Finite Group Databasebeta

← #34060045

Subgroups — #34060045

Order 19072.

230 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 62 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#23750647C211yesmaximal, characteristic, complemented
2C4×D149⋊C8C211yesmaximal, characteristic, complemented
3#23750475C212yesmaximal, complemented
4#23750473C212yesmaximal, complemented
5#23750160C211yesmaximal, characteristic
6C2×D149⋊C8—21no—
7C4⋊#11924753C2212yes—
8#18011968—21no—
9#18011966—21no—
10C4×#11924753—21no—
11C4×#11924753C2212yes—
12#18011906—21no—
13#18011899C411yescharacteristic
14#18011896—21no—
15#18011891C411yescharacteristic
16#18011886C411yescharacteristic
17#18011876C2211yescharacteristic
18#18011873—21no—
19#18011873C2211yescharacteristic
20#18011869—21no—
21C42×D149C2211yescharacteristic
22#125×C149C411yescharacteristic
23D149⋊C8—24no—
24C2×#11924753—22no—
25C2×#11924753—22no—
26C2×Dic298C2×C411yescharacteristic
27C2×D596—21no—
28C2×D596C2×C411yescharacteristic
29C2×C4×D149—21no—
30C2×C4×D149C2×C411yescharacteristic
31C2×C4×D149D411yescharacteristic
32C2×C4×D149D411yescharacteristic
33C4⋊Dic149—21no—
34#14558715—21no—
35#14558713—21no—
36#14558713—21no—
37#14558713—21no—
38#14558713—21no—
39#14558713—21no—
40C4×Dic149—21no—
41C4×Dic149D411yescharacteristic
42C4×Dic149D411yescharacteristic
43C4×Dic149C2311yescharacteristic
44C4⋊C4×C149—21no—
45C4⋊C4×C149—21no—
46C4⋊C4×C149C2×C411yescharacteristic
47C4⋊C4×C149C2×C411yescharacteristic
48C42×C149C2×C411yescharacteristic
49#11924753—24no—
50#11924753—42no—
51C22×D149—21no—
52C22×D149C22⋊C411yescharacteristic
53Dic298—22no—
54D596—22no—
55D596—42no—
56C2×Dic149—21no—
57C2×Dic149C22⋊C411yescharacteristic
58C2×Dic149C2×D411yescharacteristic
59C2×Dic149C2×D411yescharacteristic
60C4×D149—22no—
61C4×D149—22no—
62C4×D149—22no—
63C4×D149—42no—
64C2×C4×C149—21no—
65C2×C4×C149—21no—
66C2×C4×C149C22⋊C411yescharacteristic
67C2×C4×C149C22⋊C411yescharacteristic
68C2×C4×C149C22×C411yescharacteristic
69C22×C149C2×C22⋊C411yescharacteristic
70C2×D149—21no—
71C2×D149—21no—
72C2×D149—41no—
73C2×D149—41no—
74C2×D149—41no—
75C2×D149#10412yes—
76C4×C149—21no—
77C4×C149—21no—
78C4×C149—41no—
79C4×C149—41no—
80C4×C149#13112yes—
81Dic149—21no—
82Dic149—21no—
83Dic149—41no—
84Dic149#13512yes—
85C2×C149#40811yescharacteristic
86C2×C149#41611yescharacteristic
87C2×C149C2×#10411yescharacteristic
88D149—22no—
89D149—81no—
90C149#149411yescharacteristic, complemented, Sylow
91#1494—1491nomaximal, Sylow
92#529—1491no—
93#432—1491no—
94C2×C4×C8—1491no—
95Q8⋊C8—1492no—
96D4⋊C8—1492no—
97C22×C8—2981no—
98#126—2981no—
99#125#1059701011yescharacteristic
100#124—1491no—
101#123—2981no—
102C22⋊Q8—1491no—
103#121—1491no—
104C4×Q8—1491no—
105C4×D4—2981no—
106C4×D4—1491no—
107#117—2981no—
108C2×C42—1491no—
109C4⋊C8—1492no—
110C22⋊C8—2981no—
111#97—2981no—
112C4×C8—2981no—
113C4×C8—1492no—
114C2×Q8—1491no—
115C2×D4—2981no—
116C2×D4—1491no—
117C22×C4—2981no—
118C22×C4—1491no—
119C22×C4—1491no—
120C22×C4—1491no—
121C2×C8—2984no—
122C2×C8—2982no—
123C2×C8—2982no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—2981no—
127C4⋊C4—2981no—
128C4⋊C4C2×#1059701011yescharacteristic
129C4⋊C4C2×#1059701011yescharacteristic
130C22⋊C4—2981no—
131C22⋊C4—2981no—
132C22⋊C4—2981no—
133C22⋊C4—2981no—
134C22⋊C4—2981no—
135C42—2981no—
136C42—1491no—
137C42—1491no—
138C42—1491no—
139C42C2×#1059701011yescharacteristic
140C23—2981no—
141C23—1491no—
142Q8—2982no—
143D4—2982no—
144D4—5962no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—2982no—
148C2×C4—2982no—
149C2×C4—2982no—
150C2×C4—2981no—
151C2×C4—5962no—
152C2×C4—1491no—
153C2×C4—1491no—
154C2×C4—1491no—
155C2×C4C22⋊#1059701011yescharacteristic
156C2×C4C22⋊#1059701011yescharacteristic
157C2×C4C22×#1059701011yescharacteristic
158C8—2984no—
159C8—5962no—
160C22—2981no—
161C22—2981no—
162C22—5961no—
163C22—5961no—
164C22—5961no—
165C22—1492no—
166C22C2×C22⋊#1059701011yescharacteristic
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—2981no—
172C4—2981no—
173C4—5961no—
174C4—1492no—
175C4#1801199912yes—
176C2—2982no—
177C2—11921no—
178C2#2375060011yescharacteristic
179C2#2375061511yescharacteristic
180C2D149⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#125×C149C4
socleC22×C149C2×C22⋊C4
prime radical#18011886C4
cosocleC4×Dic149C23
hypercenter#125#10597010
hypocenterC149#1494
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
1. #23750647C2semidirect
2. C4×D149⋊C8C2semidirect
3. #23750475C2semidirect
4. #23750473C2semidirect
90. C149#1494semidirect

Maximal subgroups

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

subgroupindex
#237506472
C4×D149⋊C82
#237504752
#237504732
#237501602
#1494149