Finite Group Databasebeta

← #34045758

Subgroups — #34045758

Order 19072.

394 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 69 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#23750136C212yesmaximal, complemented
3#23749641C212yesmaximal, complemented
4#23749382C211yesmaximal, characteristic, complemented
5#407×C149C211yesmaximal, characteristic, complemented
6C2×#14558736C2212yes—
7#18011944—22no—
8#18011939—22no—
9#18011933—22no—
10#18011894—22no—
11#18011890—22no—
12#18011885—22no—
13#18011880—22no—
14C4×C22⋊D149—24no—
15#18011870C2212yes—
16#18011837—24no—
17C23×C4×C149C2211yescharacteristic
18C2×M16×C149C2211yescharacteristic
19C2×M16×C149C2211yescharacteristic
20C22⋊C8×C149—22no—
21#14558736—22no—
22#14558736—22no—
23#14558736—22no—
24#14558736—22no—
25C2×Dic298D412yescomplemented
26C2×D596D412yescomplemented
27C2×C22⋊D149—24no—
28C2×C22⋊D149—22no—
29C2×C4×D149—22no—
30Dic596—22no—
31#14558725—24no—
32D1192—22no—
33C4⋊Dic149—22no—
34#14558715—24no—
35C22⋊Dic149—24no—
36C22⋊Dic149—22no—
37#14558713—24no—
38C4×Dic149D414yescomplemented
39C24×C149D411yescharacteristic
40C22×C4×C149—21no—
41C22×C4×C149—22no—
42C22×C4×C149—22no—
43C22×C4×C149—21no—
44C22×C4×C149D411yescharacteristic
45C22×C4×C149C2311yescharacteristic
46M16×C149—22no—
47M16×C149—22no—
48C2×C8×C149—21no—
49C2×C8×C149D412yescomplemented
50C22×D149—22no—
51Dic298—22no—
52Dic298—22no—
53D596—22no—
54D596—22no—
55C22⋊D149—48no—
56C22⋊D149—42no—
57C22⋊D149—42no—
58C2×Dic149—22no—
59C2×Dic149—24no—
60C4×D149—42no—
61C4×D149—42no—
62C23×C149—22no—
63C23×C149—21no—
64C23×C149—42no—
65C23×C149C2×D411yescharacteristic
66C2×C4×C149—22no—
67C2×C4×C149—21no—
68C2×C4×C149—41no—
69C2×C4×C149—42no—
70C2×C4×C149—41no—
71C2×C4×C149C2×D412yes—
72C2×C4×C149C2×D412yes—
73C2×C4×C149C2×D411yescharacteristic
74C2×C4×C149#4111yescharacteristic
75C8×C149—22no—
76C8×C149—41no—
77C22×C149—22no—
78C22×C149—24no—
79C22×C149—41no—
80C22×C149—42no—
81C22×C149—41no—
82C22×C149—41no—
83C22×C149#12012yes—
84C22×C149#12111yescharacteristic
85C2×D149—44no—
86C2×D149—42no—
87C4×C149—41no—
88C4×C149#12011yescharacteristic
89C4×C149#12112yes—
90C4×C149#12711yescharacteristic
91Dic149—44no—
92Dic149—42no—
93C2×C149—22no—
94C2×C149—21no—
95C2×C149—42no—
96C2×C149#39211yescharacteristic
97D149—82no—
98C149#201011yescharacteristic, complemented, Sylow
99#2010—1491nomaximal, Sylow
100#575—1491no—
101#525—1492no—
102#421—1492no—
103#407D14911yescharacteristic, complemented
104H(3,ℤ/4)—1491no—
105C2×#41—1492no—
106C23×C4C2×D14911yescharacteristic
107#137—2982no—
108AGL(1,ℤ/8)—2982no—
109#135—2982no—
110C2×M16C2×D14911yescharacteristic
111C2×M16C2×D14911yescharacteristic
112#123—2982no—
113C22⋊Q8—2982no—
114#121—2982no—
115#120—2982no—
116C4×D4—2984no—
117#117—1492no—
118#104—2984no—
119C22⋊C8—22no—
120C24D59611yescharacteristic
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—22no—
130C22×C4—22no—
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—2982no—
134C22×C4D59611yescharacteristic
135C22×C4C22×D14911yescharacteristic
136Q16—2982no—
137SD16—2984no—
138D8—2982no—
139M16—22no—
140M16—22no—
141C2×C8—21no—
142C2×C8C22⋊D14912yescomplemented
143C4⋊C4—2984no—
144C4⋊C4—2982no—
145C22⋊C4—2984no—
146C22⋊C4—2984no—
147C22⋊C4—2982no—
148C42—1494no—
149C23—22no—
150C23—21no—
151C23—42no—
152C23—2982no—
153C23C2×D59611yescharacteristic
154Q8—2982no—
155Q8—2982no—
156D4—2982no—
157D4—2982no—
158D4—5968no—
159D4—5962no—
160D4—5962no—
161C2×C4—22no—
162C2×C4—21no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—42no—
166C2×C4—2984no—
167C2×C4—2982no—
168C2×C4—5962no—
169C2×C4—5962no—
170C2×C4D4×D14912yes—
171C2×C4D4×D14912yes—
172C2×C4C2×C22⋊D14911yescharacteristic
173C2×C4#1455873611yescharacteristic
174C8—22no—
175C8—41no—
176C22—24no—
177C22—22no—
178C22—41no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—5964no—
183C22—5962no—
184C22#1801188112yes—
185C22#1801188511yescharacteristic
186C4—41no—
187C4—5964no—
188C4—5962no—
189C4#1801187911yescharacteristic
190C4#1801188412yes—
191C4#1801190711yescharacteristic
192C2—22no—
193C2—21no—
194C2—42no—
195C2—11922no—
196C2#2374953411yescharacteristic
subgroupG/H
centerC4#18011907
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting#407×C149C2
socleC2×C149#392
hypercenter#407D149
hypocenterC149#2010
LCSG ▷ C22×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C4 ◁ C22×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #23750425C2semidirect
2. #23750136C2semidirect
3. #23749641C2semidirect
4. #23749382C2semidirect
5. #407×C149C2semidirect
25. C2×Dic298D4semidirect
26. C2×D596D4semidirect
38. C4×Dic149D4semidirect
49. C2×C8×C149D4semidirect
98. C149#2010semidirect
103. #407D149semidirect
142. C2×C8C22⋊D149semidirect

Maximal subgroups

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

subgroupindex
#237504252
#237501362
#237496412
#237493822
#407×C1492
#2010149