Finite Group Databasebeta

← #34060013

Subgroups — #34060013

Order 19072.

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

normal subgroups only

This group has 218 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#23750641C211yesmaximal, characteristic
2C4×#14558745C211yesmaximal, characteristic
3#23750475C212yesmaximal, complemented
4Q8⋊#11924753C212yesmaximal, complemented
5#23750177C211yesmaximal, characteristic
6C2×#14558745—21no—
7C4⋊#11924753C2212yes—
8C22⋊#11924753—21no—
9#18011966—21no—
10C4×#11924753—21no—
11C4×#11924753C2212yes—
12#18011910C411yescharacteristic
13#18011909C411yescharacteristic
14#18011901—21no—
15#18011890C411yescharacteristic
16#18011888—21no—
17Q8×Dic149C2211yescharacteristic
18#18011876—21no—
19#18011876C2211yescharacteristic
20#18011867—21no—
21C2×C4×Dic149C2211yescharacteristic
22C22⋊Q8×C149C411yescharacteristic
23#14558745—24no—
24C2×#11924753—22no—
25C2×#11924753—22no—
26C2×Dic298—21no—
27C2×Dic298C2×C411yescharacteristic
28C22×Dic149D411yescharacteristic
29C22×Dic149D411yescharacteristic
30C4⋊Dic149—21no—
31C4⋊Dic149C2×C411yescharacteristic
32#14558715—21no—
33#14558715—21no—
34#14558715—21no—
35#14558715—21no—
36#14558715—21no—
37C22⋊Dic149—21no—
38C4×Dic149—21no—
39C4×Dic149—21no—
40C4×Dic149C2×C411yescharacteristic
41C4×Dic149D411yescharacteristic
42C4×Dic149D411yescharacteristic
43C4×Dic149C2311yescharacteristic
44C2×Q8×C149C2×C411yescharacteristic
45C22×C4×C149C2×C411yescharacteristic
46C4⋊C4×C149—21no—
47C4⋊C4×C149C2×C411yescharacteristic
48C22⋊C4×C149—21no—
49#11924753—24no—
50#11924753—42no—
51Dic298—22no—
52Dic298—42no—
53C2×Dic149—22no—
54C2×Dic149—22no—
55C2×Dic149—21no—
56C2×Dic149—21no—
57C2×Dic149C22⋊C411yescharacteristic
58C2×Dic149C22⋊C411yescharacteristic
59C2×Dic149C2×D411yescharacteristic
60C2×Dic149C2×D411yescharacteristic
61C23×C149C22⋊C411yescharacteristic
62Q8×C149—22no—
63C2×C4×C149—22no—
64C2×C4×C149—21no—
65C2×C4×C149—21no—
66C2×C4×C149C22⋊C411yescharacteristic
67C2×C4×C149C22×C411yescharacteristic
68C22×C149—21no—
69C22×C149—21no—
70C22×C149—21no—
71C22×C149C2×C22⋊C411yescharacteristic
72C4×C149—21no—
73C4×C149—41no—
74C4×C149—41no—
75C4×C149#13112yes—
76Dic149—21no—
77Dic149—21no—
78Dic149—41no—
79Dic149—41no—
80Dic149#10412yes—
81Dic149#13712yes—
82C2×C149—41no—
83C2×C149#40811yescharacteristic
84C2×C149#41911yescharacteristic
85C2×C149C2×#10411yescharacteristic
86C149#148511yescharacteristic, complemented, Sylow
87#1485—1491nomaximal, Sylow
88#533—1491no—
89#431—1491no—
90C4×M16—1491no—
91Q8⋊C8—1492no—
92Q8⋊C8—1492no—
93C2×M16—2981no—
94C4⋊Q8—1491no—
95C4⋊Q8—1491no—
96#125—2981no—
97C22⋊Q8—2981no—
98C22⋊Q8—1491no—
99C22⋊Q8#1059701011yescharacteristic
100C4×Q8—2981no—
101C4×Q8—1491no—
102C4×Q8—1491no—
103#117—2981no—
104C2×C42—1491no—
105C4⋊C8—1492no—
106C22⋊C8—2981no—
107#97—2981no—
108C4×C8—2981no—
109C4×C8—1492no—
110C2×Q8—2981no—
111C2×Q8—1491no—
112C2×Q8C2×#1059701011yescharacteristic
113C22×C4—1491no—
114C22×C4—1491no—
115C22×C4C2×#1059701011yescharacteristic
116M16—2984no—
117C2×C8—2982no—
118C2×C8—2982no—
119C4⋊C4—21no—
120C4⋊C4—2981no—
121C4⋊C4—2981no—
122C4⋊C4—2981no—
123C4⋊C4—2981no—
124C4⋊C4—2981no—
125C4⋊C4—2981no—
126C4⋊C4—1491no—
127C4⋊C4C2×#1059701011yescharacteristic
128C22⋊C4—21no—
129C22⋊C4—2981no—
130C42—2981no—
131C42—2981no—
132C42—1491no—
133C42—1491no—
134C42—1491no—
135C42—1491no—
136C23C22⋊#1059701011yescharacteristic
137Q8—22no—
138Q8—2982no—
139Q8—5962no—
140C2×C4—22no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—2982no—
144C2×C4—2982no—
145C2×C4—2981no—
146C2×C4—2981no—
147C2×C4—1491no—
148C2×C4—1491no—
149C2×C4—1491no—
150C2×C4—1491no—
151C2×C4C22⋊#1059701011yescharacteristic
152C2×C4C22×#1059701011yescharacteristic
153C8—2984no—
154C8—5962no—
155C22—21no—
156C22—21no—
157C22—21no—
158C22C2×C22⋊#1059701011yescharacteristic
159C4—21no—
160C4—41no—
161C4—41no—
162C4—2981no—
163C4—2981no—
164C4—5961no—
165C4—5961no—
166C4—1492no—
167C4—1492no—
168C4#1801199812yes—
169C2—41no—
170C2#2375059811yescharacteristic
171C2#2375061811yescharacteristic
172C2D149⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC22⋊Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC23×C149C22⋊C4
cosocleC4×Dic149C23
hypercenterC22⋊Q8#10597010
hypocenterC149#1485
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #23750475C2semidirect
4. Q8⋊#11924753C2semidirect
86. C149#1485semidirect

Maximal subgroups

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

subgroupindex
#237506412
C4×#145587452
#237504752
Q8⋊#119247532
#237501772
#1485149