Finite Group Databasebeta

← #34059973

Subgroups — #34059973

Order 19072.

214 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 58 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#23750645C211yesmaximal, characteristic, complemented
2#23750641C211yesmaximal, characteristic, complemented
3#23750471C212yesmaximal, complemented
4#23750468C212yesmaximal
5C2×#18011904C211yesmaximal, characteristic
6#18011978—21no—
7C4⋊#11924753—21no—
8C22⋊#11924753C2212yes—
9C22⋊#11924753C2212yes—
10#18011966—21no—
11C4×#11924753—21no—
12#18011904—21no—
13#18011904—21no—
14#18011904—21no—
15#18011904—21no—
16C2×C4⋊Dic149C411yescharacteristic
17C2×#14558715C411yescharacteristic
18C2×#14558715C2211yescharacteristic
19C2×C22⋊Dic149C411yescharacteristic
20C2×C22⋊Dic149C2211yescharacteristic
21C2×C4×Dic149C2211yescharacteristic
22C2×C22⋊C4×C149C411yescharacteristic
23C2×#11924753—22no—
24C2×#11924753—22no—
25C22×Dic149C2×C411yescharacteristic
26C22×Dic149C2×C411yescharacteristic
27C22×Dic149C2×C411yescharacteristic
28C22×Dic149C2311yescharacteristic
29C4⋊Dic149—21no—
30C4⋊Dic149—21no—
31#14558715—21no—
32#14558715—21no—
33#14558715—21no—
34#14558715—21no—
35C22⋊Dic149—21no—
36C22⋊Dic149—21no—
37C22⋊Dic149—21no—
38C22⋊Dic149—21no—
39C4×Dic149D411yescharacteristic
40C4×Dic149D411yescharacteristic
41C4×Dic149D411yescharacteristic
42C4×Dic149D411yescharacteristic
43C24×C149C2×C411yescharacteristic
44C22×C4×C149C2×C411yescharacteristic
45C22×C4×C149C2×C411yescharacteristic
46C22⋊C4×C149—21no—
47C22⋊C4×C149—21no—
48#11924753—42no—
49#11924753—42no—
50C2×Dic149—21no—
51C2×Dic149—21no—
52C2×Dic149—22no—
53C2×Dic149—41no—
54C2×Dic149—41no—
55C2×Dic149—41no—
56C2×Dic149C22⋊C411yescharacteristic
57C2×Dic149C22⋊C411yescharacteristic
58C2×Dic149C2×D411yescharacteristic
59C2×Dic149C2×D411yescharacteristic
60C23×C149—21no—
61C23×C149—22no—
62C23×C149—41no—
63C23×C149—41no—
64C23×C149C22×C411yescharacteristic
65C2×C4×C149—22no—
66C2×C4×C149—21no—
67C2×C4×C149—41no—
68C2×C4×C149C22⋊C411yescharacteristic
69C2×C4×C149C22⋊C411yescharacteristic
70C22×C149—21no—
71C22×C149—21no—
72C22×C149—41no—
73C22×C149—41no—
74C22×C149—41no—
75C22×C149—82no—
76C22×C149C2×C22⋊C411yescharacteristic
77C22×C149#13112yes—
78C4×C149—21no—
79C4×C149—21no—
80C4×C149—41no—
81Dic149—21no—
82Dic149—21no—
83Dic149—21no—
84Dic149—21no—
85Dic149—41no—
86Dic149—41no—
87C2×C149—22no—
88C2×C149—81no—
89C2×C149#40811yescharacteristic
90C2×C149#41011yescharacteristic
91C2×C149#41311yescharacteristic
92C149#147311yescharacteristic, complemented, Sylow
93#1473—1491nomaximal, Sylow
94C2×#126—1491no—
95#432—1491no—
96#431—1491no—
97#324—1492no—
98#323—1492no—
99#126—2981no—
100#126—2981no—
101#126—2981no—
102#126—2981no—
103C2×C4⋊C4—1491no—
104C2×C4⋊C4—1491no—
105C2×C4⋊C4—1491no—
106C2×C22⋊C4—1491no—
107C2×C22⋊C4—1491no—
108C2×C22⋊C4#1059701011yescharacteristic
109C2×C42—1491no—
110C4⋊C8—2981no—
111C4⋊C8—2981no—
112C22⋊C8—1492no—
113C22⋊C8—1492no—
114#97—2981no—
115C4×C8—2981no—
116C24C2×#1059701011yescharacteristic
117C22×C4—1491no—
118C22×C4—1491no—
119C22×C4—1491no—
120C22×C4—1491no—
121C22×C4C2×#1059701011yescharacteristic
122C22×C4C2×#1059701011yescharacteristic
123C2×C8—2982no—
124C2×C8—2982no—
125C4⋊C4—2981no—
126C4⋊C4—2981no—
127C4⋊C4—2981no—
128C4⋊C4—2981no—
129C4⋊C4—2981no—
130C4⋊C4—2981no—
131C22⋊C4—21no—
132C22⋊C4—21no—
133C22⋊C4—2981no—
134C22⋊C4—2981no—
135C22⋊C4—2981no—
136C22⋊C4—2981no—
137C42—1491no—
138C42—1491no—
139C42—1491no—
140C42—1491no—
141C23—21no—
142C23—22no—
143C23—41no—
144C23—41no—
145C23C22×#1059701011yescharacteristic
146C2×C4—22no—
147C2×C4—21no—
148C2×C4—41no—
149C2×C4—2981no—
150C2×C4—2981no—
151C2×C4—2982no—
152C2×C4—5961no—
153C2×C4—5961no—
154C2×C4—5961no—
155C2×C4—1491no—
156C2×C4—1491no—
157C2×C4—1491no—
158C2×C4—1491no—
159C2×C4C22⋊#1059701011yescharacteristic
160C2×C4C22⋊#1059701011yescharacteristic
161C8—5962no—
162C8—5962no—
163C22—21no—
164C22—21no—
165C22—41no—
166C22—41no—
167C22—41no—
168C22—82no—
169C22C2×C22⋊#1059701011yescharacteristic
170C22#1801199812yes—
171C4—21no—
172C4—21no—
173C4—41no—
174C4—2981no—
175C4—2981no—
176C4—2981no—
177C4—2981no—
178C4—5961no—
179C4—5961no—
180C2—22no—
181C2—81no—
182C2#2375059811yescharacteristic
183C2#2375060511yescharacteristic
184C2#2375061111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC23×C149C22×C4
FrattiniC23C22×#10597010
FittingC2×C22⋊C4×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC24×C149C2×C4
cosocleC22×Dic149C23
hypercenterC2×C22⋊C4#10597010
hypocenterC149#1473
LCSG ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #23750645C2semidirect
2. #23750641C2semidirect
3. #23750471C2semidirect
92. C149#1473semidirect

Maximal subgroups

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

subgroupindex
#237506452
#237506412
#237504712
#237504682
C2×#180119042
#1473149