Finite Group Databasebeta

← #34060421

Subgroups — #34060421

Order 19072.

336 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 108 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
1C2×C22⋊#11924753C212yesmaximal
2C2×#18011966C211yesmaximal, characteristic, complemented
3C2×C4×#11924753C211yesmaximal, characteristic, complemented
4#23750491C212yesmaximal, complemented
5C2×#18011867C211yesmaximal, characteristic
6C22×#11924753C2212yes—
7C22×#11924753C2212yes—
8C22⋊#11924753C418yescomplemented
9#18011966—22no—
10C4×#11924753—22no—
11C23×Dic149C2211yescharacteristic
12#18011867—22no—
13#18011867—22no—
14C2×#14558715C411yescharacteristic
15C2×#14558715C411yescharacteristic
16C2×C22⋊Dic149C411yescharacteristic
17C2×C4×Dic149C2211yescharacteristic
18C2×C4×Dic149C2211yescharacteristic
19C2×C22⋊C4×C149C411yescharacteristic
20C2×#11924753—22no—
21C2×#11924753—22no—
22C2×#11924753—22no—
23C2×#11924753—22no—
24C2×#11924753C2×C414yes—
25C2×#11924753C2×C414yes—
26C22×Dic149—21no—
27C22×Dic149—21no—
28C22×Dic149—22no—
29C22×Dic149C2×C414yes—
30C22×Dic149C2×C411yescharacteristic
31C22×Dic149C2×C411yescharacteristic
32C22×Dic149C2×C411yescharacteristic
33C22×Dic149C2311yescharacteristic
34#14558715—22no—
35#14558715—22no—
36C22⋊Dic149—22no—
37C4×Dic149—21no—
38C4×Dic149—21no—
39C4×Dic149D412yes—
40C4×Dic149D412yes—
41C24×C149C2×C411yescharacteristic
42C22×C4×C149C2×C411yescharacteristic
43C22×C4×C149C2×C411yescharacteristic
44C22⋊C4×C149—22no—
45#11924753—24no—
46#11924753—24no—
47C2×Dic149—21no—
48C2×Dic149—21no—
49C2×Dic149—22no—
50C2×Dic149—24no—
51C2×Dic149—24no—
52C2×Dic149—21no—
53C2×Dic149—22no—
54C2×Dic149C4212yes—
55C2×Dic149C22⋊C412yes—
56C2×Dic149C22×C412yes—
57C2×Dic149C2×D411yescharacteristic
58C2×Dic149C2×D411yescharacteristic
59C2×Dic149#4112yes—
60C23×C149—21no—
61C23×C149—21no—
62C23×C149—22no—
63C23×C149—22no—
64C23×C149C4212yes—
65C23×C149C22×C411yescharacteristic
66C2×C4×C149—22no—
67C2×C4×C149—21no—
68C2×C4×C149—22no—
69C2×C4×C149C22⋊C412yes—
70C22×C149—22no—
71C22×C149—24no—
72C22×C149—41no—
73C22×C149—41no—
74C22×C149—42no—
75C22×C149C2×C4211yescharacteristic
76C22×C149C2×C22⋊C411yescharacteristic
77C22×C149#11711yescharacteristic
78C22×C149#13112yes—
79C22×C149#13112yes—
80C4×C149—22no—
81C4×C149—41no—
82Dic149—22no—
83Dic149—22no—
84Dic149—41no—
85Dic149C4×D412yes—
86Dic149C4×D412yes—
87C2×C149—42no—
88C2×C149C4×C22⋊C411yescharacteristic
89C2×C149#40512yes—
90C2×C149#40811yescharacteristic
91C2×C149#40811yescharacteristic
92C2×C149#43312yes—
93C149#175011yescharacteristic, complemented, Sylow
94#1750—1491nomaximal, Sylow
95C2×#117—1491no—
96C2×C22⋊C8—1492no—
97C2×#97—1491no—
98C2×C4×C8—1491no—
99#336—1492no—
100C23×C4—1491no—
101C22×C8—1492no—
102C22×C8—1492no—
103#117—2982no—
104#117—2982no—
105C2×C4⋊C4—1491no—
106C2×C4⋊C4—1491no—
107C2×C22⋊C4—1491no—
108C2×C22⋊C4#1059701011yescharacteristic
109C2×C42—1491no—
110C2×C42—1491no—
111C22⋊C8—1498no—
112#97—2982no—
113C4×C8—2982no—
114C24C2×#1059701011yescharacteristic
115C22×C4—2981no—
116C22×C4—2981no—
117C22×C4—2982no—
118C22×C4—1491no—
119C22×C4—1494no—
120C22×C4—1491no—
121C22×C4—1491no—
122C22×C4—1491no—
123C22×C4C2×#1059701011yescharacteristic
124C22×C4C2×#1059701011yescharacteristic
125C2×C8—2982no—
126C2×C8—2982no—
127C2×C8—2982no—
128C2×C8—2982no—
129C2×C8—1494no—
130C2×C8—1494no—
131C4⋊C4—2982no—
132C4⋊C4—2982no—
133C22⋊C4—22no—
134C22⋊C4—2982no—
135C42—2981no—
136C42—2981no—
137C42—1492no—
138C42—1492no—
139C23—21no—
140C23—21no—
141C23—22no—
142C23—22no—
143C23C4×#1059701012yes—
144C23C22×#1059701011yescharacteristic
145C2×C4—22no—
146C2×C4—21no—
147C2×C4—22no—
148C2×C4—2981no—
149C2×C4—2981no—
150C2×C4—2982no—
151C2×C4—2984no—
152C2×C4—2984no—
153C2×C4—2981no—
154C2×C4—2982no—
155C2×C4—1492no—
156C2×C4—1492no—
157C2×C4—1492no—
158C2×C4—1491no—
159C2×C4—1491no—
160C2×C4—1492no—
161C2×C4C22⋊#1059701012yes—
162C8—2984no—
163C8—2984no—
164C22—22no—
165C22—24no—
166C22—41no—
167C22—41no—
168C22—42no—
169C22C2×C4×#1059701011yescharacteristic
170C22C2×C22⋊#1059701011yescharacteristic
171C22#1801199011yescharacteristic
172C22#1801199812yes—
173C22#1801199812yes—
174C4—22no—
175C4—41no—
176C4—2982no—
177C4—2982no—
178C4—5961no—
179C4—1492no—
180C4—1492no—
181C2—42no—
182C2C4×C22⋊#1059701011yescharacteristic
183C2#2375058912yes—
184C2#2375059811yescharacteristic
185C2#2375059911yescharacteristic
186C2#2375064912yes—
subgroupG/H
center, FrattiniC23C22×#10597010
commutatorC22×C149C2×C42
FittingC2×C22⋊C4×C149C4
socleC23×C149C22×C4
prime radicalC24×C149C2×C4
cosocleC22×Dic149C23
hypercenterC2×C22⋊C4#10597010
hypocenterC149#1750
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#18011966C2semidirect
3. C2×C4×#11924753C2semidirect
4. #23750491C2semidirect
8. C22⋊#11924753C4semidirect
93. C149#1750semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊#119247532
C2×#180119662
C2×C4×#119247532
#237504912
C2×#180118672
#1750149