
50C22×C4×C149C2312yes—
51C22×C4×C149C2312yes—
52C22×C4×C149C2311yescharacteristic
53C4⋊C4×C149—22no—
54C42×C149—22no—
55Dic298—28no—
56C2×Dic149—22no—
57C2×Dic149—22no—
58C2×Dic149—22no—
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—
68C23×C149C2411yescharacteristic
69Q8×C149—28no—
70C2×C4×C149—22no—
71C2×C4×C149—22no—
72C2×C4×C149—22no—
73C2×C4×C149—22no—
74C2×C4×C149—24no—
75C2×C4×C149—22no—
76C2×C4×C149—22no—
77C2×C4×C149C22×C414yes—
78C2×C4×C149C22×C412yes—
79C2×C4×C149C2×D412yes—
80C2×C4×C149#4112yes—
81C22×C149C23×C411yescharacteristic
82C22×C149C22×D411yescharacteristic
83C22×C149C2×#4111yescharacteristic
84C22×C1492−1+412yes—
85C22×C1492−1+412yes—
86C4×C149—24no—
87C4×C149—42no—
88C4×C149—42no—
89C4×C149C4×D414yes—
90Dic149—24no—
91Dic149—24no—
92Dic149—22no—
93Dic149—22no—
94Dic149—42no—
95C2×C149C2×C4×D411yescharacteristic
96C2×C149#51912yes—
97C2×C149#53611yescharacteristic
98C2×C149#53611yescharacteristic
99C2×C149#54112yes—
100C149#232711yescharacteristic, complemented, Sylow
101#2327—1491nomaximal, Sylow
102C2×C4⋊Q8—1491no—
103C2×C4×Q8—1491no—
104C2×C4×Q8—1491no—
105#391—1491no—
106#391D14911yescharacteristic
107#387—1494no—
108#387—1494no—
109#382—1491no—
110#376—1491no—
111C22×Q8—1491no—
112C22×Q8C2×D14911yescharacteristic
113C4⋊Q8—1498no—
114C4×Q8—2984no—
115C4×Q8—2984no—
116C2×C4⋊C4—1491no—
117C2×C4⋊C4—1492no—
118C2×C4⋊C4—1492no—
119C2×C4⋊C4—1494no—
120C2×C4⋊C4C2×D14911yescharacteristic
121C2×C42—1492no—
122C2×C42—1492no—
123C2×C42—1491no—
124C2×C42—1491no—
125C2×C42C2×D14911yescharacteristic
126#95—1492no—
127#95—1492no—
128#95—1494no—
129#95—1494no—
130#95C2×D14914yes—
131C2×Q8—22no—
132C2×Q8—22no—
133C2×Q8—2982no—
134C2×Q8—2982no—
135C2×Q8—1494no—
136C2×Q8C4×D14914yes—
137C22×C4—1492no—
138C22×C4—1492no—
139C22×C4—1491no—
140C22×C4—1491no—
141C22×C4—1492no—
142C22×C4C22×D14912yes—
143C22×C4C22×D14912yes—
144C22×C4C22×D14912yes—
145C22×C4C22×D14911yescharacteristic
146C4⋊C4—22no—
147C4⋊C4—2984no—
148C4⋊C4—2984no—
149C4⋊C4—2982no—
150C4⋊C4—14916no—
151C42—22no—
152C42—2984no—
153C42—2984no—
154C42—1494no—
155C42—1494no—
156C23C23×D14911yescharacteristic
157Q8—28no—
158Q8—2988no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—24no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—2982no—
167C2×C4—2982no—
168C2×C4—2982no—
169C2×C4—2982no—
170C2×C4—2982no—
171C2×C4—2982no—
172C2×C4—2982no—
173C2×C4—2984no—
174C2×C4—1494no—
175C2×C4—1494no—
176C2×C4—1492no—
177C2×C4—1492no—
178C2×C4C2×C4×D14914yes—
179C2×C4C2×C4×D14912yes—
180C2×C4D4×D14912yes—
181C2×C4#1455873512yes—
182C22C22×C4×D14911yescharacteristic
183C22C2×D4×D14911yescharacteristic
184C22C2×#1455873511yescharacteristic
185C22#1801195812yes—
186C22#1801195912yes—
187C4—24no—
188C4—42no—
189C4—42no—
190C4—2982no—
191C4—2982no—
192C4—2984no—
193C4—2984no—
194C4—5962no—
195C4#1801187114yes—
196C2C2×#1801187111yescharacteristic
197C2#2375010112yes—
198C2#2375019511yescharacteristic
199C2#2375020011yescharacteristic
200C2#2375023512yes—
subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
Fitting#391×C149C2
socle, prime radical, cosocleC23×C149C24
hypercenter#391D149
hypocenterC149#2327
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
11. #18011909C4semidirect
100. C149#2327semidirect

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
#237495122
#237495072
#237494902
#237494712
#391×C1492
#2327149