Finite Group Databasebeta

← #34045759

Subgroups — #34045759

Order 19072.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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#23750425C211yesmaximal, characteristic, complemented
2#23750137C212yesmaximal, complemented
3#23749643C212yesmaximal, complemented
4#23749588C211yesmaximal, characteristic, complemented
5H(3,ℤ/4)×C149C211yesmaximal, characteristic, complemented
6C2×#14558736C2212yes—
7C22×C4×D149C2211yescharacteristic
8#18011944—22no—
9#18011939—22no—
10#18011933—22no—
11C2×#14558720C2211yescharacteristic
12#18011895—22no—
13#18011891—22no—
14#18011886—22no—
15#18011881—22no—
16C4×D596—24no—
17#18011839—24no—
18#18011823—22no—
19C2×M16×C149C2211yescharacteristic
20#117×C149C2212yes—
21C23×D149D411yescharacteristic
22#14558736—22no—
23#14558736—22no—
24#14558736—22no—
25#14558736—22no—
26C2×Dic298D412yescomplemented
27C2×D596—24no—
28C2×D596D412yescomplemented
29C2×C22⋊D149—22no—
30C22×Dic149D411yescharacteristic
31C2×C4×D149—21no—
32C2×C4×D149—22no—
33C2×C4×D149—22no—
34C2×C4×D149—22no—
35C2×C4×D149—21no—
36Dic596—22no—
37#14558725—24no—
38D1192—22no—
39#14558720—22no—
40C2×#11924746—21no—
41C4⋊Dic149—24no—
42#14558713—24no—
43#14558713—24no—
44C22×C4×C149C2311yescharacteristic
45M16×C149—22no—
46C2×C8×C149D412yescomplemented
47C4⋊C4×C149—22no—
48C22⋊C4×C149—22no—
49C42×C149D414yescomplemented
50C22×D149—22no—
51C22×D149—21no—
52C22×D149—22no—
53C22×D149—42no—
54Dic298—22no—
55Dic298—22no—
56D596—22no—
57D596—22no—
58D596—48no—
59C22⋊D149—42no—
60C22⋊D149—42no—
61C2×Dic149—22no—
62C2×Dic149—22no—
63C2×Dic149—21no—
64C4×D149—41no—
65C4×D149—42no—
66C4×D149—42no—
67C4×D149—41no—
68C4×D149—42no—
69#11924746—41no—
70C23×C149C2×D411yescharacteristic
71C2×C4×C149—24no—
72C2×C4×C149C2×D412yes—
73C2×C4×C149C2×D411yescharacteristic
74C2×C4×C149C2×D412yes—
75C2×C4×C149#4111yescharacteristic
76C8×C149—22no—
77C22×C149—41no—
78C22×C149#12012yes—
79C22×C149#12111yescharacteristic
80C2×D149—24no—
81C2×D149—22no—
82C2×D149—42no—
83C2×D149—41no—
84C2×D149—41no—
85C2×D149—44no—
86C2×D149—42no—
87C4×C149—44no—
88C4×C149#12011yescharacteristic
89C4×C149#12112yes—
90C4×C149#12711yescharacteristic
91Dic149—41no—
92Dic149—42no—
93C2×C149—22no—
94C2×C149—21no—
95C2×C149#39211yescharacteristic
96D149—42no—
97D149—82no—
98C149#201011yescharacteristic, complemented, Sylow
99#2010—1491nomaximal, Sylow
100#575—1491no—
101#525—1492no—
102#421—1492no—
103#407—1491no—
104H(3,ℤ/4)D14911yescharacteristic, complemented
105C2×#41—1492no—
106C23×C4—1491no—
107#137—2982no—
108AGL(1,ℤ/8)—2982no—
109#135—2982no—
110C2×M16—1491no—
111C2×M16C2×D14911yescharacteristic
112#123—2982no—
113C22⋊Q8—2982no—
114#121—2982no—
115#120—2982no—
116C4×D4—2984no—
117#117C2×D14912yes—
118#104—2984no—
119C22⋊C8—2982no—
120C24—1491no—
121#41—2982no—
122#41—2982no—
123#41—2982no—
124#41—2982no—
125C2×Q8—1492no—
126C2×D4—2984no—
127C2×D4—2982no—
128C2×D4—1492no—
129C22×C4—2982no—
130C22×C4—2981no—
131C22×C4—2982no—
132C22×C4—2982no—
133C22×C4—2981no—
134C22×C4—1491no—
135C22×C4C22×D14911yescharacteristic
136Q16—2982no—
137SD16—2984no—
138D8—2982no—
139M16—22no—
140M16—2982no—
141C2×C8—2981no—
142C2×C8D59612yescomplemented
143C4⋊C4—22no—
144C4⋊C4—2984no—
145C22⋊C4—22no—
146C22⋊C4—2984no—
147C22⋊C4—2984no—
148C42D59614yescomplemented
149C23—2982no—
150C23—2981no—
151C23—2982no—
152C23—5962no—
153C23D4×D14911yescharacteristic
154Q8—2982no—
155Q8—2982no—
156D4—2982no—
157D4—2982no—
158D4—5968no—
159D4—5962no—
160D4—5962no—
161C2×C4—24no—
162C2×C4—2982no—
163C2×C4—2982no—
164C2×C4—2981no—
165C2×C4—5961no—
166C2×C4—5962no—
167C2×C4—5961no—
168C2×C4—5962no—
169C2×C4—5962no—
170C2×C4D4×D14912yes—
171C2×C4C2×D59611yescharacteristic
172C2×C4C2×D59612yes—
173C2×C4#1455873711yescharacteristic
174C8—22no—
175C8—5961no—
176C22—41no—
177C22—2984no—
178C22—2982no—
179C22—5962no—
180C22—5961no—
181C22—5964no—
182C22—5961no—
183C22—5962no—
184C22#1801188112yes—
185C22#1801188611yescharacteristic
186C4—44no—
187C4—5961no—
188C4—5962no—
189C4#1801188111yescharacteristic
190C4#1801188612yes—
191C4#1801190811yescharacteristic
192C2—22no—
193C2—21no—
194C2—5962no—
195C2—11922no—
196C2#2374953511yescharacteristic
subgroupG/H
centerC4#18011908
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
FittingH(3,ℤ/4)×C149C2
socleC2×C149#392
hypercenterH(3,ℤ/4)D149
hypocenterC149#2010
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C4 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
1. #23750425C2semidirect
2. #23750137C2semidirect
3. #23749643C2semidirect
4. #23749588C2semidirect
5. H(3,ℤ/4)×C149C2semidirect
26. C2×Dic298D4semidirect
28. C2×D596D4semidirect
46. C2×C8×C149D4semidirect
49. C42×C149D4semidirect
98. C149#2010semidirect
104. H(3,ℤ/4)D149semidirect
142. C2×C8D596semidirect
148. C42D596semidirect

Maximal subgroups

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

subgroupindex
#237504252
#237501372
#237496432
#237495882
H(3,ℤ/4)×C1492
#2010149