Finite Group Databasebeta

← #34060101

Subgroups — #34060101

Order 19072.

274 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 60 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#23750597C211yesmaximal, characteristic
2#23750568C211yesmaximal, characteristic
3#23750479C214yesmaximal, complemented
4C2×#18011887C211yesmaximal, characteristic
5C2×#14558745—21no—
6C2×C22⋊#10597010—21no—
7#18011968—21no—
8#18011968C2212yes—
9(C2×#10597010)⋊C4—21no—
10(C2×#10597010)⋊C4C2212yes—
11C22×C4×D149C2211yescharacteristic
12#18011887—21no—
13#18011887—21no—
14#18011887C412yescomplemented
15#18011887C2212yes—
16C2×C4⋊Dic149C411yescharacteristic, complemented
17C2×#14558715—21no—
18C2×#14558713—21no—
19C22×Q8×C149C411yescharacteristic, complemented
20C22×#10597010—22no—
21#14558745—42no—
22C2×#11924753—22no—
23C22⋊#10597010—42no—
24C23×D149D411yescharacteristic
25C22×Dic149—21no—
26C22×Dic149D411yescharacteristic
27C2×C4×D149—42no—
28C2×C4×D149C2×C411yescharacteristic
29C2×C4×D149D411yescharacteristic
30C2×C4×D149D411yescharacteristic
31C2×C4×D149C2311yescharacteristic
32C4⋊Dic149—21no—
33C4⋊Dic149C2×C412yes—
34#14558715—22no—
35#14558715—22no—
36#14558713—22no—
37#14558713—22no—
38C2×Q8×C149—21no—
39C2×Q8×C149—42no—
40C2×Q8×C149C2×C412yes—
41C22×C4×C149—21no—
42C22×C4×C149C2×C411yescharacteristic
43C2×#10597010—42no—
44C2×#10597010—42no—
45C2×#10597010—42no—
46#11924753—42no—
47C22×D149—22no—
48C22×D149—22no—
49C22×D149—41no—
50C22×D149C22⋊C411yescharacteristic
51C22×D149C2×D411yescharacteristic
52C2×Dic149—22no—
53C2×Dic149—22no—
54C2×Dic149—42no—
55C2×Dic149C22⋊C411yescharacteristic
56C2×Dic149C2×D411yescharacteristic
57C4×D149—41no—
58C4×D149—41no—
59C4×D149—41no—
60C4×D149—41no—
61C23×C149C22⋊C411yescharacteristic
62Q8×C149—42no—
63Q8×C149—42no—
64C2×C4×C149—22no—
65C2×C4×C149—22no—
66C2×C4×C149—42no—
67C2×C4×C149C22⋊C411yescharacteristic
68C2×C4×C149C22×C411yescharacteristic
69C22×C149—21no—
70C22×C149—21no—
71C22×C149#9912yes—
72C22×C149C2×C22⋊C411yescharacteristic
73C2×D149—21no—
74C2×D149—21no—
75C2×D149—21no—
76C2×D149—21no—
77C2×D149—21no—
78C2×D149—44no—
79C2×D149#13712yes—
80#10597010—82no—
81C4×C149—21no—
82C4×C149—21no—
83C4×C149—42no—
84Dic149—21no—
85Dic149—21no—
86Dic149—42no—
87C2×C149—22no—
88C2×C149C2×#9911yescharacteristic
89C2×C149#41911yescharacteristic
90C2×C149#42111yescharacteristic
91D149—22no—
92D149—41no—
93C149#151111yescharacteristic, complemented, Sylow
94#1511—1491nomaximal, Sylow
95C2×C22⋊Q8—1491no—
96#407—1491no—
97#381—1491no—
98#328—1494no—
99C22×Q8#1059701011yescharacteristic, complemented
100C23×C4—1491no—
101C2×M16—2981no—
102C22⋊Q8—2981no—
103C22⋊Q8—2981no—
104C22⋊Q8—1492no—
105C22⋊Q8—1492no—
106C2×C4⋊C4—2981no—
107C2×C4⋊C4—1491no—
108C2×C22⋊C4—2981no—
109C2×C22⋊C4—2981no—
110C22⋊C8—2981no—
111C22⋊C8—1492no—
112#95—2981no—
113#95—1492no—
114C24—1491no—
115C2×Q8—21no—
116C2×Q8—42no—
117C2×Q8C2×#1059701012yes—
118C22×C4—21no—
119C22×C4—2981no—
120C22×C4—2982no—
121C22×C4—5962no—
122C22×C4—1491no—
123C22×C4—1491no—
124C22×C4—1491no—
125C22×C4—1491no—
126C22×C4—1491no—
127C22×C4C2×#1059701011yescharacteristic
128M16—5962no—
129C2×C8—2982no—
130C4⋊C4—2982no—
131C4⋊C4—2982no—
132C4⋊C4—2981no—
133C4⋊C4—1492no—
134C22⋊C4—2982no—
135C22⋊C4—2982no—
136C22⋊C4—5962no—
137C23—2982no—
138C23—2982no—
139C23—5961no—
140C23—1491no—
141C23—1491no—
142C23C22⋊#1059701011yescharacteristic
143Q8—42no—
144Q8—42no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—42no—
148C2×C4—2982no—
149C2×C4—2982no—
150C2×C4—5961no—
151C2×C4—5961no—
152C2×C4—5961no—
153C2×C4—5961no—
154C2×C4—5962no—
155C2×C4—5962no—
156C2×C4—5962no—
157C2×C4—5962no—
158C2×C4—1491no—
159C2×C4—1491no—
160C2×C4C22⋊#1059701011yescharacteristic
161C2×C4C22×#1059701011yescharacteristic
162C8—5962no—
163C22—21no—
164C22—21no—
165C22—2981no—
166C22—2981no—
167C22—2981no—
168C22—2981no—
169C22—2981no—
170C22—5964no—
171C22—1492no—
172C22#1801196912yes—
173C22C2×C22⋊#1059701011yescharacteristic
174C4—21no—
175C4—21no—
176C4—42no—
177C4—2981no—
178C4—2981no—
179C4—5962no—
180C4—11922no—
181C2—22no—
182C2—2982no—
183C2—5961no—
184C2C2×#1801196911yescharacteristic
185C2#2375061811yescharacteristic
186C2#2375062411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC22×Q8×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC23×D149D4
cosocleC2×C4×D149C23
hypercenterC22×Q8#10597010
hypocenterC149#1511
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
3. #23750479C2semidirect
14. #18011887C4semidirect
16. C2×C4⋊Dic149C4semidirect
19. C22×Q8×C149C4semidirect
93. C149#1511semidirect
99. C22×Q8#10597010semidirect

Maximal subgroups

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

subgroupindex
#237505972
#237505682
#237504792
C2×#180118872
#1511149