Finite Group Databasebeta

← #34056082

Subgroups — #34056082

Order 19072.

342 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 125 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#23749910C212yesmaximal, complemented
3#23749907C212yesmaximal, complemented
4#23749881C214yesmaximal
5#23749835C212yesmaximal, complemented
6#23749832C212yesmaximal, complemented
7#23749649C211yesmaximal, characteristic
8#533×C149C211yesmaximal, characteristic
9C2×#14558726C2214yes—
10C2×#14558720C2212yes—
11#18011911C2211yescharacteristic
12#18011911C2211yescharacteristic
13#18011903—21no—
14#18011890—21no—
15#18011890C2212yes—
16C4×Dic298—21no—
17C4×Dic298C2212yes—
18#18011870—21no—
19#18011842C2214yes—
20C4⋊#11924746C2212yes—
21C4⋊#11924746C2212yes—
22#18011835C2214yes—
23#18011834C2214yes—
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×Dic298C2312yes—
35#14558726—44no—
36#14558720—42no—
37C2×#11924746C2314yes—
38C4⋊Dic149—21no—
39C4⋊Dic149—21no—
40C4⋊Dic149—21no—
41C4⋊Dic149C2312yes—
42#14558715—22no—
43#14558715—22no—
44C22⋊Dic149—22no—
45C4×Dic149—22no—
46C2×Q8×C149—21no—
47C2×Q8×C149C2312yes—
48C22×C4×C149D411yescharacteristic
49C22×C4×C149D411yescharacteristic
50C22×C4×C149C2311yescharacteristic
51C4⋊C4×C149—21no—
52C4⋊C4×C149—21no—
53C4⋊C4×C149—21no—
54C4⋊C4×C149—22no—
55C4⋊C4×C149—22no—
56C4⋊C4×C149C2312yes—
57C22⋊C4×C149—22no—
58C42×C149—22no—
59C42×C149D411yescharacteristic
60C42×C149D411yescharacteristic
61C42×C149C2311yescharacteristic
62C42×C149C2311yescharacteristic
63Dic298—22no—
64Dic298—22no—
65Dic298—42no—
66C2×Dic149—22no—
67C2×Dic149—22no—
68#11924746—24no—
69C23×C149C2×D411yescharacteristic
70Q8×C149—22no—
71Q8×C149—22no—
72Q8×C149—42no—
73C2×C4×C149—22no—
74C2×C4×C149—22no—
75C2×C4×C149—21no—
76C2×C4×C149—21no—
77C2×C4×C149—22no—
78C2×C4×C149—22no—
79C2×C4×C149C2×D411yescharacteristic
80C2×C4×C149C2×D411yescharacteristic
81C2×C4×C149C2×D411yescharacteristic
82C2×C4×C149C2×D411yescharacteristic
83C2×C4×C149C2×D411yescharacteristic
84C2×C4×C149C2411yescharacteristic
85C22×C149—21no—
86C22×C149—21no—
87C22×C149—21no—
88C22×C149C22×D411yescharacteristic
89C4×C149—21no—
90C4×C149—21no—
91C4×C149—21no—
92C4×C149—42no—
93C4×C149—42no—
94C4×C149#13712yes—
95C4×C149#13712yes—
96C4×C149H(5,𝔽2)11yescharacteristic
97C4×C1492−1+411yescharacteristic
98Dic149—42no—
99Dic149—42no—
100C2×C149—41no—
101C2×C149#53711yescharacteristic
102C2×C149C2×#13711yescharacteristic
103C2×C149C2×#13711yescharacteristic
104C149#325511yescharacteristic, complemented, Sylow
105#3255—1491nomaximal, Sylow
106#533—1491no—
107#533D14911yescharacteristic
108#475—1492no—
109#475—1492no—
110#470—1494no—
111#462—1492no—
112#462—1492no—
113#423—1491no—
114C2×Q16—1494no—
115C2×M16—1492no—
116C4⋊Q8—1491no—
117C4⋊Q8—1491no—
118C4⋊Q8C2×D14911yescharacteristic
119C4⋊Q8C2×D14911yescharacteristic
120#125—21no—
121#125—2981no—
122C22⋊Q8—21no—
123C22⋊Q8—2981no—
124C22⋊Q8—1492no—
125C22⋊Q8C2×D14912yes—
126C4×Q8—21no—
127C4×Q8—2981no—
128C4×Q8—1492no—
129C4×Q8C2×D14912yes—
130#117—21no—
131#117—2981no—
132C2×C42C2×D14911yescharacteristic
133#106—1494no—
134C4⋊C8—1492no—
135C4⋊C8—1492no—
136#103—1494no—
137#103—1494no—
138C2×Q8—21no—
139C2×Q8—2981no—
140C2×Q8—1492no—
141C2×Q8C22×D14912yes—
142C22×C4C22⋊D14911yescharacteristic
143C22×C4C22⋊D14911yescharacteristic
144C22×C4C22×D14911yescharacteristic
145Q16—5964no—
146M16—5962no—
147C2×C8—1494no—
148C4⋊C4—21no—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—22no—
152C4⋊C4—22no—
153C4⋊C4—2981no—
154C4⋊C4—2981no—
155C4⋊C4—2981no—
156C4⋊C4—2982no—
157C4⋊C4—2982no—
158C4⋊C4—1492no—
159C4⋊C4C22×D14912yes—
160C22⋊C4—22no—
161C22⋊C4—2982no—
162C42—22no—
163C42—2982no—
164C42C22⋊D14911yescharacteristic
165C42C22⋊D14911yescharacteristic
166C42C22×D14911yescharacteristic
167C42C22×D14911yescharacteristic
168C23C2×C22⋊D14911yescharacteristic
169Q8—22no—
170Q8—22no—
171Q8—42no—
172Q8—2982no—
173Q8—2982no—
174Q8—5962no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—2982no—
182C2×C4—2982no—
183C2×C4C2×C22⋊D14911yescharacteristic
184C2×C4C2×C22⋊D14911yescharacteristic
185C2×C4C2×C22⋊D14911yescharacteristic
186C2×C4C2×C22⋊D14911yescharacteristic
187C2×C4C2×C22⋊D14911yescharacteristic
188C2×C4C23×D14911yescharacteristic
189C8—2984no—
190C22—21no—
191C22—21no—
192C22—21no—
193C22C22×C22⋊D14911yescharacteristic
194C4—21no—
195C4—21no—
196C4—21no—
197C4—42no—
198C4—42no—
199C4—5962no—
200C4—5962no—
201C4#1801194112yes—
202C4#1801194212yes—
203C4#1801195711yescharacteristic
204C4#1801195811yescharacteristic
205C2—41no—
206C2#2375020311yescharacteristic
207C2C2×#1801194111yescharacteristic
208C2C2×#1801194211yescharacteristic
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#3255
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. #23749910C2semidirect
3. #23749907C2semidirect
5. #23749835C2semidirect
6. #23749832C2semidirect
104. C149#3255semidirect

Maximal subgroups

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

subgroupindex
#237501822
#237499102
#237499072
#237498812
#237498352
#237498322
#237496492
#533×C1492
#3255149