Finite Group Databasebeta

← #34055824

Subgroups — #34055824

Order 19072.

370 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 117 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#23750028C211yesmaximal, characteristic, complemented
4#23750023C211yesmaximal, characteristic, complemented
5#23749971C211yesmaximal, characteristic, complemented
6#23749948C214yesmaximal, complemented
7#23749927C214yesmaximal, complemented
8#23749676C211yesmaximal, characteristic, complemented
9#486×C149C211yesmaximal, characteristic, complemented
10C2×#14558735—21no—
11#18011911C2211yescharacteristic
12#18011911C2211yescharacteristic
13#18011902C2212yes—
14#18011898—21no—
15#18011891—21no—
16#18011887—21no—
17#18011882—21no—
18#18011882C2212yes—
19Q8×Dic149—21no—
20#18011876—21no—
21D4×Dic149—21no—
22D4×Dic149C2212yes—
23#18011869C2212yes—
24C42×D149C2211yescharacteristic
25#18011844C2214yes—
26#18011843C2214yes—
27#18011840C2212yes—
28#18011832C2214yes—
29#18011823C2212yes—
30C4×#11924746C2211yescharacteristic
31C4⋊Q8×C149C2211yescharacteristic
32#127×C149C2211yescharacteristic
33#102×C149C2214yes—
34C4×C8×C149C2211yescharacteristic
35#14558735—44no—
36C2×Dic298—21no—
37C2×Dic298—21no—
38C2×C22⋊D149—22no—
39C22×Dic149—22no—
40C2×C4×D149D411yescharacteristic
41C2×C4×D149D411yescharacteristic
42C2×C4×D149C2311yescharacteristic
43C2×#11924746C2312yes—
44C4⋊Dic149—22no—
45C4⋊Dic149—21no—
46C4⋊Dic149—21no—
47C4⋊Dic149C2312yes—
48C4⋊Dic149C2312yes—
49#14558715—22no—
50C22⋊Dic149—22no—
51C22⋊Dic149—22no—
52#14558713—22no—
53C4×Dic149—22no—
54C4×Dic149D411yescharacteristic
55C4×Dic149D411yescharacteristic
56C4×Dic149C2311yescharacteristic
57C2×Q8×C149—21no—
58C2×D4×C149—21no—
59C2×D4×C149—21no—
60C2×D4×C149C2312yes—
61C2×C8×C149C2312yes—
62C4⋊C4×C149—21no—
63C4⋊C4×C149C2312yes—
64C42×C149C2311yescharacteristic
65C22×D149C2×D411yescharacteristic
66Dic298—42no—
67Dic298—42no—
68C22⋊D149—44no—
69C2×Dic149—22no—
70C2×Dic149—22no—
71C2×Dic149—44no—
72C2×Dic149C2×D411yescharacteristic
73C2×Dic149C2×D411yescharacteristic
74C2×Dic149C2×D411yescharacteristic
75C4×D149—22no—
76C4×D149—22no—
77C4×D149—22no—
78#11924746—22no—
79C23×C149—22no—
80Q8×C149—42no—
81D4×C149—24no—
82D4×C149—42no—
83D4×C149—42no—
84C2×C4×C149—22no—
85C2×C4×C149C2×D411yescharacteristic
86C2×C4×C149C2×D411yescharacteristic
87C2×C4×C149C2411yescharacteristic
88C8×C149—22no—
89C22×C149—42no—
90C22×C149—42no—
91C22×C149—42no—
92C22×C149C22×D411yescharacteristic
93C2×D149—21no—
94C2×D149—21no—
95C2×D149—21no—
96C4×C149—42no—
97C4×C149#13512yes—
98C4×C149AGL(1,ℤ/8)12yes—
99C4×C1492−1+412yes—
100Dic149—21no—
101Dic149—21no—
102Dic149—21no—
103Dic149—42no—
104Dic149—42no—
105C2×C149—82no—
106C2×C149#53611yescharacteristic
107C2×C149C2×#13511yescharacteristic
