Finite Group Databasebeta

← #34044004

Subgroups — #34044004

Order 19072.

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

normal subgroups only

This group has 196 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#23750035C211yesmaximal, characteristic, complemented
3#23750034C211yesmaximal, characteristic, complemented
4#23750019C211yesmaximal, characteristic
5#23749366C211yesmaximal, characteristic, complemented
6#23749364C211yesmaximal, characteristic
7#330×C149C211yesmaximal, characteristic, complemented
8C2×Dic596—21no—
9C2×#14558725—21no—
10#18011911C2211yescharacteristic
11#18011910—21no—
12#18011906—21no—
13#18011906—21no—
14#18011903C2211yescharacteristic
15#18011899C2211yescharacteristic
16#18011896—21no—
17#18011891—21no—
18#18011889—21no—
19#18011845—21no—
20#18011844—21no—
21#18011843—21no—
22#18011842—21no—
23#18011822C2211yescharacteristic
24#125×C149C2211yescharacteristic
25#97×C149C2211yescharacteristic
26#97×C149C2211yescharacteristic
27C2×Dic298—21no—
28C2×Dic298—21no—
29C2×Dic298D411yescharacteristic
30C2×D596D411yescharacteristic
31C2×C4×D149—21no—
32Dic596—42no—
33#14558725—42no—
34C2×#11924746—21no—
35C4⋊Dic149—21no—
36C4⋊Dic149—21no—
37C4⋊Dic149—21no—
38C4⋊Dic149D411yescharacteristic
39C4⋊Dic149D411yescharacteristic
40#14558715—21no—
41#14558715—21no—
42#14558715—21no—
43#14558713—21no—
44#14558713—21no—
45#14558713—21no—
46#14558713—21no—
47#14558713—21no—
48C4×Dic149—21no—
49C2×C8×C149—21no—
50C2×C8×C149—21no—
51C4⋊C4×C149—21no—
52C4⋊C4×C149—21no—
53C4⋊C4×C149D411yescharacteristic
54C4⋊C4×C149D411yescharacteristic
55C42×C149C2311yescharacteristic
56C22×D149—21no—
57Dic298—41no—
58Dic298—41no—
59Dic298—41no—
60Dic298—81no—
61D596—41no—
62C2×Dic149—21no—
63C2×Dic149—21no—
64C2×Dic149—21no—
65C2×Dic149—41no—
66C4×D149—81no—
67#11924746—22no—
68C2×C4×C149—21no—
69C2×C4×C149—21no—
70C2×C4×C149C2×D411yescharacteristic
71C2×C4×C149C2×D411yescharacteristic
72C2×C4×C149C2×D411yescharacteristic
73C8×C149—22no—
74C8×C149—22no—
75C22×C149#12011yescharacteristic
76C2×D149—41no—
77C2×D149—41no—
78C2×D149—41no—
79C4×C149—21no—
80C4×C149—21no—
81C4×C149—21no—
82C4×C149—41no—
83C4×C149—41no—
84Dic149—41no—
85Dic149—41no—
86Dic149—41no—
87Dic149—81no—
88C2×C149#45311yescharacteristic
89C2×C149#45611yescharacteristic
90C2×C149#45611yescharacteristic
91D149—81no—
92C149#166011yescharacteristic, complemented, Sylow
93#1660—1491nomaximal, Sylow
94#563—1491no—
95#501—1491no—
96#501—1491no—
97#497—1491no—
98#330—1491no—
99#330D14911yescharacteristic, complemented
100#329—1491no—
101C2×Q16—2981no—
102C2×SD16—2981no—
103C4⋊Q8—2981no—
104C4⋊Q8—1491no—
105#126—2981no—
106#126—2981no—
107#125—1491no—
108#125C2×D14911yescharacteristic
109#124—1491no—
110#123—2981no—
111C22⋊Q8—2981no—
112C22⋊Q8—2981no—
113#107—2981no—
114#107—2981no—
115#106—2981no—
116#106—2981no—
117#97—1491no—
118#97C2×D14911yescharacteristic
119#97C2×D14911yescharacteristic
120C2×Q8—2981no—
121C2×Q8—2981no—
122C2×Q8—1491no—
123C2×D4—1491no—
124C22×C4—2981no—
125Q16—5962no—
126SD16—5962no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—2981no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—2981no—
133C4⋊C4—2981no—
134C4⋊C4—2981no—
135C4⋊C4—2981no—
136C4⋊C4—2981no—
137C4⋊C4—2981no—
138C4⋊C4—1491no—
139C4⋊C4—1491no—
140C4⋊C4D59611yescharacteristic
141C4⋊C4D59611yescharacteristic
142C22⋊C4—2981no—
143C22⋊C4—2981no—
144C22⋊C4—2981no—
145C22⋊C4—2981no—
146C22⋊C4—2981no—
147C42—2981no—
148C42C22×D14911yescharacteristic
149C23—2981no—
150Q8—5961no—
151Q8—5961no—
152Q8—5961no—
153Q8—11921no—
154D4—5961no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—2981no—
158C2×C4—2981no—
159C2×C4—2981no—
160C2×C4—5961no—
161C2×C4—11921no—
162C2×C4D4×D14911yescharacteristic
163C2×C4D4×D14911yescharacteristic
164C2×C4C2×D59611yescharacteristic
165C8—22no—
166C8—22no—
167C8—2982no—
168C22—5961no—
169C22—5961no—
170C22—5961no—
171C22#1801188111yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—5961no—
178C4—5961no—
179C4—5961no—
180C4—11921no—
181C2—11921no—
182C2#2374979411yescharacteristic
183C2#2374980911yescharacteristic
184C2#2374981011yescharacteristic
subgroupG/H
centerC22#18011881
commutator, cosocleC42×C149C23
FrattiniC42C22×D149
Fitting#330×C149C2
socleC22×C149#120
prime radicalC2×D596D4
hypercenter#330D149
hypocenterC149#1660
LCSG ▷ C42×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #23750035C2semidirect
3. #23750034C2semidirect
5. #23749366C2semidirect
7. #330×C149C2semidirect
92. C149#1660semidirect
99. #330D149semidirect

Maximal subgroups

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

subgroupindex
#237503792
#237500352
#237500342
#237500192
#237493662
#237493642
#330×C1492
#1660149