Finite Group Databasebeta

← #34055157

Subgroups — #34055157

Order 19072.

572 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 165 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×#18011944C212yesmaximal, complemented
2C2×#18011939C212yesmaximal, complemented
3#23750175C211yesmaximal, characteristic, complemented
4C2×#18011899C211yesmaximal, characteristic, complemented
5#23750019C212yesmaximal, complemented
6#23750014C212yesmaximal, complemented
7#23750009C214yesmaximal, complemented
8C4×M16×C149C211yesmaximal, characteristic, complemented
9C2×#14558736C2212yes—
10C22×Dic298C2211yescharacteristic
11C22×D596C2211yescharacteristic
12#18011944—28no—
13#18011939—28no—
14C2×Dic596C2214yescomplemented
15C2×#14558725C2214yes—
16C2×#14558725C2214yescomplemented
17C2×D1192C2214yes—
18#18011911C2211yescharacteristic, complemented
19#18011908C2211yescharacteristic, complemented
20#18011899—22no—
21#18011899C2212yes—
22#18011899C2212yes—
23#18011899C2212yescomplemented
24#18011885—22no—
25C4×D596—22no—
26C2×#14558713—22no—
27C2×M16×C149C2212yes—
28C2×C42×C149C2211yescharacteristic
29#97×C149C2212yescomplemented
30C4×C8×C149C2212yescomplemented
31C23×D149—21no—
32#14558736—24no—
33#14558736—24no—
34C2×Dic298—21no—
35C2×Dic298—24no—
36C2×Dic298C2312yes—
37C2×Dic298C2312yes—
38C2×D596—24no—
39C2×D596—22no—
40C2×D596—21no—
41C2×D596C2312yes—
42C2×D596C2312yes—
43C2×C22⋊D149—22no—
44C22×Dic149—21no—
45C2×C4×D149—22no—
46Dic596—28no—
47#14558725—28no—
48#14558725—28no—
49D1192—28no—
50C4⋊Dic149—22no—
51#14558713—24no—
52#14558713—24no—
53#14558713—24no—
54C22×C4×C149D412yes—
55C22×C4×C149C2311yescharacteristic
56M16×C149D418yescomplemented
57C2×C8×C149C2314yes—
58C42×C149D412yes—
59C42×C149C2311yescharacteristic
60C42×C149C2311yescharacteristic
61C22×D149—22no—
62C22×D149—22no—
63C22×D149—44no—
64C22×D149—42no—
65Dic298—22no—
66Dic298—24no—
67Dic298—22no—
68Dic298—42no—
69D596—22no—
70D596—24no—
71D596—22no—
72D596—44no—
73D596—42no—
74C22⋊D149—44no—
75C2×Dic149—22no—
76C2×Dic149—22no—
77C2×Dic149—42no—
78C4×D149—44no—
79C23×C149C2×D411yescharacteristic
80C2×C4×C149—42no—
81C2×C4×C149C2×D412yes—
82C2×C4×C149C2×D412yes—
83C2×C4×C149C2×D411yescharacteristic
84C2×C4×C149C2×D414yes—
85C2×C4×C149C2411yescharacteristic
86C8×C149C2×D418yes—
87C22×C149—22no—
88C22×C149#12712yes—
89C22×C149C22×D411yescharacteristic
90C2×D149—42no—
91C2×D149—42no—
92C2×D149—44no—
93C2×D149—44no—
94C2×D149—84no—
95C4×C149—22no—
96C4×C149—22no—
97C4×C149#12712yes—
98C4×C149C22×D412yes—
99Dic149—42no—
100Dic149—42no—
101C2×C149—22no—
102C2×C149C2×#12711yescharacteristic
103C2×C149#57512yes—
104D149—82no—
105D149—82no—
106C149#315311yescharacteristic, complemented, Sylow
107#3153—1491nomaximal, Sylow
108C2×#137—1492no—
109C2×AGL(1,ℤ/8)—1492no—
110#532—1491no—
111C2×#124—1491no—
112#497—1492no—
113#496—1492no—
