Finite Group Databasebeta

← #34060110

Subgroups — #34060110

Order 19072.

252 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 56 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
2#23750570C211yesmaximal, characteristic, complemented
3#23750477C212yesmaximal, complemented
4#23750476C212yesmaximal, complemented
5#23750172C211yesmaximal, characteristic
6C4⋊#11924753—21no—
7#18011968C2212yes—
8#18011966—21no—
9(C2×#10597010)⋊C4—21no—
10(C2×#10597010)⋊C4—21no—
11(C2×#10597010)⋊C4C2212yes—
12C2×#14558736—21no—
13#18011910C411yescharacteristic, complemented
14#18011907C411yescharacteristic, complemented
15#18011897—21no—
16#18011886C2211yescharacteristic
17#18011884—21no—
18#18011882C2211yescharacteristic
19C4×D596C411yescharacteristic, complemented
20C4×C22⋊D149—21no—
21C42×D149C2211yescharacteristic
22C4×D4×C149C411yescharacteristic, complemented
23C22×#10597010—22no—
24C2×#11924753—22no—
25#14558736—44no—
26C2×Dic298—21no—
27C2×D596—21no—
28C2×D596C2×C411yescharacteristic
29C2×C22⋊D149—21no—
30C2×C22⋊D149—21no—
31C2×C22⋊D149—21no—
32C2×C4×D149—21no—
33C2×C4×D149D411yescharacteristic
34C2×C4×D149D411yescharacteristic
35C2×C4×D149C2311yescharacteristic
36C4⋊Dic149C2×C411yescharacteristic
37#14558715—21no—
38C22⋊Dic149—21no—
39#14558713—21no—
40#14558713—21no—
41C4×Dic149C2×C411yescharacteristic
42C4×Dic149D411yescharacteristic
43C4×Dic149D411yescharacteristic
44C2×D4×C149C2×C411yescharacteristic
45C22×C4×C149—21no—
46C4⋊C4×C149C2×C411yescharacteristic
47C22⋊C4×C149—21no—
48C42×C149C2×C411yescharacteristic
49C2×#10597010—42no—
50C2×#10597010—42no—
51C2×#10597010—42no—
52#11924753—42no—
53C22×D149—21no—
54C22×D149C2×D411yescharacteristic
55Dic298—42no—
56D596—41no—
57D596—42no—
58C22⋊D149—42no—
59C22⋊D149—42no—
60C22⋊D149—42no—
61C2×Dic149—21no—
62C2×Dic149C22⋊C411yescharacteristic
63C2×Dic149C22⋊C411yescharacteristic
64C2×Dic149C2×D411yescharacteristic
65C4×D149—22no—
66C4×D149—41no—
67C4×D149—41no—
68C4×D149—42no—
69C23×C149—21no—
70D4×C149—41no—
71C2×C4×C149—21no—
72C2×C4×C149—42no—
73C2×C4×C149C22⋊C411yescharacteristic
74C2×C4×C149C22⋊C411yescharacteristic
75C2×C4×C149C22×C411yescharacteristic
76C22×C149—41no—
77C22×C149—41no—
78C22×C149—41no—
79C22×C149C2×C22⋊C411yescharacteristic
80C2×D149—21no—
81C2×D149—21no—
82C2×D149—41no—
83C2×D149—41no—
84C2×D149—41no—
85C2×D149AGL(1,ℤ/8)12yes—
86#10597010—82no—
87C4×C149—21no—
88C4×C149—21no—
89C4×C149—21no—
90C4×C149—41no—
91Dic149—21no—
92Dic149—21no—
93Dic149—21no—
94Dic149—41no—
95C2×C149—81no—
96C2×C149#41011yescharacteristic
97C2×C149#41811yescharacteristic
98C2×C149#42111yescharacteristic
99D149—22no—
100D149—81no—
101C149#151411yescharacteristic, complemented, Sylow
102#1514—1491nomaximal, Sylow
103#532—1491no—
104#432—1491no—
105#383—1491no—
106#327—1492no—
107#327—1492no—
108C2×#41—2981no—
109C4⋊Q8—1491no—
110#127—1491no—
111#124—2981no—
112#121—2981no—
113#121—1491no—
114#121—1491no—
115C4×D4—2981no—
116C4×D4—1491no—
117C4×D4#1059701011yescharacteristic, complemented
118C2×C42—1491no—
119C4⋊C8—2981no—
120C22⋊C8—1492no—
121#97—2981no—
122#95—2981no—
123#95—2981no—
124#95—1492no—
125#41—5964no—
126C2×Q8—2981no—
127C2×D4—2981no—
128C2×D4—2981no—
129C2×D4—2981no—
130C2×D4—2981no—
131C2×D4—1491no—
132C2×D4C2×#1059701011yescharacteristic
133C22×C4—21no—
134C22×C4—2981no—
135C22×C4—2982no—
136C22×C4—1491no—
137C22×C4—1491no—
138C22×C4—1491no—
139C2×C8—2982no—
140C4⋊C4—2981no—
141C4⋊C4—1491no—
142C4⋊C4C2×#1059701011yescharacteristic
143C22⋊C4—21no—
144C22⋊C4—2981no—
145C22⋊C4—2981no—
146C22⋊C4—2981no—
147C42—1491no—
148C42—1491no—
149C42—1491no—
150C42C2×#1059701011yescharacteristic
151C23—21no—
152C23—2981no—
153C23—1491no—
154Q8—5962no—
155D4—41no—
156D4—5961no—
157D4—5962no—
158D4—5962no—
159D4—5962no—
160D4—5962no—
161C2×C4—21no—
162C2×C4—42no—
163C2×C4—2982no—
164C2×C4—2981no—
165C2×C4—5961no—
166C2×C4—5961no—
167C2×C4—5962no—
168C2×C4—5962no—
169C2×C4—5962no—
170C2×C4—5962no—
171C2×C4—1491no—
172C2×C4—1491no—
173C2×C4—1491no—
174C2×C4C22⋊#1059701011yescharacteristic
175C2×C4C22⋊#1059701011yescharacteristic
176C2×C4C22×#1059701011yescharacteristic
177C8—5962no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—2981no—
182C22—2981no—
183C22—5961no—
184C22—5961no—
185C22—5961no—
186C22—1492no—
187C22C2×C22⋊#1059701011yescharacteristic
188C4—21no—
189C4—21no—
190C4—21no—
191C4—41no—
192C4—2981no—
193C4—2981no—
194C4—2981no—
195C4—5961no—
196C4—11922no—
197C2—81no—
198C2—2982no—
199C2—11921no—
200C2#2375060411yescharacteristic
201C2#2375061711yescharacteristic
202C2#2375062211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC4×D4×C149C4
socleC22×C149C2×C22⋊C4
prime radical#23750172C2
cosocleC2×C4×D149C23
hypercenterC4×D4#10597010
hypocenterC149#1514
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #23750647C2semidirect
2. #23750570C2semidirect
3. #23750477C2semidirect
4. #23750476C2semidirect
13. #18011910C4semidirect
14. #18011907C4semidirect
19. C4×D596C4semidirect
22. C4×D4×C149C4semidirect
101. C149#1514semidirect
117. C4×D4#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506472
#237505702
#237504772
#237504762
#237501722
#1514149