Finite Group Databasebeta

← #34055010

Subgroups — #34055010

Order 19072.

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

normal subgroups only

This group has 400 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#23750180C211yesmaximal, characteristic, complemented
2#23750173C211yesmaximal, characteristic
3#23749978C214yesmaximal, complemented
4#23749977C211yesmaximal, characteristic, complemented
5#23749976C211yesmaximal, characteristic, complemented
6#23749971C211yesmaximal, characteristic, complemented
7#23749618C214yesmaximal, complemented
8C4×C8×D149C211yesmaximal, characteristic, complemented
9#486×C149C211yesmaximal, characteristic, complemented
10C2×#14558735C2212yes—
11C2×C8×D149C2212yes—
12#18011911C2211yescharacteristic
13#18011911C2211yescharacteristic
14#18011902C2212yes—
15#18011898C2212yes—
16#18011891—21no—
17#18011887—21no—
18#18011882—21no—
19#18011882—21no—
20Q8×Dic149—21no—
21#18011876—21no—
22D4×Dic149—21no—
23D4×Dic149—21no—
24#18011869C2212yes—
25C42×D149C2211yescharacteristic
26#18011836C2214yes—
27#18011834C2214yes—
28#18011832C2214yes—
29C4×#11924746C2211yescharacteristic
30C8×Dic149C2212yes—
31C4⋊Q8×C149C2211yescharacteristic
32#127×C149C2211yescharacteristic
33#102×C149C2214yes—
34C4×C8×C149C2211yescharacteristic
35#14558735—28no—
36C2×Dic298—21no—
37C2×Dic298C2312yes—
38C2×C22⋊D149—22no—
39C22×Dic149—22no—
40C2×C4×D149D411yescharacteristic
41C2×C4×D149D411yescharacteristic
42C2×C4×D149C2311yescharacteristic
43C2×#11924746C2312yes—
44C8×D149—24no—
45C4⋊Dic149—22no—
46C4⋊Dic149—21no—
47C4⋊Dic149—21no—
48C4⋊Dic149—21no—
49C4⋊Dic149C2312yes—
50#14558715—22no—
51C22⋊Dic149—22no—
52C22⋊Dic149—22no—
53#14558713—22no—
54C4×Dic149—22no—
55C4×Dic149D411yescharacteristic
56C4×Dic149D411yescharacteristic
57C4×Dic149C2311yescharacteristic
58C2×Q8×C149—21no—
59C2×D4×C149—21no—
60C2×D4×C149—21no—
61C2×D4×C149C2312yes—
62C2×C8×C149C2312yes—
63C4⋊C4×C149—21no—
64C4⋊C4×C149C2312yes—
65C42×C149C2311yescharacteristic
66C22×D149C2×D411yescharacteristic
67Dic298—24no—
68Dic298—42no—
69C22⋊D149—44no—
70C2×Dic149—22no—
71C2×Dic149—22no—
72C2×Dic149—44no—
73C2×Dic149C2×D411yescharacteristic
74C2×Dic149C2×D411yescharacteristic
75C2×Dic149C2×D411yescharacteristic
76C4×D149—22no—
77C4×D149—22no—
78C4×D149#4114yes—
79#11924746—22no—
80C23×C149—22no—
81Q8×C149—42no—
82D4×C149—24no—
83D4×C149—42no—
84D4×C149—42no—
85C2×C4×C149—22no—
86C2×C4×C149C2×D411yescharacteristic
87C2×C4×C149C2×D411yescharacteristic
88C2×C4×C149C2411yescharacteristic
89C8×C149—22no—
90C22×C149—42no—
91C22×C149—42no—
92C22×C149—42no—
93C22×C149C22×D411yescharacteristic
94C2×D149—21no—
95C2×D149—21no—
96C2×D149#12412yes—
97C4×C149—42no—
98C4×C149#13512yes—
99C4×C149#13512yes—
100C4×C149C2×#4112yes—
101Dic149—21no—
102Dic149—21no—
103Dic149—42no—
104Dic149—42no—
105Dic149#12412yes—
106C2×C149—82no—
