Finite Group Databasebeta

← #34054790

Subgroups — #34054790

Order 19072.

444 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 133 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
1#23750182C211yesmaximal, characteristic, complemented
2#23749960C212yesmaximal, complemented
3#23749905C212yesmaximal, complemented
4#23749830C212yesmaximal, complemented
5#23749776C212yesmaximal
6#23749725C214yesmaximal, complemented
7#23749682C211yesmaximal, characteristic, complemented
8C2×C4×D4×C149C211yesmaximal, characteristic
9C2×#14558724C2214yes—
10#18011911C2211yescharacteristic, complemented
11#18011911C2211yescharacteristic, complemented
12#18011903—21no—
13#18011890—21no—
14#18011890C2212yes—
15C4×Dic298—21no—
16C4×Dic298C2212yescomplemented
17#18011870—21no—
18#18011844C2214yescomplemented
19C4⋊#11924746C2212yescomplemented
20#18011834C2214yescomplemented
21#18011832C2214yes—
22C22⋊#11924746C2212yes—
23#18011822C2212yescomplemented
24C22×D4×C149C2211yescharacteristic
25C23×C4×C149—21no—
26C4×D4×C149—21no—
27C4×D4×C149—21no—
28C4×D4×C149C2212yes—
29C4×D4×C149C2212yes—
30C2×C4⋊C4×C149C2211yescharacteristic
31C2×C22⋊C4×C149—21no—
32C2×C42×C149C2211yescharacteristic
33C2×Dic298—21no—
34C2×Dic298C2312yes—
35#14558724—28no—
36C2×#11924746C2314yes—
37C4⋊Dic149—21no—
38C4⋊Dic149—21no—
39C4⋊Dic149—21no—
40C4⋊Dic149C2312yes—
41#14558715—22no—
42#14558715—22no—
43C22⋊Dic149—22no—
44C4×Dic149—22no—
45C24×C149—21no—
46C2×D4×C149—24no—
47C2×D4×C149—21no—
48C2×D4×C149C2312yes—
49C22×C4×C149—21no—
50C22×C4×C149—22no—
51C22×C4×C149—22no—
52C22×C4×C149—44no—
53C22×C4×C149D411yescharacteristic
54C22×C4×C149D411yescharacteristic
55C22×C4×C149C2311yescharacteristic
56C4⋊C4×C149—21no—
57C4⋊C4×C149C2312yes—
58C22⋊C4×C149—22no—
59C22⋊C4×C149—22no—
60C42×C149D411yescharacteristic
61C42×C149D411yescharacteristic
62C42×C149C2311yescharacteristic
63C42×C149C2311yescharacteristic
64Dic298—24no—
65Dic298—42no—
66C2×Dic149—22no—
67C2×Dic149—22no—
68#11924746—24no—
69C23×C149—24no—
70C23×C149—22no—
71C23×C149—42no—
72C23×C149—42no—
73C23×C149C2×D411yescharacteristic
74D4×C149—24no—
75D4×C149—22no—
76D4×C149#4114yes—
77C2×C4×C149—22no—
78C2×C4×C149—22no—
79C2×C4×C149—22no—
80C2×C4×C149—22no—
81C2×C4×C149—44no—
82C2×C4×C149—42no—
83C2×C4×C149—44no—
84C2×C4×C149C2×D411yescharacteristic
85C2×C4×C149C2×D411yescharacteristic
86C2×C4×C149C2×D411yescharacteristic
87C2×C4×C149C2×D411yescharacteristic
88C2×C4×C149C2×D411yescharacteristic
89C2×C4×C149C2411yescharacteristic
90C22×C149—21no—
91C22×C149—21no—
92C22×C149—24no—
93C22×C149—48no—
94C22×C149—42no—
95C22×C149—42no—
96C22×C149#13712yes—
97C22×C149C22×D411yescharacteristic
98C4×C149—21no—
99C4×C149—21no—
100C4×C149—21no—
101C4×C149—21no—
102C4×C149—42no—
103C4×C149AGL(1,ℤ/8)12yes—
104C4×C149C2×#4112yes—
105Dic149—42no—
106Dic149—42no—
107C2×C149—22no—
108C2×C149—44no—
109C2×C149#52511yescharacteristic
110C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
111C2×C149C2×#13711yescharacteristic
112C149#311011yescharacteristic, complemented, Sylow
