Finite Group Databasebeta

← #34043721

Subgroups — #34043721

Order 19072.

208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 49 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#23750224C211yesmaximal, characteristic
2#23749943C211yesmaximal, characteristic
3#23749563C211yesmaximal, characteristic, complemented
4#23749362C211yesmaximal, characteristic, complemented
5#23749360C211yesmaximal, characteristic
6#23749350C211yesmaximal, characteristic, complemented
7#484×C149C211yesmaximal, characteristic, complemented
8#18011906—21no—
9#18011902—21no—
10#18011896—21no—
11#18011895—21no—
12#18011887—21no—
13#18011885C2211yescharacteristic
14#18011871—21no—
15C2×#14558715C2211yescharacteristic
16#18011842—21no—
17#18011831—21no—
18C22⋊#11924746C2211yescharacteristic
19#18011818—21no—
20#18011818—21no—
21#18011818C2211yescharacteristic
22C22⋊Q8×C149C2211yescharacteristic
23C2×C4⋊C4×C149C2211yescharacteristic
24#107×C149—21no—
25#103×C149—21no—
26C22⋊C8×C149C2211yescharacteristic
27C2×D596D411yescharacteristic
28C2×C22⋊D149—21no—
29C22×Dic149—21no—
30C22×Dic149D411yescharacteristic
31C22×Dic149D411yescharacteristic
32C2×C4×D149—21no—
33C2×#11924746—21no—
34C4⋊Dic149—21no—
35C4⋊Dic149—21no—
36C4⋊Dic149D411yescharacteristic
37#14558715—21no—
38#14558715—21no—
39#14558715—21no—
40#14558713—21no—
41#14558713—21no—
42#14558713—21no—
43#14558713—21no—
44C4×Dic149—21no—
45C2×Q8×C149D411yescharacteristic
46C22×C4×C149—21no—
47C22×C4×C149C2311yescharacteristic
48C2×C8×C149—21no—
49C4⋊C4×C149—21no—
50C4⋊C4×C149—21no—
51C4⋊C4×C149—21no—
52C4⋊C4×C149D411yescharacteristic
53C22⋊C4×C149—21no—
54C22×D149—21no—
55D596—41no—
56C22⋊D149—41no—
57C22⋊D149—41no—
58C2×Dic149—21no—
59C2×Dic149—21no—
60C2×Dic149—21no—
61C2×Dic149—21no—
62C2×Dic149—21no—
63C2×Dic149—41no—
64C2×Dic149—41no—
65C2×Dic149—41no—
66C2×Dic149—41no—
67C4×D149—81no—
68#11924746—41no—
69C23×C149C2×D411yescharacteristic
70Q8×C149—41no—
71C2×C4×C149—21no—
72C2×C4×C149—21no—
73C2×C4×C149—41no—
74C2×C4×C149—42no—
75C2×C4×C149—41no—
76C2×C4×C149C2×D411yescharacteristic
77C2×C4×C149C2×D411yescharacteristic
78C8×C149—41no—
79C22×C149—21no—
80C22×C149—21no—
81C22×C149#12011yescharacteristic
82C22×C149#13511yescharacteristic
83C22×C149#13711yescharacteristic
84C2×D149—41no—
85C2×D149—41no—
86C2×D149—41no—
87C4×C149—21no—
88C4×C149—21no—
89C4×C149—41no—
90C4×C149—41no—
91C4×C149—81no—
92Dic149—41no—
93Dic149—41no—
94Dic149—41no—
95Dic149—81no—
96C2×C149—21no—
97C2×C149—21no—
98C2×C149#45211yescharacteristic
99C2×C149#45411yescharacteristic
100C2×C149#45811yescharacteristic
101D149—81no—
102C149#161511yescharacteristic, complemented, Sylow
103#1615—1491nomaximal, Sylow
104#539—1491no—
105#484D14911yescharacteristic, complemented
106#481—1491no—
107#400—1491no—
108#328—1491no—
109#327—1491no—
110#324—1491no—
111#126—2981no—
112#125—2981no—
113#123—2981no—
114#123—2981no—
115C22⋊Q8—2981no—
116C22⋊Q8C2×D14911yescharacteristic
117#121—1491no—
118C4×D4—2981no—
119C2×C4⋊C4—1491no—
120C2×C4⋊C4C2×D14911yescharacteristic
121#107—21no—
122#106—2981no—
123#103—21no—
124#102—2981no—
125C22⋊C8—1491no—
126C22⋊C8C2×D14911yescharacteristic
127#95—2981no—
128#95—2981no—
129#95—1491no—
130C2×Q8C22⋊D14911yescharacteristic
131C2×D4—2981no—
132C2×D4—1491no—
133C22×C4—21no—
134C22×C4—2981no—
135C22×C4—2981no—
136C22×C4—1491no—
137C22×C4—1491no—
138C22×C4C22×D14911yescharacteristic
139C2×C8—21no—
140C2×C8—2981no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—2981no—
145C4⋊C4—2981no—
146C4⋊C4—2981no—
147C4⋊C4—2981no—
148C4⋊C4—2981no—
149C4⋊C4—1491no—
150C4⋊C4C22⋊D14911yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—2981no—
153C22⋊C4—2981no—
154C22⋊C4—2981no—
155C22⋊C4—2981no—
156C42—2981no—
157C23—2981no—
158C23D4×D14911yescharacteristic
159Q8—41no—
160D4—5961no—
161D4—5961no—
162D4—5961no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—42no—
167C2×C4—41no—
168C2×C4—2981no—
169C2×C4—2981no—
170C2×C4—2981no—
171C2×C4—2981no—
172C2×C4—2981no—
173C2×C4—5961no—
174C2×C4—5961no—
175C2×C4—5961no—
176C2×C4—5961no—
177C2×C4—11921no—
178C2×C4D4×D14911yescharacteristic
179C2×C4C2×C22⋊D14911yescharacteristic
180C8—41no—
181C8—5961no—
182C22—21no—
183C22—21no—
184C22—5961no—
185C22—5961no—
186C22—5961no—
187C22#1801187911yescharacteristic
188C22#1801193411yescharacteristic
189C22#1801194311yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—81no—
195C4—5961no—
196C4—5961no—
197C4—5961no—
198C4—11921no—
199C2—21no—
200C2—21no—
201C2—11921no—
202C2#2374978611yescharacteristic
203C2#2374979611yescharacteristic
204C2#2374981411yescharacteristic
subgroupG/H
centerC22#18011879
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting#484×C149C2
socleC22×C149#120
prime radical#18011885C22
hypercenter#484D149
hypocenterC149#1615
LCSG ▷ C22×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
3. #23749563C2semidirect
4. #23749362C2semidirect
6. #23749350C2semidirect
7. #484×C149C2semidirect
102. C149#1615semidirect
105. #484D149semidirect

Maximal subgroups

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

subgroupindex
#237502242
#237499432
#237495632
#237493622
#237493602
#237493502
#484×C1492
#1615149