Finite Group Databasebeta

← #34055276

Subgroups — #34055276

Order 19072.

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

normal subgroups only

This group has 368 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#23750180C211yesmaximal, characteristic
2#23750180C211yesmaximal, characteristic
3#23750028C211yesmaximal, characteristic, complemented
4#23750004C211yesmaximal, characteristic, complemented
5#23749976C211yesmaximal, characteristic, complemented
6#23749865C214yesmaximal
7#23749717C214yesmaximal, complemented
8C4×C8×D149C211yesmaximal, characteristic
9#487×C149C211yesmaximal, characteristic, complemented
10C2×#14558726C2214yes—
11C2×C8×D149C2212yes—
12#18011911C2211yescharacteristic
13#18011911C2211yescharacteristic
14#18011902—21no—
15#18011902—21no—
16#18011891—21no—
17#18011891C2212yes—
18#18011887—21no—
19#18011887C2212yes—
20Q8×Dic149—21no—
21Q8×Dic149C2212yes—
22#18011876—21no—
23#18011876C2212yes—
24#18011869—21no—
25#18011869—21no—
26C42×D149C2211yescharacteristic
27#18011844C2214yes—
28#18011836C2214yes—
29C4×#11924746C2211yescharacteristic
30C8×Dic149C2212yes—
31C4⋊Q8×C149C2211yescharacteristic
32C4⋊Q8×C149C2211yescharacteristic
33#103×C149C2214yes—
34C4×C8×C149C2211yescharacteristic
35C2×Dic298—21no—
36C2×Dic298C2312yes—
37C2×C4×D149D411yescharacteristic
38C2×C4×D149D411yescharacteristic
39C2×C4×D149C2311yescharacteristic
40#14558726—28no—
41C2×#11924746C2312yes—
42C8×D149—24no—
43C4⋊Dic149—22no—
44C4⋊Dic149—22no—
45C4⋊Dic149—21no—
46C4⋊Dic149—21no—
47C4⋊Dic149—21no—
48C4⋊Dic149C2312yes—
49#14558715—22no—
50#14558715—22no—
51#14558713—22no—
52#14558713—22no—
53C4×Dic149—22no—
54C4×Dic149—22no—
55C4×Dic149D411yescharacteristic
56C4×Dic149D411yescharacteristic
57C4×Dic149C2311yescharacteristic
58C2×Q8×C149—21no—
59C2×Q8×C149C2312yes—
60C2×C8×C149C2312yes—
61C4⋊C4×C149—21no—
62C4⋊C4×C149—21no—
63C4⋊C4×C149—21no—
64C4⋊C4×C149C2312yes—
65C42×C149C2311yescharacteristic
66C22×D149C2×D411yescharacteristic
67Dic298—24no—
68Dic298—42no—
69C2×Dic149—22no—
70C2×Dic149—22no—
71C2×Dic149C2×D411yescharacteristic
72C2×Dic149C2×D411yescharacteristic
73C2×Dic149C2×D411yescharacteristic
74C4×D149—22no—
75C4×D149—22no—
76C4×D149Q1614yescomplemented
77#11924746#4114yes—
78Q8×C149—24no—
79Q8×C149—42no—
80C2×C4×C149—22no—
81C2×C4×C149—22no—
82C2×C4×C149C2×D411yescharacteristic
83C2×C4×C149C2×D411yescharacteristic
84C2×C4×C149C2411yescharacteristic
85C8×C149—22no—
86C22×C149C22×D411yescharacteristic
87C2×D149—21no—
88C2×D149—21no—
89C2×D149C2×Q1612yes—
90C4×C149—42no—
91C4×C149—42no—
92C4×C149C2×Q1612yes—
93C4×C149#13512yes—
94C4×C149C2×#4112yes—
95Dic149—21no—
96Dic149—21no—
97Dic149—42no—
98Dic149—42no—
99Dic149C2×Q1612yes—
100C2×C149#53211yescharacteristic
