Finite Group Databasebeta

← #34060113

Subgroups — #34060113

Order 19072.

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

normal subgroups only

This group has 208 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
2#23750570C211yesmaximal, characteristic
3#23750479C212yesmaximal
4#23750478C212yesmaximal
5#23750179C211yesmaximal, characteristic
6C4⋊#11924753—21no—
7#18011968C2212yes—
8#18011966—21no—
9(C2×#10597010)⋊C4—21no—
10(C2×#10597010)⋊C4—21no—
11(C2×#10597010)⋊C4C2212yes—
12#18011910C411yescharacteristic, complemented
13#18011909C411yescharacteristic, complemented
14#18011901—21no—
15#18011891C2211yescharacteristic
16#18011889—21no—
17#18011887C2211yescharacteristic
18C4×Dic298—21no—
19C4×Dic298C411yescharacteristic, complemented
20#18011868—21no—
21C42×D149C2211yescharacteristic
22C4×Q8×C149C411yescharacteristic, complemented
23C22×#10597010—22no—
24C2×#11924753—22no—
25C2×Dic298—21no—
26C2×Dic298C2×C411yescharacteristic
27C2×C4×D149D411yescharacteristic
28C2×C4×D149D411yescharacteristic
29C2×C4×D149C2311yescharacteristic
30C4⋊Dic149—21no—
31C4⋊Dic149C2×C411yescharacteristic
32#14558715—21no—
33#14558715—21no—
34#14558715—21no—
35#14558715—21no—
36#14558715—21no—
37#14558713—21no—
38#14558713—21no—
39C4×Dic149—21no—
40C4×Dic149C2×C411yescharacteristic
41C4×Dic149D411yescharacteristic
42C4×Dic149D411yescharacteristic
43C2×Q8×C149C2×C411yescharacteristic
44C4⋊C4×C149—21no—
45C4⋊C4×C149C2×C411yescharacteristic
46C42×C149—21no—
47C42×C149C2×C411yescharacteristic
48C2×#10597010—42no—
49C2×#10597010—42no—
50C2×#10597010—42no—
51#11924753—42no—
52C22×D149C2×D411yescharacteristic
53Dic298—42no—
54Dic298—41no—
55C2×Dic149—21no—
56C2×Dic149—21no—
57C2×Dic149C22⋊C411yescharacteristic
58C2×Dic149C22⋊C411yescharacteristic
59C2×Dic149C2×D411yescharacteristic
60C4×D149—22no—
61C4×D149—41no—
62C4×D149—41no—
63Q8×C149—41no—
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#13712yes—
73#10597010—82no—
74C4×C149—21no—
75C4×C149—21no—
76C4×C149—21no—
77C4×C149—41no—
78C4×C149—41no—
79Dic149—21no—
80Dic149—21no—
81Dic149—21no—
82Dic149—41no—
83Dic149—41no—
84C2×C149#41011yescharacteristic
85C2×C149#41911yescharacteristic
86C2×C149#42111yescharacteristic
87D149—22no—
88C149#151511yescharacteristic, complemented, Sylow
89#1515—1491nomaximal, Sylow
90#533—1491no—
91#432—1491no—
92#383—1491no—
93#328—1492no—
94#328—1492no—
95C4⋊Q8—1491no—
96C4⋊Q8—1491no—
97#125—2981no—
98C22⋊Q8—2981no—
99C22⋊Q8—1491no—
100C22⋊Q8—1491no—
101C4×Q8—2981no—
102C4×Q8—1491no—
103C4×Q8#1059701011yescharacteristic, complemented
104#117—2981no—
105C2×C42—1491no—
106C4⋊C8—2981no—
107C22⋊C8—1492no—
108#97—2981no—
109#95—2981no—
110#95—2981no—
111#95—1492no—
112C2×Q8—2981no—
113C2×Q8—1491no—
114C2×Q8C2×#1059701011yescharacteristic
115C22×C4—2982no—
116C22×C4—1491no—
117C22×C4—1491no—
118C22×C4—1491no—
119C2×C8—2982no—
120C4⋊C4—21no—
121C4⋊C4—2981no—
122C4⋊C4—2981no—
123C4⋊C4—2981no—
124C4⋊C4—2981no—
125C4⋊C4—2981no—
126C4⋊C4—2981no—
127C4⋊C4—1491no—
128C4⋊C4C2×#1059701011yescharacteristic
129C22⋊C4—2981no—
130C22⋊C4—2981no—
131C42—21no—
132C42—2981no—
133C42—1491no—
134C42—1491no—
135C42—1491no—
136C42C2×#1059701011yescharacteristic
137C23—1491no—
138Q8—41no—
139Q8—5961no—
140Q8—5962no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—2982no—
144C2×C4—2981no—
145C2×C4—2981no—
146C2×C4—5961no—
147C2×C4—5961no—
148C2×C4—5962no—
149C2×C4—5962no—
150C2×C4—5962no—
151C2×C4—1491no—
152C2×C4—1491no—
153C2×C4—1491no—
154C2×C4C22⋊#1059701011yescharacteristic
155C2×C4C22⋊#1059701011yescharacteristic
156C2×C4C22×#1059701011yescharacteristic
157C8—5962no—
158C22—2981no—
159C22—2981no—
160C22—1492no—
161C22C2×C22⋊#1059701011yescharacteristic
162C4—21no—
163C4—21no—
164C4—21no—
165C4—41no—
166C4—41no—
167C4—2981no—
168C4—2981no—
169C4—2981no—
170C4—5961no—
171C4—5961no—
172C4—11922no—
173C2—2982no—
174C2#2375060411yescharacteristic
175C2#2375061811yescharacteristic
176C2#2375062211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC4×Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC22×D149C2×D4
cosocleC2×C4×D149C23
hypercenterC4×Q8#10597010
hypocenterC149#1515
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
12. #18011910C4semidirect
13. #18011909C4semidirect
19. C4×Dic298C4semidirect
22. C4×Q8×C149C4semidirect
88. C149#1515semidirect
103. C4×Q8#10597010semidirect

Maximal subgroups

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

subgroupindex
#237506472
#237505702
#237504792
#237504782
#237501792
#1515149