Finite Group Databasebeta

← #34055639

Subgroups — #34055639

Order 19072.

384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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#23750004C212yesmaximal, complemented
3#23749975C212yesmaximal, complemented
4#23749832C214yesmaximal, complemented
5#23749781C214yesmaximal
6#23749678C211yesmaximal, characteristic
7C2×C4⋊Q8×C149C211yesmaximal, characteristic
8C2×#14558726C2218yes—
9#18011911C2211yescharacteristic
10#18011911C2211yescharacteristic
11#18011903—21no—
12#18011890—21no—
13#18011890C2212yes—
14C4×Dic298—21no—
15C4×Dic298C2212yes—
16#18011870—21no—
17C4⋊#11924746C2212yes—
18#18011835C2218yes—
19C22⋊#11924746C2212yes—
20C4×#11924746C2212yes—
21C22×Q8×C149C2212yes—
22C4⋊Q8×C149—21no—
23C4⋊Q8×C149—21no—
24C4⋊Q8×C149C2212yes—
25C4⋊Q8×C149C2212yes—
26C2×C4⋊C4×C149—21no—
27C2×C4⋊C4×C149—21no—
28C2×C42×C149C2211yescharacteristic
29C2×Dic298—21no—
30C2×Dic298C2312yes—
31#14558726—48no—
32C2×#11924746C2314yes—
33C4⋊Dic149—21no—
34C4⋊Dic149—21no—
35C4⋊Dic149—21no—
36C4⋊Dic149C2312yes—
37#14558715—22no—
38#14558715—22no—
39C22⋊Dic149—22no—
40C4×Dic149—22no—
41C2×Q8×C149—22no—
42C2×Q8×C149—44no—
43C2×Q8×C149C2314yes—
44C22×C4×C149—22no—
45C22×C4×C149D411yescharacteristic
46C22×C4×C149D411yescharacteristic
47C22×C4×C149C2311yescharacteristic
48C4⋊C4×C149—22no—
49C4⋊C4×C149—22no—
50C4⋊C4×C149—22no—
51C4⋊C4×C149—22no—
52C42×C149D411yescharacteristic
53C42×C149D411yescharacteristic
54C42×C149C2311yescharacteristic
55C42×C149C2311yescharacteristic
56Dic298—24no—
57Dic298—42no—
58C2×Dic149—22no—
59C2×Dic149—22no—
60#11924746—24no—
61C23×C149C2×D411yescharacteristic
62Q8×C149—28no—
63Q8×C149—44no—
64C2×C4×C149—22no—
65C2×C4×C149—22no—
66C2×C4×C149—24no—
67C2×C4×C149—44no—
68C2×C4×C149Q1614yescomplemented
69C2×C4×C149C2×D411yescharacteristic
70C2×C4×C149C2×D411yescharacteristic
71C2×C4×C149C2×D411yescharacteristic
72C2×C4×C149C2×D411yescharacteristic
73C2×C4×C149C2×D411yescharacteristic
74C2×C4×C149C2411yescharacteristic
75C22×C149—21no—
76C22×C149—21no—
77C22×C149C2×Q1612yes—
78C22×C149C22×D411yescharacteristic
79C4×C149—21no—
80C4×C149—21no—
81C4×C149—44no—
82C4×C149C2×Q1612yes—
83C4×C149C2×Q1612yes—
84C4×C149#13712yes—
85C4×C149H(5,𝔽2)12yes—
86Dic149—42no—
87Dic149—42no—
88C2×C149—22no—
89C2×C149#53511yescharacteristic
90C2×C149C22×Q1611yescharacteristic
91C2×C149C2×#13711yescharacteristic
92C149#320911yescharacteristic, complemented, Sylow
93#3209—1491nomaximal, Sylow
94#533—1491no—
95C2×C4⋊Q8D14911yescharacteristic
96#494—1492no—
97#487—1492no—
98#462—1494no—
99#451—1494no—
100#431—1491no—
101C22×Q8C2×D14912yes—
102C2×Q16—1498no—
103C4⋊Q8—21no—
104C4⋊Q8—21no—
105C4⋊Q8—1491no—
106C4⋊Q8—1491no—
107C4⋊Q8C2×D14912yes—
108C4⋊Q8C2×D14912yes—
109#125—2981no—
110C22⋊Q8—2981no—
111C22⋊Q8—1492no—
112C4×Q8—2981no—
113C4×Q8—1492no—
114#117—2981no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—21no—
117C2×C42C2×D14911yescharacteristic
118C4⋊C8—1492no—
119#103—1498no—
120C22⋊C8—1492no—
121C4×C8—1492no—
122C2×Q8—22no—
123C2×Q8—44no—
124C2×Q8—2981no—
125C2×Q8—1492no—
126C2×Q8C22×D14914yes—
127C22×C4—22no—
128C22×C4C22⋊D14911yescharacteristic
129C22×C4C22⋊D14911yescharacteristic
130C22×C4C22×D14911yescharacteristic
131Q16—5968no—
132C2×C8—1494no—
133C4⋊C4—22no—
134C4⋊C4—22no—
135C4⋊C4—22no—
136C4⋊C4—22no—
137C4⋊C4—2981no—
138C4⋊C4—2981no—
139C4⋊C4—2981no—
140C4⋊C4—2982no—
141C4⋊C4—2982no—
142C4⋊C4—1492no—
143C22⋊C4—2982no—
144C42—2982no—
145C42C22⋊D14911yescharacteristic
146C42C22⋊D14911yescharacteristic
147C42C22×D14911yescharacteristic
148C42C22×D14911yescharacteristic
149C23C2×C22⋊D14911yescharacteristic
150Q8—28no—
151Q8—44no—
152Q8—2984no—
153Q8—5962no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—24no—
157C2×C4—44no—
158C2×C4—2982no—
159C2×C4—2982no—
160C2×C4#1455872614yescomplemented
161C2×C4C2×C22⋊D14911yescharacteristic
162C2×C4C2×C22⋊D14911yescharacteristic
163C2×C4C2×C22⋊D14911yescharacteristic
164C2×C4C2×C22⋊D14911yescharacteristic
165C2×C4C2×C22⋊D14911yescharacteristic
166C2×C4C23×D14911yescharacteristic
167C8—2984no—
168C22—21no—
169C22—21no—
170C22C2×#1455872612yes—
171C22C22×C22⋊D14911yescharacteristic
172C4—21no—
173C4—21no—
174C4—44no—
175C4—5962no—
176C4—5962no—
177C4C2×#1455872612yes—
178C4C2×#1455872612yes—
179C4#1801194212yes—
180C4#1801195612yes—
181C2—22no—
182C2#2375019211yescharacteristic
183C2C22×#1455872611yescharacteristic
184C2C2×#1801194211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×C4⋊Q8×C149C2
socleC22×C149C22×D4
prime radicalC23×C149C2×D4
hypercenterC2×C4⋊Q8D149
hypocenterC149#3209
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #23750004C2semidirect
3. #23749975C2semidirect
4. #23749832C2semidirect
68. C2×C4×C149Q16semidirect
92. C149#3209semidirect
160. C2×C4#14558726semidirect

Maximal subgroups

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

subgroupindex
#237501822
#237500042
#237499752
#237498322
#237497812
#237496782
C2×C4⋊Q8×C1492
#3209149