101C2×C149C22×Q1611yescharacteristic
102C2×C149C2×#13511yescharacteristic
103D149—22no—
104C149#317011yescharacteristic, complemented, Sylow
105#3170—1491nomaximal, Sylow
106#533—1491no—
107#533—1491no—
108#500—1491no—
109#494—1491no—
110#487—1491no—
111#487D14911yescharacteristic, complemented
112#467—1494no—
113C4×Q16—1494no—
114C2×C4×C8—1491no—
115C2×Q16—1494no—
116C22×C8—1492no—
117C4⋊Q8—1491no—
118C4⋊Q8—1491no—
119C4⋊Q8C2×D14911yescharacteristic
120C4⋊Q8C2×D14911yescharacteristic
121#125—2981no—
122#125—2981no—
123C22⋊Q8—2981no—
124C22⋊Q8—2981no—
125C22⋊Q8—1492no—
126C22⋊Q8—1492no—
127C4×Q8—2981no—
128C4×Q8—2981no—
129C4×Q8—1492no—
130C4×Q8—1492no—
131#117—2981no—
132#117—2981no—
133C2×C42—1491no—
134#107—1494no—
135#103—1494no—
136#103C2×D14914yes—
137C4×C8—1492no—
138C4×C8—1491no—
139C4×C8C2×D14911yescharacteristic
140C2×Q8—21no—
141C2×Q8—2981no—
142C2×Q8—1492no—
143C2×Q8C22×D14912yes—
144C22×C4—1491no—
145C22×C4—1491no—
146C22×C4—1491no—
147Q16—2988no—
148C2×C8—2984no—
149C2×C8—1492no—
150C2×C8C22×D14912yes—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—21no—
154C4⋊C4—2982no—
155C4⋊C4—2982no—
156C4⋊C4—2982no—
157C4⋊C4—2982no—
158C4⋊C4—2981no—
159C4⋊C4—2981no—
160C4⋊C4—2981no—
161C4⋊C4—1492no—
162C4⋊C4C22×D14912yes—
163C22⋊C4—2982no—
164C22⋊C4—2982no—
165C42—2982no—
166C42—2982no—
167C42—1491no—
168C42—1491no—
169C42—1491no—
170C42C22×D14911yescharacteristic
171C23—1491no—
172Q8—24no—
173Q8—42no—
174Q8—2984no—
175Q8—5962no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—2982no—
179C2×C4—2982no—
180C2×C4—2982no—
181C2×C4—2982no—
182C2×C4—1491no—
183C2×C4—1491no—
184C2×C4—1491no—
185C2×C4—1494no—
186C2×C4D4×D14911yescharacteristic
187C2×C4D4×D14911yescharacteristic
188C2×C4C23×D14911yescharacteristic
189C8—22no—
190C8—1494no—
191C22—2981no—
192C22—2981no—
193C22—1492no—
194C22C2×D4×D14911yescharacteristic
195C4—42no—
196C4—42no—
197C4—2981no—
198C4—2981no—
199C4—5962no—
200C4—5962no—
201C4—1492no—
202C4Q16×D14912yes—
203C4#1801193212yes—
204C4#41×D14912yes—
205C2—2982no—
206C2#2375017411yescharacteristic
207C2C2×Q16×D14911yescharacteristic
208C2C2×#1801193211yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#487×C149C2
socleC22×C149C22×D4
prime radicalC22×D149C2×D4
hypercenter#487D149
hypocenterC149#3170
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. #23750028C2semidirect
4. #23750004C2semidirect
5. #23749976C2semidirect
7. #23749717C2semidirect
9. #487×C149C2semidirect
76. C4×D149Q16semidirect
104. C149#3170semidirect
111. #487D149semidirect

Maximal subgroups

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

subgroupindex
#237501802
#237500282
#237500042
#237499762
#237498652
#237497172
C4×C8×D1492
#487×C1492
#3170149