Finite Group Databasebeta

← #34055155

Subgroups — #34055155

Order 19072.

572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 149 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×#18011942C212yesmaximal, complemented
2C2×#18011937C212yesmaximal, complemented
3#23750175C211yesmaximal, characteristic, complemented
4#23750020C212yesmaximal, complemented
5#23750015C212yesmaximal, complemented
6#23750007C214yesmaximal, complemented
7C4×#14558720C211yesmaximal, characteristic, complemented
8C2×#124×C149C211yesmaximal, characteristic, complemented
9C2×#14558736C2212yes—
10#18011942—28no—
11#18011937—28no—
12C2×#14558726C2214yescomplemented
13C2×#14558724C2214yes—
14C2×#14558723C2214yescomplemented
15C2×#14558721C2214yes—
16C2×#14558720C2212yes—
17#18011911C2211yescharacteristic, complemented
18#18011908C2211yescharacteristic, complemented
19#18011899C2212yescomplemented
20#18011885—22no—
21C4×D596—22no—
22#18011822C2212yescomplemented
23C4×#11924746C2212yescomplemented
24C22×Q8×C149C2211yescharacteristic
25C22×D4×C149C2211yescharacteristic
26#124×C149—22no—
27#124×C149C2212yes—
28#124×C149C2212yes—
29C2×C22⋊C4×C149—22no—
30C2×C42×C149C2211yescharacteristic
31#14558736—24no—
32#14558736—24no—
33C2×Dic298C2312yes—
34C2×D596—22no—
35C2×D596C2312yes—
36C2×C22⋊D149—22no—
37C2×C4×D149—22no—
38#14558726—28no—
39#14558724—28no—
40#14558723—28no—
41#14558721—28no—
42#14558720D418yescomplemented
43C2×#11924746C2314yes—
44C4⋊Dic149—22no—
45#14558713—24no—
46C24×C149—21no—
47C2×Q8×C149—21no—
48C2×Q8×C149—24no—
49C2×Q8×C149C2312yes—
50C2×D4×C149—24no—
51C2×D4×C149—21no—
52C2×D4×C149C2312yes—
53C22×C4×C149—21no—
54C22×C4×C149D412yes—
55C22×C4×C149C2311yescharacteristic
56C22⋊C4×C149—24no—
57C22⋊C4×C149—24no—
58C42×C149D412yes—
59C42×C149C2311yescharacteristic
60C42×C149C2311yescharacteristic
61C22×D149—22no—
62Dic298—22no—
63Dic298—22no—
64D596—22no—
65D596—22no—
66D596—44no—
67C22⋊D149—44no—
68C2×Dic149—22no—
69C4×D149—44no—
70#11924746C2×D418yes—
71C23×C149—22no—
72C23×C149—44no—
73C23×C149—42no—
74C23×C149C2×D411yescharacteristic
75Q8×C149—24no—
76Q8×C149—42no—
77D4×C149—24no—
78D4×C149—42no—
79C2×C4×C149—22no—
80C2×C4×C149—42no—
81C2×C4×C149—42no—
82C2×C4×C149C2×D414yes—
83C2×C4×C149C2×D412yes—
84C2×C4×C149C2×D412yes—
85C2×C4×C149C2×D411yescharacteristic
86C2×C4×C149C2411yescharacteristic
87C22×C149—22no—
88C22×C149—42no—
89C22×C149—44no—
90C22×C149—84no—
91C22×C149#12712yes—
92C22×C149C22×D411yescharacteristic
93C2×D149—42no—
94C2×D149—44no—
95C4×C149—22no—
96C4×C149—22no—
97C4×C149—42no—
98C4×C149#12712yes—
99C4×C149C22×D412yes—
100Dic149—42no—
101C2×C149—22no—
102C2×C149—82no—
103C2×C149C2×#12711yescharacteristic
104C2×C149#57512yes—
105D149—82no—
106C149#315311yescharacteristic, complemented, Sylow
107#3153—1491nomaximal, Sylow
108C2×#137—1492no—
109C2×AGL(1,ℤ/8)—1492no—