107C2×C149C2×#12411yescharacteristic
108C2×C149C2×#13511yescharacteristic
109C2×C149C2×#13511yescharacteristic
110D149—22no—
111C149#313111yescharacteristic, complemented, Sylow
112#3131—1491nomaximal, Sylow
113#533—1491no—
114#532—1491no—
115#488—1494no—
116#487—1491no—
117#487—1491no—
118#486—1491no—
119#486D14911yescharacteristic, complemented
120#416—1494no—
121C2×C4×C8—1491no—
122C2×#41—1492no—
123C22×C8—1492no—
124C4⋊Q8—1491no—
125C4⋊Q8—1491no—
126C4⋊Q8C2×D14911yescharacteristic
127#127C2×D14911yescharacteristic
128#125—1492no—
129#124—1492no—
130C22⋊Q8—2981no—
131C22⋊Q8—2981no—
132#121—2981no—
133#121—2981no—
134C4×Q8—2981no—
135C4×Q8—2981no—
136C4×D4—2981no—
137C4×D4—2981no—
138#117—1492no—
139C2×C42—1491no—
140#103—1494no—
141#103—1494no—
142#102—1494no—
143#102C2×D14914yes—
144C4×C8—1492no—
145C4×C8—1491no—
146C4×C8C2×D14911yescharacteristic
147#41—2988no—
148C2×Q8—21no—
149C2×Q8—2981no—
150C2×Q8—1492no—
151C2×D4—21no—
152C2×D4—21no—
153C2×D4—2982no—
154C2×D4C22×D14912yes—
155C22×C4—2982no—
156C22×C4—1491no—
157C22×C4—1491no—
158C22×C4—1491no—
159C2×C8—2984no—
160C2×C8—1492no—
161C2×C8C22×D14912yes—
162C4⋊C4—21no—
163C4⋊C4—2982no—
164C4⋊C4—2982no—
165C4⋊C4—2981no—
166C4⋊C4—2981no—
167C4⋊C4—2981no—
168C4⋊C4—1492no—
169C4⋊C4C22×D14912yes—
170C22⋊C4—2982no—
171C22⋊C4—2982no—
172C22⋊C4—2982no—
173C42—2982no—
174C42—1491no—
175C42—1491no—
176C42—1491no—
177C42C22×D14911yescharacteristic
178C23—22no—
179C23—1491no—
180Q8—42no—
181Q8—2984no—
182Q8—5962no—
183D4—24no—
184D4—42no—
185D4—42no—
186D4—5964no—
187C2×C4—22no—
188C2×C4—2982no—
189C2×C4—2982no—
190C2×C4—2982no—
191C2×C4—2982no—
192C2×C4—5964no—
193C2×C4—1491no—
194C2×C4—1491no—
195C2×C4—1491no—
196C2×C4—1494no—
197C2×C4D4×D14911yescharacteristic
198C2×C4D4×D14911yescharacteristic
199C2×C4C23×D14911yescharacteristic
200C8—22no—
201C8—2982no—
202C22—42no—
203C22—42no—
204C22—42no—
205C22—2981no—
206C22—2981no—
207C22—1492no—
208C22C2×D4×D14911yescharacteristic
209C4—42no—
210C4—2981no—
211C4—2981no—
212C4—5962no—
213C4—5962no—
214C4—1492no—
215C4#1801193012yes—
216C4#1801193212yes—
217C4#41×D14912yes—
218C2—82no—
219C2—2982no—
220C2#124×D14911yescharacteristic
221C2C2×#1801193011yescharacteristic
222C2C2×#1801193211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#486×C149C2
socleC22×C149C22×D4
prime radical#23750173C2
hypercenter#486D149
hypocenterC149#3131
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #23750180C2semidirect
3. #23749978C2semidirect
4. #23749977C2semidirect
5. #23749976C2semidirect
6. #23749971C2semidirect
7. #23749618C2semidirect
8. C4×C8×D149C2semidirect
9. #486×C149C2semidirect
111. C149#3131semidirect
119. #486D149semidirect

Maximal subgroups

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

subgroupindex
#237501802
#237501732
#237499782
#237499772
#237499762
#237499712
#237496182
C4×C8×D1492
#486×C1492
#3131149