Finite Group Databasebeta

← #34055901

Subgroups — #34055901

Order 19072.

322 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 121 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#23750182C211yesmaximal, characteristic
2#23750031C212yesmaximal, complemented
3#23749993C212yesmaximal, complemented
4#23749963C214yesmaximal
5#23749920C212yesmaximal, complemented
6#23749910C212yesmaximal, complemented
7#23749682C211yesmaximal, characteristic
8#533×C149C211yesmaximal, characteristic
9#18011911C2211yescharacteristic
10#18011911C2211yescharacteristic
11#18011903C2212yes—
12#18011890—21no—
13#18011890—21no—
14C4×Dic298—21no—
15C4×Dic298—21no—
16#18011870C2212yes—
17#18011844C2214yes—
18#18011842C2214yes—
19C4⋊#11924746C2212yes—
20#18011835C2214yes—
21#18011835C2214yes—
22C22⋊#11924746C2212yes—
23#18011822C2212yes—
24C4⋊Q8×C149C2211yescharacteristic
25C4⋊Q8×C149C2211yescharacteristic
26#125×C149—21no—
27C22⋊Q8×C149—21no—
28C22⋊Q8×C149C2212yes—
29C4×Q8×C149—21no—
30C4×Q8×C149C2212yes—
31#117×C149—21no—
32C2×C42×C149C2211yescharacteristic
33C2×Dic298—21no—
34C2×Dic298—21no—
35C2×#11924746C2314yes—
36C4⋊Dic149—21no—
37C4⋊Dic149—21no—
38C4⋊Dic149C2312yes—
39C4⋊Dic149C2312yes—
40#14558715—22no—
41#14558715—22no—
42C22⋊Dic149—22no—
43C4×Dic149—22no—
44C2×Q8×C149—21no—
45C2×Q8×C149C2312yes—
46C22×C4×C149D411yescharacteristic
47C22×C4×C149D411yescharacteristic
48C22×C4×C149C2311yescharacteristic
49C4⋊C4×C149—21no—
50C4⋊C4×C149—21no—
51C4⋊C4×C149—21no—
52C4⋊C4×C149—22no—
53C4⋊C4×C149—22no—
54C4⋊C4×C149C2312yes—
55C22⋊C4×C149—22no—
56C42×C149—22no—
57C42×C149D411yescharacteristic
58C42×C149D411yescharacteristic
59C42×C149C2311yescharacteristic
60C42×C149C2311yescharacteristic
61Dic298—42no—
62Dic298—42no—
63C2×Dic149—22no—
64C2×Dic149—22no—
65#11924746—24no—
66C23×C149C2×D411yescharacteristic
67Q8×C149—24no—
68Q8×C149—42no—
69C2×C4×C149—22no—
70C2×C4×C149—22no—
71C2×C4×C149—22no—
72C2×C4×C149—22no—
73C2×C4×C149—41no—
74C2×C4×C149C2×D411yescharacteristic
75C2×C4×C149C2×D411yescharacteristic
76C2×C4×C149C2×D411yescharacteristic
77C2×C4×C149C2×D411yescharacteristic
78C2×C4×C149C2×D411yescharacteristic
79C2×C4×C149C2411yescharacteristic
80C22×C149—21no—
81C22×C149—21no—
82C22×C149—21no—
83C22×C149C22×D411yescharacteristic
84C4×C149—21no—
85C4×C149—21no—
86C4×C149—21no—
87C4×C149—21no—
88C4×C149—42no—
89C4×C149—42no—
90C4×C149#13712yes—
91C4×C1492−1+412yes—
92Dic149—42no—
93Dic149—42no—
94C2×C149—41no—
95C2×C149#53611yescharacteristic
96C2×C149C2×#13711yescharacteristic
97C2×C149#57511yescharacteristic
98C149#323711yescharacteristic, complemented, Sylow
99#3237—1491nomaximal, Sylow
100#533—1491no—
101#533D14911yescharacteristic
102#501—1492no—
103#491—1492no—
104#485—1494no—
105#477—1492no—
106#475—1492no—
107#432—1491no—
108C4⋊Q8—1491no—
109C4⋊Q8—1491no—
110C4⋊Q8C2×D14911yescharacteristic
111C4⋊Q8C2×D14911yescharacteristic
112#125—21no—
113#125—1492no—
114C22⋊Q8—21no—
115C22⋊Q8—2981no—
116C22⋊Q8—2981no—
117C22⋊Q8C2×D14912yes—
118C4×Q8—21no—
119C4×Q8—2981no—
120C4×Q8—2981no—
121C4×Q8C2×D14912yes—
122#117—21no—
123#117—1492no—
124C2×C42C2×D14911yescharacteristic
125#107—1494no—
126#106—1494no—
127C4⋊C8—1492no—
128#103—1494no—
129#103—1494no—
130C22⋊C8—1492no—
131#97—1492no—
132C2×Q8—21no—
133C2×Q8—2981no—
134C2×Q8—2981no—
135C2×Q8C22×D14912yes—
136C22×C4C22⋊D14911yescharacteristic
137C22×C4C22⋊D14911yescharacteristic
138C22×C4C22×D14911yescharacteristic
139C2×C8—1494no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—22no—
144C4⋊C4—22no—
145C4⋊C4—2982no—
146C4⋊C4—2982no—
147C4⋊C4—2981no—
148C4⋊C4—2981no—
149C4⋊C4—1492no—
150C4⋊C4—1492no—
151C4⋊C4C22×D14912yes—
152C22⋊C4—22no—
153C22⋊C4—2982no—
154C42—22no—
155C42—2982no—
156C42C22⋊D14911yescharacteristic
157C42C22⋊D14911yescharacteristic
158C42C22×D14911yescharacteristic
159C42C22×D14911yescharacteristic
160C23C2×C22⋊D14911yescharacteristic
161Q8—24no—
162Q8—42no—
163Q8—5962no—
164Q8—5962no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—41no—
170C2×C4—2982no—
171C2×C4—2982no—
172C2×C4C2×C22⋊D14911yescharacteristic
173C2×C4C2×C22⋊D14911yescharacteristic
174C2×C4C2×C22⋊D14911yescharacteristic
175C2×C4C2×C22⋊D14911yescharacteristic
176C2×C4C2×C22⋊D14911yescharacteristic
177C2×C4C23×D14911yescharacteristic
178C8—2984no—
179C22—21no—
180C22—21no—
181C22—21no—
182C22C22×C22⋊D14911yescharacteristic
183C4—21no—
184C4—21no—
185C4—21no—
186C4—21no—
187C4—42no—
188C4—42no—
189C4—5962no—
190C4—5962no—
191C4#1801194212yes—
192C4#1801195812yes—
193C2—41no—
194C2#2375019611yescharacteristic
195C2C2×#1801194211yescharacteristic
196C2#2375042311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#533×C149C2
socleC22×C149C22×D4
prime radicalC23×C149C2×D4
hypercenter#533D149
hypocenterC149#3237
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #23750031C2semidirect
3. #23749993C2semidirect
5. #23749920C2semidirect
6. #23749910C2semidirect
98. C149#3237semidirect

Maximal subgroups

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

subgroupindex
#237501822
#237500312
#237499932
#237499632
#237499202
#237499102
#237496822
#533×C1492
#3237149