110#532—1491no—
111C2×#124D14911yescharacteristic, complemented
112#497—1492no—
113#496—1492no—
114#495—1494no—
115C4×M16—1491no—
116C2×#41—1492no—
117C22×Q8C2×D14911yescharacteristic
118C22×D4C2×D14911yescharacteristic
119#137—2988no—
120AGL(1,ℤ/8)—2988no—
121C2×Q16—1494no—
122C2×SD16—1494no—
123C2×SD16—1494no—
124C2×D8—1494no—
125C2×M16—1492no—
126C4⋊Q8—1491no—
127#127—1491no—
128#124—22no—
129#124—1492no—
130#124C2×D14912yes—
131#124C2×D14912yes—
132#121—2982no—
133C4×D4—2982no—
134C2×C22⋊C4—22no—
135C2×C42C2×D14911yescharacteristic
136#97—1492no—
137C4×C8—1492no—
138C24—21no—
139#41—2984no—
140#41—2984no—
141C2×Q8—21no—
142C2×Q8—24no—
143C2×Q8—1492no—
144C2×Q8C22×D14912yes—
145C2×D4—24no—
146C2×D4—21no—
147C2×D4—2982no—
148C2×D4—2982no—
149C2×D4—1492no—
150C2×D4C22×D14912yes—
151C22×C4—21no—
152C22×C4—2982no—
153C22×C4C22⋊D14912yes—
154C22×C4C22×D14911yescharacteristic
155Q16—2988no—
156SD16—2988no—
157SD16—2988no—
158D8—2988no—
159M16—1498no—
160C2×C8—1494no—
161C4⋊C4—2982no—
162C22⋊C4—24no—
163C22⋊C4—24no—
164C22⋊C4—2984no—
165C42C22⋊D14912yes—
166C42C22×D14911yescharacteristic
167C42C22×D14911yescharacteristic
168C23—22no—
169C23—44no—
170C23—42no—
171C23—2982no—
172C23C2×C22⋊D14911yescharacteristic
173Q8—24no—
174Q8—42no—
175Q8—2982no—
176Q8—2982no—
177D4—24no—
178D4—42no—
179D4—2982no—
180D4—2982no—
181D4—5964no—
182D4—5964no—
183C2×C4—22no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—2982no—
187C2×C4—5964no—
188C2×C4D4×D14914yes—
189C2×C4C2×C22⋊D14912yes—
190C2×C4C2×C22⋊D14912yes—
191C2×C4C2×C22⋊D14911yescharacteristic
192C2×C4C23×D14911yescharacteristic
193C8—1498no—
194C22—22no—
195C22—42no—
196C22—44no—
197C22—84no—
198C22—5962no—
199C22—5964no—
200C22#1801190712yes—
201C22C22×C22⋊D14911yescharacteristic
202C4—22no—
203C4—22no—
204C4—42no—
205C4—5962no—
206C4#1801190712yes—
207C4C2×D4×D14912yes—
208C2—22no—
209C2—82no—
210C2—11922no—
211C2C2×#1801190711yescharacteristic
212C2#2375042312yes—
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×#124×C149C2
socleC22×C149C22×D4
hypercenterC2×#124D149
hypocenterC149#3153
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#18011942C2semidirect
2. C2×#18011937C2semidirect
3. #23750175C2semidirect
4. #23750020C2semidirect
5. #23750015C2semidirect
6. #23750007C2semidirect
7. C4×#14558720C2semidirect
8. C2×#124×C149C2semidirect
12. C2×#14558726C22semidirect
14. C2×#14558723C22semidirect
17. #18011911C22semidirect
18. #18011908C22semidirect
19. #18011899C22semidirect
22. #18011822C22semidirect
23. C4×#11924746C22semidirect
42. #14558720D4semidirect
106. C149#3153semidirect
111. C2×#124D149semidirect

Maximal subgroups

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

subgroupindex
C2×#180119422
C2×#180119372
#237501752
#237500202
#237500152
#237500072
C4×#145587202
C2×#124×C1492
#3153149