108C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
109D149—41no—
110C149#322811yescharacteristic, complemented, Sylow
111#3228—1491nomaximal, Sylow
112#533—1491no—
113#532—1491no—
114#500—1491no—
115#498—1491no—
116#486—1491no—
117#486D14911yescharacteristic, complemented
118#482—1494no—
119#478—1494no—
120#431—1491no—
121C2×#41—2981no—
122C4⋊Q8—1491no—
123C4⋊Q8—1491no—
124C4⋊Q8C2×D14911yescharacteristic
125#127C2×D14911yescharacteristic
126#125—1492no—
127#124—2981no—
128C22⋊Q8—2981no—
129C22⋊Q8—2981no—
130#121—2981no—
131#121—1492no—
132C4×Q8—2981no—
133C4×Q8—2981no—
134C4×D4—2981no—
135C4×D4—1492no—
136#117—1492no—
137C2×C42—1491no—
138#107—1494no—
139#106—1494no—
140C4⋊C8—1492no—
141#102—1494no—
142#102C2×D14914yes—
143C22⋊C8—1492no—
144C4×C8—1491no—
145C4×C8C2×D14911yescharacteristic
146#41—5964no—
147C2×Q8—21no—
148C2×Q8—2981no—
149C2×Q8—2981no—
150C2×D4—21no—
151C2×D4—21no—
152C2×D4—2982no—
153C2×D4C22×D14912yes—
154C22×C4—2982no—
155C22×C4—1491no—
156C22×C4—1491no—
157C22×C4—1491no—
158C2×C8—1492no—
159C2×C8C22×D14912yes—
160C4⋊C4—21no—
161C4⋊C4—2982no—
162C4⋊C4—2982no—
163C4⋊C4—2981no—
164C4⋊C4—2981no—
165C4⋊C4—1492no—
166C4⋊C4—1492no—
167C4⋊C4C22×D14912yes—
168C22⋊C4—2982no—
169C22⋊C4—2982no—
170C22⋊C4—2982no—
171C42—2982no—
172C42—1491no—
173C42—1491no—
174C42—1491no—
175C42C22×D14911yescharacteristic
176C23—22no—
177C23—1491no—
178Q8—42no—
179Q8—5962no—
180Q8—5962no—
181D4—24no—
182D4—42no—
183D4—42no—
184D4—5964no—
185C2×C4—22no—
186C2×C4—2982no—
187C2×C4—2982no—
188C2×C4—2982no—
189C2×C4—2982no—
190C2×C4—2982no—
191C2×C4—5964no—
192C2×C4—1491no—
193C2×C4—1491no—
194C2×C4—1491no—
195C2×C4D4×D14911yescharacteristic
196C2×C4D4×D14911yescharacteristic
197C2×C4C23×D14911yescharacteristic
198C8—22no—
199C8—2982no—
200C22—42no—
201C22—42no—
202C22—42no—
203C22—2981no—
204C22—2981no—
205C22—2981no—
206C22C2×D4×D14911yescharacteristic
207C4—42no—
208C4—2981no—
209C4—2981no—
210C4—2981no—
211C4—5962no—
212C4—5962no—
213C4#1801193212yes—
214C4#1801193512yes—
215C4#1801195812yes—
216C2—82no—
217C2—5961no—
218C2#2375019511yescharacteristic
219C2C2×#1801193211yescharacteristic
220C2C2×#1801193511yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#486×C149C2
socleC22×C149C22×D4
prime radical#23750173C2
hypercenter#486D149
hypocenterC149#3228
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. #23750028C2semidirect
4. #23750023C2semidirect
5. #23749971C2semidirect
6. #23749948C2semidirect
7. #23749927C2semidirect
8. #23749676C2semidirect
9. #486×C149C2semidirect
110. C149#3228semidirect
117. #486D149semidirect

Maximal subgroups

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

subgroupindex
#237501802
#237501732
#237500282
#237500232
#237499712
#237499482
#237499272
#237496762
#486×C1492
#3228149