Finite Group Databasebeta

← #34060039

Subgroups — #34060039

Order 19072.

232 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 72 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#23750628C211yesmaximal, characteristic
2C2×C4×#11924753C211yesmaximal, characteristic
3#23750475C212yesmaximal, complemented
4Q8⋊#11924753C212yesmaximal, complemented
5#23750177C211yesmaximal, characteristic
6C2×#14558745—21no—
7C22×#11924753—21no—
8#18011978—21no—
9C4⋊#11924753C2212yes—
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—42no—
24C2×#11924753—24no—
25C2×#11924753—22no—
26C2×#11924753—22no—
27C2×Dic298—21no—
28C2×Dic298C2×C411yescharacteristic
29C22×Dic149D411yescharacteristic
30C22×Dic149D411yescharacteristic
31C4⋊Dic149—21no—
32C4⋊Dic149C2×C411yescharacteristic
33#14558715—21no—
34#14558715—21no—
35#14558715—21no—
36#14558715—21no—
37#14558715—21no—
38C22⋊Dic149—21no—
39C4×Dic149—21no—
40C4×Dic149—21no—
41C4×Dic149C2×C411yescharacteristic
42C4×Dic149D411yescharacteristic
43C4×Dic149D411yescharacteristic
44C4×Dic149C2311yescharacteristic
45C2×Q8×C149C2×C411yescharacteristic
46C22×C4×C149C2×C411yescharacteristic
47C4⋊C4×C149—21no—
48C4⋊C4×C149C2×C411yescharacteristic
49C22⋊C4×C149—21no—
50#11924753—24no—
51#11924753—42no—
52Dic298—22no—
53Dic298—42no—
54C2×Dic149—22no—
55C2×Dic149—21no—
56C2×Dic149—21no—
57C2×Dic149C22⋊C411yescharacteristic
58C2×Dic149C22⋊C411yescharacteristic
59C2×Dic149SD1612yes—
60C2×Dic149Q1612yes—
61C2×Dic149C2×D411yescharacteristic
62C2×Dic149C2×D411yescharacteristic
63C23×C149C22⋊C411yescharacteristic
64Q8×C149—22no—
65C2×C4×C149—22no—
66C2×C4×C149—21no—
67C2×C4×C149—21no—
68C2×C4×C149C22⋊C411yescharacteristic
69C2×C4×C149C22×C411yescharacteristic
70C22×C149—21no—
71C22×C149—21no—
72C22×C149#10312yes—
73C22×C149C2×C22⋊C411yescharacteristic
74C4×C149—21no—
75C4×C149—41no—
76C4×C149—41no—
77C4×C149#13112yes—
78Dic149—21no—
79Dic149—41no—
80Dic149—41no—
81Dic149#10312yes—
82Dic149#10412yes—
83Dic149C2×SD1611yescharacteristic
84Dic149C2×Q1611yescharacteristic
85C2×C149—22no—
86C2×C149#40811yescharacteristic
87C2×C149C2×#10311yescharacteristic
88C2×C149C2×#10411yescharacteristic
89C149#149311yescharacteristic, complemented, Sylow
90#1493—1491nomaximal, Sylow
91#533—1491no—
92#423—1491no—
93C2×C4×C8—1491no—
94Q8⋊C8—1492no—
95Q8⋊C8—1492no—
96C2×M16—2981no—
97C22×C8—2981no—
98C4⋊Q8—1491no—
99C4⋊Q8—1491no—
100#125—2981no—
101C22⋊Q8—2981no—
102C22⋊Q8—1491no—
103C22⋊Q8#1059701011yescharacteristic
104C4×Q8—2981no—
105C4×Q8—1491no—
106C4×Q8—1491no—
107#117—2981no—
108C2×C42—1491no—
109C4⋊C8—2981no—
110C4⋊C8—1492no—
111C4×C8—2981no—
112C4×C8—1492no—
113C2×Q8—2981no—
114C2×Q8—1491no—
115C2×Q8C2×#1059701011yescharacteristic
116C22×C4—1491no—
117C22×C4—1491no—
118C22×C4C2×#1059701011yescharacteristic
119M16—5962no—
120C2×C8—2984no—
121C2×C8—2982no—
122C2×C8—2982no—
123C4⋊C4—21no—
124C4⋊C4—2981no—
125C4⋊C4—2981no—
126C4⋊C4—2981no—
127C4⋊C4—2981no—
128C4⋊C4—2981no—
129C4⋊C4—2981no—
130C4⋊C4—1491no—
131C4⋊C4C2×#1059701011yescharacteristic
132C22⋊C4—21no—
133C22⋊C4—2981no—
134C42—2981no—
135C42—2981no—
136C42—1491no—
137C42—1491no—
138C42—1491no—
139C42—1491no—
140C23C22⋊#1059701011yescharacteristic
141Q8—22no—
142Q8—2982no—
143Q8—5962no—
144C2×C4—22no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—2982no—
148C2×C4—2981no—
149C2×C4—2981no—
150C2×C4—1491no—
151C2×C4—1492no—
152C2×C4—1492no—
153C2×C4—1491no—
154C2×C4—1491no—
155C2×C4—1491no—
156C2×C4C22⋊#1059701011yescharacteristic
157C2×C4C22×#1059701011yescharacteristic
158C8—2984no—
159C8—5962no—
160C22—21no—
161C22—21no—
162C22#1801197412yes—
163C22C2×C22⋊#1059701011yescharacteristic
164C4—21no—
165C4—41no—
166C4—41no—
167C4—2981no—
168C4—5961no—
169C4—5961no—
170C4—1491no—
171C4—1492no—
172C4—1491no—
173C4—1492no—
174C4#1801199812yes—
175C2—22no—
176C2#2375059811yescharacteristic
177C2C2×#1801197411yescharacteristic
178C2D149⋊#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#1493
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
89. C149#1493semidirect

Maximal subgroups

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

subgroupindex
#237506282
C2×C4×#119247532
#237504752
Q8⋊#119247532
#237501772
#1493149