113#3110—1491nomaximal, Sylow
114#533—1491no—
115C2×C4×D4D14911yescharacteristic
116#484—1492no—
117#474—1492no—
118#461—1492no—
119#450—1492no—
120#440—1494no—
121#432—1491no—
122C22×D4C2×D14911yescharacteristic
123C23×C4—21no—
124C2×SD16—1494no—
125C4⋊Q8—1491no—
126C4⋊Q8—1491no—
127#125—2981no—
128C22⋊Q8—2981no—
129C22⋊Q8—1492no—
130C4×Q8—2981no—
131C4×Q8—1492no—
132C4×D4—21no—
133C4×D4—21no—
134C4×D4C2×D14912yes—
135C4×D4C2×D14912yes—
136#117—2981no—
137C2×C4⋊C4C2×D14911yescharacteristic
138C2×C22⋊C4—21no—
139C2×C42C2×D14911yescharacteristic
140#107—1494no—
141C4⋊C8—1492no—
142#103—1494no—
143#102—1494no—
144C22⋊C8—1492no—
145#97—1492no—
146C24—21no—
147C2×Q8—2981no—
148C2×Q8—1492no—
149C2×D4—24no—
150C2×D4—21no—
151C2×D4C22×D14912yes—
152C22×C4—21no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—44no—
156C22×C4C22⋊D14911yescharacteristic
157C22×C4C22⋊D14911yescharacteristic
158C22×C4C22×D14911yescharacteristic
159SD16—2988no—
160C2×C8—1494no—
161C4⋊C4—21no—
162C4⋊C4—2981no—
163C4⋊C4—2981no—
164C4⋊C4—2981no—
165C4⋊C4—2982no—
166C4⋊C4—2982no—
167C4⋊C4—1492no—
168C4⋊C4C22×D14912yes—
169C22⋊C4—22no—
170C22⋊C4—22no—
171C22⋊C4—2982no—
172C42—2982no—
173C42C22⋊D14911yescharacteristic
174C42C22⋊D14911yescharacteristic
175C42C22×D14911yescharacteristic
176C42C22×D14911yescharacteristic
177C23—24no—
178C23—22no—
179C23—42no—
180C23—42no—
181C23C2×C22⋊D14911yescharacteristic
182Q8—2984no—
183Q8—5962no—
184D4—24no—
185D4—22no—
186D4#1455873614yes—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—44no—
192C2×C4—42no—
193C2×C4—44no—
194C2×C4—2982no—
195C2×C4—2982no—
196C2×C4C2×C22⋊D14911yescharacteristic
197C2×C4C2×C22⋊D14911yescharacteristic
198C2×C4C2×C22⋊D14911yescharacteristic
199C2×C4C2×C22⋊D14911yescharacteristic
200C2×C4C2×C22⋊D14911yescharacteristic
201C2×C4C23×D14911yescharacteristic
202C8—2984no—
203C22—21no—
204C22—21no—
205C22—24no—
206C22—48no—
207C22—42no—
208C22—42no—
209C22#1801194112yes—
210C22C22×C22⋊D14911yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—21no—
215C4—42no—
216C4—5962no—
217C4—5962no—
218C4#1801193712yes—
219C4C2×#1455873612yes—
220C2—22no—
221C2—44no—
222C2#2375013611yescharacteristic
223C2C2×#1801193711yescharacteristic
224C2C2×#1801194111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×C4×D4×C149C2
socleC22×C149C22×D4
prime radicalC22×D4×C149C22
hypercenterC2×C4×D4D149
hypocenterC149#3110
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #23750182C2semidirect
2. #23749960C2semidirect
3. #23749905C2semidirect
4. #23749830C2semidirect
6. #23749725C2semidirect
7. #23749682C2semidirect
10. #18011911C22semidirect
11. #18011911C22semidirect
16. C4×Dic298C22semidirect
18. #18011844C22semidirect
19. C4⋊#11924746C22semidirect
20. #18011834C22semidirect
23. #18011822C22semidirect
112. C149#3110semidirect

Maximal subgroups

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

subgroupindex
#237501822
#237499602
#237499052
#237498302
#237497762
#237497252
#237496822
C2×C4×D4×C1492
#3110149