114#495—1494no—
115C4×M16D14911yescharacteristic, complemented
116C2×#41—1492no—
117C22×Q8—1491no—
118C22×D4—1491no—
119#137—2988no—
120AGL(1,ℤ/8)—2988no—
121C2×Q16—1494no—
122C2×SD16—1494no—
123C2×SD16—1494no—
124C2×D8—1494no—
125C2×M16C2×D14912yes—
126C4⋊Q8—1491no—
127#127—1491no—
128#124—2982no—
129#124—1492no—
130#124—1492no—
131#124—1492no—
132#121—2982no—
133C4×D4—2982no—
134C2×C22⋊C4—2982no—
135C2×C42C2×D14911yescharacteristic
136#97C2×D14912yescomplemented
137C4×C8C2×D14912yescomplemented
138C24—2981no—
139#41—2984no—
140#41—2984no—
141C2×Q8—2981no—
142C2×Q8—2984no—
143C2×Q8—1492no—
144C2×Q8—1492no—
145C2×D4—2982no—
146C2×D4—2984no—
147C2×D4—2982no—
148C2×D4—2981no—
149C2×D4—1492no—
150C2×D4—1492no—
151C22×C4—2981no—
152C22×C4—2982no—
153C22×C4D59612yes—
154C22×C4C22×D14911yescharacteristic
155Q16—2988no—
156SD16—2988no—
157SD16—2988no—
158D8—2988no—
159M16D59618yescomplemented
160C2×C8C22×D14914yes—
161C4⋊C4—2982no—
162C22⋊C4—2984no—
163C22⋊C4—2984no—
164C22⋊C4—2984no—
165C42D59612yes—
166C42C22×D14911yescharacteristic
167C42C22×D14911yescharacteristic
168C23—2982no—
169C23—2982no—
170C23—5964no—
171C23—5962no—
172C23C2×D59611yescharacteristic
173Q8—2982no—
174Q8—2984no—
175Q8—2982no—
176Q8—5962no—
177D4—2982no—
178D4—2984no—
179D4—2982no—
180D4—5964no—
181D4—5964no—
182D4—5962no—
183C2×C4—42no—
184C2×C4—2982no—
185C2×C4—2982no—
186C2×C4—5962no—
187C2×C4—5964no—
188C2×C4C2×D59612yes—
189C2×C4C2×D59612yes—
190C2×C4C2×D59611yescharacteristic
191C2×C4C2×D59614yes—
192C2×C4C23×D14911yescharacteristic
193C8C2×D59618yes—
194C22—22no—
195C22—5962no—
196C22—5962no—
197C22—5964no—
198C22—5964no—
199C22—11924no—
200C22#1801190812yes—
201C22C22×D59611yescharacteristic
202C4—22no—
203C4—22no—
204C4—5962no—
205C4—5962no—
206C4#1801190812yes—
207C4C22×D59612yes—
208C2—22no—
209C2—11922no—
210C2—11922no—
211C2C2×#1801190811yescharacteristic
212C2#2375042512yes—
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC4×M16×C149C2
socleC22×C149C22×D4
hypercenterC4×M16D149
hypocenterC149#3153
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
1. C2×#18011944C2semidirect
2. C2×#18011939C2semidirect
3. #23750175C2semidirect
4. C2×#18011899C2semidirect
5. #23750019C2semidirect
6. #23750014C2semidirect
7. #23750009C2semidirect
8. C4×M16×C149C2semidirect
14. C2×Dic596C22semidirect
16. C2×#14558725C22semidirect
18. #18011911C22semidirect
19. #18011908C22semidirect
23. #18011899C22semidirect
29. #97×C149C22semidirect
30. C4×C8×C149C22semidirect
56. M16×C149D4semidirect
106. C149#3153semidirect
115. C4×M16D149semidirect
136. #97C2×D149semidirect
137. C4×C8C2×D149semidirect
159. M16D596semidirect

Maximal subgroups

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

subgroupindex
C2×#180119442
C2×#180119392
#237501752
C2×#180118992
#237500192
#237500142
#237500092
C4×M16×C1492
#3153149