Finite Group Databasebeta

← #34055269

Subgroups — #34055269

Order 19072.

456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 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#23750176C211yesmaximal, characteristic, complemented
2#23750173C211yesmaximal, characteristic, complemented
3#23750028C211yesmaximal, characteristic, complemented
4#23750001C211yesmaximal, characteristic, complemented
5#23749972C211yesmaximal, characteristic, complemented
6#23749860C214yesmaximal, complemented
7#23749705C214yesmaximal, complemented
8C4×C8×D149C211yesmaximal, characteristic, complemented
9#486×C149C211yesmaximal, characteristic, complemented
10C2×#14558737—21no—
11C2×#14558735—21no—
12C2×#14558721C2214yes—
13C2×C8×D149C2212yes—
14#18011911C2211yescharacteristic
15#18011908C2211yescharacteristic
16#18011900—21no—
17#18011898—21no—
18#18011886—21no—
19#18011886C2212yes—
20#18011882—21no—
21#18011882C2212yes—
22D4×Dic149—21no—
23D4×Dic149C2212yes—
24#18011873—21no—
25#18011873C2212yes—
26C42×D149C2211yescharacteristic
27#18011844C2214yes—
28#18011833C2214yes—
29C4×#11924746C2211yescharacteristic
30C8×Dic149C2212yes—
31C4⋊Q8×C149C2211yescharacteristic
32#127×C149C2211yescharacteristic
33#102×C149C2214yes—
34C4×C8×C149C2211yescharacteristic
35#14558737—44no—
36#14558735—44no—
37C2×Dic298—21no—
38C2×D596—22no—
39C2×D596—21no—
40C2×D596—21no—
41C2×D596C2312yes—
42C2×C22⋊D149—22no—
43C22×Dic149—22no—
44C2×C4×D149—22no—
45C2×C4×D149D411yescharacteristic
46C2×C4×D149D411yescharacteristic
47C2×C4×D149C2311yescharacteristic
48#14558721—28no—
49C2×#11924746C2312yes—
50C8×D149—24no—
51C4⋊Dic149—21no—
52C4⋊Dic149C2312yes—
53C22⋊Dic149—22no—
54C22⋊Dic149—22no—
55#14558713—22no—
56#14558713—22no—
57C4×Dic149D411yescharacteristic
58C4×Dic149D411yescharacteristic
59C4×Dic149C2311yescharacteristic
60C2×Q8×C149—21no—
61C2×D4×C149—21no—
62C2×D4×C149—21no—
63C2×D4×C149C2312yes—
64C2×C8×C149C2312yes—
65C4⋊C4×C149—21no—
66C4⋊C4×C149C2312yes—
67C42×C149C2311yescharacteristic
68C22×D149—22no—
69C22×D149C2×D411yescharacteristic
70Dic298—42no—
71D596—24no—
72D596—44no—
73D596—42no—
74D596—42no—
75C22⋊D149—44no—
76C2×Dic149—22no—
77C2×Dic149—44no—
78C2×Dic149C2×D411yescharacteristic
79C2×Dic149C2×D411yescharacteristic
80C2×Dic149C2×D411yescharacteristic
81C4×D149—22no—
82C4×D149—22no—
83C4×D149—44no—
84C4×D149D814yescomplemented
85#11924746#4114yescomplemented
86C23×C149—22no—
87Q8×C149—42no—
88D4×C149—24no—
89D4×C149—42no—
90D4×C149—42no—
91C2×C4×C149—22no—
92C2×C4×C149C2×D411yescharacteristic
93C2×C4×C149C2×D411yescharacteristic
94C2×C4×C149C2411yescharacteristic
95C8×C149—22no—
96C22×C149—42no—
97C22×C149—42no—
98C22×C149—42no—
99C22×C149C22×D411yescharacteristic
100C2×D149—21no—
101C2×D149—21no—
102C2×D149—42no—
103C2×D149—42no—
104C2×D149—42no—
105C2×D149C2×D812yes—
106C4×C149—42no—
107C4×C149C2×D812yes—
108C4×C149#13512yes—
109C4×C149C2×#4112yes—
110Dic149—21no—
111Dic149—21no—
112Dic149—42no—
113Dic149C2×D812yes—
114C2×C149—82no—
115C2×C149#53211yescharacteristic
