Finite Group Databasebeta

← #34060094

Subgroups — #34060094

Order 19072.

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

normal subgroups only

This group has 242 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#23750648C211yesmaximal, characteristic, complemented
2C4×C4⋊#10597010C211yesmaximal, characteristic, complemented
3#23750478C212yesmaximal, complemented
4#23750477C212yesmaximal
5#23750160C211yesmaximal, characteristic
6C2×C4⋊#10597010—21no—
7C2×C4×#10597010—21no—
8#18011978—21no—
9#18011968C2212yes—
10#18011966—21no—
11(C2×#10597010)⋊C4C2212yes—
12#18011906—21no—
13#18011899C411yescharacteristic, complemented
14#18011896—21no—
15#18011891C2211yescharacteristic
16#18011886C2211yescharacteristic
17#18011876C411yescharacteristic, complemented
18#18011873—21no—
19#18011873C411yescharacteristic, complemented
20#18011869—21no—
21C42×D149C2211yescharacteristic
22#125×C149C411yescharacteristic, complemented
23C22×#10597010—22no—
24C2×#11924753—22no—
25C4⋊#10597010—24no—
26C4×#10597010—42no—
27C2×Dic298C2×C411yescharacteristic
28C2×D596—21no—
29C2×D596C2×C411yescharacteristic
30C2×C4×D149—21no—
31C2×C4×D149D411yescharacteristic
32C2×C4×D149D411yescharacteristic
33C2×C4×D149C2311yescharacteristic
34C4⋊Dic149—21no—
35#14558715—21no—
36#14558713—21no—
37#14558713—21no—
38#14558713—21no—
39#14558713—21no—
40#14558713—21no—
41C4×Dic149—21no—
42C4×Dic149C2×C411yescharacteristic
43C4×Dic149D411yescharacteristic
44C4×Dic149D411yescharacteristic
45C4⋊C4×C149—21no—
46C4⋊C4×C149—21no—
47C4⋊C4×C149C2×C411yescharacteristic
48C4⋊C4×C149C2×C411yescharacteristic
49C42×C149C2×C411yescharacteristic
50C2×#10597010—24no—
51C2×#10597010—42no—
52C2×#10597010—42no—
53#11924753—42no—
54C22×D149—21no—
55C22×D149C2×D411yescharacteristic
56Dic298—41no—
57D596—41no—
58D596—41no—
59D596—41no—
60C2×Dic149—21no—
61C2×Dic149C22⋊C411yescharacteristic
62C2×Dic149C22⋊C411yescharacteristic
63C2×Dic149C2×D411yescharacteristic
64C4×D149—21no—
65C4×D149—21no—
66C4×D149—22no—
67C4×D149—41no—
68C4×D149—42no—
69C2×C4×C149—21no—
70C2×C4×C149—21no—
71C2×C4×C149C22⋊C411yescharacteristic
72C2×C4×C149C22⋊C411yescharacteristic
73C2×C4×C149C22×C411yescharacteristic
74C22×C149C2×C22⋊C411yescharacteristic
75C2×D149—21no—
76C2×D149—21no—
77C2×D149—41no—
78C2×D149—41no—
79C2×D149—41no—
80C2×D149AGL(1,ℤ/8)11yescharacteristic
81C2×D149#13711yescharacteristic
82#10597010—44no—
83C4×C149—21no—
84C4×C149—21no—
85C4×C149—21no—
86C4×C149—41no—
87C4×C149—41no—
88Dic149—21no—
89Dic149—21no—
90Dic149—41no—
91Dic149#10412yes—
92C2×C149#41011yescharacteristic
93C2×C149#41711yescharacteristic
94C2×C149C2×#10411yescharacteristic
95D149—21no—
96D149—21no—
97D149—81no—
98C149#150911yescharacteristic, complemented, Sylow
99#1509—1491nomaximal, Sylow
100#529—1491no—
101#432—1491no—
102C4×C4⋊C4—1491no—
103#328—1492no—
104#327—1492no—
105#126—2981no—
106#125#1059701011yescharacteristic, complemented
107#124—1491no—
108#123—2981no—
109C22⋊Q8—1491no—
110#121—1491no—
111C4×Q8—1491no—
112C4×D4—2981no—
113C4×D4—1491no—
114#117—2981no—
115C2×C4⋊C4—2981no—
116C2×C42—2981no—
117C2×C42—1491no—
118C4⋊C8—2981no—
119C22⋊C8—1492no—
120#97—2981no—
121#95—1492no—
122C2×Q8—1491no—
123C2×D4—2981no—
124C2×D4—1491no—
125C22×C4—2981no—
126C22×C4—2982no—
127C22×C4—1491no—
128C22×C4—1491no—
129C22×C4—1491no—
130C2×C8—2982no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—2981no—
134C4⋊C4—2981no—
135C4⋊C4—2984no—
136C4⋊C4C2×#1059701011yescharacteristic
137C4⋊C4C2×#1059701011yescharacteristic
138C22⋊C4—2981no—
139C22⋊C4—2981no—
140C22⋊C4—2981no—
141C22⋊C4—2981no—
142C22⋊C4—2981no—
143C42—2981no—
144C42—5962no—
145C42—1491no—
146C42—1491no—
147C42—1491no—
148C42C2×#1059701011yescharacteristic
149C23—2981no—
150C23—1491no—
151Q8—5961no—
152D4—5961no—
153D4—5961no—
154D4—5961no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—2981no—
158C2×C4—2981no—
159C2×C4—2982no—
160C2×C4—2984no—
161C2×C4—2981no—
162C2×C4—5961no—
163C2×C4—5962no—
164C2×C4—5962no—
165C2×C4—5962no—
166C2×C4—1491no—
167C2×C4—1491no—
168C2×C4—1491no—
169C2×C4C22⋊#1059701011yescharacteristic
170C2×C4C22⋊#1059701011yescharacteristic
171C2×C4C22×#1059701011yescharacteristic
172C8—5962no—
173C22—2981no—
174C22—2981no—
175C22—5961no—
176C22—5961no—
177C22—5961no—
178C22—1491no—
179C22—1491no—
180C22C2×C22⋊#1059701011yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—41no—
185C4—41no—
186C4—2981no—
187C4—2981no—
188C4—5964no—
189C4—5961no—
190C4—1492no—
191C2—2981no—
192C2—2981no—
193C2—11921no—
194C2#2375060611yescharacteristic
195C2#2375061611yescharacteristic
196C2D149⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
Fitting#125×C149C4
socleC22×C149C2×C22⋊C4
prime radical#18011886C22
cosocleC2×C4×D149C23
hypercenter#125#10597010
hypocenterC149#1509
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
1. #23750648C2semidirect
2. C4×C4⋊#10597010C2semidirect
3. #23750478C2semidirect
13. #18011899C4semidirect
17. #18011876C4semidirect
19. #18011873C4semidirect
22. #125×C149C4semidirect
98. C149#1509semidirect
106. #125#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506482
C4×C4⋊#105970102
#237504782
#237504772
#237501602
#1509149