Finite Group Databasebeta

← #34044022

Subgroups — #34044022

Order 19072.

184 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 45 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#23750379C211yesmaximal, characteristic
2#23750031C211yesmaximal, characteristic, complemented
3#23749987C211yesmaximal, characteristic
4#23749367C211yesmaximal, characteristic, complemented
5#23749366C211yesmaximal, characteristic, complemented
6#23749364C211yesmaximal, characteristic
7#491×C149C211yesmaximal, characteristic, complemented
8#18011910—21no—
9#18011906—21no—
10#18011906—21no—
11#18011903C2211yescharacteristic
12#18011899C2211yescharacteristic
13#18011896—21no—
14#18011891—21no—
15#18011889—21no—
16#18011844—21no—
17#18011842—21no—
18#18011834—21no—
19#18011831—21no—
20#18011822C2211yescharacteristic
21#18011822C2211yescharacteristic
22C4⋊Q8×C149C2211yescharacteristic
23#125×C149C2211yescharacteristic
24#103×C149—21no—
25#103×C149—21no—
26#97×C149C2211yescharacteristic
27C2×Dic298—21no—
28C2×Dic298D411yescharacteristic
29C2×D596D411yescharacteristic
30C2×C4×D149—21no—
31C2×#11924746—21no—
32C2×#11924746—21no—
33C4⋊Dic149—21no—
34C4⋊Dic149D411yescharacteristic
35C4⋊Dic149D411yescharacteristic
36#14558715—21no—
37#14558715—21no—
38#14558715—21no—
39#14558713—21no—
40#14558713—21no—
41#14558713—21no—
42#14558713—21no—
43#14558713—21no—
44C4×Dic149—21no—
45C2×Q8×C149—21no—
46C2×C8×C149—21no—
47C4⋊C4×C149—21no—
48C4⋊C4×C149—21no—
49C4⋊C4×C149—21no—
50C4⋊C4×C149—21no—
51C4⋊C4×C149D411yescharacteristic
52C4⋊C4×C149D411yescharacteristic
53C42×C149C2311yescharacteristic
54C22×D149—21no—
55Dic298—41no—
56Dic298—81no—
57D596—41no—
58C2×Dic149—21no—
59C2×Dic149—21no—
60C2×Dic149—21no—
61C4×D149—81no—
62#11924746—22no—
63#11924746—41no—
64Q8×C149—42no—
65C2×C4×C149—21no—
66C2×C4×C149—21no—
67C2×C4×C149—41no—
68C2×C4×C149C2×D411yescharacteristic
69C2×C4×C149C2×D411yescharacteristic
70C2×C4×C149C2×D411yescharacteristic
71C8×C149—41no—
72C22×C149#12011yescharacteristic
73C2×D149—41no—
74C2×D149—41no—
75C2×D149—41no—
76C4×C149—21no—
77C4×C149—21no—
78C4×C149—21no—
79C4×C149—41no—
80C4×C149—41no—
81C4×C149—81no—
82Dic149—41no—
83Dic149—41no—
84Dic149—41no—
85C2×C149#45411yescharacteristic
86C2×C149#45511yescharacteristic
87C2×C149#45611yescharacteristic
88D149—81no—
89C149#166411yescharacteristic, complemented, Sylow
90#1664—1491nomaximal, Sylow
91#563—1491no—
92#501—1491no—
93#491D14911yescharacteristic, complemented
94#489—1491no—
95#330—1491no—
96#330—1491no—
97#329—1491no—
98C4⋊Q8—2981no—
99C4⋊Q8C2×D14911yescharacteristic
100#126—2981no—
101#126—2981no—
102#125—1491no—
103#125C2×D14911yescharacteristic
104#124—1491no—
105#123—2981no—
106C22⋊Q8—2981no—
107C22⋊Q8—2981no—
108#107—2981no—
109#106—2981no—
110#103—21no—
111#103—21no—
112#103—2981no—
113#102—2981no—
114#97—1491no—
115#97—1491no—
116#97C2×D14911yescharacteristic
117C2×Q8—21no—
118C2×Q8—2981no—
119C2×Q8—1491no—
120C2×D4—1491no—
121C22×C4—2981no—
122C2×C8—21no—
123C2×C8—2981no—
124C2×C8—2981no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—2981no—
130C4⋊C4—2981no—
131C4⋊C4—2981no—
132C4⋊C4—2981no—
133C4⋊C4—1491no—
134C4⋊C4—1491no—
135C4⋊C4C22⋊D14911yescharacteristic
136C4⋊C4C22⋊D14911yescharacteristic
137C22⋊C4—2981no—
138C22⋊C4—2981no—
139C22⋊C4—2981no—
140C22⋊C4—2981no—
141C22⋊C4—2981no—
142C42—2981no—
143C42C22×D14911yescharacteristic
144C23—2981no—
145Q8—42no—
146Q8—5961no—
147Q8—11921no—
148D4—5961no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—2981no—
153C2×C4—2981no—
154C2×C4—2981no—
155C2×C4—11921no—
156C2×C4D4×D14911yescharacteristic
157C2×C4D4×D14911yescharacteristic
158C2×C4C2×C22⋊D14911yescharacteristic
159C8—41no—
160C8—2982no—
161C8—5961no—
162C22—5961no—
163C22—5961no—
164C22—5961no—
165C22#1801187911yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—81no—
172C4—5961no—
173C4—5961no—
174C4—5961no—
175C2—11921no—
176C2#2374979711yescharacteristic
177C2#2374980111yescharacteristic
178C2#2374980611yescharacteristic
subgroupG/H
centerC22#18011879
commutator, cosocleC42×C149C23
FrattiniC42C22×D149
Fitting#491×C149C2
socleC22×C149#120
prime radicalC2×D596D4
hypercenter#491D149
hypocenterC149#1664
LCSG ▷ C42×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
2. #23750031C2semidirect
4. #23749367C2semidirect
5. #23749366C2semidirect
7. #491×C149C2semidirect
89. C149#1664semidirect
93. #491D149semidirect

Maximal subgroups

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

subgroupindex
#237503792
#237500312
#237499872
#237493672
#237493662
#237493642
#491×C1492
#1664149