116C2×C149C22×D811yescharacteristic
117C2×C149C2×#13511yescharacteristic
118D149—22no—
119D149—82no—
120C149#316911yescharacteristic, complemented, Sylow
121#3169—1491nomaximal, Sylow
122#532—1491no—
123#532—1491no—
124#500—1491no—
125#493—1491no—
126#486—1491no—
127#486D14911yescharacteristic, complemented
128#466—1494no—
129C4×D8—1494no—
130C2×C4×C8—1491no—
131C2×#41—2981no—
132C2×#41—2981no—
133C2×D8—1494no—
134C22×C8—1492no—
135C4⋊Q8—1491no—
136C4⋊Q8C2×D14911yescharacteristic
137#127—1491no—
138#127C2×D14911yescharacteristic
139#124—2981no—
140#124—2981no—
141#121—2981no—
142#121—2981no—
143#121—1492no—
144#121—1492no—
145C4×D4—2981no—
146C4×D4—2981no—
147C4×D4—1492no—
148C4×D4—1492no—
149C2×C42—1491no—
150#107—1494no—
151#102—1494no—
152#102C2×D14914yes—
153C4×C8—1492no—
154C4×C8—1491no—
155C4×C8C2×D14911yescharacteristic
156#41—5964no—
157#41—5964no—
158C2×Q8—21no—
159C2×Q8—2981no—
160C2×D4—21no—
161C2×D4—21no—
162C2×D4—2982no—
163C2×D4—2982no—
164C2×D4—2981no—
165C2×D4—2981no—
166C2×D4—1492no—
167C2×D4C22×D14912yes—
168C22×C4—2982no—
169C22×C4—2982no—
170C22×C4—1491no—
171C22×C4—1491no—
172C22×C4—1491no—
173D8—2988no—
174C2×C8—2984no—
175C2×C8—1492no—
176C2×C8C22×D14912yes—
177C4⋊C4—21no—
178C4⋊C4—2981no—
179C4⋊C4—1492no—
180C4⋊C4C22×D14912yes—
181C22⋊C4—2982no—
182C22⋊C4—2982no—
183C22⋊C4—2982no—
184C22⋊C4—2982no—
185C42—1491no—
186C42—1491no—
187C42—1491no—
188C42C22×D14911yescharacteristic
189C23—22no—
190C23—2982no—
191C23—1491no—
192Q8—42no—
193Q8—5962no—
194D4—24no—
195D4—42no—
196D4—42no—
197D4—2984no—
198D4—5964no—
199D4—5964no—
200D4—5962no—
201D4—5962no—
202C2×C4—22no—
203C2×C4—2982no—
204C2×C4—2982no—
205C2×C4—2982no—
206C2×C4—5964no—
207C2×C4—5964no—
208C2×C4—1491no—
209C2×C4—1491no—
210C2×C4—1491no—
211C2×C4—1494no—
212C2×C4D4×D14911yescharacteristic
213C2×C4D4×D14911yescharacteristic
214C2×C4C23×D14911yescharacteristic
215C8—22no—
216C8—1494no—
217C22—42no—
218C22—42no—
219C22—42no—
220C22—2981no—
221C22—2981no—
222C22—5962no—
223C22—5962no—
224C22—5962no—
225C22—1492no—
226C22C2×D4×D14911yescharacteristic
227C4—42no—
228C4—2981no—
229C4—2981no—
230C4—5962no—
231C4—1492no—
232C4D8×D14912yes—
233C4#1801193212yes—
234C4#41×D14912yes—
235C2—82no—
236C2—2982no—
237C2—11922no—
238C2#2375017411yescharacteristic
239C2C2×D8×D14911yescharacteristic
240C2C2×#1801193211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#486×C149C2
socleC22×C149C22×D4
hypercenter#486D149
hypocenterC149#3169
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. #23750176C2semidirect
2. #23750173C2semidirect
3. #23750028C2semidirect
4. #23750001C2semidirect
5. #23749972C2semidirect
6. #23749860C2semidirect
7. #23749705C2semidirect
8. C4×C8×D149C2semidirect
9. #486×C149C2semidirect
84. C4×D149D8semidirect
85. #11924746#41semidirect
120. C149#3169semidirect
127. #486D149semidirect

Maximal subgroups

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

subgroupindex
#237501762
#237501732
#237500282
#237500012
#237499722
#237498602
#237497052
C4×C8×D1492
#486×C1492
#3169149